A model for global biomass burning in preindustrial time: LPJ-LMfire ...

Geosci Model Dev 6 643ndash685 2013wwwgeosci-model-devnet66432013doi105194gmd-6-643-2013copy Author(s) 2013 CC Attribution 30 License

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A model for global biomass burning in preindustrial timeLPJ-LMfire (v10)

M Pfeiffer 1 A Spessa23 and J O Kaplan1

1ARVE Group Ecole Polytechnique Federale de Lausanne Lausanne Switzerland2Department of Atmospheric Chemistry Max Planck Institute for Chemistry Mainz Germany3Biodiversity and Climate Research Centre (BiK-F) Frankfurt am Main Germany

Correspondence toM Pfeiffer (mirjampfeifferepflch)

Received 8 August 2012 ndash Published in Geosci Model Dev Discuss 23 August 2012Revised 15 April 2013 ndash Accepted 19 April 2013 ndash Published 17 May 2013

Abstract Fire is the primary disturbance factor in many ter-restrial ecosystems Wildfire alters vegetation structure andcomposition affects carbon storage and biogeochemical cy-cling and results in the release of climatically relevant tracegases including CO2 CO CH4 NOx and aerosols One wayof assessing the impacts of global wildfire on centennial tomulti-millennial timescales is to use process-based fire mod-els linked to dynamic global vegetation models (DGVMs)Here we present an update to the LPJ-DGVM and a newfire module based on SPITFIRE that includes several im-provements to the way in which fire occurrence behaviourand the effects of fire on vegetation are simulated The newLPJ-LMfire model includes explicit calculation of naturalignitions the representation of multi-day burning and coa-lescence of fires and the calculation of rates of spread indifferent vegetation types We describe a new representationof anthropogenic biomass burning under preindustrial con-ditions that distinguishes the different relationships betweenhumans and fire among hunter-gatherers pastoralists andfarmers We evaluate our model simulations against remote-sensing-based estimates of burned area at regional and globalscale While wildfire in much of the modern world is largelyinfluenced by anthropogenic suppression and ignitions inthose parts of the world where natural fire is still the dom-inant process (eg in remote areas of the boreal forest andsubarctic) our results demonstrate a significant improvementin simulated burned area over the original SPITFIRE Thenew fire model we present here is particularly suited for theinvestigation of climatendashhumanndashfire relationships on multi-millennial timescales prior to the Industrial Revolution

1 Introduction

Fire is one of the most important disturbance processes af-fecting the terrestrial biosphere Fires affect most ecosys-tems from tropical forests to tundra (Bond and van Wilgen1996 Dwyer et al 2000) and the evolution of fire overthe Phanerozoic is likely to have had a major control onboth the global carbon budget and the present distribution ofplants on earth (Bond and Keeley 2005 Pausas and Keeley2009 Bond and Scott 2010 Bond and Midgley 2012)Wildfires alter vegetation composition structure and dis-tribution biomass productivity plant diversity and biogeo-chemical cycles (Johnson et al 1998 Moreira 2000 Ojimaet al 1994 Wan et al 2001 Neary et al 2005 Bondet al 2005) Biomass burning (both wildfires and intentionalcombustion of biofuels) influences the spatial and interan-nual variability in the emissions of climatically relevant tracegases and aerosols including CO2 CO CH4 NOx and blackcarbon (Crutzen and Andreae 1990 Penner et al 1992Andreae and Merlet 2001 Jain et al 2006) Because of theclose relationship between fire vegetation and climate un-derstanding the causes and consequences of fires is criticalfor any assessment of the past present and future state ofthe Earth system (Bowman et al 2009)

Quantitative observations of wildfire are severely limitedboth in time and space coverage in global data sets basedon satellite observations began in the last decades of the20th century To improve our understanding of the driversof fire and fire-related trace gas and aerosol emissions it istherefore imperative to use numerical models of fire occur-rence behaviour and impacts But process-based modelling

Published by Copernicus Publications on behalf of the European Geosciences Union

644 M Pfeiffer et al Global biomass burning in preindustrial time LPJ-LMfire (v10)

of fire and fire emissions is challenging Fire occurrence isinfluenced by climate vegetation structure and compositionand human activities fire behaviour is affected by weathertopography and the characteristics of the fuel fire distur-bance alters vegetation composition and structure and ulti-mately climate (Archibald et al 2009 Bowman et al 2009Spessa et al 2012) Thus modelling fire requires represen-tations of vegetation fire and climate that interact and feedback upon one another

Mathematical models of wildfire dynamics have existedfor over 40 yr (Rothermel 1972) The original models offire behaviour were motivated by needs for operational fireforecasting for firefighting and forest management applica-tions These models were applied at relatively small spatialscales of 100 minus 103 ha and have been extensively revisedand updated over subsequent years (Burgan and Rothermel1984 Andrews 1986 Burgan 1987 Andrews and Chase1989 Reinhardt et al 1997 Finney 1998 Andrews et al2003 Andrews 2007 Andrews et al 2008 Heinsch andAndrews 2010) Fire modelling at field scale is an essentialpart of fire management and mitigation worldwide and mod-ern operational fire models such as BehavePlus (Heinsch andAndrews 2010) can be used for a wide range of fire man-agement applications including projecting the behaviour ofongoing fire planning prescribed fire assessing fuel hazardand training

More recently fire models have been developed for ap-plication at larger spatial scales eg for integration into dy-namic global vegetation models (DGVMs) in order to simu-late the fundamental ecosystem disturbance process that firerepresents and in some cases to estimate the emissions ofclimate-relevant trace gases and aerosols at continental toglobal scale Depending on the goals for application of theparticular DGVM the detail with which fire is representedvaries but all large-scale fire models include a representationof three key processes

1 fire occurrence

2 fire behaviour and

3 fire impacts on vegetation

The most complex representations of fire currently adaptedfor DGVMs incorporate and generalize many of the con-cepts and equations developed for operational fire forecast-ing models into a large-scale framework The RegFIRM firemodel (Venevsky et al 2002) originally developed as anembedded module within the Lund-Potsdam-Jena DGVM(LPJ Sitch et al 2003) was one of the first global firemodels that contained explicit representations of climatic firedanger and lightning- and human-caused wildfire ignitionsBuilding on RegFIRM the SPITFIRE (SPread and InTensityof FIRE) fire model (Thonicke et al 2010) included a morecomplete process representation of fire ignitions and be-haviour and further contained new representations of the im-

pacts of fire on vegetation including plant mortality as a re-sult of crown scorch and cambial damage and routines forestimating trace gas and aerosol emissions SPITFIRE wasdesigned to overcome many of the limitations in previousfire models set within DGVM frameworks and be flexibleenough to permit simulation analyses at sub-continental toglobal scales with minimal input data requirements

SPITFIRE is one of the most comprehensive fire mod-ules for DGVMs currently available and has been the fo-cus of numerous studies on the role of fire in terrestrialecosystems and the Earth systemThonicke et al(2010) pre-sented the SPITFIRE model description and global assess-ments of simulated burned area and wildfire trace gas emis-sionsGomez-Dans et al(2013) used SPITFIRE in combi-nation with MODIS burned area and tree cover data to im-prove the modelrsquos predictions of burned area at selected sitesin different biomes using parameter calibration-optimizationtechniques SPITFIRE has also been driven with L3JRCburned area data (Tansey et al 2008) and MODIS burnedarea data (Roy et al 2008 Roy and Boschetti 2009) aspart of the LPJ-GUESS vegetation model (Smith et al2001 Hickler et al 2006) in a study examining emis-sions from biomass burning in Africa (Lehsten et al 2009)Using LPJ-GUESS-SPITFIRELehsten et al(2013) ex-amined how changes to fire frequency including fire ex-clusion affect treendashgrass ratios in Africa RecentlySpessaet al (2012) benchmarked LPJ-GUESS-SPITFIRE againstremote-sensing-based tree biomass data for pan-tropicalforests and savannas (Saatchi et al 2011 Baccini et al2012) The model was driven by a combination of monthlyburned area from the Global Fire and Emissions Database(GFEDv31Giglio et al 2010 van der Werf et al 2010)and long-term annual fire statistics (Mouillot and Field2005)

In addition to LPJ and its variants SPITFIRE hasbeen incorporated into other vegetation modelsSpessa andFisher(2010) coupled SPITFIRE to a global version of theEcosystem Demography (ED) vegetation model (Moorcroftet al 2001) ED has been incorporated into the MOSES22land surface model (Met Office Surface Exchange SchemeEssery et al 2001 Fisher et al 2010) and the CommunityLand Surface Model (CLMOleson et al 2010) SPITFIREis currently being integrated into ED-CLM (Spessa andFisher in preparation) With minor modifications SPITFIREhas also been incorporated into the LPX-DGVM (Prenticeet al 2011) and applied in global experiments to quantifythe contribution of wildfires to the global landndashatmosphereCO2 flux

In the following sections we describe LPJ-LMfire whichis a revised version of LPJ-SPITFIRE that we designedfor simulating global fire and vegetationndashfire interactionson centennial to multi-millennial timescales primarily dur-ing prehistoric and preindustrial time The purpose of thismanuscript is to present a complete description of our cur-rent model code to facilitate referencing of the model in

Geosci Model Dev 6 643ndash685 2013 wwwgeosci-model-devnet66432013

M Pfeiffer et al Global biomass burning in preindustrial time LPJ-LMfire (v10) 645

our future publications and promote easier dissemination ofour methods to other researchers who may be interested inusing our model We perform a detailed evaluation of thenew model based on simulations and observations of fire inAlaska and compare the results of a global simulation overrecent decades to data sets of observed burned area We con-clude with recommendations for future model development

2 Rationale for modifying SPITFIRE

We were motivated to modify SPITFIRE for two main rea-sons (1) in some parts of the world with very little humanimpact on the landscape most notably in boreal and sub-arctic North America both LPJ-SPITFIRE and LPX simu-lated little or no burned area where observations show thatlarge fires do occur however infrequently This indicated tous that the fundamental behaviour of the model andor thedata sets used to drive the model could be improved (2) Wewanted to describe a scheme for simulating anthropogenicfire during the preindustrial period The formulation for an-thropogenic fire ignitions based on population density and asingle spatially variable parametera(Nd) did not seem appro-priate to us based on what is known about the way humansused fire during preindustrial time In updating SPITFIRE totackle these goals we had to make several changes to the firemodule and to LPJ itself In addition to these changes weintroduce new formulations for lightning occurrence rate ofspread in herbaceous fuels and anthropogenic burning A de-tailed description of our changes from the original SPITFIREfollows

3 Methods

Here we present a new fire module LPJ-LMfire that is de-signed to be used with LPJ and similar DGVMs The mod-ule is largely based on SPITFIRE (Thonicke et al 2010)but has been substantially altered in a number of impor-tant ways We made changes that improved the simulationof daily lightning ignitions fuel bulk density fire rate ofspread and fire mortality In order to simulate human fireduring preindustrial and prehistoric time we replace the sim-ple population-density-based formulation for anthropogenicignitions with a classification of humans by their subsis-tence lifestyle and introduce specific goals for each groupin terms of fire management of their landscape We furtherintroduce a new scheme to track the progression of individ-ual fires over the entire fire season and simulate smolderingignitions Fires in LPJ-LMfire continue burning for multipledays once ignited and are extinguished only by changes inweather by merging with other active fires or by running outof fuel when encountering previously burned area Finallywe account for passive fire suppression as a result of land-scape fragmentation from anthropogenic land use These newmethods for calculating wildfire occurrence behaviour and

impacts required changes not only to SPITFIRE but also toLPJ which we detail below

The model description that follows is presented in the fol-lowing order

ndash Fire occurrence and ignitions (Sect31)

ndash Fire behaviour (Sect32)

ndash Fire impacts on vegetation (Sect33)

In each section we detail the representations in LPJ-LMfirethat are different from the original SPITFIRE followed byany changes we needed to make to LPJ to accommodatethe requirements of the fire model The description belowis intended to stand alone (ie the entire model can bereconstructed on the basis of the equations and parame-ters presented in this paper without relying on earlier pub-lished descriptions) A comprehensive list of abbreviationsis provided in Table 1 a flowchart illustrating the struc-ture of LPJ-LMfire depicted in Fig1 and a table listingthe plant functional type (PFT)-specific parameters presentedin Table A1 The remaining equations that were unchangedfrom original SPITFIRE are detailed in Appendix A alongwith a table of supplementary symbols and abbreviations(TableA2)

As a note on random numbers LPJ-LMfire as withSPITFIRE and some versions of LPJ (egGerten et al2004) uses random numbers to calculate certain processesincluding precipitation occurrence and daily precipitationamount In LPJ-LMfire we additionally use random num-bers in the calculation of lightning fire ignitions In this paperwhen we describe the use of random numbers we are refer-ring to values drawn from a pseudo-random sequence thatdisplays statistical randomness To guarantee reproducibilityof simulation runs in LPJ-LMfire across platforms ratherthan using a built-in function we include random numbergenerators in the model code for sampling uniform distri-butions (Marsaglia 1991) and for other distributions basedon the uniformly distributed sequence (Dagpunar 1988) Weseed the random sequence at the beginning of each model runusing a four-byte integer hash that is calculated from the ge-ographic coordinates of the grid cell and is unique to at least30 arc seconds of precision The state of the random numbersequence is stored separately for each grid cell so the se-quence of random numbers is preserved even if the modelruns grid cells in parallel or a different order This procedureensures that every grid cell run with the same longitude andlatitude will have exactly the same sequence of random num-bers every time the model is run

31 Fire occurrence and ignitions

311 Factors excluding fire

As with SPITFIRE the LMfire routine is designed to oper-ate on a daily timestep However to save computation time

wwwgeosci-model-devnet66432013 Geosci Model Dev 6 643ndash685 2013


Table 1Explanation of variable and parameter abbreviations

variable variable explanation variable unit

lm monthly number of lightning flashes [gridcellminus1monthminus1]LISOTDm monthly number of lightning flashes from LISOTD data set [gridcellminus1monthminus1]CAPEanom normalized CAPE anomaly of given month [gridcellminus1monthminus1]ieffavg average ignition efficiency [ndash]ieffpft PFT-specific ignition efficiency [ndash]fpcgrid foliar projected cover fraction of PFT on grid cell [ndash]ieffbf ignition efficiency determined by burned area fraction of grid cell [ndash]ieff overall ignition efficiency [ndash]burnedf cumulative fraction of total grid cell area burned during the year [ndash]FDI Fire danger index [ndash]rf risk factor [ndash]igp number of ignitions per fire-lighting person [personminus1dayminus1]Dwalk average walking distance per fire-lighting person [m]Wf width of a single fire (shorter axis of burn ellipse) [m]DT distance travelled by fire (length of major axis of burn ellipse) [m]LB length-to-breadth ratio of the burn ellipse [ndash]Abpd potential area that one person can burn [hadayminus1]af average size of a single fire on a given day [ha]targetdgroup daily burning target [hadayminus1groupminus1]targetygroup annual burning target [hayrminus1groupminus1]bf20 20 yr running mean of annual burned area fraction [ndash]nhig number of human-caused ignitions [dminus1]people 10 of all people within a given lifestyle group [ndash]ac area average contiguous area size of patches with natural vegetation [ha]fnat fraction of grid cell covered with natural vegetation [ndash]Agc grid cell area [ha]ρlivegrass fuel bulk density of live grass [kgmminus3]GDD20 20 yr-average number of growing degree days [C]Uf mean wind speed [mminminus1]ROSfsg forward rate of spread of fire in herbaceous fuels [mminminus1]rm moisture content of the fuel relative to its moisture of extinction [ndash]ωnl mean relative moisture content of 1 h fuel class and live grass [ndash]menl mass-weighted average moisture of extinction for live grass and 1 h fuel [ndash]ω(1) moisture content of the 1 h fuel class [ndash]woi(1) dead fuel mass in 1 h fuel class [gmminus2]ωlg relative moisture content of live grass [ndash]wlifegrass mass of live grass [gmminus2]wfinefuel sum of live grass mass and 1 h dead fuel class [gmminus2]SOMsurf mass of organic matter in the O horizon [gmminus2]mefc(1) moisture of extinction for 1 h fuel size class (0404) [ndash]melf moisture of extinction for live grass fuels (02) [ndash]ωo relative daily litter moisture [ndash]meavg mass-weighted average moisture of extinction over all fuels [ndash]α drying parameter for the fuel size classes (15times 10minus3 813times 10minus5 222times 10minus5 15times 10minus6) [Cminus2]wn total fuel (live mass of herbaceous plus dead mass including all PFTs and fuel size classes 1ndash3) [gmminus2]woi(1 3) 1 10 and 100 h dead fuel mass summed across all PFTs [gmminus2]wo total mass of dead fuel summed across the first three fuel classes and all PFTs [gmminus2]wtot total dead fuel mass within the first three fuel size classes plus mass of the live grass [gmminus2]mefc moisture of extinction for the four fuel size classes (0404 0487 0525 05440) [ndash]melf moisture of extinction for live grassherbaceous fuels (02) [ndash]ROSfsw surface forward rate of spread in woody fuels [mminminus1]ROSfsg surface forward rate of spread in herbaceous fuels [mminminus1]treecover fraction of grid cell area covered by tree PFTs [ndash]grasscover fraction of grid cell covered by grass PFTs [ndash]livefuel1h 1 h live fuel summed across all tree PFTs [gmminus2]



Table 1Continued


ROSf rate of forward spread [mminminus1]ROSfs rate of surface forward spread [mminminus1]slf slope factor [ndash]γ slope angle [degrees]firesd number of fires on current day [dayminus1]firesdminus1 number of fires on previous day [dayminus1]iresnew newly ignited fires on current day [dayminus1]

we implemented several checks to ensure that the fire rou-tine is only called when fires are possible We exclude firewhen there is snow cover in the model assuming that a snowlayer will not allow the ignition and spread of surface firesAs the current version of LPJ updates living biomass and thelitter pools annually we further skip calling the fire routineif the total vegetation foliar projected cover (FPC) of the gridcell is less than 50 or if the total amount of fuel includ-ing live fuel all four dead fuel classes and the soil surfacecarbon pool is less than 1 kgm2 These thresholds similar tothose used in LPX (Prentice et al 2011) are based on theassumption that if fuels are discontinuous or insufficient inquantity a fire might start but will not be able to spread farenough from the starting point to cause a significantly largewildfire We calibrated our thresholds by running the modelfor individual grid cells and evaluating the modelled firelineintensity (Isurface) in environments with low vegetation coverandor total fuel load These minimum fuel load and continu-ity thresholds are almost always met except in hot and polardeserts where vegetation reaches its bioclimatic limits

312 Calculation of daily lightning ignitions

Lightning ignitions in SPITFIRE are calculated from asatellite-based climatology of monthly lightning flash den-sity (Christian et al 2003) that is interpolated betweenmonths and scaled to yield a quasi-daily climatology of light-ning strikes (Thonicke et al 2010) This daily number oflightning strikes is further reduced to fire ignitions basedon a constant scaling factor This approach takes into ac-count neither the observation that lightning can be highlyvariable from year to year particularly in regions where thetotal amount of lightning strikes is comparably low nor thatlightning occurrence is clustered in time (ie it is linked toprecipitation events and times of atmospheric instability)nor that observations of fire ignitions suggest that a certainamount of stochasticity characterizes lightning-caused firesHere we describe our new approach for estimating the in-terannual variability of lightning its daily occurrence and arepresentation of the stochastic nature of lightning fire igni-tions

Thonicke et al(2010) argued that they expected the modelsensitivity to inter-annual variability in lightning ignitions to

be small compared to the overall model outcome and thusneglected interannual variability in lightning However wefound that in places where fires are infrequent but importantin terms of ecosystem impacts and are generally caused bylightning (eg in boreal and subarctic North America) inter-annual variability in lightning occurrence is a key componentof fire occurrence In these regions between 72 and 93 of all fires observed at present day are attributed to lightningignitions (Stocks et al 2003 Boles and Verbyla 2000) andlarge interannual variability in burned area is visible in theGFEDv3 data set (Giglio et al 2010) Using the SPITFIREor LPX formulations for lightning ignitions results in sim-ulated burned area that is much smaller than observations inboreal and subarctic North America and Siberia even thoughFDI is nonzero (Thonicke et al 2010 Fig 3cPrentice et al2011 Fig 2) This inconsistency can be explained by thevery low density of lightning strikes in the input climatol-ogy which leads to an estimation of lightning ignitions thatis well below one event per grid cell per month

We therefore believe that it is essential to capture inter-annual variability in lighting activity in order to simulatefire in boreal and subarctic regions that is consistent withobservations The only globally homogenized observationof lightning occurrence that is currently freely available isthe LISOTD satellite-based data set (Christian et al 2003)though other data sets eg WWLLN (Virts et al 2013) andGLD360 (Holle et al 2011) are under development andcould be applied in the future The LISOTD data are avail-able at the 05 spatial resolution we use for LPJ-LMfire butonly as a climatology (the HRMC data set) Lower resolutionLISOTD data are available as a multi-year monthly time se-ries However for the extratropics (north and south of 42 lat-itude) this time series and the climatology is based on only4 yr of satellite observations Because of the limited temporalcoverage and low spatial resolution of available global light-ning data we developed a method of imposing interannualvariability on climatological mean lightning frequency usingancillary meteorological data

Peterson et al(2010) describe the correlation betweenconvective available potential energy (CAPE) and cloud-to-ground lightning flashes for Alaska and northern Canadaindicating that lightning strikes are more common at timeswith positive CAPE anomalies Based on this observationwe produce an interannually variable time series of lightningby scaling the climatological mean lightning flash rate withmonthly anomalies of CAPE The magnitude of the imposedvariability is based on observed lightning strikes from theAlaska Lightning Detection System (ALDSAlaska Bureauof Land Management 2013)

To estimate the range of interannual variability in lightningamount we analysed ALDS strike data for the time periodbetween 1986 and 2010 for June the peak lightning monthin most of Alaska Point observations of lightning strikes inthe ALDS were aggregated on a 05 grid and grid cellswith more than 5 yr of lightning strike observations (approx



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l bu

rnin

g(o

nce

annu

ally

)

Bur

ned

area

20

o

f the

cro

p la

nd a

fter h

arve

st

Fuel

con

sum

ptio

n20

o

f ann

ual

abov

egro

und

biom

ass

(har

vest

re

mai

nder

s)

Fire

impa

ct

Car

bon

loss

tar

ea

burn

ed

Scal

ing

land

use

cov

er fr

actio

ns

(nat

ural

agr

icul

tura

l re

cove

ring)

annu

al g

rid c

ell l

evel

ac

cum

ulat

ion

burn

ed a

rea

em

issi

ons

Tota

l bur

ned

area

and

trac

e ga

sem

issi

ons

no fi

re

spre

ad

yes

no

Fig 1Flowchart of LPJ-LMfire



1750 valid cells) were analysed with respect to the mini-mum maximum and mean number of observed lightningstrikes over all available years For each grid cell the min-imum and maximum observed values were set into a ratioto the temporal mean The two boxplots in Fig2 show theminimum-to-mean ratio and maximum-to-mean ratio distri-bution for all grid cells The total range in interannual vari-ability spanned four orders of magnitude from 1 of to 10-times the mean We used this range to scale climatologicalmean lightning strikes based on CAPE anomalies

Using CAPE from the 20th Century Reanalysis Project(Compo et al 2011) we determined monthly anomalies on agrid cell level compared to the 1961ndash1990 mean CAPE valuefor a given month The largest positive or negative CAPE-anomaly value within the time series for a specific grid cellis used to normalize CAPE anomalies to a range betweenminus1and+1 for the entire time series available for a given gridcell Applying the normalized CAPE anomaly with the scal-ing factor described above the monthly number of lightningflashes is estimated as

lm=

LISOTDm (1+9CAPEanom) CAPEanomge0

LISOTDm (1+099CAPEanom) CAPEanomlt0 (1)

With the lightning flash density given by Eq (1) wedisaggregate the monthly values to a daily amount andscale lightning flashes to cloud-to-ground lightning strikesNoting that lightning and precipitation are closely corre-lated (egJayaratne and Kuleshov 2006 and referencestherein Michaelides et al 2009 Katsanos et al 2007)we allow lightning strikes to occur only on days with pre-cipitation Daily precipitation occurrence is simulated witha weather generator following the original SPITFIRE for-mulation (Thonicke et al 2010) Simultaneous observa-tions show that the quantity of lightning strikes is furtherpositively correlated with precipitation amount (Piepgrasset al 1982 Rivas Soriano et al 2001 Zhou et al 2002Lal and Pawar 2009) Therefore to estimate the numberof daily lightning strikes we scale the total monthly light-ning amount by the daily fraction of monthly total precipita-tion as simulated by the weather generator With daily light-ning flashes we estimate ground strikes by using a flash-to-strike ratio of 20 as in the original SPITFIRE We con-firmed this flash-to-strike ratio as realistic through a quali-tative comparison of satellite-derived lightning flash densityin the LISOTD LRMTS monthly time series with lightningground-strike observations from the ALDS and from an ex-tract of the North American Lightning Detection Network(NALDN Orville et al 2011) data set covering the south-eastern United States

With an estimate of lightning ground strikes SPITFIREcalculates fire starts as a function of a fixed ignition efficiencyof 4 yielding a total lightning flash-to-ignition ratio of08 In contrast the LPX fire model specifies a 3 flash-to-ignition ratio and further reduces the number of fire starts

001

01

1

10

ratio

of

str

ike

s t

o t

em

po

ral m

ea

n

Fig 2 Maximum-to-mean ratio (top box plot) and minimum-to-mean ratio (bottom box plot) for ALDS strike data in June between1986 and 2010 based on approx 1750 grid cells with more than5 yr of observations

using the factorP+ which reduces the effectiveness of igni-tion events in wet months (Prentice et al 2011 Eq 1) Bothof these methods result in a deterministic simulation of firestarts on any given day that is directly linked to lightningamount The initiation of lighting-ignited fires is howeveralso influenced by other factors including the spatial distri-bution of lightning on the landscape the temporal evolutionof burned area during the fire season and by a componentthat is observed but cannot be explained by large-scale vari-ables something that we term stochastic ignition efficiency

These additional controls on fire starts are apparent whenanalysing patterns of lightning strikes and burned area in bo-real and subarctic regions where lightning is rare but largefires develop these are places where human impact is lowbut both SPITFIRE and LPX fail to simulate burned area inagreement with observations In attempting to improve ourability to model lightning-caused fire in the high latitudeswe made a series of changes to the way fire starts are calcu-lated in LPJ-LMfire Our new formulation accounts for thedifferential flammability of different plant types fuel mois-ture the spatial autocorrelation of lightning strikes and pre-viously burned area All of these terms are combined to anestimate of ignition probability against which we comparea uniformly distributed random number that represents thestochastic component of wildfire ignition

Plant types differ in their intrinsic flammability as a resultof leaf and stem morphology typical canopy hydration sta-tus and presence of phenols and other flammable compoundsin the fuel (Diaz-Avalos et al 2001) We noticed that treatingall PFTs the same way with respect to ignition efficiency wasproblematic especially when comparing the tropics (wherelightning strikes are extremely frequent) to the extratropics(where fewer strikes appear in some cases to cause equalor more amounts of fire) In assigning PFT-specific ignitionefficiency parameters we took a top-down approach wherewe qualitatively optimized the ignition efficiency parameter



to match the performance of the model with respect tosatellite-based observations of mean annual burned area frac-tion at the level of a few grid cells in areas where we judgedhuman impact to be low (see Sect45 Fig S9) This op-timization of the parameters led to a large range of valuesbetween 005 and 05 (ieffpft TableA1) The individual igni-tion efficiencies are combined into an FPC-weighted average

ieffavg =

npftsumpft=1

(fpcgridieffpft

)npftsum

pft=1fpcgrid

(2)

Lightning strikes display a large degree of spatial auto-correlation tending to cluster on mountaintops and otherhigh terrain tall buildings water bodies etc (Kotroni andLagouvardos 2008 Mazarakis et al 2008 Uman 2010)Because of this autocorrelation successive thunderstormsover the course of a fire season become less likely to start newfires because lightning will strike places that have alreadyburned As such we decrease the likelihood of lightning-ignited fires as a function of the area already burned to date

ieffbf =1minus burnedf

1+ 25burnedf (3)

This equation is based on an empirical evaluation of NALDNdata for Florida where we investigated the spatial autocorre-lation of lightning strikes in relation to strike density

Similarly to LPX the probability that a lightning strikewill result in an ignition also depends on fuel moisture LPXuses an additional parameterβ based on a single transectacross the Sahel and applied globally to influence the rela-tionship between fuel moisture and ignitions Given the un-certainty in this formulation and to avoid using another pa-rameter in LPJ-LMfire we use the fire danger index (FDI) asan indicator of fuel moisture The overall ignition probabilityon a given day is therefore calculated as

ieff = FDIieffavgieffbf (4)

As explained above this probability is compared with auniformly distributed random number that represents thestochastic component of wildfire ignitions that helps to ex-plain why in certain cases a single lightning strike can be suf-ficient to cause a fire whereas in other cases many lightningstrikes within one thunderstorm do not cause a single fire(Nickey 1976 Keeley et al 1989 Kourtz and Todd 1991Jones et al 2009 Hu et al 2010) The net effect of thisapproach is that lightning will sometimes cause a fire eventhough conditions are not very favourable and vice versaBy allowing either zero or one ignition per grid cell and daywe account for the fact that lightning ignitions are discreteevents

313 Anthropogenic ignitions

Humans have used fire since the Palaeolithic as a tool formanaging landscapes optimizing hunting and gathering op-portunities cooking hunting and defense and communica-tion (Pyne 1994 Anderson 1994 Pyne 1997 Carcailletet al 2002 Tinner et al 2005 Roos et al 2010) The re-lationship beween humans and fire has changed over historyparticularly after the Neolithic revolution when people begancultivating domesticated plants and animals (Iversen 1941Kalis and Meurers-Balke 1998 Luning 2000 Rosch et al2002 Kalis et al 2003) and during the 20th century fol-lowing the widespread mechanization of agriculture and in-stitution of industrial fire suppression Since our goal is todevelop a model capable of simulating fire in prehistoric andpreindustrial time we attempt to quantify the way in whichhumans in the past used fire For us the main question is notsimply how much fire people can cause as it only takes afew dedicated individuals to cause significant amounts of fire(egEva et al 1998) but rather ndash how much fire would hu-mans want to cause given certain environmental conditionsand subsistence lifestyles We further account for the physi-cal limits to anthropogenic fire ignitions

Subsistence lifestyle is a very important factor determin-ing why humans light fires and to what extent they light firesin order to manage their environment (Head 1994 Bowman1998 Bowman et al 2004) Hunter-gatherers use fire to pro-mote habitat diversity and grass for game keep landscapesopen to ease their own mobility and help prevent high-intensity wildfires late in the season that could completelydestroy vegetation resources They accomplish these goalsby lighting low-intensity fires early in the fire season thatremove only understorey vegetation and prevent dangerousbuild-up of fuels (Lewis 1985 Pyne 1997 Williams 2000Kimmerer and Lake 2001 Stewart et al 2002) Pastoralistsuse fire to kill unpalatable species and stop woody encroach-ment to promote the growth of fresh grass to control para-sites and animal movements and to increase visibility whilemustering (Crowley and Garnett 2000 ) Farmers will burncrop residues after harvest and pastures for domesticatedgrazers and depending on population density and availabilityof unused land may use fire to prepare new cropland whileold areas are abandoned eg in systems of shifting cultiva-tion

Thus modelling human burning in preindustrial time iscomplex as different groups of people had different goalsfor fire management and these probably changed in spaceand time and because few quantitative observations existthat enable us to directly calibrate our model It is there-fore necessary to make assumptions on the relationship be-tween humans and fire based on qualitative information egfrom ethnographic anthropological and archaeological stud-ies Theoretically the only limit to how much people canburn depends on population density average daily walkingrange of people fire weather conditions and fuel availability



and structure In most cases people will not fully exploitthe potential maximum amount of fires they can cause asthey will try to use fire in a constructive way to manage theirhabitat rather than destroying it by overburning (Head 1994Bowman 1998 Bowman et al 2004) We define this con-structive use of fire in terms of burn targets for the three sub-sistence lifestyle groups described above

For foragers we assume that their goal is to use fire tocreate and maintain semi-open landscapes as this was thehabitat most preferred by prehistoric people because habi-tat diversity and foraging opportunities increase with mod-erate disturbance but decrease again if disturbance becomestoo severe (egGrime 1973 Connell 1978 Huston 1979Collins 1992 Roxburgh et al 2004 Perry et al 2011Faivre et al 2011) We therefore link the annual amount thatforagers will try to burn to the simulated degree of landscapeopenness ie tree cover and the effectiveness of fires to openup forest ie the rate of change of vegetation cover over timeThe annual burn target for foragers is calculated as

tann=max

(min

((1minusgrass)max

(d(grass)

dt0

)201

)0

) (5)

with the change in grass cover being estimated as

d(grass)

dt= grass(tminus1) minus

(09grass(tminus1) + 01grasst

) (6)

These equations imply that foragers living in an area withhigh forest cover will initially try to use fire to open the land-scape As the forest cover is reduced the annual amount ofanthropogenic fire will be reduced to maintain an equilib-rium level of openness of the landscape Alternatively if an-thropogenic burning has little effect on forest cover eg inwet environments humans will ldquogive uprdquo trying to burn theirlandscape after a short period of time This quantification ofhunter-gatherer fire use is based on suggestions that nativeNorth Americans repeatedly made controlled surface burnson a cycle of 1ndash3 yr broken by occasional catastrophic firesthat escaped the area intended to burn and periodic conflagra-tions during times of drought (Pyne 1982 Williams 2002b)

Pastoralists are assigned a constant burn target of 20 (equal to a 5 yr fire return interval) that they will try to reachbefore they stop igniting fires assuming that their interestin causing fires is less pronounced as they will try to pre-serve biomass for their domesticated grazers while at thesame time trying to maintain good pasture quality and avoidfuel accumulation in fire-prone environments Present-dayrecommendations for prescribed fire maintenance of prairiesand pastures suggest that a fire return interval target of 5 yrmay even be on the more conservative side of estimates(Prairiesourcecom 1992 Government of Western AustraliaDepartment for Agriculture and Food 2005)

Farmers may burn unused land to expand their area undercultivation or prepare new fields as old ones are abandonedeg in shifting cultivation systems They may also light fires

to control fuel build-up and mitigate the possibility of devas-tating wildfires in areas adjacent to their cultivated land oruse fire to maintain pastures To account for these processeswe assign farmers an annual burn target of 5 on land notused for agriculture corresponding to a fire return interval of20 yr

Given the assumption that people burn purposely toachieve a certain goal it is unlikely that all people who arepresent in a grid cell will cause fire When 10 or more peo-ple are present in a grid cell we therefore allow only ev-ery 10th person present to purposely ignite fires Amongall groups of people cognitive genetic and economic fac-tors mean that human social organization leads to hierarchiesof group sizes Numerous archaeological and ethnographicstudies have demonstrated that these relationships are re-markably stable over time (egHamilton 2007 Whiten andErdal 2012) Marlowe(2005) suggests that the optimal sizeof a hunter-gatherer group is 30 persons We assume thatthree members of this group eg able-bodied young maleswill be responsible for fire management in the territory ofthe group We allow for the possibility that the total numbercould be smaller at times eg during colonization of new ter-ritory if less than 10 people are present in a grid cell thenone person is responsible for fire ignitions This 10 scalingfactor on active human agents of fire is most important whencalculating ignitions among forager populations In agricul-tural and pastoral groups population density will nearly al-ways be high enough to ensure that an overabundance of po-tential arsonists is available to aim for the burn targets wespecify

Anthropogenic ignitions are determined after the calcula-tion of the average size of single fires and their geometryon a given day The number of individual ignitions per fire-lighting person is calculated as

igp =Dwalk

Wf (7)

where

Wf =DT

LB (8)

The area that one fire-lighting person potentially can burn inone day is given by the equation

Abpd = igpaf (9)

where the average distance that one person lighting fire walksin one day is limited to 10 km

How much fire people will start on a given day will de-pend on the environment in which they live People who livein an environment that naturally has a lot of fire will takeinto account that some part of the landscape will burn natu-rally and adjust their burn target accordingly in order to avoidoverburning In order to take into account that people have acollective memory of the fire history in their habitat we keep



track of the 20 yr running mean of the burned area fraction ina given grid cell and define the daily burn target for a givenlifestyle group as

targetdgroup= Agcmax(targetygroupminus bf20minus burnedf

) (10)

with Agc being the grid cell area in ha This function servesto reduce the target over the course of the year as people ap-proach it Once the target has been reduced to zero peoplewill stop igniting fires The 20 yr-average burned area frac-tion is subtracted to let people stay conservative with theirburning by taking into account that there can be some base-line amount of lightning-caused fire as well thereby avoidingoverburning of their target

Ethnographic and historical studies have shown that prein-dustrial humans lit fires for landscape management purposeswhen fires were not likely to become severe ie when me-teorological conditions allowed burning but the overall firedanger was not too high To represent this observation werestrict anthropogenic burning to days when the averagesize of single firesaf will not become larger than 100 haAdditionally the number of fires started by people on a givenday is linked to the FDI via a multiplication factor that re-duces the ignitions as FDI increases

rf =

1 FDI le 025

1122πFDIe

minus(ln(FDI)+129)2

018 FDI gt 025 (11)

The decline of the risk factor rf follows a log-normal dis-tribution with a maximum value of 1 at an FDI of 025 thatthen declines toward zero as FDI increases which thereforemakes it increasingly unlikely that people will keep caus-ing fires when conditions for causing out-of-control firesbecome more risky We developed this equation based onethnographic studies from Australia showing that Aboriginespreferentially cause fires at the beginning of the dry seasonwhen fire danger is still moderate and decrease their ignitionactivities as FDI increases (Bowman 1998 Yibarbuk et al2002 Bowman et al 2004) We chose a log-normal curveto describe the relationship between anthropogenic ignitionsand FDI because even with high fire risk the chance thatsomeone causes a fire will not be completely zero

In cases where enough fire-lighting people are available toreach or exceed the burn target for the given day the numberof human-caused ignitions is derived from

nhig = rftargetdgroup

af (12)

and in cases where the burn target of the day cannot beachieved due to a lack of enough fire-lighting people from

nhig = igppeoplerf (13)

Anthropogenic ignitions can be optionally specified forany given model run but are always excluded in the modelspinup before year 800 of the simulation in order to allow thedevelopment of a stable vegetation cover

314 Burning of cropland

All of the equations presented in Sect313concern anthro-pogenic burning on the fraction of the grid cell where po-tential natural vegetation is simulated by LPJ We prescribeadditional burn targets to account for anthropogenic burn-ing on the part of the grid cell that is occupied by croplandEvidence suggests that the usage of fire in cropland manage-ment was widespread in preindustrial times (egDumond1961 Sigaut 1979 Otto and Anderson 1982 Johnston2003 Williams 2002a) and even nowadays is common inparts of the world where agriculture is largely unmechanizedeg in Sub-Saharan Africa and parts of South and SoutheastAsia Indonesia and Latin America (Conklin 1961 Seilerand Crutzen 1980 Dove 1985 Smittinand et al 1978Unruh et al 1987 Kleinman et al 1995 Van Reuler andJanssen 1996 Cairns and Garrity 1999 Akanvou et al2000 Fox 2000 Rasul and Thapa 2003)

Depending on agricultural practices crop residues maybe burned in situ or collected and burned throughout theyear eg as a fuel (Yevich and Logan 2003) Fields that areburned may be burned immediately after harvest or shortlybefore planting and in some places where double or triplecropping is practised possibly even several times per yearCropland burning can be achieved largely independently offire weather for example managed fire was historically im-portant in places with hypermaritime climate such as the up-lands of northwestern Europe (Mather 2004 Dodgshon andOlsson 2006)

In LPJ-LMfire 20 of the total simulated crop biomassproduced within 1 yr remains on the fields as residues andthis remaining biomass becomes potential fuel for agricul-tural burning Farmers are assumed to burn 20 of the to-tal cropland area within a grid cell every year We derivedthis value from a qualitative comparison between total annualarea burned observed in GFEDv3 and our simulated burn-ing on natural land for regions in Africa where agriculturalburning is commonly practised after harvest It is a conser-vative first approximation for the past when people did nothave modern-day technology available to prepare fields forthe next crop planting after harvest and likely could be muchhigher in places where for example multi-cropping is prac-tised and all fields are burned after every harvest

As described above cropland and crop residue burningpractices vary with space and time We therefore make noattempt to estimate the seasonality of cropland burningaside from excluding cropland burning when snow coveris present or temperatures are below 0C and assume thatburning is evenly distributed across all other days of theyear Future improvements to the model could attempt toresolve the temporal pattern of cropland burning by using amore sophisticated crop module for LPJ (egBondeau et al2007) For studies that focus on fire seasonality or trace gasemissions from biomass burning on a sub-annual scale thetiming of anthropogenic activities affecting seasonal patterns



of fire cannot be neglected and will need to be accounted forexplicitly

32 Fire behaviour

As described above boreal and subarctic regions are charac-terized by infrequent lightning ignitions that may still leadto large amounts of burned area because individual fires per-sist over the course of several weeks or months (Alaska FireService 2013) On the other hand both SPITFIRE and LPX(Prentice et al 2011) allow fires to burn for a maximum du-ration of 241 min after which individual fire starts are extin-guished Combined with the fractional occurrence of light-ning ignitions described above this representation of fire du-ration may be one of the main reasons why these models sim-ulate burned area that is inconsistent with observations Thelargest change we made from the original SPITFIRE was theimplementation of a scheme for multi-day burning and thecoalescence of fires After making this fundamental changeto the model we had to revise other SPITFIRE formulationsto make them consistent with our new approach These revi-sions included changes to the representation of fuel composi-tion and amount to meteorological influences on fuel mois-ture and rate of spread and the introduction of representationof the role of topography in influencing fire size The newfunctionality and changes are detailed below

321 Multi-day burning and coalescence of fires

Once a wildfire is started it typically continues burning aslong as fire weather conditions and availability of fuel do notrestrict the progress of the fire (egTodd and Jewkes 2006Desiles et al 2007 Jones et al 2009) Wildfires display acharacteristic diurnal cycle with the most active period be-ing around midday and early afternoon when humidity is ata minimum and wind speeds are higher (Pyne et al 1996)To account for these observations we remove the 241 minlimitation on fire duration specified in SPITFIRE but main-tain this value as an active burning period on any given dayin calculating daily burned area Individual ignitions persistfrom one day to the next until they are extinguished due to(1) merging with other fires (2) running out of fuel fromburning into areas already burned during the current year or(3) as a result of sustained precipitation

In LPJ-LMfire the total number of fires burning on a spe-cific day is therefore defined as the number of fires that werestarted on previous days that have not yet been extinguishedplus any potential additional ignitions on the current day Asindividual fires grow in size the likelihood of one fire burn-ing into another or into an area that has already burned in-creases To take this into account we reduce the number offires burning on any given day by the product of the grid cellfraction that has already burned in the current year and thetotal number of fires on this day Thus the total number of

fires on any given day is calculated as

firesd=firesdminus1+firesnewminusburnedf(firesdminus1+firesnew) (14)

In allowing fires to burn for multiple days we needed todefine threshold amounts of precipitation above which ongo-ing fires will be extinguished Field observations have shownthat while small amounts of precipitation will impede firespread fires may keep smoldering and start spreading as soonas conditions dry out again and that the amount of precipi-tation required to slow or stop wildfires differs depending onthe type of fuel that is burning (Latham and Rothermel 1993Hall 2007 Hadlow 2009 Pyne et al 1996) LPJ-LMfireextinguishes burning fires when the precipitation sum overconsecutive days exceeds 10 mm for grid cells that have agrass cover of less than 60 and 3 mm for grid cells withmore than 60 grass cover (ie fires are extinguished afteras many rain days in a row as it takes to reach the extinctionthreshold)

322 Fuel quantity and density

While testing development versions of LPJ-LMfire we no-ticed that simulated burned area greatly exceeded GFEDv3observations in parts of Siberia and the seasonal tropicalforests of South America We diagnosed the cause as veryhigh simulated fuel loads that in turn propagated extremelylarge fires High fuel loads in the tropics were the resultof unrealistic accumulation of biomass in living vegetationwhereas in the boreal regions slow decomposition of lit-ter with low bulk density led to an unrealistically deep andloosely packed fuel bed To improve the simulation of firewe therefore made several changes to the way LPJ simulatesbiomass and fuel bed density

In LPJ the amount of live woody biomass in a grid cellis determined by the PFT state variables of the average indi-vidual that represents the mean of the PFT population withrespect to all state variables describing the PFT and by theindividual density that represents the number of individualsin a unit area (Sitch et al 2003) Accumulation of biomassin the average individual is limited by the maximum crownarea parameter Density is limited by space in the grid cellwith the assumption that individuals do not overlap in space(packing constraint) Thus at equilibrium individual densitystabilizes as the size of the average individual approachesmaximum crown area In our tests simulated biomass ac-cumulated to very high levels in areas where disturbance israre and growth rates are high such as the perennially humidparts of the Amazon Basin

To reduce biomass in LPJ-LMfire we allow trees to reacha maximum crown area of 30 m2 instead of the 15 m2 usedin the original LPJ parameterization At the same timewe increased the maximum sapling establishment rate from012 individualsmminus2 to 015 individualsmminus2 As leaves haveless biomass per unit area than stems increasing the maxi-mum crown area parameter in the model decreases density



a)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24

live biomass [kg C mminus2]

b)

Fig 3 Simulated aboveground C-storage in living biomass(a) after corrections to maximum establishment rate and maximum crown diam-eter in LPJ compared to aboveground live biomass values derived fromSaatchi et al(2009) (b)

and therefore simulated total biomass Adjusting these twoparameters leads to an overall decrease in total biomass be-tween 5 and 15 for the area shown in Fig3 with high-est reduction percentages in areas of high biomass such asthe upper Amazon Basin As described above the reduc-tion effect caused by the increase of maximum crown area ismost relevant for the wet tropics where trees experience littledisturbance and optimal growth conditions In most extra-tropical regions the new limit for maximum crown area isusually not reached due to climate-induced mortality and dis-turbance

In boreal regions where we noticed very high amounts ofburned area in our development simulations we traced thisback to high rates of fire spread simulated in an unrealisti-cally deep and loosely packed fuel bed In LPJ litter decom-position is controlled by temperature and moisture so thatunder cold dry conditions very slow effective decomposi-tion rates are simulated and litter tends to accumulate fordecades to centuries In boreal regions particularly in thedrier parts of Alaska and Siberia the model therefore sim-ulated large accumulations of aboveground litter with valuesas high as 7 kgCmminus2 Following the original SPITFIRE pa-rameterization fuel bulk density is relatively low 2 kgmminus3

for herbaceous litter and 25 kgmminus3 for woody litter Largeaccumulations of litter therefore lead to the formation of adeep loosely packed fuel bed This problem is exacerbatedwhen frequent fires result in widespread tree mortality andshift the vegetation cover towards being dominated by herba-ceous PFTs

Cold dry climates lead to the accumulation of largeamounts of organic matter but the assumption that thesewould not be mechanically and chemically altered with timeis unrealistic (Berg 2000 Berg et al 2001 Akselsson et al2005)To account for changes in the physical properties ofthe fuel bed with time we introduce an aboveground or-ganic matter pool in LPJ that schematically represents anO horizon After having calculated decomposition in the

Table 2Rate of spread (ROS) calculations before and after imple-mentation of the O horizon

relative fuel moisture () ROS (msminus1)

without O horizon fine fuel load 42 kgmminus2

10 92950 514

with O horizon fine fuel load 02 kgmminus2

10 04750 024

All calculations performed with wind speed of 3msminus1 and fine fuel bulk densityof 2kgmminus3

three litter pools (fast litter slow litter and belowground finelitter) following Sitch et al(2003) the remaining carbon inthe fast litter pool is transferred to the O horizon where it de-composes with a nominal turnover time of 2 yr at a tempera-ture of 10C This way an organic layer can build up in coldplaces where litter decomposition is slow and unrealisticallylarge accumulations of litter are avoided Carbon that wastransferred to the O horizon does not contribute to the rate ofspread calculations as it is considered to be densely packedcompared to the fuels in the regular fuel size classes but itis included into the overall fuel combustion term As shownin Table2 reducing the amount of dead fuel by transferringolder litter into the O horizon strongly affects the simulatedrate of spread and therefore fire size and burned area

We also noticed that our implementation of the originalSPITFIRE resulted in high rates of fire spread in tundraecosystems and consequently simulation of burned areathat exceeded observations (GFEDv3Alaska Fire Service2013) As the standard version of LPJ does not have atundra shrub PFT subarctic vegetation is primarily repre-sented by the C3-grass PFT for which SPITFIRE assigns aconstant fuel bulk density of 2 kgmminus3 In tundra ecosystemsherbaceous plants and shrubs grow close to the ground and



typically have a dense life form eg as tussocks as an adap-tation against damage from frost and snow burden (Bliss1962 Sonesson and Callaghan 1991 Sturm et al 2000)To account for the dense growth form of tundra and the gen-eral tendency of herbaceous vegetation to grow more denselyand closer to the ground with decreasing temperatures we in-troduced a dependency between the bulk density of the twoherbaceous PFTs and the 20 yr running mean of the annualsum of degree-days on a 5C base (GDD20Sitch et al2003)

ρlivegrass=20000

GDD20+ 1000minus 1 (15)

In the tropics the annual GDD sum can be as high as 10 000whereas in high latitudes values are typically 1000 or lessWith fewer GDDs we decrease bulk density from typical val-ues in tundra areas of 10ndash12 kgmminus3 to 1ndash2 kgmminus3 in warmtropical regions where tall grasses grow These endpoint val-ues are estimated based on abundant field evidence demon-strating that tropical grasses are typically tall whereas herba-ceous tundra is short and often grows in dense tussocks (egBreckle 2002 Gibson 2009) We use GDD20 because grassbulk density should not be influenced by interannual variabil-ity in climate as individual species have a relatively stablegrowth habit over time The modification of grass fuel bulkdensity affects simulated rate of spread For example givena fuel load of 1 kgmminus2 a wind speed of 3 msminus1 and a fuelbulk density of 2 kgmminus3 the resulting ROS is 236 msminus1 atan rm of 01 and 122 msminus1 at an rm of 05 With a fuel bulkdensity of 12 kgmminus3 ROS is reduced by roughly one orderof magnitude to 027 msminus1 and 014 msminus1

323 Fuel moisture

For herbaceous fuels we set the relative moisture content ofthe fuel to be equal to the ratio

rm =ωnl

menl (16)

whereωnl is the mean relative moisture content of the 1 hfuel class and the live grass and menl is the mass-weightedaverage moisture of extinction for live grass and 1 h fuelωnland menl are calculated as follows

ωnl =ω(1)woi(1) + ωlg

(wlivegrass+ SOMsurf

)wfinefuel+ SOMsurf

(17)

menl =mefc(1)woi(1) + melf


)wfinefuel+ SOMsurf

(18)

As discussed above the implementation of multi-day burn-ing in LPJ-LMfire led to simulations of fires that were overlylarge and frequent compared to observations This overburn-ing was partly solved by introducing the O horizon for sur-face litter and by adjusting the bulk density of live herba-ceous fuels However in drier boreal and subarctic regions

we also noticed that herbaceous live fuel moisture was verylow in the middle of the growing season This low moisturewas a result of LPJrsquos standard representation of soil hydrol-ogy where all soils are considered to be free draining In real-ity much of the boreal and subarctic regions are underlain bypermafrost which acts as a barrier to water drainage (Kaneand Stein 1983 Niu and Yang 2006) To approximate theeffects of permafrost on soil moisture and therefore herba-ceous live fuel moisture we impede all drainage of soil waterin LPJ where permafrost is present We define permafrost asoccurring in any grid cell where the 20 yr running mean an-nual temperature is less than 0C

For woody fuels relative moisture content is calculated as

rm =ωo

meavg (19)

Instead of resetting the relative daily litter moisture to satu-ration as soon as daily precipitation exceeds 3 mm ie whenthe Nesterov Index (NI) is set to zero we calculateωo as amass balance between drying and wetting of the fuel assum-ing that at a threshold of 50 mm precipitation all fuel will becompletely wet and lesser amounts of rain will partially wetthe fuel according to the amount of precipitation The dry-ing term is estimated as a function of daily maximum andminimum temperature similar to the way the Nesterov Indexis calculated in original SPITFIRE based on the differencebetween the dayrsquos minimum and maximum temperature thefuel water content and a fuel drying parameter integratedover theα-parameters given inThonicke et al(2010) ac-cording to fuel composition

dryo = tmax(tmaxminus tmin minus 4)cafωodminus1 (20)

wet=

1 precgt 50mm

prec50 precle 50mm

(21)

with 50 mm of daily precipitation being the threshold def-inition for heavy rain given by the World MeteorologicalOrganization (httpsevereworldweatherorgrain) at whichwe assume all fuel to be water-saturated independent of itsprevious water status

The water balance between drying and wetting is calcu-lated as follows

balance= ωodminus1 minus dryo + wet (22)

which is essentially a simple water bucket approach similarto the way the soil water balance is calculated in LPJ Thefuel moisture on the current day is defined as

wet=

1 balancegt 1

balance 0 le balancele 1

0 balancelt 0

(23)



The variable caf representsα combined over all fuels and iscalculated as

caf=

3sumi=1

αwoi

wn

wo

wtot+ αlg

wlivegrass

wtot (24)

The mass-weighted average moisture of extinction over allfuels meavg is calculated as

meavg =

fcsumi=1

(woimefc)

fcsumi=1

woi

middotwo

wtot+

melfwlivegrass

wtot (25)

Depending on the grass cover fraction of the grid cell FDI iscalculated as

FDI =

max(0(1minus

ωnlmenl

) grasscoverge 06

max(0(1minus

ωomeavg

) grasscoverlt 06

(26)

324 Fire rate of spread

In contrast to SPITFIRE we assume that fires will be mostlycarried in light fuels as these are easily ignited due to theirhigh surface area-to-volume (SAV) ratio and low fuel bulkdensity whereas heavier fuel components will sustain burn-ing once fire has started at a given place As each PFT in LPJoccupies an exclusive space on the grid cell the possibilitythat their fuels are spatially collocated is also excluded OurMonte Carlo simulations on the continuity of natural land de-pending on the fraction that is occupied by agricultural land(Sect326 Eq33) revealed that in a randomly distributedspatial arrangement of two differing entities the fractionaloccupation ratio has an influence on the continuity of bothentities This result also applies to the distribution of herba-ceous versus woody PFTs and thus fuels

For example if a herbaceous PFT occupies more than60 of the grid cell fire rate of spread is determined bythe properties of the herbaceous fuel because it is not pos-sible to arrange the remaining 40 ie the woody PFTsin a way that interrupts the continuity of the herbaceous fuelBelow 60 herbaceous cover the average contiguous size ofpatches of herbaceous vegetation rapidly decreases as longas areas occupied by grass or trees are assumed to be dis-tributed more or less randomly and the influence of woodyfuels on the overall rate of spread becomes more dominantWe therefore calculate rate of fire spread for herbaceous andwoody fuel components separately and then average the twocalculated rates of spread according to the coverage of theherbaceous and woody PFTs on the landscape

To calculate rate of spread in grass we use a modified formof the equation given inMell et al (2012) setting the fuel

bulk density for these light fuels equal to theρlivegrassvaluecalculated in Eq (15)

ROSfsg =

((0165+ 0534

Uf

60

)eminus0108rm100gs60 (27)

where

gs = minus00848min(ρlivegrass12

)+ 10848 (28)

Equation (28) accounts for the variable density of live grassdepending on GDD20 as calculated in Eq (15) Comparedto SPITFIRE the rate of spread in this new equation requiresfewer parameters (wind speed ratio of relative fuel moistureto its moisture of extinction and fuel bulk density) and typ-ically results in slower rate of spread when all other condi-tions are equal

The rate of spread in woody fuel is calculated as inSPITFIRE with the exception that we use a fixed value of5 cm2cmminus3 for SAV assuming that fire will be carried pri-marily by the finest component of the fuel bed For detailson the calculation of rate of spread see the equations inAppendixA

We determine the surface forward rate of spread as theweighted average of the rate of spread in the woody andherbaceous fuel according to the cover fractions of tree- andgrass-PFTs on the landscape

ROSfs =ROSfswtreecover+ ROSfsggrasscover

treecover+ grasscover (29)

In addition we introduced a wind multiplier for high-windconditions at a wind speed of 10 msminus1 and above the cal-culated ROS will be doubled as the BEHAVE-based ROS isincreasingly too low at higher wind speeds (see Fig 13 inMorvan et al 2008)

windfact=

1+ e2Uforward minus 20 Uforward

60 le 10

2Uforward

60 gt 10 (30)

325 Effect of terrain on average fire size

Terrain can be an important factor influencing the spread offires (Pyne et al 1996) We argue that areas with high re-lief energy should have smaller average fire sizes comparedto areas that are completely flat as dissected topography willinhibit fire propagation Although fire rate of spread is usu-ally faster upslope due to more fuel surface being exposedto the flames than on flat terrain and additional upslope windeffects at 05 spatial resolution no individual grid cell ofsim1000ndash3000 km2 represents one single slope Rather all up-slopes will be accompanied by downslopes on the opposingside where fire spread will be slowed or impeded Terrainwith high relief energy is also characterized by varying slopeexposures A dry sun-exposed slope will be opposed by ashady slope with wetter fuel conditions different vegetation



and in some cases a sparsely vegetated crest that separatesboth slopes and impedes the spread of fires from one catch-ment into a neighbouring one (Guyette et al 2002) Fuelcontinuity also can be broken by areas of unvegetated rockand cliffs which are more likely to occur in complex terrain

Our qualitative observations of remotely sensed burnedscars (Alaska Fire Service 2013) databases of individual firesize (National Interagency Fire Service 2013) and previousmodelling studies (Parks et al 2012) show that very largefires ie those that would consume an entire 05 grid cellare rare in mountainous regions To capture this effect wecalculate a terrain impedance factor

slf =

1 γ lt 17

159πγminus2

γ ge 17 (31)

which affects mean fire sizeaf as a downscaling factor

af = afslf (32)

We determined the median slope angleγ of a 05 grid cellby aggregating the maximum D8 slope (Zhang et al 1999)at 1 arc minute resolution from the ETOPO1 global digitalelevation model (Amante and Eakins 2009) Median slopeangle at this scale ranges roughly from 0 to 17 from hori-zontal A world map of slf is shown in Fig S2

With the size of individual fires scaled according to theaverage slope angle more fires will be required to burn anequivalently sized total area in more complex terrain as com-pared to flat terrain

326 Passive fire suppression through landscapefragmentation

For the first time in human history modern technology al-lows people to actively suppress and extinguish wildfiresto protect their lives and properties In the past possibili-ties to actively suppress and extinguish wildfires were lim-ited (Skinner and Chang 1996 Pausas and Keeley 2009)Nevertheless increases in population densities and paral-lel increases in land use eventually contributed to landscapefragmentation and thereby indirect suppression of wildfiresFollowingArchibald et al(2009) we simulate the effect thatanthropogenic landscape fragmentation has on fire spreadand therefore burned area

In order to estimate the effects of anthropogenic landscapefragmentation here defined as the fraction of cropland vsunused land we performed a Monte Carlo simulation on agrid of 100times 100 pixels where we increased the fraction ofcropland by 1 increments from 0 to 1 For each step werandomly assigned pixels within the grid to either be crop-land or unused land and calculated the average contiguousarea size of natural patches based on an 8-cell neighbour-hood To estimate the final average contiguous area size ofnatural patches we performed 1000 repetitions of the exper-iment at each land use fraction The resulting relationship

between the cropland fraction of a grid cell and the averagecontiguous area size of unused patches can be approximatedby the following equation

ac area=(1003+ e(16607minus41503fnat)

)minus2169Agc (33)

with Agc being the grid cell area in ha The equation accountsfor changing land use as fragmentation is recalculated everyyear based on the information on how much land within agrid cell is agricultural land The average contiguous areasize of natural patches is used to set an upper limit toaf thesize of individual fires in the fire routine At very high landuse fractions we limit the minimum allowed averaged patchsize to a kernel size of 10 ha not allowing any fragmentationthat causes natural patches smaller than this size The conceptof connectivity and fragmentation being related to the pro-portions of two different phases in our case agricultural landand unused land is well known in other scientific contextseg in soil science where unsaturated soil water conductivitydepends on the ratio between water-filled and air-filled porespace (Richards 1931 Newman and Ziff 2000) For a de-tailed depiction of the Monte Carlo simulation results seeSupplement Fig S1

33 Fire mortality

Fire mortality in the original version of SPITFIRE was simu-lated through a combination of cambial damage and scorch-ing of tree crowns followingPeterson and Ryan(1986)where tree kill is a function of fire intensity bark thicknessand tree height Thus to simulate realistic amounts of treekill it is essential to have a representation of the size andshape of trees in the model that is realistic However the pop-ulation averaging of the allometric equations in LPJ leads tothe simulation of average individuals that are much shorterand thinner than mature trees in nature To overcome thislimitation SPITFIRE applied an unpublished scheme to dis-aggregate the biomass represented by the average individualinto a series of size classes with height and diameter that arerelative to the height of the average individual simulated byLPJ We use an adaptation of this scheme to approximate re-alistic tree heights in LPJ-LMfire

We begin by prescribing a PFT-specific relationship be-tween the simulated range in height for the average indi-vidual and the typical range in height from sapling to ma-ture tree of a real individual of that PFT as it is observedin the field Thus any given height of the average individ-ual can be mapped to a mean real height (Hreal) for the PFTRecognizing that the average individual represents a range oftree ages and sizes we disaggregate the biomass of each av-erage individual into seven height classes following a skew-normal distribution centred onHreal estimated above Theheights of each height class are equally spaced and rangefrom 50 of Hreal for the shortest class to 125 ofHrealfor the tallest class



Stem diameter is calculated separately for each heightclass based on the observed relationship between maximumtree height and diameter for each PFT Bark thickness iscalculated using the PFT-specific bark thickness parametersgiven in Thonicke et al(2010) (par1 par2 TableA1) Asin SPITFIRE mortality resulting from cambial kill is calcu-lated separately for each height class and the total mortal-ity over all classes is summed up across all classes per PFTApart from bark thickness the probability of mortality dueto cambial damage also depends on the residence time ofthe fireτl in relation to the critical time for cambial dam-ageThonicke et al(2010) do not provide the exact equationused in SPITFIRE to calculateτl but refer toPeterson andRyan(1986) In LPJ-LPMfire we calculateτl using Eq (8)of Peterson and Ryan(1986)

τl = 394fcsum

i=1

woi(1minus (1minus CF)05

) (34)

With our revised height class scheme we needed to re-parameterize the PFT-specific RCK- andp values that de-scribe the probability of mortality due to crown damageWhen we used the SPITFIRE RCK parameters close to1 for all woody PFTs with the exception of the tropicalbroadleaf raingreen PFT an undesired result of our multiple-day burning scheme was that excessive crown kill resultedin much of the simulated global vegetation cover being con-verted to grasslands in places with frequent fire occurrenceObservational data eg from vegetation maps and the GlobalLand Cover Facility (GLCF) tree cover data set (DeFrieset al 2000) showed that many of these places clearly shouldbe forested While we acknowledge that using parametersfrom observed plant traits is a good strategy given the unre-alistic allometry simulated for LPJrsquos average individual andthe simplification presented by our height class scheme di-rect representation of the characteristics of individual treesis not strictly possible Future model development should in-clude better representation of the size and shape of trees inthe model eg by using a cohort-based approach such as thatused in LPJ-GUESS (Smith et al 2001) In LPJ-LMfire weset RCK to a constant value of 05 for all tree PFTs andp

to a constant value of 03 We further add the restriction thatdeciduous trees can only be killed by crown scorch if greenleaves are present at the time of fire occurrence

In nature most grasses grow quickly enough to finish theirlife cycle within one growing season (Gibson 2009) Someherbs and grasses are annual species that sprout from seedsevery year while for many perennial herbaceous plants theentire aboveground biomass dies back after the growing sea-son and then resprouts from the root mass during the nextgrowing season (Cheney and Sullivan 2008 Gibson 2009)In LPJ however herbaceous PFTs take 3ndash10 yr to reach equi-librium potential aboveground biomass under constant cli-mate soil and CO2 forcing in part because establishmentand allocation are updated only once annually In SPITFIRE

herbaceous biomass is removed as a result of combustionIn areas with frequent fire LPJ-SPITFIRE simulates herba-ceous biomass and FPC that are lower than observationsThis inconsistency affects not only fire behaviour but alsogeneral biogeochemical cycling in ecosystems where herba-ceous vegetation is present

To avoid an unrealistic reduction in herbaceous biomassin LPJ-LMfire as a result of fire we convert combusted livegrass biomass to carbon but do not remove the grass biomassfrom the live biomass pool at the end of year similarly to thescheme used byKaplan et al(2011) to simulate the harvestof agricultural crops This correction results in more realisticbiomass and coverage of grasses when simulating fire In thefuture a new and more realistic implementation for the de-velopment and senescence of grasses within LPJ should beimplemented which will require moving to a daily time stepfor grass allocation as for example has been done for cropsin LPJ-ML (Bondeau et al 2007)

34 Data sets and model runs used for model evaluation

Evaluating a complex DGVM and fire model such asLPJ-LMfire requires suitable input data for driving themodel including information on climate including light-ning soils topography atmospheric CO2 concentrationsand human population density and anthropogenic land useUnfortunately not all parts of the world where fire is ob-served are equally well represented in terms of quality datafor driving and testing DGVMs with fire In the simulationsdescribed below we prepared a standard global driver dataset for LPJ-LMfire using the data sets listed in Table3 Todrive the model with the best possible approximation of ac-tual climate conditions we use a baseline long-term meanclimatology with a native spatial resolution of at least 05 towhich interannual variability is added in the form of anoma-lies from a lower resolution reanalysis climate simulationthat covers the period 1871ndash2010 We calculated anomaliesin the reanalysis data relative to a 1961ndash1990 standard pe-riod and linearly interpolated the 2 reanalysis grid to 05

using the CDO software (Schulzweida et al 2012)In all of the simulations presented in this paper the model

was spun up for 1020 yr with a detrended version of the20th Century Reanalysis climatology with the atmosphericCO2 concentrations of 1871 and then run in a transient sim-ulation from 1871 to 2010 For the Alaska case study we re-placed LISOTD with the ALDS data set for the time periodof record that overlapped with our experiments (1986ndash2010)

Since we focus on the overall performance of the modelin simulating fire behaviour and impacts on ecosystems andsince the development of the demographic history data setsis the subject of a separate publication we exclude anthro-pogenic ignitions from the simulations presented here

We needed model-independent data to evaluate simulatedfire frequency and behaviour eg satellite-derived or ground-based data of annual burned area To evaluate LPJ-LMfirersquos



Table 3Data sets used to drive LPJ-LMfire

Variables Data sets References

Baseline climatologyLong-term monthly means

temperature precipitationdiurnal temperature range WorldClim 21 Climate WNA Wang et al(2011) Hijmans et al(2005)

number of days per monthwith precipitation wind speed CRU CL 20 New et al(2002)

total cloud cover Wisconsin HIRS Cloud ClimatologyWylie et al(2005)

lightning flashes LISOTD HRMC Christian et al(2003)

Climate interannual variabilityDetrended and transient (1871ndash2010)

temperature precipitationcloud cover wind speed CAPE 20th Century Reanalysis Compo et al(2011)

Elevation and Slope ETOPO1 Amante and Eakins(2009)

Soil particle size distribution andvolume fraction of coarse fragments Harmonized World Soil DatabaseFAOIIASAISRICISSCASJRC(2008)

Atmospheric CO2 concentrations Composite CO2 time series Krumhardt and Kaplan(2012)

Land use HYDE v31 Klein Goldewijk et al(2010)

performance in Alaska we compared simulated area burnedbetween 1986 and 2010 with the AFS historical burned areapolygon data set (Alaska Fire Service 2013) For globalmodel evaluation we used GFEDv3 (Giglio et al 2010) andthe global burned area data set published byRanderson et al(2012)

4 Model results and evaluation

In the following sections we first present and discuss LPJ re-sults for simulated aboveground biomass and the O horizonWe then present our case study for Alaska where we evalu-ate LPJ-LMfire simulation results with reference to the high-quality data sets on lightning strikes that we used to drive themodel and detailed maps of annual burned area that we usedto test model output We present and discuss a world mapof potential natural fire return interval that could be used forecosystem management and restoration and finally comparea global fire scenario to global observations of burned area

41 Aboveground biomass

As noted in Sect322 living aboveground biomass sim-ulated by LPJ was consistently overestimated compared tovalues reported in literature especially in places with highbiomass such as the Amazon Basin where simulated val-ues reached a maximum of more than 30 kgCmminus2 Afterthe modifications we made to maximum crown radius andmaximum establishment rate aboveground biomass sim-ulated in the central Amazon Basin ranged between 18and 21 kgCmminus2 (Fig 3a) Comparisons of our simulated

biomass with satellite-derived observations (Saatchi et al2009) show that even after the modifications LPJrsquos estimatesof aboveground live biomass are likely to be still on the highend of estimates Aboveground biomass carbon estimatescollected byMalhi et al (2006) for old-growth Amazonianforests range between 85 and 167 kgCmminus2 Estimates ofbiomass carbon for tropical moist forests in the BrazilianAmazon collected byHoughton et al(2001) range between10 and 232 kgCmminus2 with a mean of 177 kgCmminus2 In re-gions with generally lower biomass eg in the Caatinga ofnortheast Brazil or in the Andes simulated and satellite-derived biomass values reported bySaatchi et al(2009) aregenerally in good agreement although the model underesti-mates biomass in parts of the Andes

42 The organic soil layer

Figure4 shows the global amount of carbon stored in the newLPJ O horizon The highest values are found in northeast-ern Siberia and northern North America with values rang-ing between 2 and 35 kgCmminus2 In northern Europe sim-ulated values range between 1 and 2 kgCmminus2 These val-ues do not capture the high end of values reported in lit-erature but are well within the observed range For exam-ple Makipaa (1995) reported a range of 05 to 3 kgCmminus2

for the organic layers of forest soils in southern Finland de-pending on nutrient status and site wetness For the arctictundra of North America Ping et al (2008) reported val-ues as low as 07 kgCmminus2 for mountain sites and reach-ing 151 kgCmminus2 for lowland sitesPregitzer and Euskirchen(2004) summarize organic soil horizon stocks from a number



of studies giving a range between 02 and 195 kgCmminus2 forboreal forests The values simulated by LPJ are thereforewithin a realistic range although site-specific variability can-not be reproduced at 05 spatial resolution

43 Fire in boreal ecosystems the Alaska case study

Fire is an important process in the boreal region and con-trols a variety of different ecosystem processes such assuccession tree recruitment vegetation recovery carbonstorage soil respiration and emission of atmospheric tracegases (Landhaeuser and Wein 1993 Kurz and Apps 1999Johnson 1992 Harden et al 2000 Turetsky et al 2002Bergner et al 2004 Kasischke et al 2005) Alaska wasparticularly suitable for our model evaluation first becauseneither SPITFIRE nor LPX was able to simulate adequateamounts and realistic variability of burned area in boreal andsubarctic environments and also because the availability ofdata to drive and evaluate the fire model is excellent for thisregion

Because sufficiently dry conditions occur comparativelyrarely fire is highly episodic in boreal and subarctic Alaskaand northern Canada (Kasischke et al 2002) and hence theobservational record is dominated by relatively few big fireyears Lightning is the main source of ignitions for largefires in boreal ecosystems For the period 1950ndash1969Barney(1971) showed thatsim 24 of all fire ignitions in Alaskawere caused by lightning but fires started by lightning ac-counted for more than 80 of total area burnedTodd andJewkes(2006) provide an extensive year-by-year overviewfrom 1950 to 2005 listing the total number of wildfires peryear caused by humans and lightning and the correspondingnumber of acres burned by these wildfires A total of 89 ofall burned area between 1950 and 2005 can be attributed tolightning-caused fires (Todd and Jewkes 2006) From 1986to 2005 11 yr had more than 95 of the total annual areaburned attributed to lightning fires 13 yr more than 90 and16 yr more than 80 One of the reasons why the highlyvariable fluctuations in burned area could not be reproducedby the original version of SPITFIRE could be because inter-annual variability in lightning occurrence was neglected asdescribed in Sect312above Furthermore smoldering firesare an important part of fire behaviour in boreal and subarc-tic environments For example the recent Anaktuvuk Rivertundra fire smoldered for nearly two months as the tundradried out before spreading rapidly at the end of the sum-mer (Jones et al 2009) With the high-quality data sets thatare available on fire in Alaska we set out to see if the im-provements we made to LPJ-LMfire substantially improvedthe model performance in this ecologically important region

431 Simulated and observed area burned

Since the majority of burned area in Alaska is due tolightning-ignited fires (Todd and Jewkes 2006) we set themodel up only to simulate ignition and spread of naturalie lightning-ignited fires on land not subject to human landuse We distinguish the following seven major ecoregions(Fig 5) based on the ecoregions distinguished by the AlaskaInteragency Coordination Center (2013)

1 Intermontane Boreal (IB)

2 Arctic Tundra (AT)

3 Alaska Range Transition (ART)

4 Bering Taiga (BTA)

5 Bering Tundra (BTU)

6 Coastal Rainforest (CR)

7 Aleutian Meadows (AM)

Depending on the ecoregion in consideration the simu-lated and observed area burned on average over the time pe-riod from 1986 to 2010 varies considerably In the followingsections we compare and discuss simulated fire occurrencewith observed burned area by ecoregion

Intermontane Boreal ecoregion

The Intermontane Boreal ecoregion situated between theAlaska Range and the Brooks Range is the most importantregion of Alaska for fire On average 93 of the total areaburned in Alaska is located in this area Both the observa-tional data and the simulation results identify this area asthe region most affected by fire In this region observationsshow an average annual burned area of 4834 km2 over 25 yrand a standard deviation of 6285 km2 or 096plusmn 125 ofthe total area of the region (Table4) Our simulated annualburned area of 4736plusmn 5654 km2 or 094plusmn 113 agreeswell with observations slightly underestimating both the to-tal amount and the magnitude of the interannual variabilityin burned area The absolute range of area burned in this re-gion is approximately the same for both the observations andsimulation with a minimum of 136 vs 0 km2 and a max-imum of 26 464 vs 25 500 km2 respectively (Fig6) Forboth observations and simulation the annual mean burnedarea is larger than the median indicating that the annual fireregime is characterized by relatively low area burned occa-sionally interrupted by extreme years during which large ar-eas burn In contrast to the mean where simulated burnedarea is slightly less than observations the median and 75 percentile burned area are slightly higher in the simulationthan in the observations (Fig6)



0 1 200 400 600 800 1000 1500 2000 2500 3000 3500

C stored in Ominushorizon [g mminus2]

Fig 4Simulated C-storage in the organic topsoil layer (O horizon) newly implemented in LPJ

Table 4 Observed and simulated mean (standard deviation) area burned and burned percent of total ecoregion area over the time period1986ndash2010 by ecoregion

IB AT ART BTA BTU CR AM

observation (km2) 4834 (6285) 138 (281) 91 (109) 86 (146) 48 (104) 13 (38) 1 (5)observation ( area) 096 (125) 004 (008) 004 (005) 003 (006) 005 (010) 001 (002) 000 (000)simulated (km2) 4736 (5654) 680 (1782) 134 (393) 22 (70) 15 (33) 10 (47) 0 (0)simulated ( area) 094 (113) 019 (051) 006 (019) 001 (003) 001 (003) 001 (003) 000 (000)

In Fig 7 we show the simulated and observed timeseries of burned area in the Intermontane Boreal regionLPJ-LMfire reproduces observations of burned area well notonly in terms of the average area burned over the 25 yr pe-riod but also in terms of the interannual variability

Arctic Tundra

Compared to the Intermontane Boreal ecoregion describedabove burned area in the other six ecoregions is very smallin terms of total area burned as well as percent of the ecore-gion burned (Fig6 Table4) Our simulations therefore cor-rectly identify the location of the most important ecoregionfor fire in Alaska However our simulations overestimate themean annual area burned as well as the maximum annualarea burned for ecoregion AT (Arctic Tundra) compared tothe observation data This is due to 2 yr within the simu-lated time series 2008 and 2009 for which we largely over-estimate the total area burned whereas in most other yearswe simulate low amounts of burning that match the obser-vational data in magnitude and variability Exceptional yearswith very large single tundra fires are known to occur eg theAnaktuvuk River fire in 2007 (Jones et al 2009) AlthoughLPJ-LMfire is capable of simulating years with exceptionally

large amounts of fire in Alaskarsquos arctic tundra we are notable to reproduce burned area in exactly those years whenlarge burned area was observed

Bering Taiga and Bering Tundra

Burning in the westernmost part of Alaska (ecoregions BTAand BTU) is generally low in the observational data (Fig6Table4) with a maximum of 675 km2 burned during the pe-riod 1986ndash2010 with an average of 86 km2yrminus1 and a me-dian of 27 km2yrminus1 for the Bering Taiga and a maximumof 367 km2yrminus1 an average of 48 km2yrminus1 and a medianof 0 km2yrminus1 for the Bering Tundra This implies that anaverage of 003 of the Bering Taiga and 005 of theBering Tundra region burned over the 25 yr period Our sim-ulations underestimate burning in these regions especiallyfor the Bering Taiga where the simulated maximum burnedarea is 329 km2yrminus1 with an average of 22 km2yrminus1 and amedian of 0 km2yrminus1 For the Bering Tundra we simulate amaximum of 148 km2yrminus1 an average of 15 km2yrminus1 and amedian of 0 km2yrminus1 therefore also underestimating obser-vations



AT

IB

AM

ART

BTA

BTU

CR

Fig 5 Alaska ecoregions following the scheme used bythe Alaska Fire Service IB = Intermontane Boreal AT = ArcticTundra ART = Alaska Range Transition BTA = Bering TaigaBTU = Bering Tundra CR = Coastal Rainforest AM = AleutianMeadows

Ecoregions ART CR and AM

For ecoregion ART (Alaska Range Transition) LPJ-LMfiresimulates a mean annual burned area of 134plusmn 393 km2yrminus1

and a median of 4 km2yrminus1 compared to an observed meanannual burned area of 91plusmn 109 km2yrminus1 and a median of37 km2yrminus1 (Fig 6 Table 4) We therefore underestimatethe median while overestimating the mean with the latteragain being augmented due to one single fire year 2007 forwhich we simulate a maximum of 1907 km2yrminus1 against anobservation value of only 299 km2yrminus1 All other 24 yr forecoregion ART are within the range of observation concern-ing total area burned and interannual variability EcoregionsCR (Coastal Rainforest) and AM (Aleutian Meadows) areecoregions with extremely low amounts of burned areaboth observed and simulated in total as well as percent-age of regionrsquos area For ecoregion CR an average of 13plusmn

38 km2yrminus1 in the observation data compares to a simulatedaverage of 10plusmn 47 km2yrminus1 In ecoregion AM burned areais recorded in 4 out of the 25 yr of observation compared to2 yr of fire simulated by LPJ-LMfire These results reveal thatthough we may not be able to reproduce exact numbers forarea burned at the very low end of fire observations we arestill able to simulate fire occurrence behaviour realisticallyeven in areas where burning is rare and reproducing any fireat all in the simulations is challenging

432 Discussion of Alaska burned area results

While overall mean simulated burned area was close to thatobserved peak fire years in our simulated time series did notalways match observed peak fire years (Fig7) The causefor this mismatch may be linked to the uncertainty in dailyweather conditions resulting from the usage of a weathergenerator and monthly climate data Using monthly climateforcing constrains total precipitation amount and number ofwet days but the timing of rainy days within a given monthmay be very different in the simulation compared to the trueweather situation eg if simulated wet days all come clus-tered at the beginning or end of the month whereas in real-ity they had been more equally distributed over the monthIn such a case the consequences for fuel wetting and dry-ing are different between observation and simulation withsimulation overestimating fuel dryness and FDI and there-fore leading to higher amounts of area burned Moreoverthe timing and amount of precipitation matters for simulat-ing fire extinction in LPJ-LMfire as either one day with morethan 10 mm precipitation (3 mm precipitation with more than60 grass cover) or several consecutive days with a sumof more than 10 mm precipitation are required to extinguishfires in our simulation If for example a fire is burning ina given month and the simulated clustering of rainy dayswithin this month is less pronounced than the clustering thatoccurred in reality the fire may continue burning althoughin reality it was extinguished This may also be true for theopposite case where fires are extinguished although theyshould have kept burning Another uncertainty is linked towind speed as we lack the capability in our weather genera-tor to disaggregate wind speed to daily or hourly values weuse climatological mean wind speed which may underesti-mate the infrequent high-wind events that are responsible forthe largest episodes of fire spread Finally LPJ-LMfire doesnot simulate the feedback mechanism between fire and windfor example large intense fires such as those observed inboreal forests may produce strong convection that increaseswind speeds in the vicinity of the fire which in turn enhancesfire spread

Correct simulation of fires in tundra regions is challeng-ing for several reasons The most significant problem lead-ing to a general overestimation of simulated burned area onthe Alaska North Slope is the simple soil water scheme ofLPJ that is not able to explicitly simulate permafrost or wet-lands Detailed analyses of grid pixels in northern Alaska re-vealed that soils dry out very quickly as soon as all snowhas melted in May or beginning of June and because it islinked to soil moisture the water content of the live grassdrops quickly Summers in northern Alaska are dry while atthe same time day length is long therefore simulated evapo-transpiration is high and helps to draw down soil moisturein combination with surface runoff and drainage Overallthis leads to simulation of environmental conditions that arefar drier than in reality where thawing of the active layer



minus81000

minus72000

minus63000

minus54000

minus45000

minus36000

minus27000

minus18000

minus9000

0

9000

18000

27000

0

1000

2000

3000

4000

5000

6000

7000

are

a b

urn

ed

[km

2]


0

100

200

300

400

500

600

700

BTA BTU CR AM

Fig 6 Boxplots showing the observed (left box plot) and simulated (right box plot) minimum maximum median and quartiles of areaburned between 1986 and 2010 for each of the seven ecoregions Black stars indicate the statistical mean value

0

5000

10000

15000

20000

25000

30000

Are

a b

urn

ed

[km

2 y

rminus1]

1990 1995 2000 2005 2010

Fig 7 Simulated (orange) and observed (black) time series of totalannual area burned in ecoregion IB between 1986 and 2010

proceeds slowly down the soil column over the course of thesummer and by limiting evapotranspiration keeps soils andvegetation wetter than would otherwise be the case If light-ning occurs in the period between May and July simulatedfires spread very fast and therefore lead to an overestimationof burned area In most of the cases where we overestimateburning fires are ignited early in summer when in realityconditions are likely still too wet the simulated fires spreadquickly due to the fuel being dry and keep burning throughsummer due to the lack of precipitation In addition to thepoor representation of wetlands and permafrost in LPJ thetundra on Alaska North Slope is characterized by a high den-sity of water bodies including many lakes peatlands streamsand rivers which is not taken into account in LPJ In realitythese water bodies will limit the spread of fires as can beobserved for the Anaktuvuk River fire which is bordered byrivers on its western and eastern margins Future improve-ments to LPJ and the fire model therefore should focus on

the implementation of adequate permafrost and wetland sim-ulation modules (egWania et al 2009 Koven et al 2009Ringeval et al 2010) and the incorporation of some spatialstatistic representing water body distribution on a grid celllevel as a limiting factor to the spread of fires This could beaccomplished similarly to the way in which we account forthe effects of landscape fragmentation on fire size as a re-sult of topography (Sect325) or land use (Sect326) AsLPJ-LMfire has no PFT that specifically represents it tundravegetation in the model is simulated with the C3-grass PFTAs described in Sect322 we tried to improve the repre-sentation of tundra vegetation with respect to fuel conditionsby scaling the density of live grasses to the number of grow-ing degree-days and by accounting for permafrost-impededdrainage of soil water Eventually woody shrub vegetationand tussocks could be represented by one or more separatetundra PFTs (egKaplan et al 2003 Wania et al 2009) aseach of the constituent tundra vegetation plants have diffe-rent density height and flammability that would affect firespread

Comparing the Bering Taiga and Bering Tundra ecore-gion to the Arctic Tundra in northern Alaska reveals thatall three ecoregions are characterized by generally very lowamounts of lightning They can therefore all be classified asignition-limited fire regimes In contrast to the Arctic Tundraregion the two western regions have their precipitation max-imum in summer which coincides with the potential fire sea-son As a consequence of frequent rainfall events with often-substantial daily precipitation amounts fuels stay wet andsoil water status is high (Fig8) In the already rare case of alightning ignition fires therefore tend to spread slowly staysmall and are soon extinguished especially when comparedto fires started in the Arctic Tundra



0

5

10

15

20

25

30

pre

cip

ita

tio

n [

mm

dminus

1]

01 02 03 04 05 06 07 08 09 10 11 12

snowpack

no burning

00

01

02

03

04

05

06

07

08

09

10

FD

I (s

tars

)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

ligh

tnin

g s

trik

es (

red

circle

s)

[grid

ce

llminus1 d

minus1]

Fig 8 Typical daily diagnostics for a grid pixel located in ecoregion BTA showing the daily amount of precipitation (blue bars) FDI (pinkstars) lightning strikes (red circles) duration of snow cover (turquoise line at top of panel) and the snow-free time potentially available forburning (yellow line at top of panel) The year shown had a short dry period in July with FDI values high enough for burning but no lightningstrike that potentially could have started a fire occurred during this year

Rare but important fires in boreal and subarctic environ-ments develop during particular conditions eg an excep-tionally long string of dry weather As LPJ-LMfire uses aweather generator to disaggregate monthly climate variablesto daily values it is possible that the specific circumstancesthat in reality led to a fire ie having an ignition while at thesame time simulating a sufficiently long dry period after theignition so that the fire can spread are not captured by themodel simulation With only few lightning sensors locatedin the far west of Alaska it is also possible that the actualamount of lighting occurring in these two ecoregions is un-derestimated and not all lighting is recorded

Apart from the limitations discussed here using daily andinterannually variable lightning as described in Sect312al-lows us to simulate fire in boreal regions with results show-ing considerable interannual variability in total burned areaAlthough we may not be able to reproduce observed annualarea burned exactly on a year-to-year basis because of thelimitations highlighted above with LPJ-LMfire we capturethe overall behaviour of boreal fires well in terms of beingable to simulate long-term averages and variability that areconsistent with observations

433 Simulated fire return intervals in Alaska

Fire return interval (FRI) ie the number of years betweensuccessive fires in an area is widely used to characterize nat-ural fire regimes and assess the changes in fire frequencycaused by climate change For the recent past efforts to re-construct FRIs based on fire scar data sets have been per-formed byBalshi et al(2007) who present maps of fire re-turn intervals in boreal North America and Eurasia using his-torical fire records for the second half of the 20th centuryIn places where fire is infrequent however FRIs may ex-

12 25 50 100 200 300 400 500 700 1000 2000

fire return interval (years)

Fig 9 Simulated fire return intervals in Alaska for a 1000 yr runwith detrended 20th century climate To facilitate comparison thecolour schemes used here and in Fig 11 are the same as those usedin Balshi et al(2007)

ceed the period of modern observations Detailed historicalrecords of burned area in the boreal forest in the best casehold a little more than 70 yr of data in Alaska and Canada



and even less than that in Eurasia Short records may be notrepresentative of the overall average fire regime as by chancethey may for example represent a time of relatively highor low fire activity and therefore lead to an overestimationor underestimation of average FRIs over longer time scalesThe need to perform spatial interpolation of FRIs over largespatial scales introduces further uncertainty

Analysis of charcoal accumulation rates from sedimen-tary archives has been applied successfully on local to re-gional scales to reconstruct FRIs over longer time scales (egHiguera et al 2009 Lynch et al 2004 Tinner et al 2006Higuera et al 2008 Brubaker et al 2009) However centen-nial to millennial scale climate variability probably affectedFRIs as ecosystems adjusted to changing climate It is there-fore difficult to characterize steady-state equilibrium FRIs orestimate how future climate changes could affect burningbased solely on palaeo-archives The advantage of DGVMscontaining fire models is that they can be run for long timeperiods using detrended steady-state climate allowing vege-tation and fire regime to equilibrate so that conclusions canbe made as to what the equilibrium FRI would be if climateat any given time stayed constant

To estimate FRIs for Alaska we made a model run over1000 yr with steady-state climate after vegetation and fireregime had equilibrated FollowingBalshi et al(2007) wedefine FRI as the time required to burn an area equal to theentire 05 grid cell The FRI within a grid cell is conse-quently calculated as the ratio of 1000 yr and the numberof times a grid cell area burned during these 1000 yr Wepresent our simulated fire return intervals in Fig9 using thesame colour scheme as inBalshi et al(2007) but withoutapplying any smoothing Agreeing withBalshi et al(2007)we simulate frequent burning with return intervals between12 and 50 yr in eastern Alaska located in the IntermontaneBoreal ecoregion between Brooks Range and Alaska RangeTowards the west of ecoregion IB the FRIs predicted fromour simulation become more heterogeneous from less than50 yr to more than 500 therefore being slightly lower thanthe FRIs estimated byBalshi et al(2007) Towards the ex-treme west of mainland Alaska we simulate FRIs between900 and 2000 yr for some grid cells but mostly FRIs arelonger than 2000 yr Compared toBalshi et al(2007) we es-timate significantly longer FRIs in some grid cells especiallyfor ecoregion BTU (Bering Tundra) This may be linked tothe possibility that the already low amounts of lightning areunderestimated in the LISOTD lightning climatology usedfor this experiment due to the limited 4 yr length of recordof the lightning climatology and the low detection efficiencyat high latitudes In contrast we simulate shorter fire re-turn intervals for the Arctic Tundra which typically fall inthe 100ndash200 yr and 500ndash700 yr categories Given the modelshortcomings related to the simulation of tundra vegetationand permafrost (see Sect432) these results may be biasedsomewhat towards shorter FRIs than are actually observed

44 Global fire under natural conditions

To characterize the behaviour of LPJ-LMfire globally andplace it in the context of previous fire modelling work weperformed an experiment analogous to that presented byBond et al(2005) contrasting global biomass in a ldquoworldwithout firerdquo to one where natural fires are simulated Theglobal effects of fire on aboveground live biomass are shownin Fig 10 Both panels represent a world with potential nat-ural vegetation and no anthropogenic land use Panel (a)shows biomass with natural fires caused by lightning igni-tions while panel (b) shows a world without fire Panel (c)shows the difference in biomass between a world with andwithout fire The maps clearly reveal the parts of the worldthat are mostly affected by fire disturbance and thereforehave less biomass than they potentially could have in a worldwithout fire On a 100 yr basis the total amount of globalcarbon stored in aboveground living biomass is 208plusmn 2 Pgless for the simulation with fire compared to the simulationwithout fire totaling 948plusmn3 PgC with fire No impact of fireon biomass is simulated for the wet tropics where very littlefire is simulated such as the Amazon and Congo basins orin Indonesia all places that naturally store large amounts ofcarbon in forests Most of the biomass loss related to fire dis-turbance is simulated in the seasonal tropics and subtropicsin the Miombo woodland region south of the Congo Basinin the east and southeast of the Amazon Basin in the Sahelin India and Southeast Asia and in northern and southernAustralia The impact of fire on biomass is also clearly vis-ible in the grassland regions of central and western NorthAmerica the western Mediterranean southwestern RussiaKazakhstan and Uzbekistan Fires in the boreal regions canbe extensive but the return interval is too long to have adiscernible impact on carbon storage in aboveground livebiomass compared to ecosystems with short fire return in-tervals

The results we present here are broadly consistent withthose inBond et al(2005) who showed in a series of ex-periments running a DGVM with and without fire that thelargest reductions in tree cover as a result of natural fire are inthe seasonal subtropicsBond et al(2005 Fig 6) also show alarge reduction in forest cover in central Europe and the east-ern United States areas where fire impacts in LPJ-LMfire aremore muted In contrast LPJ-LMfire shows a large reductionin biomass in the grassland areas of central North Americaon the Eurasian steppe in central and southern Australia andin southern South America when comparing ldquofire onrdquo withldquofire offrdquo scenariosBond et al(2005) state that FRIs simu-lated by their model in these natural grassland areas are muchtoo long with respect to observations (75ndash200 yr modelledwhere 2ndash5 yr are observed) LPJ-LMfire shows much shorterFRIs (Fig11) of 1ndash5 yr in much of these natural grasslandregions that are more consistent with field observations



a)

b)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24

Aboveground living biomass [kg C mminus2]

c)

minus10 minus7 minus6 minus5 minus4 minus3 minus2 minus15 minus1 minus05

Aboveground living biomass reduction [kg C mminus2]

Fig 10Simulated biomass C(a) human absence lightning fires(b) human absence no fire(c) reduction in biomass C between(a) and(b)

The map of global FRIs in Fig11shows that fires are mostfrequent in places where three factors are coincident

a enough biomass to sustain frequent burning

b sufficient amounts of lightning ignitions

c seasonally varying meteorological conditionsspecifically a pronounced dry season that allows fueldrying

If any of these three conditions is not present wildfires areunlikely to occur As noted above fire is rare in the Amazonand Congo basins and on the Indonesian archipelago In theseregions lightning ignitions and biomass are not limiting butmeteorological conditions are typically too wet for the deve-lopment of wildfires with the exception of relatively infre-quent severe drought events eg in extreme El Nino years(Page et al 2002 2012) In the desert and high-mountain



1 5 12 25 50 100 200 300 400 500 700 1000 2000

fire return interval [years]

Fig 11Simulated global fire return intervals for a model run over a time period of 1000 yr using the detrended 20th century reanalysis andLISOTD-derived lightning climatology

regions of the world eg in the Sahara desert the southernpart of the Arabian Peninsula and on the Tibetan Plateau theabsence of biomass is the limiting factor for fire Large partsof the worldrsquos boreal and subarctic ecosystems have enoughbiomass to support frequent burning but the number of light-ning ignitions generally tends to be low compared to lowerlatitudes with snow and temperatures below 0C occurringfor half a year or more and the summer season is frequentlythe wettest time of the year

In contrast in any part of the world where all three factorsare met fire return intervals are short eg in the Sahel thewestern Mediterranean the Near East in the Miombo wood-lands south and east of the Congo Basin in most of Australiaand in the xerophytic Caatinga shrublands of northeasternBrazil

45 Comparison to contemporary observationsof burned area

While LPJ-LMfire has been primarily designed to simulatefire behaviour during preindustrial time we compared the re-sults of a global model run with satellite-based estimates ofburned area that cover recent decades In our model experi-ments we did not attempt to account for either anthropogenicignitions or active suppression of wildfires but we did ac-count for passive fire suppression through landscape frag-mentation as a result of agricultural land use The differencesbetween simulated and observed burned area may thereforein certain regions highlight the importance of human influ-ence on the geographic distribution of fire at present In a fewparts of the world where human impact is minimal we werefurther able to identify potential shortcomings of the currentversion of LPJ-LMfire and priorities for future model deve-lopment

As described in Sect34 above we ran LPJ-LMfire withclimate and soils data that reflect the late 20th and early21st centuries (Table3) The model was spun up for 1020 yrwith 1871 CO2 concentrations and land use and then runin a transient climate CO2 and land use scenario for theperiod 1871ndash2010 Used land was defined as the sum ofthe agricultural and urban fractions and was specified fromthe HYDE v31 anthropogenic land cover change scenario(Klein Goldewijk et al 2010) In our simulations fires wereonly allowed to burn on the unused fraction of each grid celland the only ignition source was lightning

We compare our model results with the global burned areaproducts GFEDv31 (Giglio et al 2010 hereafter GFED)and the data set presented byRanderson et al(2012 here-after JR12) GFED provides complete annual coverage forthe years 1997ndash2011 while JR12 covers the period 2001ndash2010 The main difference between the two observationalburned area products is that JR12 accounts for numerous ad-ditional small fires not included in GFED which results in anincrease in mean annual burned area of up to 30 in someregions mainly in the tropics and subtropics

We compare modelled with observed burned area on thebasis of a multi-year mean of the annual total burned areafraction of each 05 grid cell We extracted the time peri-ods from our LPJ-LMfire run overlapping with the periodcovered by the observational data sets summed the monthlyvalues in the observational data sets to create annual totalsand calculated average burned area over the number of yearsof record In comparing LPJ-LMfire with GFED we maskedthe difference between model and observation where the dif-ferences were less than the aggregate uncertainty specified inthe GFED database For comparison with JR12 we maskedareas where the modelndashdata mismatch was less than 1



a)

minus100 minus75 minus50 minus25 0 25 50 75 100

percent difference in mean annual burned area fraction

b)

LPJ underestimates observations

Areas without human impact

Areas with human impact

LPJ overestimates observations



Fig 12 (a)Residuals between observed average annual area burned in GFED and simulated burned area(b) Residuals between observedand simulated annual area burned in context of anthropogenic imprint on the global land surface

The differences between LPJ-LMfire and GFED areshown in panel a of Fig12 differences with JR12 are inFig S8 Overall the spatial pattern and magnitude of theresidual between model and observations are similar regard-less of the observational data set we used The greatest differ-ences between model and observations are found in the sea-sonal tropics of Africa both north and south of the Equatorwhere LPJ-LMfire shows substantially less burned area thanthe observations Further large negative residuals are seenin northern Australia along the steppe belt of Eurasia fromUkraine to Kazakhstan in Southeast Asia particularly inCambodia in the Amur region of the Russian Far East and inthe lowlands of Bolivia and Paraguay In contrast the modelshows relatively more burned area compared to observationsin several regions notably in the Caatinga region of north-

eastern Brazil in Iran and western Turkmenistan in most ofsouthern Australia in the western United States and in theChaco dry forest region of northwestern Argentina

In panel b of Figs12 and S8 we place these differencesbetween model and observations in the context of the anthro-pogenic imprint on the global land surface by means of a sim-ple classification of the residual based on human impact Wespecified human impact based on the GLOBIO methodology(Ahlenius 2005 Fig S9) which identifies the presence ofanthropogenic features on the ground including urban areasopen cast mines airports roads railroads canals and utilitylines Half-degree grid cells covered 1 or more by anthro-pogenic features were classified as being substantially influ-enced by human activities On the basis of this classification75 (347 out of 464 Mha) of the mean annual global burned



area in JR12 occurs on land influenced by human impact (forGFED the amount is 71 or 258 of 363 Mha) The areasof largest disagreement between model and observations areeven more concentrated in regions of human impact In gridcells where the difference between LPJ-LMfire and the ob-servational data sets is greater than 1 human impact isvisible on 93 of the area

As discussed above where LPJ-LMfire underestimatesobserved burned area in much of the seasonal tropics this ismost likely the result of regular intentional burning of crop-land and pastures and in some cases deforestation fires Inthe Sahel extensive agricultural burning is common practiceand occurs annually for several months during the NorthernHemisphere autumn and winter when people ignite firesto remove crop residues and to renew pasture grasses andstop woody encroachment on pastures for hunting and tocontrol pests and wildfires (Menaut et al 1991 Klop andPrins 2008 Kull and Laris 2009 NASA 2011) This isalso the case for the Miombo woodlands south of the CongoBasin and on Madagascar where intentional burning playsan important role (Eriksen 2007 Le Page et al 2010) VanWilgen et al(1990) estimate that humans cause 70 of allannual fires in African savannas Likewise the large under-estimate in burned area in the Eurasian steppe and Amurvalley is related to agricultural burning (Tansey et al 2004Warneke et al 2009)

In places where LPJ-LMfire overestimates burned area rel-ative to observations and human impact is considered impor-tant three processes that are not included in LPJ-LMfire mayexplain the differences (1) removal of biomass from graz-ing and land degradation (2) industrial fire suppression and(3) landscape fragmentation from roads and other anthro-pogenic features that are not classified as agricultural landuse by HYDE Eastern Brazil northern Argentina south-ern Australia East Africa northern Mexico and the westernGreat Plains of the United States are occupied by extensiveopen rangelands (Klein Goldewijk et al 2010 Ramankuttyet al 2008) where livestock grazing leads to a reduction offine fuel load that is not accounted for in our model sim-ulations Furthermore the semiarid regions of the northernSahel Central Asia and the Near East are characterized byextensive soil degradation as a result of overgrazing and mil-lennia of land use (Dregne 2002) This degradation is notaccounted for in our simulations and the model simulatesmore biomass than is actually present and therefore morefire Industrial fire suppression is common in Europe NorthAmerica and Australia and may explain much of the addi-tional LPJ-LMfire overestimate relative to observations inthese areas In the US alone expenditure on wildfire suppres-sion has increased continually over the last 70 yr (Stephensand Ruth 2005 Calkin et al 2005 Westerling et al 2006Nazzaro 2007 Gebert et al 2007 2008) Finally while weaccounted for landscape fragmentation as a result of agricul-tural land use in our simulations additional fragmentation ef-fects caused by the presence of human infrastructure such as

roads were not included The combination of industrial firesuppression with a high magnitude of human impact is thelikely cause for the overestimate in burned area in developedcountries of the temperate regions

On the remaining 7 of land area that may be classified ashaving insignificant human impact we show overestimates inburned area in subarctic western Canada and eastern Siberiain a small area along the southern margin of the Sahara inMali and Niger and markedly in the southeastern AmazonBasin in the transition zone between tropical forests and theCerrado savanna In contrast the model underestimates firein boreal Canada in the eastern Central African Republiccentral Australia and in central Brazil These residuals areuseful for understanding the limitations of both our modeland the observational data sets

The unprojected maps in Figs12 and S8 exaggerate thearea but the overestimate in burned area in the subarctic maybe caused by several factors that were already discussed inour analysis of LPJ-LMfire results for Alaska These includean inadequate representation of permafrost that influencessoil hydrology and therefore fuel moisture an overall over-estimate in modelled aboveground biomass also caused bypermafrost andor lack of soil and fine-scale landscape frag-mentation caused by the rivers lakes and wetlands that areextensive in this region (Papa et al 2010) Permafrost is im-portant in all of these northern areas where LPJ-LMfire over-estimates observations (Tarnocai et al 2009) In areas of bo-real Canada further south where LPJ-LMfire underestimatesburned area several factors not included in our simulationsmay influence the model results including tree kill events asa result of insect infestations and remote industrial activitiesincluding logging and hydroelectric and oil and gas develop-ment Furthermore in the boreal and subarctic areas wheremodelled burned area is both under- and overestimated thevery short 4 yr period upon which our lighting climatologyis based for the extratropics means that we may misestimatethe number of ignitions in these regions The large interan-nual variability and differences in spatial pattern in lightningwe observed using the ALDS data for Alaska shows that theLISOTD climatology is at best a rough approximation of theactual amount of lighting strikes and that in certain yearsour LISOTD-based estimates could result in a substantialover- or underestimate in the actual number of potential ig-nition events

As described above most of the temperate regions of theworld are so extensively impacted by human activities bothat present and historically that it is impossible to disentan-gle the natural fire regime from anthropogenic influences atthe 05 spatial resolution used in our model simulations Abetter test of our process fire model in mid-latitude settingscould be to perform case studies in protected regions suchas national parks or wilderness areas at very high (sim 1 km)spatial resolution

In the subtropics and tropics the largest area of disagree-ment between model and observations is in the transition



zone between Cerrado savannas and tropical forests in thesoutheastern Amazon in northern Mato Grosso and southernPara states of Brazil In this region a pronounced dry sea-son of three to four months combined with high temperaturesleads to rapid fuel drying and high FDI in our simulationsCombined with lightning activity in all seasons as seen in theLISOTD climatology modelled fire frequencies and burnedarea in this region are high In reality several factors precludethe development of large fires in this region and should be in-cluded in future improvements to the model In this regiontropical forests tend to develop on lowland environmentswith deep soils the maximum rooting depth in LPJ-LMfire is2 m but much more deeply rooted trees have been commonlyobserved in the Amazon (Kleidon and Heimann 2000) Moredeeply rooted trees would extend the period of greenness fortropical raingreen vegetation the dominant PFT in this re-gion in our model simulations effectively limiting the lengthof the dry season for the vegetation

Furthermore green forest vegetation will effectively shadethe litter and other fuel in the understorey reducing the rate atwhich it will dry out In experiments in the seasonal tropics ofthe southeastern AmazonUhl and Kauffman(1990) showedthat land cover controls fuel moisture and that under equiv-alent climate conditions fuels in intact forests would neverbecome dry enough to burn while in grasslands only 24 hof dry weather was required to support sustained burning Inthis sense the Nesterov Index approach used for estimatingfuel moisture in SPITFIRE may be inadequate We suggestthat future models would benefit from an energy balance ap-proach to estimating fuel moisture particularly in forest un-derstoreys On the other hand it is possible that the observa-tions of burned area in this region are underestimates of theactual situationRanderson et al(2012) suggest that burnedarea in their data set may be particularly underestimated inregions where small fires occur in forest understorey Thecombination of these limitations in both the model and thedata sets probably leads to the large positive residual ob-served in this region

Adjacent to this region of overestimated modelled burnedarea in central Brazil is a discontinuous region of underesti-mated burning in areas shown on our map to be largely freeof human influence This region in Mato Grosso Goias andTocantins states is an area where rapid land cover changein the form of deforestation and conversion to agricultureand pasture has been important in recent decades (de Souzaet al 2013) This recent deforestation has been documentedas being associated with an increase in burned area (Limaet al 2012) Our human influence map is based on theVMAP0 data product (NIMA 2000) that was largely assem-bled from data collected during the period 1974ndash1994 Wesuggest that the negative residual in burned area in this re-gion is a result of recent human activities not currently cap-tured by our human impact database

Similarly the large areas of underestimated burned areain the easternmost Central African Republic and northern

Australia have been attributed to human action though notas a result of anthropogenic land cover change In Africalarge savanna fires are intentionally lit to facilitate huntingin sparsely populated areas (Eva et al 1998) Likewise innorthern Australia frequent intentional human burning is animportant part of traditional landscape management that iswidespread in sparsely populated areas at present (McKeonet al 1990 Dyer 1999 Yibarbuk et al 2002 Bowmanet al 2004 Bowman and Prior 2004 Crowley and Garnett2000)

In summary our simulations of burned area over recentdecades caused only by lightning ignitions and only pas-sively suppressed through agricultural and urban land useshow substantial differences with observational data sets offire We expect these differences because the complex hu-man relationship with fire at present is well known and wehave made no attempt to prescribe this in our simulationsIn parts of the world where human impact is limited mod-elled mean burned area fraction often agrees within 10 ofobservations on a decadal average In those areas of low hu-man impact where we do show important disagreement be-tween model and observations we can identify limitationsin our model and driver data sets In boreal and subarcticCanada and Russia we may overestimate fire because of ourover-simplistic treatment of permafrost and because of thepresence of lakes wetlands and barren ground that are notaccounted for in our model input In the tropics and sub-tropics we may overestimate burning because of an inade-quate representation of the effects that canopy shading anddeeply rooted vegetation have on fuel moisture Future de-velopments to the model should address these issues by im-proving the soil hydrology scheme by using recently devel-oped methods for simulating permafrost (Wania et al 2009)or deep tropical soils (Poulter et al 2009)

5 General discussion

Realistic simulation of global vegetation dynamics requiresthe inclusion of disturbance regimes that influence vegetationdevelopment alter vegetation structure and composition andaffect global carbon budgets Simulation of fire arguably themost important disturbance process that affects the terrestrialbiosphere is of crucial importance for a complete model rep-resentation of terrestrial vegetation dynamics Starting withSPITFIRE we developed LPJ-LMfire to overcome some ofthe shortcomings of the original model LPJ-LMfire includesmajor changes to the process representations of fire occur-rence fire spread and fire impact In boreal and subarcticregions in particular LPJ-LMfire results are in much bet-ter agreement with observations compared to SPITFIRE orLPX In other parts of the world the changes that we madeto SPITFIRE in developing LPJ-LMfire are harder to distin-guish at the coarse resolution at which we run the modelbecause of the pervasive nature of human impact on fire atpresent both through ignitions and fire suppression



Under a natural fire regime excluding human interferencelightning is the most common ignition source for wildfiresAccounting for interannual variability in lightning and theoccurrence of lightning on a daily timescale is important es-pecially in regions where the total amount of monthly light-ning strikes is low and therefore an equal distribution oflightning strikes on all days within a month may result ina significant underestimate of lightning ignitions By corre-lating the occurrence of lightning strikes with the occurrenceof precipitation we provide a more realistic way to simu-late lightning ignitions In boreal and subarctic environmentswhere lightning ignitions are rare SPITFIRE and LPX showunrealistically little fire compared to observations With me-teorological forcing that is similar to that used by these mod-els but by accounting for intra-monthly and interannual vari-ability in lighting ignitions in LPJ-LMfire we show that sim-ulation of realistic fire behaviour is possible This is illus-trated by our time series of burned area for central Alaska(Fig 7) that includes single years with significant amountsof area burned while many other years have no or only verylittle fire It is possible that the meteorological forcing usedby all three models is unrealistic but the inclusion of ob-served variability in lightning strikes in the model providesa parsimonious solution that results in a better match withobservations

By allowing the ignition of smoldering fires during wetconditions and simulating fires that persist over the course ofmultiple days instead of extinguishing each fire after a lengthof time that is limited to 241 min LPJ-LMfire more closelyreflects the true behaviour of fire Likewise the calculationof fuel wetness as a mass balance function of wetting anddrying in LPJ-LMfire rather than relying on a precipitationthreshold of 3 mm as suggested byNesterov(1949) and usedin SPITFIRE made a substantial improvement in the agree-ment of the model results with observations

Eventually the introduction of additional shrub PFTs asintermediates between herbaceous vegetation and tree PFTsshould be considered especially for an appropriate represen-tation of tundra and xerophytic vegetation Introduction ofshrub PFTs will help ameliorate the current tendency of themodel to overestimate herbaceous vegetation cover in fire-prone areas and the strong positive feedback between fire andvegetation that results in an overestimate of fire frequencyand the prevalence of grasses a problem sometimes still ob-served for example in the Arctic tundra of northern Alaskaor in southern Spain and central Australia Further improve-ments should also focus on the inclusion of a scheme to sim-ulate wetlands and permafrost in order to capture the way inwhich permafrost keeps tundra organic matter wet even un-der dry meteorological conditions Since our version of LPJdoes not represent permafrost dynamics soil and fuel dryingand hence fire occurrence are overestimated in tundra areassuch as northern Alaska where wetlands and permafrost arecommon Other future improvements to LPJ-LMfire shouldinclude development of a scheme to simulate crown fires in

addition to the surface fires simulated by the current versionof the model

By introducing a slope factor related to the median slopeangle of each 05 grid cell we present a simple way to ac-count for the role that topographic complexity plays in lim-iting fire size and rate of spread Eventually a representationof other natural firebreaks such as rivers and lakes should bebuilt into the fire module An approximation of the number ofrivers that could act as fire breaks could be handled by usingdrainage density information extracted from a digital eleva-tion model That rivers constrain the spread of fires can beobserved for example in case of the large Anaktuvuk Riverfire from 2007 in the Alaskan tundra that was ultimately con-strained by the two rivers Nanushuk to the west and Itkillikto the east (Jones et al 2009) A measure of fragmenta-tion by water bodies could be indirectly accounted for usingEq (14) which links the numbers of fires burning at any timeto the degree to which the landscape has been fragmented dueto previous burns in the fire season

Grass PFTs should be implemented such that they are ableto reach full cover and complete their life cycle within onegrowing season Our overall simulation results indicate thatthis would be particularly important for mesic tropical savan-nas where fire is a prevalent feature of the ecosystem andmost species of grass have annual lifecycles (Scholes et al1997) To accomplish this it would be necessary to run theentire model at a monthly or shorter timestep Calculatingprocesses such as allocation turnover and mortality thatare currently updated annually in LPJ on a shorter timestepwould also provide the additional advantage that burned areacould be tracked continuously over time rather than reset-ting calculated burned area at the beginning of each calendaryear While the Northern Hemisphere summer fortunatelyroughly corresponds with the fire season for a large part ofthe world it is not correct for southern South America south-ern Australia and parts of Southeast Asia and the Sahel

Our comparison of the LPJ-LMfire results with observa-tional data sets of burned area shows that anthropogenic im-pact on controlling the spatial pattern of fire observed in re-cent decades may be important in many parts of the worldAbout three-quarters of the earthrsquos surface where fire is ob-served at present occurs on lands influenced by human activ-ities and human interactions with fire range from rigoroussuppression eg in the US Europe or parts of Australia toliberal intentional burning on agricultural and natural landeg in Sub-Saharan Africa The sheer variety of examplesfor humanndashfire interactions makes it clear that modellingthe spatial and temporal pattern of fire at the present daywould require detailed parameterizations of the human rela-tionships with fire at sub-national level Prescription of hu-man behaviour with respect to fire could likely overcomemost of the differences between observed and simulated re-sults but would no longer be process-based fire modellingMoreover such a detailed parameterization of anthropogenicbehaviour would reflect present-day customs and policies



with respect to fire but would not have predictive power forthe future or for the past as human preferences and subsis-tence strategies change over time Our main interest in de-veloping LPJ-LMfire was to model fire including anthro-pogenic fire in the preindustrial past when humans had nei-ther present-day technology to suppress and control wild-fires nor modern-day agricultural technologies that allowpeople to abstain from using fire for agricultural purposes

We therefore decided to develop a more general schemefor representing humanndashfire interactions in the past that isbased on observations and knowledge on people who stilluse fire in traditional ways at present day such as AustralianAborigines or subsistence farmers in developing countriesor on historical ethnographic observations of fire usage egof the native North Americans Literature research evidencefrom palaeoproxies such as charcoal preserved in sedimentsand discussions with anthropologists and archaeologists ledus to the conclusion that humans in the past used fire for avariety of different reasons depending on their lifestyles andhabitat and that terrestrial biomass burning related to hu-man activity must have been very common By developinga method of representing the way in which people with diffe-rent subsistence lifestyles interact with fire with LPJ-LMfirewe are able to perform quantitative estimates on the impactof anthropogenic burning on vegetation carbon pools andtrace gas emissions on a global scale during preindustrialtime We realize that this approach may be too simplisticto address specific local-scale peculiarities of human burn-ing behaviour but believe nonetheless that our approach toclassifying peoplersquos relationship with fire based on their sub-sistence lifestyle is a more appropriate way of addressing theimplementation of human burning in the past than prescrib-ing the patterns of human-influenced fire observed in the 21stcentury

6 Conclusions

Beginning with LPJ-SPITFIRE (Thonicke et al 2010) wemade improvements to several aspects of the original formu-lation and achieved a more realistic process representation offire occurrence fire behaviour and fire impacts particularlyin boreal and subarctic ecosystems With our updated modelLPJ-LMfire we were able to simulate realistic fire regimes inAlaska one of the key regions of the world where SPITFIREresults did not agree with observations We also developed ascheme to distinguish among the ways in which preindustrialpeople with different subsistence strategies interact with fireto achieve their land management goals LPJ-LMfire is a ma-jor improvement on past global fire models and will be par-ticularly useful for studying changes in global fire on millen-nial timescales providing a basis for further improvementsmodifications and model development

Appendix A

In this appendix we provide the equations used inLPJ-LMfire that were not changed from the originalSPITFIRE With these we provide a complete documen-tation of LPJ-LMfire Variable and parameter abbreviationsused in addition to those in Table1 are provided in TableA2

A1 Fuel load and moisture

Fuel calculation by PFT and by fuel type (ldquoslow abovegroundlitterrdquo includes all woody litter whereas ldquofast abovegroundlitterrdquo is leaves only)

df(PFT1) = 222middot (s(1) middot las(PFT) + laf(PFT)) (A1)

df(PFT2 4) = 222middot (s(2 4) middot las(PFT)) (A2)

lf(PFT1) = 222middot Nind middot (s(1) middot (hmind(PFT)

+smind(PFT)) + lmind(PFT)) (A3)

lf(PFT2 4) = 222middot Nind middot s(2 4) middot (hmind(PFT)+smind(PFT))

(A4)

where s = 0045 0075 021 067 for fuel size classes 1ndash4(1 1 h fuel 2 10 h fuel 3 100 h fuel 4 1000 h fuel) Deadfuel load per fuel size class

woi(class) =

npftsumpft=1

df(PFTclass) (A5)

Relative moisture content of live grass fuel

ωlg =10

9middot ωs1minus

1

9 (A6)

Recalculation ofαlg

αlg =

minuslogωlg

NI ωlg gt 0 and NIgt 00 else

(A7)

Calculation of total fine fuel amount

wfinefuel = woi(1) + wlivegrass (A8)

Total mass of dead fuel summed across the first three fuelclasses and all PFTs

wo =

3sumclass=1

(woi(class)) (A9)

Total dead fuel mass within the first three fuel size classesplus mass of the live grass

wtot = wo+ wlivegrass (A10)



Table A1 PFT-specific parameters TrBE = tropical broadleaf evergreen TrBR = tropical broadleaf raingreen TeNE = temperate needle-leaf evergreen TeBE = temperate broadleaf evergreen TeBS = temperate broadleaf summergreen BoNE = boreal needleleaf evergreenBoS = boreal summergreen C3gr = C3 perennial grass C4gr = C4 perennial grass

TrBE TrBR TeNE TeBE TeBS BoNE BoS C3gr C4gr

F 0160 0350 0094 0070 0094 0094 0094 ndash ndashCLf 033 010 033 033 033 033 033 ndash ndashieffpft 005 040 010 010 050 044 044 050 050emfactCO2 1580 1664 1568 1568 1568 1568 1568 106 1664emfactCO 103 63 106 106 106 106 106 106 63emfactCH4 68 22 48 48 48 48 48 48 22emfactVOC 81 34 57 57 57 57 57 57 34emfactTPM 85 85 176 176 176 176 176 176 85emfactNOx 20 254 324 324 324 324 324 324 254ρbPFT 15 15 15 15 15 15 15 ρlivegrass ρlivegrasspar1 00301 01085 00367 00451 00347 00292 00347 ndash ndashpar2 00281 00281 00281 00281 00281 00281 00281 ndash ndash

A2 Rate of spread

For the calculation of ROSfsw σ = 5

relm =ωo

meavg (A11)

wn = livemass+ deadmass (A12)

livemass=9sum

PFT=8

pftlivefuel(PFT) (A13)

deadmass=9sum

PFT=1

pftdeadfuel(PFT) (A14)

pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)

ρPFT(PFT) =ρbPFT(PFT) middot Z

3sumclass=1

df(PFTclass)

(A17)

Z=df(PFT1)+12 middot df(PFT2)+14 middot df(PFT3) (A18)

ρb =

ρlivegrassmiddot livemass+npftsumi=1

(ρPFT(i) middot pftdeadfuel(i)

)wn

(A19)

For the calculation of ROSfc σ = 66 relm = 099ρb = 01and

wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)

The actual rate of spread calculation is based on Eqs (A21)ndash(A37)

Packing ratio

β =ρb

ρp (A21)

Optimum packing ratio

βop = 0200395middot σminus08189 (A22)

Ratio of packing ratio to optimum packing ratio

pratio =β

βop (A23)

Maximum reaction velocity

0primemax =

1

00591+ 2926middot σminus15 (A24)

Optimum reaction velocity

0prime= 0prime

max middot pAratio middot eA

middot (1minus pratio) (A25)

A = 89033middot σminus07913 (A26)



Table A2 Explanation of variable and parameter abbreviations


df(PFTclass) dead fuel load per PFT in 1 10 100 and 1000 h fuel class [gDMmminus2]lf(PFTclass) live fuel load per PFT in 1 10 100 and 1000 h fuel class [gDMmminus2]laf(PFT) fast-decomposing aboveground litter per PFT [gCmminus2]las(PFT) slow-decomposing aboveground litter per PFT [gCmminus2]lbg(PFT) belowground litter per PFT [gCmminus2]Nind(PFT) individual density per PFT [mminus2]lmind(PFT) leaf mass of the average individual [gCindminus1]smind(PFT) sapwood mass of the average individual [gCindminus1]hmind(PFT) heartwood mass of the average individual [gCindminus1]rmind(PFT) root mass of the average individual [gCindminus1]woi(class) 1 10 100 and 1000 h dead fuel mass summed across all PFTs [gmminus2]ωs1 relative moisture content of top soil layer [ndash]αlg drying parameter for live grass fuel [Cminus2]NI Nesterov fuel dryness index [ C2]relm relative moisture content of the fuel relative to its moisture of extinction [ndash]ρb fuel bulk density [kgmminus3]σ surface-to-volume ratio of the fuel [cm2cmminus3]ρPFT(PFT) bulk density of dead fuel per PFT mass-weighted over first 3 fuel size classes [kgmminus3]pftdeadfuel(PFT) mass of dead fuel per PFT summed over the first 3 fuel size classes [gmminus2]β packing ratio (fuel bulk densityoven dry particle density) [ndash]ρp oven-dry particle density 513 [kgmminus3]βop optimum packing ratio [ndash]pratio ratio of packing ratio to optimum packing ratio [ndash]0prime

max maximum reaction velocity [minminus1]0prime optimum reaction velocity [minminus1]νM moisture dampening coefficient [ndash]IR reaction intensity [kJmminus2minminus1]νs mineral dampening coefficient 041739 [ndash]h heat content of fuel 18 [kJgminus1]ξ ratio of propagating flux to reaction intensity [ndash]8w wind coefficient [ndash]ε effective heating number [ndash]Qig heat of pre-ignition [kJkgminus1]ROSbs rate of backward surface spread [mminminus1]LBtree length-to-breadth ratio of burn ellipse with tree cover [ndash]LBgrass length-to-breadth ratio of burn ellipse with grass cover [ndash]tfire fire duration [min]CFlg live grass fraction consumed by fire [ndash]CF(class) fractional consumption of dead fuel per fuel class [ndash]ω(class) moisture content per fuel class [ndash]FC(class) amount of dead fuel consumed [gmminus2]ST mineral fraction of total vegetation mass 0055 [ndash]Isurface surface fire line intensity [kWmminus1]PmCK(PFT) probability of mortality due to crown damage [ndash]RCK(PFT) PFT-specific crown damage parameter [ndash]CK(PFT) crown scorch fraction [ndash]dphen(PFT) leaf phenology status per PFT [ndash]SH(PFT) scorch height [m]height(PFT) tree height [m]CL(PFT) crown length of woody PFTs [m]F(PFT) scorch height parameter [ndash]BBdead(PFT15) biomass burned from dead fuel by PFT and fuel type [gmminus2]BBlive(PFT13) biomass burned from live fuel by PFT and fuel type [gmminus2]ABfrac fractional area burned on the grid cell [dayminus1]



Table A2 Continued


annkill(PFT) annual total probability of mortality [ndash]Nind-kill(PFT) fraction of PFT killed by fire [ndash]BBtot total C-emissions from burning across all PFTs [gCmminus2]BBpft(PFT) total burned biomass per PFT [kgdrymattermminus2]acfluxfire annual C-flux from biomass burning [gmminus2]Mx(spec) trace gas emissions per species (CO2 CO CH4 VOC TPM NOx) [gxmminus2]aMx(spec) annual trace gas emissions per species [gxmminus2]

Moisture dampening coefficient

νM = 1minus 259middot relm + 511middot relm2minus 352middot relm

3 (A27)

Reaction intensity

IR = 0primemiddot wn middot h middot νM middot νs (A28)

Ratio of propagating flux to reaction intensity

ξ =e(0792+37597middot

radicσ middot(β+01))

192+ 79095middot σ (A29)

Wind coefficient

8w = C middot (3281middot Uforward)B

middot pratiominusE (A30)

C = 747middot eminus08711middotσ055 (A31)

B = 015988middot σ 054 (A32)

E = 0715middot eminus001094middotσ (A33)

Effective heating number

ε = eminus4528

σ (A34)

Heat of pre-ignition

Qig = 581+ 2594middot ωo (A35)

The rate of spread is then calculated as follows

ROSx =IR middot ξ middot (1+ 8w) middot windfact

ρb middot ε middot Qig (A36)

Backward rate of spread (decreases with increasing windspeed)

ROSbs = ROSfs middot eminus0012middotUforward (A37)

A3 Fire geometry and duration

Length-to-breadth ratio of burn ellipse in cases when windspeed exceeds 1 kmhrminus1

LBtree= 1+ 8729middot

(1minus eminus003middot006middotUforward

)2155 (A38)

LBgrass= 11+ 006middot Uforward00464 (A39)

LB = min(LBtreemiddot treecover+ LBgrassmiddot grasscover8

) (A40)

In cases when wind speed is slower than 1 kmhrminus1LB = 1 The maximum daily fire duration is derived as a func-tion of FDI

tfire =241

1+ 240middot eminus1106middotFDI (A41)

The total distance travelled by a fire within a day is esti-mated as

DT = tfire middot (ROSf+ ROSb) (A42)

The mean area burned by one single fire is calculated as

af = min( π

4 middot LBmiddot DT2

middot 00001ac area)

(A43)

A4 Combustion of dead fuel

Fraction of live grass consumed by surface fire

rm =ωlg

melf (A44)

CFlg =

1 rm le 018

245minus 245middot rm rm gt 073

110minus 062middot rm else

(A45)



Fraction of 1 h fuel consumed by surface fire

rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =

098minus 085middot rm rm le 038106minus 106middot rm else

(A51)


rm =ω(4)

mefc(4) (A52)

CF(4) = minus08 middot rm+ 08 (A53)

Total fuel consumed in each fuel size class (gmminus2)

FC(class) = CF(class) middot woi(class) middot (1minus ST) (A54)

To calculate how much fuel has been consumed in totalwithin one grid cell over the course of a year FC(class) needsto be multiplied with the annual area burned (in mminus2)

Calculation of surface fire intensity

Isurface= h middot ROSfs middot

3sumclass=1

FC(class) middot1

60 (A55)

If the surface fire intensity is less than 50 kWmminus1 it isconsidered to be too low for burning and fires are extin-guished

A5 Fire mortality and combustion of live fuel

Crown scorch is calculated per PFT For seasonally leaf-bearing trees crown scorch is relevant as long as there areleaves on the tree

Probability of mortality due to crown damage calculatedper PFT

PmCK(PFT) = RCK(PFT) middot CK(PFT)3middot dphen(PFT) (A56)

CK(PFT) =SH(PFT) minus height(PFT) + CL(PFT)

CL(PFT) (A57)

SH(PFT) = F(PFT) middot Isurface0667 (A58)

CL(PFT) = max(height(PFT) middot CLf(PFT)001) (A59)

The probability of mortality due to cambial damage isgiven by

Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)

whereτlτc is the ratio of the residence time of the fire to thecritical time for cambial damage (Peterson and Ryan 1986)The critical time for cambial damageτc(min) depends on thebark thickness (BT) (cm)

τc = 29 middot BT2 (A61)

(Peterson and Ryan 1986 Johnson 1992) which is cal-culated from the diameter at breast height (DBH cm) using

BT = par1middot DBH + par2 (A62)

where par1 and par2 are PFT-specific constants (TableA1)

The total probability of mortality due to crown damagePmCK and cambial damagePm(τ ) is calculated as

Pm = Pm(τ ) + PmCK minus Pm(τ ) middot PmCK (A63)

A6 Fuel consumption

Biomass burned from dead fuel by fuel type and PFT

BBdead(PFT1) = ABfrac middot CF(1) middot laf(PFT) (A64)

BBdead(PFT2) = ABfrac middot CF(1) middot las(PFT) middot 0045 (A65)






These are calculated on a daily basis To calculate the an-nual total the daily sum is accumulated over the course ofthe year

annBBdead(PFT) = annBBdead(PFT) + BBdead(PFT) (A69)

Biomass is burned from live fuel by fuel type and PFT Fortree-type PFTs

BBlive(PFT1) = ABfrac middot CK(PFT) middot lmind(PFT) middot Nind(PFT) (A70)

BBlive(PFT2) = ABfrac middot CK(PFT) middot smind(PFT) middot Nind(PFT) middot 004875 (A71)

BBlive(PFT3) = ABfrac middot CK(PFT) middot hmind(PFT) middot Nind(PFT) middot 004875 (A72)

For grass-type PFTs

BBlive(PFT1) = ABfrac middot CF(1) middot lmind(PFT) (A73)

Annual totals are continuously summed over the course ofthe year

annBBlive(PFT) = annBBlive(PFT) + BBlive(PFT) (A74)

The annual running sum of mortality probability is calcu-lated as

annkill (PFT) = annkill (PFT) + PmCK(PFT) middot ABfrac (A75)

Updating of the litter pools is done once at the end of theyear

laf(PFT) = max(laf(PFT) minus annBBdead(PFT1)0

) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)

For the tree-type PFTs live biomass that was killed butnot consumed by burning is transferred to the litter poolsand the individual density is updated based on the fraction ofindividuals that were killed over the course of the year

Nindminuskill (PFT) = annkill (PFT) middot Nind(PFT) (A78)

laf(PFT) = laf(PFT) + Nindminuskill (PFT) middot lmind(PFT) (A79)

las(PFT) = las(PFT) + Nindminuskill (PFT) middot(smind(PFT) + hmind(PFT)

) (A80)

lbg(PFT) = lbg(PFT) + Nindminuskill (PFT) middot rmind(PFT) (A81)

Nind(PFT) = max(Nind(PFT) minus Nindminuskill (PFT)0

) (A82)

In case of a PFT being killed off completely by fire re-set presence to ldquofalserdquo and set all biomass pools of that PFT(lmind(PFT) smind(PFT) hmind(PFT) rmind(PFT)) to zero

A7 Trace gas emissions

Total carbon emissions from burning across all PFTs

BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)

To calculate annual total carbon flux from biomass burn-ing keep updating the running sum

acfluxfire = acfluxfire + BBtot (A84)

Amount of carbon emissions from burning per PFT

BBpft(PFT) = 0001middot 222middot

5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)

Daily trace gas emissions per species

Mx(spec) =

npftsumPFT=1

(emfact(PFTspec) middot BBpft(PFT)

) (A86)

Annual trace gas emissions per species are calculated asrunning sum over the year

aMx(spec) = aMx(spec) + Mx(spec) (A87)

Supplementary material related to this article isavailable online athttpwwwgeosci-model-devnet66432013gmd-6-643-2013-supplementpdf



AcknowledgementsWe thank Ron Holle for providing accessto a subset of the NALDN lightning data set and Jim Randersonfor providing his global burned area data We are grateful toKirsten Thonicke and two anonymous referees for their extensivereview and discussion comments which improved this manuscriptFunding for this work was provided by grants from the SwissNational Science Foundation (PP0022-1190049) and the ItalianMinistry for Research and Education (FIRB RBID08LNFJ) for theResearch Project CASTANEA

Edited by D Lawrence

References

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Boles S H and Verbyla D L Comparison of Three AVHRR-Based Fire Detection Algorithms for Interior Alaska RemoteSens Environ 72 1ndash16doi101016S0034-4257(99)00079-62000

Bond W J and Keeley J E Fire as a global rsquoherbivorersquo the ecol-ogy and evolution of flammable ecosystems Trends Ecol Evol20 387ndash394 2005

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Bond W J and Scott A C Fire and the spread of flower-ing plants in the Cretaceous New Phytol 188 1137ndash1150doi101111j1469-8137201003418x 2010

Bond W J and van Wilgen B W Fire and Plants Chapman ampHall London UK 1996

Bond W J Woodward F I and Midgley G F The global distri-bution of ecosystems in a world without fire New Phytol 165525ndash538doi101111j1469-8137200401252x 2005



Bondeau A Smith P C Zaehle S Schaphoff S LuchtW Cramer W Gerten D Lotze-Campen H Muller CReichstein M and Smith B Modelling the role of agri-culture for the 20th century global terrestrial carbon bal-ance Glob Change Biol 13 679ndash706doi101111j1365-2486200601305x 2007

Bowman D M J S Tansley Review No 101 ndash The impactof Aboriginal landscape burning on the Australian biota NewPhytol 140 385ndash410 1998

Bowman D M J S and Prior L D Impact of Aboriginal land-scape burning on woody vegetation in Eucalyptus tetrodonta sa-vanna in Arnhem Land northern Australia J Biogeogr 31807ndash817doi101111j1365-2699200401077x 2004

Bowman D M J S Walsh A and Prior L D Landscape anal-ysis of Aboriginal fire management in Central Arnhem Landnorth Australia J Biogeogr 31 207ndash223doi101046j0305-0270200300997x 2004

Bowman D M J S Balch J K Artaxo P Bond W J CarlsonJ M Cochrane M A DrsquoAntonio C M DeFries R S DoyleJ C Harrison S P Johnston F H Keeley J E KrawchuckM A Kull C A Marston J B Moritz M A Prentice I CRoos C I Scott A C Swetnam T W van der Werf G Rand Pyne S J Fire in the Earth System Science 324 481ndash485doi101126science1163886 2009

Breckle S W Walterrsquos Vegetation of the Earth The EcologicalSystems of the Geo-Biosphere Springer Verlag BerlinHeidelberg 2002

Brubaker L Higuera P E Rupp T S Olson M A AndersonP M and Hu F S Linking sediment-charcoal records and eco-logical modeling to understand causes of fire-regime change inboreal forests Ecology 90 1788ndash1801doi10189008-079712009

Burgan R E Concepts and Interpreted Examples In AdvancedFuel Modeling United States Department of Agriculture ForestService Intermountain Research Station Ogden UT 84401General Technical Report INT-283 1987

Burgan R E and Rothermel R C BEHAVE Fire BehaviorPrediction and Fuel Modeling System ndash Fuel SubsystemNational Wildfire Coordinating Group United StatesDepartment of Agriculture United States Department ofthe Interior Intermountain Forest and Range ExperimentStation Ogden UT 84401 General Technical Report INT-1671984

Cairns M and Garrity D P Improving shifting cultivation inSoutheast Asia by building on indigenous fallow managementstrategies Agroforest Syst 47 37ndash48 1999

Calkin D E Gebert K M Jones J G and Neilson R P ForestService Large Fire Area Burned and Suppression ExpenditureTrends 1970ndash2002 J Forest 103 179ndash183 2005

Carcaillet C Almquist H Asnong H Bradshaw R H WCarrion J S Gaillard M-J Gajewski K Haas J N HaberleS G Hadorn P Muller S D Richard P J H Richoz IRosch M Sanchez Goni M F von Stedingk H StevensonA C Talon B Tardy C Tinner W Tryterud E Wick Land Willis K J Holocene biomass burning and global dynam-ics of the carbon cycle Chemosphere 49 845ndash863 2002

Cheney P and Sullivan A Grassfires Fuel Weather and FireBehavior 2nd Edn CSIRO Publishing 2008

Christian H J Blakeslee R J Boccippio D J Boeck W LBuechler D E Driscoll K T Goodman S J Hall J MKoshak W J Mach D M and Stewart M F Global fre-quency and distribution of lightning as observed from space bythe Optical Transient Detector J Geophys Res 108 4005doi1010292002JD002347 2003

Collins S L Fire Frequency and Community Heterogeneity inTallgrass Prairie Vegetation Ecology 73 2001ndash2006 1992

Compo G P Whitacker J S Sardeshmukh P D Matsui NAllan R J Yin X Gleason Jr B E Vose R S RutledgeG Bessemoulin P Bronnimann S Brunet M CrouthamelR I Grant A N Groisman P Y Jones P D Kruk M CKruger A Marshall G J Maugeri M Mok H Y NordliOslash Ross T F Trigo R M Wang X L Woodruff S D andWorley S J The Twentieth Century Reanalysis Project Q JRoy Meteor Soc 137 1ndash28doi101002qj776 2011

Conklin H C The Study of Shifting Cultivation Curr Anthropol2 27ndash61 1961

Connell J H Diversity in Tropical Rain Forests and Coral ReefsScience 199 1302ndash1310doi101126science199433513021978

Crowley G M and Garnett S T Changing Fire Management inthe Pastoral Lands of Cape York Peninsula of northeast Australia1623 to 1996 Aust Geogr Stud 38 10ndash26doi1011111467-847000097 2000

Crutzen P J and Andreae M O Biomass Burning in the TropicsImpact on Atmospheric Chemistry and Biogeochemical CyclesScience 250 1669ndash1678doi101126science250498816691990

Dagpunar J Principles of Random Variate Generation OxfordScience Publications Clarendon Press Oxford 1988

DeFries R S Hansen M C Townshend J R G Janetos A Cand Loveland T R A new global 1-km dataset of percentagetree cover derived from remote sensing Glob Change Biol 6247ndash254doi101046j1365-2486200000296x 2000

Desiles S L E Nijssen B Ekwurzel B and Ferre T P APost-wildfire changes in suspended sediment rating curvesSabino Canyon Arizona Hydrological Processes 21 1413ndash1423doi101002hyp6352 2007

de Souza R A Miziara F and De Marco Junior P Spatial vari-ation of deforestation rated in the Brazilian Amazon A com-plex theater for agrarian technology agrarian structure and gov-ernance by surveillance Land Use Policy 30 915ndash924 2013

Diaz-Avalos C Peterson D L Alvarado E Ferguson S A andBesag J E Spacetime modelling of lightning-caused ignitionsin the Blue Mountains Oregon Can J Forest Res 31 1579ndash1593 2001

Dodgshon R A and Olsson G A Heather moorland in theScottish Highlands the history of a cultural landscape 1600-1880 J Hist Geogr 32 21ndash37 2006

Dove M R Swidden agriculture in Indonesia the subsistencestrategies of the Kalimantan Kantu Mouton de Gruyter BerlinGermany 1985

Dregne H E Land Degradation in the Drylands Arid Land ResManag 16 99ndash132 2002

Dumond D E Swidden agriculture and the rise of the Maya civi-lization Southwest J Anthrop 17 301ndash316 1961

Dwyer E Pinnock S Gregoire J-M and Pereira J M CGlobal spatial and temporal distribution of vegetation fire as de-



termined from satellite observations Int J Remote Sens 211289ndash1302doi101080014311600210182 2000

Dyer R The Role of Fire on Pastoral Lands in Northern Australiain Fire and Sustainable Agricultural and Forestry Developmentin Eastern Indonesia and Northern Australia ACIAR Proc 91108ndash113 1999

Eriksen C Why do they burn the rsquobushrsquo Fire rural livelihoodsand conservation in Zambia Geogr J 173 242ndash256 2007

Essery R Best M and Cox P MOSES 22 TechnicalDocumentation Tech rep Hadley Center Technical Note 30Hadley Center Met Office Bracknell UK 2001

Eva H D Malingreau J P Gregoire J M Belward A S andMutlow C T Cover The advance of burnt areas in CentralAfrica as detected by ERS-1 ATSR-1 Int J Remote Sens 191635ndash1637 1998

Faivre N P R Boer M M McCaw L and Grierson P FCharacterization of landscape pyrodiversity in Mediterraneanenvironments contrasts and similarities between south-westernAustralia nd south-eastern France Landscape Ecol 26 557ndash571doi101007s10980-011-9582-6 2011

FAOIIASAISRICISSCASJRC Harmonized World SoilDatabase (version 10) 2008

Finney M A FARSITE Fire Area Simulator ndash ModelDevelopment and Evaluation USDA Forest Service ResearchPaper Missoula MT RMRS-RP-4 Revised 52 1998

Fisher J B Sitch S Malhi Y Fisher R A HungtingfordC and Tan S-Y Carbon cost of plant nitrogen acquisitionA mechanistic globally applicable model of plant nitrogen up-take retranslocation and fixation Global Biogeochem Cy 24GB1014doi1010292009gb003621 2010

Fox J M How Blaming rsquoSlash and Burnrsquo Farmers is DeforestingMainland Southeast Asia AsiaPacific Issues 47 1ndash8 2000

Gebert K M Calkins D E and Yoder J Estimating SuppressionExpenditures for Individual Large Wildland Fires West J ApplFor 22 188ndash196 2007

Gebert K M Calkin D E Huggett R J and Abt K LEconomic analysis of federal wildfire management programs inThe economics of forest disturbance wildfires storms and inva-sive species Springer Verlag Dordrecht The Netherlands 2008

Gerten D Schaphoff S Haberlandt U Lucht W and Sitch STerrestrial vegetation and water balance - hydrological evalua-tion of a dynamic global vegetation model J Hydrol 286 249ndash270doi101016jjhydrol200309029 2004

Gibson D J Grasses and grassland ecology Oxford UniversityPress Oxford UK 2009

Giglio L Randerson J T van der Werf G R Kasibhatla PS Collatz G J Morton D C and DeFries R S Assessingvariability and long-term trends in burned area by mergingmultiple satellite fire products Biogeosciences 7 1171ndash1186doi105194bg-7-1171-2010 2010

Gomez-Dans J Spessa A Wooster M and Lewis P A sensi-tivity analysis study of the coupled vegetation-fire model LPJ-SPITFIRE Ecological Modeling in review 2013

Government of Western Australia Department for Agricultureand Food Fire Management Guidelines for Kimberley PastoralRangelands Best Management Practice Guide 2005

Grime J P Control of species density in herbaceous vegetation JEnviron Manage 1 151ndash167 1973

Guyette R P Muzika R M and Dey D C Dynamicsof an Anthropogenic Fire Regime Ecosystems 5 472ndash486doi101007s10021-002-0115-7 2002

Hadlow A M Changes in Fire Season Precipitation in Idahoand Montana from 1982ndash2006 PhD thesis Colorado SateUniversity Fort Collins Colorado 2009

Hall B L Precipitation associcated with lightning-ignited wild-fires in Arizona and New Mexico Int J Wildland Fire 16 242ndash254doi101071WF06075 2007

Hamilton M J The complex structure of hunter-gatherer social networks P R Soc B 274 2195ndash2203doi101098rspb20070564 2007

Harden J W Trumbore S E Stocks B J Hirsch A GowerS T OrsquoNeill K P and Kasischke E S The role of firein the boreal carbon budget Glob Change Biol 6 174ndash184doi101046j1365-2486200006019x 2000

Head L M Landscapes socialised by fire post-contact changesin Aboriginal fire use in northern Australia and implications forprehistory Archaeol Ocean 29 172ndash181 1994

Heinsch F A and Andrews P L BehavePlus fire modeling sys-tem version 50 design and features General Technical ReportRMRS-GTR-249 United States Department of AgricultureForest Service Rocky Mountain Research Station Fort CollinsCO 2010

Hickler T Prentice I C Smith B Sykes M T and ZaehleS Implementing plant hydraulic architecture within the LPJDynamic Global Vegetation Model Global Ecol Biogeogr 15567ndash577 2006

Higuera P E Brubaker L B Anderson P M BrownT A Kennedy A T and Hu F S Frequent Firesin Ancient Shrub Tundra Implications of Paleorecords forArctic Environmental Change PLoS One 3 e0001744doi101371journalpone0001744 2008

Higuera P E Brubaker L B Anderson P M Hu F S andBrown T A Vegeation mediated the impacts of postglacial cli-mate change on fire regimes in the south-central Brooks RangeAlaska Ecol Monogr 79 201ndash219doi10189007-201912009

Hijmans R J Cameron S E Parra J L Jones P Gand Jarvis A Very high resolution interpolated climate sur-faces for global land areas Int J Climatol 25 1965ndash1978doi101002joc1276 2005

Holle R L Cummins K L and Demetriades N W S Monthlydistribution of NLDN and GLD360 cloud-to-ground lightningTech rep Vaisala Inc Tucson Arizona 85756 2011

Houghton R A Lawrence K T Hackler J L and BrownS The spatial distribution of forest biomass in the BrazilianAmazon a comparison of estimates Glob Change Biol 7 731ndash746 2001

Hu F S Higuera P E Walsh J E Chapman W L Duffy P ABrubaker L B and Chipman M L Tundra burning in AlaskaLinkages to climatic change and sea ice retreat J Geophys Res115 G04002doi1010292009JG001270 2010

Huston M A General Hypothesis of Species Diversity Am Nat113 81ndash101 1979

Iversen J Landnam i Danmarks Stenalder En pollenana-lytisk Undersoslashgelse over det foslashrste Landbrugs Indvirkningpaa Vegetationsudviklingen (Land occupation in DenmarkrsquosStone Age A Pollen-Analytical Study of the Influence of



Farmer Culture on the Vegetational Development) DanmarksGeologiske Undersoslashlgelse Raekke II 1941 (in Danish)

Jain A K Tao Z Yang X and Gillespie C Estimates of globalbiomass burning emissions for reactive greenhouse gases (CONMHCs and NOx) and CO2 J Geophys Res 111 D06304doi1010292005JD006237 2006

Jayaratne E R and Kuleshov Y Geographical and seasonal char-acteristics of the relationship between lightning ground flash den-sity and rainfall within the continent of Australia Atmos Res79 1ndash14doi101016jatmosres200503004 2006

Johnson D W Susfalk R B Dahlgren R A and KlopatekJ M Fire is more important than water for nitrogenfluxes in semi-arid forests Environ Sci Policy 1 79ndash86doi101016S1462-9011(98)00008-2 1998

Johnson E A Fire and vegetation dynamics studies from theNorth American boreal forest Cambridge University PressCambridge 1992

Johnston K J The intensification of pre-industrial cereal agri-culture in the tropics Boserup cultivation lengthening andthe Classic Maya J Anthropol Archaeol 22 126ndash161doi101016S0278-4165(03)00013-8 2003

Jones B M Kolden C A Jandtt R Abatzoglout J T UrbansF and Arp C D Fire Behavior Weather and Burn Severityof the 2007 Anaktuvuk River Tundra Fire North Slope AlaskaArct Antarct Alp Res 41 309ndash318doi101657l938-4246-413309 2009

Kalis A J and Meurers-Balke J Die ldquoLandnamrdquo-Modelle vonIversen und Troels-Smith zur Neolithisierung des westlichenOstseegebietes ndash ein Versuch ihrer Aktualisierung Praehist Z73 1ndash24 1998 (in German)

Kalis A J Merkt J and Wunderlich J Environmental changesduring the Holocene climatic optimum in central Europe ndash hu-man impact and natural causes Quaternary Sci Rev 22 33ndash79doi101016S0277-3791(02)00181-6 2003

Kane D L and Stein J Water Movement Into SeasonallyFrozen Soils Water Resour Res 19 1547ndash1557doi101029WR019i006p01547 1983

Kaplan J O Bigelow N H Prentice I C Harrison S PBartlein P J Christensen T R Cramer W Matveyeva N VMcGuire A D Murray D F Razzhivin V Y Smith BWalker D A Anderson P M Andreev A A BrubakerL B Edwards M E and Lozhkin A V Climate changeand Arctic ecosystems 2 Modeling paleodata-model compar-isons and future projections J Geophys Res 108 8171doi1010292002JD002559 2003

Kaplan J O Krumhard K M Ellis E C Ruddiman W FLemmen C and Klein Goldewijk K Holocene carbon emis-sions as a result of anthropogenic land cover change Holocene21 775ndash791 2011

Kasischke E S Williams D and Barry D Analysis of the pat-terns of large fires in the boreal forest of Alaska Int J WildlandFire 11 131ndash144 2002

Kasischke E S Hyer E J Novelli P C Bruhwiler L P FrenchN H F Sukhinin A I Hewson J H and Stocks B JInfluences of boreal fire emissions on Northern Hemisphere at-mospheric carbon and carbon monoxide Global BiogeochemCy 19 GB1012doi1010292004GB002300 2005

Katsanos D Lagouvardos K Kotroni V and Argiriou A ACombined analysis of rainfall and lightning data produced by

mesoscale systems in the central and eastern MediterraneanAtmos Res 83 55ndash63doi101016jatmosres2006010122007

Keeley J E Zedler P H Zammit C A and Stohlgren T JFire and Demography in The California Chapararal ParadigmsReexamined edited by Keeley S C Science Series No 34Natural History Museum of Los Angeles County 1989

Kimmerer R W and Lake F K The Role of Indigenous Burningin Land Management J Forest 99 36ndash41 2001

Kleidon A and Heimann M Assessing the role of deep rootedvegetation in the climate system with model simulationsmechanisms comparison to observations and implications forAmazonian deforestation Clim Dynam 16 183ndash199 2000

Klein Goldewijk K Beusen A van Drecht G and de Vos MThe HYDE 31 spatially explicit database of human-inducedglobal land-use change over the past 12000 years Global EcolBiogeogr 20 73ndash86doi101111j1466-8238201000587x2010

Kleinman P J A Pimentel D and Bryant R B The ecolog-ical sustainability of slash-and-burn agriculture Agr EcosystEnviron 52 235ndash249doi1010160167-8809(94)00531-I1995

Klop E and Prins H H T Diversity and species composition ofWest African ungulate assemblages effects of fire climate andsoil Global Ecol Biogeogr 17 778ndash787doi101111j1466-8238200800416x 2008

Kotroni V and Lagouvardos K Lightning occurrence in re-lation with elevation terrain slope and vegetation coverin the Mediterranean J Geophys Res 113 D21118doi1010292008JD010605 2008

Kourtz P and Todd B Predicting the daily occurrenceof lightning-caused forest fires Forestry Canada PetawawaNational Forestry Institute Information Report No PI-X-11218 pp 1992

Koven C Friedlingstein P Ciais P D K Krinner Gand Tarnocai C On the formation of high-latitude carbonstocks Effects of cryoturbation and insulation by organic mat-ter in a land surface model Geophys Res Lett 36 L21501doi1010292009GL040150 2009

Krumhardt K M and Kaplan J O A spline fit to atmo-spheric CO2 records from Antarctic ice cores and measuredconcentrations for the last 25000 years ARVE TechnicalReport 2 ARVE Group Environmental Engineering InstituteEcole Polytechnique Federale de Lausanne EPFL Station2 1015 Lausannehttpgrkapweb1epflchpubARVEtechreport2co2splinepdf last access 10 May 2013 2012

Kull C A and Laris P Fire ecology and fire politics in Mali andMadagascar in Tropical Fire Ecology Springer Verlag BerlinHeidelberg 171ndash226doi101007978-3-540-77381-87 2009

Kurz W A and Apps M J A 70-year retrospec-tive analysis of carbon fluxes in the Canadian for-est sector Ecol Appl 9 526ndash547doi1018901051-0761(1999)009[0526AYRAOC]20CO2 1999

Lal D M and Pawar S D Relationship between rain-fall and lightning over central Indian region in mon-soon and premonsoon seasons Atmos Res 92 402ndash410doi101016jatmosres200812009 2009

Landhaeuser S M and Wein R M Postfire vegetation recoveryand tree establishment at the Arctic treeline Climatic-change-



vegetation-response hypothesis J Ecol 81 665ndash672 1993Latham D J and Rothermel R C Probability of Fire-Stopping

Precipitation Events Tech rep US Forest Service UtahRegional Depository Paper 354 8 pp 1993

Lehsten V Tansey K Balzter H Thonicke K Spessa AWeber U Smith B and Arneth A Estimating carbonemissions from African wildfires Biogeosciences 6 349ndash360doi105194bg-6-349-2009 2009

Lehsten V Arneth A Thonicke K and Spessa A The effect offire on tree-grass coexistence in savannas a simulation study JVeg Sci in review 2013

Le Page Y Oom D Silva J N M Jonsson P andPereira J M C Seasonality of vegetation fires as mod-ified by human action observing the deviation from eco-climatic fire regimes Global Ecol Biogeogr 19 575ndash588doi101111j1466-8238201000525x 2010

Lewis H T (Ed) Why Indians burned specific versus gen-eral reasons GTR-INT-182 in Proceedings ndash Symposium andWorkshop on Wilderness Fire Missoula Montana OgdenUT USDA Forest Service Intermountain Forest and RangeExperiment Station 1985

Lima A Freire Silva T S Oliveira L E and de Aragao C Landuse and land cover changes determine the spatial relationshipbetween fire and deforestation in the Brazilian Amazon ApplGeogr 34 239ndash246doi101016japgeog201110013 2012

Luning J Steinzeitliche Bauern in Deutschland dieLandwirtschaft im Neolithikum Universitatsforschungenzur prahistorischen Archaologie Bonn Vol 58 285 pp 2000(in German)

Lynch J A Hollis J L and Hu F S Climatic and landscapecontrols of the boreal forest fire regime Holocene records fromAlaska J Ecol 92 477ndash489 2004

Makipaa R Effect of nitrogen input on carbon accumulation ofboreal forest soils and ground vegetation Forest Ecol Manag79 217ndash226doi1010160378-1127(95)03601-6 1995

Malhi Y Wood D Bakers T R Wright J Phillips O LCochrane T Meir P Chave J Almeida S Arroyo LHiguchi N Killeen T J Laurance S G Laurance W FLewis S L Monteagudo A Neill D A Vargas P NPitman N C A Quesada C A Salomao R Silva J N MLezama A T Terborgh J Vasquez-Martinez R and VincetiB The regional variation of aboveground live biomass in old-growth Amazonian forests Glob Change Biol 12 1107ndash1138doi101111j1365-2486200601120x 2006

Marlowe F W Hunter-Gatherers and Human EvolutionEvolutionary Anthropology 14 54ndash67doi101002evan200462005

Marsaglia G Normal (Gaussian) Random Variablesfor Supercomputers The J Supercomput 5 49ndash55doi101007BF00155857 1991

Mather A S Forest transition theory and the refor-estation of Scotland Scot Geogr J 120 83ndash98doi10108000369220418737194 2004

Mazarakis N Kotroni V Lagouvardos K and Argiriou A AStorms and Lightning Activity in Greece during the WarmPeriods of 2003ndash06 J Appl Meteorol Clim 47 3089ndash3098doi1011752008JAMC17981 2008

McKeon G M Day K A Howden S M Mott J J Orr D Mand Scattini W J Northern Australia savannas management for

pastoral production J Biogeogr 17 355ndash372 1990Mell W E Charney J J Jenkins M A Cheney P and Gould

J Numerical Simulations of Grassland Fire Behavior fromthe LANL ndash FIRETEC and NIST-WFDS Models in RemoteSensing Modeling and Applications to Wildland Fires SpringerVerlag Berlin Heidelberg 2012

Menaut J-C Abbadie L Lavenu F Loudjani P and PodaireA Biomass burning in West African savannas MIT PressCambridge Massachusetts USA 133ndash142 1991

Michaelides S C Savvidou K Nicolaides K A andCharalambous M In search for relationships between light-ning and rainfall with a rectangular grid-box methodology AdvGeosci 20 51ndash56doi105194adgeo-20-51-2009 2009

Moorcroft P R Hurtt G C and Pacala S W A methodfor scaling vegetation dynamics the ecosystem demographymodel (ED) Ecol Monogr 71 557ndash586doi1018900012-9615(2001)071[0557AMFSVD]20CO2 2001

Moreira A G Effects of Fire Protection on Savanna Structure inCentral Brazil J Biogeogr 27 1021ndash1029doi101046j1365-2699200000422x 2000

Morvan D Meradji S and Accary G Physical model-ing of fire spread in Grasslands Fire Safety J 44 50ndash61doi101016jfiresaf200803004 2008

Mouillot F and Field C B Fire history and the global car-bon budget a 1 times 1 fire history reconstruction for the 20thcentury Global Change Biol 11 398ndash420doi101111j1365-2486200500920x 2005

NASA Understanding Earth Biomass Burning NationalAeronautics and Space Administration Goddard SpaceFlight Center Greenbelt Maryland Tech Rep NP-2011-10-250-GSFC 2011

National Interagency Fire Service 1997ndash2012 large fires (100000+ acres) httpwwwnifcgovfireInfofireInfostatslgFireshtml(last access 10 May 2013) 2013

Nazzaro R M Wildland Fire ndash Management Improvements CouldEnhance Federal Agenciesrsquo Efforts to Contain the Costs ofFighting Fires Testimony before the Committee on Energy andNatural Re sources US Senate GAO-07-922T 15 pp 2007

Neary D G Ryan K C and DeBano L F Wildland Fire inEcosystems ndash Effects of Fire on Soil and Water United StatesDepartment of Agriculture Forest Service Rocky MountainResearch Station Ogden UT 84401 General Technical ReportRMRS-GTR-42-volume 4 2005

Nesterov V G Gorimostrsquo lesa i metody eio opredeleniaGoslesbumaga Moscow 1949 (in Russian)

New M Lister D Hulme M and Makin I A high-resolutiondata set of surface climate over global land areas Climate Res21 1ndash25doi103354cr021001 2002

Newman M E J and Ziff R M Efficient Monte Carlo Algorithmand High-Precision Results for Percolation Phys Rev Lett 854104ndash4107doi101103PhysRevLett854104 2000

Nickey B B Occurrences of lightning fires ndash Can they be simu-lated Fire Technol 12 321ndash330 1976

NIMA Vector Map Level 0 database (VMAP0) Digital Chart ofthe World 5th Edn Tech rep National Imagery and MappingAgency Bethesda MD 2000

Niu G-Y and Yang Z-L Effects of Frozen Soil on SnowmeltRunoff and Soil Water Storage at a Continental Scale JHydrometeorol 7 973ndash952 2006



Ojima D S Schimel D S Parton W J and OwensbyC E Long- and short-term effects of fire on nitrogencycling in tallgrass prairie Biogeochemistry 24 67ndash84doi101007BF02390180 1994

Oleson K W M L D Bonan G B Flanner M G KluzekE Lawrence P J Levis S Swenson S C Thornton P EDai A Decker M Dickinson R Feddema J J HealdC L Hoffman F Lamarque J-F Mahowald N Niu G-YQian T Randerson J T Running S Sakaguchi K SlaterA Stockli R Wang A Yang Z-L Zeng X and ZengX Technical Description of version 40 of the CommunityLand Model (CLM) NCAR TECHNICAL NOTE NCARTN-478+STR Boulder CO 80307-3000 2010

Orville R E Huffins G R Burrows W R and Cummins K LThe North American Lightning Detection Network (NALDN)ndash Analysis of Flash Data 2001ndash09 Mon Weather Rev 1391305ndash1322doi1011752010MWR34521 2011

Otto J S and Anderson N E Slash-and-Burn Cultivationin the Highlands South A Problem in ComparativeAgricultural History Comp Stud Soc Hist 24 131ndash147doi101017S0010417500009816 1982

Page S Siegert F Boehm H Jaya A and Limin S Theamount of carbon released from peat and forest fires in Indonesiaduring 1997 Nature 420 61ndash65doi101038nature011312002

Page S Rieley J Hoscilo A Spessa A and Weber U Fire andGlobal Change Chapter IV Current Fire Regimes in Impactsand Likely Changes in Tropical Southeast Asia Springer VerlagBerlin Heidelberg 2012

Papa F Prigent C Aires F Jimenez C Rossow W B andMatthews E Interannual variability of surface water extent atthe global scale 1993ndash2004 J Geophys Res 115 D12111doi1010292009JD012674 2010

Parks S A Parisien M-A and Miller C Spatial bottom-upcontrols on fire likelihood vary across western North AmericaEcosphere 3 art12doi101890ES11-002981 2012

Pausas J G and Keeley J E A burning story The roleof fire in the history of life BioScience 59 593ndash601doi101525bio200959710 2009

Penner J E Dickinson R E and OrsquoNeill C A Effects ofAerosol from Biomass Burning on the Global Radiation BudgetScience 256 1432ndash1434doi101126science256506214321992

Perry D A Hessburg P F Skinner C N Spies T A StephensS L Taylor A H Franklin J F McComb B and RiegelG The ecology of mixed severity fire regimes in WashingtonOregon and Northern California Forest Ecol Manag 262 703ndash717doi101016jforeco201105004 2011

Peterson D Wang J Ichoku C and Remer L A Effects oflightning and other meteorological factors on fire activity in theNorth American boreal forest implications for fire weather fore-casting Atmos Chem Phys 10 6873ndash6888doi105194acp-10-6873-2010 2010

Peterson D L and Ryan K C Modeling postfire conifer mor-tality for long-range planning Environ Manage 10 797ndash808doi101007BF01867732 1986

Piepgrass M V Krider E P and Moore C B Lightning andSurface Rainfall During Florida Thunderstorms J GeophysRes 87 11193ndash11201doi101029JC087iC13p11193 1982

Poulter B Heyder U and Cramer W Modeling the Sensitivityof the Seasonal Cycle of GPP to Dynamic LAI and SoilDepth in Tropical Rainforests Ecosystems 12 517ndash333doi101007s10021-009-9238-4 2009

Prairiesourcecom Prescribed Burning 101 An Introduction toPrescribed Burning Spring 1992httpwwwprairiesourcecomnewsletters92spr01htm last access 10 May 2013 1992

Pregitzer K S and Euskirchen E S Carbon cycling andstorage in world forests biomae patterns related to forestage Glob Change Biol 10 2052ndash2077doi101111j1365-2486200400866x 2004

Prentice I C Kelley D I Foster P N Friedlingstein PHarrison S P and Bartlein P J Modeling fire and the ter-restrial carbon balance Global Biogeochem Cy 25 GB3005doi1010292010GB003906 2011

Pyne S J Fire in America A Cultural History of Wildland andRural Fire Princeton University Press Princeton NJ 1982

Pyne S J Maintaining Focus An Introduction to AnthropogenicFire Chemosphere 29 889ndash911doi1010160045-6535(94)90159-7 1994

Pyne S J World Fire The Culture of Fire on Earth University ofWashington Press Seattle WA 384 pp 1997

Pyne S J Andrews P L and Daven R D Introduction toWildland Fire Wiley London 1996

Ramankutty N Evan A T Monfreda C and Foley J AFarming the planet 1 Geographic distribution of global agri-cultural lands in the year 2000 Global Biogeochem Cy 22GB1003doi1010292007GB002952 2008

Randerson J T Chen Y van der Werf G R Rogers B Mand Morton D C Global burnedf area and biomass burn-ing emissions from small fires J Geophys Res 117 G04012doi1010292012JG002128 2012

Rasul G and Thapa G B Shifting Cultivation in the Mountainsof South and Southeast Asia Regional patterns and factorsinfluencing the change Land Degrad Dev 14 495ndash508doi101002ldr570 2003

Reinhardt E D Keane R E and Brown J K FirstOrder Fire Effects Model FOFEM 40 United StatesDepartment of Agriculture Forest Service Missoula Montana59807 Intermountain Research Station Userrsquos Guide GeneralTechnical Report INT-GTR-344 1997

Richards L A Capillary conduction of liquids through porousmediums Physics 1 318ndash333doi10106311745010 1931

Ringeval B de Noblet-Ducoudre N Ciais P Bousquet PPrigent C Papa F and Rossow W B An attempt to quantifythe impact of changes in wetland extent on methane emissionson the seasonal and interannual time scales Global BiogeochemCy 24 GB2003doi1010292008GB003354 2010

Rivas Soriano L De Pablo F and Garcıa Dıez E Relationshipbetween Convective Precipitation and Cloud-to-GroundLightning in the Iberian Peninsula Mon Weather Rev 1292998ndash3003 2001

Roos C I Sullivan A P and NcNamee C PaleoecologicalEvidence for Systematic Indigenous Burning in the UplandSouthwest The Archaeology of Anthropogenic EnvironmentsSouthern Illinois University Press Carbondale 142ndash171 2010

Rosch M Ehrmann O Herrmann L Schulz E BogenriederA Goldammer J P Hall M Page H and Schier W An ex-perimental approach to Neolithic shifting cultivation Veg Hist



Archaebot 11 143ndash154 2002Rothermel R C A mathematical model for predicting fire spread

in wildland fuels USDA Forest Service Research Paper OgdenUT 84401 INT-115 48 pp 1972

Roxburgh S H Shea K and Wilson J B The IntermediateDisturbance Hypothesis Patch Dynamics and Mechanisms ofSpecies Coexistence Ecology 85 359ndash371doi10189003-0266 2004

Roy D P and Boschetti L Southern Africa Validation of theMODIS L3JRC and GlobCarbon Burned-Area Products IEEET Geosci Remote 47 1032ndash1044 2009

Roy D P Boschetti L Justice C O and Ju J The collection 5MODIS burned area product ndash Global evaluation by comparisonwith the MODIS active fire product Remote Sens Environ 1123690ndash3707doi101016jrse200805013 2008

Saatchi S S Houghton R A Alves D and Nelson B AmazonBasin Aboveground Live Biomass Distribution Map 1999ndash2000 Data Set from Oak Ridge National Laboratory DistributedActive Archive Center Oak Ridge Tennessee USA 2009

Saatchi S S Harris N L Brown S Lefsky M Mitchard E TA Salas W Buermann W Lewis S L Hagen S Petrova SWhite L Silman M and Morel A Benchmark map of forestcarbon stocks in tropical regions across three continents P NatlAcad Sci USA 108 1ndash6doi101073pnas1019576108 2011

Scholes M C Martin R Scholes R J Parsons D andWinstead E NO and N2O emissions from savanna soils fol-lowing the first simulated rains of the season Nutr CyclAgroecosys 48 115ndash122 1997

Schulzweida U Kornblueh L and Quast R CDO Userrsquos Guide2012

Seiler W and Crutzen P J Estimates of gross and netfluxes of carbon between the biosphere and the atmo-sphere from biomass burning Climatic Change 2 207ndash247doi101007BF00137988 1980

Sigaut F Swidden cultivation in Europe A question fortropical anthropologists Soc Sc Inform 18 679ndash694doi101177053901847901800404 1979

Sitch S Smith B Prentice I C Arneth A Bondeau ACramer W Kaplan J O Levis S Lucht W Sykes M TThonicke K and Venevsky S Evaluation of ecosystem dynam-ics plant geography and terrestrial carbon cycling in the LPJ dy-namic global vegetation model Glob Change Biol 9 161ndash185doi101046j1365-2486200300569x 2003

Skinner C N and Chang C-R Fire Regimes Past and PresentSierra Nevada Ecosystem Project Final Report to CongressVol II in Assessments and scientific basis for managementoptions Sierra Nevada Ecosystem Project Final Report toCongress Wildland Resources Center Report No 37 Centers forWater and Wildland Resources University of California DavisCalifornia USA 1996

Smith B Prentice I C and Sykes M T Representation ofvegetation dynamics in the modelling of terrestrial ecosystemscomparing two contrasting approaches within European climatespace Global Ecol Biogeogr 10 621ndash637doi101046j1466-822X2001t01-1-00256x 2001

Smittinand T Ratanakhon S Banijbatana D Komkris T ZinkeP J Hinton P Keen F B Charley J L McGarity J Wand Pelzer K J Farmers in the Forest Economic develop-ment and marginal agriculture in Northern Thailand edited by

Kunstaedter P Chapman E C and Sabhasri S University ofHawairsquoi Press Honolulu HI 96822 402 pp 1978

Sonesson M and Callaghan T V Strategies of Survival in Plantsof the Fennoscandian Tundra Arctic 44 95ndash105 1991

Spessa A and Fisher R On the relative role of fire and rainfallin determining vegetation patterns in tropical savannas a sim-ulation study Geophysical Research Abstracts 12 EGU2010-7142-6 2010

Spessa A van der Werf G Thonicke K Gomez-Dans J FisherR and Forrest M Fire and Global Change in ModelingVegetation Fires and Emissions Chapter XIV Springer publish-ers 2012

Stephens S L and Ruth L W Federal Forest-Fire Policy in theUnited States Ecol Appl 15 532ndash542 2005

Stewart O C Lewis H T and Anderson K Forgotten FiresNative Americans and the Transient Wilderness University ofOklahoma Press Norman OK 73069 364 pp 2002

Stocks B J Mason J A Todd J B Bosch E M WottonB M Amiro B D Flannigan M D Hirsch K GLogan K A Martell D L and Skinner W R Large for-est fires in Canada 1959ndash1997 J Geophys Res 108 8149doi1010292001JD000484 2003

Sturm M McFadden J P Liston G E ChapinF S Racine C H and Holmgren J Snow-ShrubInteractions in Arctic Tundra A Hypothesis with ClimaticImplications J Climate 14 336ndash344doi1011751520-0442(2001)014lt0336SSIIATgt20CO2 2000

Tansey K Gregoire J-M Stroppiana D Sousa A Silva JPereira J M C Boschetti L Maggi M Brivio P A PraserR Flasse S Ershov D Binaghi E Graetz D and PeduzziP Vegetation burning in the year 2000 Global burned area es-timates from SPOT VEGETATIOM data J Geophys Res 109D14S03doi1010292003JD003598 2004

Tansey K Gregoire J-M Defourny P Leigh R Pekel Jvan Bogaert J F O van Bogaert E and Bartholome EA new global multi-annual (2000-2007) burnt area prod-uct at 1 km resolution Geophys Res Lett 35 L01401doi1010292007GL031567 2008

Tarnocai C Canadell J G Schuur E A G Kuhry PMazhitova G and Zimov S Soil organic carbon pools in thenorthern circumpolar permafrost region Global BiogeochemCy 23 GB2023doi1010292008GB003327 2009

Thonicke K Spessa A Prentice I C Harrison S P DongL and Carmona-Moreno C The influence of vegetation firespread and fire behaviour on biomass burning and trace gasemissions results from a process-based model BiogeosciencesDiscuss 7 697ndash743doi105194bgd-7-697-2010 2010

Tinner W Conedera M Ammann B and Lotter A F Fire ecol-ogy north and south of the Alps since the last ice age Holocene15 1214ndash1226doi1011910959683605hl892rp 2005

Tinner W Hu F S Beer R Kaltenrieder P Scheurer B andKrahenbuhl U Postglacial vegetational and fire history pollenplant macrofossil and charcoal records from two Alaskan lakesVeg Hist Archaebot 15 279ndash293doi101007s00334-006-0052-z 2006

Todd S K and Jewkes H A Wildland Fire in Alaska AHistory of Organized Fire Suppression and Management inthe Last FrontierAgricultural and Forestry Experiment StationUniversity of Alaska Fairbanks Tech Rep Bulletin No 114



2006Turetsky M Wieder K Halsey L and Vitt D Current distur-

bance and the diminishing peatland carbon sink Geophys ResLett 29 279ndash293doi101007s00334-006-0052-z 2002

Uhl C and Kauffman J B Deforestation Fire Susceptibilityand Potential Tree Responses to Fire in the Eastern AmazonEcology 71 437ndash449doi1023071940299 1990

Uman M A The Art and Science of Lightning ProtectionCambridge University Press Cambridge 2010

Unruh J D Treacy J M Alcorn J B and Flores Paitan SSwidden-fallow agroforestry in the Peruvian Amazon Vol 5New York Botanical Garden PressDept 1987

van der Werf G R Randerson J T Giglio L Collatz G J MuM Kasibhatla P S Morton D C DeFries R S Jin Y andvan Leeuwen T T Global fire emissions and the contribution ofdeforestation savanna forest agricultural and peat fires (1997ndash2009) Atmos Chem Phys 10 11707ndash11735doi105194acp-10-11707-2010 2010

Van Reuler H and Janssen B H Comparison of the fertilizingeffects of ash from burnt secondary vegetation and of mineralfertilizers on upland rice in south-west Cote drsquoIvoire Fert Res45 1ndash11doi101007BF00749875 1996

van Wilgen B W Everson C S and Trollope W S W Firemanagement in southern Africa some examples of current objec-tives practices and problems in Fire Management in SouthernAfrica Some Examples of Current Objectives Practices andProblems Springer Verlag Berlin 79ndash212 1990

Venevsky S Thonicke K Sitch S and Cramer W Simulatingfire regimes in human-dominated ecosystems Iberian Peninsulacase study Glob Change Biol 8 984ndash998 2002

Virts K S Wallace J M Hutchins M L and HolzworthR H Highlights of a new ground-based hourlyglobal lightning climatology B Amer Meteorol Socdoihttpdxdoiorg101175BAMS-D-12-000821 accepted2013

Wan S Hui D and Luo Y Fire Effects on NitrogenPools and Dynamics in Terrestrial Ecosystems A Meta-Analysis Ecol Appl 11 1349ndash1365doi1018901051-0761(2001)011[1349FEONPA]20CO2 2001

Wang T Hamann A Spittlehouse D L and Murdock T QClimateWNA ndash High-Resolution Spatial Climate Data forWestern North America J Appl Meteorol Clim 51 16ndash29doi101175JAMC-D-11-0431 2011

Wania R Ross I and Prentice I C Integrating peat-lands and permafrost into a dynamic global vegetationmodel 1 Evaluation and sensitivity of physical land sur-face processes Global Biogeochem Cy 23 GB3014doi1010292008GB003412 2009

Warneke C Bahreini R Brock C A de Gouw J A FaheyD W Froyd K D Holloway J S Middlebrook A MillerL Montzka S Murphy D M Peischl J Ryerson T BSchwarz J P Spackman J R and Veres P Biomass burningin Siberia and Kazakhstan as important source for haze over theAlaskan Arctic in April 2008 Geophys Res Lett 36 L02813doi1010292008GL036194 2009

Westerling A L Hidalgo H G Cayan D R and SwetnamT W Warming and Earlier Spring Increase WesternUS Forest Wildfire Activity Science 313 940ndash943doi101126science1128834 2006

Whiten A and Erdal D The human socio-cognitive niche andits evolutionary origins Philos T R Soc B 367 2119ndash2129doi101098rstb20120114 2012

Williams G W Introduction to Aboriginal Fire Use in NorthAmerica Fire Management Today 60 8ndash12 2000

Williams G W Aboriginal use of fire are there any ldquonaturalrdquo plantcommunities in Wilderness and Political Ecology AboriginalLand Management ndash Myths and Reality University of UtahPress Logan UT 2002a

Williams M Deforesting the Earth From Prehistory to GlobalCrisis University of Chicago Press Chicago IL 2002b

Wylie D Jackson D L Menzel W P and Bates J J Trends inGlobal Cloud Cover in Two Decades of HIRS Observations JClimate 18 3021ndash3031doi101175JCLI34611 2005

Yevich R and Logan J A An assessment of biofuel use andburning of agricultural waste in the developing world GlobalBiogeochem Cy 17 1095doi1010292002GB001952 2003

Yibarbuk D Whitehead P J Russell-Smith J Jackson DGodjuwa C Fisher A Cooke P D C and Bowman DM J S Fire ecology and Aboriginal land management incentral Arnhem Land northern Austalia a tradition of ecosys-tem management J Biogeogr 28 325ndash343doi101046j1365-2699200100555x 2002

Zhang X Drake N A Wainwright J and Mulligan MComparison of slope estimates from low resolution DEMS scal-ing issues and a fractal method for their solution Earth SurfProc Land 24 763ndash779 1999

Zhou Y Qie X and Soula S A study of the relationship be-tween cloud-to-ground lightning and precipitation in the con-vective weather system in China Ann Geophys 20 107ndash113doi105194angeo-20-107-2002 2002



of fire and fire emissions is challenging Fire occurrence isinfluenced by climate vegetation structure and compositionand human activities fire behaviour is affected by weathertopography and the characteristics of the fuel fire distur-bance alters vegetation composition and structure and ulti-mately climate (Archibald et al 2009 Bowman et al 2009Spessa et al 2012) Thus modelling fire requires represen-tations of vegetation fire and climate that interact and feedback upon one another

Mathematical models of wildfire dynamics have existedfor over 40 yr (Rothermel 1972) The original models offire behaviour were motivated by needs for operational fireforecasting for firefighting and forest management applica-tions These models were applied at relatively small spatialscales of 100 minus 103 ha and have been extensively revisedand updated over subsequent years (Burgan and Rothermel1984 Andrews 1986 Burgan 1987 Andrews and Chase1989 Reinhardt et al 1997 Finney 1998 Andrews et al2003 Andrews 2007 Andrews et al 2008 Heinsch andAndrews 2010) Fire modelling at field scale is an essentialpart of fire management and mitigation worldwide and mod-ern operational fire models such as BehavePlus (Heinsch andAndrews 2010) can be used for a wide range of fire man-agement applications including projecting the behaviour ofongoing fire planning prescribed fire assessing fuel hazardand training

More recently fire models have been developed for ap-plication at larger spatial scales eg for integration into dy-namic global vegetation models (DGVMs) in order to simu-late the fundamental ecosystem disturbance process that firerepresents and in some cases to estimate the emissions ofclimate-relevant trace gases and aerosols at continental toglobal scale Depending on the goals for application of theparticular DGVM the detail with which fire is representedvaries but all large-scale fire models include a representationof three key processes

1 fire occurrence

2 fire behaviour and

3 fire impacts on vegetation

The most complex representations of fire currently adaptedfor DGVMs incorporate and generalize many of the con-cepts and equations developed for operational fire forecast-ing models into a large-scale framework The RegFIRM firemodel (Venevsky et al 2002) originally developed as anembedded module within the Lund-Potsdam-Jena DGVM(LPJ Sitch et al 2003) was one of the first global firemodels that contained explicit representations of climatic firedanger and lightning- and human-caused wildfire ignitionsBuilding on RegFIRM the SPITFIRE (SPread and InTensityof FIRE) fire model (Thonicke et al 2010) included a morecomplete process representation of fire ignitions and be-haviour and further contained new representations of the im-

pacts of fire on vegetation including plant mortality as a re-sult of crown scorch and cambial damage and routines forestimating trace gas and aerosol emissions SPITFIRE wasdesigned to overcome many of the limitations in previousfire models set within DGVM frameworks and be flexibleenough to permit simulation analyses at sub-continental toglobal scales with minimal input data requirements

SPITFIRE is one of the most comprehensive fire mod-ules for DGVMs currently available and has been the fo-cus of numerous studies on the role of fire in terrestrialecosystems and the Earth systemThonicke et al(2010) pre-sented the SPITFIRE model description and global assess-ments of simulated burned area and wildfire trace gas emis-sionsGomez-Dans et al(2013) used SPITFIRE in combi-nation with MODIS burned area and tree cover data to im-prove the modelrsquos predictions of burned area at selected sitesin different biomes using parameter calibration-optimizationtechniques SPITFIRE has also been driven with L3JRCburned area data (Tansey et al 2008) and MODIS burnedarea data (Roy et al 2008 Roy and Boschetti 2009) aspart of the LPJ-GUESS vegetation model (Smith et al2001 Hickler et al 2006) in a study examining emis-sions from biomass burning in Africa (Lehsten et al 2009)Using LPJ-GUESS-SPITFIRELehsten et al(2013) ex-amined how changes to fire frequency including fire ex-clusion affect treendashgrass ratios in Africa RecentlySpessaet al (2012) benchmarked LPJ-GUESS-SPITFIRE againstremote-sensing-based tree biomass data for pan-tropicalforests and savannas (Saatchi et al 2011 Baccini et al2012) The model was driven by a combination of monthlyburned area from the Global Fire and Emissions Database(GFEDv31Giglio et al 2010 van der Werf et al 2010)and long-term annual fire statistics (Mouillot and Field2005)

In addition to LPJ and its variants SPITFIRE hasbeen incorporated into other vegetation modelsSpessa andFisher(2010) coupled SPITFIRE to a global version of theEcosystem Demography (ED) vegetation model (Moorcroftet al 2001) ED has been incorporated into the MOSES22land surface model (Met Office Surface Exchange SchemeEssery et al 2001 Fisher et al 2010) and the CommunityLand Surface Model (CLMOleson et al 2010) SPITFIREis currently being integrated into ED-CLM (Spessa andFisher in preparation) With minor modifications SPITFIREhas also been incorporated into the LPX-DGVM (Prenticeet al 2011) and applied in global experiments to quantifythe contribution of wildfires to the global landndashatmosphereCO2 flux

In the following sections we describe LPJ-LMfire whichis a revised version of LPJ-SPITFIRE that we designedfor simulating global fire and vegetationndashfire interactionson centennial to multi-millennial timescales primarily dur-ing prehistoric and preindustrial time The purpose of thismanuscript is to present a complete description of our cur-rent model code to facilitate referencing of the model in






3 Methods



















Table 1Continued













LPJ

CA

LL T

O

FIR

E R

OU

TIN

E (d

aily

)sn

owco

ver

no fi

re

yes

slop

e gt=

003

no

slf =

10

lt= s

lf lt1

noye

s

ρ lg

f(GD

D20

)

A unbu

rned

ƒ(A

Ato

tbur

n)

calc

of f

uel p

ools

an

d ve

g c

over

fra

ctio

ns

totfu

el

lt 10

00or

vegc

over

lt

05

Ligh

tnin

g ig

nitio

ns

ƒ(ig

n e

ffici

ency

FD

I A to

tbur

n)

fuel

moi

stur

eƒ(α

wet

ting

dryi

ng

term

top

soil

moi

stur

e)

Fire

Dan

ger (

FDI)

ƒ(fu

el m

oist

ure

m

oist

ure

of

extin

ctio

n)

gras

scov

ergt=

60

FD

I ƒ(Ѡ

o m

e_av

g)FD

I ƒ(Ѡ

nl m

e_nl

)

yes

no

FDI =

0

no fi

re

yes

no fi

re

spre

ad

yes

fuel

bul

k de

nsity

ƒ(d

eadf

uel(p

ftcl

ass)

ρ b

PFT

)

df(P

FTc

lass

) ƒ(la

f la

s)

lf(PF

Tcl

ass)

ƒ(N

ind

hm

ind

sm

ind

lmin

d)

per P

FT a

nd fu

el s

ize

clas

s

per f

uel s

ize

clas

s

woi

(14

)w

oigr

assy

woi

woo

dy

herb

aceo

usw

oody

de

adfu

el

tota

l fue

l

totfu

el

veg

cov

er fr

actio

ns

treec

over

gra

ssco

ver

totc

over

per f

uel s

ize

clas

s

Ѡ(fc

) ƒ(α

wet

ting

dryi

ng te

rm)

for l

iveg

rass

Ѡlg

ƒ(to

psoi

l m

oist

ure)

all 1

-hr f

uel

Ѡnl

ƒ(Ѡ

(1) Ѡ

lg

woi

(1)

wliv

egra

ss

SOM

surf)

wei

ghte

d av

erag

eѠ

o f(α(

clas

s)

α lg

woi

(cla

ss)

wliv

egra

ss)

moi

stur

e of

ext

inct

ion

me

ƒ(w

oi(c

l) m

e(fc

)) m

e_av

g ƒ

(me

woi

(cl)

me_

lf w

liveg

r)

me _

nl ƒ

(me(

1) w

oi(1

) m

e_lf

wliv

egr

)

Fire

Occ

urre

nce

Rat

e of

forw

ard

spre

ad

RO

Sfsw

RO

Sfsg

gras

s fu

elw

oody

fue

l

RO

Sfs

ƒ(R

OSf

sg

RO

Sfsw

tre

ecov

er

gras

scov

er)

treec

over

gt=

60

ampw

scal

lt

1

RO

Sfc

yes

no

RO

Sfs

ltR

OSf

c

RO

Sf =

RO

Sfc

cr

ownfi

re =

true

RO

Sf =

RO

Sfs

cr

ownfi

re =

fals

e

yes

no

Fire

Beh

avio

r

Rat

e of

bac

kwar

d sp

read

ƒ(R

OSf

win

d)

t fire

ƒ(F

DI)

DT

ƒ(t fi

re R

OSf

RO

Sb)

LB ƒ

(win

d tr

eeco

ver

gras

scov

er)

ā f ƒ

(LB

DT

slf

ker

nel

size

)

Hum

an Ig

nitio

ns

hfire

= tr

ueamp

ā f lt

100

dayb

urnt

arge

tƒ(a

nnta

rget

bf2

0

cum

frac)

yes

Ab_

day(

pers

on)

ƒ(D

T L

B w

alkd

ist

ā f)

hum

an ig

nitio

ns

nhig

=

ƒ(d

aybu

rnta

rget

pe

ople

ā f

)

nhig

= 0

no

num

ber o

f fire

s c

umfir

es =ƒ(c

umfir

es

natfi

res

hum

fires

A t

otbu

rn)

daily

are

a bu

rned

AB

ƒ(c

umfir

es ā

f A u

nbur

ned)

Fuel

con

sum

ptio

nFC

ƒ(fu

el m

oist

ure

m

oist

ure

of e

xtin

ctio

n

fuel

load

)

Fire

inte

nsity

I s

urfa

ce ƒ

(FC

RO

Sf)

Isur

face

gt

50

Fire

Impa

ct

Fire

mor

talit

yP m

CK

ƒ(R

CK

I sur

face

he

ight

CL

F d

phen

)

Fire

impa

ct

Car

bon

loss

tra

ce g

as

emis

sion

s a

nnua

l are

a bu

rned

Agr

icul

tura

l bu

rnin

g(o

nce

annu

ally

)

Bur

ned

area

20

o

f the

cro

p la

nd a

fter h

arve

st

Fuel

con

sum

ptio

n20

o

f ann

ual

abov

egro

und

biom

ass

(har

vest

re

mai

nder

s)

Fire

impa

ct

Car

bon

loss

tar

ea

burn

ed

Scal

ing

land

use

cov

er fr

actio

ns

(nat

ural

agr

icul

tura

l re

cove

ring)

annu

al g

rid c

ell l

evel

ac

cum

ulat

ion

burn

ed a

rea

em

issi

ons

Tota

l bur

ned

area

and

trac

e ga

sem

issi

ons

no fi

re

spre

ad

yes

no






lm=





001

01

1

10

ratio

of

str

ike

s t

o t

em

po

ral m

ea

n








ieffavg =

npftsumpft=1

(fpcgridieffpft

)npftsum

pft=1fpcgrid

(2)



1+ 25burnedf (3)













tann=max

(min

((1minusgrass)max

(d(grass)

dt0

)201

)0

) (5)


d(grass)



) (6)







igp =Dwalk

Wf (7)

where

Wf =DT

LB (8)


Abpd = igpaf (9)







) (10)



rf =

1 FDI le 025

1122πFDIe

minus(ln(FDI)+129)2

018 FDI gt 025 (11)




af (12)












32 Fire behaviour














a)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


b)









10 92950 514


10 04750 024







ρlivegrass=20000

GDD20+ 1000minus 1 (15)


323 Fuel moisture


rm =ωnl

menl (16)




)wfinefuel+ SOMsurf

(17)



)wfinefuel+ SOMsurf

(18)




rm =ωo

meavg (19)



wet=

1 precgt 50mm

prec50 precle 50mm

(21)





wet=

1 balancegt 1


0 balancelt 0

(23)




caf=

3sumi=1

αwoi

wn

wo

wtot+ αlg

wlivegrass

wtot (24)


meavg =

fcsumi=1

(woimefc)

fcsumi=1

woi

middotwo

wtot+

melfwlivegrass

wtot (25)


FDI =

max(0(1minus

ωnlmenl

) grasscoverge 06

max(0(1minus

ωomeavg

) grasscoverlt 06

(26)






ROSfsg =

((0165+ 0534

Uf

60


where


)+ 10848 (28)







windfact=


60 le 10

2Uforward

60 gt 10 (30)







slf =

1 γ lt 17

159πγminus2

γ ge 17 (31)


af = afslf (32)








)minus2169Agc (33)


33 Fire mortality






τl = 394fcsum

i=1


) (34)
























































0 1 200 400 600 800 1000 1500 2000 2500 3000 3500







Arctic Tundra







AT

IB

AM

ART

BTA

BTU

CR











minus81000

minus72000

minus63000

minus54000

minus45000

minus36000

minus27000

minus18000

minus9000

0

9000

18000

27000

0

1000

2000

3000

4000

5000

6000

7000

are

a b

urn

ed

[km

2]


0

100

200

300

400

500

600

700

BTA BTU CR AM


0

5000

10000

15000

20000

25000

30000

Are

a b

urn

ed

[km

2 y

rminus1]

1990 1995 2000 2005 2010







0

5

10

15

20

25

30

pre

cip

ita

tio

n [

mm

dminus

1]

01 02 03 04 05 06 07 08 09 10 11 12

snowpack

no burning

00

01

02

03

04

05

06

07

08

09

10

FD

I (s

tars

)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

ligh

tnin

g s

trik

es (

red

circle

s)

[grid

ce

llminus1 d

minus1]






12 25 50 100 200 300 400 500 700 1000 2000














a)

b)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


c)











1 5 12 25 50 100 200 300 400 500 700 1000 2000












a)



b)












































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References





































































































































































































































































3 Methods



















Table 1Continued













LPJ

CA

LL T

O

FIR

E R

OU

TIN

E (d

aily

)sn

owco

ver

no fi

re

yes

slop

e gt=

003

no

slf =

10

lt= s

lf lt1

noye

s

ρ lg

f(GD

D20

)

A unbu

rned

ƒ(A

Ato

tbur

n)

calc

of f

uel p

ools

an

d ve

g c

over

fra

ctio

ns

totfu

el

lt 10

00or

vegc

over

lt

05

Ligh

tnin

g ig

nitio

ns

ƒ(ig

n e

ffici

ency

FD

I A to

tbur

n)

fuel

moi

stur

eƒ(α

wet

ting

dryi

ng

term

top

soil

moi

stur

e)

Fire

Dan

ger (

FDI)

ƒ(fu

el m

oist

ure

m

oist

ure

of

extin

ctio

n)

gras

scov

ergt=

60

FD

I ƒ(Ѡ

o m

e_av

g)FD

I ƒ(Ѡ

nl m

e_nl

)

yes

no

FDI =

0

no fi

re

yes

no fi

re

spre

ad

yes

fuel

bul

k de

nsity

ƒ(d

eadf

uel(p

ftcl

ass)

ρ b

PFT

)

df(P

FTc

lass

) ƒ(la

f la

s)

lf(PF

Tcl

ass)

ƒ(N

ind

hm

ind

sm

ind

lmin

d)

per P

FT a

nd fu

el s

ize

clas

s

per f

uel s

ize

clas

s

woi

(14

)w

oigr

assy

woi

woo

dy

herb

aceo

usw

oody

de

adfu

el

tota

l fue

l

totfu

el

veg

cov

er fr

actio

ns

treec

over

gra

ssco

ver

totc

over

per f

uel s

ize

clas

s

Ѡ(fc

) ƒ(α

wet

ting

dryi

ng te

rm)

for l

iveg

rass

Ѡlg

ƒ(to

psoi

l m

oist

ure)

all 1

-hr f

uel

Ѡnl

ƒ(Ѡ

(1) Ѡ

lg

woi

(1)

wliv

egra

ss

SOM

surf)

wei

ghte

d av

erag

eѠ

o f(α(

clas

s)

α lg

woi

(cla

ss)

wliv

egra

ss)

moi

stur

e of

ext

inct

ion

me

ƒ(w

oi(c

l) m

e(fc

)) m

e_av

g ƒ

(me

woi

(cl)

me_

lf w

liveg

r)

me _

nl ƒ

(me(

1) w

oi(1

) m

e_lf

wliv

egr

)

Fire

Occ

urre

nce

Rat

e of

forw

ard

spre

ad

RO

Sfsw

RO

Sfsg

gras

s fu

elw

oody

fue

l

RO

Sfs

ƒ(R

OSf

sg

RO

Sfsw

tre

ecov

er

gras

scov

er)

treec

over

gt=

60

ampw

scal

lt

1

RO

Sfc

yes

no

RO

Sfs

ltR

OSf

c

RO

Sf =

RO

Sfc

cr

ownfi

re =

true

RO

Sf =

RO

Sfs

cr

ownfi

re =

fals

e

yes

no

Fire

Beh

avio

r

Rat

e of

bac

kwar

d sp

read

ƒ(R

OSf

win

d)

t fire

ƒ(F

DI)

DT

ƒ(t fi

re R

OSf

RO

Sb)

LB ƒ

(win

d tr

eeco

ver

gras

scov

er)

ā f ƒ

(LB

DT

slf

ker

nel

size

)

Hum

an Ig

nitio

ns

hfire

= tr

ueamp

ā f lt

100

dayb

urnt

arge

tƒ(a

nnta

rget

bf2

0

cum

frac)

yes

Ab_

day(

pers

on)

ƒ(D

T L

B w

alkd

ist

ā f)

hum

an ig

nitio

ns

nhig

=

ƒ(d

aybu

rnta

rget

pe

ople

ā f

)

nhig

= 0

no

num

ber o

f fire

s c

umfir

es =ƒ(c

umfir

es

natfi

res

hum

fires

A t

otbu

rn)

daily

are

a bu

rned

AB

ƒ(c

umfir

es ā

f A u

nbur

ned)

Fuel

con

sum

ptio

nFC

ƒ(fu

el m

oist

ure

m

oist

ure

of e

xtin

ctio

n

fuel

load

)

Fire

inte

nsity

I s

urfa

ce ƒ

(FC

RO

Sf)

Isur

face

gt

50

Fire

Impa

ct

Fire

mor

talit

yP m

CK

ƒ(R

CK

I sur

face

he

ight

CL

F d

phen

)

Fire

impa

ct

Car

bon

loss

tra

ce g

as

emis

sion

s a

nnua

l are

a bu

rned

Agr

icul

tura

l bu

rnin

g(o

nce

annu

ally

)

Bur

ned

area

20

o

f the

cro

p la

nd a

fter h

arve

st

Fuel

con

sum

ptio

n20

o

f ann

ual

abov

egro

und

biom

ass

(har

vest

re

mai

nder

s)

Fire

impa

ct

Car

bon

loss

tar

ea

burn

ed

Scal

ing

land

use

cov

er fr

actio

ns

(nat

ural

agr

icul

tura

l re

cove

ring)

annu

al g

rid c

ell l

evel

ac

cum

ulat

ion

burn

ed a

rea

em

issi

ons

Tota

l bur

ned

area

and

trac

e ga

sem

issi

ons

no fi

re

spre

ad

yes

no






lm=





001

01

1

10

ratio

of

str

ike

s t

o t

em

po

ral m

ea

n








ieffavg =

npftsumpft=1

(fpcgridieffpft

)npftsum

pft=1fpcgrid

(2)



1+ 25burnedf (3)













tann=max

(min

((1minusgrass)max

(d(grass)

dt0

)201

)0

) (5)


d(grass)



) (6)







igp =Dwalk

Wf (7)

where

Wf =DT

LB (8)


Abpd = igpaf (9)







) (10)



rf =

1 FDI le 025

1122πFDIe

minus(ln(FDI)+129)2

018 FDI gt 025 (11)




af (12)












32 Fire behaviour














a)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


b)









10 92950 514


10 04750 024







ρlivegrass=20000

GDD20+ 1000minus 1 (15)


323 Fuel moisture


rm =ωnl

menl (16)




)wfinefuel+ SOMsurf

(17)



)wfinefuel+ SOMsurf

(18)




rm =ωo

meavg (19)



wet=

1 precgt 50mm

prec50 precle 50mm

(21)





wet=

1 balancegt 1


0 balancelt 0

(23)




caf=

3sumi=1

αwoi

wn

wo

wtot+ αlg

wlivegrass

wtot (24)


meavg =

fcsumi=1

(woimefc)

fcsumi=1

woi

middotwo

wtot+

melfwlivegrass

wtot (25)


FDI =

max(0(1minus

ωnlmenl

) grasscoverge 06

max(0(1minus

ωomeavg

) grasscoverlt 06

(26)






ROSfsg =

((0165+ 0534

Uf

60


where


)+ 10848 (28)







windfact=


60 le 10

2Uforward

60 gt 10 (30)







slf =

1 γ lt 17

159πγminus2

γ ge 17 (31)


af = afslf (32)








)minus2169Agc (33)


33 Fire mortality






τl = 394fcsum

i=1


) (34)
























































0 1 200 400 600 800 1000 1500 2000 2500 3000 3500







Arctic Tundra







AT

IB

AM

ART

BTA

BTU

CR











minus81000

minus72000

minus63000

minus54000

minus45000

minus36000

minus27000

minus18000

minus9000

0

9000

18000

27000

0

1000

2000

3000

4000

5000

6000

7000

are

a b

urn

ed

[km

2]


0

100

200

300

400

500

600

700

BTA BTU CR AM


0

5000

10000

15000

20000

25000

30000

Are

a b

urn

ed

[km

2 y

rminus1]

1990 1995 2000 2005 2010







0

5

10

15

20

25

30

pre

cip

ita

tio

n [

mm

dminus

1]

01 02 03 04 05 06 07 08 09 10 11 12

snowpack

no burning

00

01

02

03

04

05

06

07

08

09

10

FD

I (s

tars

)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

ligh

tnin

g s

trik

es (

red

circle

s)

[grid

ce

llminus1 d

minus1]






12 25 50 100 200 300 400 500 700 1000 2000














a)

b)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


c)











1 5 12 25 50 100 200 300 400 500 700 1000 2000












a)



b)












































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References







































































































































































































































































Table 1Continued













LPJ

CA

LL T

O

FIR

E R

OU

TIN

E (d

aily

)sn

owco

ver

no fi

re

yes

slop

e gt=

003

no

slf =

10

lt= s

lf lt1

noye

s

ρ lg

f(GD

D20

)

A unbu

rned

ƒ(A

Ato

tbur

n)

calc

of f

uel p

ools

an

d ve

g c

over

fra

ctio

ns

totfu

el

lt 10

00or

vegc

over

lt

05

Ligh

tnin

g ig

nitio

ns

ƒ(ig

n e

ffici

ency

FD

I A to

tbur

n)

fuel

moi

stur

eƒ(α

wet

ting

dryi

ng

term

top

soil

moi

stur

e)

Fire

Dan

ger (

FDI)

ƒ(fu

el m

oist

ure

m

oist

ure

of

extin

ctio

n)

gras

scov

ergt=

60

FD

I ƒ(Ѡ

o m

e_av

g)FD

I ƒ(Ѡ

nl m

e_nl

)

yes

no

FDI =

0

no fi

re

yes

no fi

re

spre

ad

yes

fuel

bul

k de

nsity

ƒ(d

eadf

uel(p

ftcl

ass)

ρ b

PFT

)

df(P

FTc

lass

) ƒ(la

f la

s)

lf(PF

Tcl

ass)

ƒ(N

ind

hm

ind

sm

ind

lmin

d)

per P

FT a

nd fu

el s

ize

clas

s

per f

uel s

ize

clas

s

woi

(14

)w

oigr

assy

woi

woo

dy

herb

aceo

usw

oody

de

adfu

el

tota

l fue

l

totfu

el

veg

cov

er fr

actio

ns

treec

over

gra

ssco

ver

totc

over

per f

uel s

ize

clas

s

Ѡ(fc

) ƒ(α

wet

ting

dryi

ng te

rm)

for l

iveg

rass

Ѡlg

ƒ(to

psoi

l m

oist

ure)

all 1

-hr f

uel

Ѡnl

ƒ(Ѡ

(1) Ѡ

lg

woi

(1)

wliv

egra

ss

SOM

surf)

wei

ghte

d av

erag

eѠ

o f(α(

clas

s)

α lg

woi

(cla

ss)

wliv

egra

ss)

moi

stur

e of

ext

inct

ion

me

ƒ(w

oi(c

l) m

e(fc

)) m

e_av

g ƒ

(me

woi

(cl)

me_

lf w

liveg

r)

me _

nl ƒ

(me(

1) w

oi(1

) m

e_lf

wliv

egr

)

Fire

Occ

urre

nce

Rat

e of

forw

ard

spre

ad

RO

Sfsw

RO

Sfsg

gras

s fu

elw

oody

fue

l

RO

Sfs

ƒ(R

OSf

sg

RO

Sfsw

tre

ecov

er

gras

scov

er)

treec

over

gt=

60

ampw

scal

lt

1

RO

Sfc

yes

no

RO

Sfs

ltR

OSf

c

RO

Sf =

RO

Sfc

cr

ownfi

re =

true

RO

Sf =

RO

Sfs

cr

ownfi

re =

fals

e

yes

no

Fire

Beh

avio

r

Rat

e of

bac

kwar

d sp

read

ƒ(R

OSf

win

d)

t fire

ƒ(F

DI)

DT

ƒ(t fi

re R

OSf

RO

Sb)

LB ƒ

(win

d tr

eeco

ver

gras

scov

er)

ā f ƒ

(LB

DT

slf

ker

nel

size

)

Hum

an Ig

nitio

ns

hfire

= tr

ueamp

ā f lt

100

dayb

urnt

arge

tƒ(a

nnta

rget

bf2

0

cum

frac)

yes

Ab_

day(

pers

on)

ƒ(D

T L

B w

alkd

ist

ā f)

hum

an ig

nitio

ns

nhig

=

ƒ(d

aybu

rnta

rget

pe

ople

ā f

)

nhig

= 0

no

num

ber o

f fire

s c

umfir

es =ƒ(c

umfir

es

natfi

res

hum

fires

A t

otbu

rn)

daily

are

a bu

rned

AB

ƒ(c

umfir

es ā

f A u

nbur

ned)

Fuel

con

sum

ptio

nFC

ƒ(fu

el m

oist

ure

m

oist

ure

of e

xtin

ctio

n

fuel

load

)

Fire

inte

nsity

I s

urfa

ce ƒ

(FC

RO

Sf)

Isur

face

gt

50

Fire

Impa

ct

Fire

mor

talit

yP m

CK

ƒ(R

CK

I sur

face

he

ight

CL

F d

phen

)

Fire

impa

ct

Car

bon

loss

tra

ce g

as

emis

sion

s a

nnua

l are

a bu

rned

Agr

icul

tura

l bu

rnin

g(o

nce

annu

ally

)

Bur

ned

area

20

o

f the

cro

p la

nd a

fter h

arve

st

Fuel

con

sum

ptio

n20

o

f ann

ual

abov

egro

und

biom

ass

(har

vest

re

mai

nder

s)

Fire

impa

ct

Car

bon

loss

tar

ea

burn

ed

Scal

ing

land

use

cov

er fr

actio

ns

(nat

ural

agr

icul

tura

l re

cove

ring)

annu

al g

rid c

ell l

evel

ac

cum

ulat

ion

burn

ed a

rea

em

issi

ons

Tota

l bur

ned

area

and

trac

e ga

sem

issi

ons

no fi

re

spre

ad

yes

no






lm=





001

01

1

10

ratio

of

str

ike

s t

o t

em

po

ral m

ea

n








ieffavg =

npftsumpft=1

(fpcgridieffpft

)npftsum

pft=1fpcgrid

(2)



1+ 25burnedf (3)













tann=max

(min

((1minusgrass)max

(d(grass)

dt0

)201

)0

) (5)


d(grass)



) (6)







igp =Dwalk

Wf (7)

where

Wf =DT

LB (8)


Abpd = igpaf (9)







) (10)



rf =

1 FDI le 025

1122πFDIe

minus(ln(FDI)+129)2

018 FDI gt 025 (11)




af (12)












32 Fire behaviour














a)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


b)









10 92950 514


10 04750 024







ρlivegrass=20000

GDD20+ 1000minus 1 (15)


323 Fuel moisture


rm =ωnl

menl (16)




)wfinefuel+ SOMsurf

(17)



)wfinefuel+ SOMsurf

(18)




rm =ωo

meavg (19)



wet=

1 precgt 50mm

prec50 precle 50mm

(21)





wet=

1 balancegt 1


0 balancelt 0

(23)




caf=

3sumi=1

αwoi

wn

wo

wtot+ αlg

wlivegrass

wtot (24)


meavg =

fcsumi=1

(woimefc)

fcsumi=1

woi

middotwo

wtot+

melfwlivegrass

wtot (25)


FDI =

max(0(1minus

ωnlmenl

) grasscoverge 06

max(0(1minus

ωomeavg

) grasscoverlt 06

(26)






ROSfsg =

((0165+ 0534

Uf

60


where


)+ 10848 (28)







windfact=


60 le 10

2Uforward

60 gt 10 (30)







slf =

1 γ lt 17

159πγminus2

γ ge 17 (31)


af = afslf (32)








)minus2169Agc (33)


33 Fire mortality






τl = 394fcsum

i=1


) (34)
























































0 1 200 400 600 800 1000 1500 2000 2500 3000 3500







Arctic Tundra







AT

IB

AM

ART

BTA

BTU

CR











minus81000

minus72000

minus63000

minus54000

minus45000

minus36000

minus27000

minus18000

minus9000

0

9000

18000

27000

0

1000

2000

3000

4000

5000

6000

7000

are

a b

urn

ed

[km

2]


0

100

200

300

400

500

600

700

BTA BTU CR AM


0

5000

10000

15000

20000

25000

30000

Are

a b

urn

ed

[km

2 y

rminus1]

1990 1995 2000 2005 2010







0

5

10

15

20

25

30

pre

cip

ita

tio

n [

mm

dminus

1]

01 02 03 04 05 06 07 08 09 10 11 12

snowpack

no burning

00

01

02

03

04

05

06

07

08

09

10

FD

I (s

tars

)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

ligh

tnin

g s

trik

es (

red

circle

s)

[grid

ce

llminus1 d

minus1]






12 25 50 100 200 300 400 500 700 1000 2000














a)

b)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


c)











1 5 12 25 50 100 200 300 400 500 700 1000 2000












a)



b)












































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References


































































































































































































































































Table 1Continued













LPJ

CA

LL T

O

FIR

E R

OU

TIN

E (d

aily

)sn

owco

ver

no fi

re

yes

slop

e gt=

003

no

slf =

10

lt= s

lf lt1

noye

s

ρ lg

f(GD

D20

)

A unbu

rned

ƒ(A

Ato

tbur

n)

calc

of f

uel p

ools

an

d ve

g c

over

fra

ctio

ns

totfu

el

lt 10

00or

vegc

over

lt

05

Ligh

tnin

g ig

nitio

ns

ƒ(ig

n e

ffici

ency

FD

I A to

tbur

n)

fuel

moi

stur

eƒ(α

wet

ting

dryi

ng

term

top

soil

moi

stur

e)

Fire

Dan

ger (

FDI)

ƒ(fu

el m

oist

ure

m

oist

ure

of

extin

ctio

n)

gras

scov

ergt=

60

FD

I ƒ(Ѡ

o m

e_av

g)FD

I ƒ(Ѡ

nl m

e_nl

)

yes

no

FDI =

0

no fi

re

yes

no fi

re

spre

ad

yes

fuel

bul

k de

nsity

ƒ(d

eadf

uel(p

ftcl

ass)

ρ b

PFT

)

df(P

FTc

lass

) ƒ(la

f la

s)

lf(PF

Tcl

ass)

ƒ(N

ind

hm

ind

sm

ind

lmin

d)

per P

FT a

nd fu

el s

ize

clas

s

per f

uel s

ize

clas

s

woi

(14

)w

oigr

assy

woi

woo

dy

herb

aceo

usw

oody

de

adfu

el

tota

l fue

l

totfu

el

veg

cov

er fr

actio

ns

treec

over

gra

ssco

ver

totc

over

per f

uel s

ize

clas

s

Ѡ(fc

) ƒ(α

wet

ting

dryi

ng te

rm)

for l

iveg

rass

Ѡlg

ƒ(to

psoi

l m

oist

ure)

all 1

-hr f

uel

Ѡnl

ƒ(Ѡ

(1) Ѡ

lg

woi

(1)

wliv

egra

ss

SOM

surf)

wei

ghte

d av

erag

eѠ

o f(α(

clas

s)

α lg

woi

(cla

ss)

wliv

egra

ss)

moi

stur

e of

ext

inct

ion

me

ƒ(w

oi(c

l) m

e(fc

)) m

e_av

g ƒ

(me

woi

(cl)

me_

lf w

liveg

r)

me _

nl ƒ

(me(

1) w

oi(1

) m

e_lf

wliv

egr

)

Fire

Occ

urre

nce

Rat

e of

forw

ard

spre

ad

RO

Sfsw

RO

Sfsg

gras

s fu

elw

oody

fue

l

RO

Sfs

ƒ(R

OSf

sg

RO

Sfsw

tre

ecov

er

gras

scov

er)

treec

over

gt=

60

ampw

scal

lt

1

RO

Sfc

yes

no

RO

Sfs

ltR

OSf

c

RO

Sf =

RO

Sfc

cr

ownfi

re =

true

RO

Sf =

RO

Sfs

cr

ownfi

re =

fals

e

yes

no

Fire

Beh

avio

r

Rat

e of

bac

kwar

d sp

read

ƒ(R

OSf

win

d)

t fire

ƒ(F

DI)

DT

ƒ(t fi

re R

OSf

RO

Sb)

LB ƒ

(win

d tr

eeco

ver

gras

scov

er)

ā f ƒ

(LB

DT

slf

ker

nel

size

)

Hum

an Ig

nitio

ns

hfire

= tr

ueamp

ā f lt

100

dayb

urnt

arge

tƒ(a

nnta

rget

bf2

0

cum

frac)

yes

Ab_

day(

pers

on)

ƒ(D

T L

B w

alkd

ist

ā f)

hum

an ig

nitio

ns

nhig

=

ƒ(d

aybu

rnta

rget

pe

ople

ā f

)

nhig

= 0

no

num

ber o

f fire

s c

umfir

es =ƒ(c

umfir

es

natfi

res

hum

fires

A t

otbu

rn)

daily

are

a bu

rned

AB

ƒ(c

umfir

es ā

f A u

nbur

ned)

Fuel

con

sum

ptio

nFC

ƒ(fu

el m

oist

ure

m

oist

ure

of e

xtin

ctio

n

fuel

load

)

Fire

inte

nsity

I s

urfa

ce ƒ

(FC

RO

Sf)

Isur

face

gt

50

Fire

Impa

ct

Fire

mor

talit

yP m

CK

ƒ(R

CK

I sur

face

he

ight

CL

F d

phen

)

Fire

impa

ct

Car

bon

loss

tra

ce g

as

emis

sion

s a

nnua

l are

a bu

rned

Agr

icul

tura

l bu

rnin

g(o

nce

annu

ally

)

Bur

ned

area

20

o

f the

cro

p la

nd a

fter h

arve

st

Fuel

con

sum

ptio

n20

o

f ann

ual

abov

egro

und

biom

ass

(har

vest

re

mai

nder

s)

Fire

impa

ct

Car

bon

loss

tar

ea

burn

ed

Scal

ing

land

use

cov

er fr

actio

ns

(nat

ural

agr

icul

tura

l re

cove

ring)

annu

al g

rid c

ell l

evel

ac

cum

ulat

ion

burn

ed a

rea

em

issi

ons

Tota

l bur

ned

area

and

trac

e ga

sem

issi

ons

no fi

re

spre

ad

yes

no






lm=





001

01

1

10

ratio

of

str

ike

s t

o t

em

po

ral m

ea

n








ieffavg =

npftsumpft=1

(fpcgridieffpft

)npftsum

pft=1fpcgrid

(2)



1+ 25burnedf (3)













tann=max

(min

((1minusgrass)max

(d(grass)

dt0

)201

)0

) (5)


d(grass)



) (6)







igp =Dwalk

Wf (7)

where

Wf =DT

LB (8)


Abpd = igpaf (9)







) (10)



rf =

1 FDI le 025

1122πFDIe

minus(ln(FDI)+129)2

018 FDI gt 025 (11)




af (12)












32 Fire behaviour














a)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


b)









10 92950 514


10 04750 024







ρlivegrass=20000

GDD20+ 1000minus 1 (15)


323 Fuel moisture


rm =ωnl

menl (16)




)wfinefuel+ SOMsurf

(17)



)wfinefuel+ SOMsurf

(18)




rm =ωo

meavg (19)



wet=

1 precgt 50mm

prec50 precle 50mm

(21)





wet=

1 balancegt 1


0 balancelt 0

(23)




caf=

3sumi=1

αwoi

wn

wo

wtot+ αlg

wlivegrass

wtot (24)


meavg =

fcsumi=1

(woimefc)

fcsumi=1

woi

middotwo

wtot+

melfwlivegrass

wtot (25)


FDI =

max(0(1minus

ωnlmenl

) grasscoverge 06

max(0(1minus

ωomeavg

) grasscoverlt 06

(26)






ROSfsg =

((0165+ 0534

Uf

60


where


)+ 10848 (28)







windfact=


60 le 10

2Uforward

60 gt 10 (30)







slf =

1 γ lt 17

159πγminus2

γ ge 17 (31)


af = afslf (32)








)minus2169Agc (33)


33 Fire mortality






τl = 394fcsum

i=1


) (34)
























































0 1 200 400 600 800 1000 1500 2000 2500 3000 3500







Arctic Tundra







AT

IB

AM

ART

BTA

BTU

CR











minus81000

minus72000

minus63000

minus54000

minus45000

minus36000

minus27000

minus18000

minus9000

0

9000

18000

27000

0

1000

2000

3000

4000

5000

6000

7000

are

a b

urn

ed

[km

2]


0

100

200

300

400

500

600

700

BTA BTU CR AM


0

5000

10000

15000

20000

25000

30000

Are

a b

urn

ed

[km

2 y

rminus1]

1990 1995 2000 2005 2010







0

5

10

15

20

25

30

pre

cip

ita

tio

n [

mm

dminus

1]

01 02 03 04 05 06 07 08 09 10 11 12

snowpack

no burning

00

01

02

03

04

05

06

07

08

09

10

FD

I (s

tars

)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

ligh

tnin

g s

trik

es (

red

circle

s)

[grid

ce

llminus1 d

minus1]






12 25 50 100 200 300 400 500 700 1000 2000














a)

b)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


c)











1 5 12 25 50 100 200 300 400 500 700 1000 2000












a)



b)












































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References


































































































































































































































































LPJ

CA

LL T

O

FIR

E R

OU

TIN

E (d

aily

)sn

owco

ver

no fi

re

yes

slop

e gt=

003

no

slf =

10

lt= s

lf lt1

noye

s

ρ lg

f(GD

D20

)

A unbu

rned

ƒ(A

Ato

tbur

n)

calc

of f

uel p

ools

an

d ve

g c

over

fra

ctio

ns

totfu

el

lt 10

00or

vegc

over

lt

05

Ligh

tnin

g ig

nitio

ns

ƒ(ig

n e

ffici

ency

FD

I A to

tbur

n)

fuel

moi

stur

eƒ(α

wet

ting

dryi

ng

term

top

soil

moi

stur

e)

Fire

Dan

ger (

FDI)

ƒ(fu

el m

oist

ure

m

oist

ure

of

extin

ctio

n)

gras

scov

ergt=

60

FD

I ƒ(Ѡ

o m

e_av

g)FD

I ƒ(Ѡ

nl m

e_nl

)

yes

no

FDI =

0

no fi

re

yes

no fi

re

spre

ad

yes

fuel

bul

k de

nsity

ƒ(d

eadf

uel(p

ftcl

ass)

ρ b

PFT

)

df(P

FTc

lass

) ƒ(la

f la

s)

lf(PF

Tcl

ass)

ƒ(N

ind

hm

ind

sm

ind

lmin

d)

per P

FT a

nd fu

el s

ize

clas

s

per f

uel s

ize

clas

s

woi

(14

)w

oigr

assy

woi

woo

dy

herb

aceo

usw

oody

de

adfu

el

tota

l fue

l

totfu

el

veg

cov

er fr

actio

ns

treec

over

gra

ssco

ver

totc

over

per f

uel s

ize

clas

s

Ѡ(fc

) ƒ(α

wet

ting

dryi

ng te

rm)

for l

iveg

rass

Ѡlg

ƒ(to

psoi

l m

oist

ure)

all 1

-hr f

uel

Ѡnl

ƒ(Ѡ

(1) Ѡ

lg

woi

(1)

wliv

egra

ss

SOM

surf)

wei

ghte

d av

erag

eѠ

o f(α(

clas

s)

α lg

woi

(cla

ss)

wliv

egra

ss)

moi

stur

e of

ext

inct

ion

me

ƒ(w

oi(c

l) m

e(fc

)) m

e_av

g ƒ

(me

woi

(cl)

me_

lf w

liveg

r)

me _

nl ƒ

(me(

1) w

oi(1

) m

e_lf

wliv

egr

)

Fire

Occ

urre

nce

Rat

e of

forw

ard

spre

ad

RO

Sfsw

RO

Sfsg

gras

s fu

elw

oody

fue

l

RO

Sfs

ƒ(R

OSf

sg

RO

Sfsw

tre

ecov

er

gras

scov

er)

treec

over

gt=

60

ampw

scal

lt

1

RO

Sfc

yes

no

RO

Sfs

ltR

OSf

c

RO

Sf =

RO

Sfc

cr

ownfi

re =

true

RO

Sf =

RO

Sfs

cr

ownfi

re =

fals

e

yes

no

Fire

Beh

avio

r

Rat

e of

bac

kwar

d sp

read

ƒ(R

OSf

win

d)

t fire

ƒ(F

DI)

DT

ƒ(t fi

re R

OSf

RO

Sb)

LB ƒ

(win

d tr

eeco

ver

gras

scov

er)

ā f ƒ

(LB

DT

slf

ker

nel

size

)

Hum

an Ig

nitio

ns

hfire

= tr

ueamp

ā f lt

100

dayb

urnt

arge

tƒ(a

nnta

rget

bf2

0

cum

frac)

yes

Ab_

day(

pers

on)

ƒ(D

T L

B w

alkd

ist

ā f)

hum

an ig

nitio

ns

nhig

=

ƒ(d

aybu

rnta

rget

pe

ople

ā f

)

nhig

= 0

no

num

ber o

f fire

s c

umfir

es =ƒ(c

umfir

es

natfi

res

hum

fires

A t

otbu

rn)

daily

are

a bu

rned

AB

ƒ(c

umfir

es ā

f A u

nbur

ned)

Fuel

con

sum

ptio

nFC

ƒ(fu

el m

oist

ure

m

oist

ure

of e

xtin

ctio

n

fuel

load

)

Fire

inte

nsity

I s

urfa

ce ƒ

(FC

RO

Sf)

Isur

face

gt

50

Fire

Impa

ct

Fire

mor

talit

yP m

CK

ƒ(R

CK

I sur

face

he

ight

CL

F d

phen

)

Fire

impa

ct

Car

bon

loss

tra

ce g

as

emis

sion

s a

nnua

l are

a bu

rned

Agr

icul

tura

l bu

rnin

g(o

nce

annu

ally

)

Bur

ned

area

20

o

f the

cro

p la

nd a

fter h

arve

st

Fuel

con

sum

ptio

n20

o

f ann

ual

abov

egro

und

biom

ass

(har

vest

re

mai

nder

s)

Fire

impa

ct

Car

bon

loss

tar

ea

burn

ed

Scal

ing

land

use

cov

er fr

actio

ns

(nat

ural

agr

icul

tura

l re

cove

ring)

annu

al g

rid c

ell l

evel

ac

cum

ulat

ion

burn

ed a

rea

em

issi

ons

Tota

l bur

ned

area

and

trac

e ga

sem

issi

ons

no fi

re

spre

ad

yes

no






lm=





001

01

1

10

ratio

of

str

ike

s t

o t

em

po

ral m

ea

n








ieffavg =

npftsumpft=1

(fpcgridieffpft

)npftsum

pft=1fpcgrid

(2)



1+ 25burnedf (3)













tann=max

(min

((1minusgrass)max

(d(grass)

dt0

)201

)0

) (5)


d(grass)



) (6)







igp =Dwalk

Wf (7)

where

Wf =DT

LB (8)


Abpd = igpaf (9)







) (10)



rf =

1 FDI le 025

1122πFDIe

minus(ln(FDI)+129)2

018 FDI gt 025 (11)




af (12)












32 Fire behaviour














a)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


b)









10 92950 514


10 04750 024







ρlivegrass=20000

GDD20+ 1000minus 1 (15)


323 Fuel moisture


rm =ωnl

menl (16)




)wfinefuel+ SOMsurf

(17)



)wfinefuel+ SOMsurf

(18)




rm =ωo

meavg (19)



wet=

1 precgt 50mm

prec50 precle 50mm

(21)





wet=

1 balancegt 1


0 balancelt 0

(23)




caf=

3sumi=1

αwoi

wn

wo

wtot+ αlg

wlivegrass

wtot (24)


meavg =

fcsumi=1

(woimefc)

fcsumi=1

woi

middotwo

wtot+

melfwlivegrass

wtot (25)


FDI =

max(0(1minus

ωnlmenl

) grasscoverge 06

max(0(1minus

ωomeavg

) grasscoverlt 06

(26)






ROSfsg =

((0165+ 0534

Uf

60


where


)+ 10848 (28)







windfact=


60 le 10

2Uforward

60 gt 10 (30)







slf =

1 γ lt 17

159πγminus2

γ ge 17 (31)


af = afslf (32)








)minus2169Agc (33)


33 Fire mortality






τl = 394fcsum

i=1


) (34)
























































0 1 200 400 600 800 1000 1500 2000 2500 3000 3500







Arctic Tundra







AT

IB

AM

ART

BTA

BTU

CR











minus81000

minus72000

minus63000

minus54000

minus45000

minus36000

minus27000

minus18000

minus9000

0

9000

18000

27000

0

1000

2000

3000

4000

5000

6000

7000

are

a b

urn

ed

[km

2]


0

100

200

300

400

500

600

700

BTA BTU CR AM


0

5000

10000

15000

20000

25000

30000

Are

a b

urn

ed

[km

2 y

rminus1]

1990 1995 2000 2005 2010







0

5

10

15

20

25

30

pre

cip

ita

tio

n [

mm

dminus

1]

01 02 03 04 05 06 07 08 09 10 11 12

snowpack

no burning

00

01

02

03

04

05

06

07

08

09

10

FD

I (s

tars

)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

ligh

tnin

g s

trik

es (

red

circle

s)

[grid

ce

llminus1 d

minus1]






12 25 50 100 200 300 400 500 700 1000 2000














a)

b)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


c)











1 5 12 25 50 100 200 300 400 500 700 1000 2000












a)



b)












































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References




































































































































































































































































lm=





001

01

1

10

ratio

of

str

ike

s t

o t

em

po

ral m

ea

n








ieffavg =

npftsumpft=1

(fpcgridieffpft

)npftsum

pft=1fpcgrid

(2)



1+ 25burnedf (3)













tann=max

(min

((1minusgrass)max

(d(grass)

dt0

)201

)0

) (5)


d(grass)



) (6)







igp =Dwalk

Wf (7)

where

Wf =DT

LB (8)


Abpd = igpaf (9)







) (10)



rf =

1 FDI le 025

1122πFDIe

minus(ln(FDI)+129)2

018 FDI gt 025 (11)




af (12)












32 Fire behaviour














a)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


b)









10 92950 514


10 04750 024







ρlivegrass=20000

GDD20+ 1000minus 1 (15)


323 Fuel moisture


rm =ωnl

menl (16)




)wfinefuel+ SOMsurf

(17)



)wfinefuel+ SOMsurf

(18)




rm =ωo

meavg (19)



wet=

1 precgt 50mm

prec50 precle 50mm

(21)





wet=

1 balancegt 1


0 balancelt 0

(23)




caf=

3sumi=1

αwoi

wn

wo

wtot+ αlg

wlivegrass

wtot (24)


meavg =

fcsumi=1

(woimefc)

fcsumi=1

woi

middotwo

wtot+

melfwlivegrass

wtot (25)


FDI =

max(0(1minus

ωnlmenl

) grasscoverge 06

max(0(1minus

ωomeavg

) grasscoverlt 06

(26)






ROSfsg =

((0165+ 0534

Uf

60


where


)+ 10848 (28)







windfact=


60 le 10

2Uforward

60 gt 10 (30)







slf =

1 γ lt 17

159πγminus2

γ ge 17 (31)


af = afslf (32)








)minus2169Agc (33)


33 Fire mortality






τl = 394fcsum

i=1


) (34)
























































0 1 200 400 600 800 1000 1500 2000 2500 3000 3500







Arctic Tundra







AT

IB

AM

ART

BTA

BTU

CR











minus81000

minus72000

minus63000

minus54000

minus45000

minus36000

minus27000

minus18000

minus9000

0

9000

18000

27000

0

1000

2000

3000

4000

5000

6000

7000

are

a b

urn

ed

[km

2]


0

100

200

300

400

500

600

700

BTA BTU CR AM


0

5000

10000

15000

20000

25000

30000

Are

a b

urn

ed

[km

2 y

rminus1]

1990 1995 2000 2005 2010







0

5

10

15

20

25

30

pre

cip

ita

tio

n [

mm

dminus

1]

01 02 03 04 05 06 07 08 09 10 11 12

snowpack

no burning

00

01

02

03

04

05

06

07

08

09

10

FD

I (s

tars

)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

ligh

tnin

g s

trik

es (

red

circle

s)

[grid

ce

llminus1 d

minus1]






12 25 50 100 200 300 400 500 700 1000 2000














a)

b)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


c)











1 5 12 25 50 100 200 300 400 500 700 1000 2000












a)



b)












































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References



































































































































































































































































ieffavg =

npftsumpft=1

(fpcgridieffpft

)npftsum

pft=1fpcgrid

(2)



1+ 25burnedf (3)













tann=max

(min

((1minusgrass)max

(d(grass)

dt0

)201

)0

) (5)


d(grass)



) (6)







igp =Dwalk

Wf (7)

where

Wf =DT

LB (8)


Abpd = igpaf (9)







) (10)



rf =

1 FDI le 025

1122πFDIe

minus(ln(FDI)+129)2

018 FDI gt 025 (11)




af (12)












32 Fire behaviour














a)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


b)









10 92950 514


10 04750 024







ρlivegrass=20000

GDD20+ 1000minus 1 (15)


323 Fuel moisture


rm =ωnl

menl (16)




)wfinefuel+ SOMsurf

(17)



)wfinefuel+ SOMsurf

(18)




rm =ωo

meavg (19)



wet=

1 precgt 50mm

prec50 precle 50mm

(21)





wet=

1 balancegt 1


0 balancelt 0

(23)




caf=

3sumi=1

αwoi

wn

wo

wtot+ αlg

wlivegrass

wtot (24)


meavg =

fcsumi=1

(woimefc)

fcsumi=1

woi

middotwo

wtot+

melfwlivegrass

wtot (25)


FDI =

max(0(1minus

ωnlmenl

) grasscoverge 06

max(0(1minus

ωomeavg

) grasscoverlt 06

(26)






ROSfsg =

((0165+ 0534

Uf

60


where


)+ 10848 (28)







windfact=


60 le 10

2Uforward

60 gt 10 (30)







slf =

1 γ lt 17

159πγminus2

γ ge 17 (31)


af = afslf (32)








)minus2169Agc (33)


33 Fire mortality






τl = 394fcsum

i=1


) (34)
























































0 1 200 400 600 800 1000 1500 2000 2500 3000 3500







Arctic Tundra







AT

IB

AM

ART

BTA

BTU

CR











minus81000

minus72000

minus63000

minus54000

minus45000

minus36000

minus27000

minus18000

minus9000

0

9000

18000

27000

0

1000

2000

3000

4000

5000

6000

7000

are

a b

urn

ed

[km

2]


0

100

200

300

400

500

600

700

BTA BTU CR AM


0

5000

10000

15000

20000

25000

30000

Are

a b

urn

ed

[km

2 y

rminus1]

1990 1995 2000 2005 2010







0

5

10

15

20

25

30

pre

cip

ita

tio

n [

mm

dminus

1]

01 02 03 04 05 06 07 08 09 10 11 12

snowpack

no burning

00

01

02

03

04

05

06

07

08

09

10

FD

I (s

tars

)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

ligh

tnin

g s

trik

es (

red

circle

s)

[grid

ce

llminus1 d

minus1]






12 25 50 100 200 300 400 500 700 1000 2000














a)

b)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


c)











1 5 12 25 50 100 200 300 400 500 700 1000 2000












a)



b)












































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References




































































































































































































































































tann=max

(min

((1minusgrass)max

(d(grass)

dt0

)201

)0

) (5)


d(grass)



) (6)







igp =Dwalk

Wf (7)

where

Wf =DT

LB (8)


Abpd = igpaf (9)







) (10)



rf =

1 FDI le 025

1122πFDIe

minus(ln(FDI)+129)2

018 FDI gt 025 (11)




af (12)












32 Fire behaviour














a)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


b)









10 92950 514


10 04750 024







ρlivegrass=20000

GDD20+ 1000minus 1 (15)


323 Fuel moisture


rm =ωnl

menl (16)




)wfinefuel+ SOMsurf

(17)



)wfinefuel+ SOMsurf

(18)




rm =ωo

meavg (19)



wet=

1 precgt 50mm

prec50 precle 50mm

(21)





wet=

1 balancegt 1


0 balancelt 0

(23)




caf=

3sumi=1

αwoi

wn

wo

wtot+ αlg

wlivegrass

wtot (24)


meavg =

fcsumi=1

(woimefc)

fcsumi=1

woi

middotwo

wtot+

melfwlivegrass

wtot (25)


FDI =

max(0(1minus

ωnlmenl

) grasscoverge 06

max(0(1minus

ωomeavg

) grasscoverlt 06

(26)






ROSfsg =

((0165+ 0534

Uf

60


where


)+ 10848 (28)







windfact=


60 le 10

2Uforward

60 gt 10 (30)







slf =

1 γ lt 17

159πγminus2

γ ge 17 (31)


af = afslf (32)








)minus2169Agc (33)


33 Fire mortality






τl = 394fcsum

i=1


) (34)
























































0 1 200 400 600 800 1000 1500 2000 2500 3000 3500







Arctic Tundra







AT

IB

AM

ART

BTA

BTU

CR











minus81000

minus72000

minus63000

minus54000

minus45000

minus36000

minus27000

minus18000

minus9000

0

9000

18000

27000

0

1000

2000

3000

4000

5000

6000

7000

are

a b

urn

ed

[km

2]


0

100

200

300

400

500

600

700

BTA BTU CR AM


0

5000

10000

15000

20000

25000

30000

Are

a b

urn

ed

[km

2 y

rminus1]

1990 1995 2000 2005 2010







0

5

10

15

20

25

30

pre

cip

ita

tio

n [

mm

dminus

1]

01 02 03 04 05 06 07 08 09 10 11 12

snowpack

no burning

00

01

02

03

04

05

06

07

08

09

10

FD

I (s

tars

)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

ligh

tnin

g s

trik

es (

red

circle

s)

[grid

ce

llminus1 d

minus1]






12 25 50 100 200 300 400 500 700 1000 2000














a)

b)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


c)











1 5 12 25 50 100 200 300 400 500 700 1000 2000












a)



b)












































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References




































































































































































































































































) (10)



rf =

1 FDI le 025

1122πFDIe

minus(ln(FDI)+129)2

018 FDI gt 025 (11)




af (12)












32 Fire behaviour














a)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


b)









10 92950 514


10 04750 024







ρlivegrass=20000

GDD20+ 1000minus 1 (15)


323 Fuel moisture


rm =ωnl

menl (16)




)wfinefuel+ SOMsurf

(17)



)wfinefuel+ SOMsurf

(18)




rm =ωo

meavg (19)



wet=

1 precgt 50mm

prec50 precle 50mm

(21)





wet=

1 balancegt 1


0 balancelt 0

(23)




caf=

3sumi=1

αwoi

wn

wo

wtot+ αlg

wlivegrass

wtot (24)


meavg =

fcsumi=1

(woimefc)

fcsumi=1

woi

middotwo

wtot+

melfwlivegrass

wtot (25)


FDI =

max(0(1minus

ωnlmenl

) grasscoverge 06

max(0(1minus

ωomeavg

) grasscoverlt 06

(26)






ROSfsg =

((0165+ 0534

Uf

60


where


)+ 10848 (28)







windfact=


60 le 10

2Uforward

60 gt 10 (30)







slf =

1 γ lt 17

159πγminus2

γ ge 17 (31)


af = afslf (32)








)minus2169Agc (33)


33 Fire mortality






τl = 394fcsum

i=1


) (34)
























































0 1 200 400 600 800 1000 1500 2000 2500 3000 3500







Arctic Tundra







AT

IB

AM

ART

BTA

BTU

CR











minus81000

minus72000

minus63000

minus54000

minus45000

minus36000

minus27000

minus18000

minus9000

0

9000

18000

27000

0

1000

2000

3000

4000

5000

6000

7000

are

a b

urn

ed

[km

2]


0

100

200

300

400

500

600

700

BTA BTU CR AM


0

5000

10000

15000

20000

25000

30000

Are

a b

urn

ed

[km

2 y

rminus1]

1990 1995 2000 2005 2010







0

5

10

15

20

25

30

pre

cip

ita

tio

n [

mm

dminus

1]

01 02 03 04 05 06 07 08 09 10 11 12

snowpack

no burning

00

01

02

03

04

05

06

07

08

09

10

FD

I (s

tars

)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

ligh

tnin

g s

trik

es (

red

circle

s)

[grid

ce

llminus1 d

minus1]






12 25 50 100 200 300 400 500 700 1000 2000














a)

b)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


c)











1 5 12 25 50 100 200 300 400 500 700 1000 2000












a)



b)












































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References



































































































































































































































































32 Fire behaviour














a)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


b)









10 92950 514


10 04750 024







ρlivegrass=20000

GDD20+ 1000minus 1 (15)


323 Fuel moisture


rm =ωnl

menl (16)




)wfinefuel+ SOMsurf

(17)



)wfinefuel+ SOMsurf

(18)




rm =ωo

meavg (19)



wet=

1 precgt 50mm

prec50 precle 50mm

(21)





wet=

1 balancegt 1


0 balancelt 0

(23)




caf=

3sumi=1

αwoi

wn

wo

wtot+ αlg

wlivegrass

wtot (24)


meavg =

fcsumi=1

(woimefc)

fcsumi=1

woi

middotwo

wtot+

melfwlivegrass

wtot (25)


FDI =

max(0(1minus

ωnlmenl

) grasscoverge 06

max(0(1minus

ωomeavg

) grasscoverlt 06

(26)






ROSfsg =

((0165+ 0534

Uf

60


where


)+ 10848 (28)







windfact=


60 le 10

2Uforward

60 gt 10 (30)







slf =

1 γ lt 17

159πγminus2

γ ge 17 (31)


af = afslf (32)








)minus2169Agc (33)


33 Fire mortality






τl = 394fcsum

i=1


) (34)
























































0 1 200 400 600 800 1000 1500 2000 2500 3000 3500







Arctic Tundra







AT

IB

AM

ART

BTA

BTU

CR











minus81000

minus72000

minus63000

minus54000

minus45000

minus36000

minus27000

minus18000

minus9000

0

9000

18000

27000

0

1000

2000

3000

4000

5000

6000

7000

are

a b

urn

ed

[km

2]


0

100

200

300

400

500

600

700

BTA BTU CR AM


0

5000

10000

15000

20000

25000

30000

Are

a b

urn

ed

[km

2 y

rminus1]

1990 1995 2000 2005 2010







0

5

10

15

20

25

30

pre

cip

ita

tio

n [

mm

dminus

1]

01 02 03 04 05 06 07 08 09 10 11 12

snowpack

no burning

00

01

02

03

04

05

06

07

08

09

10

FD

I (s

tars

)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

ligh

tnin

g s

trik

es (

red

circle

s)

[grid

ce

llminus1 d

minus1]






12 25 50 100 200 300 400 500 700 1000 2000














a)

b)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


c)











1 5 12 25 50 100 200 300 400 500 700 1000 2000












a)



b)












































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References


































































































































































































































































a)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


b)









10 92950 514


10 04750 024







ρlivegrass=20000

GDD20+ 1000minus 1 (15)


323 Fuel moisture


rm =ωnl

menl (16)




)wfinefuel+ SOMsurf

(17)



)wfinefuel+ SOMsurf

(18)




rm =ωo

meavg (19)



wet=

1 precgt 50mm

prec50 precle 50mm

(21)





wet=

1 balancegt 1


0 balancelt 0

(23)




caf=

3sumi=1

αwoi

wn

wo

wtot+ αlg

wlivegrass

wtot (24)


meavg =

fcsumi=1

(woimefc)

fcsumi=1

woi

middotwo

wtot+

melfwlivegrass

wtot (25)


FDI =

max(0(1minus

ωnlmenl

) grasscoverge 06

max(0(1minus

ωomeavg

) grasscoverlt 06

(26)






ROSfsg =

((0165+ 0534

Uf

60


where


)+ 10848 (28)







windfact=


60 le 10

2Uforward

60 gt 10 (30)







slf =

1 γ lt 17

159πγminus2

γ ge 17 (31)


af = afslf (32)








)minus2169Agc (33)


33 Fire mortality






τl = 394fcsum

i=1


) (34)
























































0 1 200 400 600 800 1000 1500 2000 2500 3000 3500







Arctic Tundra







AT

IB

AM

ART

BTA

BTU

CR











minus81000

minus72000

minus63000

minus54000

minus45000

minus36000

minus27000

minus18000

minus9000

0

9000

18000

27000

0

1000

2000

3000

4000

5000

6000

7000

are

a b

urn

ed

[km

2]


0

100

200

300

400

500

600

700

BTA BTU CR AM


0

5000

10000

15000

20000

25000

30000

Are

a b

urn

ed

[km

2 y

rminus1]

1990 1995 2000 2005 2010







0

5

10

15

20

25

30

pre

cip

ita

tio

n [

mm

dminus

1]

01 02 03 04 05 06 07 08 09 10 11 12

snowpack

no burning

00

01

02

03

04

05

06

07

08

09

10

FD

I (s

tars

)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

ligh

tnin

g s

trik

es (

red

circle

s)

[grid

ce

llminus1 d

minus1]






12 25 50 100 200 300 400 500 700 1000 2000














a)

b)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


c)











1 5 12 25 50 100 200 300 400 500 700 1000 2000












a)



b)












































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References



































































































































































































































































ρlivegrass=20000

GDD20+ 1000minus 1 (15)


323 Fuel moisture


rm =ωnl

menl (16)




)wfinefuel+ SOMsurf

(17)



)wfinefuel+ SOMsurf

(18)




rm =ωo

meavg (19)



wet=

1 precgt 50mm

prec50 precle 50mm

(21)





wet=

1 balancegt 1


0 balancelt 0

(23)




caf=

3sumi=1

αwoi

wn

wo

wtot+ αlg

wlivegrass

wtot (24)


meavg =

fcsumi=1

(woimefc)

fcsumi=1

woi

middotwo

wtot+

melfwlivegrass

wtot (25)


FDI =

max(0(1minus

ωnlmenl

) grasscoverge 06

max(0(1minus

ωomeavg

) grasscoverlt 06

(26)






ROSfsg =

((0165+ 0534

Uf

60


where


)+ 10848 (28)







windfact=


60 le 10

2Uforward

60 gt 10 (30)







slf =

1 γ lt 17

159πγminus2

γ ge 17 (31)


af = afslf (32)








)minus2169Agc (33)


33 Fire mortality






τl = 394fcsum

i=1


) (34)
























































0 1 200 400 600 800 1000 1500 2000 2500 3000 3500







Arctic Tundra







AT

IB

AM

ART

BTA

BTU

CR











minus81000

minus72000

minus63000

minus54000

minus45000

minus36000

minus27000

minus18000

minus9000

0

9000

18000

27000

0

1000

2000

3000

4000

5000

6000

7000

are

a b

urn

ed

[km

2]


0

100

200

300

400

500

600

700

BTA BTU CR AM


0

5000

10000

15000

20000

25000

30000

Are

a b

urn

ed

[km

2 y

rminus1]

1990 1995 2000 2005 2010







0

5

10

15

20

25

30

pre

cip

ita

tio

n [

mm

dminus

1]

01 02 03 04 05 06 07 08 09 10 11 12

snowpack

no burning

00

01

02

03

04

05

06

07

08

09

10

FD

I (s

tars

)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

ligh

tnin

g s

trik

es (

red

circle

s)

[grid

ce

llminus1 d

minus1]






12 25 50 100 200 300 400 500 700 1000 2000














a)

b)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


c)











1 5 12 25 50 100 200 300 400 500 700 1000 2000












a)



b)












































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References



































































































































































































































































caf=

3sumi=1

αwoi

wn

wo

wtot+ αlg

wlivegrass

wtot (24)


meavg =

fcsumi=1

(woimefc)

fcsumi=1

woi

middotwo

wtot+

melfwlivegrass

wtot (25)


FDI =

max(0(1minus

ωnlmenl

) grasscoverge 06

max(0(1minus

ωomeavg

) grasscoverlt 06

(26)






ROSfsg =

((0165+ 0534

Uf

60


where


)+ 10848 (28)







windfact=


60 le 10

2Uforward

60 gt 10 (30)







slf =

1 γ lt 17

159πγminus2

γ ge 17 (31)


af = afslf (32)








)minus2169Agc (33)


33 Fire mortality






τl = 394fcsum

i=1


) (34)
























































0 1 200 400 600 800 1000 1500 2000 2500 3000 3500







Arctic Tundra







AT

IB

AM

ART

BTA

BTU

CR











minus81000

minus72000

minus63000

minus54000

minus45000

minus36000

minus27000

minus18000

minus9000

0

9000

18000

27000

0

1000

2000

3000

4000

5000

6000

7000

are

a b

urn

ed

[km

2]


0

100

200

300

400

500

600

700

BTA BTU CR AM


0

5000

10000

15000

20000

25000

30000

Are

a b

urn

ed

[km

2 y

rminus1]

1990 1995 2000 2005 2010







0

5

10

15

20

25

30

pre

cip

ita

tio

n [

mm

dminus

1]

01 02 03 04 05 06 07 08 09 10 11 12

snowpack

no burning

00

01

02

03

04

05

06

07

08

09

10

FD

I (s

tars

)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

ligh

tnin

g s

trik

es (

red

circle

s)

[grid

ce

llminus1 d

minus1]






12 25 50 100 200 300 400 500 700 1000 2000














a)

b)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


c)











1 5 12 25 50 100 200 300 400 500 700 1000 2000












a)



b)












































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References




































































































































































































































































slf =

1 γ lt 17

159πγminus2

γ ge 17 (31)


af = afslf (32)








)minus2169Agc (33)


33 Fire mortality






τl = 394fcsum

i=1


) (34)
























































0 1 200 400 600 800 1000 1500 2000 2500 3000 3500







Arctic Tundra







AT

IB

AM

ART

BTA

BTU

CR











minus81000

minus72000

minus63000

minus54000

minus45000

minus36000

minus27000

minus18000

minus9000

0

9000

18000

27000

0

1000

2000

3000

4000

5000

6000

7000

are

a b

urn

ed

[km

2]


0

100

200

300

400

500

600

700

BTA BTU CR AM


0

5000

10000

15000

20000

25000

30000

Are

a b

urn

ed

[km

2 y

rminus1]

1990 1995 2000 2005 2010







0

5

10

15

20

25

30

pre

cip

ita

tio

n [

mm

dminus

1]

01 02 03 04 05 06 07 08 09 10 11 12

snowpack

no burning

00

01

02

03

04

05

06

07

08

09

10

FD

I (s

tars

)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

ligh

tnin

g s

trik

es (

red

circle

s)

[grid

ce

llminus1 d

minus1]






12 25 50 100 200 300 400 500 700 1000 2000














a)

b)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


c)











1 5 12 25 50 100 200 300 400 500 700 1000 2000












a)



b)












































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References



































































































































































































































































τl = 394fcsum

i=1


) (34)
























































0 1 200 400 600 800 1000 1500 2000 2500 3000 3500







Arctic Tundra







AT

IB

AM

ART

BTA

BTU

CR











minus81000

minus72000

minus63000

minus54000

minus45000

minus36000

minus27000

minus18000

minus9000

0

9000

18000

27000

0

1000

2000

3000

4000

5000

6000

7000

are

a b

urn

ed

[km

2]


0

100

200

300

400

500

600

700

BTA BTU CR AM


0

5000

10000

15000

20000

25000

30000

Are

a b

urn

ed

[km

2 y

rminus1]

1990 1995 2000 2005 2010







0

5

10

15

20

25

30

pre

cip

ita

tio

n [

mm

dminus

1]

01 02 03 04 05 06 07 08 09 10 11 12

snowpack

no burning

00

01

02

03

04

05

06

07

08

09

10

FD

I (s

tars

)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

ligh

tnin

g s

trik

es (

red

circle

s)

[grid

ce

llminus1 d

minus1]






12 25 50 100 200 300 400 500 700 1000 2000














a)

b)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


c)











1 5 12 25 50 100 200 300 400 500 700 1000 2000












a)



b)












































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References












































































































































































































































































































0 1 200 400 600 800 1000 1500 2000 2500 3000 3500







Arctic Tundra







AT

IB

AM

ART

BTA

BTU

CR











minus81000

minus72000

minus63000

minus54000

minus45000

minus36000

minus27000

minus18000

minus9000

0

9000

18000

27000

0

1000

2000

3000

4000

5000

6000

7000

are

a b

urn

ed

[km

2]


0

100

200

300

400

500

600

700

BTA BTU CR AM


0

5000

10000

15000

20000

25000

30000

Are

a b

urn

ed

[km

2 y

rminus1]

1990 1995 2000 2005 2010







0

5

10

15

20

25

30

pre

cip

ita

tio

n [

mm

dminus

1]

01 02 03 04 05 06 07 08 09 10 11 12

snowpack

no burning

00

01

02

03

04

05

06

07

08

09

10

FD

I (s

tars

)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

ligh

tnin

g s

trik

es (

red

circle

s)

[grid

ce

llminus1 d

minus1]






12 25 50 100 200 300 400 500 700 1000 2000














a)

b)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


c)











1 5 12 25 50 100 200 300 400 500 700 1000 2000












a)



b)












































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References




















































































































































































































































































0 1 200 400 600 800 1000 1500 2000 2500 3000 3500







Arctic Tundra







AT

IB

AM

ART

BTA

BTU

CR











minus81000

minus72000

minus63000

minus54000

minus45000

minus36000

minus27000

minus18000

minus9000

0

9000

18000

27000

0

1000

2000

3000

4000

5000

6000

7000

are

a b

urn

ed

[km

2]


0

100

200

300

400

500

600

700

BTA BTU CR AM


0

5000

10000

15000

20000

25000

30000

Are

a b

urn

ed

[km

2 y

rminus1]

1990 1995 2000 2005 2010







0

5

10

15

20

25

30

pre

cip

ita

tio

n [

mm

dminus

1]

01 02 03 04 05 06 07 08 09 10 11 12

snowpack

no burning

00

01

02

03

04

05

06

07

08

09

10

FD

I (s

tars

)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

ligh

tnin

g s

trik

es (

red

circle

s)

[grid

ce

llminus1 d

minus1]






12 25 50 100 200 300 400 500 700 1000 2000














a)

b)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


c)











1 5 12 25 50 100 200 300 400 500 700 1000 2000












a)



b)












































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References


































































































































































































































































0 1 200 400 600 800 1000 1500 2000 2500 3000 3500







Arctic Tundra







AT

IB

AM

ART

BTA

BTU

CR











minus81000

minus72000

minus63000

minus54000

minus45000

minus36000

minus27000

minus18000

minus9000

0

9000

18000

27000

0

1000

2000

3000

4000

5000

6000

7000

are

a b

urn

ed

[km

2]


0

100

200

300

400

500

600

700

BTA BTU CR AM


0

5000

10000

15000

20000

25000

30000

Are

a b

urn

ed

[km

2 y

rminus1]

1990 1995 2000 2005 2010







0

5

10

15

20

25

30

pre

cip

ita

tio

n [

mm

dminus

1]

01 02 03 04 05 06 07 08 09 10 11 12

snowpack

no burning

00

01

02

03

04

05

06

07

08

09

10

FD

I (s

tars

)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

ligh

tnin

g s

trik

es (

red

circle

s)

[grid

ce

llminus1 d

minus1]






12 25 50 100 200 300 400 500 700 1000 2000














a)

b)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


c)











1 5 12 25 50 100 200 300 400 500 700 1000 2000












a)



b)












































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References


































































































































































































































































AT

IB

AM

ART

BTA

BTU

CR











minus81000

minus72000

minus63000

minus54000

minus45000

minus36000

minus27000

minus18000

minus9000

0

9000

18000

27000

0

1000

2000

3000

4000

5000

6000

7000

are

a b

urn

ed

[km

2]


0

100

200

300

400

500

600

700

BTA BTU CR AM


0

5000

10000

15000

20000

25000

30000

Are

a b

urn

ed

[km

2 y

rminus1]

1990 1995 2000 2005 2010







0

5

10

15

20

25

30

pre

cip

ita

tio

n [

mm

dminus

1]

01 02 03 04 05 06 07 08 09 10 11 12

snowpack

no burning

00

01

02

03

04

05

06

07

08

09

10

FD

I (s

tars

)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

ligh

tnin

g s

trik

es (

red

circle

s)

[grid

ce

llminus1 d

minus1]






12 25 50 100 200 300 400 500 700 1000 2000














a)

b)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


c)











1 5 12 25 50 100 200 300 400 500 700 1000 2000












a)



b)












































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References


































































































































































































































































minus81000

minus72000

minus63000

minus54000

minus45000

minus36000

minus27000

minus18000

minus9000

0

9000

18000

27000

0

1000

2000

3000

4000

5000

6000

7000

are

a b

urn

ed

[km

2]


0

100

200

300

400

500

600

700

BTA BTU CR AM


0

5000

10000

15000

20000

25000

30000

Are

a b

urn

ed

[km

2 y

rminus1]

1990 1995 2000 2005 2010







0

5

10

15

20

25

30

pre

cip

ita

tio

n [

mm

dminus

1]

01 02 03 04 05 06 07 08 09 10 11 12

snowpack

no burning

00

01

02

03

04

05

06

07

08

09

10

FD

I (s

tars

)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

ligh

tnin

g s

trik

es (

red

circle

s)

[grid

ce

llminus1 d

minus1]






12 25 50 100 200 300 400 500 700 1000 2000














a)

b)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


c)











1 5 12 25 50 100 200 300 400 500 700 1000 2000












a)



b)












































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References


































































































































































































































































0

5

10

15

20

25

30

pre

cip

ita

tio

n [

mm

dminus

1]

01 02 03 04 05 06 07 08 09 10 11 12

snowpack

no burning

00

01

02

03

04

05

06

07

08

09

10

FD

I (s

tars

)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

ligh

tnin

g s

trik

es (

red

circle

s)

[grid

ce

llminus1 d

minus1]






12 25 50 100 200 300 400 500 700 1000 2000














a)

b)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


c)











1 5 12 25 50 100 200 300 400 500 700 1000 2000












a)



b)












































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References










































































































































































































































































a)

b)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


c)











1 5 12 25 50 100 200 300 400 500 700 1000 2000












a)



b)












































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References


































































































































































































































































a)

b)

0 02 05 1 15 2 25 3 6 9 12 15 18 21 24


c)











1 5 12 25 50 100 200 300 400 500 700 1000 2000












a)



b)












































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References


































































































































































































































































1 5 12 25 50 100 200 300 400 500 700 1000 2000












a)



b)












































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References


































































































































































































































































a)



b)












































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References

































































































































































































































































































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References























































































































































































































































































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References













































































































































































































































































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References




































































































































































































































































6 Conclusions


Appendix A









(A4)


woi(class) =

npftsumpft=1

df(PFTclass) (A5)


ωlg =10

9middot ωs1minus

1

9 (A6)


αlg =

minuslogωlg


(A7)




wo =

3sumclass=1

(woi(class)) (A9)








A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References





































































































































































































































































A2 Rate of spread


relm =ωo

meavg (A11)


livemass=9sum

PFT=8


deadmass=9sum

PFT=1


pftlivefuel(PFT) =

3sumclass=1

lf(PFTclass) (A15)

pftdeadfuel(PFT) =

3sumclass=1

df(PFTclass) (A16)


3sumclass=1

df(PFTclass)

(A17)


ρb =



)wn

(A19)


wn = min

(7sum

PFT=1

lf(PFT1)8000

) (A20)


Packing ratio

β =ρb

ρp (A21)




pratio =β

βop (A23)


0primemax =

1



0prime= 0prime












Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References








































































































































































































































































Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References


































































































































































































































































Table A2 Continued





3 (A27)

Reaction intensity



ξ =e(0792+37597middot


192+ 79095middot σ (A29)

Wind coefficient




B = 015988middot σ 054 (A32)



ε = eminus4528

σ (A34)












)2155 (A38)



) (A40)


tfire =241





af = min( π



(A43)



rm =ωlg

melf (A44)

CFlg =

1 rm le 018



(A45)




rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References



































































































































































































































































rm =ω(1)

mefc(1) (A46)

CF(1) =

1 rm le 018



(A47)


rm =ω(2)

mefc(2) (A48)

CF(2) =

1 rm le 012



(A49)


rm =ω(3)

mefc(3) (A50)

CF(3) =


(A51)


rm =ω(4)

mefc(4) (A52)







3sumclass=1

FC(class) middot1

60 (A55)







CL(PFT) (A57)




Pm (τ ) =

0

τl

τcle 022

0563middotτl

τcminus 0125 τl

τcgt 022

1τl

τcge 20

(A60)








A6 Fuel consumption















For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








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For grass-type PFTs








) (A76)

las(PFT) = max

(las(PFT) minus

5sumi=2

annBBdead(PFTi)0

)

(A77)





) (A80)



) (A82)




BBtot =

npftsumPFT=1

5sumi=1

BBdead(PFTi) +

npftsumPFT=1

3sumj=1

BBlive(PFTj) (A83)





5sumiminus1

BBdead(PFTi) +

3sumj=1

BBlive(PFTj) (A85)


Mx(spec) =

npftsumPFT=1


) (A86)








References




































































































































































































































































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Date post:	17-Jan-2017
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A model for global biomass burning in preindustrial time: LPJ-LMfire ...

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