W. Chen et al. / Ecological Modelling 135 (2000) 55–7956
1. Introduction
Global land use changes (LUC) was estimated torelease 1.691.0 Pg per year (1 Pg=1015 g) carbon(C) to the atmosphere during 1980s (Houghton etal., 1996). This estimate, along with that of fossilfuel emissions, accumulation in the atmosphere,and ocean sink, suggested that during 1980s amissing sink of 1.891.6 Pg C per year existed inthe terrestrial biomes that were not subject to LUC(Houghton et al., 1996).
In searching for the missing sink, the effects ofdisturbances (e.g. fire, insect-induced mortality,and harvest), climatic variations (e.g. growing sea-son length lg, growing season temperature Ta,g,annual precipitation APPT, abiotic decompositionfactor L), and changes in atmospheric chemistry(atmospheric CO2 concentration and nitrogen (N)deposition) were each investigated (e.g. Bazzaz,1990; Kurz et al., 1992; Dai and Fung, 1993;Kolchugina and Vinson, 1993; Turner et al., 1995;Townsend et al., 1996; Kurz and Apps, 1999). Forexample, the 1995 IPCC report estimated that theNorthern hemisphere forest regrowth as a result ofchanges in age class distribution, caused by varia-tions in disturbance rates, increased terrestrial Csink by 0.590.5 Pg C per year during the 1980s(Houghton et al., 1996). In the same IPCC report,N deposition was suggested to increase globalterrestrial C sink by 0.2–1.0 Pg C per year, CO2
fertilization by 0.5–2.0 Pg C per year, and climaticchanges by 0–1.0 Pg C per year during the 1980s.Other studies have investigated the effects of somecombinations of these factors. For example,Melillo et al. (1993) and Post et al. (1997) inte-grated the effects of changes in CO2, climate, andN deposition. Aber and Driscoll (1997) investi-gated land use, climatic variation, and N deposi-tion on C storage for six northern hardwood forestsites. However, no existing model has attempted tointegrate the effects of all these disturbance andnon-disturbance factors on the C cycle of a forestregion. Due to the complex interactions and feed-back among these effects, accurate regional andglobal terrestrial ecosystem C balance cannot beobtained by simply summing the estimates forindividual factors. Therefore, a comprehensiveanalysis, which mechanistically integrates all of
these disturbance and non-disturbance factors, isneeded (Fung, 1996; Schimel et al., 1997; Potter,2000).
This paper describes an Integrated TerrestrialEcosystem C-budget model (InTEC), which inte-grates the effects of all these factors on the forestcarbon cycle. Realizing that InTEC is a complexmodel, which involves a large number of variablesand processes at different spatial and temporalscales, we first provide a brief road map in Section2 by outlining the model strategy. Detailed modeldescription is then given in Section 3. The modelhas been applied to Canada’s 417.6 Mha forests(Canadian Forest Service, 1993), with applicationresults being reported in Section 4.
2. Model strategy
The C balance of a forest region is the sum ofchanges in all biomass, soil, and product C pools(Fig. 1). The C in soil and product pools comefrom biomass pools, which in turn are resultedfrom NPP. NPP changes with climate, atmosphericconditions, and stand age which in turn is a resultof disturbances. Therefore, the C balance of aforest region is a function of these external forcingfactors. In this study, we use the response functionof NPP to changes in disturbance rates in year i,fNPPd(i ), and the response function of NPP toclimatic and atmospheric changes in year i,fNPPn(i ), to describe the effects of the correspond-ing factors. The value of fNPPd(i ) is determinedonly by the changes in disturbance rates whilekeeping the climatic and atmospheric variables attheir mean pre-industrial levels, while that offNPPn(i ) is determined only by the climatic andatmospheric changes while keeping disturbances attheir mean pre-industrial rates. Therefore, underthe mean pre-industrial disturbance rates and cli-matic and atmospheric conditions, fNPPd(0) andfNPPn(0) equal 1, and NPP(0) was a constant. Forany year since the industrialization, NPP was givenby
NPP(i )=fNPPd(i )fNPPn(i )NPP(0). (1)
The details of how to determine fNPPd(i ) fromrelationships between age class composition and
W. Chen et al. / Ecological Modelling 135 (2000) 55–79 57
disturbance rates and an age–NPP relationshipare given in Section 3.1. The Farquhar’s leafphotosynthesis model is used for describing theeffects of climatic and atmospheric changes onNPP in Section 3.2 (Farquhar et al., 1980; Bonan,1995). To upscale the leaf photosynthesis to aregion at an annual time step at which C and Ncycles are investigated in this study, a spatial andtemporal scaling algorithm is developed. Becauseleaf N content is a very important variable affect-ing fNPPn(i ), and involves the entire N cycle inforest ecosystems, a separate section (i.e. Section3.3) is devoted to it. With known values offNPPd(i ) and fNPPn(i ), the value of NPP(0) canbe determined if NPP in a calibration year isknown. In the case of Canada’s forests, we choose1994 as the calibration year, and NPP in this yearis used as a base to calculate NPP(0)retrospectively.
Fig. 2 shows a more detailed structure of In-TEC. As Fig. 2 shows, disturbances also affect Ctransfer from biomass to soil and product pools.For example, fires release a fraction of biomassand soil C into the atmosphere, and transfer theremaining biomass C into soil pools. Harvest
transfers a fraction of biomass into forest productC pools, and the remaining to soil C pools, whileinsect-induced mortality transfers all biomass tosoil C pools. We describe the C cycle in Section3.4, patterned to the widely tested Century model(Parton, et al., 1987; Schimel et al., 1996), exceptfor the following four modifications. (1) NPP isdetermined every year since the industrializationusing procedures discussed above; (2) Instead ofusing a constant Q10 to calculate L, we use amodified Arrhenius-type equation of Lloyd andTaylor (1994); (3) Disturbance effects on inter-pool C transfer are considered in the C cycle; (4)The soil structural C pool is divided into coarseand fine components to better characterize forestdetritus of different residence times.
3. Model description
3.1. The response function of NPP todisturbances fNPPd
The stand age distribution A(y, i ) can be deter-mined using a Weibull distribution:
A(y, i )=Atq(i )e− (q(i )y)s
8(1/s+1), (2)
where q is the total fire and insect occurrencefrequency, 8 is the gamma function, and s is theshape parameter (Kasischke et al., 1995). Wefurther assume that only mature forests are har-vested. At y=0 (i.e. for areas disturbed and yet toregenerate), A(0, i ) was the difference betweenthe disturbed and planted areas in previous nyears, where n is the average age that a forest mayneed to start to regenerate. For example, n=5 forCanada’s forests, with a range of 1–10 years(Bunce, 1989). For each subsequent year, A(y, i )is calculated by increasing the age by one year fornot disturbed forest areas, returning the age tozero for newly disturbed forest areas, and enteringage one for previously disturbed forest areaswhich at that time begin to regenerate. In thisstudy, all areas are treated equally, and no spatialdetail is involved. With the calculated A(y, i ) andFNPP(y), the overall effect of disturbances on NPPis then given by
Fig. 1. Concept chart of an Integrated Terrestrial EcosystemC-budget model (InTEC) for estimating the effects of changesin disturbance rates, climate, and atmospheric chemistry.Dished arrows indicate influences, and solid arrows showC–N flows.
W. Chen et al. / Ecological Modelling 135 (2000) 55–7958
Fig. 2. Same as Fig. 1 except with a more detailed structure.
fNPPd(i ) =&�
0
FNPP(y)A(y,i )dy/&�
0
FNPP(y)
A(y,0)dy. (3)
3.2. The response function of NPP tonon-disturbances fNPPn
For C3 plants, which include all Canada’sforests species, the instantaneous photosynthesisrate of a single leaf p is limited by the minimum ofthe two values (Farquhar et al., 1980; Bonan,
1995; Luo et al., 1996):
ÁÃÍÃÄ
p1=Jci−G
4.5ci+10.5G
p2=Vm
ci−G
ci+kco
, (4)
where p1 and p2 are leaf gross photosynthesislimited by electron transport and rubisco activity,respectively. The values of J, Vm, ci, G, and kco inEq. (4) are given by (Sellers et al., 1992; Bonan,1995):
W. Chen et al. / Ecological Modelling 135 (2000) 55–79 59
ÁÃÃÃÃÃÍÃÃÃÃÃÄ
J=[Jm+0.38S−(Jm+0.38S)2−1.064JmS ]/1.4
Vm=Vm25
Nl
Nlmax
aVm
Ta−25
10 /[1+e85.4Ta−3147.7
Ta+273 ]
G=40.2×1.75Ta−25
10
kco=300×2.1Ta−25
10 +209×1.75Ta−25
10
ci=aca
,
(5)
where Jm= [Jm25(Nl/Nlmax)ajm(Ta−25)/10]/[1+exp
((85.4Ta−3147.7)/(Ta+273))]. The meanings ofother terms are listed in Notation. Eq. (5) showsthat p is affected by climatic variables (i.e. Ta, S,and hr) and atmospheric variables (i.e. ca and Ndeposition). The effect of N deposition on p isincorporated through Nl/Nlmax (see details in Sec-tion 3.3).
The area-averaged annual gross photosynthesisrate of a forest region in year i, P(i ), is thengiven by integrating p for all leaves (x) over thewhole forest region (y) and time periods duringthe year (t)
P(i )=1At
&t
&y
&x
p dx dy dt, (6)
There are many ways to carry out this integra-tion for all leaves in a stand (Norman, 1993).One way, simple yet effective, is to stratify acanopy into sunlit and shaded leaves (Norman,1993), since Ta, ca, and hr are more or less thesame for all leaves in a canopy because canopyair is often well mixed during daytime. Thisstratification is essential because irradiationchanges greatly for different leaves dependingon their positions relative to the sun, resultingin different J values for different leaves inthe canopy. With this stratification and canopyradiation models (Black et al., 1991; Chen etal., 1999a), we calculate the instantaneouscanopy photosynthesis rate, pcan, by the mini-mum of
ÁÃÍÃÄ
pcan1= (JsunLsun+JshadLshad)ci−G
4.5ci+10.5G,
pcan2=Vm
ci−G
ci+kco
Lt,(7)
where Lsun is the sunlit leaf area index, given byLAIsun=2(1−P(u))cosu, where P(u)is the gapfraction at the view zenith angle u, calculated asP(u)=e−G(u)VLAIt /cosu (Nilson, 1971; Chen et al.,1997). The shaded leaf area index, Lshad, thusequals the difference of total leaf area index Lt
and Lsun. Assuming no significant changes inmorphology of leaves occurred since the industri-alization, we can calculate the change in area-av-eraged Lt in year i by
dLt(i )/Lt(i )=dCl(i )/Cl(i ). (8)
The values of J for sunlit leaves and shadedleaves, Jsun and Jshad, are calculated by replacingS in Eq. (5) with Ssun and Sshad respectively,where Ssun and Sshad are calculated followingBlack et al. (1991) and Chen et al. (1999a).
Assuming fp is the fraction of canopy photo-synthesis limited by Pcan1, we calculate thecanopy photosynthesis rate over the time periodby
pcan= fppcan1+ (1− fp)pcan2. (9)
With pcan, we reduce Eq. (6) to
P(i )=1At
&t
&y
pcan(y,t) dx dt. (10)
While it is theoretically possible to calculate P(i )for each year since the industrialization, such anoperation is practically limited by data availability.An alternative is to calculate P(i ) only for a recentyear for which quality data are available, and todetermine P(i ) in other years using a relationshipbetween the interannual relative change in P(i ),(dP(i )/[P(i )di ]), and the external forcing factors.Differentiating Eq. (10) gives
dP(i )di
=&
t
&y
dpcan(y, t)At
dy dt
(I)
+&
t
pcan(y, t)At
(y(i
dt
(II)
+&
y
pcan(y, t)At
(t(i
dy
(III)
, (11)
W. Chen et al. / Ecological Modelling 135 (2000) 55–7960
where term I represents the effect on dP(i )/dicaused by changes in pcan(y, t), while term II andIII represent, respectively, the effects caused bychanges in forest cover area and growing seasonlength (lg). The value of dpcan(y, t) is given bydifferentiating Eq. (9):
dpcan(y, t)
= fppcan[L1dca+ (LT1,1+LT1,2+LT1,3)dTa
+LN1dNl+LL1,1dLsun+LL1,2dLshad]
+ (1− fp)
pcan[L2dca+ (LT2,1+LT2,2+LT2,3+LT2,4)dTa
+LN2dNl+LL2dLt ], (12)
where L1, L2, LT1,1, LT1,2, LT1,3, LN1, LL1,1, LL1,2,LT2,1, LT2,2, LT2,3, LT2,4, LN2, and LL2 are coeffi-cients for the effects of CO2 fertilization, climatevariability, N availability, and leaf area changes(see Appendix A). Due to the lack of historicaldata about changes in hr, Ssun, and Sshad sinceindustrialization, we omit their impacts in thisstudy. All these L terms (shortened as Lx) andpcan vary diurnally and seasonally as well as be-tween locations. Due to the covariance betweenLx and pcan, Lx cannot be factored out of thetwo-dimension integration in Eq. (11). To carryout this integration, detailed data for Lx and pcan
are required. In reality, this is not feasible, espe-cially for the long historical periods in thisstudy. To avoid this difficulty, we use a 3-stepspatial and temporal scaling algorithm: (1) Toreplace the integration by a discrete summation;(2) To estimate the discrete summation using thecorrelation coefficient, r, between the two vari-ables Lx and pcan, namely,
%n
j=1
Lx( j )pcan( j )=nLx pcan�
1+rsLx
sp can
nLx pcan
�=nLx pcanzLx,p can
,
where n is the number of data points in terms ofboth time periods and spatial locations, �Lx(i )�is the spatial and temporal assemble average ofLx in year i, and s is the standard deviation;and (3) To introduce a conversion coefficient,cLx, that gives �Lx(i )�=cLx
Lx(i ), where Lx(i )
is calculated using annual mean values of cli-mate, N availability, and CO2 concentration. Us-ing this algorithm, we express term I as follows:
Term II in Eq. (11) is the effect of the changein forest area on the total photosynthesis. Sincewe consider only the existing forests, and LUCeffects are outside the scope of this study. Thechanges in forest area due to disturbances areconsidered in Section 3.1.
Term III in Eq. (11) is the result of growingseason length changes, i.e.
Term III=P(i )+P(i−1)lg(i )+ lg(i−1)
Dlg(i )
=x3(i )P(i )+P(i−1)
2. (14)
This term can be very important at high lati-tudes where the growing season is short and airtemperature increased at a higher rate than thatat low and middle latitudes (Frolking, 1997;Chen et al., 1999b). Inserting Eqs. (13) and (14)into Eq. (11), we calculate the interannual rela-tive change in P(i ) by
W. Chen et al. / Ecological Modelling 135 (2000) 55–79 61
dP(i )di
= [x1(i )+x3(i )]�P(i )+P(i−1)
2n
=x(i )�P(i )+P(i−1)
2n
. (15)
So far, we have considered only gross photo-synthesis rate P(i ). NPP is only about 25–60% ofP(i ), dependent on plant species, because a largepart of P(i ) is consumed by autotrophic respira-tion (Ryan et al., 1997). Yet, the ratio of NPP toP(i ) is conservative with climate change and Nstatus (Ryan et al., 1997), so that
dNPP(i )NPP(i )di
=dP(i )P(i )di
. (16)
From Eq. (1) and Eqs. (15) and (16), the effects ofnon-disturbance factors on NPP can then be cal-culated as
fNPPn(i )= 5i
j=1
2+x( j )2−x( j )
. (17)
3.3. N cycle and leaf N content
The total available N in the soils in year i,Na6,s(i ), is the sum of atmospheric N depositionNdep(i ), biotic N fixation Nfix(i ), and net N min-eralization Nmin(i )
Na6,s(i )=Ndep(i )+Nfix(i )+Nmin(i ). (18)
We use measured Ndep(i ) values (Ro et al.,1995). The value of Nfix(i ) is calculated based onthe studies of Van Cleve and Alexander (1981),Parton et al. (1987), and Chapin and Bledsoe(1992) (see detail in Chen et al., 2000b). Net Nmineralization is stochastically related to the Ccycle through the C/N ratios and is calculated by:
This equation follows the same principle as thatof Townsend et al. (1996) and Holland et al.(1997), but differs in two aspects. One is thatadditional soil C pools are included in this equa-tion. The second aspect is that we allow C/Nratios of biomass and soil C pools to vary, basedon recent experimental findings. Many recentstudies revealed that when grown in higher CO2,plant issues (including green leaves) had consis-tently lower N concentration (e.g. Curtis et al.,1995). Yet leaf litter quality is essentially the sameunder different CO2 levels because N is withdrawnprior to leaf senescence (O’Neill, 1994). In con-trast, N in fine roots is not mobilized prior tosenescence (Nambiar, 1987), and the C/N ratiowas found to be much higher in fine roots grownunder higher CO2 environments (Norby, 1994).Experimental evidence also showed that C/N ra-tios of soil C pools vary from year to year(Schimel et al., 1994), and vary at different N andCO2 levels (Pregitzer et al., 1995). Some recentmodels (e.g. Schimel et al., 1996; Comins, 1997)have incorporated these experimental findings ofvarying C/N ratios. In this study, we calculate aC/N ratio for each of the biomass and soil Cpools as the ratio of total C content to total Ncontent of the C pool in the year of concern.
Due to N loss as a result of wildfire, harvest,gas emission, and leaching, only a fraction ofNa6,s(i ) will be taken up by the plants. The valueof Nup(i ) can be determined through solving threerelated equations: (1) Nav,s(i )=Nup(i )+Nloss(i );(2) a Michaelis–Menten relationship between
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Nup(i ) and the inorganic N concentration in thesoil (Rastetter et al., 1991; Hudson et al., 1994);and (3) a linear relationship between Nloss(i ) andthe inorganic N concentration in the soil. Thesolution for Nup(i ) is given by:
Nup(i )=Nup,max(i )
1+2Na6,sb2
Nav,s−Nup,max(i )−b2
,
+(Nav,s−Nup,max(i )−b2)2+4Nav,sb2 (20)
where the maximum uptake capacity Nup,max(i ) isgiven by b1[Cfr(i )/Cfr(0)] [CNfr(i )/CNfr(0)]-Q
10,Nup
(Ts (i )−Ts (0))/10, b1 and b2 are constants determinedby equaling N input into and export from theforest ecosystems during the pre-industrial peri-ods. In addition to the Nup(i ), the N transferredfrom senesced leaves in year i−1, Ntr(i ), alsocontributes to the total available N in plants inyear i, Nav,p(i ).
We use the same coefficients partitioning Nav,p
to green leaf, fine roots, wood, and coarse roots inyear i as in year i−1 because there is no evidencethat these coefficients vary in one way or another.Equations for calculating C/N ratio of green leaf,fine roots, wood, coarse roots, fine structure de-tritus, coarse structure detritus, and slow soil Care given in Appendix A. The C/N ratios ofmicrobe, metabolic detritus, passive soil C, andcharcoal are assumed to be constant. With theknown values of CNl(i ) and Lt(i ), and Cl(i ), themean leaf N content per unit leaf area at year i,Nl(i ), can be calculated as follows
Nl(i )=Cl(i )
CNl(i )Lt(i ), (21)
where the value of Nl(i ) is constrained to 5Nlmax(i ). Since the relationship between age andNPP is empirically pre-determined, the interac-tions between changes in NPP caused by age classshift and N cycle have already been included in theage–NPP relationship. Therefore, the value ofNl(i ) is calculated after considering only the cli-matic and atmospheric changes.
3.4. C cycle
The change in the size of each C pool in InTEC
is described by the first-order rate kinetics (Pauland Clark, 1996)
DCx(i )=Input(i )−kx(i )Cx(i ), (22)
where Input(i ) is a fraction of NPP transferred tobiomass C pools or a fraction of upstream C poolsto soil and forest product C pools. It is importantto note that if inventory-based Cx(i ) and esti-mated NPP are used, which can only be measuredor estimated with limited accuracy, a large errorcan be introduced in DCx(i ), which is usuallymuch smaller than NPP or kx(i )Cx(i ) in a givenyear. To avoid this error, we rearrange Eq. (22) bytaking Cx(i ) as Cx(i−1)+DCx(i ), so that
DCx(i )=Input(i )−kx(i )Cx(i−1)
1+kx(i ). (23)
To calculate Cx(i−1), Cx(i−2) and NPP(i−1)are needed. This procedure continues, until thepre-industrial period is reached during which weassume DCx(0)=0 under the mean disturbancerates and climatic and atmospheric conditions.This procedure shows that DCx(i ) depends onhistorical changes in disturbance rates and climaticconditions over the entire time period since theindustrialization. Following this procedure, thechanges in biomass, soil, and forest products Cpools are calculated by subtracting C output terms(i.e. transfer to downstream pools, and fire emis-sion, oxidation, and respiration to the atmo-sphere) from the input terms (i.e. fraction of NPPpartitioned to the C pool concerned, and C trans-fer from upstream pools). Farquhar and Henry(1997) estimated that �10% of remaining woodafter burning will become charcoal instead of Ccd,and we adopt this percentage in this study. Thevalue of Fm(i ) affects the partitioning of leave andfine roots litter to detritus C pools, and is given byFm(i )=0.85−0.018LN(i ) (Schimel et al., 1996).Equations for calculating changes in biomass, soil,and forest products C pools are given in AppendixA. For the five product pools, the changes in thesizes of lumber (DClu(i )), pulp-wood (DCpw(i )),and landfills (DClf(i )) C pools are calculated alsousing the first-order rate kinetics in the same wayas for ecosystem C pools, while the bio-energy andburned-as-waste release C within a year.
W. Chen et al. / Ecological Modelling 135 (2000) 55–79 63
Summation of these C pool changes gives thearea-averaged annual C balance or NBP in year i.The cumulative change in each of these C pools isobtained by integrating the change since theindustrialization.
4. Model application for Canada’s forests
To apply the model for Canada’s forests, modelparameters have been calibrated using experimen-tal data obtained from Canada’s forest ecosys-tems (see detail in Chen et al., 2000b). Onemodification made to these parameters is allowingfp to change with LAI (Fig. 3). The ratio shadedleave to sunlit leave increases with total LAI andthe photosynthetic rate of shaded leave are usu-ally limited electron transport, so that fp increaseswith total LAI. The description of data sources ofthe ten external variables can be found in Chen etal. (2000a), with Figs. 4–6 showing the temporalvariations of these variables, and Fig. 7 showingthe spatial distribution of N deposition.
4.1. Short-term and long-term effects of eachfactor
To better understand the role played by each of
Fig. 4. Area of Canada’s forests disturbed by forest fire,harvest, and insect-induced mortality during the period from1800 to 1998. Measurements were available from 1920, andvalues before 1920 were inferred from age-class distribution in1920 (Chen et al., 2000a).
these external factors in the C cycle, and also tofacilitate model comparison and validation, theeffects of each factor need to be investigated.When different time scales are concerned, theeffects of each factor may be different. For exam-ple, the direct effect of fire may last only a short
Fig. 5. National mean growing season air temperature Ta,g,growing season length lg, and annual precipitation APPT,shown as departure relative to 1895 levels. Also shown is andabiotic decomposition factor L as the ratio to its 1895 value.
Fig. 3. Fraction of canopy photosynthesis limited by electrontranspot, fp, as a function of leaf area index, calculated usingmeasurements made at the BOREAS old black spruce (OBS)site in 1995 and 1996, and at the old aspen (OA) site in 1994and 1996.
W. Chen et al. / Ecological Modelling 135 (2000) 55–7964
Fig. 6. Atmospheric CO2 concentration and N deposition from1895 to 1998. N deposition during 1984–1994 was determinedbased on measurements made at 30 sites across Canada (seeFig. 7), and was extended to 1895 based on the trend ofnational greenhouse gas emission records. The mean rateduring 1984–1994 was used for 1995–1998 since the measure-ments indicated that N deposition had been stable since 1980s.
ppm, and N deposition by 0.02 g N m−2 per year.Fig. 8 shows the short-term and long-term
effects of each factor on NPP. Because thedisturbances destroy forest stands in the yearwhen they occur, and since the forest standsregenerated thereafter grow slowly in the first 20years, the area-averaged NPP in year 1 and thenext �20 years is reduced. As the regeneratedforests enter more productive ages, the NPPincreases, reaching a maximum around 40–60years after disturbance, and decreasing againthereafter as the forests age. Planting eliminatesthe regeneration delay period, and so shifts theproductive stage forward by 5–9 years (Bunce,1989). As a result, planting increases NPP in thefirst �50 years, and reduces it thereafter becausenaturally regenerated forest stands will beyounger and more productive than planted standsat the later stages.
The perturbations in lg, Ta,g, and CO2 increaseNPP significantly in the perturbation year, butreduce it in the subsequent years. Numerousmeasurements showed that increases in lg andCO2 enhanced NPP in the same year (Frolking,1997; Wullschleger et al., 1997; Chen et al.,1999b). Yet, over a period of \2 years, theenhancement of CO2 was reduced even if CO2 wasmaintained at the same elevated level (McKane etal., 1997; Idso, 1999), indicating the negativelong-term effect of an increase in CO2 on growth.If there were not a negative long-term effect, thenthe enhancement should be always the same whenCO2 was kept at the same elevated level,indifferent to the previous CO2 concentration.This negative long-term effect has also beenobserved for plants growing near a natural CO2
spring with a CO2 concentration at �790 ppm(Cook et al., 1998). Various hypotheses have beenproposed to explain these variable short- andlong-term effects of elevated CO2 concentrations(Luo et al., 1999). From the perspective of C–Ncycles at the ecosystem level, the long-termnegative effect of increasing CO2 can be explainedthrough its influence on the state variables of leafN content and leaf area. The positive short-termeffect on NPP in the perturbation year results inlarger leaf area and higher C/N ratios in rootsand wood detritus in year 2. The higher C/N
time period, its ‘after’ effect may continues fordecades to centuries by altering the state variablesof the forest ecosystem: the age of the forest standdisturbed and sizes of biomass and soil C pools.In this study, we define the effect on C cyclecaused by a change in an external factor in theyear when the change occurs as a ‘short-term’effect, and the effect in years after its occurrenceas a ‘long-term’ effect. Due to the largeinterannual variations in many of the externalforcing factors, distinguishing between short-termand long-term effects becomes very difficult ifactual historical data are used. To simplify thematter, we analyze the short-term and long-termeffects for each of these factors by perturbing oneof the 10 factors in year 1 since theindustrialization while keeping this factor in allother years and all other factors in all years atpre-industrial levels. The perturbation studyincludes increases in burned area andinsect-induced mortality each by 2 Mha, harvestand planting each by 0.5 Mha, Ta,g by 1°C, lg by7 days, APPT by 50 mm, L by 5%, CO2 by 2
W. Chen et al. / Ecological Modelling 135 (2000) 55–79 65
ratios in roots and wood detritus reduce the net Nmineralization rate. Both reduced net N mineral-ization rate and increased leaf area reduced thearea-based leaf N content. Since the majority ofthe increased leaf area is shaded leaves, theircontribution to NPP is usually not enough tocompensate for the decrease in leaf N content,and consequently NPP is reduced. For the subse-quent years, the reduction in the net N mineral-ization rate caused by higher C/N ratios in rootsand wood detritus has greater negative effects onNPP. The effects of lg and Ta,g can be explained inthe same way, except that in reality their changesare often accompanied by soil temperaturechanges which have effects opposite to those of lgand Ta,g. In addition, the interannual variations inlg and Ta,g are usually large. As a result, thelong-term effects of lg and Ta,g are masked by
their short-term effects, and therefore measure-ments that show their long-term effects are rare.
N deposition, L (affecting net N mineraliza-tion), and APPT (affecting N fixation) influenceNPP through leaf N content, which is an ecosys-tem internal state variable and represents the cu-mulative effects of climatic and atmosphericfactors over many years. As a result, perturba-tions in N deposition, L, and APPT usually mod-ify the leaf N content only slightly in theperturbation year (depending on the amount of Nadded), but their effects can last for many years.For example, fertilization trials conducted during1970s and 1980s in Canada showed that measur-able growth enhancements of fertilization maylast for over 10 years (Weetman et al., 1987;Gardner, 1990). For a Douglas-fir ecosystem inBritish Columbia, significant enhancements were
Fig. 7. Map showing the wet deposition of NO3− and NH4
+ measured at 30 sites across Canada during 1984–1994.
W. Chen et al. / Ecological Modelling 135 (2000) 55–7966
Fig. 8. Short-term long-term effects on NPP of Canada’sforests by a single-year perturbation imposed on each offollowing ten disturbances and climatic and atmospheric fac-tors in year 1: burned area and insect-induced mortality eachincreasing by 2 Mha, harvest and planting each by 0.5 Mha,mean growing season air temperature (Ta,g) by 1°C, growingseason length (lg) by 7 days, annual precipitation (APPT) by50 mm, abiotic decomposition factor by 0.1, atmospheric CO2
concentration by 2 ppm, and N deposition by 0.02 g N m−2
per year. In year 0 and all years after year 2, all factors remainat their pre-industrial levels.
effect of a factor on NBP is positive in yearsimmediately after the perturbation, an additionalC soil release is expected during the period there-after, or vice versa.
4.2. Integrated effects of all 10 factors
4.2.1. NPPAs Fig. 4 shows, the disturbance rates during
1860–1920 and during 1970–1998 were high, andwere low during early 1800s and 1920–1970. Thistemporal distribution of disturbance rates resultedin significant variations in the percentages ofyoung and less productive stands (i.e. B20 yearsold), productive stands (i.e. 20–100 years old),and old and less productive stands (i.e. \100years old) (Fig. 10). From 1800–1820, fire andinsect-induced mortality rates were lower thantheir pre-industrial averages. Consequently, thepercentage of young stands decreased while thatof productive stands increased. The increasingdisturbance rates from 1820 to 1880 reduced thepercentage of productive stands to a minimum of41% around 1880. The decreasing trends in thepercentage of productive stands was reversedsince then and reached a maximum of 71% in1940, as fire and insect-induced mortality rates
Fig. 9. Same with Fig. 8 except for the cumulative effects ofperturbations on NBP of Canada’s forests.
measured for the period 12–15 years after theinitial fertilization (Gardner, 1990).
The short-term and long-term effects of the tendisturbance and non-disturbance factors on NBPare largely similar to those on NPP (Fig. 9),except for the following three aspects: (1) Theincrease in annual burned area releases a substan-tial amount of C into the atmosphere in the yearit occurs, and so has more negative short-termeffect on NBP than on NPP; (2) The increase in L
has a negative effect on NBP in the perturbationyear because of the resultant increase in soil respi-ration, compared to a positive short-term effecton NPP; (3) For NPP, the long-term effects ofthese factors are achieved through altering age,C/N ratios of biomass and soil C pools, leaf area,and leaf N content. For NBP, another importantecosystem state variable, the sizes of biomass andsoil C pools, is added to the list. Therefore, if the
W. Chen et al. / Ecological Modelling 135 (2000) 55–79 67
Fig. 10. Histogram of age class composition of Canada’sforests from 1800 to 1998, resulted from the rate changes infire, insect-induced mortality, harvest, and planting.
used in determining fNPPd, the error caused bythe assumption gradually diminished. Therefore,the estimates of fNPPd during the 20th centuryshould be more accurate than those during the19th century.
As Figs. 5 and 6 shows that from 1895 to1998, the national mean Ta,g increased by �1°C,lg by 1 week, APPT by 5 mm, L by 14%, CO2
concentration by 74 ppm, and N deposition by0.2 g N m−2 per year. The resultant fNPPn in-creased gradually from 1895 to 1940, mainly inresponse to climatic changes (Fig. 12). It de-creased slightly during the next three decadesbecause of the tradeoff between the increasing Ndeposition effect and decreasing climatic effects.In the recent two decades, both N depositionand climatic changes increased NPP, resulting infNPPn increasing faster than during 1895–1940.The effect of CO2 was small throughout the pe-riod from 1895–1998, as its positive short-termeffect being counterbalanced by its long-termnegative effect.
decreased in this period. From 1940–1970, thefire and insect-induced mortality rates were stilllow, but the stands disturbed during 1860–1920high rate period entered into old and less pro-ductive ages, reducing the percentage of produc-tive stands. The increases in fire andinsect-induced mortality rates during the last twodecades increased the percentage of young standssubstantially and reduced the percentage of pro-ductive stands further.
The resultant temporal distribution of fNPPd
resembled that of the percentage of productivestands, because after all the later was the largestcontribution to the regional mean NPP (Fig. 11).This fact indicates that the importance of thelong-term effect of disturbance rates on NPP.Among these disturbance factors, fire and insect-induced mortality were the two biggest contribu-tors. The effects of harvest and planting on NPPhad been minimal until 1970s, since then theireffects have become significant.
Because fNPPd was affected by long-term ef-fects of disturbance rates, and the disturbancerates before 1800 were unlikely to be constantsas assumed, the accuracy of fNPPd was expectedto be low in the early part of the 19th century.As the year of interest becomes further awayfrom 1800 and more real disturbance rates were
Fig. 11. Response of NPP of Canada’s forests to all distur-bances during 1800–1998, where a fNPPd value of 1 indicatesno effect, and 1.1 (or 0.9) indicates a 10% enhancement (orreduction). Also plotted are the responses of NPP of Canada’sforests to fire, insect-induced mortality, harvest, and planting,considered individually while assuming others remain at theirpre-industrial levels.
W. Chen et al. / Ecological Modelling 135 (2000) 55–7968
Fig. 12. Response of NPP of Canada’s forests to all ‘non-dis-turbance’ climatic and atmospheric changes during 1895–1998where fNPPn=1 indicating no effect, \1 positive effect, andB1 negative effect. Also plotted are the responses of NPP ofCanada’s forests to growing season air temperature Ta,g, grow-ing season length lg, abiotic decomposition factor L, annualprecipitation, CO2, and N deposition, each of which is consid-ered by assuming others remain at their pre-industrial levels.
The �1.8 g N m−2 per year net N mineralizationrate was the largest component of available N forplants in Canada’s forest ecosystems, similar tofindings for other mid-high latitude forest ecosys-tems (Aber and Driscoll, 1997). Observed rates ofnet N mineralization cited by Bonan (1990)ranged from 0.8 to 5.8 g N m−2 per year: 0.8–1.8g N m−2 per year in mature black spruce forests(Picea mariana (Mill.) B.S.P) in the upland ofinterior Alaska; 1.1 g N m−2 per year in a blackspruce forest in central Quebec; 1.7–2.0 g N m−2
per year in mature white spruce forests (Piceaglauca (Moench) Voss) in the upland of interiorAlaska; and 2.4–5.8 in mature birch forests (Be-tula papyrifera Marsh.) in the upland of interiorAlaska. Our result was in the range of theseobservations, especially close to those in spruceforests, which are the dominant species ofCanada’s forests.
After integrating the short-term and long-termeffects of all disturbance and non-disturbance fac-tors, we found that the national mean NPP ofCanada’s forests increased slightly during 1800–
Table 1Averaged effects of disturbances and climatic and atmosphericchanges on NPPa
1990–19981800–1998
−2.4Fire 0.79−2.10.11Insects
Harvest −0.1−0.040.60.10Planting
0.85 −4.3Disturbances0.80.09Ta,g
3.60.06lg15.63.99L
0.07 1.0APPT0.21CO2 0.6
N deposition 12.12.508.1 39.1Non-disturbances
Integrated effect 9.30 32.2
a The effects on NPP are shown as percentages relative to itspre-industrial level. The effects of each individual factor arecalculated by assuming all other factors remained at theirpre-industrial levels. The effects of disturbances (or non-distur-bances) are calculated by assuming all non-disturbance factors(or disturbance factors) remained at their pre-industrial levels.The final values integrate both short- and long-term effects ofall factors.
When averaged over the entire period from1800 to 1998, disturbances increased fNPPd by lessthan 1%, with the highest contribution due to fire(Table 1). These values were calculated by allow-ing only the factor considered to change while allother factors were maintained at their pre-indus-trial levels. Insect-induced mortality was the sec-ond most important factor causing the variationsin fNPPd, although much less on average. Harvestreduced the mean fNPPd by 0.04%, whereas plant-ing increased it by 0.1% during 1800–1998. Overthe same period, fNPPn increased by 8.1%. Theeffect of L on fNPPn was the largest at 4.0%,followed by N deposition and CO2 at 2.5 and0.2% respectively, while the other three were allless than 0.1%. If only L changed and all otherfactors remained at their pre-industrial levels, thenet N mineralization rate would have increased by5.5% from 1800 to 1998. With actual climatic andatmospheric data, the net N mineralization rateincreased by 2.9% for the same period (Fig. 13).
W. Chen et al. / Ecological Modelling 135 (2000) 55–79 69
Fig. 13. Available N in soil and in plant, during 1895–1998.Available N in soil is the sum of net N mineralization, Ndeposition, and N fixation, while available in plant is the sumof N uptake and N retranslocation from the senescing leavesin the previous year.
which considered both errors from NPP calcula-tion and in original data of disturbances andclimatic and atmospheric variables (Chen et al.,2000a).
Among the four disturbance factors, fire hadthe most important contribution to the interan-nual and decadal variations of NBP, followed byinsect-induced mortality (Fig. 15). Our estimatesof disturbance effects are similar to those of Kurzet al. (1995) for the period of 1920–1989, if thesame assumptions are made (Chen et al., 2000a).For non-disturbance factors, N deposition wasthe largest contributor to NBP on average, whilemost of the interannual variations in NBP werecaused by climatic factors (Fig. 16). N saturationhas been observed in Central and Eastern Europeand Northeast United States (Aber et al., 1989).Based on the measurement of N deposition acrossCanada (Fig. 7) and the established criteria(Baron et al., 1994), N saturation has not been aproblem for Canada’s forests. The same conclu-sion was also reached by the Acid Rain NationalEarly Warning System, which did not detect anysign of pollution damage in boreal forests (Hall,
1820, decreased during 1820–1880, increasedagain from 1880 to 1940, and remained at thislevel since then (Fig. 14).
4.2.2. NBPFig. 14 also shows that the total C loss (i.e. sum
of soil heterotrophic respiration, fire emission,and forest product oxidation) remained approxi-mately at the same level, during 1800–1820 as aresult of tradeoff between decrease in fire emissionand increase in soil respiration. The same was trueduring 1820–1900 except as a result of tradeoffbetween an increase in fire emission and decreasein soil respiration. After 1900, total C loss in-creased because of the increases in L and soil Cstock from increasing NPP. As the residue ofNPP and the total C loss, the NBP of Canada’sforests was 40920 Tg C per year (i.e. a sink) in1810s, reduced to −131966 Tg C per year (i.e. asource) in 1870s, increased thereafter to a maxi-mum of 2009100 Tg C per year in 1930s, anddecreased again to 57929 Tg C per year in1990s. The uncertainties of �50% of these valuesare given based on a previous sensitivity analysis,
Fig. 14. Annual and decadal NBP of Canada’s forests, afterintegrating the short- and long-term effects of disturbancesand climatic and atmospheric changes, during 1800–1998.Also plotted are annual total C gain (i.e. NPP) and annualtotal C loss (soil respiration, fire C emission, and productoxidation).
W. Chen et al. / Ecological Modelling 135 (2000) 55–7970
Fig. 15. Effect of disturbance factors on NBP of Canada’sforests during 1800–1998. Also included are the effects of fire,insect-induced mortality, harvest, and planting on NBP ofCanada’s forests, each of which is considered by assumingothers remain at their pre-industrial levels. Fig. 16. Effect of ‘non-disturbance’ climatic and atmospheric
factors on NBP of Canada’s forests during 1800–1998. Alsoincluded are the effects of growing season air temperature Ta,g,growing season length lg, abiotic decomposition factor L,annual precipitation, CO2, and N deposition, when each ofthem is considered by assuming others remain at their pre-in-dustrial levels.
1995). Overall, the contribution of CO2 to NBPwas small, because of the counterbalance betweenthe positive short-term effect and negative long-term effect of increases in CO2 concentration.During 1910–1930 and 1960–1998 CO2 increasedat fast rates, consequently its short-term effectoutbalanced its long-term effect and a relativelarge CO2 contribution was found. These resultsare consistent with findings from studies whichconsidered coupled C–N cycles, such as TEM(McGuire et al., 1992; Melillo et al., 1993).Melillo et al. (1993) found that the response intropical and dry temperate ecosystems was domi-nated by CO2, but those in northern and moisttemperate ecosystems reflected the effects of tem-perature on N availability. The underlying reasonfor this is that most ecosystems, except for sometropical ecosystems, are N limited, and the limita-tion is greater at higher latitudes (McGuire et al.,1992).
Averaged over the entire period during 1800–1998, NBP was 40 Tg C per year. N depositionwas the largest contributor by �36%, followedby L by �20% and fire by �17%. The contribu-tions of other factors were less than 10%, with aremaining 9% due to interactions between allthese effects (Table 2). These partitioning percent-
ages changed for different time periods. In 1990s,the effect of N deposition of �70 Tg C per yearexceeded the magnitude of NBP by �57 Tg Cper year (Table 2). Again, a simple summation ofall these effects would have overestimated NBP by
Table 2Same as Table 1 except for NBP (Tg C per year)
1800–1998 1990–1998
−52.0Fire 6.71.7Insects −22.7
−1.8Harvest −9.20.6 3.7Planting
−81.16.7Disturbances1.3 11.3Ta,g
25.81.5lgL 13.57.9
0.8 1.7APPT3.2 11.3CO2
14.3N deposition 70.014931.9Non-disturbances
39.7Integrated effect 57.1
W. Chen et al. / Ecological Modelling 135 (2000) 55–79 71
Fig. 17. Cumulative stock changes of Canada’s forest C poolssince 1800: overall, soil, biomass, and products, as well asindividual soil and biomass C pool.
resulted in immediate C loss from soil, but en-hanced NPP and biomass C stock. It would bemany years before the increased biomass C stockwould be transferred to soil. All other climaticand atmospheric factors increased first thebiomass C stock, which would be transferred tosoil C pools many years later. Such time lag wasalso found between detritus C pools and slow soilC pool, because the later was at the lower end thecarbon transfer cascade.
For biomass, the largest C stock change oc-curred in the wood pool, since it was the largestamong biomass C pools. Yet, although the pas-sive soil C pool was largest among soil C pools,its extremely long residence time made it inert tochanges. The largest soil C stock changes oc-curred in detritus and slow soil C pools. Averagedover the entire period from 1800 to 1998, the slowsoil C pool accounted for 47% of the C stockchange in soil, followed by coarse and fine struc-tural detritus at 31 and 21%, respectively (Table3). Overall, the soil C stock increased 4.321 Pgfrom 1800 to 1998, or 2.1% of the current soil Cstock of 206.5 Pg, while the above-groundbiomass increased 2.473 Pg, or 19.1% of current
28%, demonstrating the necessity of integratedanalysis.
4.2.3. C stockThe cumulative stock changes of C pools in
Canada’s forests as a result of changes in distur-bance rates and climatic and atmospheric condi-tions are shown in Fig. 17. A time lag between theC stock change in biomass and that in soil wasclearly evident here. The biomass C stock startedto increase gradually around 1880, whereas thatof soil did not increase until around 1930. Around1970, the biomass C stock decreased slightly andstabilized thereafter, while soil C stock continuedto increase. The primary reason for this time lagwas the differences in the ways biomass and soil Cpools respond to disturbances and climatic andatmospheric changes. For example, fire, insect-in-duced mortality, and harvest reduced biomass Cstock, but increased soil C stock in the distur-bance year through transferring biomass C to soil.Over the decades after the disturbances, however,biomass was restored gradually, yet soil C stockwould continue to decline for up to �50 yearsbefore it started to recover again. Increasing L
Table 3Cumulative stock changes of Canada’s forest biomass, soil,and product C pools for periods during 1800–1998 and during1990–1998
W. Chen et al. / Ecological Modelling 135 (2000) 55–7972
inventory-based value of 13 Pg. During the 1990s,the aboveground biomass C stock, however, de-creased by 0.4% of its current total (Table 3).With the accuracy of forest volume inventorydata being �6% (Auclair and Bedford, 1997),such a small variation in aboveground biomass Cstock cannot be detected using forest volume in-ventory techniques. Table 3 also shows that thesoil C stock during 1990s increased by 0.434 Pg,or on average at the rate of 11.5 g C m−2 peryear, which is consistent with recent BorealEcosystem-Atmosphere Study (BOREAS) sitemeasurements (Nakane et al. 1997; Trumbore andHarden, 1997). Nakane et al. (1997) estimatedthat the soil of a black spruce forest stand nearthe south boreal boundary in Saskatchewan wasaccumulating C at 3–13 C m−2 per year. Atanother BOREAS site near the northern borealboundary, Trumbore and Harden (1997) foundthat the soil of a black spruce stand was accumu-lating C at rate of 3–30 C m−2 per year, depen-dent on drainage conditions.
5. Concluding remarks
This study presents a regional forest C-budgetmodel, InTEC, which integrates the effects ofdisturbance and non-disturbance factors. Distur-bance factors considered include fire, insect-in-duced mortality, and harvest. Planting is alsoincluded here. Non-disturbance factors include lg,Ta,g, APPT, and L, CO2, and N deposition. Fourbiomass C pools (i.e. leaf, coarse root, and fineroots), seven soil C pools (i.e. coarse structuraldetritus, fine structural detritus, metabolic de-tritus, microbe, slow, charcoal, and passive), andfive product C pools (i.e. lumber, pump-wood,bio-energy, burned-as-waste, and landfills) areconsidered.
InTEC is based on the Farquhar’s leaf photo-synthesis model, the Century C cycle model, thenet N mineralization model of Townsend et al.(1996) and Holland et al. (1997), and an age–NPP relationship derived from forestry inventory-based age–biomass relationships. To integratethese models and relationships developed for dif-ferent purposes and for different spatial and tem-
poral scales into a coherent model, we (1) developa spatial and temporal up-scaling algorithm forannual and regional calculations using leaf levelmodels; and then (2) combine the upscaled resultswith an age–NPP relationship derived fromforestry inventory-based age–biomass relation-ships to obtain the annual NPP of a forest region.
The C balance of a forest region is usually onlya few percent of fluxes involved (e.g. NPP, soilrespiration), and the percentage changes in thevarious C pools are even smaller. Because thesefluxes or C pool sizes can only be evaluated withlimited accuracy, estimates of the C balance froma single-year data of these fluxes or C pool sizesare often degraded by large uncertainties. Toavoid this type of uncertainty, we use a historicalchange approach, in which the C balance is deter-mined from the changes in the disturbances andnon-disturbances factors, and is assumed to be atthe equilibrium state under the mean pre-indus-trial conditions of these disturbances and non-dis-turbances factors. Using the historical changeapproach not only improves the accuracy of thepast and present regional forest C balance esti-mates, but also enables us to predict the futureregional forest C balance for projected changes indisturbance rate, climate, and atmospheric condi-tions. Both present estimates and future predic-tions of regional forest C balance are critical informulating mitigation and adaptation strategiesfor global changes.
The short-term (i.e. in the perturbation year)effects of increases in fire, insect-induced mortal-ity, and harvest on NPP and NBP are negative.Planting has little short-term effects on NPP andNBP. The short-term effects of increases in lg,Ta,g, APPT, CO2, and N deposition increase NPPand NBP, while increase in L increases NPP butreduces NBP. The long-term (i.e. in years after theperturbation) effects of increases in fire, insect-in-duced mortality, and harvest reduce NPP andNBP in the first 20 years after disturbances, thenincrease them to a maximum around 40–60 yearsafter disturbances, and the positive effects onNPP decline afterwards. Through shifting the age-growth curve by 5–9 years, planting increasesNPP and NBP in the first 40–50 years and re-duces them thereafter. The long-term effects of
W. Chen et al. / Ecological Modelling 135 (2000) 55–79 73
increases in lg, Ta,g, and CO2 reduce NPP andNBP, whereas those in L, APPT and N deposi-tion increase them. The short-term effects directlychange photosynthesis (CO2, lg, Ta,g), N availabil-ity (APPT and N deposition), respiration rate (L),and C transfer and emission rates (disturbances)in the perturbation year, while the long-term ef-fects on NPP and NBP are realized through mod-ifying internal ecosystem state variables, includingage class, leaf N content, leaf area, and soil Cstock. These state variables represent cumulativeeffects of external forcing factors, and so anyperturbation to them require a very long time torespond fully.
Most of the Free Air CO2 Enrichment (FACE)studies were designed to quantify the short-termand long-term responses of vegetation to doubleCO2 conditions. To maintain such studies areexpensive, and the results from year 2 afterwardsare in fact a complex mixture of short-term andlong-term effects. A more cost-efficient, and easy-to-interpret alternative is a perturbation study:enriching CO2 in one year and returning it to theoriginal level for more years as desired. Perturba-tion studies can also serve as a means for modelcomparison and validation, both of which arecritical in order to obtain accurate regional andglobal C budgets (Rastetter, 1996).
Using the historical data of disturbances during1800–1998, and climatic and atmospheric vari-ables during 1895–1998, we estimate the inte-grated effects of all these external forcing factorsand draw the following conclusions on the Cbudget of Canada’s forests.
During 1800–1998, the relative importance ofeach factor varied from year to year. Overall, firewas the most important disturbance factor influ-encing NPP and NBP of Canada’s forest, fol-lowed by insect-induced mortality. The effects ofharvest and planting were small in 19th century,but increased in recent decades. Most of the inter-annual variability in NBP was caused by fire andclimatic variables, while N deposition was themost important non-disturbance factor when av-eraged over the entire period 1800–1998. CO2
contributed significantly to NBP during 1910–1930 and during 1960–1998, during which CO2
increased at fast rates.
The annual mean NBP of Canada’s forestsduring 1810s was 40916 Tg C per year (i.e. a sink),reduced to −131952 Tg C per year by the 1870s(source), increased thereafter to a maximum of200980 Tg C per year by the 1930s, and decreasedagain since then. During 1980–1998, the negativeeffects of disturbance rate increases and the positiveeffects of non-disturbance climatic and atmo-spheric changes were nearly in balance, resulting inan almost constant NBP (sink) of 65926 Tg C peryear in 1980s and of 57923 Tg C per year in 1990s.
During the entire period from 1800 to 1998,biomass, soil, and product C stocks increased by�3.1, 4.3, and 0.5 Pg, respectively. The changes inaboveground biomass and soil C pools represented�19% and�2% increases, relative to their currentinventory values.
Although we have made great efforts to includein InTEC all known factors affecting terrestrial Ccycle, some less well understood factors, such asozone, soil degradation, are not considered in thisstudy. The effect of hydrological cycle is wellknown at the stand level, but is difficult to beincorporated at a regional scale model. High-reso-lution topographical maps are needed in order toconsider the hydrological effects, and it representsa major challenge for the next step. The lack of dataabout historical changes in forest species composi-tion prevents its inclusion in InTEC. The LUCeffect can be very important in a regional C budget,and so deserves a separate study.
Notation
symbol definition and unitdisturbed forest area, burnedAd, Af, At
forest area, total forest area (m2)APPT annual precipitation mm
coefficients for partitioning avail-b1, b2
able N into N uptake and N lossci, ca intercellular and atmospheric CO2
concentration mmol mol−1
CN, LN C/N ratio, Lignin to N ratioCx C content in pool x (subscript) (g
C m−2)partitioning fraction of leaf andFm
fine-root litterfall to metabolicdetritus C pool
W. Chen et al. / Ecological Modelling 135 (2000) 55–7974
FNPP(y) normalized NPP as a function ofage yfraction of pcan limited by pcan1fp
mmol electron (m−2 s−1)coefficient associated with enzymekco
kinetics (mmol mol−1)C transfer coefficient from pool xkx,y
to y per yearcoefficients accounting for the cli-Lx
matic and atmospheric changes onNPP
Lt, Lsun total and sunlit leaf area index(m2 m−2)
Lshad shaded leaf area index (m2 m−2)growing season length daylgavailable N, N deposition (g NNav, Ndep
m−2 per year)N fixation, net N mineralizationNfix, Nmin
(g N m−2 per year)N uptake, and N loss (g N m−2Nup, Nloss
per year)N transfer from previous year’sNtr
senesced leaves (g N m−2 per year)
Nl, Nlmax actual and optimal leaf N contentper unit leaf area (g N m−2)net primary productivity (g CNPPm−2 per year)
P(u) gap fraction at view zenith angle u
mean annual gross photosynthesisP(i)rate (g C m−2 per year)
p, p1, p2 instantaneous leaf gross photosyn-thesis rate, and that limited byelectron transport and rubisco ac-tivity (g C m−2 s−1)instantaneous canopy gross pho-Pcan
tosynthesis rate (g C m−2 s−1)mean occurrence frequency of fireqand insect-induced mortality, peryear
gross respiration rate (g C m−2Rs−1)above-canopy photosynthetic ac-Stive radiation (PAR) (mmol pho-ton m−2 s−1)absorbed PAR by sunlit andSsun, Sshad
shaded leaves mmol photon m−2
s−1)soil and air temperature (°C)Ts, Ta
maximum carboxylation rateVm
(mmol CO2 m−2 s−1)VPD air water vapour deficit (kPa)
scaling factor accounting for thezLx,p can,
effect of diurnal and seasonalvariations in Lx and Pcan on dpcan/pcan
ratio of assemble average of LxcLx
calculated using half-hourly envi-ronmental conditions to Lx calcu-lated using annual meanenvironmental conditionstotal wood C removed due to har-h
vest per year (g C per year)abiotic decomposition factorL
fNPPd, response functions of NPP tochanges in disturbance rates, andfNPPn,‘non-disturbance’ climatic and at-mospheric changes
G CO2 compensation point withoutdark respiration (mmol mol−1)
a ratio of ci to ca
leaf clumping factorV
relative change rate of P as ax
function of changes in non-distur-bance factors
jx C loss from pool x due to fire (gC m−2 per year)
Subscriptdenoting Cpoolsa, cr, fr, l Atmosphere, coarse root, fine
W. Chen et al. / Ecological Modelling 135 (2000) 55–79 75
Acknowledgements
Funding for this project is provided by CCRS(Canada Centre for Remote Sensing) and PERD(Penal for Energy Research and Development,Canada). Peter White helped with editing. JaneLiu provided useful comments on an early version
of the manuscript. We wish also to thank thefollowing individuals for their invaluable assis-tance and insights: Robert Steward, Andy Black,Alan Barr, Mike Novak, Yiqi Luo, David Price,and Ted Hogg. We thank Yuri Svirezhev and ananonymous reviewer for their constructive com-ments on the manuscript.
Appendix A. Equations for calculating Lx, C/N ratio, and DCx
L1=15aG
(aca−G)(4.5aca+10.5G), (A1)
LT1,1= −0.056caL1, (A2)
LT1,2=LT2,3= −L1ca
198.2hr
(240.97+Ta)2e17.502Ta
240.97+Ta, (A3)
LT1,3=!Lsun Jm
Lt J�
0.714−0.714Jm−0.1086Ssun
(Jm+0.38Ssun)2−1.064JmSsun
n+
Lshad Jm
Lt J�
0.714−0.714Jm−0.1086Sshad
(Jm+0.38Sshad)2−1.064JmSshad
n"<0.0531−
26461.9
(Ta+273)2(1+e3147.7−85.4Ta
Ta+273 )
=,
(A4)
LN1=JmLsun
JNlLt
�0.714−
0.714Jm−0.1086Ssun
(Jm+0.38Ssun)2−1.064JmSsun
n+
JmLshad
JNlLt
�0.714−
0.714Jm−0.1086Sshad
(Jm+0.38Sshad)2−1.064JmSshad
n, (A5)
LL1,1=Jsun
JLt
(A6)
LL1,2=Jshad
JLt
(A7)
L2=a(kco+G)
(aca−G)(aca+kco), (A8)
LT2,1= −0.056G(aca+kco)
a(kco+G)L2, (A9)
LT2,2= −(0.074kco−0.291G)(aca−G)
a(kco+G)L2, (A10)
LT2,4=0.0875−26461.9
(Ta+273)2(1+e3147.7−85.4Ta
Ta+273 ), (A11)
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