A review of sampling designs for the measurement of soil organic … · 2016. 7. 13. · A review...

A review of sampling designs for the measurement of soilorganic carbon in Australian grazing lands

D E AllenA M J PringleA K L PageA and R C DalalABC

ADepartment of Environment and Resource Management 80 Meiers Rd Indooroopilly Qld 4068 AustraliaBLand Crop and Food Sciences University of Queensland St Lucia Qld 4072 AustraliaCCorresponding author Email RamDalalqldgovau

Abstract The accuratemeasurement of the soil organic carbon (SOC) stock inAustralian grazing lands is important due tothemajor role that SOC plays in soil productivity and the potential influence of soil C cycling onAustraliarsquos greenhouse gasemissions However the current sampling methodologies for SOC stock are varied and potentially conflicting It was theobjective of this paper to review thenature of and reasons for SOCvariability the samplingmethodologies commonlyusedand to identify knowledge gaps for SOC measurement in grazing lands Soil C consists of a range of biological materialsin various SOC pools such as dissolved organic C micro- and meso-fauna (microbial biomass) fungal hyphae and freshplant residues in or on the soil (particulate organic C light-fraction C) the products of decomposition (humus slow pool C)and complexed organic C and char and phytoliths (inert passive or resistant C) and soil inorganic C (carbonates andbicarbonates) Microbial biomass and particulate or light-fraction organic C are most sensitive to management or land-usechange resistant organicC and soil carbonates are least sensitive TheSOCpresent at any location is influenced by a series ofcomplex interactions between plant growth climate soil type or parent material topography and sitemanagement Becauseof this SOCstock andSOCpools are highlyvariable onboth spatial and temporal scales This creates a challenge for efficientsampling Samplingmethods are predominantly based on design-based (classical) statistical techniques crucial towhich is arandomised sampling pattern that negates biasAlternatively amodel-based (geostatistical) analysis can be usedwhich doesnot require randomisation Each approach is equally valid to characterise SOC in the rangelands However given that SOCreporting in the rangelands will almost certainly rely on average values for some aggregated scale (such as a paddock orproperty)we contend that thedesign-basedapproachmight bepreferredWealso challenge soil surveyors and their sponsorsto realise that (i) paired sites are themost efficientwayof detecting a temporal change inSOCstock but destructive samplingand cumulative measurement errors decrease our ability to detect change (ii) due to (i) an efficient sampling scheme toestimate baseline status is not likely to be an efficient sampling scheme to estimate temporal change (iii) samples should becollected aswidely as possiblewithin the area of interest (iv) replicate of laboratory analyses is a critical step in being able tocharacterise temporal change Sampling requirements for SOC stock in Australian grazing lands are yet to be explicitlyquantified and an examination of a range of these ecosystems is required in order to assess the sampling densities andtechniques necessary to detect specified changes in SOC stock and SOC pools An examination of techniques that can helpreduce sampling requirements (such as measurement of the SOC fractions that are most sensitive to management changesandor measurement at specific times of the year ndash preferably before rapid plant growth ndash to decrease temporal variability)and new technologies for in situ SOC measurement is also required

Introduction

For the purposeof this review rangelands are definedas relativelyundisturbed ecosystems containing savannas woodlands andshrublands where rainfall is too low or unreliable and soils toopoor to support regular cropping (Beeton et al 2006 Bastin2008) One of the major threats to the sustainability of Australiangrazing lands and particularly rangelands where inputs such asfertiliser are not economically feasible is the depletion of soilorganic carbon (SOC) Soil organic matter contains ~58 SOCand ismadeupof a range of biologicalmaterials livingorganisms(micro- and meso-fauna) fresh plant residues in or on the soilparticulate organic matter the products of decomposition(humus) and inert (humic and char) substances (Gregorich et al

1994) and silica-occluded plant C or phytoliths (Parr andSullivan 2005) It plays an important role in maintaining thesustainability of grazing lands due to the function it plays withinthe soil For example it provides a primary source of many plantnutrients improves the water-holding capacity of the soil isresponsible for the formation of stable aggregates that protect thesoil from erosion and provides a habitat for soil microbialbioversity (Weil and Magdoff 2004)

In addition to its role in maintaining soil productivity inrecent years there has been a focus on the ability of SOC to act as aCO2 lsquosinkrsquo and thus assist in the reduction of atmosphericgreenhousegases (Follett 2001)Changes tograzingmanagementpractices that increase SOC storage may have the potential to

Australian Rangeland Society 2010 101071RJ09043 1036-987210020227

CSIRO PUBLISHING Review

wwwpublishcsiroaujournalstrj The Rangeland Journal 2010 32 227ndash246

reduce Australiarsquos net greenhouse gas emissions and thuscontribute towards Australia achieving its greenhouse gasemissions targets

Because of its important role the effect of managementpractices onSOCstock (ie the product of SOCconcentration andsoil bulk density and sampling depth) in grazing lands has beenstudied extensively for many years However one issue that hascontinually been encountered by researchers is the high spatialand temporal variability of SOC stock and the difficulties that thiscreates when using statistical techniques to measure relativelysmall differences between land uses or management treatmentsIt is desirable to be able to detect relatively small changes in SOCstock since across large areas of rangelands these can representa substantial sequestration or loss of C In addition being able todetect small SOC changes enables the effect of managementpractices to be assessed within shorter timescales

Numerous and varied approaches have been used whensampling for SOC stock and we are faced with what canbe a confusing array of choices when selecting samplingmethodology Thus there is a need for greater understanding ofthe sampling methodologies available to estimate SOC stock ingrazing lands It is the objective of this review to (i) examine thenature of and reasons for SOC variability (ii) examine thestrengths and weaknesses of the sampling methods commonlyused for SOC stock and (iii) identify knowledge gaps and areasfor future research for SOC measurement in grazing lands

Characteristics of soil C

Soil C consists of organic C as organic matter containing arange of organic materials and inorganic C as carbonates andbicarbonates Organic C stocks are ~1500Gt (1015 g) C andinorganic C stocks are ~720Gt C in the top 1m of soil depth(Batjes 1996)

Soil organic C is heterogeneous in nature and consists ofseveral SOC pools which can be broadly grouped based on theirturnover rates in soil For example Parton et al (1987) postulated3 SOC pools (i) the active or labile C pool (ii) the slow C pooland (iii) the resistant or passive pool These have turnoverperiods of respectively lt10 years 10ndash200 years and gt100 years(Table 1)

The labile pool consists of soluble fresh plant residuesincluding fine roots living organisms (microbial biomass)particulate organic C andor light fraction in varying proportionsof lt5 lt10 and up to 30ndash40 of SOC respectively These aremeasured as soluble and microbial products and root exudatesmicrobial biomass and lt53mm organic C fraction (particulateorganic C) andor light fraction (lt16ndash2 gcm3 density) ofsoil respectively (Parton et al 1987 Cambardella and Elliott1992 Baldock and Skjemstad 1999 Dalal and Chan 2001Franzluebbers and Stuedemann 2003)

Dissolved organic C usually lt1 from root exudatesmicrobial products and plant materials forms the most labilefraction in soil It is transported within the soil profile and in run-off waters to streams and eventually to oceans (Hopkinson andVallino 2005) Within the soil profile it is immediately availableto soil microbes and is rapidly mineralised within hours to daysotherwise it enters into or forms soil microaggregates (Smuckeret al 2007)

Microbial biomassC compriseslt5of theSOC (Dalal 1998)It is considered as a sensitive indicator of SOC changes due toland-use change andor management (Sparling 1992) In mostsoils light-fraction C is essentially similar to particulate organicC and rarely exceeds 30of the total SOCwith turnover periodsof lt10 years in mesic subhumid and semi-arid environments(Dalal and Chan 2001)

Humus or clay-sorbed C forms the slow C pool which variesfrom 30 to 60 depending on soil type clay content claymineralogy and iron and aluminiumoxideswith turnover periodsfrom 10 years to 200 years or more depending on climaticconditions (Parton et al 1987) Three possible mechanisms havebeen suggested for slow turnover rates of this C pool These arechemical nature of SOC with increasing aromaticity increasingspatial inaccessibility to microorganisms and extracellularenzymes due to microaggregation and physical separation andsorption of C on mineral surfaces andor interaction with mineralparticles (Sollins et al 1996 von Lutzow et al 2007)

The resistant or passive SOC pool comprises primarilycharcoal C up to 30 (Skjemstad et al 1999) with turnoverperiods generally gt100 years depending on the charcoal sourceand quality although charcoal C dynamics in soil is not knownA proportion of organo-mineral-metal complexed SOC also

Table 1 Soil carbon (C) pools soil C fractions forms measured and sensitivity to management change

Soil C pool Soil C fraction Pool Ctotal C () Form measured Turnoverperiod (year)

Sensitivity tomanagementchange

Labile (active) CA Soluble fresh residues 05ndash5 Microbial and root exudates lt01 Very rapidA

Living micro- andmeso-flora and fauna

1ndash10 Microbial biomass lt5 RapidAC

Particulate organic C 1ndash40 gt53mm lt10 RapidBDE

Light fraction 1ndash30 lt16ndash2 gcm3 lt10 RapidC

Slow CA Humus 30ndash50 Total organic C ndash particulate organic C 10ndash200 MediumB

Clay-complexed C 30ndash60 lt2mm 10ndash100 MediumC

Resistant (passive) CA Charcoal C 1ndash30 Resistant to chemical oxidation gt100 SlowB

Phytoliths 1ndash30 Oxidised at ~13008C Millenia Very slowFG

Carbonates 0ndash30 Release of CO2 by acid treatment gt1000 Very slowHIJ

AParton et al (1987) BBaldock andSkjemstad (1999) CDalal andChan (2001) DCambardella andElliott (1992) EFranzluebbers andStuedemann (2003) FDreeset al (1989) GParr and Sullivan (2005) HCerling (1984) IDalal and Mayer (1986b) JKnowles and Singh (2003)

228 The Rangeland Journal D E Allen et al

forms the passive SOC pool (Koumlgel-Knabner et al 2008) Thephytolith C pool is generally small up to 3 (Drees et al 1989)although some reports suggest much higher amounts up to 60in the soil profile (Parr and Sullivan 2005) Since phytoliths arevery stable in soil these have been used to reconstruct thepaleovegetation during the Holocene andor Pleistocene periods(Piperno and Becker 1996) However the role of phytoliths inSOCdynamics in response to land use andmanagement change islittle understood

Soil carbonates and bicarbonates are the primary pools of soilinorganic C and comprise a substantial total C pool (gt30) inmesic semi-arid and arid regions (Knowles and Singh 2003)These are derived both from parent material as well as formedin situ as pedogenic carbonates Similar to phytolith C andcharcoal C pedogenic carbonate C is used to reconstruct region-wide paleoenvironments (Zhou and Chafetz 2010) Sincepedogenic carbonates are relatively stable with turnover periodsgt1000 years (Cerling 1984 Amundson et al 1994 Zhou andChafetz 2010) the carbonate stocks in soil are generally similarfollowing land-use andmanagement changes For exampleDalalandMayer (1986a) and Knowles and Singh (2003) found similarcarbonate stocks in soil after 60 years of agriculture followingconversion of land use from native vegetation even though initialSOC stocks declined by up to 60 during this period Thereforecarbonate C is not considered in this review although furtherstudies may elucidate the role of carbonate C in the rangelandsoils especially if the legume component of the vegetationincreases which may enhance the acidification of the soil profileand dissolution of carbonate C

Depth distribution of SOC

Spain et al (1983) summarised SOC concentrations of severalAustralian soils They noted that SOC stocks generally decreasedexponentially with soil depth but the magnitude of this change

depends on soil type and vegetation and generally follows rootdensity distribution of the dominant vegetation For example inFig 1 SOC stocks under Queensland blue grass (Dicanthiumsericeum L) vegetation changed less with depth as comparedwith that under Brigalow (Acacia harpohylla L) vegetationwhere SOC stocks were higher in the top 03-m depths althoughtotal SOC stocks in the top 12-m depths were similar (104 tha)under both vegetations (Dalal and Carter 2000) Generally IPCC(2006) recommends the samplingof the top03-mdepthof soil forSOC stock measurement or estimation since changes in SOCstock due to land-use change or management are primarilyconfined to the top 01- or 03-m depths in most soils (Dalal andMayer 1986b Knowles and Singh 2003 Dalal et al 2005)

The depth distribution of SOC pools generally follow the totalSOC trends except that in the top 01-m depth labile organic Cmay be proportionally greater than the total SOC mainly due tothemixing of litter with the soil in the top layer (Dalal et al 2005)

Soil bulk density

Soil bulk density expressed asmass per unit volume of soil (unitsof gcm3 or tm3) is used to calculate soil C density or SOC stockfor a given depth (kgm2 or tha) from SOC concentration ()bulk density and soil depth For measurement of soil bulk densityin the field including soils containing coarse fragments suchas gravel refer to McKenzie et al (2000) and Cresswell andHamilton (2002) Precisemeasurement of bulk density in thefieldis time consuming and expensive and remains a challengealthough recent developments in the in situmeasurement of bulkdensity using gamma-ray attenuation and electromagneticinduction appears to be promising across a range of landscapes(Tyler et al 2001 Pires et al 2009)

Soil bulk density is affected by farming systems such ascropping (through tillage residue management vehicular traffic)and grazing (through pasture type grazing intensity compaction

00

02

04

06

08

10

12

0 5 10 15 20 25 30 35 40 45 50

SOC stock (tha)

Soi

l dep

th (

m)

Dicanthium sericeum

EucalyptusndashDicanthiumAcacia harpophylla

Fig 1 Depth distribution of soil organic carbon under three native vegetations Dicanthiumsericeum (Queensland blue grass) on black Vertosol Eucalyptus populneandashDicanthium sericeum(Eucalypt woodland-savanna) on grey Vertosol Acacia harpophylla (Brigalow) on grey Vertosolin southern Queensland Australia (data from Dalal and Carter 2000)

A review of sampling designs for measuring soil organic carbon The Rangeland Journal 229

fire drought) and forestry systems (through land preparation forplantation and harvesting operations) besides the natural factorssuch as soil characteristics climate and vegetation In shrink-swell soils such as Vertosols bulk density is also affected by soilwater content Thismeans that in these soils themoisture contentneeds to be explicitly considered when attempting to compareSOC stocks of paired-sites or for chronosequence-sampled sitesor treatments with variable moisture content and bulk density onan equivalent soil mass basis to assess management effects onSOCstocks (Dalal andMayer 1986bGifford andRoderick 2003Wuest 2009) as shown in Fig 2 (Dalal et al 2005)

Spatial and temporal variability of SOC and SOC poolsin Australian grazing lands

The SOC that is present at any particular location is a result ofthe balance between (i) inputs of SOC from plant growth ormaterial deposited during erosion and (ii) losses of SOC dueto soil respiration or export of SOC offsite due to erosion andleaching This balance is affected by a series of complexinteractions between plant growth climate soil type topographyand site management (Baldock and Skjemstad 1999) Theseprocesses affect SOC concentrations and stocks on a range ofdifferent temporal and spatial scales ranging from plantpedonscales (mmndash200m) to community scales (20mndashkm) and tolandscape and regional scales (gtkm) (Bird et al 2001) (Fig 3)

Spatial variability

Plantpedon scale (up to 200m)

At the plantpedon scale the main contributors to the spatialvariability of SOC are vegetative patterns and plant communitydynamics Plant material provides the main source of SOCthrough litter drop the production of root exudates and rootmortality (Bird et al 2001) Consequently the size morphology(eg tree shrub grass) and spatial distribution of plants affects theareas where C is input into the soil (Jackson and Caldwell 1993Hook and Burke 2000)

In grazing areas and particularly rangelands strongheterogeneity at the plantpedon scale is often a characteristic ofsites with sparsely distributed plants In these sites C enrichment

tends to occur in the area surrounding plants with areas of lowerC content in interplant areas (Hook and Burke 2000 Lechmere-Oertel et al 2005) In semi-arid woodland areas for example thespatial distribution of resources may operate on several levelsAt the largest scale (~100m2) distinct groves of trees separatedby open intergroves may be responsible for a concentration oforganicC In addition at a plant level individual trees shrubs andgrasses create distinct areas where organic C will accumulateinterspersed with areas that are relatively nutrient-poor (Ludwigand Tongway 1995) This occurs not only due to the direct inputsof organicC fromplants but also due to the entrapment of organicmaterial that is moved across the landscape by wind and water(LudwigandTongway1995)Thus JacksonandCaldwell (1993)found that SOC stocks varied by as much as 5-fold within a120-m2 area of sagebrush-steppe vegetation

The pattern of plant growth also affects the location ofother sources of SOC such as the soil microbial biomass and soilfauna These components will tend to congregate around areasalready high in organic C content further contributing to SOCheterogeneity (Bird et al 2001) Soil macro- and micro-faunaalso contribute to SOC heterogeneity due to the soil mixing orbioturbation they cause (VandenBygaart 2006)

Community scale (20mndashkm)

At the community scale spatial variability is primarilyaffected by soil type and sitemanagement Soil type is influentialdue to the effect that soil nutrition can have on biomassproductionwith soil types higher in clay content generally able toprovide more nutrients and higher moisture retention and thusact as a better substrate for plant growth (Burke et al 1995)

Areas of high C sequestration

Scale

Floodplain

Mountaintop

Matrix

Landscape(km wide)

Community(20 m to landscape)

Plant(2 mm to 200 m)

Patchtype B

Patchtype A

Fig 3 Schematic representation of soil carbon features at the pedonplantcommunity and landscape scale as affected by vegetation soil typeenvironment and management (adapted from Bird et al 2001)

Soil C (tha)0 10 20 30 40 50

Soi

l mas

s (t

ha)

0

2000

4000

6000

8000

10 000

12 000

14 000

Soi

l dep

th (

m)

00

02

04

06

08

10

Fig 2 Relationship between soil carbon and soil depth and soil mass(soil depth bulk density) on Kandosol at a mulga (Acacia aneura L) sitefor estimation of soil organic carbon stocks on equivalent soil mass usingpolynomial equation (from Dalal et al 2005)


In addition the sorptionofSOC toclay its isolation inmicroporesand its physical protection within stable macro- andmicroaggregates can reduce SOC availability and hencedecomposition rates Consequently SOC is generally lower incoarse textured and poorly structured soils and numerousauthors have observed positive correlations between SOC andclay content (Burke et al 1989 Hook and Burke 2000VandenBygaart and Kay 2004 Don et al 2007) This trend hasalso been observed in Australian grazing environments Forexample in Queensland rangeland environments sites with finetextured soils had significantly greater SOC stocks than coarsetextured soils (Harms and Dalal 2003)

At the community scale landmanagement also starts to play arole in SOC variability In grazing lands management practicesthat increase yield such as fertiliser use lime application or theuse of more productive species can increase SOC particularlywhere soil has inherently low soil fertility (Chan 1997 Schnabelet al 2001) However such strategies can also decrease SOC incertain situations due to increases in the decomposability of theorganic material or decreases in root biomass sometimesassociated with increases in fertility (Schnabel et al 2001) Theactivities of grazing animals will also influence SOC variabilityHoof action creates surface disturbances that can both increaseerosion (and thus decrease SOC) and help incorporate surfacelitter into the soil (potentially increasing SOC) (Dormaar et al1977 Schuman et al 2009) Consequently grazing intensity canalter SOC concentrations with the direction of change a result ofthe balance between SOC loss due to overgrazing and the SOCgains due to incorporation of litter into the soil (Schnabel et al2001) The accumulation of SOC from animal excreta aroundanimal camps or watering places also contributes substantially toSOC variability (Schnabel et al 2001 Bisigato et al 2008)

Although natural bushfires occur infrequently in semi-aridgrazing lands fire as a grazingmanagement tool is used regularlyin large areas of northern rangelands (Bradstock 2010) Up to40 of tropical rangelands are burned every year (Bastin 2008)Fire frequency in semi-arid woodlands affects the woodlandthickening (Bastin 2008) and vegetation communities and grasscomposition (Rossiter et al 2003) and increases landscapespatial variability (Ludwig and Tongway 1995) and hence SOCvariability For example Coetsee et al (2010) found that frequentfires in savannas over a 50-year period changed the distribution ofSOC (and N) under canopies and away from canopies but had nosignificant effect on total SOC stocks However Williams et al(2004) surmised that frequent and extensive fires reduced thepotential net ecosystem productivity by ~2 t Cha by decreasingboth SOC stocks and aboveground C stocks in mesic savanna inthe Northern Territory Australia Actual data on SOC stocks andSOCpools (labileC charcoalC) and transfer between them in thisregion are currently not available to verify their assessment

Regional and landscape scales (gtkm)

On a regional or landscape scale topography and climate arethe main factors responsible for SOC variability Topography isparticularly influential due to the effects that slope and aspect canhave on soil moisture and depth and hence biomass productionand C input Steeper slopes have been found to have lowerSOC and down-slope positions higher SOC due to erosion(Burke et al 1995Hook andBurke 2000 Jia andAkiyama 2005

Liu et al 2006) The highermoisture contents and hence biomassproduction in down-slope position also contribute to the higherSOC concentrations (VandenBygaart 2006) and stocks

In addition to water erosion wind erosion can also beresponsible formoving soil and its associated organicC around inthe landscape and thus contribute to SOC variability (Zuo et al2008) Grazing areas are particularly susceptible to wind erosion(Webb et al 2009) during periods of lowvegetation cover such asafter fire during drought or due to overgrazing (Bastin 2008 Zuoet al 2008)

Climate also plays a large role in SOC variability particularlyon regional scales Temperature and rainfall effects have a largeinfluence on both plant biomass production and soil respirationand generally SOC tends to be higher in cold wet climates andlower in warm dry ones (Amundson 2001) With increasingtemperature both plant biomass production and soil respirationrates tend to be higher Adequate moisture will also increasebiomass production and decomposition rates Howeverexcessively high moisture contents will lead to anaerobicconditions within the soil and a decrease in decomposition ratesthus increasing SOC storage (Amundson 2001)

Temporal variability

Where distinct growing seasons exist due to the seasonality oftemperature or rainfall plant biomass production and the activityof the soil microbial biomass can vary throughout the year andpotentially impact on SOC concentrations (Dormaar et al 1977Saggar and Hedley 2001 Jacobs et al 2007) and stock In areaswhere distinct warm and cold periods exist pasture productionand root growth is often observed to vary during the year beinghighest in spring or summer and lowest in winter (Saggar andHedley 2001 Jacobs et al 2007) In addition where plants havedistinct growing periods litter fall is often higher at certain timesof the year (Wilson and Thompson 2005) Similarly microbialgrowth and soil respiration also show distinct seasonality beinginfluenced by temperature the availability of organic substrates(eg root exudates) andmoisture availability (Kaiser et al 1995Corre et al 2002) One feature of Australian grazing landsparticularly relevant to variation on a temporal scale is theinherent climatic variability Cycles of drought and rainfall arecommon and contribute to periods of low followed by highorganic matter input (Bastin 2008) Thus rangelands are subjectto SOC losses during drought and this should be consideredwhencomparing long-term SOC stocks from different grazingmanagements (Schuman et al 2009)

While the seasonality ofC input into and cycling through soilsystems is generally acknowledged there are currently very fewstudies that have quantified the subsequent changes to SOC andSOC pools in Australian grazing systems and the effect that thiscould potentially have on the measurement of SOC In overseasgrazing systems however total SOC has been observed toincrease by over 60 in the upper humus layer (Ah) betweensummer and winter sampling times (Dormaar et al 1977)possibly due to increase mostly in particulate organic C or labilepool A corollary to these studies from cropping soils in Australiashows that SOC stocks in the top 01-m depth decreased by 10during the fallow period primarily as a result of substantialdecomposition of labile organic C and lack of fresh plant C input


(Wang et al 2004) This emphasises the importance of samplingthe soil for SOC stock at the same time each year (preferablybefore rapid plant growth) to minimise the temporal (seasonal)variation to discern the land-use andmanagement effects on SOCstock

Spatial variability of SOC in grazing lands comparedwith other land uses

Grazing lands may encompass a wide range of differentecosystems ranging from the intensivelymanaged andhigh inputdairy pastures in eastern Australia through to the grazing ofrangeland ecosystems in central and northern Australia Variedgrazing management was noted as a possible explanation forspatial variability in SOC found in Australiarsquos unclearedlandscapes in some of the National Carbon Accounting Systemstudies (Griffin et al 2003 Harms and Dalal 2003 Murphy et al2003) However there is very little published information on thevariability of SOC in Australian grazing lands compared withother land uses In addition from the international literature it isdifficult to draw conclusions regarding the variability of SOC inone type of land use comparedwith another as this often dependson the characteristics of the area in question However as ageneralised statement SOC in grazing areas is often found to bemore heterogeneous than in cropped locations (Miao et al 2000Bird et al 2001) particularly where mixing and homogenisationby cultivation occurs

Comparison of grazing and forest lands suggests the degree ofspatial variability in SOC tends to depend more on the type offorest and the characteristic of the grazing land For examplesome studies have observed greater spatial heterogeneity inungrazed rangeland soils compared with protected forested areas(oak) (Nael et al 2004) This observation was explained by thefact that the protected forests were relatively homogeneous over-and understorey creating a more homogeneous input of organicCThe rangelandarea however had a significant amount of shrubvegetation and also grass tussocks (Ludwig and Tongway 1995)resulting in the concentration of organic C under shrubs andtussocks and thus a greater heterogeneity of SOC Other studiesof more typical grassland pastures however have been observedto have a lower degree of spatial heterogeneity under pasturecompared to forested sites (Conant and Paustian 2002) Mostlikely comparison of the extent of SOC spatial variabilitybetween different ecosystems is complicated by variation in soiltype landscape and topographic position andvegetation typeanddistribution amongother factors such as seasonality temperatureand rainfall amount and distribution

The degree of spatial variability of SOC observed in grazinglands may also depend on grazing management Where stockingrates are too high and not sustainable grazing can change thenature of the surface vegetation for example leading to anincrease in the invasion of shrub species (Schlesinger et al 1990)species composition (annual v perennial grasses slow-rooted vdeep-rooted vegetation) (Schuman et al 2009) or decreasingplant cover so that plant growth becomes lsquopatchyrsquo and ischaracterised by areas of greater fertility interspersed withbare infertile soil (Schlesinger et al 1990 Ludwig and Tongway1995 Su et al 2006) In such cases an increase in the spatialheterogeneity of SOC can be expected In other instances grazing

pressuresmay reduce vegetation cover to such an extent that SOCdistribution starts to become more homogeneous due to thelimited input of organic material and the compaction andhomogenisation of soil due to hoof action (Nael et al 2004 Zhaoet al 2007) In instances where ecosystems are naturallycharacterised by shrub vegetation and overgrazing leads to thereplacement of shrubs by grassland decreased spatial variabilityhas also been observed (Lechmere-Oertel et al 2005)

The above discussion indicates that the spatial variability ofSOC in grazed areas and particularly rangeland areas with shrubvegetation is likely to be high in all but the most degraded areasConsequently sampling methodologies need to be designed inorder to adequately characterise this variation and must becapable of doing so at a variety of spatial scales This is importantfor C accounting purposes since SOC stock is usually expressedat larger spatial scales and estimated according to relative land-use area

Sampling designs to characterise SOC

Without an appropriate sampling design the ability forinference about SOC is compromised de Gruijter et al (2006)note that there are three ways to choose where to sample(i) choosing by convenience (ii) choosing at randomor (iii) choosing those locations thought to be the mostinformative (ie choosing purposively) The advantages ofchoosing locations by convenience are self-evident ndash soilsampling by the roadside is a typical example ndash but its statisticalproperties are questionable and we will not deal with it furtherChoosing locations at random or purposively give rise torespectively two contrasting philosophies of statisticalinvestigation the design-based approach and the model-basedapproach Papritz andWebster (1995a) summarised the essentialdifference between the two lsquo the random character of anobservation arises in the design-based approach fromrandomising the selection of the sampling positions In model-based estimation in contrast each observed value per se isconsidered tobe the outcomeof a randomvariable postulated for agiven position in spacersquoNeither approach is lsquobestrsquo to characteriseSOC although depending on themotivation for sampling one isusually more appropriate than the other de Gruijter et al (2006)note that the suitability of the two approaches to a particular taskchanges with the spatial resolution of interest for example thedesign-based approach might be favoured to estimate the meanSOC stock for a paddock (lsquoglobal estimationrsquo) but the model-based approach might be favoured to map SOC stock withina paddock (lsquolocal estimationrsquo) But it is misleading to classifytheir roles so crisply the design-based approach can be usedfor local estimation just as the model-based approach can beused for global estimation A summary of the advantages anddisadvantages of each approach are presented in Table 2

Design-based approach

The design-based approach evolved in the first half of the 20thCentury largely through the pioneering ideas of R A Fisher(1890ndash1962) For illustrative purposes let us say that our variableof interest is SOC stock In the simplest case of sampling for thisvariable where all locations in an area of interest have equalprobability of being chosen the sample mean sample variance


and estimation variance of the sample mean [ms s2s and s2

s (ms)respectively] are computed without bias by (after de Gruijteret al 2006)

ms frac141n

Xnifrac141

yi eth1THORN

s2s frac14

1n 1

Xnifrac141

ethyi msTHORN2 eth2THORN

s2s ethmsTHORN frac14

s2s

neth3THORN

where yi is the ith of n observations of SOC stock Moreinformationon these quantities canbe found in standard statisticaltexts such as Snedecor and Cochran (1989) and Zar (1999)Through randomisation we ensure that the deviations about themean (the errors) form an independent random variable (ie onesample has no relation to another) a necessary assumption fordesign-based inference The most familiar application of thedesign-based approach is ANOVA (Snedecor and Cochran1989) due to Fisher In part the design-based approach was anattempt to overcome historical constraints on the gathering andprocessing of information contemporaries of Fisher needed away to interpret and extrapolate results from what wouldnow be considered relatively small sample sizes Fisherrsquostechniques were tremendously successful and have sincebecome convention Besides unbiasedness the advantage ofthe design-based approach is that because it is conventionmany of its accompanying statistical analyses have beenpackaged in commercial software as lsquoone-clickrsquo procedures Thedisadvantage of simple random sampling is that it tends to clusterthe samples which can result in undesirably large parts of thestudy area remaining unsampled (Fig 4a)

To circumvent the clustering effect of simple randomsampling the study area can be stratified ie split into strata thatare ideally as homogeneous as possible Two samples (at least)are then selected at random from each stratum An unbiasedestimate of the sample mean of SOC stock through stratifiedrandom sampling mst is computed by (after de Gruijter et al2006)

mst frac14XHhfrac141

ahmh eth4THORN

where H is the number of strata and ah and mh are respectivelythe proportion of the study area and the mean SOC stockassociated with the hth stratum Equation 1 is used to estimate mh

the variance and estimation variance of the hth stratum s2h and

s2h(mh) are estimated according toEqns 2 and 3 respectively The

estimation variance of mst is computed without bias by

s2stethmstTHORN frac14

XHhfrac141

a2hs2hethmhTHORN eth5THORN

and an unbiased estimate of the sample variance s2st is given by

s2st frac14

1n

Xnifrac141

yi2

m2

st thorn s2stethmstTHORN eth6THORN

There are two ways in which strata can be delineated (deGruijter et al 2006) (i) through geographic coordinates (Fig 4b)or (ii) through ancillary data (Fig 4c) de Gruijter et al (2006)recommend the use of a k-means classifier (eg Hartigan andWong 1979) to derive the strata which we have followed hereIn Fig 4b we see that stratification by geographic coordinateshas dispersed the sampling locations about the study area morethan simple random sampling When stratifying by an ancillaryvariable the ancillary variable should have a plausible correlationwith the target variable we used here an estimate of the long-termmean vegetative cover of the ground surface () (Scarth et al2006) derived from 20 years of Landsat satellite imageryunder the hypothesis that SOCwill increase proportionately Theresulting sample locations are not guaranteed to dispersespatially however they are dispersed over the range of variationof the ancillary variable

A systematic grid can be used as part of a design-basedsampling approach but only on the condition that the initiallocation of the grid is chosen randomly (deGruijter et al 2006) Itmay be necessary to permute the initial location and the gridspacingmany timesbefore thedesirednumberof samplesfit in thearea of interest In the example in Fig 4d the samples are spreadadequately through the study areawith a spacing of 247m but thechoice of initialising location has meant that one sample is veryclose to the field boundary To move this sample away fromthe boundary would introduce bias Under systematic randomsampling as this design is known the user can estimate thesample mean without bias according to Eqn 1 but there is nounbiased estimate of sample variance de Gruijter et al (2006)note that Eqn 2 can be used but it will generally overestimateHowever if there is periodic variation in the study area that occursat a wavelength coincident to the sampling interval (eg waterdrains hedge rows) then Eqn 2 will severely underestimate Analternative less-biased approximation is the method of balanceddifferences (Yates 1981 Papritz and Webster 1995a) The

Table 2 A summary of the two sampling approaches to characterise soil organic carbon stock

Approach Site selection Advantages Disadvantages Ideal useA Inference

Design-based Random UnbiasedA In its simplest form provides Non-spatial summary Analysis ofpoor spatial coverageA of a study area varianceA

Model-based Purposive Optimises the Not a safeguard against biasA Mapping of a Linear mixedspatial coverageA study area modelA

Obtaining the lsquomodelrsquo can bedifficultA

Analysis is complexA

AIdeal though not exclusive


technique is related closely to signal processing whereengineers commonly filter the informative component of data(lsquosignalrsquo) from background variation (lsquonoisersquo) In the context ofestimating the sample variance of a systematic design it is thelsquonoisersquo that is relevantWebster andOliver (2001) describe afilterof the form

025 thorn050 050 thorn025

thorn050 100 thorn100 050



Note that each row and column of the filter sum to zero Thisfilter moves over the systematic grid in J steps (where J lt n therecan be some overlap between the steps) At the jth location thevalues of the 16 nearest sample locations are convolved with thefilter coefficients to yield a single valuedj The sample variance isthen computed as

s2sy frac14

1J 625

XJjfrac141

d2j eth7THORN

where lsquo625rsquo is the sum of the squared coefficients in the filtergiven above The method may be less biased than Eqn 2 but has

its own problems such as how to handle the data at the edge of thestudy area and the arbitrary choice of the dimension of the filter

Another commonly used design-based strategy is nestedsampling Webster and Oliver (2001) provide an overview of thetechnique The simplest form of nested sampling involvesselecting a set of n1 locations separated by distance d1 These arecalled lsquofirst-stagersquo samples At a distance d2 (where d2lt d1) fromeach first-stage sample with random orientation one sample istaken to form the collection of n2 samples Then at a distance d3(where d3lt d2) from each first- and second-stage sample withrandom orientation one sample is taken to form the collection ofn3 samples The process is repeated for any number of stagesalthough the total sample number quickly becomes large Thisbasic scheme forms a lsquobalancedrsquo hierarchy which means thatthere is full replication at each stage For three stages labelled ab and c respectively the model of variation is

zijk frac14 mthorn ai thorn bij thorn cijk eth8THORN

where zijk is the value of the kth unit in the cth stage in the jth unitof the bth stage in the ith unit of the ath stage m is the overallmean ai is the difference betweenm and themean of the ath stagebij is the difference between the mean of the first stage and themean of the jth subclass in class i and cijk is the differencebetween the observed value and its class mean at the third stage

ndash500

Y (

m)

ndash500 0 500

X (m)

ndash500 0 500

500

0

ndash500

500

0

(a) (b)

(c) (d )

Fig 4 Examples of four different kinds of design-based sampling (each with n= 10) for a hypothetical paddock(a) simple random sampling (b) random sampling stratified by classified geographical coordinates (shown in thebackground shading) (c) random sampling stratified by a classified ancillary variable (in this case an estimate oflong-termmean ground cover shown in the background shading) (d) systematic random sampling (with the initiallocation shown as an open circle)


The quantities ai bij and cijk are independent random variablesassociated with the three stages Each stage has zero meanand the respective variance components s2

as2bs2

c The overallvariance of z is

s2frac14s2a thorn s2

b thorn s2c eth9THORN

Analysis of a balanced hierarchy is relatively straightforwardthrough ANOVA However full replication is wasteful ofresources and a user might prefer to concentrate resources atparticular stagesThis creates anunbalancedhierarchy Pettitt andMcBratney (1993) proposed a form of unbalanced nested designfor soil sampling suited to situations where the variability ofthe target process is not known To summarise their method thestudy area is divided into strata and within each stratum arandomly oriented transect is placed Individual samples are thencollected at exponential spacings along the transect Howeveranalysis of an unbalanced hierarchy is complex Garrett andGoss (1980) provided a computer program to tackle the taskUnfortunately the method suffers the possibility of returningnegative estimates for some variance components Spijker et al(2005) circumvented the issue by substituting zeros for thenegative estimates Amore elegant way to ensure valid estimatesof the variance components is through residual maximumlikelihood (eg Pettitt and McBratney 1993) although thistechnically makes the scheme a hybrid of the design-based andmodel-based sampling approaches

There are other types of design-based sampling schemebesides those we have outlined above We refer the reader to deGruijter et al (2006) for a comprehensive treatment

Model-based approach

The model-based approach evolved through advances incomputing and the ability to collect and process large amounts ofinformation quickly Choosing sampling locations purposivelynecessitates the existence of prior knowledge in the form of amodel In its least tractable form this model might reside in themind of expert More commonly we will derive the modelthrough statistical procedures For SOC stock arguably the mostrelevantmodel is born of geostatistical theory which is discussedin detail below

The advantage of the model-based approach is thatsamples can be spread optimally throughout the area of interest(although this does assume that the model is sensible and can beextrapolated) Compared with design-based sampling thedisadvantages of the model-based approach are (i) the latter isnot as secure a safeguard against bias and (ii) the statisticalanalyses that accompany themodel-based approach are relativelycomplicated and less prevalent in commercial software deGruijter et al (2006) note that to gain advantage over the design-based approach the model-based approach must satisfy threeconditions (i) theremust bemany samples (ii) the target variablemust display spatial autocorrelation and (iii) a large proportionof the samplesmust be taken at spatial intervalsmuch smaller thanthe range of the variogram The concepts of lsquoautocorrelationrsquolsquovariogramrsquo and lsquorangersquo are introduced below

The basic tenet of geostatistical theory is that if you observeSOC stock at location x in a paddock then step h= 1m (in somearbitrary direction) and make another observation the pair of

recorded values will probably be quite similar However if youwalk h= 100m from x and make an observation of SOC stockyouwill probablyfind that the recordedvalue is quite dissimilar tothe value at x This is the concept of autocorrelation Over manypairs of observations we can compute the average dissimilaritybetween each pair (based on half their squared difference) as afunction of h which is known as the experimental (semi)-variogram (Webster and Oliver 2001)

gethhTHORN frac14 1

2nethhTHORNXnethhTHORNifrac141

fzethxiTHORN zethxi thorn hTHORNg2 eth10THORN

where g(h) denotes the average semi-variance as a function of hn(h) is the number of pairs as a function of h z(xi) is the ith valueof the observed variable and z(xi +h) is another observationof z located h units from z(xi) The experimental variogram isusually quite noisy and to be useful has to be idealised withwhat is known as an lsquoauthorised functionrsquo to form the theoreticalvariogram It is the theoretical variogram that lends itself soreadily to the lsquomodelrsquo of model-based sampling in that itsummarises the available knowledge about the spatial variabilityof SOC stock in an area of interest Webster and Oliver (2001)describe the various authorised functions how to fit them tothe experimental variogram and then choose the best theoreticalmodel Figure 5 illustrates how the theoretical variogramsummarises the spatial variability of observations under differentamounts of autocorrelation In each case the authorisedfunction is a spherical model (Webster and Oliver 2001)When aprocess is autocorrelated strongly as in the top row of Fig 5the observations show a distinct spatial pattern The variogram ofthis process shows that the lsquonuggetrsquo variance component ndash they-intercept ndash is relatively small Nugget variance describesuncorrelated variation and is due to the combined effects ofmeasurement error and fluctuations in the process that occur overintervals smaller than the minimum sampling distance As theproportionof nuggetvariance increases uncorrelatedfluctuationssupersede the autocorrelated fluctuations (the middle and bottomrowsof Fig 5) In each of the three cases the variogram rises fromthe nugget variance to a maximum known as the lsquosillrsquo varianceIf the samplemeanand sample varianceof the observations canbeassumed constant within the area of interest the sill variancetheoretically equals the sample variancewhen this is not the caseit indicates that the spatial variability of the process is complexand the usermight wish to consult a statistician for advice on howto proceed The separation distance at which the sill is reached iscalled the lsquorangersquo Samples separated by distances larger than therange can be considered independent under the model-basedapproach For simplicity we have ensured that the range of thethree variograms in Fig 5 is constant at a 30-m distance

The theoretical variogram relates to purposive samplingthrough the interpolation method known as kriging Kriging is atype of moving average that interpolates estimates at unsampledlocations conditional on the values observed at sampledlocations (Webster and Oliver 2001) The moving average isweighted inversely by the semi-variances between observedlocations which as we have seen are a function of h accordingto the model of spatial variation The uncertainty associatedwith a kriging estimate ndash the kriging variance analogous tothe estimation variance of the sample mean in design-based


statistics ndash depends not on the values of the observations but onthe theoretical variogram and on the spatial arrangement of thesample locations Therefore if one is lucky enough to knowthe variogram in advance a set of locations for purposivesampling can be proposed and kriging used to ensure that thekriging variance for the entire area of interest is smaller thansome nominated threshold (McBratney et al 1981) Often thevariogram is not known in advance of sampling and must begleaned from ameta-analysis or estimated with a reconnaissancesurvey McBratney and Pringle (1999) surveyed the publishedliterature for variograms of topsoil attributes and createdaverages that could serve as an initial guess about the spatialvariability of an attribute before sampling Pringle and Lark(2008) updated the averages and placed those for SOCconcentration () and bulk density (gcm3)mdashas noted aboveboth variables are needed to estimate SOC stock on a mass-per-area basismdashin the context of a lsquolinear model of coregionalisationrsquo(LMCR) (Journel and Huijbregts 1978) (Table 3) A LMCR is aconstruct that describes how the theoretical variogram of oneattribute relates to another through their cross-variogram Of thetwo variables bulk density has the largest proportion of nuggetvariance to sill variance at 025 This reflects the inherentrandomness of bulk density at the scale of a soil core The LMCRof SOC concentration and bulk density enables optimisationof a model-based sampling strategy for both variablessimultaneously McBratney and Webster (1983a) explored thisidea in the context of the components of soil texture

In regard to reconnaissance surveyMarchant andLark (2006)developed an adaptivemethod An initial theoretical variogram is

computed from a bare minimum of samples in the first phase andused to propose a set of optimum sample locations for the secondphase Following their collection the second-phase samples areused to update the variogram which then optimises the samplelocations for the third phase and so on The method could beextended to cater formore thanonevariable but cannot escape thefact that it is suited ideally tovariables that canbemeasured in situor to variables not expected to vary substantially between onephase of sampling and the next SOC concentration fails to meetboth of these criteria as the variable (i) has to be estimatedthrough laboratory analysis and (ii) has been shown to changeseasonally (Leinweber et al 1994 Saggar and Hedley 2001) In

Small

Large

Nugget variance = 005

Val

ue

Small

Large

Sem

ivar

ianc

e


0 20 40 60 80 100

Position (m)

Small

Large

h (m)

0 50


0

1

0

1

0

1

Fig 5 Spatial variability described by the variogram Panels on the left show hypothetical observations of a variableat 100 locations along a transect Panels on the right show the associated theoretical (standardised) variogramThe process is autocorrelated strongly in the first row moderately in the second row and weakly in the third rowThe range parameter of variogram is 30m in each case

Table 3 Coregionalisation matrices of topsoil organic carbonconcentration (SOC units of2) and bulk density [BD units of (gcm3)2]The authorised function that links the three matrices is a double-spherical

model (Webster and Oliver 2001)

SOC BD

(a) Nugget structured0 = 0m SOC 0009 ndash0005

BD ndash 0010

(b) 1st autocorrelated structured1 = 30m SOC 0009 ndash0005

BD ndash 0010

(c) 2nd autocorrelated structured2 = 300m SOC 0090 ndash0023

BD ndash 0020


regard to the former Gehl andRice (2007) reviewed the ability ofproximal sensing to measure SOC content in situ and concludedthat laboratory techniques will be needed for some time yet

An alternative reconnaissance method for estimating thevariogram is nested sampling introduced above The variancecomponents of Eqn 9 can be plotted as a function of separationdistance thus approximating the variogram (Oliver andWebster1987) Unbalanced schemes are generally favoured becausethey allow the concentration of sampling resources at the finestspatial scales which are crucial for variogram estimation(de Gruijter et al 2006) The studies of Schoumlning et al (2006)and Rossi et al (2009) both used unbalanced nested schemesto create variograms of SOC stock which were then used topropose optimum model-based sampling schemes Corstanjeet al (2007) used the variograms obtained from an unbalancednested ANOVA to examine how SOC concentration correlatedwith the activity of the urease enzyme an important component ofN-cycling They found that for a pasture site the variables werecorrelated only weakly and that the correlation did not changesignificantly with spatial scale

We mentioned above how the LMCR of SOC concentrationand bulk density (Table 3) enables optimisation of amodel-basedstrategy for simultaneous sampling of both variables Figure 6presents an example Because there are two variables we aredealing with cokriging variance rather than kriging variance(Webster and Oliver 2001) Central to optimisation is thedefinition of an objective function ie a quantity that we want tominimise (or perhaps maximise) through the action of samplingIn a univariate context vanGroenigen et al (1999) used themeankriging variance across the study site as an objective function onthe basis that kriging variance represents uncertainty whichobviously we want to minimise A more rigorous objective

functionmight be conceived (eg Lark 2002) butwehave chosenhere to follow the idea of van Groenigen et al (1999) At any onelocation in the study area there will be two values of cokrigingvariance one for each variable The objective function must be asingle value To integrate the two variables we computed theproportion of cokriging variance to sill variance averaged overboth variables over the study site The optimisation procedureinvolved (i) proposing a set of n= 20 initial sampling locationsfor both variables based on stratified random sampling bygeographic coordinates (Fig 4b) (nb it is not necessary to specifythe same number of samples for both variables but we have doneso here for illustrative purposes) (ii) calculating the objectivefunction based on the LMCR and the proposed samplinglocations and (iii) using spatial simulated annealing (vanGroenigen et al 1999) to minimise the objective function Theinitial proposed locations returned mean cokriging variances of00802 and 0037 (gcm3)2 for SOC concentration and bulkdensity respectively The initial value of the objective functionwas 0828 Following optimisation the samples are spread evenlythroughout the study site (Fig 6) on a roughly triangular gridvan Groenigen et al (1999) demonstrated the same effect whichreflects the fact that a triangular grid is the most efficient wayto implement systematic sampling (McBratney et al 1981)The mean cokriging variances reduced to 00682 and 0034(gcm3)2 for SOC concentration and bulk density respectivelywhile the final value of the objective function was 0745

Number of samples needed to estimate SOC

We have seen above the basic sampling arrangements that mightbe used by the design-based approachWe have also seen how themodel-based approach might be used to optimise a samplingarrangement for a study area But howmany samples do we needto takeWemust ensure we have adequate samples for inferencebut we do not want to be wasteful of resources Both samplingapproaches provide answers to this question


Let us say that we need to estimate the mean SOC stock for anarea of interest The optimum number of samples to collect willdepend on the sample variance of SOC stock and on what sortof uncertainty we can tolerate Usually we know in advance atleast roughly the tolerable uncertainty Against the uncertainbackground we need to sample enough locations to ensure thatwe can detect a case of SOC stock departing from the mean Theprobability of correct detection is known as lsquostatistical powerrsquo(Snedecor andCochran1989) Statistical power in this context isa function of four quantities (i) the number of samples (ii) thetolerable uncertainty scaled by the square-root of the samplevariance (iii) the significance level (a) and (iv)whether the test isone-tailed or two-tailed For a given dataset the only variablewillbe the number of samples the rest are constant The choice of (iii)and (iv) are somewhat arbitrary although two tailed-tests aregenerally used at a= 005

Consider the simple random sampling scheme in Fig 4a Inimplementing this strategywewould observe SOC concentrationand bulk density (gcm3) at all 10 locations then make thenecessary conversion to SOC stock In our experience this lattervariable has a log-Normal distribution but statistical power

Mean CKV SOC = 0068 ()2 BD = 0034 (gcm3)2 Objective function = 0745

X (m)

Y (

m)

ndash500 0 500

ndash500

0

500

Fig 6 Model-based sampling scheme that minimises the mean cokrigingvariance for soil organic carbon concentration and bulk density We haveassumed that both variables will be collected at the same locations but this isnot essential


requires a Normal distribution Therefore we transform thedata to SOC [log(Mgha)] We used the LMCR in Table 3 inconjunction with the method of Lark (2002) to generate arealisation of SOC [log(Mgha)] for the paddock in Fig 2 Themean and variance of the realisation were m = 3762 log(Mgha)and s2 = 0141 [log(Mgha)]2 respectively although we couldnever know this in realityWe then sampled the area according tothe scheme in Fig 4a where we found that the sample mean wasms= 3840 log(Mgha) and the sample variance was s2

s = 0099[log(Mgha)]2 Following Larsen et al (2001) we used tolerableuncertainty of 10 above and below the sample mean SnedecorandCochran (1989) present the computational steps for statisticalpower For a particular number of samples we start by findingthe values of ms that constitute a significant deviation ata= 005 a significant deviation lies outside the intervalms 196

ffiffiffiffiffiffiffiffiffiffiffiffiffis2s ethmsTHORN

p which corresponds to ms lt 3645 and

ms gt 4035 in our example We then calculate the probabilityof ms being outside this interval when the mean is at the limitof tolerance ms+ 01ms= 4224 For ms= 3645 the normaldeviate is zl = (36454224)


p=5807 For ms= 4035

the normal deviate is zu = (40354224)ffiffiffiffiffiffiffiffiffiffiffiffiffis2s ethmsTHORN

p=1896

The probabilities associated with these deviates are P(zl) lt zl 0andP(zu)gt zu = 0971 respectively These quantities are summedto yield the statistical power to detect a deviation greater thanthe tolerable uncertainty with 95 confidence (two-tailed test)We repeated this process for various sample sizes andplotted the results (Fig 7) Also shown in Fig 7 are the statisticalpower functions for the stratified and systematic samplingschemes shown in Fig 4b and d respectively where weobserved mst= 3683 log(Mgha) s2

st = 0087 [log(Mgha)]2msy= 3748 log(Mgha) and s2

sy = 0156 [log(Mgha)]2 (wherefor simplicity the latter was calculated according to Eqn 2)A statistical power of 08 is used conventionally as a benchmarkfor minimum sampling effort (Lenth 2001) Simple random

sampling and stratified random sampling both require 5 samplesto estimate mean SOC stock with a statistical power of 08 whilesystematic random sampling requires 8 samples These numbersserve only as an illustrative example and should not be construedas a recommendation

An alternative expression of statistical power is the minimumdetectable difference (MDD) which to paraphrase Garten andWullschleger (1999) is defined as the smallest difference that canbe detected between means with a certain amount of confidenceThe conventional formula for determining the optimum samplesize to estimate a mean is (Cline 1944 Snedecor and Cochran1989 Zar 1999)

n frac14s2t2a=2ethn1THORN

d2eth11THORN

wheres2 is the sample variance t2a=2ethn1THORN is Studentrsquos t-value at aconfidence level of a (two-sided) with n1 degrees of freedomand d is half the width of the desired confidence interval Thevalue of n has to be determined iteratively because it appearson both sides of the equation (Zar 1999) Equation 11 can bereformulated in terms of statistical power (Zar 1999)

n frac14 s2

d2ethta=2ethn1THORN thorn teth1bTHORNethn1THORNTHORN2 eth12THORN

where 1b is the desired statistical power (say 08) TheMDD isobtained by rearranging Eqn 12 (Zar 1999)

MDD frac14ffiffiffiffiffis2

n

rethta=2ethn1THORN thorn teth1bTHORNethn1THORNTHORN2 eth13THORN

The equation needs to be modified if computing the MDDfor multiple treatments see Zar (1999) for details The study ofGarten and Wullschleger (1999) who examined SOC stocksunder different types of plant cover is often cited for its use ofMDD They showed how the MDD decreases asymptoticallywith increasing sample size

Finally it is possible to derive a model-based solution foroptimal design-based sampling provided that a variogram of thetarget variable can be used as prior knowledge (de Gruijter et al2006) The first step is to compute themean semi-variance for the(two-dimensional) area of interest B (Webster and Oliver 2001)

gethBBTHORN frac14 1

jB2jethB

ethB

gethx x0THORNdxdx0 eth14THORN

where g(xx0) represents the theoretical semi-variance at theseparation distance between a pair of locations x and x0 Thequantity g(B B) is known as the lsquodispersion variancersquo ingeostatistical terminology The integration is usually donenumerically over a large number of pairs If simple randomsampling is the desired arrangement the estimation variance forthe observations will be (after de Gruijter et al 2006)


gethBBTHORNn

eth15THORN

If stratified random sampling is desired the estimationvariance will be


XHhfrac141

a2h gethb bTHORN eth16THORN

0 5 10 15 20 25 30

00

02

04

06

08

10

n

Pow

er

Fig 7 Statistical power to detect a deviation within 10 of the samplemean with 95 confidence (two-tailed test) solid line = simple randomsampling (Fig 4a) dashed line = random sampling stratified by geographicalcoordinates (Fig 4b) dotted line = systematic random sampling (Fig 4d)


where g(b b) denotes the dispersion variance for the hth stratumUnder systematic random sampling the estimation variance willbe

s2syethmsyTHORN frac14 gethBBTHORN gethb bTHORN eth17THORN

whereg(bb) denotes here the dispersion variance of the proposedlocations in the grid (Actually multiplying s2

sy(msy) by n yieldsanotherwayof approximating the sample varianceof a systematicrandom design besides Eqn 2 and the method of balanceddifferences)


The method of McBratney et al (1981) for optimising a model-based sampling scheme uses a pre-specified maximum krigingvariance to propose n arranged in a grid pattern Rossi et al(2009) recently used this method to derive optimum samplingschemes for SOC stocks in Tanzanian forests But because manysoil surveyors know in advance roughly howmany samples theycan afford to collect it is arguably better to reverse the method ofMcBratney et al (1981) This was done by McBratney andWebster (1983b) who showed how under the model-basedapproach a geostatistical analogue of the classical estimator inEqn 11 returned relatively efficient estimates of the optimum n fora study area The approach was adopted recently by Worshamet al (2010) to describe SOC stocks associated with differenttypes of land cover in a forest in Georgia USA Mooney et al(2007) proposed amethod to optimise sampling for SOC stock byreducing the estimate of variance while circumventing the needfor a formal geostatistical analysis They argued that this wasnecessary on the (rather flimsy) basis that geostatistics requiresspecialised software To reduce variance they first had to infer avalue for the range of spatial correlation In our opinion thework-around needed to avoid computing a variogram is not worth thetrouble

Power analysis can also be used with the model-basedapproach Schoumlning et al (2006) examined variograms of SOCstock then substituted estimates of semi-variance at particular lagdistances to compute the MDD Stroup (2002) detailed a methodfor power analysis under a model-based approach based on theoutput of a linearmixedmodel (Lark andCullis 2004) It is not ourintention to describe the details of a linear mixed model otherthan to say that it is a regression model that accounts explicitlyfor spatial variability by simultaneously estimating regressionparameters and the parameters of the theoretical variogram Thekey advantage of a linearmixedmodel is that as under the design-based approach one can test hypotheses about the regressioncoefficients The disadvantages of the linear mixed model arethat the method is relatively complex computationally intenseand relies on iterative fitting that if done without care mightreturn a suboptimal solution Kravchenko et al (2006) followedthe method of Stroup (2002) to find the optimum sample size todescribe total soil C content They found that for a particularsample size MDD decreased as the range of the variogramincreased

Wehave seen inFig 6howa theoretical variogramcanbeusedin conjunction with simulated annealing to optimise a model-based sampling scheme In that example we assumed from

simplicity that n= 20 for both variables but noted that this did nothave to be the case To find the optimum number of samples foreach variable the method we outlined above could be run fordifferent combinations of n for both SOC concentration andbulk density and the most satisfactory outcome chosen A moreelegant approach would be to explicitly incorporate n as aparameter to optimise

Sampling in space and time

In the above discussion of adequate sample sizes we havepurposefully conveyed only the lsquospatialrsquo component of samplingBut what about the lsquotimersquo component Assuming that we sampleadequately to establish the baseline status of SOC stock we willultimatelywant to sample adequately todetect a changeover time

Papritz and Webster (1995a) provided a theoreticallyrigorous treatment of how to estimate change under both thedesign-based approach and the model-based approach andprovided some pointers on how to choose the right approach fora certain situation de Gruijter et al (2006) discuss four basicarrangements for space-time sampling (i) static (spatial positionsare fixed but temporal positions change) (ii) synchronous(temporal positions are fixed but the spatial positions changesuch that they might never be revisited) (iii) static-synchronous(a combination most easily related as a space-time grid) and(iv) rotational (a compromise where the spatial positionssampled at a particular time are partially replaced at the nextsampling time) A static design in the strictest sense cannot beimplemented for SOC stocks because of destructive samplingie we can never sample the same location twice For generalflexibility and ease of statistical inference de Gruijter et al(2006) recommend the synchronous pattern however eachpattern has its own advantages and disadvantages which dependsomewhat on the nature of the variable being monitored and onthe objective of themonitoring programmeWe refer the reader tode Gruijter et al (2006) for further details about calculatingsample means sample variances and estimation variances undereach arrangement


In the context of design-based analysis it is recommended thatwhen revisiting an already sampled study area with the intentionof detecting SOC change one should sample as close as possibleto the original baseline locations This approximates the lsquostaticrsquoapproach described above but might also be termed lsquotemporallypaired sitesrsquo (Conteh 1999) Such a scheme increases theprecision of the estimates of change (Papritz andWebster 1995bLark 2009) Note the words estimates of change What makeschange detection particularly difficult is that we are interested inneither the baseline observations nor the revisit observationsrather we are interested in their differenceY which is distributedas (Lark 2009)

Y ethmY s2Y thorn 2s2

e thorn s2LTHORN eth18THORN

where mY is the mean difference and s2Y thorn 2s2

e thorn s2L represents

the total variance of Y The variance component s2Y is the sample

variance of Y the variance component s2e represents sampling

and measurement errors accrued in the baseline and revisitobservations (multiplied by 2 because they are independent in


space and time) and the variance component s2L represents

location error (necessary due to destructive sampling) Note thatestimation of s2

e entails a proportion of replicated laboratoryanalysis for both the baseline survey and the revisit It is unlikely(in the extreme) that the term s2

Y thorn 2s2e thorn s2

L will equal thesample variance of the baseline observations The importance ofthis cannot be overstated to quote Lark (2009) lsquoSoil scientistsand the administrators who sponsor surveys should not fall intothe trap of assuming that a survey planned to estimate status willalso suffice for estimating change or that the requirements forestimating change can be computed in a simple way from data onstatus alonersquo Similar sentiments were echoed by deGruijter et al(2006) who noted that rotational sampling patterns are relativelyefficient for estimating the current mean of a target variable butstatic synchronous patterns are relatively efficient for detectingchange in the mean Lark (2009) recommended adoptingstratified reconnaissance sampling where only a proportion ofbaseline sites are initially revisited in any one stratum Strata thatshow a large change could then sampled more intensively andvice versa

At this point it is worth returning briefly to MDD (Eqn 13)Garten and Wullschleger (1999) applied the method to assessSOCstock spatially but speculated that it couldbeused todetect achange in SOC stock Many studies have since promoted MDDfor the elucidation of change (for example Conant et al 2003Kucharik et al 2003 Poussart et al 2004 Homann et al 2008Heim et al 2009) Schoumlning et al (2006) did the same in termsof amodel-based analysis But as none of these studies considered theimplications of Eqn 18 they have used an incorrect estimate ofvariance and so their conclusions are flawed

We refer the reader to Stewart-Oaten et al (1992) for furtherdiscussion of the statistical pitfalls of estimating change in pairedsamples collected under the design-based approach


Papritz and Fluumlhler (1994) presented a model-based method forestimating the change of a spatially autocorrelated target quantitybetween two dates say baseline sampling and a revisit Themethod is a modification of cokriging As such it requires that theobserved variables associated with each date are described by anLMCR (Table 3) However due to the necessity for destructivesampling that accompanies estimates of SOC stock the standardcross-variogram in the LMCR will have to be replaced withthe pseudo-cross-variogram (Myers 1991) There are threeadvantages to the method of Papritz and Fluumlhler (1994) Firstbecause the temporally paired samples are not collocatedcokrigingwill always return amore precise estimate of the changethan kriging the two variables independently and subtracting oneinterpolated surface from another (de Gruijter et al 2006) Thesecond advantage is that the LMCR can be used to optimise amodel-based sampling scheme to detect further change in SOCstock The third advantage relates to the concept of geostatisticalblocking (Webster and Oliver 2001) Geostatistical blockingshould not be confused with the blocking that is applied toexperimental designs Through geostatistical blocking the usercan effectively scale the predictions of the method of Papritz andFluumlhler (1994) to represent global estimates of the change in themean (as opposed to the local estimates that would usually be

returned) This is an example of the model-based approachlending itself to a task that many would associate readily with thedesign-based approach

Krigersquos relation

Soil monitoring programmes are expensive to maintain Anobvious way to reduce costs is to limit the amount of time spenttravelling from site to site Thus the financial benefit of samplingin a relatively small area say 25 25m is self-evident This hasthe added advantage of being easily communicated whichincreases its adoptability as a standard procedure Advocates ofthis approach argue that byminimising spatial effects the chanceof detecting a changeover time is increasedUnfortunately due tothe geostatistical principle of Krigersquos relation the method isflawed if wishing to describe temporal change over an area largerthan 25 25m

Let us say that we have been asked to estimate the baselinemean SOC stock for a paddock This paddock is part of a largerproperty From a random part of the paddock we choose a site forthe 25 25-m area from which we will collect 10 samples Wedenote the property paddock and sample area as R B and brespectively In Eqn 14 we described how to compute thedispersion variance for an area of interest B The same formulaapplies for thedispersionvariance associatedwith eachofR andbKrigersquos relation describes how the dispersion variance ispartitioned according to the spatial scale of interest (afterWebsterand Oliver 2001) that is

s2ethb 2 RTHORN frac14 s2ethb 2 BTHORN thorn s2ethB 2 RTHORN eth19THORNwhere s2 (b2R) = g(R R)g(b b) s2 (b2B) = g(B B)g(b b)and s2(B2R) = g(R R)g(B B) The term s2 (b2B) is the keyhere because it relates the uncertainty of the sample mean of thepaddock estimated under a particular sampling pattern

What is the implication of Krigersquos relation For thehypothetical paddock of Fig 4 we demonstrate in Table 4 howthe s2(b2B) component of Eqn 19 changes according totwo contrasting sampling arrangements (i) selecting n= 10locations from within a b = 25 25-m area within the paddockand (ii) selecting n = 10 locations from the entire paddock(ie b=B 1000 1000-marea)We assume that the theoreticalvariogram is described by a spherical function with a sill of 1 unitand a nugget variance of 05 units but alter the range parameter totake values of a = 5 10 30 50 100 1000 (in units of m) Forsimplicity we have used simple random sampling (Fig 4a) to

Table 4 Dispersion variance (uncertainty) of a hypothetical variablewhen estimated from samples spread over an area b within a paddock

of B 1000 1000m

Range (m) b25 25m 1000 1000m

5 0115 009810 0143 009830 0310 009850 0397 0097100 0468 00941000 0347 0085


derive the estimates of s2 (b2B) although the same principleapplies to anydesign-basedormodel-basedarrangementThere issome fluctuation in the values of s2 (b2B) (Table 4) inheritedfrom the process of random site selection in b but the generalpattern is clear Krigersquos relation implies that we obtain relativelyprecise estimates of the paddock mean by sampling as widely aspossible within the paddock This is a simple and sensiblemessage but it is easily supplanted by the desire for conveniencewhich as noted by de Gruijter et al (2006) creates samples withweak statistical properties

Further considerations for optimum sampling

In addition to statistical issues two important considerationsrelate to (i) sample compositing and (ii) the temporal variabilityof SOCand its constituent pools Sample compositing (lsquobulkingrsquo)has been used by numerous authors in order to reduce lateralvariability (eg Webster and Burgess 1984 Dalal and Mayer1986b Studdert et al 1997 Brus et al 1999 Conant et al 2003Harms and Dalal 2003) Compositing involves collecting severalsoil cores in close proximity then mixing the cores together toform a single sample The effect of compositing is to smoothshort-range fluctuations which increases the chance of detectinglonger-range treatment differences A variogram can be used asprior knowledge to help decide the optimum way in whichsamples should be composited (Webster and Burgess 1984) Theprincipal reason for compositing is that analytical costs arereduced A user must be aware of the implicit assumption that thecomposite sample upon analysis must yield the same value asthe mean of the individual cores that comprise the composite(disregarding sampling and measurement errors) (de Gruijteret al 2006) Fortunately this is the case for both SOCconcentration and bulk density (A notable soil attribute to beaffected by this assumption is pH due to the log transformapplied to the activity of the H+ ions a composite sample of soilpH will not equal the mean of individual observations)

In regard to temporal variability we expect that amanagement-induced change to SOC stock will in generalmanifest itself slowly over several years Somemay consider thisto be too long Encouragingly in several studies it has been foundthat the particulate fraction of SOCor light-fraction C (labile C) islost preferentially under a change in management (Chan 1997Franzluebbers and Stuedemann 2003 Dalal et al 2005)Research is needed to verify whether this applies to northernAustralian rangeland conditions If so then concentratinganalytical effort on this fraction of SOC might expedite theprocess of detecting change

FollowingConteh (1999) VandenBygaart (2006) andGoidtset al (2009) some additional considerations for sampling forSOCstock include (i)whether it is better to sample byfixeddepthintervals (IPCC default value is a 0ndash03-m depth) or sample byhorizon (ii) the sampling process cannot be streamlined byassuming that bulk densities or SOC pools such as labile C aretemporally constant (consider sampling at the same time ofthe year) (iii) clay particles play an important role in C cycling(Sollins et al 1996) and their concentration should not beassumed temporally stable particularly in areas prone to erosion(iv) plant litter and roots are importantC sinks (contribute to labileC pool) and should be sampled concomitantly with soil (v) rocky

soil is a major source of uncertainty due to its influence on bulkdensity ndash affected areas may require estimation by spatialinterpolation or by a calibrated pedotransfer function and (vi) themore background information one collects about a site the better(two of the more obvious for rangelands are historical stockingrates and rainfall) In addition the background informationgathered from electromagnetic surveys (clay content salinityetc) biomass and yield maps (Dang et al 2009) and remotesensing (Fisher et al 2009) can be employed to stratify soilsampling An example of utilising the variability in long-termground cover for designing a sampling scheme is shown in Fig 4

Sampling and analytical costs and time required to estimateSOC stocks (and other soil properties) may be reduced byemploying emerging technologies for in situ estimation(surrogate measures) of soil C (Gehl and Rice 2007) Thesetechniques include laser-induced breakdown spectroscopy(Ebinger et al 2003) inelastic neutron scattering (Wielopolskiet al 2001) visible-near infrared spectroscopy (Morgan et al2009) and remote sensing for surface cover and plant biomassnormalised difference vegetation index (NDVI) and hencepotential C input (Chen et al 2000)

Conclusion

We have discussed the nature and the causes of spatial andtemporal variability in SOC stock and SOC pools and thestatistical issues that arisewhen theyare sampledAt thevery leastwe hope that we have shown how statistical considerationspervade every aspect of sampling and enlightened the reader tothe contrast between the design-based approach and the model-based approach and how they might apply to his or her ownresearch

McKenzie et al (2000) proposed a broad soil samplingstrategy for terrestrial C accounting to support the NationalCarbon Accounting System This strategy recommended astratified random sampling scheme with a minimum of 4replicates per strata Due to a dearth of information it is not yetknown whether this is too few or too many for Australianrangelands Ultimately we should be able to detect with theconfidence afforded by statistical rigour whether the SOC stockand SOC pools at a certain location have increased or decreaseddue to management effect or following land-use change incomparison with a baseline value MDD is an appropriate tool bywhich this can be achieved However before we arrive at thisgoal the discussion above has highlighted several importantissues(i) At the outset which approach dowewant to follow design-

based or model-based The ultimate objective is todetermine a change in the mean SOC stock over someaggregated area (eg a paddock a farm a region) Thisimplies that we are interested in global estimationConsequently the design-based approach might bepreferred provided of course that the principle of randomsite selection can be adhered to strictly We have seen thata model-based approach can also lend itself to globalestimation of change If random site selection cannot beguaranteed then the model-based approach is the soleoption although it will require a greater sampling intensitythan the design-based approach


(ii) Sample as widely as possible with the unit of interest(respecting of course the principles of the particularapproach that is being used) This principle will ensure thatthe mean is estimated precisely and applies to intensivelygrazed dairy pasture paddocks aswell as extensively grazedrangeland paddocks If working under the model-basedapproach we recommend that at a proportion of samplingsites an additional adjacent sample is collected Theseadditional samples will help improve the accuracy of thevariogram of the target variable which will in turnimprove future sampling schemes

(iii) A proportion of the samples must be replicated duringlaboratory analysis in order to quantify laboratorymeasurement error It is easy to overlook this considerationbut it is critically important when making inference aboutchange

(iv) Temporally paired sites are the most efficient way ofdetecting a change in SOC stock but destructive samplingand cumulative measurement errors decrease our ability todetect change Tominimise the effect of seasonal variationespecially for labile C pools we recommend that revisitsamples are collected at the same timeof year as the baselinesamples

(v) Research is needed to establish an appropriate MDD forAustralian rangelands

Acknowledgments

We thankMeat andLivestockAustralia for their partial fundingof this reviewThis review has benefitted immensely fromnumerous constructive commentsand suggestions fromBeverley HenryMickQuirk Adrian Chappell and twoanonymous reviewers and the journal editor

References

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Batjes N H (1996) Total carbon and nitrogen in the soils of the worldEuropean Journal of Soil Science 47 151ndash163 doi101111j1365-23891996tb01386x

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Bird S B Herrick J E and Wander M M (2001) ExploitingHeterogeneity of Soil Organic Matter in Rangelands Benefits forCarbon Sequestration In lsquoThe Potential of US Grazing Lands toSequester Carbon andMitigate the Greenhouse Effectrsquo (Eds R F FolletJ M Kimble and R Lal) pp 121ndash138 (CRC Press Boca Raton FL)

Bisigato A J Laphitz R M L and Carrera A L (2008) Non-linearrelationships between grazing pressure and conservation of soil resourcesin Patagonian Monte shrublands Journal of Arid Environments 721464ndash1475 doi101016jjaridenv200802016

Bradstock R A (2010) A biogeographic model of fire regimes in Australiacurrent and future implications Global Ecology and Biogeography 19145ndash158 doi101111j1466-8238200900512x

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Chan K Y (1997) Consequences of changes in particulate organic carbonin vertisols under pasture and cropping Soil Science Society of AmericaJournal 61 1376ndash1382

Chen F Kissel D E West L T and Adkins W (2000) Field-scalemapping of surface soil organic carbon using remotely sensed imagerySoil Science Society of America Journal 64 746ndash753

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Conant R T and Paustian K (2002) Spatial variability of soil organiccarbon in grasslands implications for detecting change at different scalesEnvironmental Pollution 116 S127ndashS135 doi101016S0269-7491(01)00265-2

Conant R T Smith G R and Paustian K (2003) Spatial variability of soilcarbon in forested and cultivated sites implications for change detectionJournal of Environmental Quality 32 278ndash286

Conteh A (1999) Discussion paper 3 evaluation of the paired siteapproach to estimating changes in soil carbon In lsquoEstimation of changesin soil carbon due to changed land usersquo Technical Report No 2(Ed Webbnet Resource Services Pty Ltd) pp 65ndash79 (National CarbonAccounting System Technical Report Australian Greenhouse OfficeCanberra)

Corre M D Schnabel R R and Stout W L (2002) Spatial and seasonalvariation of gross nitrogen transformations and microbial biomass in aNortheastern US grassland Soil Biology amp Biochemistry 34 445ndash457doi101016S0038-0717(01)00198-5

Corstanje R Schulin R and Lark R M (2007) Scale-dependentrelationships between soil organic carbon and urease activity EuropeanJournal of Soil Science 58 1087ndash1095 doi101111j1365-2389200700902x

Cresswell H P and Hamilton G J (2002) Bulk density and pore spacerelations In lsquoSoil Physical Measurement and Interpretation for LandEvaluationrsquo (Eds N McKenzie K Coughlan and H Cresswell)pp 35ndash58 (CSIRO Publishing Melbourne)

Dalal R C (1998) Soil microbial biomass ndash what do the numbers reallymean Australian Journal of Experimental Agriculture 38 649ndash665doi101071EA97142


Dalal RC andCarter J O (2000) Soil organicmatter dynamics and carbonsequestration in Australian tropical soils In lsquoGlobal Climate Changeand Tropical Ecosystemsrsquo Advances in Soil Science (Eds R LalJ M Kimble and B A Stewart) pp 283ndash314 (CRC Press Boca RatonFL)

Dalal R C and Chan K Y (2001) Soil organic matter in rainfed croppingsystems of the Australian cereal belt Australian Journal of Soil Research39 435ndash464 doi101071SR99042

Dalal R C Harms B P Krull E and Wang W J (2005) Total organicmatter and its labile pools following mulga (Acacia aneura) clearing forpasture development and cropping 1 Total and labile carbon AustralianJournal of Soil Research 43 13ndash20 doi101071SR04044

Dalal R C and Mayer R J (1986a) Long-term trends in fertility of soilsunder continuous cultivation and cereal cropping in southernQueenslandI Overall changes in soil properties and trends in winter cereal yieldsAustralian Journal of Soil Research 24 265ndash279 doi101071SR9860265

Dalal R C and Mayer R J (1986b) Long-term trends in fertility of soilsunder continuous cultivation and cereal cropping in southernQueenslandII Total organic carbon and its rate of loss from the soil profileAustralianJournal of Soil Research 24 281ndash292 doi101071SR9860281

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de Gruijter J J Brus D J Bierkens M F P and Knotters M (2006)lsquoSampling for Natural Resource Monitoringrsquo (Springer TheNetherlands)

Don A Schumacher J Scherer-Lorenzen M Scholten T and SchulzeE D (2007) Spatial and vertical variation of soil carbon at two grasslandsites ndash implications for measuring soil carbon stocks Geoderma 141272ndash282 doi101016jgeoderma200706003

Dormaar J F Johnston A and Smoliak S (1977) Seasonal variation inchemical characteristics of soil organic matter of grazed and ungrazedmixed prairie and fescue grassland Journal of Range Management30 195ndash198 doi1023073897467

Drees L RWilding L P SmeckN E and Senkayi A L (1989) Silica insoils quartz and disordered silica polymorphs In lsquoMineral in SoilEnvironmentsrsquo 2nd edn (Eds J B Dixon and S BWeed) pp 471ndash552(Soil Science Society of America Madison WI)

EbingerMHNorfleetMLBreshearsDDCremersDA FerrisM JUnkefer P J Lamb M S Goddard K L and Meyer C W (2003)Extending the applicability of laser-induced breakdown spectroscopy fortotal soil carbon measurement Soil Science Society of America Journal67 1616ndash1619

Fisher P D Abuzar M Best F and Rab M A (2009) Advances inprecision agriculture in south-easternAustralia Part I Amethodology forthe combined use of historical paddock yields and normalised differencevegetation index to simulate spatial variation in cereal yields Crop ampPasture Science 60 844ndash858 doi101071CP08347

Follett R F (2001) Organic carbon pools in grazing land soils In lsquoPotentialof US Grazing Lands to Sequester Carbon and Mitigate the GreenhouseEffectrsquo (Eds R F Follet J M Kimble and R Lal) pp 121ndash138 (CRCPress Boca Raton FL)

Franzluebbers A J and Stuedemann J A (2003) Bermudagrassmanagement in the southern piedmont USA III Particulate andbiologically active soil carbon Soil Science Society of America Journal67 132ndash138

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Gehl R J and Rice C W (2007) Emerging technologies for in situmeasurement of soil carbon Climatic Change 80 43ndash54 doi101007s10584-006-9150-2

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GriffinEAVerboomWH andAllenDG (2003) lsquoPairedSiteSamplingfor Soil Carbon (and Nitrogen) Estimation ndashWestern AustraliarsquoNationalCarbon Accounting System Technical Report No 38 (AustralianGreenhouse Office Canberra)

Harms B and Dalal R C (2003) lsquoPaired Site Sampling for Soil Carbon(and Nitrogen) Estimation ndash Queenslandrsquo National Carbon AccountingSystem Technical Report No 37 (Australian Greenhouse OfficeCanberra)

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Heim A Wehrli L Eugster W and Schmidt M W I (2009) Effects ofsampling design on the probability to detect soil carbon stock changes atthe Swiss CarboEurope site Laumlgaren Geoderma 149 347ndash354doi101016jgeoderma200812018

Homann P S BormannB T Boyle J R Darbyshire R L andBigleyR(2008) Soil C and N minimum detectable changes and treatmentdifferences in a multi-treatment forest experiment Forest Ecology andManagement 255 1724ndash1734 doi101016jforeco200711037

Hook P B and Burke I C (2000) Biogeochemistry in a shortgrasslandscape control by topography soil texture andmicroclimateEcology81 2686ndash2703 doi1018900012-9658(2000)081[2686BIASLC]20CO2

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IPCC (2006) lsquo2006 IPCC Guidelines for National Greenhouse GasInventories Vol 4 Agriculture Forestry and Other Land Usersquo(Eds S Eggleston L Buendia K Miwa T Ngara and K Tanabe)(IGES Japan)

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Jia S and Akiyama T (2005) A precise unified method for estimatingcarbon storage in cool-temperate deciduous forest ecosystemsAgricultural and Forest Meteorology 134 70ndash80 doi101016jagrformet200508014

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Knowles T A and Singh B (2003) Carbon storage in cotton soils ofnorthern New South Wales Australian Journal of Soil Research 41889ndash903 doi101071SR02023

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Lenth R V (2001) Some practical guidelines for effective sample sizedetermination The American Statistician 55 187ndash193 doi101198000313001317098149

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McBratney A B and Webster R (1983b) How many observations areneeded for regional estimation of soil properties Soil Science 135177ndash183 doi10109700010694-198303000-00007

McBratney A B Webster R and Burgess T M (1981) The design ofoptimal sampling schemes for local estimation and mapping ofregionalized variables ndash I Theory andmethodComputersampGeosciences7 331ndash334 doi1010160098-3004(81)90077-7

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Miao Y Robinson C A Stewart B A and Evett S R (2000)Comparison of soil spatial variability in crop and rangeland InlsquoProceedings of the 5th International Conference on PrecisionAgriculturersquo Bloomington Minnesota USA 16ndash19 July 2000(Eds P C Robert R H Rust and W E Larson) pp 1ndash10 (AmericanSociety of Agronomy Madison WI)

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MurphyB RawsonARavenscroft L RankinM andMillardR (2003)lsquoPaired site sampling for soil carbon estimationrsquo National CarbonAccounting System Technical Report No 34 (Australian GreenhouseOffice Canberra)

Myers D E (1991) Pseudo-cross variograms positive-definitenessand cokriging Mathematical Geology 23 805ndash816 doi101007BF02068776

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Papritz A and Webster R (1995b) Estimating temporal change in soilmonitoring II Sampling from simulated fields European Journal ofSoil Science 46 13ndash27 doi101111j1365-23891995tb01809x

Parr J F and Sullivan L A (2005) Soil carbon sequestration in phytolithsSoil Biology amp Biochemistry 37 117ndash124 doi101016jsoilbio200406013

PartonWP SchimelD SColeCV andOjimaDS (1987)Analysis offactors controlling soil organic matter levels in Great Plains grasslandsSoil Science Society of America Journal 51 1173ndash1179

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Piperno D and Becker P (1996) Vegetation history of a site in the centralAmazon basin derived from phytolith and charcoal records from naturalsoils Quaternary Research 45 202ndash209 doi101006qres19960020

Pires L F Rosa J A Pereira A B Arthur R C J and Bacchi O O S(2009) Gamma-ray attenuation method as an efficient tool to investigatesoil bulk density spatial variability Annals of Nuclear Energy 361734ndash1739 doi101016janucene200908016

Poussart J N Ardo J and Olsson L (2004) Verification of soil carbonsequestration sample requirements Environmental Management 33S416ndashS425 doi101007s00267-003-9149-7


Pringle M J and Lark R M (2008) The effects of simple perturbations ofa process model on the spatial variability of its output Geoderma 145267ndash277 doi101016jgeoderma200803014

Rossi J Govaerts A De Vos B Verbist B Vervoort A Poesen JMuys B andDeckers J (2009) Spatial structures of soil organic carbonin tropical forests ndash a case study of Southeastern Tanzania Catena 7719ndash27 doi101016jcatena200812003

Rossiter N A Setterfield S A Douglas M M and Hurley L B (2003)Testing the grass-fire cycle alien grass invasion in the tropical savannas ofnorthern Australia Diversity amp Distributions 9 169ndash176 doi101046j1472-4642200300020x

Saggar S and Hedley C B (2001) Estimating seasonal and annual carboninputs and root decomposition rates in a temperate pasture followingfield 14C pulse-labelling Plant and Soil 236 91ndash103 doi101023A1011942619252

Scarth P Byrne M Danaher T Henry B Hassett R Carter J andTimmers P (2006) State of the paddock monitoring condition andtrend in groundcover across Queensland In lsquoProceedings of the 13thAustralasian Remote Sensing and Photogrammetry ConferencersquoCanberra (Organizer 13th Australasian Remote Sensing andPhotogrammetry Conference Canberra)

Schlesinger W H Reynolds J F Cunningham G L Huenneke L FJarrell W M Virginia R A and Whitford W G (1990) Biologicalfeedbacks inglobaldesertificationScience247 1043ndash1048doi101126science24749461043

Schnabel R R Franzluebbers A J Stout W L Sanderson M A andStuedemann J A (2001) The effects of pasture management practicesIn lsquoPotential of US Grazing Lands to Sequester Carbon and Mitigatethe Greenhouse Effectrsquo (Eds R F Follet J M Kimble and R Lal)(CRC Press LLC USA)

Schoumlning I Uwe Totsche K and Koumlgel-Knabner I (2006) Smallscale spatial variability of organic carbon stocks in litter and solum of aforested Luvisol Geoderma 136 631ndash642 doi101016jgeoderma200604023

Schuman G E Ingram L J Stahl P D Derner J D Vance G F andMorgan J A (2009) Influence of management on soil organic carbondynamics in northern mixed-grass rangeland In lsquoSoil CarbonSequestration and the Greenhouse Effectrsquo SSSA Special Publication 572nd edn pp 169ndash180 (American Society of Agronomy Madison WI)

Skjemstad J O Taylor J A and Smernik R J (1999) Estimation ofcharcoal (Char) in soils Communications in Soil Science and PlantAnalysis 30 2283ndash2298 doi10108000103629909370372

Smucker A JM Park E J Dorner J andHorn R (2007) Soil microporedevelopment and contributions to soluble carbon transport withinmicroaggregates Vadose Zone Journal 6 282ndash290 doi102136vzj20070031

Snedecor G W and Cochran W G (1989) lsquoStatistical Methodsrsquo 8th edn(Iowa State University Press Ames IA)

Sollins P Homann P and Caldwell B A (1996) Stabilization anddestabilization of soil organic matter mechanisms and controlsGeoderma 74 65ndash105 doi101016S0016-7061(96)00036-5

Spain A V Isbell R F and Probert M E (1983) Soil organic matterIn lsquoSoils An Australian viewpointrsquo (Ed CSIRO Australia Division ofSoils) pp 551ndash564 (CSIRO Publishing Melbourne)

Sparling G P (1992) Ratio of microbial biomass carbon to soil organiccarbonas a sensitive indicator of changes in soil organicmatterAustralianJournal of Soil Research 30 195ndash207 doi101071SR9920195

Spijker J Vriend S P and van Gaans P F M (2005) Natural andanthropogenic patterns of covariance and spatial variability of minor andtrace elements in agricultural topsoilGeoderma127 24ndash35 doi101016jgeoderma200411002

Stewart-Oaten A Bence J R and Osenberg C W (1992) Assessingeffects of unreplicated perturbations no simple solutions Ecology 731396ndash1404 doi1023071940685

StroupWW (2002) Power analysis based on spatial effects mixed modelsa tool for comparing design and analysis strategies in the presence ofspatial variability Journal of Agricultural Biological amp EnvironmentalStatistics 7 491ndash511 doi101198108571102780

StuddertGA EcheverriaH E andCasanovas EM (1997) Crop-pasturerotation for sustaining the quality and productivity of a Typic ArgiudollSoil Science Society of America Journal 61 1466ndash1472

Su Y Z Li Y L and Zhao H L (2006) Soil properties and their spatialpattern inadegradedsandygrasslandunderpost-grazing restoration InnerMongolia northern China Biogeochemistry 79 297ndash314 doi101007s10533-005-5273-1

Tyler A N Davidson D A and Grieve I C (2001) In situ radiometricmapping of soil erosion and field-moist bulk density on cultivated fieldsSoil Use and Management 17 88ndash96

van Groenigen J W Siderius W and Stein A (1999) Constrainedoptimisation of soil sampling for minimisation of the kriging varianceGeoderma 87 239ndash259 doi101016S0016-7061(98)00056-1

VandenBygaart A J (2006) Monitoring soil organic carbon stock changesin agricultural landscapes Issues and a proposed approach CanadianJournal of Soil Science 86 451ndash463

VandenBygaart A J and Kay B D (2004) Persistence of soil organiccarbon after plowing a long-termno-tillfield in southernOntario CanadaSoil Science Society of America Journal 68 1394ndash1402

vonLutzowMKoumlgel-Knabner I EkschmittK FlessaHGuggenbergerG Matzner E and Marschner B (2007) SOM fractionation methodsrelevance to functional pools and to stabilization mechanisms SoilBiology amp Biochemistry 39 2183ndash2207 doi101016jsoilbio200703007

WangW J DalalRC andMoodyPW (2004) Soil carbon sequestrationand density distribution in a Vertosol under different farming practicesAustralian Journal of Soil Research 42 875ndash882 doi101071SR04023

Webb N PMcGowan H A Phinn S R Leys J F andMcTainsh G H(2009) A model to predict land susceptibility to wind erosion in westernQueensland Australia Environmental Modelling amp Software 24214ndash227 doi101016jenvsoft200806006

Webster R and Burgess T M (1984) Sampling and bulking strategies forestimating soil properties in small regions Journal of Soil Science 35127ndash140 doi101111j1365-23891984tb00267x

Webster R and Oliver M A (2001) lsquoGeostatistics for EnvironmentalScientistsrsquo (John Wiley amp Sons Ltd Chichester)

Weil R R andMagdoff F (2004) Significance of soil organicmatter to soilquality and health In lsquoSignificance of Soil OrganicMatter to Soil QualityandHealthrsquo (EdsFMagdoff andRRWeil) pp 1ndash43 (CRCPressBocaRaton FL)

Wielopolski L P Drees L R and Nordt L C (2001) Soil carbonmeasurements using inelastic neutron scattering IEEE Transactions onNuclear Science 47 914ndash917 doi10110923856717

WilliamsR JHutleyLBCookGDRussell-Smith JEdwardsA andChen X (2004) Assessing the carbon sequestration potential of mesicsavannas in the Northern Territory Australia approaches uncertaintiesand potential impacts of fire Functional Plant Biology 31 415ndash422doi101071FP03215

Wilson T B and Thompson T L (2005) Soil nutrient distributions ofmesquite-dominated desert grasslands changes in time and spaceGeoderma 126 301ndash315 doi101016jgeoderma200410002

Worsham LMarkewitz D andNibbelink N (2010) Incorporating spatialdependence into estimates of soil carbon contents under different landcovers Soil Science Society of America Journal 74 635ndash646doi102136sssaj20080412

Wuest S B (2009) Correction of bulk density and sampling method biasesusing soil mass per unit area Soil Science Society of America Journal73 312ndash316 doi102136sssaj20080063

Yates F (1981) lsquoSampling Methods for Censuses and Surveysrsquo 4th edn(Griffin London)


Zar J H (1999) lsquoBiostatistical Analysisrsquo 4th edn (Prentice HallInternational Inc Upper Saddle River NJ)

Zhou J and Chafetz H S (2010) Pedogenic carbonates in Texas stable-isotope distributions and their implications for reconstructing region-widepaleoenvironments Journal of Sedimentary Research 80 137ndash150doi102110jsr2010018

Zhao Y Peth S Kruumlmmelbein J Horn R Wang Z Steffens MHoffmann C and Peng X (2007) Spatial variability of soil propertiesaffected by grazing intensity in Inner Mongolia grassland EcologicalModelling 205 241ndash254 doi101016jecolmodel200702019

Zuo X Zhao H Zhao X Zhang T Guo Y Wang S and Drake S(2008) Spatial pattern and heterogeneity of soil properties in sand dunesunder grazing and restoration inHorqin SandyLandNorthernChina Soilamp Tillage Research 99 202ndash212 doi101016jstill200802008

Manuscript received 3 July 2009 accepted 20 May 2010


httpwwwpublishcsiroaujournalstrj

reduce Australiarsquos net greenhouse gas emissions and thuscontribute towards Australia achieving its greenhouse gasemissions targets

Because of its important role the effect of managementpractices onSOCstock (ie the product of SOCconcentration andsoil bulk density and sampling depth) in grazing lands has beenstudied extensively for many years However one issue that hascontinually been encountered by researchers is the high spatialand temporal variability of SOC stock and the difficulties that thiscreates when using statistical techniques to measure relativelysmall differences between land uses or management treatmentsIt is desirable to be able to detect relatively small changes in SOCstock since across large areas of rangelands these can representa substantial sequestration or loss of C In addition being able todetect small SOC changes enables the effect of managementpractices to be assessed within shorter timescales

Numerous and varied approaches have been used whensampling for SOC stock and we are faced with what canbe a confusing array of choices when selecting samplingmethodology Thus there is a need for greater understanding ofthe sampling methodologies available to estimate SOC stock ingrazing lands It is the objective of this review to (i) examine thenature of and reasons for SOC variability (ii) examine thestrengths and weaknesses of the sampling methods commonlyused for SOC stock and (iii) identify knowledge gaps and areasfor future research for SOC measurement in grazing lands

Characteristics of soil C

Soil C consists of organic C as organic matter containing arange of organic materials and inorganic C as carbonates andbicarbonates Organic C stocks are ~1500Gt (1015 g) C andinorganic C stocks are ~720Gt C in the top 1m of soil depth(Batjes 1996)

Soil organic C is heterogeneous in nature and consists ofseveral SOC pools which can be broadly grouped based on theirturnover rates in soil For example Parton et al (1987) postulated3 SOC pools (i) the active or labile C pool (ii) the slow C pooland (iii) the resistant or passive pool These have turnoverperiods of respectively lt10 years 10ndash200 years and gt100 years(Table 1)

The labile pool consists of soluble fresh plant residuesincluding fine roots living organisms (microbial biomass)particulate organic C andor light fraction in varying proportionsof lt5 lt10 and up to 30ndash40 of SOC respectively These aremeasured as soluble and microbial products and root exudatesmicrobial biomass and lt53mm organic C fraction (particulateorganic C) andor light fraction (lt16ndash2 gcm3 density) ofsoil respectively (Parton et al 1987 Cambardella and Elliott1992 Baldock and Skjemstad 1999 Dalal and Chan 2001Franzluebbers and Stuedemann 2003)

Dissolved organic C usually lt1 from root exudatesmicrobial products and plant materials forms the most labilefraction in soil It is transported within the soil profile and in run-off waters to streams and eventually to oceans (Hopkinson andVallino 2005) Within the soil profile it is immediately availableto soil microbes and is rapidly mineralised within hours to daysotherwise it enters into or forms soil microaggregates (Smuckeret al 2007)

Microbial biomassC compriseslt5of theSOC (Dalal 1998)It is considered as a sensitive indicator of SOC changes due toland-use change andor management (Sparling 1992) In mostsoils light-fraction C is essentially similar to particulate organicC and rarely exceeds 30of the total SOCwith turnover periodsof lt10 years in mesic subhumid and semi-arid environments(Dalal and Chan 2001)

Humus or clay-sorbed C forms the slow C pool which variesfrom 30 to 60 depending on soil type clay content claymineralogy and iron and aluminiumoxideswith turnover periodsfrom 10 years to 200 years or more depending on climaticconditions (Parton et al 1987) Three possible mechanisms havebeen suggested for slow turnover rates of this C pool These arechemical nature of SOC with increasing aromaticity increasingspatial inaccessibility to microorganisms and extracellularenzymes due to microaggregation and physical separation andsorption of C on mineral surfaces andor interaction with mineralparticles (Sollins et al 1996 von Lutzow et al 2007)

The resistant or passive SOC pool comprises primarilycharcoal C up to 30 (Skjemstad et al 1999) with turnoverperiods generally gt100 years depending on the charcoal sourceand quality although charcoal C dynamics in soil is not knownA proportion of organo-mineral-metal complexed SOC also

Table 1 Soil carbon (C) pools soil C fractions forms measured and sensitivity to management change

Soil C pool Soil C fraction Pool Ctotal C () Form measured Turnoverperiod (year)

Sensitivity tomanagementchange

Labile (active) CA Soluble fresh residues 05ndash5 Microbial and root exudates lt01 Very rapidA

Living micro- andmeso-flora and fauna

1ndash10 Microbial biomass lt5 RapidAC

Particulate organic C 1ndash40 gt53mm lt10 RapidBDE

Light fraction 1ndash30 lt16ndash2 gcm3 lt10 RapidC

Slow CA Humus 30ndash50 Total organic C ndash particulate organic C 10ndash200 MediumB

Clay-complexed C 30ndash60 lt2mm 10ndash100 MediumC

Resistant (passive) CA Charcoal C 1ndash30 Resistant to chemical oxidation gt100 SlowB

Phytoliths 1ndash30 Oxidised at ~13008C Millenia Very slowFG

Carbonates 0ndash30 Release of CO2 by acid treatment gt1000 Very slowHIJ

AParton et al (1987) BBaldock andSkjemstad (1999) CDalal andChan (2001) DCambardella andElliott (1992) EFranzluebbers andStuedemann (2003) FDreeset al (1989) GParr and Sullivan (2005) HCerling (1984) IDalal and Mayer (1986b) JKnowles and Singh (2003)








Soil bulk density



00

02

04

06

08

10

12

0 5 10 15 20 25 30 35 40 45 50

SOC stock (tha)

Soi

l dep

th (

m)

Dicanthium sericeum







Spatial variability









Scale

Floodplain

Mountaintop

Matrix

Landscape(km wide)



Patchtype B

Patchtype A


Soil C (tha)0 10 20 30 40 50

Soi

l mas

s (t

ha)

0

2000

4000

6000

8000

10 000

12 000

14 000

Soi

l dep

th (

m)

00

02

04

06

08

10





























ms frac141n

Xnifrac141

yi eth1THORN

s2s frac14

1n 1

Xnifrac141



s2s

neth3THORN




ahmh eth4THORN






XHhfrac141



s2st frac14

1n

Xnifrac141

yi2

m2


















s2sy frac14

1J 625

XJjfrac141

d2j eth7THORN






ndash500

Y (

m)

ndash500 0 500

X (m)

ndash500 0 500

500

0

ndash500

500

0

(a) (b)

(c) (d )




as2bs2











gethhTHORN frac14 1









Small

Large


Val

ue

Small

Large

Sem

ivar

ianc

e


0 20 40 60 80 100

Position (m)

Small

Large

h (m)

0 50


0

1

0

1

0

1




SOC BD


BD ndash 0010


BD ndash 0010


BD ndash 0020












X (m)

Y (

m)

ndash500 0 500

ndash500

0

500









p=5807 For ms= 4035


p=1896







d2eth11THORN


n frac14 s2




n





jB2jethB

ethB




gethBBTHORNn

eth15THORN



XHhfrac141


0 5 10 15 20 25 30

00

02

04

06

08

10

n

Pow

er









































of B 1000 1000m

Range (m) b25 25m 1000 1000m

5 0115 009810 0143 009830 0310 009850 0397 0097100 0468 00941000 0347 0085









Conclusion









Acknowledgments


References



















































































































































Soil bulk density



00

02

04

06

08

10

12

0 5 10 15 20 25 30 35 40 45 50

SOC stock (tha)

Soi

l dep

th (

m)

Dicanthium sericeum







Spatial variability









Scale

Floodplain

Mountaintop

Matrix

Landscape(km wide)



Patchtype B

Patchtype A


Soil C (tha)0 10 20 30 40 50

Soi

l mas

s (t

ha)

0

2000

4000

6000

8000

10 000

12 000

14 000

Soi

l dep

th (

m)

00

02

04

06

08

10





























ms frac141n

Xnifrac141

yi eth1THORN

s2s frac14

1n 1

Xnifrac141



s2s

neth3THORN




ahmh eth4THORN






XHhfrac141



s2st frac14

1n

Xnifrac141

yi2

m2


















s2sy frac14

1J 625

XJjfrac141

d2j eth7THORN






ndash500

Y (

m)

ndash500 0 500

X (m)

ndash500 0 500

500

0

ndash500

500

0

(a) (b)

(c) (d )




as2bs2











gethhTHORN frac14 1









Small

Large


Val

ue

Small

Large

Sem

ivar

ianc

e


0 20 40 60 80 100

Position (m)

Small

Large

h (m)

0 50


0

1

0

1

0

1




SOC BD


BD ndash 0010


BD ndash 0010


BD ndash 0020












X (m)

Y (

m)

ndash500 0 500

ndash500

0

500









p=5807 For ms= 4035


p=1896







d2eth11THORN


n frac14 s2




n





jB2jethB

ethB




gethBBTHORNn

eth15THORN



XHhfrac141


0 5 10 15 20 25 30

00

02

04

06

08

10

n

Pow

er









































of B 1000 1000m

Range (m) b25 25m 1000 1000m

5 0115 009810 0143 009830 0310 009850 0397 0097100 0468 00941000 0347 0085









Conclusion









Acknowledgments


References
















































































































































Spatial variability









Scale

Floodplain

Mountaintop

Matrix

Landscape(km wide)



Patchtype B

Patchtype A


Soil C (tha)0 10 20 30 40 50

Soi

l mas

s (t

ha)

0

2000

4000

6000

8000

10 000

12 000

14 000

Soi

l dep

th (

m)

00

02

04

06

08

10





























ms frac141n

Xnifrac141

yi eth1THORN

s2s frac14

1n 1

Xnifrac141



s2s

neth3THORN




ahmh eth4THORN






XHhfrac141



s2st frac14

1n

Xnifrac141

yi2

m2


















s2sy frac14

1J 625

XJjfrac141

d2j eth7THORN






ndash500

Y (

m)

ndash500 0 500

X (m)

ndash500 0 500

500

0

ndash500

500

0

(a) (b)

(c) (d )




as2bs2











gethhTHORN frac14 1









Small

Large


Val

ue

Small

Large

Sem

ivar

ianc

e


0 20 40 60 80 100

Position (m)

Small

Large

h (m)

0 50


0

1

0

1

0

1




SOC BD


BD ndash 0010


BD ndash 0010


BD ndash 0020












X (m)

Y (

m)

ndash500 0 500

ndash500

0

500









p=5807 For ms= 4035


p=1896







d2eth11THORN


n frac14 s2




n





jB2jethB

ethB




gethBBTHORNn

eth15THORN



XHhfrac141


0 5 10 15 20 25 30

00

02

04

06

08

10

n

Pow

er









































of B 1000 1000m

Range (m) b25 25m 1000 1000m

5 0115 009810 0143 009830 0310 009850 0397 0097100 0468 00941000 0347 0085









Conclusion









Acknowledgments


References







































































































































































ms frac141n

Xnifrac141

yi eth1THORN

s2s frac14

1n 1

Xnifrac141



s2s

neth3THORN




ahmh eth4THORN






XHhfrac141



s2st frac14

1n

Xnifrac141

yi2

m2


















s2sy frac14

1J 625

XJjfrac141

d2j eth7THORN






ndash500

Y (

m)

ndash500 0 500

X (m)

ndash500 0 500

500

0

ndash500

500

0

(a) (b)

(c) (d )




as2bs2











gethhTHORN frac14 1









Small

Large


Val

ue

Small

Large

Sem

ivar

ianc

e


0 20 40 60 80 100

Position (m)

Small

Large

h (m)

0 50


0

1

0

1

0

1




SOC BD


BD ndash 0010


BD ndash 0010


BD ndash 0020












X (m)

Y (

m)

ndash500 0 500

ndash500

0

500









p=5807 For ms= 4035


p=1896







d2eth11THORN


n frac14 s2




n





jB2jethB

ethB




gethBBTHORNn

eth15THORN



XHhfrac141


0 5 10 15 20 25 30

00

02

04

06

08

10

n

Pow

er









































of B 1000 1000m

Range (m) b25 25m 1000 1000m

5 0115 009810 0143 009830 0310 009850 0397 0097100 0468 00941000 0347 0085









Conclusion









Acknowledgments


References



























































































































































ms frac141n

Xnifrac141

yi eth1THORN

s2s frac14

1n 1

Xnifrac141



s2s

neth3THORN




ahmh eth4THORN






XHhfrac141



s2st frac14

1n

Xnifrac141

yi2

m2


















s2sy frac14

1J 625

XJjfrac141

d2j eth7THORN






ndash500

Y (

m)

ndash500 0 500

X (m)

ndash500 0 500

500

0

ndash500

500

0

(a) (b)

(c) (d )




as2bs2











gethhTHORN frac14 1









Small

Large


Val

ue

Small

Large

Sem

ivar

ianc

e


0 20 40 60 80 100

Position (m)

Small

Large

h (m)

0 50


0

1

0

1

0

1




SOC BD


BD ndash 0010


BD ndash 0010


BD ndash 0020












X (m)

Y (

m)

ndash500 0 500

ndash500

0

500









p=5807 For ms= 4035


p=1896







d2eth11THORN


n frac14 s2




n





jB2jethB

ethB




gethBBTHORNn

eth15THORN



XHhfrac141


0 5 10 15 20 25 30

00

02

04

06

08

10

n

Pow

er









































of B 1000 1000m

Range (m) b25 25m 1000 1000m

5 0115 009810 0143 009830 0310 009850 0397 0097100 0468 00941000 0347 0085









Conclusion









Acknowledgments


References















































































































































ms frac141n

Xnifrac141

yi eth1THORN

s2s frac14

1n 1

Xnifrac141



s2s

neth3THORN




ahmh eth4THORN






XHhfrac141



s2st frac14

1n

Xnifrac141

yi2

m2


















s2sy frac14

1J 625

XJjfrac141

d2j eth7THORN






ndash500

Y (

m)

ndash500 0 500

X (m)

ndash500 0 500

500

0

ndash500

500

0

(a) (b)

(c) (d )




as2bs2











gethhTHORN frac14 1









Small

Large


Val

ue

Small

Large

Sem

ivar

ianc

e


0 20 40 60 80 100

Position (m)

Small

Large

h (m)

0 50


0

1

0

1

0

1




SOC BD


BD ndash 0010


BD ndash 0010


BD ndash 0020












X (m)

Y (

m)

ndash500 0 500

ndash500

0

500









p=5807 For ms= 4035


p=1896







d2eth11THORN


n frac14 s2




n





jB2jethB

ethB




gethBBTHORNn

eth15THORN



XHhfrac141


0 5 10 15 20 25 30

00

02

04

06

08

10

n

Pow

er









































of B 1000 1000m

Range (m) b25 25m 1000 1000m

5 0115 009810 0143 009830 0310 009850 0397 0097100 0468 00941000 0347 0085









Conclusion









Acknowledgments


References



















































































































































s2sy frac14

1J 625

XJjfrac141

d2j eth7THORN






ndash500

Y (

m)

ndash500 0 500

X (m)

ndash500 0 500

500

0

ndash500

500

0

(a) (b)

(c) (d )




as2bs2











gethhTHORN frac14 1









Small

Large


Val

ue

Small

Large

Sem

ivar

ianc

e


0 20 40 60 80 100

Position (m)

Small

Large

h (m)

0 50


0

1

0

1

0

1




SOC BD


BD ndash 0010


BD ndash 0010


BD ndash 0020












X (m)

Y (

m)

ndash500 0 500

ndash500

0

500









p=5807 For ms= 4035


p=1896







d2eth11THORN


n frac14 s2




n





jB2jethB

ethB




gethBBTHORNn

eth15THORN



XHhfrac141


0 5 10 15 20 25 30

00

02

04

06

08

10

n

Pow

er









































of B 1000 1000m

Range (m) b25 25m 1000 1000m

5 0115 009810 0143 009830 0310 009850 0397 0097100 0468 00941000 0347 0085









Conclusion









Acknowledgments


References














































































































































as2bs2











gethhTHORN frac14 1









Small

Large


Val

ue

Small

Large

Sem

ivar

ianc

e


0 20 40 60 80 100

Position (m)

Small

Large

h (m)

0 50


0

1

0

1

0

1




SOC BD


BD ndash 0010


BD ndash 0010


BD ndash 0020












X (m)

Y (

m)

ndash500 0 500

ndash500

0

500









p=5807 For ms= 4035


p=1896







d2eth11THORN


n frac14 s2




n





jB2jethB

ethB




gethBBTHORNn

eth15THORN



XHhfrac141


0 5 10 15 20 25 30

00

02

04

06

08

10

n

Pow

er









































of B 1000 1000m

Range (m) b25 25m 1000 1000m

5 0115 009810 0143 009830 0310 009850 0397 0097100 0468 00941000 0347 0085









Conclusion









Acknowledgments


References
















































































































































Small

Large


Val

ue

Small

Large

Sem

ivar

ianc

e


0 20 40 60 80 100

Position (m)

Small

Large

h (m)

0 50


0

1

0

1

0

1




SOC BD


BD ndash 0010


BD ndash 0010


BD ndash 0020












X (m)

Y (

m)

ndash500 0 500

ndash500

0

500









p=5807 For ms= 4035


p=1896







d2eth11THORN


n frac14 s2




n





jB2jethB

ethB




gethBBTHORNn

eth15THORN



XHhfrac141


0 5 10 15 20 25 30

00

02

04

06

08

10

n

Pow

er









































of B 1000 1000m

Range (m) b25 25m 1000 1000m

5 0115 009810 0143 009830 0310 009850 0397 0097100 0468 00941000 0347 0085









Conclusion









Acknowledgments


References























































































































































X (m)

Y (

m)

ndash500 0 500

ndash500

0

500









p=5807 For ms= 4035


p=1896







d2eth11THORN


n frac14 s2




n





jB2jethB

ethB




gethBBTHORNn

eth15THORN



XHhfrac141


0 5 10 15 20 25 30

00

02

04

06

08

10

n

Pow

er









































of B 1000 1000m

Range (m) b25 25m 1000 1000m

5 0115 009810 0143 009830 0310 009850 0397 0097100 0468 00941000 0347 0085









Conclusion









Acknowledgments


References



















































































































































p=5807 For ms= 4035


p=1896







d2eth11THORN


n frac14 s2




n





jB2jethB

ethB




gethBBTHORNn

eth15THORN



XHhfrac141


0 5 10 15 20 25 30

00

02

04

06

08

10

n

Pow

er









































of B 1000 1000m

Range (m) b25 25m 1000 1000m

5 0115 009810 0143 009830 0310 009850 0397 0097100 0468 00941000 0347 0085









Conclusion









Acknowledgments


References



















































































































































































of B 1000 1000m

Range (m) b25 25m 1000 1000m

5 0115 009810 0143 009830 0310 009850 0397 0097100 0468 00941000 0347 0085









Conclusion









Acknowledgments


References





























































































































































of B 1000 1000m

Range (m) b25 25m 1000 1000m

5 0115 009810 0143 009830 0310 009850 0397 0097100 0468 00941000 0347 0085









Conclusion









Acknowledgments


References




















































































































































Conclusion









Acknowledgments


References

















































































































































Acknowledgments


References


































































































































































































































































































































































































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