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1、ecological modelling 2 0 9(2 0 0 7)264276available at journal homepage: local spatial autocorrelation to compareoutputs from a forest growth modelMichael A.Wuldera,Joanne C.Whitea,Nicholas C.Coopsb,Trisalyn Nelsonc,Barry BootsdaCanadian Forest Service(Pacific Forestry Centre),Natural Resources Canad
2、a,Victoria,British Columbia,Canada V8Z 1M5bUniversity of British Columbia,Department of Forest Resource Management,Vancouver,British Columbia,Canada V6T 1Z4cUniversity of Victoria,Department of Geography,Victoria,British Columbia,Canada V8W 3P5dWilfrid Laurier University,Department of Geography and
3、Environmental Studies,Waterloo,Ontario,Canada N2L 3C5a r t i c l ei n f oArticle history:Received 26 July 2006Received in revised form19 April 2007Accepted 29 June 2007Published on line 17 August 2007Keywords:Physiological model3PGLAIStand volumeLocal spatial autocorrelationGetis statistica b s t r
4、a c tComparing model outputs is a critical precursor to successfully applying models to environ-mental issues.In this paper,we applied a calibrated physiological model(3PG)and predictedtwo fundamental forest growth attributes(leaf area index(LAI)and stand volume).As partof this simulation,we systema
5、tically changed two key model input parameters(soil waterholdingcapacityandsoilfertilityrating)andcomparedthemodeloutputsutilisingamethodthat accounts for local spatial autocorrelation.The use of the Getis statistic(Gi*)providesinsights on the spatial ramifications of an aspatial change to model inp
6、uts.Specifically,thelocation of significant Gi*values identified areas where the differences in LAI and standvolume occur and are spatially clustered.When soil water is doubled and soil fertility isunchanged,both LAI and stand volume increase;conversely,when soil water is doubledand soil fertility i
7、s halved,both LAI and stand volume decrease.The increase and decreasein these model outputs occurred differentially across the study area,although there is asimilar pattern to the location of the significant Gi*values(p=0.10)in both LAI and standvolume outputs,for each model scenario.Analyzing the l
8、ocal spatial autocorrelation of thedifferences between model outputs identified those areas that have systematic sensitivityto specific model inputs.This information may then be used to aid in the interpretation ofmodel outputs,or to direct the collection of additional data to refine model predictio
9、ns.2007 Published by Elsevier B.V.1.IntroductionThe past 10 years have seen significant new developmentsin the use of models investigating carbon dynamics interrestrial ecosystems.In addition,recent advances in soft-ware and hardware technology have dramatically increasedopportunities to undertake s
10、imulations and compare modelassumptions and behaviours in a consistent and standardizedCorresponding author at:506 West Burnside Road,Victoria,British Columbia,Canada V8Z 1M5.Tel.:+1 250 363 6090;fax:+1 250 363 0775.E-mail address:mwuldernrcan.gc.ca(M.A.Wulder).way.The comparison of model outputs is
11、 therefore becomingan important,if not a critical step,in developing,testing,andultimately applying models to environmental issues.In basic situations where the same model framework isapplied,yet input variables are varied(resulting in a rangeof output predictions),it is possible to simply subtract
12、orratio the two model predictions,and observe and analysethe differences in the predictions.In this paper,we describe0304-3800/$see front matter 2007 Published by Elsevier B.V.doi:10.1016/j.ecolmodel.2007.06.033ecological modelling 2 0 9(2 0 0 7)264276265and apply a method of model comparison that a
13、llows aninvestigation of the differences in predictions,as well as thespatial patterns associated with the differences.The methodemployed is a measure of local spatial autocorrelation,whichindicateswhetherthedifferencesbetweenthecontrolandthemodelscenarioswererandomlylocatedoverthestudyarea,orfollow
14、edsomespatialpattern,therebyindicatingsomeunder-lying physical or ecological process.To develop and demonstrate the approach of using a mea-sure of local spatial autocorrelation for comparison of modeloutputs,we examined predictions from a process-basedmodel that simulates the growth of forest stand
15、s in terms ofthe underlying physiological processes.Process-based mod-els are typically driven by climatic data and constrained bysoil properties that affect the storage and availability of waterand nutrients(see review by Makela et al.,2000).These mod-els assume that primary production can be descr
16、ibed in termsof radiation interception,photosynthesis,and carbon alloca-tion(Landsberg and Gower,1997).A key advantage of thesetypes of light-use interception models is that by modeling theunderlying physiological processes,the model can be appliedat many locations over a landscape.In addition,by ut
17、ilizingactual meteorological and environmental conditions,changesin forest structure resulting from climate change,manage-ment,or other effects,may also be modeled.Landsberg andWaring(1997)developed a deterministic forest growth model,3PG(Physiological Principles for Predicting Growth)based ona numb
18、er of established biophysical relationships and con-stants.3PGdiffersfrommostprocessmodelsinthatitpredictsstand properties measured by foresters(tree density,basalarea,mean diameters,standing volume,and mean annualincrement),as well as those of interest to ecologists(carbonallocation and water balan
19、ce).In this paper,we applied a calibrated version of the 3PGphysiological model and predicted two fundamental forestgrowth attributes(leaf area index(LAI)and stand volume)forponderosa pine(Pinus ponderosa Doug.ex Loud).As part of thissimulation,we systematically changed two key model inputparameters
20、(soil water holding capacity and soil fertility rat-ing)and compared the model outputs utilising a method ofmodel comparison that accounts for local spatial autocorre-lation.Our objective was to determine how aspatial changesin model inputs manifest spatially in the model outputs,ormore specifically
21、,were there spatial locations of systematicmodel sensitivity to aspatial changes in model inputs?Theadvantages of using this type of approach are then discussed.2.Study area,data,and methodsThe study area for this investigation is located on the westerncoast of the United States and spans the states
22、 of Washington,Oregon,and Northern California(Fig.1).Within this region,ponderosa pine represents the major forest type,occurringin nearly pure stands in a 1530km wide band along theeastern flanks of the Cascade Mountains where annual pre-cipitation is generally between 300 and 800mm.Historically,gr
23、ound fires at 820 year intervals maintained the ponderosapine forest type free of other potential competing conifers.However,on more moist sites,ponderosa pine occurs in amixturewithDouglasfir(Pseudotsugamenziesii(Mirb.)Franco),grand fir(Abies grandis(Dougl.)Lindl.),and other conifers.Onmore arid si
24、tes,juniper(Juniperus occidentalis Hook.)and/orsagebrush(Purshia tridentata(Pursh)D.C.)replace ponderosapine as drought becomes more severe and fires more frequent(Franklin and Dyrness,1973).Today,ponderosa pine occupiesan extensive range,yet it maintains an ecologically precari-ous position,constra
25、ined to the east by more arid conditionsthat favour juniper woodlands,to the west by mountains withmore moderate precipitation that favour a mixture of otherconifers,and by elevation,where heavy snow loads can dam-age ponderosa pine branches(Waring et al.,1975).Ponderosapine,along with Douglasfir,ha
26、s served as a basis for eval-uating growth potential across a wide range of forests in thewestern United States(e.g.,Waring et al.,2002).The ecologicaldistributions and growth of ponderosa pine is therefore crit-ically important(Franklin and Dyrness,1973 and see specialissue on“The ponderosa pine ec
27、osystem and environmentalstress:past,present,and future”published in Tree Physiol.vol.21,2001)and monitoring the current and future distributionof species in this region is a high priority for forest resourcemangers concerned with future forest distribution and pro-ductivity(Coops et al.,2005).2.1.T
28、he 3PG modelAll ecosystem models are simplified versions of reality withthe choice of which process based model to utilize beingdependentupontheirinputandoutputparameters,minimumspatial and temporal units of operation,maximum spatialextent and time period of application(Nightingale et al.,2004).In a
29、ddition,the scale at which the model operates(leaftree,plotstand,regional and ecosystem levels)is also critical,withmodel complexity generally decreasing as the time-step andspatial extent of model operation increases(Nightingale etal.,2004;Coops et al.,2005).Given the large spatial extent ofthe stu
30、dy area,and the subsequent requirement for coarsespatial resolution input data we believe a monthly time step,stand-level,process based model is an appropriate choice forour analysis.Within this specification a number of processbased models exist(Nightingale et al.,2004)including HYBRID(Friend et al
31、.,1997),FOREST-BGC(Running and Coughlan,1988),BIOME-BGC(Running and Hunt,1993)amongst others).There are however two features that together distinguish 3PGfrom all other process-based models(some share one feature)include(Landsberg et al.,2003):The simplifying assumption that respiration is a fixed f
32、ac-tion of gross photosynthesis(Waring et al.,1998;Gifford,2003).This simplification removes the difficulty in pre-dicting belowground growth,protein turnover rates,andseparating carbon dioxide generated by microbial activity.Detailed forest inventory variables are readily predicted bythe 3PG model(
33、such as standing volume)and indirectlysupport its simplifying assumptions.Confidence in the 3PGstructure and function is gained as it accurately predictsmeasured change in LAI,litterfall,stocking density,basalarea,andmeantreediameters,inadditiontoannualgrowthin managed and unmanaged stands(Landsberg
34、 et al.,2003).266ecological modelling 2 0 9(2 0 0 7)264276Fig.1 Extent of the study area in the Pacific Northwest with a Digital Elevation Model(DEM).We therefore have confidence that the 3PG model occupiesthe middle ground between conventional mensuration-basedgrowth and yield models,and process-ba
35、sed carbon balancemodels(LandsbergandWaring,1997).Detailedinformationonthe 3PG is available(Landsberg and Waring,1997;Landsberget al.,2003);however,for completeness a short overviewis provided here.3PG is a monthly time step model whichrequires average daily short-wave incoming radiation for eachmon
36、th,daily mean vapor pressure deficits(D),temperatureextremes,total monthly precipitation,and estimates of soilwaterstoragecapacity(mm)andsoilfertility.Absorbedphoto-synthetically active radiation(APAR)is estimated from globalsolar radiation and LAI;the utilized portion,APARu,is calcu-lated by reduci
37、ng APAR by an amount determined by a seriesof modifiers that take values between 0(system shutdown)and 1(no constraint)to limit gas exchange via canopy stom-atal conductance(Landsberg and Waring,1997).The modifiersinclude:(a)high averaged daytime D,(b)the frequency of sub-freezingconditions,and(c)so
38、ildrought.LimitationsonAPARuareimposedeachmonthbythemodifierwiththelowestvalue.Drought limitations are imposed as a function of soil texturewhen the total monthly precipitation and soil water sup-ply is significantly less than transpiration estimated with thePenmanMonteith equation.Gross primary pro
39、duction(PG)iscalculated by multiplying APARu by a canopy quantum effi-ciency coefficient(),with a maximum value set by the soilfertility ranking and reduced monthly when mean tempera-tures are suboptimal for photosynthesis and growth.A majorsimplification in the 3-PG model is that it does not requir
40、edetailed calculation of respiration from knowledge of rootturnover,but rather assumes that autotrophic respiration(Ra)and total net primary production(PN)in temperate forests areapproximately fixed fractions(0.53 and 0.47,S.E.0.04)of PG(Landsberg and Waring,1997,Waring et al.,1998;Law et al.,2000a)
41、.The model partitions PN into root and abovegroundbiomass.The fraction of total PN allocated to root growthincreases from 0.25 to 0.6 as the ratio APARu/APAR decreasesfrom 1.0 to 0.2.Under more favourable climatic conditions,the fraction of photosynthate allocated to roots increases withinfertility
42、of the soil(Landsberg and Waring,1997).The role of nutrition is an important variable within 3PGhowever our capacity to link soil nutrient status within quan-ecological modelling 2 0 9(2 0 0 7)264276267titative models of plant growth is limited(Landsberg et al.,2003).This is partly due to a lack of
43、good quality spatialinformation about soil physical and chemical properties,andsecond,the characterisation of simple relationships betweenstandard measures of soil fertility and tree growth is diffi-cult and depends upon geochemical cycling(see Waring andSchlesinger,1985;LandsbergandGower,1997;andWa
44、ringandRunning,1998),particularly in relation to nitrogen.As a resultin 3PG,although chemical analyses may provide a guide to fer-tility ranking,a degree of expert knowledge is required.Thefertility ranking therefore(set between 0 and 1)can be usedas a tuneable parameter in the model(Landsberg et al
45、.,2003)andscaledaccordingtotheinformationonsoilnutrientstatusavailable at a site or across a region.3-PG(and variations of this model)has been used exten-sively to model the productivity of a wide range of forest typesacross regions of North America including:ponderosa pine(Law et al.,2000a,2000b);l
46、odgepole pine(Pinus contorta Dougl.ex Loud.var.latifolia Engelm.)(Hall et al.,2006);loblolly pine(Pinus taeda)(Landsberg et al.,2000);Douglasfir(Coops et al.,2005);and jack pine(Pinus banksiana)(Peng et al.,2002).Modelproductivity estimates have exhibited a high degree of accu-racy when compared to
47、site index data and in addition,themodel water balance has been shown to accurately demon-strate the general trends in regional soil water depletion usinglimited monthly climate datasets(Coops et al.,2001a;Coopsand Waring,2001a;Coops et al.,2001b;Coops and Waring,2001b).2.2.Input dataWhile many agen
48、cies are routinely producing average cli-mate surfaces over large spatial areas using state of the artmathematical modeling approaches such as DAYMET in theUnited States(Thornton et al.,1997;Thornton and Running,1999),and spline fitting in Canada(McKenney et al.,2001),theinclusion and integration of
49、 soil information is an ongoingissue.Information on soil fertility and soil water holding capacityis critically important to models of plant production;however,consistent data on soil properties at a fine spatial resolutionis typically unavailable for many regional studies.Soils mapsdelineated at sc
50、ales of 1km2or coarser generally mask sig-nificant spatial variation in physical and chemical properties.Even with more precise mapping the fertility of forest soilswould be difficult to judge as the same soil type may be com-merciallyfertilized,maysupportnitrogen-fixingvegetation,orreceive signific