Processes influencing model data mismatch in drought

Processes influencing model‐data mismatch in drought‐stressed,fire‐disturbed eddy flux sites

Stephen Mitchell,1 Keith Beven,2,3 Jim Freer,4 and Beverly Law5

Received 15 September 2009; revised 12 November 2010; accepted 14 January 2011; published 7 May 2011.

[1] Semiarid forests are very sensitive to climatic change and among the most difficultecosystems to accurately model. We tested the performance of the Biome‐BGC modelagainst eddy flux data taken from young (years 2004–2008), mature (years 2002–2008),and old‐growth (year 2000) ponderosa pine stands at Metolius, Oregon, andsubsequently examined several potential causes for model‐data mismatch. We used theGeneralized Likelihood Uncertainty Estimation methodology, which involved 500,000model runs for each stand (1,500,000 total). Each simulation was run with randomlygenerated parameter values from a uniform distribution based on published parameterranges, resulting in modeled estimates of net ecosystem CO2 exchange (NEE) that werecompared to measured eddy flux data. Simulations for the young stand exhibited thehighest level of performance, though they overestimated ecosystem C accumulation(−NEE) 99% of the time. Among the simulations for the mature and old‐growth stands,100% and 99% of the simulations underestimated ecosystem C accumulation. Oneobvious area of model‐data mismatch is soil moisture, which was overestimated by themodel in the young and old‐growth stands yet underestimated in the mature stand.However, modeled estimates of soil water content and associated water deficits did notappear to be the primary cause of model‐data mismatch; our analysis indicated that grossprimary production can be accurately modeled even if soil moisture content is not.Instead, difficulties in adequately modeling ecosystem respiration, mainly autotrophicrespiration, appeared to be the fundamental cause of model‐data mismatch.

Citation: Mitchell, S., K. Beven, J. Freer, and B. Law (2011), Processes influencing model‐data mismatch in drought‐stressed,fire‐disturbed eddy flux sites, J. Geophys. Res., 116, G02008, doi:10.1029/2009JG001146.

1. Introduction

[2] A predictive science of atmosphere‐biosphere inter-actions is essential for an understanding of how climaticchange will alter earth’s ecosystems and the continuedprovision of ecosystem services, but this has not yet beenachieved [Moorcroft, 2006]. As a result, the future of theglobal C cycle is a matter of ongoing debate, and a dis-agreement remains about whether earth’s surface will becomea source or sink of atmospheric CO2 in the coming century[Cox et al., 2000; Friedlingstein et al., 2003; Moorcroft,2006; Sitch et al., 2008]. Fortunately, long‐term studies ofnet ecosystem CO2 exchange throughout a wide variety ofbiomes [Baldocchi, 2008] hold significant potential forunderstanding terrestrial ecosystems and their role in miti-

gating or exacerbating current and future atmospheric CO2

concentrations.[3] Net ecosystem CO2 exchange, hereafter referred to as

NEE, is the net exchange of CO2 between ecosystems and theatmosphere, calculated as the difference between gross pri-mary production and ecosystem respiration, excluding lossesof respiration‐derived dissolved inorganic carbon [Chapinet al., 2006]. Note that our use of NEE, based on Chapinet al. [2006], is almost identical to net ecosystem produc-tion, NEP, except with signs reversed (−NEE ∼= NEP),where a negative NEE represents a transfer of atmospheric Cto a terrestrial ecosystem. Continuous field measurements ofNEE have been taken from over 400 locations using theeddy covariance method and offer a valuable baselineagainst which model assumptions, parameters, and perfor-mance can be ascertained [Schulz et al., 2001; Wang et al.,2001; Thornton et al., 2002; Braswell et al., 2005; Knorrand Kattge, 2005; Sacks et al., 2006]. Employing NEE asa metric against which terrestrial ecosystem model perfor-mance can be tested is useful for constraining estimates ofC cycling, and not just because it gives an estimate of netgain (or loss) of C for a terrestrial ecosystem. NEE is,however, a derived variable, dependent upon uncertainty inthe estimation of other metrics of the C cycle such as gross

1Nicholas School of the Environment, Duke University, Durham, NorthCarolina, USA.

2Lancaster Environment Centre, Lancaster University, Lancaster, UK.3Department of Earth Sciences, Uppsala University, Uppsala, Sweden.4School of Geographical Sciences, University of Bristol, Bristol, UK.5Department of Forest Ecosystems and Society, College of Forestry,

Oregon State University, Corvallis, Oregon, USA.

Copyright 2011 by the American Geophysical Union.0148‐0227/11/2009JG001146

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116, G02008, doi:10.1029/2009JG001146, 2011

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http://dx.doi.org/10.1029/2009JG001146

primary production, autotrophic respiration, and heterotro-phic respiration. Potential sources of model failure, there-fore, are numerous and interdependent, as errors producedin one step almost inevitably lead to a propagation of errorscarried into a succeeding step.[4] One way to ascertain the extent of these uncertainties

is through a model‐data synthesis. Model‐data synthesis,according to Raupach et al. [2005], operates under theassumption that the inherent uncertainties in any data set arejust as important as the data values and should thereby beincluded in both parameter estimation and data assimilation.For an ecosystem model (or any environmental model), thisuncertainty lies not just with the observed data but also withthe parameters on which the data are conditioned, affectingboth the predictive uncertainty of a model‐data synthesis andthe predicted best estimate. An effective analysis of theseuncertainties requires an acknowledgment of the potentialfor equifinality in model predictions. The concept of equi-finality implies that, within the current capacity of mecha-nistic modeling, there may be many model structures anddifferent parameter sets for a particular ecosystem process,representing different hypotheses about system functioning,that may be acceptable in reproducing the observed behaviorof an environmental system [Beven, 2002, 2006]. Given thelimitations of observed data to fully represent the naturalsystem, the approximate process descriptions within models,the temporal propagation of model/data errors, and lack ofindependent estimates of the effective parameter values by amodel, it may not be possible to determine the most plausiblehypothesis. However, by exploring a range of model pre-dictions, parameter combinations that fail to predict observedresponses adequately can be rejected and hence classed asunacceptable hypotheses.[5] Semiarid forest ecosystems are a particularly inter-

esting case for testing hypotheses about system functioningand pose a difficult challenge for the production of accurateecosystem simulations. Fluctuations in above or below-ground biomass, physiological characteristics of vegetation,or community composition that may be insignificant in moremesic, more productive ecosystems, can have substantialfeedbacks that affect water balances and other ecosystemprocesses [Kremer and Running, 1996]. Additionally, minorvariations in precipitation, potential evapotranspiration, andother environmental factors may significantly alter com-munity phenology and productivity [Kremer and Running,1996]. Even though they do not represent a particularlylarge carbon pool compared to more mesic ecosystems, theyare nevertheless significant in global change studies becauseof their vulnerability to a changing climate, particularlydrought [Fischlin et al., 2007]; extended water deficits inponderosa pine woodlands in New Mexico have beenobserved to result in widespread tree mortality, producinglandscape‐level shifts to pinyon‐juniper woodland [Allenand Breshears, 1998]. Further drought in this region haseven resulted in a widespread mortality of Pinyon pine, aspecies that is already highly drought‐resistant [Breshearset al., 2005].[6] Research at the Metolius sites indicates that the old‐

growth site is less sensitive to drought, and the mature andyoung pine sites experience seasonal water stress beginningin June/July that triggers a rapid decline in net carbonuptake associate with gross primary production (GPP) lev-

eling off while total ecosystem respiration (TER) continuesto increase. GPP responds to the onset of seasonal droughtsooner than TER at these sites. Seasonal and diel analysis ofGPP, water use efficiency and transpiration indicates thatthe young site experiences seasonal drought earlier and to amore severe degree, presumably because the younger standhas a shallower root system [Thomas et al., 2009; Vickerset al., 2009].[7] The accurate simulation of such coupled climate‐

ecosystem changes is challenging and will depend on anumber of different factors: the forcing data used to drive anecosystem model (whether they come from observations orclimate predictions), the initial conditions and disturbancehistory at the site, the limitations of the process representa-tions in a model based on current understanding, the effectiveparameter values provided to the model, and the limitationsof any observational data used to evaluate the model. Theseare all sources of uncertainty in simulations and their influ-ence will depend on the ecosystem type and the spatiotem-poral scale of the simulation.[8] Our goals in this study were twofold. First, we ana-

lyzed the extent to which equifinality in parameter valuescan influence the reproduction of ecosystem processes in awidely used terrestrial ecosystem model. We examined thisby performing multiple simulations (500,000) with multiplecombinations of ecophysiological parameter values withinplausible parameter ranges for a young (∼20 years old),mature (∼90 years old) and old‐growth stand (>250 yearsold). Second, we analyze these results to determine the keyecosystem processes that are responsible for any model‐datamismatch in these semiarid forests over multiple years ofdata.

2. Materials and Methods

2.1. The GLUE Methodology

[9] The Generalized Likelihood Uncertainty Estimation(GLUE) methodology [Beven and Binley, 1992] wasdeveloped from the generalized sensitivity analysis of Spearand Hornberger [1980] to assess the possibility that morethan one unique parameter set for a given environmentalmodel may provide good (behavioral) predictions. Studiesof parameter responses have shown that the assumption ofa single well‐defined optimal parameter set rarely holds,resulting in model equifinality, where many parameter setcombinations give similar predictions of observed responses[Freer et al., 1996; Franks et al., 1997; Beven and Freer,2001; Schulz et al., 2001; Beven, 2006]. GLUE provides ameans of assessing the predictive uncertainty of a model bycomparing simulations to available observations using aperformance measure within a Monte Carlo framework.GLUE has been used for a wide range of environmentalmodeling problems [see Beven and Freer, 2001; Freer et al.,2004; Beven, 2006], including the prediction of CO2 fluxdata [Franks et al., 1997; Schulz et al., 2001], tree mortalityunder drought conditions [Martínez‐Vilalta et al., 2002] andforest fires [Piñol et al., 2004, 2007]. Application of theGLUE method involves a large number (typically >100,000)of model simulations, each of which is characterized by a setof randomly sampled parameters usually drawn from uni-form (noninformative) prior distributions across the rangeof each parameter since information regarding the likely

MITCHELL ET AL.: PROCESSES CAUSING MODEL‐DATA MISMATCH G02008G02008

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effective parameter values is normally highly limited orunknown (Figure 1). The performance of each run isthereafter deemed behavioral or nonbehavioral based uponthe comparison of simulated versus observed data. Modelruns that do not meet specified acceptability criteria arerejected as nonbehavioral and are thus given zero likeli-hood, removing them from further analysis [Beven, 2006].Within GLUE, a model as hypothesis is always associatedwith a set of parameter values. Retained parameter sets canstill exhibit a wide spread of values and the associatedsimulated responses can be quite variable between param-eter sets over the simulated period. The sensitivity of modelparameters and the interactions between the parametersdetermines the variability in the posterior likelihoods of theparameter sets.

2.2. Evaluation of Parameter Sensitivities

[10] In a complex model such as Biome‐BGC it is in-evitable that many randomly generated parameter sets willresult in a simulation that is physiologically unsustainable,thus simulations that had an annual GPP of less than 10 g Cm−2 yr−1 were excluded from additional analysis a priori.Once we screened parameter combinations that resulted innonliving simulations, we calculated the resultant likelihood

weights for the remaining simulations using the followingequation:

L QjjY� �

¼PJ

j¼1

PIi¼1 Ci

o � Ci;jm

� �2� �PI

i¼1 Cio � Ci;j

m� �2� � ð1Þ

where Coi is observed NEE for day i, and Cm

i,j is modeledNEE of day i for parameter set j, and L(QjjY ) is the likeli-hood of simulating data Y given parameter set Qj. Note thatwe do not consider simulations that are merely “living” to beindicative of satisfactory model performance. Until theapplication of an additional performance criteria, we onlyconsider them to be worthy of further analysis.[11] Our method is similar to the sensitivity analysis of

Spear and Hornberger [1980] except that there is an addi-tional step of calculating a likelihood weight for eachparameter set. Equation (1) is calculated on a daily time stepfor the extent of the available data, which in this study iscomposed of carbon flux data measured by the eddy covari-ance technique for the years simulated (2004–2008 for theyoung stand, 2002–2008 for the mature stand, and 2000 forthe old‐growth stand).[12] We imposed an additional criterion for what would

be considered a satisfactory model performance in relation

Figure 1. Schematic of the GLUE procedure.


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to inherent errors in the observed data. We did this bycomparing annual estimates of NEE from the model toestimates obtained from field measurements. We used thecoefficient of variation (cv) to represent the uncertainty inannual estimates of NEE. The term cv (calculated as s/m) isbased on the coefficient of variation calculated for annualNEE estimates and includes estimates of errors incurred bythe instrumentation used in the eddy covariance technique,gap‐filling, as well as spatial and temporal variability[Oren et al., 2006; Thomas et al., 2009]. This “effectiveobservation error” criterion is an example of the approachto model evaluation proposed by Beven [2006] but theconcept of including observational uncertainties to con-struct model performance criteria has been applied previ-ously [Page et al., 2003; Freer et al., 2004]. Mean annualNEE is calculated for the years during which the model‐data synthesis was performed (2004–2008 for the youngstand, 2002–2008 for the mature stand, and 2000 for theold‐growth stand). Modeled estimates of annual NEE forthose years are deemed to be satisfactory if they fall withinthe bounds of uncertainty (mean annual NEE ± cv).

2.3. Parameter Estimates

[13] Biome‐BGC requires 37 ecophysiological parametervalues for the simulation of evergreen needleleaf forests. Ofthese 37, 13 were allowed to vary (Table 1) assumingindependent uniform prior distributions across feasibleranges of the parameters in the absence of any stronginformation about effective parameter values and theircovariation. White et al. [2000] performed a sensitivityanalysis of model parameters, showing that LAI, FLNR, andC:Nleaf were among the most sensitive parameters, and thesewere some of the parameters we included. Additionalselection of parameters that were allowed to vary was basedon the range in variation of parameters in the literature. Forinstance, parameters with a wide range of variability, suchas FRC:LC, were chosen for this reason, and literaturevalues that exhibited little to no variability were likewiseexcluded. Our study site has a canopy comprised primarily ofPinus ponderosa, a species with input parameters that aregenerally provided in the compilation byWhite et al. [2000],many of which were also available from site measurements.Each parameter range was subsequently expanded to allowfor the possibility of yet‐unpublished values that may bepresent in the field. However, it must also be stressed that

field observations may not be commensurate with theeffective parameter values required in a particular modelstructure to give a good fit to the observed carbon flux data.

2.4. Study Sites

[14] The Metolius Research National Area is locatedapproximately 64 km north of Bend, Oregon. Net ecosystemCO2 exchange data for the young stand at Metolius werecollected from 2004 to 2008. Data from the mature stand atMetolius were collected 2002–2008, and data for the old‐growth stand were collected in 2000. The young stand isrecovering from a clear‐cut performed in 1987 while themature stand is recovering from a harvest in ∼1905. Allsites are dominated primarily by Ponderosa pine (Pinusponderosa) and have a complex disturbance history. Pon-derosa pine forests in central Oregon typically are subject tofrequent, low‐severity wildfires that occur naturally approx-imately every 16 years [Bork, 1985]. High‐severity firesoccur with considerably less frequency. In the old‐growthstand at Metolius, a stand replacing fire appears to haveoccurred in 1750, killing 99% of all overstory trees in thestand. Additional moderate severity burns occurred in 1850and 1950. More recently, anomalously warm, dry years(1985–1994, 2000–2005) contributed to regional droughtstress [Thomas et al., 2009]. Low‐intensity underburns wereimplemented in small areas of the old‐growth forest (e.g.,1 ha) at the Research Natural Area since the 1950s. The agedistribution in the tower footprint at the time of eddycovariance measurements was ∼50% mixed age (45 and250 years), 25% young (45 years) and 25% pure stands ofold trees (250+) [Law et al., 1999]. Soils are well drained.Descriptions of site‐specific data are referred to as they were

Table 1. Biome‐BGC Parameters Randomly Sampled Between Limitsa

Symbol Variable Estimated Literature Values Measured Values

FM annual leaf and fine root turnover fraction (1/yr) 0.1–0.9 0.25FRC:LC new fine root C: new leaf C (ratio) 0.1–6.0 3.0SC:LC new stem C: new leaf C (ratio) 0.2–2.0 0.96CRC:NSC new croot C: new stem C (ratio) 0.2–0.5 N/AC:Nleaf C:N of leaves (kgC/kgN) 20–90 53.53C:Nlitter C:N of leaf litter, after retranslocation (kgC/kgN) 90–150 88.6C:Nfine root C:N of fine roots (kgC/kgN) 20–90 79C:Ndead wood C:N of dead wood (kgC/kgN) 200–1800 330LAI canopy average specific leaf area, projected area basis (m2/kgC) 0.5–4.0 2.25FLNR fraction of leaf N in Rubisco (unitless) 0.01–0.15 N/Agsmax maximum stomatal conductance, projected area basis (m/s) 0.002–0.012 0.008Ys leaf water potential: start of conductance reduction (MPa) −0.85 to −0.2 −1.5Yc leaf water potential: complete conductance reduction (MPa) −2.3 to −0.9 N/A

aFor description of data collection procedures, see Law et al. [2003].

Table 2. Site Characteristics for the Metolius AmeriFlux SitesSimulated

Young Stand Mature Stand Old Stand

Latitude 44.32 44.45 44.49Longitude −121.61 −121.56 −121.62Elevation 1008 m 1253 m 915 mAnalysis period 2004–2008 2002–2008 2000Stand age(90th percentile)

23 90 250

Overstory LAI 1.1 m2 m−2 2.8 m2 m−2 2.1 m2 m−2

Dominant species ponderosa pine ponderosa pine ponderosa pineSoil texture sandy loam sandy loam sandy loam


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during the time in which the system was simulated. Addi-tional site characteristics are summarized in Table 2.

2.5. Modeling Protocol

[15] All simulations used version 4.1.2 of the Biome‐BGC model [Thornton et al., 2002], a widely used terrestrialecosystem model. Biome‐BGC simulates water, carbon, andnitrogen dynamics in plants, litter, and soil, using a dailytime step for all processes [Running and Coughlin, 1988;White et al., 2000]. Biome‐BGC allows for the option of aspin‐up simulation to serve as a basis for an initial estimateof soil C content. Spin‐up time is determined by the amountof time it takes to allow soil C to reach equilibrium[Thornton and Rosenbloom, 2005]. We incorporated thesame randomly generated parameter values in the spin‐upsimulations for each of our GLUE analysis simulations.Among the young and mature stands, we incorporated arepresentation of the stand’s disturbance history into theregular (non‐spin‐up) simulations. Our methodology for thiswas similar to, but not an exact replicate of, the methodol-ogy developed by Law et al. [2001].[16] The incorporation of disturbance history for the old‐

growth stand was more complex. Thornton et al. [2002]report a disturbance history involving a stand replacing(∼99% mortality) fire in 1750, a medium‐severity fire(∼25% mortality) in 1850, and another medium‐severity fire(∼25% mortality) in 1950. We incorporated this disturbancehistory by running the spin‐up simulation and then begin-ning the normal simulation in the year 1750. The simulationwas then run for 100 years until 1850, at which point adisturbance resulted in a stem mortality of between 20 and30% (to account for the uncertainty in the disturbanceseverity estimate of 25%). The mortality percentage gener-ated for the disturbance in 1850 was then multiplied by theestimates of stem C to estimate the contribution of newlydead stem C and leaf C to the coarse woody debris and litterpools, respectively. Next, a new initialization file was gen-erated that incorporated these estimates of newly createdcoarse woody debris C and litter C, which were then addedto the pools left over from the simulation before the fire.The amount of stem C and leaf C remaining after the dis-turbance was calculated by multiplying the amount of leaf Cremaining after the simulation to 1850 (1 ‐ disturbancemortality fraction) and was also incorporated into the newinitialization file. Prefire estimates of soil C, fine root C, andsoil N, although likely to have marginally changed in thedisturbance, were not modified from their values at the endof the simulation ending in 1850. The same procedure wasperformed from 1851 until 1950, when another fire with∼25% mortality occurred. Finally, starting in 1951, a newsimulation was run with no major disturbances apart fromthe annual fire mortality fraction applied to every year. Thefinal simulation was run until the end of the year 2000, theyear in which the eddy covariance data were collected.

2.6. Data Collection

[17] Flux data collection protocols are described byAnthoni et al. [2002] and Thomas et al. [2009]. In brief, theeddy covariance method estimates NEE flux from thecovariance of high‐frequency fluctuations in vertical windvelocity and CO2 concentrations. NEE is calculated as thesum of this flux term and a canopy CO2 storage term, the

latter of which is calculated from the change in CO2 con-centration in the canopy air space as a function of height[Law et al., 1999; Anthoni et al., 2002]:

NEE ¼ $′c′þZz

0

dc

dtdz ð2Þ

where $′c′ is the time‐averaged eddy flux for CO2

[covariance between the turbulent fluctuations for verticalwind speed (w′) and scalar concentration (c′)] and dc/dt is avertical storage term that is a function of canopy height (z),which approximates change in CO2 storage in the canopy airspace. The scalar concentrations were measured at 20 Hzand NEE are averaged in 30 min intervals which form thedata set of daily estimates of NEE for each respective stand.[18] There are several potential sources of error in NEE

estimates that form the basis of our uncertainty estimate todetermine model acceptability. First, the fluxes that arecomputed over half‐hour intervals to minimize samplingerrors are associated with nonstationarity in the effectivefootprint over time; micrometeorological sampling errors[Baldocchi, 2003]; and statistical sampling errors from gap‐filling methodologies [Falge et al., 2001]. We used theuncertainty estimates calculated by Thomas et al. [2009] forthe Metolius sites, where the uncertainty (coefficient ofvariation) for annual NEE is estimated to be 16% of themean. All sites have been evaluated for accuracy and con-sistency of eddy covariance‐based GPP and ecosystemrespiration with biometric measurements of NPP, autotro-phic respiration, and heterotrophic respiration, includingclosure of the CO2 balance to account for errors in each ofthe component fluxes, and the sites passed both tests[Luyssaert et al., 2009; Vickers et al., 2009].

2.7. Meteorological Data

[19] The driving meteorological data for Biome‐BGC iscomposed of the following inputs given on a daily time step:maximum temperature (Tmax), minimum temperature (Tmin),average temperature (Tavg), average vapor pressure deficit(VPD) (MPa), average incoming shortwave radiation (Srad)(W m−2), total precipitation (mm), and day length (s).Meteorological instrumentation did not exist at the Metoliussite prior to its establishment as an AmeriFlux site, requiringthe generation of such data for the years before the eddycovariance instrumentation was installed at the site. Thisneed was met using the DAYMET climate model, a modelwhich gathers data for a user‐specified location by extrapo-lating meteorological readings from surrounding climatestations and adjusting for any changes in elevation [Thorntonand Running, 1999; Thornton et al., 2000]. DAYMETgenerated daily climate data from 1980 through 2000. Forthe young stand, meteorological data was used starting in1987. For the mature and old‐growth stands, the meteoro-logical data was recycled so that it could provide a record ofappropriate length for each stand. Meteorological data takenfrom the AmeriFlux instrumentation then replaced the datagenerated by the DAYMET model for the time span of ouranalysis. In addition to incorporating meteorological data,Biome‐BGC allows for the user to specify yearly CO2 con-centrations at the site, based on annual CO2 concentrationsrecorded since 1901, and we utilized this feature to account


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for changes in atmospheric CO2 at this point. CO2 con-centrations prior to 1901 were based on the inferred CO2

concentrations from Intergovernmental Panel on ClimateChange [2007].[20] We suggest that the assumptions made in setting up

Biome‐BGC for this study are rather typical of this type ofecosystem simulation. Unique to this study is the explora-tion of uncertainty and potential equifinality of differentmodels as hypotheses about functioning of the Pinus pon-derosa system (see alsoMitchell et al. [2009] for applicationto an additional Pinus ponderosa ecosystem). The inputsdescribed above were the basis for 500,000 simulationsperformed with different randomly chosen parameter setsfrom the ranges specified in Table 1. A complete list of theparameter values used in the simulations can be found inTable S1 (available as auxiliary material).1 We recognize

that there will be an interaction between errors in the inputsand any parameter sets that are identified as behavioralwithin the GLUE methodology (see discussions in theworks of Beven [2006]) but, as in very many environmentalmodeling studies, there is little information available withwhich to assess the potential input errors.

3. Results

3.1. Parameter Sensitivities

[21] Of the simulations that were run for the young,mature, and old‐growth stands, 80.77%, 79.26%, and73.00% were nonliving (GPP < 10 g C m−2 yr−1) and werethus excluded from further analysis. The direction in whichthe errors were propagated differed for the simulations(Figure 2). In the young stand, 99.73% of the simulationsoverestimated the magnitude of measured NEE. However,among the living simulations for the mature and old‐growth

Figure 2. Time series of soil moisture content, evapotranspiration, GPP, TER, and GPP‐TER for theyoung and mature stands during 2004–2008. Data are from live simulations only.

1Auxiliary materials are available in the HTML. doi:10.1029/2009JG001146.


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stands, 100% and 99.84% underestimated the magnitude ofmeasured NEE.[22] Beven [2006] has suggested an approach to model

rejection based on setting prior limits of acceptability. Herethis approach has been implemented by defining such limitson the basis of the effect of error in the field measurementsas in condition above. Such an approach allows a refinementof the set of retained models to treat as behavioral only thoseproviding predictions that are satisfactory in the sense ofbeing consistent with the estimated errors in the measure-ments and that might therefore be considered as providingreliable simulations. Among the living simulations in theyoung stand, 14.04% of the estimates of mean annual GPPwere within 16% of the measured estimate of 745 g C m−2

yr−1. For the living simulations in the mature stand, 2.89%of the estimates of mean annual GPP were within 16% of themeasured estimate of 1583 g C m−2 yr−1 (Figure 3). For theliving simulations in the old‐growth stand, 19.79% ofthe estimates of GPP (year 2000) were within 16% of themeasured estimate of 938 g C m−2 yr−1. Perhaps surpris-ingly, estimates of total ecosystem respiration (TER) weremore accurate than estimates of GPP. Among the livingsimulations in the young stand, 16.64% of the estimates ofmean annual TER were within 16% of the measured esti-mate of 1049 g C m−2 yr−1. Among the living simulations inthe mature stand, 15.90% of the estimates of mean annualTER were within 16% of the measured estimate of 1115 g Cm−2 yr−1. Among the living simulations for the old‐growthstand, 25.00% of the estimates of mean annual TER werewithin 16% of the measured estimate of 430 g C m−2 yr−1

(Figure 3).[23] Reproduction of estimates of GPP and TER were

considerably more accurate than estimates of NEE. This isdue, in part, to the fact that estimates of NEE are dependenton the estimates of both GPP and TER. An accurate estimateof NEE does not imply accurate estimates of both GPP andTER; it only means that the difference between the two isequal to the difference between the two estimates measuredin the field. Among the living simulations for the youngstand, a mere 1.04% of the simulations resulted in satis-factory (±16% of mean annual NEE) estimates for the stand(Figure 3) while 0.63% of living old‐growth simulations hadreproductions of mean annual NEE that were satisfactory.None (0.00%) of the simulations for the mature stand werewithin 16% of the mean annual NEE (Figure 3).[24] Estimates of NEE at the Metolius sites show signif-

icant interannual variability, and part of the model‐datamismatch may result from an inability to respond to inter-annual climatic fluctuations. Thomas et al. [2009] demon-strated that soil water content is the main determinant ofecosystem carbon flux in the Metolius sites, and that theinterannual variability of the onset of the growing season islarge (45 days). From 2002 to 2008, annual NEE at themature stand ranged from −250 g C m−2 yr−1 in 2003 to−603 g C m−2 yr−1 in 2008, with an average annual NEE of−471 g C m−2 yr−1 for the overall time period. Also worthnoting are the findings of Vickers et al. [2009], whichdemonstrate that the young stand may be even more sensi-tive to drought than the mature stand. From 2004 to 2008,NEE at the young stand varied from 45 g C m−2 yr−1

in 2005 to 189 g C m−2 yr−1 in 2008, with an average of119 g C m−2 yr−1 for that time period. (Note that nonnegative

NEE values imply a transfer of terrestrial ecosystem C to theatmosphere.)

3.2. Uncertainties in Disturbance History

[25] To ascertain the role of disturbance history on thevalidity of NEE estimates for the old‐growth site, we tookthe parameter set that best emulated NEE estimates and ran10,000 simulations, each with different fire severities. Unlikethe previous GLUE exercise, which simulated disturbanceswith severities of 20–30% during the years of 1850 and 1950(see section 2.5 above), we simulated the effects of variationin disturbance history simulating disturbances with severitiesof 0–100% in 1850 and 1950. We also allowed annual fire‐related tree mortality to vary from 0.1 to 2.0% to incorporatethe variation in fire‐related mortality that results from fre-quent (MFRI = 16 years), low‐severity fires among Pinusponderosa trees, which are well adapted to low‐intensitysurface fires. In a study on recent fires in Ponderosa pine nearthe site, mean basal area mortality ranged from 14% in low‐severity stands to 50% in moderate severity and 100% inhigh‐severity stands [Meigs et al., 2009]. Results indicatethat annual fire‐related tree mortality was a highly sensitiveparameter, with lower mortality estimates resulting in greatlyimproved estimates of NEE (Figure 4). Similarly, low esti-mates of fire severity in both 1850 and 1950 resulted in thebest reproduction of NEE data (Figure 4), but the sensitivitiesof these parameters were much lower than that of annual fire‐related tree mortality.

4. Discussion

[26] Semiarid ecosystems are a particularly challengingcase study in ecosystem modeling, and a failure to reproducedata for one semiarid ecosystem does not indict the model’sperformance for all ecosystem types. However, assuming ourmethodology for parameterization is representative of typicalmodel applications, and that we characterized disturbancehistory sufficiently, the model performed inadequately in thissensitivity test because there does not appear to be a singleinstance in which both GPP and TER were accuratelymodeled (Figure 5) in the mature and old‐growth stands,even if certain combinations of them could result in accurateestimates of NEE for the old‐growth stand.

4.1. Soil Hydrology

[27] We initially suspected that difficulties in modelingthe soil hydrology in the Metolius ecosystem accounted fora large proportion of model‐data mismatch, as the sensitivityof this ecosystem to soil hydrology has been documented[Irvine et al., 2004; Thomas et al., 2009]. We investigatedthis possibility by examining the estimates of mean annualsoil water content (�m) and mean annual GPP. In the youngand old‐growth stands, modeled estimates of mean annualsoil water content were universally higher than the measuredvalues. Conversely, the model reproduced a lower amountof soil water content at the mature stand, though the dif-ference was not nearly as dramatic as it was for the youngand old‐growth stands.[28] Much of the discrepancy may be due to difficulties in

reproducing taproot dynamics of semiarid forests. Taprootscan extend deep into the soil in semiarid ecosystems as anadaptation for chronic water limitations, and it is striking


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Figure

3.Proportions

ofcarbon

flux

values

forliv

esimulations

reproduced

bythemodel.Nonliv

ingsimulations

arenot

show

n.Black

lines

representrangeof

values

that

couldbe

deem

edsatisfactory(±cv).


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that, in the old‐growth stand, the model produced a highersoil water content than that observed in the field. We suspectthat this may be due to the inability to account for, andrespond to, the availability of deep soil water, which isassociated with precipitation at longer timescales than thedaily precipitation that is used in the simulations; Biome‐BGC simulates water availability with a simplified repre-sentation of the soil water column and associated wateruptake.[29] Fortunately, even though the model did not accu-

rately simulate mean soil water content, this does not meanthat all of the simulated estimates of mean annual GPP wereinaccurate. On the contrary, there were many estimates ofannual GPP that were comparable to field data. Similarly,successful reproductions of the ratio of annual GPP toannual evapotranspiration (ET) were found in an earlierGLUE analysis of the Biome‐BGC model for young andmature aged ponderosa pine stands, even when no simula-tion accurately reproduced the relationship between soilwater content and ET [Mitchell et al., 2009].

4.2. Soil Respiration

[30] Approximately 80% of global GPP is respired back tothe atmosphere, and soil respiration, which incorporateselements of both Ra and Rh, accounts for more than two‐thirds of this flux [Law et al., 1999; Janssens et al., 2001;Xu et al., 2001]. Difficulties in modeling soil respiration arewell‐documented. Braswell et al. [2005] applied nonlinearinversion to the eddy covariance flux measurements fromHarvard Forest using a simplified model of photosynthesis

and evapotranspiration and concluded that multiyear eddyflux measurements allow for a tight constraint on photo-synthesis, but poor constraints on parameters relating to soildecomposition, which varies at considerably longer time-scales than photosynthesis and evapotranspiration. Simi-larly, Verbeeck et al. [2006] found that the parameterresponsible for the greatest amount of uncertainty in theFORUG model was related to soil respiration, and Williamset al. [2005] concluded that long‐term measurements ofcarbon pool sizes are needed to estimate parameters relatingto soil decomposition.[31] We investigated the extent to which modeled esti-

mates of soil respiration contributed to model‐data mis-match by performing a subseries of GLUE analyses for10,000 runs. While the simulations for the young standoverlapped with the field data, the vast majority of thesimulations for the mature stand and all of the simulationsfor the old‐growth stand underestimated soil respirationestimates from the field (Figure 6). We note that onlyperiodic soil respiration measurements were made at thesesites, and scaling with temperature response curves over theyear can lead to larger uncertainty in annual estimates thanuse of continuous measurements. Likewise, Law et al.[1999] showed that on calm nights, soil respiration couldexceed eddy covariance estimates of total respiration, sug-gesting periods of nocturnal cold air drainage. However,even though soil respiration was underestimated in most ofthe 10,000 runs for both the mature and old‐growth stands,this underestimation actually improved model performance.Even though modeled estimates of soil respiration were

Figure 4. Uncertainties in disturbance history for the best sample set of parameter values for 10,000simulations. Year‐specific mortality fractions represent the percent of live stem biomass killed in eachgiven year. Observed mortality is an estimate of actual mortality for that year, deduced from age‐classreconstructions [see Thornton et al., 2002]. Annual fire mortality fraction is the average fire‐relatedpercent tree mortality resulting from fires of lower severity than those in 1850 and 1950. Results indicatethat the aggregated annual mortality fraction is a highly sensitive parameter, with low values producingthe best performing simulations. Like the aggregated estimate of annual mortality, year‐specific mortalityalso produces better performing simulations when mortality fractions are low, but with considerably lesssensitivity.


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Figure

5.Meanannual

GPPplottedagainsttotalecosystem

respiration(TER),meanannual

GPPplottedagainstautotro-

phic

respiration(R

a),andmeanannu

alNPPplottedagainstheterotrop

hicrespiration(R

h)estim

ates

forallthreestands.

Modeled

values

areshow

nin

blue,while

therangein

uncertainty(±cv)regardingthemeasuredvalues

isshow

nin

black.

Notethatfield‐derivedestim

ates

ofRain

theoldstandarenearly

0andarelik

elyto

besignificantly

underestim

ated,m

ean-

ingthat

eddy

flux

estim

ates

ofGPPand/or

TERfortheoldstandareprobably

inaccurate.


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underestimated, it was an inaccuracy that actually increasedthe accuracy of the estimates of NEE, since TER was almostalways overestimated. Thus, even though our results lendsupport to prior findings [Braswell et al., 2005; Williamset al., 2005; Verbeeck et al., 2006] that suggest that theframeworks for modeling soil respiration are inadequate, wecannot attribute the entirety of mismatch in our study to soilrespiration.

4.3. Gross Primary Production and Total EcosystemRespiration

[32] While some of the simulations for the young standwere successful in reproducing the relationship between

GPP and TER, none of the modeled estimates for the matureand old‐growth stands were successful in reproducing themean annual GPP: mean annual TER ratio (Figure 5).Similar results were found in an earlier GLUE analysis ofthe Biome‐BGC model for two younger stands by Mitchellet al. [2009]. To determine what component of ecosystemrespiration (autotrophic or heterotrophic) is causing model‐data mismatch, we utilized field estimates of NPP to deter-mine autotrophic respiration. Once autotrophic respiration(Ra) was known, the heterotrophic portion of ecosystemrespiration (Rh) was calculated (Rh = TER − Ra).[33] Our results demonstrate that autotrophic respiration is

not being simulated reliably in both the mature and old‐

Figure 7. Modeled estimates Ra/GPP compared to field estimates. Note that Ra/GPP is increasinglyoverestimated in the mature and old‐growth stands, indicating that Ra is a significant source of model‐data mismatch. Note that field‐derived estimates of GPP in the old stand may be significantly underes-timated (see Figure 5), meaning that field estimates of TER for the old stand are probably inaccurate.

Figure 6. Mean annual GPP plotted against mean annual soil respiration for all three stands. Eventhough soil respiration was underestimated in most of the 10,000 simulations for the mature stand andall of the simulations for the old‐growth stand, this underestimation actually improved model performancesince total ecosystem respiration (TER) was almost always overestimated for these stands.


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growth stands. Simulations for both stands showed that themodel almost always overestimated the portion of GPP thatwas lost via Ra for the mature and old‐growth stands(Figure 7). The trend of simulated fluxes observed in Figure 7runs contrary to field observations where Ra/GPP is initiallylow [DeLucia et al., 2007]. The role of Ra in model‐datamismatch is further illustrated in Figure 8, which shows thatwhen estimates of Ra and Rh are adjusted according to esti-mates of field measurements of Ra/GPP and Rh/Ra, estimatesof GPP − TER (i.e., GPP − Ra − Rh) are substantiallyimproved. Evidence for a failure to adequately simulate Ra

was also found byWang et al. [2009], who calibrated Biome‐BGC to produce highly accurate estimates of GPP andevapotranspiration (ET), but noted that NPP (GPP − Ra) wasnevertheless underestimated when compared to field mea-surements. An overestimation of Ra also explains why our

simulations for the mature and old‐growth stands were runbest with parameter values that were often on the extremeends of value ranges, as they resulted in an increase in GPPthat compensated for an overestimation of Ra. Consequently,parameters that have a more direct control over potentialGPP, such as those that control leaf production and leafnitrogen concentration, are clearly among the most sensitivemodel parameters in Biome‐BGC [White et al., 2000]. Theframework for modeling Ra was largely derived from thatoutlined by Ryan [1991].[34] Of the living simulations for the mature and old‐

growth stands, 100% and 99.84% underestimated themagnitude of NEE. An underestimation of NEE in forestecosystems is not unprecedented for the Biome‐BGC model.Thornton et al. [2002] reported that, in the year 2000,Biome‐BGC estimated an annual NEE of −25 g C m−2 y−1

Figure 8. (top left) Scatterplot showing the modeled values of Ra and Rh plotted against GPP for theliving simulations for the mature stand, with (bottom left) the histogram representing the distribution ofthe corresponding modeled values of GPP − Ra − Rh. (top right) Scatterplot showing the adjusted valuesof Ra, calculated by multiplying the modeled value of Ra by the ratio of measured Ra/GPP to modeledRa/GPP. Adjusted Rh was calculated by multiplying the adjusted modeled value of Ra by the field mea-surements of Rh/Ra. (bottom right) Histogram showing the distribution of the corresponding values ofGPP − Ra − Rh obtained from the adjusted values of Ra and Rh from the scatterplot in Figure 8 (topright). Note that when the estimates of Ra and Rh are adjusted according to the ratio observed from fieldmeasurements, the new estimates of GPP − Ra − Rh are substantially improved.


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for the old‐growth stand at Metolius, a significant under-estimation of the −508 g C m−2 yr−1 that was recorded. Anoverestimation of both autotrophic and heterotrophic respi-ration cascades through the years simulated, as each inaccu-rate year of simulation inevitably carries over into thefollowing year. The results of these cascading errors canresult in a significant deviation from field‐based estimatesof total ecosystem C storage. Thornton et al. [2002] pro-vided modeled estimates of total C storage (not to beconfused with annual NEE) for the old‐growth site atMetolius at 140 Mg C ha−1, while the field‐based estimatesof Law et al. [2001, 2003] are 210 and 239 Mg C ha−1

(different years of measurement), ∼50% higher than themodeled estimates. A similar tendency for estimates of themagnitude of annual NEE to be underestimated appears tobe present in modeled estimates of other ecosystems aswell. Simulations performed by Thornton et al. [2002] forthe Wind River Experimental Forest in the western CascadeRange of Washington estimated stand biomass to be443 Mg C ha−1, while field measurements reported bySmithwick et al. [2002] estimated stand C storage to be614 Mg C ha−1, 39% higher than the modeled estimates.[35] Finally, the frequency and severity of previous dis-

turbances, such as high‐frequency low‐severity wildfires, aswell as moderate‐frequency wildfires of moderate‐to‐highseverity, exert significant influence on estimates of NEE,particularly at stands with long and complex disturbancehistories, like the old‐growth stand. Our work on the sen-sitivity of disturbance history to NEE estimates reiteratedthe findings by Thornton et al. [2002], which emphasizedthe importance of incorporating site‐specific patterns ofdisturbance into simulations. After running 10,000 simula-tions with the highest likelihood model parameter set, wefound that, for the disturbances simulated in 1850 and 1950,lower‐severity disturbances resulted in simulations withhigher likelihood (Figure 4). This was true even for distur-bance severity values that were significantly lower than theactual severities of the disturbances. Similarly, the annualrate of fire disturbance had the higher likelihoods at thelower end of the parameter value range (Figure 4). Thereason for this confluence is likely similar to the reasons forother shaping in parameter values, as lower mortality fromdisturbance results in more photosynthetic machinery, thushigher GPP to offset the model’s inability to compensate forthe difficulties in simulating ecosystem respiration.[36] However, there is an important difference in the

application of field‐based measurements of year‐specificmortality from average annual mortality. Ascertaining theextent of significant disturbances, such as those that occurredin 1750, 1850, and 1950, can be done with considerablymore certainty than estimating the fine‐scale mortality pro-cesses that occur with a high‐frequency, low‐severity fireregime endemic to the east Cascades; reconstructing a stand‐level disturbance with moderate to high severity can be easilydone through dendrochronology, while estimating the annualfraction of fire‐related mortality from fires of lower severityis more difficult and may yet prove to be essential to esti-mates of NEE in terrestrial ecosystem models. Since thefine‐scale annual rate of fire‐related mortality is a sensitivemodel parameter that is difficult to estimate, incorporatingsuch disturbances, while necessary, is likely to be a major

challenge to finding behavioral estimates of NEE. We sus-pect the same is true for other fine‐scale mortality processes,such as pest outbreaks (i.e., pine beetle infestations). Sim-ulating an aggregated estimate of the annual disturbance‐related mortality, rather than simulating the full magnitudeof actual disturbances in the years in which they occur, islikely too coarse a representation of the disturbance pro-cesses. Furthermore, the frequency and extent of both ofthese mortality agents is likely to have changed over thetime period in which they were measured, and may changein the future as a result of continued climatic change,making a reconstruction difficult and a future projection ofthem even more challenging.

5. Conclusions

[37] We have incorporated the uncertainty that arises fromdisturbance history, multidimensional parameter variability,and eddy flux measurement uncertainty by simulating500,000 combinations of 13 parameter values for three ageclasses of semiarid forest and tested to see if estimates ofNEE from those simulations can fall within the bounds ofmeasurement uncertainty inherent in estimates of NEEbased on eddy flux measurements. Studies that provide anevaluation of the sources of uncertainty to this extent arerare, and our simulations of net ecosystem CO2 exchange inthese semiarid forests with Biome‐BGC were challenged bysome inconsistencies with observations. We note that themodel can provide accurate reproductions of GPP, meaningthat what is arguably the most critical ecosystem process,photosynthesis, is reasonably well understood. Nevertheless,it is clear that substantial uncertainties remain in modelingecosystem respiration, as our results indicate that respirationframeworks, particularly those for autotrophic respiration,require modification. However, even if both autotrophic andheterotrophic respiration can be accurately modeled, copingwith the equifinality that results from multidimensionalparameter variability may still present obstacles to theaccurate reproduction of ecosystem processes. We also notethat uncertainties in disturbance history can undermine theaccuracy of even the most robustly calibrated models. Forthese reasons, we contend that an incorporation of mea-surement uncertainty, multidimensional parameter variabil-ity, and uncertainties in ecosystem disturbance history mayprove valuable in efforts to detect specific problems inmodel structure and we encourage such a procedure infuture model assessments.

[38] Acknowledgments. The Metolius AmeriFlux sites are supportedby the U.S. Department of Energy Terrestrial Carbon Program (grant DE‐FG02‐03ER63653). Discussions regarding Biome‐BGC with Ron Neilsonat the United States Forest Service Pacific Northwest Research Station werealso very helpful, as was his generosity in letting us use his Linux cluster.Biome‐BGC version 4.1.2 was provided by Peter Thornton at the NationalCenter for Atmospheric Research (NCAR), and by the Numerical Terrady-namic Simulation Group (NTSG) at the University of Montana. NCAR issponsored by the National Science Foundation. Support for this researchwas provided by an NSF IGERT graduate fellowship to S. R. Mitchell(NSF award 0333257) in the Ecosystem Informatics IGERT program atOregon State University, a NASA New Investigator Program grant toK. E. B. O’Connell (NN604GR436) at Oregon State University, and theH. J. Andrews LTER (DEB‐0218088). Development of the GLUE method-ology has been supported by UK NERC grant NER/L/S/2001/00658 andNE/E002242/1.


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K. Beven, Lancaster Environment Centre, Lancaster University,Lancaster LA1 4YQ, UK.J. Freer, School of Geographical Sciences, University of Bristol, Bristol

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Processes influencing model data mismatch in drought