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Ecological Modelling 220 (2009) 3259–3270

Contents lists available at ScienceDirect

Ecological Modelling

journa l homepage: www.e lsev ier .com/ locate /eco lmodel

ultiple sources of predictive uncertainty in modeled estimates of netcosystem CO2 exchange

tephen Mitchell a,∗,1, Keith Bevenb,c, Jim Freerd

Department of Forest Ecosystems and Society, Oregon State University, Corvallis, OR 97331, USADepartment of Environmental Science, Lancaster University, Lancaster LA1 4YQ, UKGeoCentrum, Uppsala University, Uppsala 73236, SwedenSchool of Geographical Sciences, University of Bristol, Bristol BS8 1SS, UK

r t i c l e i n f o

rticle history:eceived 14 August 2008eceived in revised form 21 January 2009ccepted 24 August 2009vailable online 14 October 2009

eywords:et ecosystem exchangeiome-BGCcosystem ModelncertaintyLUEinus ponderosaodel-data synthesis

a b s t r a c t

Net ecosystem CO2 exchange (NEE) is typically measured directly by eddy covariance towers or isestimated by ecosystem process models, yet comparisons between the data obtained by these two meth-ods can show poor correspondence. There are three potential explanations for this discrepancy. First,estimates of NEE as measured by the eddy-covariance technique are laden with uncertainty and canpotentially provide a poor baseline for models to be tested against. Second, there could be fundamen-tal problems in model structure that prevent an accurate simulation of NEE. Third, ecosystem processmodels are dependent on ecophysiological parameter sets derived from field measurements in which asingle parameter for a given species can vary considerably. The latter problem suggests that with suchbroad variation among multiple inputs, any ecosystem modeling scheme must account for the possibilitythat many combinations of apparently feasible parameter values might not allow the model to emulatethe observed NEE dynamics of a terrestrial ecosystem, as well as the possibility that there may be manyparameter sets within a particular model structure that can successfully reproduce the observed data.We examined the extent to which these three issues influence estimates of NEE in a widely used ecosys-tem process model, Biome-BGC, by adapting the generalized likelihood uncertainty estimation (GLUE)methodology. This procedure involved 400,000 model runs, each with randomly generated parametervalues from a uniform distribution based on published parameter ranges, resulting in estimates of NEEthat were compared to daily NEE data from young and mature Ponderosa pine stands at Metolius, Oregon.Of the 400,000 simulations run with different parameter sets for each age class (800,000 total), over 99%of the simulations underestimated the magnitude of net ecosystem CO2 exchange, with only 4.07% and0.045% of all simulations providing satisfactory simulations of the field data for the young and mature

stands, even when uncertainties in eddy-covariance measurements are accounted for. Results indicatefundamental shortcomings in the ability of this model to produce realistic carbon flux data over thecourse of forest development, and we suspect that much of the mismatch derives from an inability torealistically model ecosystem respiration. However, difficulties in estimating historic climate data arealso a cause for model-data mismatch, particularly in a highly ecotonal region such as central Oregon.This latter difficulty may be less prevalent in other ecosystems, but it nonetheless highlights a challenge

amic

in trying to develop a dyn

. Introduction

Increases in atmospheric CO2 concentrations have long beenbserved (Revelle and Suess, 1957; Revelle, 1982) and there isuch evidence that they are causing significant changes in earth’s

∗ Corresponding author. Current address: Nicholas School of the Environment,uke University, Durham, NC 27708, USA. Tel.: +1 919 613 8069.

E-mail address: stephen.mitchell@duke.edu (S. Mitchell).1 Tel.: +1 919 491 0398; fax: +1 919 684 8741.

304-3800/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.ecolmodel.2009.08.021

representation of the terrestrial biosphere.© 2009 Elsevier B.V. All rights reserved.

climate (IPCC, 2007). Approximately half of all annual fossil fuelemissions remain in the atmosphere, leaving the rest to be absorbedby oceanic and terrestrial ecosystems (Schimel et al., 2001). Thepotential for terrestrial ecosystems to mitigate current and futureatmospheric CO2 concentrations is a matter of ongoing enquiry,necessitating long-term studies of net ecosystem CO2 exchange

throughout a wide variety of biomes (Goulden et al., 1996; Lawet al., 2003; Baldocchi, 2003). Net ecosystem CO2 exchange (NEE)is the net CO2–C exchange from an ecosystem to the atmosphere,calculated as the difference between gross primary productionand ecosystem respiration, excluding losses of respiration-derived

3 Mode

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260 S. Mitchell et al. / Ecological

issolved inorganic carbon (Chapin et al., 2006). Continuous fieldstimates of NEE have been measured from over 100 locations usinghe eddy-covariance method and offer a valuable baseline againsthich model assumptions, parameters, and performance can be

scertained (Schulz et al., 2001; Wang et al., 2001; Thornton et al.,002; Braswell et al., 2005; Knorr and Kattge, 2005; Sacks et al.,006).

Biophysical models, even those designed to simulate the samehenomena, can differ widely in their structure, assumptions, andhilosophy, leading to substantial uncertainty in their predictionsFranks et al., 1997; Schulz et al., 2001; Raupach et al., 2005).or many terrestrial ecosystem models, a predominant source ofodel uncertainty stems from an insufficient capacity to provide

eliable estimates of total ecosystem respiration (TER) (Davidsont al., 2006; Trumbore, 2006). TER, defined as the sum of het-rotrophic respiration (Rh) and autotrophic respiration (Ra), posesdifficulty to environmental modelers. A large source of the uncer-

ainty in estimates of TER involves the respiratory processes ofoots and soil organisms, collectively referred to as soil respira-ion. While it is known that temperature as well as soil moisturexert significant control over soil respiration, efforts at modelinguch dynamics are difficult because of the intricacies involved inisentangling the interactions between seasonal variations in tem-erature from accompanying variations in soil moisture (Davidsont al., 1998).

Uncertainties inherent in calculations of TER do not end in theoil. Any modeled estimate of TER requires knowledge of the preciseuantities of each respiring component (Law et al., 1999; Litton etl., 2007) and estimates of the growth and maintenance respirationf constituent woody tissues are often calculated and distributed byay of stationary allometric ratios that determine the patterns of

iomass allocation. In reality, allometric ratios are not static. Treesith a high capacity for biomass storage can exhibit substantial

ariation in such ratios due to variation among site conditions asell as stand age; Law et al. (2004a,b) found that xeric systems

xhibited decreased below-ground biomass allocation with agehile mesic systems exhibited increased below-ground biomass

llocation with age. Similarly, Comeau and Kimmons (1989) foundhat patterns of new fine root C: new leaf C in Pinus contorta can varyonsiderably as a function of site water availability. Non-allometricarameters can also vary by site and/or stand age. In Pinus pon-erosa, leaf and fine root turnover varies by elevation (Whittakernd Niering, 1968, 1975), and percentages of leaf nitrogen in rubiscoary with irradiance (Poorter and Evans, 1998). Furthermore, sig-ificant differences in transpiration per unit leaf area have beenbserved between young and mature stands when water is readilyvailable (Irvine et al., 2004), which may partially explain why leafater potentials during conductance reactions can show significant

nter-site variation within species (DeLucia et al., 1988; DeLucia andchlessinger, 1990).

Issues such as these have prompted model-data synthesis stud-es. Model-data synthesis, according to Raupach et al. (2005),perates under the assumption that the inherent uncertainties inny dataset are just as important as the data values and shouldhereby be included in both parameter estimation and data assim-lation. For an ecosystem model (and/or in fact any environmental

odel), this uncertainty lies not just with the observed data butlso with the parameters on which the data is conditioned, affectingoth the predictive uncertainty of a model-data synthesis and theredicted best estimate. Analyzing these uncertainties effectivelyequires an acknowledgment of the potential for equifinality in

odel predictions. The concept of equifinality implies that, within

he current capacity of mechanistic modeling, there may be manyodel structures and parameter sets within a given model struc-

ure that may be acceptable in reproducing the observed behaviorf an environmental system (Beven, 2002, 2006).

lling 220 (2009) 3259–3270

Acknowledgement of model equifinality is essential to predic-tions drawn from environmental models in that competing modelsand parameter sets can be considered as multiple working hypothe-ses about how the system is functioning. Given the limitations ofobservational data, approximate model assumptions, and lackingindependent estimates of the effective parameter values requiredby a model, it may not be possible to determine uniquely the mostlikely hypothesis, even if many models can be rejected as unac-ceptable or non-behavioral. Our goal was to explore the respectivecontributions of measurement uncertainty, model structure, andparameter equifinality to modeled estimates of NEE. We used theGLUE framework (Fig. 1) in conjunction with a terrestrial ecosystemmodel, Biome-BGC, to (1) examine model equifinality for combi-nations of ecophysiological parameter values with respect to NEEdynamics in a semi-arid forest ecosystem, (2) compare differencesin parameter uncertainty between two distinct age classes of thisecosystem and (3) ascertain the cause(s) of any model-data mis-match.

2. Materials and methods

2.1. The GLUE methodology

The GLUE method (Beven and Binley, 1992) was developed fromthe generalized sensitivity analysis of Spear and Hornberger (1980)to deal with multiple acceptable parameter sets within environ-mental models. Studies of parameter responses have shown thatthe assumption of a single well-defined optimal parameter setrarely holds, resulting in the condition of model equifinality (Freeret al., 1996; Franks et al., 1997; Beven and Freer, 2001; Schulz et al.,2001). GLUE provides a means of assessing the predictive uncer-tainty based on a generalized likelihood measure within a MonteCarlo framework. GLUE has been used for a wide range of envi-ronmental modeling problems (see Beven and Freer, 2001; Freer etal., 2004; Beven, 2006, 2008), including the prediction of CO2 fluxdata (Schulz et al., 2001), tree mortality under drought conditions(Martínez-Vilalta et al., 2002) and forest fires (Pinol et al., 2004,2007).

Utilization of the GLUE method involves a large number of modelruns, each of which is driven by randomly generated input param-eter values drawn from uniform prior distributions across therange of each parameter. The performance of each run is thereafterdeemed behavioral or non-behavioral based upon the comparisonof simulated versus observed data. Model runs that do not meetspecified acceptability criteria are rejected as non-behavioral andare thus given zero likelihood, removing them from further anal-ysis. Parameter sets must then satisfy an additional performancecriterium to be considered as behavioral and used in prediction.Within the GLUE methodology, each behavioral simulation can beassociated with a likelihood weight that depends on performanceduring comparisons with available observations.

2.2. Evaluation of parameter sensitivities

Many randomly generated parameter sets will result in a sim-ulation that is physiologically unsustainable within the appliedmodeling framework, thus simulations that resulted in a NEE of 0.0were excluded from additional analysis a priori. For the remainingsimulations we used the Nash-Sutcliffe model efficiency coefficient(Nash and Sutcliffe, 1970) to determine whether or not a given setof parameters should be retained for further analysis. It is defined

as:

Ej = 1 −∑I

i=1(Cio − Ci,j

m )2

∑Ii=1(Ci

o − Co)2

(1)

S. Mitchell et al. / Ecological Modelling 220 (2009) 3259–3270 3261

of the

wNS(dacawnt

L

wtsSopswp

Fig. 1. Schematic

here Cio is observed NEE for day i, Co is the mean of daily observed

EE, and Ci,jm is modeled NEE of day i for parameter set j. Nash-

utcliffe efficiencies can range from −∞ to 1. An efficiency of 1E = 1) indicates a perfect match of modeled data to the observedata. An efficiency of 0 (E = 0) indicates that the model predictionsre as accurate as the mean of the observed data, while an effi-iency less than zero (E < 0) occurs when the observed mean isbetter predictor than the model. Simulations where (0 ≤ E < 1)ere retained for further analysis. Once these parameter combi-ations were found, we calculated their likelihood weights usinghe following equation:

(�j|Y) =∑J

j=1

(∑Ii=1(Ci

o − Ci,jm )

2)

(∑Ii=1(Ci

o − Ci,jm )

2) (2)

here L(�j|Y) is the likelihood of simulating data Y given parame-er set �j , assuming a uniform prior distribution for all parameterets where E > 0. Our method is similar to the sensitivity analysis ofpear and Hornberger (1980) except that there is an additional step

f calculating a likelihood weight for each parameter set. This sam-ling strategy allows any covariation that is important in providingimulations with 0 ≤ E < 1 to be apparent in the likelihood weightshether or not prior covariation has been specified in sampling thearameter sets.

GLUE procedure.

This first threshold condition for a model to be retained for fur-ther analysis (0 ≤ E < 1) is very relaxed. It might be considered lessthan the minimal requirement for a model to be useful in prediction,since it indicates that the model predictions are merely as accurateas or better than the mean of the observed data. Here, however,we are using it primarily to reveal information about the sensi-tivity of the simulations to different parameters and combinationsof parameters. We later impose an additional criterion for a modelperformance to be considered behavioral in relation to errors in theobserved data. The second threshold criterion is based on compar-ing annual estimates of NEE from the model to estimates obtainedfrom field measurements, the latter of which includes a term ε, rep-resenting the uncertainty in annual estimates of NEE. The term ε isbased on the propagation of uncertainty in annual NEE estimatesand includes estimates of errors incurred by the instrumentationused in the eddy covariance technique, gap-filling, as well as spatialand temporal variability, calculated from the estimates of annualmeasurements of net ecosystem CO2 exchange uncertainty fromOren et al. (2006). This ‘effective observation error’ criterion is anexample of the approach to model evaluation proposed by Beven

(2006) but the concept of including observational uncertainties toconstruct model performance criteria has been applied previously(Page et al., 2003; Freer et al., 2004). We included this second step inour evaluation procedure to help decide whether or not our modelshould be consulted as a reliable simulator of NEE. Thus, only sim-

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lated annual estimates of NEE that met the following criteria areonsidered in the behavioral model set:

N

i=1Ci

o − 2ε <∑N

i=1Ci

m <∑N

i=1Ci

o + 2ε (3)

.3. Parameter estimates

Biome-BGC requires 37 ecophysiological parameter values forhe simulation of evergreen needle-leaf forests. Of these 37, 13ere allowed to vary (Table 1) assuming independent uniformrior distributions across feasible ranges of the parameters inhe absence of any strong information about effective parame-er values and their covariation. White et al. (2000) performed aensitivity analysis of model parameters, showing that LAI, FLNR,nd C:Nleaf were among the most sensitive parameters, and theseere some of the parameters we included. Additional selection

f parameters that were allowed to vary was based on the rangen variation of parameters in the literature. For instance, parame-ers with a wide range of variability, such as FRC:LC, were chosenor this reason, and parameters for which literature values exhib-ted little to no variability were excluded. Our study site has aanopy comprised primarily of Pinus ponderosa, a species withnput parameters that are generally provided in the compilation by

hite et al. (2000), and in cases where published parameter valuesere unavailable, we substituted them from other Pinus species.

ach parameter range was subsequently expanded to allow forhe possibility of yet-unpublished values that might be observedn the field in the future, the uncertainty that may arise fromubstituting species types when necessary, and the commensu-ability error between field-measured values and the effectivearameter values required to give good results in this model struc-ure.

.4. Study sites

Data were collected from two sites with eddy covariance towerst Metolius, Oregon, located approximately 64 km north of Bend,regon. Data from the young stand, aged ∼22 years, were col-

ected in 2000, while data from the mature stand, aged ∼89 years,ere collected in 2002. Both sites are dominated primarily by Pon-erosa pine (Pinus ponderosa) and both have naturally regeneratedrom clear-cuts. Soils are well drained at both sites. Descriptionsf site-specific data are referred to as they were during the time inhich the system was simulated. Additional site characteristics are

ummarized in Table 2.

.5. Modeling

All simulations used version 4.1.2 of the Biome-BGC modelThornton et al., 2002), a widely used terrestrial ecosystem model.iome-BGC simulates water, carbon, and nitrogen dynamics inlants, litter, and soil, using a daily time step for all processesRunning and Coughlin, 1988; Thornton, 1998; White et al., 2000).iome-BGC allows for the option of a spin-up simulation to serves a basis for an initial estimate of soil C content. Spin-up time isetermined by the amount of time it takes to allow soil C to reachquilibrium (Thornton and Rosenbloom, 2005). We incorporatedhe same randomly generated parameter values in the spin-up sim-lations for each of our GLUE analysis simulations. In addition toimulating initial estimates of soil C content for each parameter,e incorporated a representation of each stand’s disturbance his-

ory into the regular (non-spinup) simulations. Our methodologyor this was similar to, but not an exact replicate of, the method-logy developed by Law et al. (2001). At both stands, a clear-cutas simulated upon the completion of each spin-up simulation by

tarting a new simulation that included estimates of post-harvest

lling 220 (2009) 3259–3270

amounts of coarse woody debris, leaf litter, dead fine roots, and soilC pools taken from the amounts of these materials remaining at theend of the spin-up simulation.

2.6. Data collection

Descriptions of NEE collection protocols are described for theyoung stand in Anthoni (2002) and mature stand data are describedin Vickers et al. (submitted for publication). In brief, the eddycovariance method estimates NEE flux from the covariance ofhigh-frequency fluctuations in vertical wind velocity and CO2 con-centrations. NEE is calculated as the sum of this flux term and acanopy CO2 storage term, the latter of which is calculated from thechange in CO2 concentration in the canopy air space as a functionof height (Law et al., 1999; Anthoni et al., 2002):

NEE = � ′c′ +∫ z

0

dc

dtdz (4)

where � ′c′ is the time-averaged eddy flux for CO2 [covariancebetween the turbulent fluctuations for vertical wind speed (ω′) andscalar concentration (c′)] and dc/dt is a vertical storage term thatis a function of canopy height (z), which approximates change inCO2 storage in the canopy air space. NEE, like other measurementstaken from an eddy flux tower, is measured at 20 Hz and is there-after averaged into 30-min intervals which form the dataset of dailyestimates of NEE for each respective stand.

2.7. Meteorological data

The driving meteorological data for Biome-BGC is composed ofthe following inputs given on a daily time step: maximum temper-ature (Tmax), minimum temperature (Tmin), average temperature(Tavg), average vapor pressure deficit (VPD) (MPa), average incom-ing shortwave radiation (Srad) (W m−2), total precipitation (mm),and day length (s). Meteorological instrumentation did not exist atthe Metolius site prior to its establishment as an AmeriFlux site,requiring the generation of such data for the years before the eddycorrelation instrumentation was installed at the site. This needwas met using the DAYMET climate model, a model which gathersdata for a user-specified location by extrapolating meteorologi-cal readings from surrounding climate stations and adjusting forany changes in elevation (Thornton and Running, 1999; Thorntonet al., 2000). DAYMET generated daily climate data from 1980through 2003 specific to each site. Such a climate record is of suffi-cient length to capture inter-annual El Nino-Southern Oscillationdynamics, which exert considerable control over the vegetationdynamics of the US Pacific Northwest (Greenland, 1994). Mete-orological data taken from the AmeriFlux instrumentation thenreplaced the data generated by the DAYMET model for the timespan of our analysis. In addition to incorporating meteorologicaldata, Biome-BGC allows for the user to specify yearly CO2 concen-trations at the site, based on annual CO2 concentrations recordedsince 1901, and we utilized this feature to account for changes inatmospheric CO2.

These inputs were the basis of all 400,000 simulations we per-formed for each of the two stands. We recognize that there willbe an interaction between errors in the inputs and any parametersets that are identified as behavioral within the GLUE methodology(see discussion in Beven, 2006) but, as in very many environmentalmodeling studies, there is little information available with which to

assess the potential input errors. Each Pinus ponderosa simulationhad 24 fixed ecophysiological parameter values and 13 that wereallowed to vary by way of the Fortran90 “rand” random numbergenerator that sampled from a uniform range in potential modelparameter values. Ranges for these parameters are given in Table 2.

S. Mitchell et al. / Ecological Modelling 220 (2009) 3259–3270 3263

Table 1Biome-BGC parameters allowed to vary.

Symbol Variable Parameter Value Range Values from Young Stand

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 6.00SC:LC New stem C: new leaf C (ratio) 0.2–2.0 1.48CRC:NSC New croot C: new stem C (ratio) 0.2–0.5 N/AC:Nleaf C:N of leaves (kgC/kgN) 20–90 50.50C:Nlitter C:N of leaf litter, after retranslocation (kgC/kgN) 90–150 95.60C:Nfine root C:N of fine roots (kgC/kgN) 20–90 46.00C:Ndead wood C:N of dead wood (kgC/kgN) 200–1800 287.00LAI Canopy average specific leaf area, projected area basis (m2/kgC) 0.5–4.0 0.89FLNR Fraction of leaf N in Rubisco (unitless) 0.01–0.15 0.075gs max Maximum stomatal conductance, projected area basis (m/s) 0.002–0.012 0.007

Pa)(Mpa)

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S

� s Leaf water potential: start of conductance reduction (M� c Leaf water potential: complete conductance reduction

ite values from Law (personal communication). Values not available for the matur

he 800,000 total simulations of Biome-BGC and the GLUE analy-is were performed on a Linux cluster at the USDA Forest Serviceacific Northwest Research Station in Corvallis, Oregon.

. Results

Of the simulations that were run, 73.15% and 77.06% of simula-ions resulted in a non-living and thus rejected simulation for theoung and mature stands respectively; 12.40% and 21.81% resultedn live but rejected (∞ ≤ E < 0) simulations. 14.45% and 1.13% of allimulations resulted in live simulations that could be retained forurther analysis (0 ≤ E < 1), shown in Fig. 2. Of the retained simula-ions, 98.63% and 99.71% underestimated the magnitude of the NEEstimated by observation for the young and mature stands.

Fig. 3 shows plots of the randomly sampled parameter valuesgainst posterior likelihood projections. Parameter values for theetained combinations (E ≥ 0) are shown in grey and behavioralombinations that satisfied both performance citeria are shown inlack. Each of these plots represents points on the posterior multi-imensional surface, projected onto single parameter axes. In all,of the 13 varying parameters show no sensitivities within their

ange (C:Nlitter, C:Ndead wood, CRC:SC, � c, � s), 2 of the 13 parame-ers show slight preference (C:Nleaf and C:Nfine roots), and 6 of the 13arameters (FLNR, FM, FRC:LC, SC:LC, LAI, and gsmax) show strongreference for a certain parameter value (Fig. 3). Exhibition of pref-rences for these 6 parameter values appears more pronouncedn the mature stand, particularly in the likelihood projections ofehavioral (annual NEE ± 2ε) parameter value combinations. Theifference between the sets of parameter combinations is less obvi-us in the young stand since a much higher proportion of parameter

ombinations were behavioral. In the mature stand, clustering ofhese behavioral likelihood projections within a certain parame-er value range is pronounced, and this clustering tends to occurn the parameter value ranges that produce the highest likelihoodstimates.

able 2ite characteristics from Law et al. (2003).

Young Mature

Latitude 44.44 44.45Longitude −121.57 −121.56Elevation (m) 1165 1232Mean DBH (cm) 11.3 29.0Analysis Period 2000 2002Stand Age (90th %tile) 23 89Overstory LAI (m2 m−2) 0.89 2.96Species Composition Pipo Pipo, CadeSoil Porosity Sandy Loam Sandy Loam

pecies codes: Pipo, Pinus ponderosa; Cade, Calocedrus decurrens.

−0.85 to −0.20 N/A−2.3 to −0.9 -1.14

d.

C:Nleaf exhibits a slight preference for low values in the youngstand and a slight preference for high values in the mature stand.C:Nlitter and C:Ndead wood showed no slope across the sampled rangein their posterior likelihood projections. C:Nfine root in the youngstand also lacked any strong conditioning in the posterior likeli-hood projections, though lower parameter values in the maturestand showed a tendency to have higher likelihood values. Thelikelihood projections for the parameter controlling FLNR showa slight absence of lower values for low parameter values in theyoung stand. A similar absence of low FLNR values is seen for themature stand, which also show slightly increasing likelihood valuesfor higher parameter values.

FM shows similarity among age classes in the projection of like-lihood estimates, with both showing a slight downward slopingpattern for high likelihood values and an absence of low likelihoodvalues for high parameter values. FRC:LC shows high values for lowparameter values and an absence of lower likelihood values for highparameter values. SC:LC shows a slight preference for high valuesin the young stand and a downward sloping likelihood projection inthe mature stand. In contrast, likelihood estimates of CRC:SC do notshow any curvature in the posterior likelihood projections acrossthe full range sampled.

Likelihood projections for LAI have a slight downward slope forthe young stand and a rapidly increasing slope with an absenceof low likelihood values in the mature stand. LAI estimates takenat these sites, however, were measured to be 0.89 and 2.96 forthe young and mature stands, respectively. Maximum stomatalconductance (gsmax) however, exhibits a slightly upward-slopingpattern with an absence of low likelihood values for low parametervalues in the young stand, while the mature stand shows a rapidlyincreasing slope to values of ∼3.0 × 10−3 that thereafter tapers offinto a gradually decreasing slope across the upper bounds of highlikelihood values, also with a lack of low likelihood values for lowparameter values. Plant water stress (�1) is a cause of stomatal clo-sure and is related to leaf water potentials at the initial and finalreductions to stomatal conductance (�s, �c) in Biome-BGC. Bothof these values are assumed to be negative, since plants are rarelyat full hydration. Likelihood projections for both of these values donot show any shaping across the values range.

Parameters that have relatively uniform posterior likelihoodprojections are those that have less to do with the dynamics of pri-mary production and affected non-photosynthetic biomass, dealingwith either stoichiometry or allocation ratios. CRC:SC, a parame-ter that deals exclusively with non-photosynthetic biomass, merely

controls patterns of biomass allocation in coarse roots and stems,thus has little impact on primary production and respiration.C:Nfine root had only a very slight shaping in its posterior likeli-hood projections, and C:Ndead wood and C:Nlitter show no discernableinfluence on NEE, probably due to the comparatively long time scale

3264 S. Mitchell et al. / Ecological Modelling 220 (2009) 3259–3270

EE es

aCaitcwttyf

3

aItrsbdbboiaao

t

Fig. 2. Time series of cumulative distribution percentiles for daily N

t which decomposition operates. On a multi-year time scale, a low:N ratio of dead biomass would, holding climate constant, result inn increased decomposition rate k for these components, increas-ng the respiration of CO2 to the atmosphere. However, it is clearhat this effect is difficult to detect due to the influence of climaticonstraints. Sun et al. (2004) found that measurements of coarseoody debris respiration in this ecosystem were negligible unless

he wood was saturated with water under warm climatic condi-ions, thus decomposition only occurs during a small part of theear and contributes a marginal amount to TER in this semi-aridorest.

.1. Prediction uncertainties

As noted earlier, the range of models included in the sensitivitynalysis includes many models that have limited predictive power.t is clear, however, that for many parameters the ‘best’ models forhe chosen performance measures are distributed throughout theanges of parameter values tried. The GLUE methodology allows foruch equifinality of models in estimating prediction uncertaintiesy keeping a set of behavioral models thought to be useful in pre-iction. Beven (2006) has suggested an approach to model rejectionased on setting prior limits of acceptability. Here this approach haseen implemented by defining such limits on the basis of the effectf error in the field measurements on estimates of annual NEE asn condition (3) above. Behavioral models are then consistent with

nnual NEE allowing for the estimated errors in the measurementsnd might therefore be considered as providing reliable simulationsf net ecosystem CO2 exchange.

There are several potential sources of error in NEE estimateshat form the basis of our uncertainty estimate ε that we use in our

timates of retained model runs in comparison with observed data.

Eq. (3) to determine model acceptability. First, the fluxes that arecomputed over half-hour intervals with the intention of describ-ing ecosystem activities in the sampling footprint are known toinclude sampling errors, including micrometeorological samplingerrors (Baldocchi, 2003) as well as statistical sampling errors fromgap-filling methodologies (Falge et al., 2001). These errors are dis-tinct from uncertainties in the spatial and temporal variability inecosystem activity. Uncertainties in the spatial and temporal vari-ability should not be significantly changed through an increase inaveraging time, while micrometeorological sampling errors can bepotentially reduced by sampling a greater proportion of eddiesand averaging them over a longer time scale (Katul et al., 2001).Oren et al. (2006) separated the contribution of these two fac-tors through temporal averaging of NEE data from towers withoverlapping ecosystem activity footprints to ascertain the magni-tude of each source of measurement uncertainty, which therebyallowed a calculation of total measurement uncertainty. We cal-culated ε from averaging the uncertainty propagation estimatesof Oren et al. (2006) for the years 1998–2004, calculated to be101 g C m−2 yr−1.

After application of this term ε into condition (3), a mere 4.07%and 0.0045% (16,276 and 179 out of 400,000) of the simulationsresulted in behavioral (±2ε of annual NEE) estimates for the youngand mature stands, respectively (Fig. 4). We note that some mayconsider this acceptability criterion still to be too generous, andwe add that the percent of stands with NEE estimates that were

±50 g C m2 of annual NEE were 0.31% and 0.000023% (1256 and 9out of 400,000) for the young and mature stands, respectively. Thus,an overwhelming majority of parameter combinations resultedin an inadequate reproduction of observed data and could berejected.

S. Mitchell et al. / Ecological Modelling 220 (2009) 3259–3270 3265

Fig. 3. Posterior likelihood (L) projections (from top left) of leaf C:N ratio (C:Nleaf), litter C:N ratio (C:Nlitter), fine root C:N ratio (C:Nfine root), dead wood C:N ratio (C:Ndead wood),f w leafl waterp ioral pp

4

4s

(urmttdtrptitba

a

raction of leaf nitrogen in Rubisco (FLNR), foliage mortality (FM), new fine root C/neeaf area index-projected area basis (LAI), stomatal conductance (gsmax), and leafoints represent retained parameter combinations and black points represent behavarameter in multidimensional parameter space.

. Discussion

.1. Can Biome-BGC be considered a satisfactory model of thesetands?

In using the Generalized Likelihood Uncertainty EstimationGLUE) technique to analyze the uncertainty that arises when sim-lating a forest ecosystem at two different age classes with the ter-estrial ecosystem model, Biome-BGC, only a very small number ofodel parameter sets have survived the chosen, rather relaxed, cri-

eria for acceptability. On the basis of the wide range of simulationsried, we do not think that this model provides an adequate repro-uction of observed data at these sites. We note that the failure ofhe many simulations to produce a live stand does not necessarilyeflect poorly on the Biome-BGC model, as our range of potentialarameter values was large and inevitably leads to many parame-er combinations that are physiologically unsustainable. However,t was clear from our posterior likelihood estimates that many of

he parameters, despite a broad range in their uniform prior distri-utions, exhibited little or no sensitivity to variation in their valuesnd thus bear little or no responsibility for model failures.

In the young and mature stands, Biome-BGC does not reli-bly simulate the magnitude of NEE during the summer months;

C (FRC:LC), new stem C/new leaf C (SC:LC), new coarse root C/new stem C (CSC:SC),potential at the completion (� c) and start (� s) of a conductance reaction. Greyarameter combinations. All points represent the likelihood projection for a specific

simulations in the young and mature stands, whether behavioralor non-behavioral, underestimated the magnitude of annual NEE99.77% and 99.90% of the time. Biome-BGC’s tendency to underesti-mate the magnitude of NEE is apparent in other studies as well. In anearlier study, Law et al. (2001) performed a model-data comparisonof NEE data from an old-growth Pinus ponderosa stand at Metolius,OR and found that Biome-BGC underestimated the magnitude ofNEE flux by 240 g C m−2 yr−1.

Substantial differences were observed in the shaping of boththe retained (E ≥ 0) and behavioral likelihood projections betweenthe young and mature stands, indicating the difficulties involvedin finding a parameter set that can simulate estimates of NEEover the course of forest development. Differences in the poste-rior likelihood projections are due to a variety of factors, the mostsignificant of which appears to be Biome-BGC’s low capacity forsimulating the magnitude of summertime NEE. We found this ten-dency for an underestimation of the magnitude of NEE when wetested Biome-BGC’s default model parameter values for an ever-

green needle-leaf forest in both the young and mature stands. Theyoung stand produced a NEE estimate of −168 g C m−2 yr−1 com-pared to −273 g C m−2 yr−1, while the mature stand produced aNEE estimate of −286 g C m−2 yr−1, compared to a measured esti-mate of −413 g C m−2 yr−1. Such results are quite superior to the

3266 S. Mitchell et al. / Ecological Modelling 220 (2009) 3259–3270

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Fig. 4. Histograms of NEE estimates resu

stimates of most parameter combinations, but it is striking howuch default model parameter values differed from the values

aken directly from the site itself.Using site specific estimates for 11 of the 13 varying param-

ter values for the young stand (see Table 2), along with everyther substitutable parameter value measured at the site, the sim-lation produced a non-living simulation. (Parameter values fromhe mature stand were not available to allow a similar test). Thisuggests that, at the very least, there is a commensurability issueetween measured values of parameters and the effective valuesequired to produce a successful simulation; at worst that there issignificant structural deficiency in the model.

.2. Investigating model failure: simulation of soil hydrology

We initially suspected that difficulties in modeling soilydraulics in the Metolius ecosystem accounted for the bulk ofodel-data mismatch. Irvine et al. (2004) showed that while there

re substantial inter-stand differences in transpiration that occurhen water is readily available at the Metolius sites, cumula-

ive tree transpiration does not differ greatly among differentlyged-stands during the growing season, suggesting that water lim-tations ultimately inhibit GPP. We investigated the possibility of

failure to sufficiently reproduce soil hydrology and evapotran-piration by running 5000 additional simulations. We evaluatedodel performance by comparing simulated estimates of soil water

otential and evapotranspiration (ET) to measured data in bothtands. Results were divergent: the ratio of the modeled estimatesf soil water potential to ET were higher than the ratio of theeasured values for the young stand and lower than the ratio of

he measured values for the mature stand (Fig. 5). Such a resultlearly shows an inability to model soil water storage and uptakey not only getting the ratios wrong, but by getting them wrong inifferent ways for differently aged stands. However, this is not nec-ssarily the dominant factor in the model’s inability to reproduce

EE. Plots of annual ET plotted against annual GPP show that mea-

ured data can be well within the range of the modeled data plottedor both stands (Fig. 5), so it is clear that the model can accuratelyeproduce estimates of the water use efficiency of photosynthesisWUEP), even if soil hydrology is misrepresented.

rom acceptable (±2ε) parameter values.

4.3. Investigating model failure: simulation of Total EcosytemRespiration (TER)

Another possible cause of the limited success of the Biome-BGC in predicting the observed NEE data is an inability to modelTER successfully. On average, ∼80% of GPP is respired back to theatmosphere, and soil respiration, which incorporates elements ofboth Ra and Rh, accounts for more than two-thirds of this flux(Law et al., 1999; Janssens et al., 2001; Xu et al., 2001). Contem-porary frameworks for modeling soil respiration, such as the Lloydand Taylor (1994) function used in our version of Biome-BGC, basecalculations on temperature and moisture data, ignoring some ofthe contributions of canopy processes to soil CO2 efflux that maybe crucial to modeled estimates of NEE. Recent research indicatesthat failure to incorporate a more direct link between canopy andsoil processes in ecosystem simulation models may be problem-atic. Ekblad and Hogberg (2001) and Bowling et al. (2002) usedan isotopic technique to show that photosynthate takes only daysto become available for root respiration, indicating a relativelytight coupling of above and below-ground processes. Irvine et al.(2005) observed that daily soil CO2 efflux was linearly relatedto GPP as measured by the eddy covariance technique (r2 = 0.55,p < 0.01), furthering the evidence that GPP makes significant short-term contributions to soil respiration. Our results are an additionalindication that the connection between canopy processes and soilrespiration is not being made. Even though GPP can be reasonablyreproduced, there is still a significant mismatch between mod-eled and measured respiration data. This is especially visible whenGPP is plotted against TER (Fig. 5), as the ratio between GPP andTER is too large; too much of GPP is respired back to the atmo-sphere, thus yielding the low estimates of the magnitude of NEE.Difficulties in modeling soil respiration are present in other model-data syntheses as well. Braswell et al. (2005) applied nonlinearinversion to the eddy covariance flux measurements from HarvardForest using a simplified model of photosynthesis and evapotran-

spiration and concluded that multi-year eddy flux measurementsallow for a tight constraining of photosynthesis, but poor con-straints on parameters relating to soil decomposition, which variesat considerably longer time scales than photosynthesis and evap-otranspiration. Similarly, Verbeeck et al. (2006) found that the

S. Mitchell et al. / Ecological Modelling 220 (2009) 3259–3270 3267

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ig. 5. Scatterplots of the relationship between annual values for mean soil waterroduction (GPP), and gross primary production (GPP) and total ecosystem respirat

arameter responsible for the greatest amount of uncertainty inhe FORUG model was related to soil respiration, and Williams etl. (2005) concluded that long-term measurements of carbon poolizes are needed to estimate parameters relating to soil decompo-ition.

As a result, the simulations performed best with parameter val-es that were often on the extreme ends of their specified rangesroducing an increase in GPP that compensated for an overestima-ion of the magnitude of TER. Parameters that have a more directontrol over potential GPP, such as those that control leaf produc-ion and leaf nitrogen concentration, are clearly are among the mostensitive model parameters in Biome-BGC (White et al., 2000) anday be even more so under conditions of chronic water limitation.

or instance, low values of FRC:LC imply increased allocation toeaves and thus had high likelihoods in both stands. Like FRC:LC,smax showed inter-stand similarities among the posterior likeli-ood projections, and high-likelihood values associated with lowalues for gsmax were consistent with the workings of a water-imited system, since a lower maximal stomatal conductance willesult in decreased water loss. Furthermore, low values of FM implyow leaf (and fine root) turnover and had the highest likelihood

eights, probably due to reduced growth respiration costs for theeaves that could be used in constructing other biomass compo-ents, thereby increasing the magnitude of NEE. Field values of leafurnover were similar to the high likelihood values in the model,

ndicating a mean residence times of 3.6 years (FM = 0.28) (Law etl., 2001). Field values of fine root mean residence time were dif-erent from leaf values and were estimated at 1.6 years (FM = 0.63)Law et al., 2001), though estimates of fine root turnover are oftenroblematic (Strand et al., 2008).

ntial (�) and evapotranspiration (ET), evapotranspiration (ET) and gross primaryER). A total of 5000 simulations, retained and non-retained, are plotted.

Projections for these and other parameters exhibit not only ashaping of maximal values that can be attributed to certain param-eter values generating high likelihood estimates, but also stronginteraction effects with other parameter values. Both FRC:LC andFM showed high and low likelihoods for low values while showingan absence of low likelihood values for high parameter values whilegsmax showed a lack of low likelihood values for low parameter val-ues due to the interaction effects between other parameters. Theshaping of the behavioral likelihood projection (shown in black) forgsmax in the mature stand is an exceptional example of the stronginteractions that take place with other parameter values. Similarly,while high likelihood values were found for C:Nleaf in the youngstand, there was a slight tendency for higher likelihood values tobe found among high parameter values of C:Nleaf in the maturestand, a phenomenon which we suspect is due to a sensitivity inthe interaction with FLNR.

4.4. Investigating model failure: stand history data

We also recognize that one perceived source of model-datamismatch in our analysis may be related to the incorporationof clear-cutting disturbance and its potential effects on legaciesof remaining coarse woody debris and their contribution to TER.Even though we incorporated Biome-BGC’s pre-disturbance esti-mates of dead fine roots, leaf litter, soil C, and coarse woody debris

into our simulation, our estimates of coarse woody debris didnot include the potential contribution of tree stump biomass thatwould remain following a clear-cut. We know of no appropriatemethod for estimating the stump biomass that would remain fol-lowing a clear-cut in a single-life form model such as Biome-BGC

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268 S. Mitchell et al. / Ecological

ince estimates of stem biomass and allometry vary substantiallyhen generated by multiple sets of ecophysiological parameter

ombinations. However, we do not think that this alters our gen-ral conclusions for two reasons. First, as stated above, Sun et al.2004) found that coarse wood decomposition contributes only a

arginal amount to TER in this semi-arid forest, and our modeledesults likewise demonstrated the model’s insensitivity to param-ters such as CRC:SC and C:Ndead wood. Second, even if estimatesf NEE in this ecosystem were sensitive to the release of CO2 byoarse woody debris, the incorporation of additional amounts ofO2 release by decomposing stump materials would merely serveo further decrease the magnitude of NEE and result in even greater

odel-data mismatch, thereby strengthening our current conclu-ion.

.5. Investigating model failure: modeled past climate inputs

There is additional uncertainty in the generation of climaticata via the DAYMET model (Thornton and Running, 1999). TheAYMET model estimates meteorological data by taking measure-ents from surrounding weather stations and subsequently using

his data to estimate the meteorological data at a point near thoseeather stations. This method is most reliable when there are manyeather stations close to the point of interest and when the area

ver which the meteorological data are extrapolated is homoge-eous in its climatic patterns. Neither of these conditions is met

n an estimation of meteorological data at the Metolius sites. Theetolius sites occur in the eastern Cascade mountain range, where

ainfall patterns are tightly coupled to the rain-shadow effect thatharacterizes Pacific Northwest climate gradients (Waring andranklin, 1979), making reliable generations of site-specific mete-rological data difficult, particularly in a region with a relativelyparse population and [presumably] few weather stations.

We ran an informal test of the extent to which an exclusionf DAYMET data resulted in a different number of retained runsy running the model 5000 times with continuous data takenolely from the Ameriflux instrumentation. Of the simulations forhe young stand, 4.56% were retained and 3.94% were behavioral,ompared to 14.45% that were retained and 4.07% that were behav-oral in the simulations run with climate data generated with theAYMET model. The mature stand had 7.22% retained and 3.68%ere behavioral simulations, compared to 1.13% that were retained

nd 0.0045% that were behavioral in the simulations run with cli-ate data generated with the DAYMET model. In other words,

sing one year’s worth of site climate data resulted in a significanteduction of retained runs and a slight reduction in the number ofehavioral runs for the young stand. However, this same substitu-ion for the mature stand significantly increased the number of bothhe retained and behavioral simulations. Furthermore, 67% and 49%f these retained simulations underestimated the magnitude ofEE for the young and mature stands, respectively, which is a muchore even error distribution compared to the simulations run with

he more complete, though distantly estimated, historical climateata. Such a result partly vindicates the performance of the model

f only to raise new questions about the future difficulties of pre-icting meteorological data throughout the terrestrial biosphere,hough we acknowledge that the difficulties involved in predict-ng climate at our particular points could, in fact, be indicative of acenario in which such a task is uncharacteristically difficult. Nev-rtheless, one of the goals of ecological modeling is to simulate ancosystem, including future changes in response to climate forc-

ng, without any eddy covariance data to aid in model calibration,nd we think that our initial modeling exercise that included theAYMET data is more indicative of the common practices of ecosys-

em modeling and thus does not represent an extreme case in termsf procedure.

lling 220 (2009) 3259–3270

4.6. Investigating model failure: lack of temporal parametervariation

Wang et al. (2007) has noted that the CSIRO Biosphere model(CBM) can have very strong performance when photosyntheticparameters (maximum potential carboxylation rate and maximalelectron transport rate) are allowed to have different values forthe growing season and the dormant season. Such an innovationin the photosynthetic parameters of Biome-BGC may come at theexpense of introducing more parameters to be identified, but maynevertheless result in improved model performance. Our version ofBiome-BGC might also benefit from having allometric parameters(SC:LC, FRC:LC, CRC:SC) that vary with age, as such parameters areknown to vary significantly in the field. As stated previously, Lawet al. (2004a,b) found that xeric Pinus ponderosa systems exhib-ited decreased below-ground biomass allocation with age whilemesic systems exhibited increased below-ground biomass alloca-tion with age, and Comeau and Kimmons (1989) found that patternsof FRC:LC in Pinus contorta can greatly vary as a function of sitewater availability. Likewise, the likelihood projections for FRC:LCand SC:LC are shaped differently for the two stands, making it clearthat accounting for temporal changes in parameter values may benecessary to improve model performance.

5. Conclusions

We have incorporated the uncertainty that arises from bothmultidimensional parameter variability and eddy flux measure-ment uncertainty by simulating 400,000 combinations of 13parameter values for two differently-aged stands and testing tosee if estimates of NEE from those simulations can fall within thebounds of measurement uncertainty inherent in estimates of NEEbased on eddy flux measurements. Studies that provide an accountof uncertainty to this extent are rare, and our results suggest thatBiome-BGC should not be considered to be a reliable simulator ofnet ecosystem CO2 exchange in these semi-arid forests and possiblyadditional ecosystems as well. It is clear that substantial uncertain-ties remain in this terrestrial ecosystem modeling scheme and itsrepresentation of forest stand development. While recognizing thereal need for predictions regarding the dynamics of global change,scientists are often attempting to make predictions under condi-tions of incomplete knowledge for the ecosystems of concern. Itwould seem that, in the case of Biome-BGC, there is not only a prob-lem of multidimensional parameter variability that is shared withother models, but also a fundamental deficiency in model structure.We think that the model does not provide a realistic representationof ecosystem respiration at the study sites, and the only parametersets that can emulate NEE dynamics are those that manage to com-pensate for this shortcoming by allocating resources that maximizeGPP, no doubt skewing the simulation of other metrics of ecosystemprocess and function. We think that a rethinking of model structureand parameterization schemes, especially with regard to ecosystemrespiration, may be required to adapt Biome-BGC to meet the needof accurate estimates of net ecosystem CO2 exchange, and we sus-pect that this is true for other models as well. An incorporation ofboth measurement uncertainty and parameter variability can playa valuable role in detecting specific problems in model structureand we encourage such a procedure in future ecosystem processmodel assessments.

Acknowledgements

We would like to thank Beverly Law for access to her data fromMetolius and for her helpful insights about the site and modelingwith Biome-BGC. We would also like to thank Kari O’Connell andMark Harmon for their comments on this manuscript, as well as

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aul Smith and Sarah Dean at Lancaster University for their assis-ance with some of the technical aspects of the GLUE programming

ethodology. Discussions regarding Biome-BGC with Ron Neilsont the United States Forest Service Pacific Northwest Research Sta-ion were also very helpful, as was his generosity in letting us useis Linux cluster. Biome-BGC version 4.1.2 was provided by Peterhornton at the National Center for Atmospheric Research (NCAR),nd by the Numerical Terradynamic Simulation Group (NTSG) athe University of Montana. NCAR is sponsored by the National Sci-nce Foundation. Support for this research was provided by an NSFGERT graduate fellowship to S.R. Mitchell (NSF award #0333257)n the Ecosystem Informatics IGERT program at Oregon State Uni-ersity. Development of the GLUE methodology has been supportedy UK NERC grant NER/L/S/2001/00658.

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