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Ecological Modelling 260 (2013) 50– 61

Contents lists available at SciVerse ScienceDirect

Ecological Modelling

jo ur nal home p ag e: www.elsev ier .com/ locate /eco lmodel

Modelling the decadal trend of ecosystem carbon fluxes demonstratesthe important role of functional changes in a temperatedeciduous forest

J. Wua,∗, P.E. Janssonb, L. van der Lindena,c, K. Pilegaarda, C. Beiera, A. Ibroma

a Technical University of Denmark, Department of Chemical and Biochemical Engineering, Centre for Ecology and Environmental Sustainability, 4000Roskilde, Denmarkb Royal Institute of Technology (KTH), Department of Land and Water Resources Engineering, 10044 Stockholm, Swedenc Australian Water Quality Centre, 5000 Adelaide, Australia

a r t i c l e i n f o

Article history:Received 15 November 2012Received in revised form 5 March 2013Accepted 25 March 2013

Keywords:Net ecosystem exchangeCoupModelFunctional changeModel data fusionMultiple constraints approach

a b s t r a c t

Temperate forests are globally important carbon sinks and stocks. Trends in net ecosystem exchangehave been observed in a Danish beech forest and this trend cannot be entirely attributed to changingclimatic drivers. This study sought to clarify the mechanisms responsible for the observed trend, usinga dynamic ecosystem model (CoupModel) and model data fusion with multiple constraints and modelexperiments. Experiments with different validation datasets showed that a multiple constraints modeldata fusion approach that included the annual tree growth, the seasonal canopy development, the latentand sensible heat fluxes and the CO2 fluxes decreased the parameter uncertainty considerably comparedto using CO2 fluxes as validation data alone. The fitted model was able to simulate the observed carbonfluxes well (R2 = 0.8, mean error = 0.1 g C m−2 d−1) but did not reproduce the decadal (1997–2009) trendin carbon uptake when global parameter estimates were used. Annual parameter estimates were ableto reproduce the decadal scale trend; the yearly fitted posterior parameters (e.g. the light use efficiency)indicated a role for changes in the ecosystem functional properties. A possible role for nitrogen demandduring mast years is supported by the inter-annual variability in the estimated parameters. The inter-annual variability of photosynthesis parameters was fundamental to the simulation of the trend in carbonfluxes in the investigated beech forest and this demonstrates the importance of functional change incarbon balance.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Terrestrial ecosystems are dynamic components of the globalcarbon (C) cycle, acting as a net C sink of 1.0–2.6 Pg C yr−1 glob-ally (Metz, 2007). Forests are important C stocks, covering 31%of the Earth’s land surface (FAO, 2010) and storing approximately861 Pg C (Pan et al., 2011), more than the total atmospheric C stockof 805 Pg (Houghton, 2007). The estimated net C uptake by theworld’s forests (excluding the emission of 3 Pg C yr−1 due to tropi-cal deforestation) is on average 4 Pg C yr−1 in 1990–2007 (Pan et al.,2011), equivalent to almost half of the anthropogenic C emissionsin 2009 (Friedlingstein et al., 2010). Temperate forests contributeroughly 20% and 14% to the global forest area and forest C stock,respectively (Pan et al., 2011). The C sink in temperate forests hasincreased by 17% during the past two decades, contrary to borealand tropical forests, which were either unchanged or decreased by

∗ Corresponding author. Tel.: +45 46774223; fax: +45 46774100.E-mail address: jiwu@kt.dtu.dk (J. Wu).

23%, respectively (Pan et al., 2011). Temperate forests span largeareas of Europe (FAO, 2010). Historically, the natural composition offorests in Europe was mainly deciduous, until human managementresulted in an increase in the proportion of conifers, predomi-nantly for economic reasons (Spiecker, 2003). Today the fraction ofconiferous species in European temperate forests far exceeds theirnatural range. This has stimulated concerns about their ecologicalfunctioning and new management plans to reverse the compo-sitional change of European forests to contain more deciduoustree species (Spiecker, 2003). Given the high C sink potential andincreasing importance of temperate deciduous forests in the future,questions such as how they will respond to the changing climateand whether or not they can continue to serve as a strong sink ofatmospheric CO2 is of interest to scientists, policy makers and thepublic in general.

Process-based models are important tools to simulate ecosys-tem responses and states under future climatic conditions.Eco-physiological processes can be described either mechanis-tically, e.g. CO2 diffusion through the stomata and leaf surface(Collatz et al., 1991) or semi-empirically, e.g. the light response of

0304-3800/$ – see front matter © 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.ecolmodel.2013.03.015

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J. Wu et al. / Ecological Modelling 260 (2013) 50– 61 51

stomatal conductance (Jarvis, 1976) or environmental controls onplant phenology (Hänninen, 1995; Richardson et al., 2012). Manydifferent process-based ecosystem models have been developedand validated against measured C fluxes in different ecosystems.Generally, the models perform reasonably well at the site levelto predict the seasonal or short-term interannual variability ofecosystem C fluxes (e.g. Williams et al., 2005; Wu et al., 2011).However, they have been found to be less able to reproduce thelong-term variability (Keenan et al., 2012a). Keenan et al. (2012b)assessed the ability of 16 ecosystem models to simulate 11 long-term flux datasets and found that none of the models couldconsistently reproduce the observed interannual variability in theC fluxes. Similarly, several cross-site model inter-comparison stud-ies demonstrated strong divergences in model predictions (Krameret al., 2002; Morales et al., 2005; Siqueira et al., 2006). Anotherrecent modelling study in a boreal pine forest showed howeverexceptional good model performance for the long-term ecosystemC dynamics as the boreal ecosystem processes were found to bestrongly controlled by the interannual variation in the soil and airtemperature (Wu et al., 2012b).

The optimisation of process models and the investigation offuture ecosystem C cycling can be integrated in what are knownas model data fusion (MDF) studies (Wang et al., 2009). The uncer-tainty in the model projections can be reduced if the observedecological datasets are assimilated by the model to constrain theparameter ranges, determine parameter sensitivity and indentifypotential model structural deficits (Beven and Freer, 2001; Keenanet al., 2012a). MDF studies are especially beneficial when conductedat sites that have been intensively studied for long periods. Forinstance, the models can be applied at sites which have experiencedsummer heat waves (Reichstein et al., 2007) to evaluate whetherthey could capture the extreme or lagged ecosystem responses.Model data fusion can also be applied to separate the influenceof climatic effects and spatially-varying nitrogen deposition onforest growth by analyzing the model-data mismatch (Eastaughet al., 2011). In addition, for some sites that have a systematic phe-nomenon, e.g. a trend of increasing carbon uptake (Pilegaard et al.,2011; Keenan et al., 2012a), it is also particularly interesting toinvestigate whether models could identify the possible causes forthe ecosystem responses, e.g. whether the trend is caused by thedirect effect of climatic forcing or by changes of ecosystem func-tional properties (termed as functional change). Functional changescan be changes in the canopy structure, canopy photosyntheticcapacity or species composition (Wu et al., 2012a) which couldbe caused by aging, interventions (e.g. nitrogen deposition) or theindirect or lagged effects of climatic forcing (e.g. extreme weatherevents).

In a temperate deciduous forest near Sorø, Zealand Denmark,net ecosystem exchange of CO2 (NEE) was continuously measuredover the past 13 years (1997–2009), showing a trend of increasing Cuptake of 23 g C m−2 yr−2 (Pilegaard et al., 2011). Extended C uptakeperiod and enhanced canopy photosynthetic capacity were identi-fied as the main drivers of the trend (Pilegaard et al., 2011). Using asemi-empirical model, Wu et al. (2012a) confirmed that the long-term ecosystem C dynamics at this site cannot be solely explainedby the direct effect of climate variability and trends whereas thefunctional changes during the 13-year period were the most impor-tant drivers. The objective of this study was to evaluate whetherprocess-based models could dynamically simulate the changes inthe ecosystem functioning (e.g. phenology and canopy develop-ment and physiology) and the long-term variability in the carbonuptake at this site. We hypothesize that both functional changesand climate variability contributed to the observed long-term trendin CO2 uptake and that these contributions can be distinguishedusing a dynamic process-based model. Implicit in this hypothesisis that the process based model can simulate both the short-term

(i.e. diurnal or seasonal time scales) and the long-term (i.e. inter-annual time scales) carbon dynamics. We expect that the degree ofrealism in the model simulation increases, if the parameter estima-tion includes multiple response data such as LAI development, treegrowth and CO2 fluxes, i.e. a multiple constraints MDF approachis used. In order to test our hypothesis, firstly a process-basedmodel was optimized and applied to simulate the ecosystem Cdynamics with the model parameters globally fitted using a mul-tiple constraints approach. Secondly, the model parameters werefitted for each year separately and allowed to vary between years(as an approximation of ecosystem functional change) during thesimulation. The results of these two modelling experiments wereexamined to identify the drivers of short-term variability and thelong-term trend of increasing carbon uptake.

2. Materials and methods

2.1. Site

The data used in this study were measured in a temperate decid-uous forest in the Danish long-term CO2 flux investigation site, Sorø(55◦29′13′ N, 11◦38′45′ E). The major tree species in the forest isEuropean beech (Fagus sylvatica L.), mixed with a small propor-tion of coniferous species such as Norway spruce (Picea abies L.)and European Larch (Larix decidua Mill.). In 2011, the stand aroundthe flux tower was 90 years old, the average tree height was 28 mand the average diameter at breast height was 42 cm. Annual meantemperature and precipitation sum (1997–2009) at the site were8.5 ◦C and 564 mm, respectively. The soils are classified as alfisolsor mollisols (depending on the base saturation) with a 10–40 cmdeep organic layer. Further information about the site can be foundin Pilegaard et al. (2001, 2003, 2011).

2.2. Driver and validation data

Hourly gap-filled meteorological data from August 1996 toDecember 2009 (Pilegaard et al., 2011) were used as drivers of themodel. Carbon, latent and sensible heat fluxes from the years 1997to 2009 were quality controlled and corrected for below-canopystorage and low turbulence mixing (Pilegaard et al., 2011) andused for model calibration. Data of the aboveground and below-ground biomass stocks were estimated from tree ring data, heightmeasurements and biomass expansion functions (Skovsgaard andNord-Larsen, 2012). Peak leaf area index (LAI) was measured with aLAI-2000 canopy analyser (LI-COR, NE, USA) during overcast days inthe main growing season, i.e. June–August (Pilegaard et al., 2011);together with the continuously measured PAR transmission, the LAItime series was modelled using the Lambert and Beer law (Monsiand Saeki, 1953) and continuously measured photosyntheticallyactive radiation (PAR) fluxes below (Q) and above (Q0) the canopy(Eq. (1)). From the two PAR measurements the relative PAR trans-mission was calculated. The value of the light extinction coefficient(k) was calibrated by fitting the simulated peak LAI values againstthose measured in the years 2004 and 2007–2010 (see also inPilegaard et al., 2011).

LAI = − ln(Q/Q0)k

(1)

Soil temperatures were measured in the top 5 and 10 cm and thesoil water content was measured by TDR-probes (TRIME-EZ, Imkoand Theta Probe ML-2x, Delta-T Devices) at 0–15 cm. The carbonuptake periods (CUP) were calculated from both the measured andsimulated NEE time series after Pilegaard et al. (2011).

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52 J. Wu et al. / Ecological Modelling 260 (2013) 50– 61

Table 1Calibration model parameters and their prior ranges (with uniform distribution); the parameters marked with * were also fitted annually in the second model experiment.

Parameter Unit Symbol Eq./note Prior

Min Max

Plant biotic processesRadEfficiency(1)* g Dw MJ−1 ε1 Eq. (A1) 1 8RadEfficiency(2) g Dw MJ−1 ε2 Eq. (A1) 1 8T Lmin ◦C pmn Eq. (A2) –5 5T Lopt1 ◦C po1 Eq. (A2) 10 20Allocation leaf – fl Eq. (A5) 0.2 0.6Allocation root – fr Eq. (A5) 0.2 0.6Maitaince Res. leaf* d−1 rm,l Eq. (A6) 5.00E−04 0.005Maitaince Res. root* d−1 rm,r Eq. (A6) 5.00E−04 0.005Emerge Tsum(1)* ◦C tel Eq. (A8) 100 200LeafTsum2(1)* ◦C tL2 Eq. (A9) 100 200LeafRate1(1) d−1 lLc1 Eq. (A9) 1.00E−04 0.01LeafRate2(1) d−1 lLc2 Eq. (A9) 0.05 0.5

Plant abiotic processesCritThresholdDry cm water c Eq. (A16) 100 1.00E+04TempCoefA – tWA Eq. (A17) 0.2 1.5TempCoefC – Ttrig Eq. (A17) 0 6Conduct Ris(1) J m−2 d−1 gris Eq. (A18) 1.00E+06 1.00E+07Conduct VPD(1) Pa gvpd Eq. (A18) 50 300Conduct Max(1) m s−1 gmax Eq. (A18) 0.01 0.03

Soil carbon processesRateCoefLitter1* d−1 kl Eq. (A21) 0.02 0.05RateCoefHumus* d−1 kh Eq. (A22) 1.0E−05 5.0E−04TempMin ◦C tmin Eq. (A23) –10 0TempMax ◦C tmax Eq. (A23) 20 30SaturationActivity – pqSatact Eq. (A24) 0 0.5ThetaLowerRange % pqLow Eq. (A24) 3 20ThetaUpperRange % pqUp Eq. (A24) 3 20

Soil physical processesAir entry (0–0.05 m) cm water a Eq. (A26) 1 20Air entry (0.05–0.15 m) cm water a Eq. (A26) 1 20DrainLevel m zp Eq. (A27) –2 –1DrainSpacing m dp Eq. (A27) 0 100

2.3. Model description

The CoupModel is a one-dimensional process-based ecosys-tem model that can be used to simulate the coupled biologicaland physical processes in soil-plant-atmosphere systems (Janssonand Karlberg, 2004; Jansson et al., 2008; Jansson, 2012). Hourlymeteorological measurements of air temperature, global radia-tion, relative humidity, wind speed and precipitation were used asmodel drivers. The basic structure of the model represents verticallayers of the soil profiles and plants, where heat and water fluxes arecalculated. The simulated soil temperature and moisture, togetherwith the climatic drivers regulate the biotic ecosystem processessuch as phenology, photosynthesis, plant respiration and decom-position of litter and soil organic matter. In addition, the bioticecosystem dynamics feedback to the simulated physical environ-ment. For instance, the simulated plant structure will affect theaerodynamic conductance at the atmosphere and leaf surface; like-wise, changes in LAI alter the energy and water balance at the soilsurface. Photosynthesis in the model is simulated by a light useefficiency function that is further limited by unfavourable weatherconditions. The simulated respiration includes both growth res-piration (as fixed fractions of total assimilates) and maintenancerespiration (as rate coefficients). The assimilated carbon is allo-cated to the different components of the vegetation (leaf, stem,coarse root and fine roots) in fixed fractions. A detailed descrip-tion of CoupModel can be found in Jansson and Moon (2001),Jansson and Karlberg (2004) and Wu et al. (2011). The modelequations and parameters relevant to this paper are given inAppendix 1.

2.4. Model setup and calibration

The model was initialized as of August 1996 and calibrated forthe period 1997–2009. The initial C pools in vegetation and soilwere given as parameters based on the measured and estimateddata in August 1996. The soil physical parameters were either mea-sured, e.g. parameters for the water retention curve or estimated bysoil texture data, e.g. the soil thermal properties. Some other bio-logical parameters such as the specific leaf area (28.5 m2 kg−1) andplant height (28 m) were also measured on site. The data necessaryfor the model initialisation are available in BADM (Biological-ancillary-disturbance-management) format at the European FluxDatabase (http://gaia.agraria.unitus.it/).

Two modelling experiments were performed. In the first, themodel was calibrated against the whole 13 year (1997–2009) data,where 29 parameters that were expected to be sensitive to the car-bon and water dynamics (Table 1) were selected for calibrationaccording to experiences of model application and a sensitivitystudy by Svensson et al. (2008b). The prior distributions of themodel parameters (Table 1) were set to reasonably wide rangeswith uniform distribution based on literature and previous modelapplications (e.g. Svensson et al., 2008a; Wu et al., 2011). A totalnumber of 30,000 model runs were performed in the first modellingexperiment. The acceptance of behavioural models (i.e. modelssimulation with the same structure but different parameter val-ues) was based on specific user-defined criteria (Beven and Freer,2001; Liu et al., 2009). Two different constraints were consid-ered: (1) only the hourly NEE data (denoted as ˝NEE) and (2) thehourly daytime and night-time NEE, latent (�E) and sensible heat

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J. Wu et al. / Ecological Modelling 260 (2013) 50– 61 53

(H) fluxes and other biological data (denoted as ˝Multiple) wereused to select the behavioural models to determine the posteriorparameter distributions. The detailed acceptance criteria are givenin Table 2.

In order to test the hypothesis that functional changes in theecosystem have occurred over the observation period and affectedthe annual C uptake capacity of the forest, a second modellingexperiment (3000 model runs) was designed based on the opti-mized posterior parameter sets in the first modelling experiment.In this modelling experiment, the number of sampled parameterswas reduced to seven of those that control photosynthesis and res-piration and they were allowed to vary between years (Table 1).Only seven parameters were included in the model calibrationbecause it is difficult to constrain all 29 parameters with singleyear datasets. The selected seven parameters were all biologicallyrelated and thus are considered more susceptible to change overtime than the physical parameters calibrated in the first modelexperiment. Furthermore, these biological parameters are closelylinked with our hypotheses about the potential functional changesin the forest such as changes in the canopy photosynthetic capacity,canopy structure or base respiration. The inter-annual variabil-ity of ecosystem functioning is captured and represented by theparameter estimates generated for each year. Systematic variationof the model residuals with time indicates the temporal changeof ecosystem functional properties that are not represented in themodel.

3. Results

3.1. Model simulation using the multiple constraints approach

The posterior distribution of most parameters was differ-ent from their prior uniform distributions after the calibration(Fig. 1). With the single constraint, ˝NEE, only a few parame-ters (e.g. ε1, lLc1 and c) were constrained; the posterior rangesof most other parameters were still similar to their prior. Thislow degree of parameter identification was improved when themultiple constraints approach was imposed (˝Multiple). The pos-terior ranges of 9 key parameters controlling photosynthesis (e.g.ε1, pol), humus and litter decomposition (e.g. kl and kh), phen-ology (e.g. tel), allocation (e.g. fl and fr) and transpiration (e.g.Ttrig and gvpd) were clearly narrowed down as the day-time NEE,night-time NEE, yearly LAI, yearly biomass stocks, and �E werejointly used to constrain the model (˝Multiple, Table 2). Com-pared to the first model calibration, separating the daytime andnight-time NEE for the model calibration resulted in better con-strained estimates of respiration related parameters. In addition, allthe remaining 20 calibrated parameters were also more preciselydetermined, as the posterior distributions were changed from theirprior uniform distributions to normal or log normal type distribu-tions.

With both of the two different constraints, ˝NEE and ˝Multiple,the ensemble mean of the modelled outputs represented the mea-surements well, with almost equally good R2 and mean error (ME).The variability of the hourly NEE during the 13-year period wascaptured by the model (R2: 0.72 and 0.75), partly as a product ofthe good simulation of LAI dynamics (R2: 0.86 and 0.88). The soilheat processes were better simulated than the soil water trans-port and storage. The model explained approximately 92% and60% of the variability in the measured soil temperature and soilwater content, respectively. In contrast, the uncertainty (i.e. therange of the R2 and ME for the accepted runs) of all the modeloutputs was significantly lower with ˝Multiple compared to ˝NEE(Table 2). The model simulation using the modes of the poste-rior parameters of ˝Multiple (see Fig. 1) performed equally well Ta

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54 J. Wu et al. / Ecological Modelling 260 (2013) 50– 61

Fig. 1. Posterior parameter distributions (density plots) after fitting the model globally to the 13-year datasets using two different constraints, ˝NEE and ˝Multiple (see textfor details). The prior parameter distributions are set as uniform and the parameter descriptions are given in Table 1. The dashed vertical lines are the modes of the posteriorparameter distributions. Acceptance criteria of the behavioural models are given in Table 2.

as the ensemble mean of the accepted runs (Table 2). However,the simulation using the mode of the posterior parameters of˝NEE performed worse than the corresponding ensemble means(Table 2).

3.2. Model performance at diurnal and seasonal time scale

The correlation between the daily modelled and measured NEEwas higher than that at hourly time scale with R2 = 0.8 (Fig. 2).The model residuals showed an overestimation of carbon uptake athigh radiation (Fig. 2), which was also seen in the monthly diurnalcourse for the model-data mismatch (Fig. 3) where the simulatedC uptake was higher than the measurements at mid-day duringthe growing season. In general, the diurnal cycle was well sim-ulated throughout the year except in April when the simulateddaytime NEE was apparently lower than the measurements. Theinitiation and termination of photosynthesis were correctly rep-resented by the model (Fig. 3). The magnitude of night-time NEEwas also well simulated during both the winter and the growingseason.

Apart from the diurnal pattern, the flux and LAI seasonality wasalso reasonably well simulated. In all years, the peak LAI duringsummer was within the simulated uncertainty range. However, theensemble mean of the simulated LAI was higher in 2004–2005 andlower in 2009 than the observations. The interannual variabilityin the leaf flush dates was correctly identified, except in 2006 and

2007 when the model predictions were earlier and later than theobservations, respectively (Fig. 4). The leaf fall during autumn wasless well represented in the model than the leaf flush. The simu-lated leaf fall was earlier (ca.15-30 days) than the measurementsin 2002, 2003, 2004 and 2009, while it was later (ca. 20 days) in2000. In addition to the well simulated phenology, the estimatedcarbon uptake periods (CUP) based on the modelled NEE (Fig. 5a)also showed a similar trend as the measurements (Pilegaard et al.,2011), with an extension of the CUP of 1.7 d yr−1 during the 13-yearperiod.

3.3. Model performance at interannual time scale

With the globally fitted parameter sets in the first modellingexperiment (i.e. calibrated against the whole 13-year dataset), thedecadal trend of increasing carbon uptake of the forest was notreproduced by the model (Fig. 5b). The carbon uptake was over-estimated in 1997–2000 and underestimated in 2005–2009. Inthe second step of the model calibration, the interannual vari-ability in the carbon uptake was successfully simulated withyearly fitted model parameters (Fig. 5b). Out of the 7 yearlyfitted parameters, only light use efficiency showed an increas-ing trend in 1997–2009 (Fig. 5c). The other 6 parameters wereless well constrained and the mode of the posterior parame-ter distributions did not show a trend over the 13-year period(Table 3).

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J. Wu et al. / Ecological Modelling 260 (2013) 50– 61 55

Fig. 2. Observed and simulated (ensemble mean of accepted models) NEE (daily value) from 1997 to 2009; model residuals (simulated-observed) plotted against climaticvariables.

4. Discussion

By constraining the process-based model with long-term mea-surements of NEE datasets, the ensemble mean of the modeloutputs produced reasonably good estimates for both the NEEand other validation datasets. However, the accepted ensemble ofbehavioural models showed a high degree of equifinality, i.e. a num-ber of different models could produce equally good results whencompared to calibrated variables (Beven and Freer, 2001), resultingin high uncertainties in the estimates of other validated variables.This indicated that some behavioural models with certain parame-terisations were accepted for the wrong reasons. For instance, themodel could well represent the NEE (R2: 0.71–0.73) even when

Table 3Linear regression fit statistics for the analysis of the trend in the annually fittedparameters in 1997–2009.

Parameter Unit Symbol Slope R2 p value

RadEfficiency(1) g C MJ−1 ε1 0.13 0.72 0.0001Emerge Tsum(1) ◦C tel 0.71 0.31 0.051LeafTsum2(1) ◦C tL2 0.21 0.15 0.20RateCoefLitter1 d−1 kl 0 0.16 0.18RateCoefHumus d−1 kh 0 0.01 0.72MCoefRoot(1) d−1 rm,r 0 0 1.00MCoefLeaf(1) d−1 rm,l 0 0.06 0.41

the LAI dynamics were incorrectly represented (lowest R2 = 0.46).The problem of equifinality was also shown in the high number ofunconstrained posterior parameters (Fig. 1) which was similar tomany other MDF studies, where it was shown that the informa-tion content of the high frequency NEE datasets was not sufficientenough to constrain the parameters related to the different ecosys-tem component C fluxes, e.g. the autotrophic and heterotrophicrespirations from different C pools (Sacks et al., 2007; Wang et al.,2009; Keenan et al., 2012a; Richardson et al., 2012).

On the other hand, the success of MDF studies also dependson how efficiently the information in the assimilated datasetswas used. For example, the uncertainty in the model outputs wasreduced when the NEE datasets were averaged in time (e.g. monthlyand annually) and added to the model calibration (Keenan et al.,2012a). Sacks et al. (2007) showed that optimizing the model ona twice daily (instead of hourly or daily) time step significantlyimproved the model’s ability to accurately predict the componentC fluxes. Mahecha et al. (2010) proposed a method to quantify themodel-data disagreements at various time-frequency domains; thedecomposed high or low frequency signals could also potentiallybe used to optimize the model parameters. In this study, we moreefficiently used the NEE datasets by separating it into daytime andnight-time values in the model calibration (in ˝Multiple). In this way,the parameters controlling the litter and humus decomposition ratewere better constrained.

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56 J. Wu et al. / Ecological Modelling 260 (2013) 50– 61

Fig. 3. Thirteen year averages of observed and simulated mean monthly diurnal courses of NEE (ensemble means and single run using the modes of the posterior parameterdistributions).

In general, the parameter uncertainties were significantlyreduced when additional constraints were incorporated. Includ-ing the yearly LAI, yearly biomass stock and �E in the calibrationstrongly constrained 9 key model parameters and successfullyreduced posterior uncertainty in all of the remaining 20 parame-ters. The way the parameters were constrained could be attributedto the specific information content of the assimilated data whichwere related to certain ecosystem processes. For instance, the respi-ration parameters (rml, rmr, kl and kh) were better constrained whenthe night-time NEE was separately included in the calibration.However, because the autotrophic and heterotrophic respirationwere not distinguished in the data, these parameters were stillcorrelated. Nevertheless, the additionally constrained posteriorparameters are more meaningful as shown by the more realis-tic distribution of these parameters. The inclusion of LAI into thecalibration specifically constrained 4 parameters controlling thephenology (tel, tL2), litter fall rate during the growing season (lLC1),and allocation (fl). Using the multiple constraints approach, some ofthe constrained parameters shifted their distributions. For instance,the light use efficiency, ε1 shifted its distribution to a higher magni-tude when the daytime NEE was explicitly used in the calibration.In a ideal situation, using the multiple constraints approach isexpected to facilitate the process-based model optimisation, and itis interesting to investigate, for example, which additional datasetsare most beneficial for the model calibration. However, addingmore constraints does not necessarily always lead to a better modeloptimisation because the data quality, e.g. the consistency of theecosystem C budget datasets (Luyssaert et al., 2009) is of crucialimportance for the MDF.

With the multiple constraints approach, the diurnal and sea-sonal dynamics of the ecosystem C fluxes could be well representedby the model. The diurnal cycle of NEE was correctly simulated inall different seasons, except in the winter-spring transition periods,

as the small amount of the emerging coniferous photosynthesiswas not accounted for in the model. In May–August, the mea-sured NEE at mid-day was lower than the modelled value, probablybecause linear light use efficiency models in general tend to overes-timate the photosynthesis when the radiation is already saturated(Ibrom et al., 2008). On the other hand, as the model was calibratedagainst the daytime NEE, the underestimation during the winterperiods (i.e. the unaccounted coniferous photosynthesis) was pos-sibly compensated by an overestimation of the daytime NEE duringthe growing season. The uncertainty of the measured NEE wasshown to be higher during night, thus the criteria for acceptanceof the night-time NEE was also less strictly set. Nevertheless, themagnitude of night-time NEE was correctly simulated.

The seasonality of the ecosystem dynamics was also well simu-lated in the diurnal patterns. The leaf flush dates were reasonablywell estimated with the temperature sum function (Eq. (A8)). Aninteresting model data mismatch was in 2007 when the spring tem-perature was the warmest during the 13-year period (see fig. 1 inWu et al., 2012a), the predicted leaf flush date was apparently ear-lier than the observation (Fig. 3). One possible explanation for the“delayed” leaf flush could be the effect of late frosts (Linkosalo et al.,2000). However, after a screening of the temperature datasets, nosuch late frost events were recorded from March–May 2007. There-fore, it is likely that the phenology sub-model is over sensitive inperiods with extreme temperature records. This was also the casefor the spring 2006 (coolest during the 13-year), when the modelpredicted a late leaf flush. The prediction of phenology has provenchallenging. Richardson et al. (2012) analyzed the performance of14 different models and showed that almost all the models con-sistently predicted a too early leaf flush. In our case, the modeldid not show a systematic bias but a poor performance in periodswith extreme air temperatures (i.e. warmest and coldest withindecades). As the average and variability of global temperature is

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J. Wu et al. / Ecological Modelling 260 (2013) 50– 61 57

Fig. 4. Observed (black) and simulated ensemble mean (red line and grey area for the maximum and minimum) of the LAI development in 1999–2009. The blue dashed linesare the averaged seasonal LAI dynamics for 1999–2009. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of thearticle.)

expected to increase, it is unlikely that the phenology model usedwill correctly project the seasonality of future ecosystem responses.The simulated interannual variation in the peak LAI was lowerthan the estimated LAI based on measured PAR transmission data(LAIpar). For instance, in 2008 and 2009, the LAIpar was higher andlower than the 13-year average, respectively, while the simulatedLAI did not show considerable differences. A possible reason for thislower variability in the simulated LAI is that the CoupModel usesa fixed allocation scheme. This could be improved by incorporat-ing a more dynamic allocation algorithm that is able to simulatethe plant behaviour under different environmental conditions, e.g.more belowground allocation in response to water stress. This isparticularly important for modelling ecosystems that have expe-rienced extreme events, such as the heat wave in 2003. Duringour study period, the Sorø forest did not experience such extremeevents, thus, it is likely that the fixed allocation scheme was ade-quate.

Although the process-based model performed reasonably wellat diurnal and seasonal time scales, it failed to accurately repro-duce the interannual variability in the ecosystem C uptake (Fig. 5).The small systematic short-term model errors accumulated in someyears and resulted in a large bias in the simulated annual C balancesat the interannual time scale; similar results have been found inmany other modelling studies (e.g., Siqueira et al., 2006; Keenanet al., 2012a,b). This indicated that the long-term C dynamics couldneither be fully explained by the climate variables included inthis study, as demonstrated in our previous study using semi-empirical modelling (Wu et al., 2012a), nor by the dynamic changesof ecosystem that are represented in the current CoupModel ver-sion.

The failure to predict the long-term C dynamics can be causedby the inaccurate representation of the biotic ecosystem responsesin the model (Richardson et al., 2007; Wu et al., 2012a). Onehypothesis for this model-data mismatch is that the applied modelstructures (within CoupModel) used a fixed nitrogen response tophotosynthesis, and thus did not dynamically simulate the effectsof, e.g., changing canopy nitrogen contents. In the second modelexperiment, the 7 parameters controlling photosynthesis, phen-ology and respiration, were allowed to vary inter-annually andconsidered proximate for the ecosystem functional change. Theestimated light use efficiency varied between years and showeda systematic trend during the 13-year period, corresponding to thehypothesis presented by Pilegaard et al. (2011). On the other hand,this model-data mismatch could also be caused by missing modeldrivers. For instance the fertilisation effects of CO2 during the 13-year period were not accounted in the model as the present versionof CoupModel used a light use efficiency dependent photosynthesismodule. On a global scale the atmospheric CO2 concentration hasincreased by 25 ppm during the study period (Friedlingstein et al.,2010). This small concentration increase could only partly havecontributed to the increased light use efficiency over 1997–2009.Therefore, it is most likely the ecosystem internal nitrogen cyclinghas affected light use efficiency. The measured N deposition at thesite was about 20 kg N ha−1 yr−1 in 2007 while the overall N depo-sition to Danish land surface decreased by 28% during 1989–2007(Ellermann et al., 2009). However, the estimated N leaching waslow (Beier et al., 2001), which means that N is still accumulat-ing in the ecosystem. This could probably explain the increasinglight use efficiency. An interesting finding was that the strong neg-ative light use efficiency fluctuations were strongly associated with

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58 J. Wu et al. / Ecological Modelling 260 (2013) 50– 61

Fig. 5. (a) Observed and simulated carbon uptake periods (CUP) in 1997–2009. (b)Observed and simulated (using globally and yearly fitted parameter sets) annual NEEin 1997–2009. The trend lines were linear regressions of the observation and modeloutputs with yearly fitted parameters. (c) Interannual variation in the yearly fittedlight use efficiency, ε1 the solid grey dots represent mast years and the horizontaldashed line was the globally fitted ε1.

the occurrence of mast years. This indicates that the reallocationof nitrogen to the nuts might deplete stored nutrients and lowerthe N content of the leaves. To provide support for this hypoth-esis, direct measurements of nut production and its role in theN-turnover of the ecosystem are needed. The litterfall during nor-mal and mast years were measured and the results showed thatin this beech forest, intensive fruit production increased the N fluxin the litter by 60% compared to normal years (Wang et al., 2013).Other direct evidence of resource depletion in the masting treesis rare. Sala et al. (2012) examined the timing and magnitude ofstored nutrient depletion after a heavy mast events in a coniferforest and confirmed that mast events deplete stored tree internalnutrients (including nitrogen and phosphorus) and reduced the leafphotosynthetic rates. Therefore, changes in the biophysical param-eters such as the canopy photosynthetic capacity, leaf chlorophyllcontent and canopy nitrogen distribution need to be monitored,using both field observations or remote sensing (Houborg andBoegh, 2008). The processes governing nitrogen dynamics andtheir interaction with photosynthesis needs to be incorporated intoprocess-based models.

5. Conclusions

Process-based models are needed for the projection of futureecosystem responses to climate change. We used a 13-year datasetfrom Sorø to test whether the model could simulate the short-termand long-term ecosystem C dynamics. After the model calibra-tion, the diurnal and seasonal patterns of carbon were successfullysimulated, while the degree of equifinality was reduced using themultiple constraints model data fusion approach. The interann-ual variability in the ecosystem C uptake could not be correctlysimulated unless the biological parameters were allowed to varytemporally. Our results confirmed that the long-term trend ofincreasing C uptake at Sorø was strongly driven by the changesin the ecosystem functional properties. Processes such as thenitrogen cycling and varying allocation patterns in the ecosys-tem need to be further investigated and their effects on thecanopy physiology need to be incorporated into process-basedmodels.

Acknowledgements

This work is supported by the EU FP7 project CARBO-Extreme,the DTU Climate Centre and the Danish National project ECOCLIM(Danish Council for Strategic Research). We thank two review-ers for their constructive comments on a former version of themanuscript.

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J. Wu et al. / Ecological Modelling 260 (2013) 50– 61 59

Appendix 1.

CoupModel equations.Equations No. Description

Plant biotic processesCAtm→a = εLf (Tl)f (CNl)f (Eta/Etp)Rs,pl (A1) Rate of photosynthesis (g C m−2 d−1)where εL is the radiation use efficiency and Rs,pl is the global radiation absorbed by the plant canopy.

f (Tl) =

0 Tl < pmn(Tl) − pmn)/(po1 − pmn) pmn ≤ Tl ≤ po1

1 po1 ≤ Tl ≤ po21 − (Tl − po2)/(pmx − po2) po2 ≤ Tl ≤ pmx

0 Tl > pmx

(A2) Response function for leaf temperature(–)

where pmn , po1 , po2 and pmx are parameters.f(CNl) = pfixedN (A3) Response function for fixed leaf C:N

ratio (–)where pfixedN is a parameter.

f(EtaEtp

)= Eta

Etp(A4) Response function for transpiration (–)

Ca→Leaf = flCAtm→a (A5) Carbon allocation to leaf root and stem(g C m−2 d−1)

where f l is the fixed allocation parameter to leaf, the carbon allocated to roots and stem can be calculated byexchanging f l to f r and f s.

Cresleaf = kmrespleaf · f(T) · Cleaf + kgresp · Ca→Leaf (A6) Plant growth and maintenancerespiration from leaves (g C m−2 d−1)

where kmrespleaf is the maintenance respiration coefficient for leaves, kgresp is the growth respiration coefficient,and f(T) is the temperature response function. The equation calculates respiration from stem, roots byexchanging kmrespleaf to kmrespstem , kmresproo and using the corresponding stocks.

f (T) =1 T > tmax(

T − tmin

tmax − tmin

)2

tmin ≤ T ≤ tmax

0 T < tmin

(A7) Response function for air temperature(Ratkowsky function) (–)

where tmaxandtmin are parameters and T is the air temperature.DOYlf = DOYi if

∑DOYi

DOYstartT = Tem,sum (A8) Leaf flush date (–)

where DOYlf is the day of year when leaf flushes; DOYstart is the date when the air temperature is higher than5 ◦C for 3 consecutive days; T is the air temperature and Tem, sum is the temperature threshold.

f (lLc) = lLc1 + (lLc2 − lLc1) min

(1,

max(0,Tdorm,sum−tL1)max(1,tL2−tL1)

)(A9) Leaf litter fall rate (d−1)

where lLc1 is a average rate parameter for leaf litterfall throughout the year and lLc2 is the litterfall rate duringautumn when the dorming temperature sum reaches a threshold value. Tdorm , sum is calculated at the end ofthe growing season when the air temperature is below 5 ◦C as the accumulated difference between Ta and5 ◦C. tL1 and tL2 are model parameters controlling the temperature threshold.

At = Blpl,sp

(A10) Leaf area index (m2 m−2)

where pl,sp is a parameter and Bl is the total mass of leaf.

Plant abiotic processesRs,pl = 1 − e−km(Al /fcc) · fcc(1 − apl)Ris (A11) Plant interception of global radiation

(MJ m−2 d−1)where krn is the light use extinction coefficient given as a single parameter common for all plants, fcc is the

surface canopy cover, and apl is the plant albedo.fcc = pc max(1 − e−pckAl ) (A12) Surface canopy cover (m2 m−2)where pcmax is a parameter that determines the maximum surface cover and pck is a parameter the governs the

speed at which the maximum surface cover is reached. Al is the leaf area index of the plant.Si max = iLAIAl + ibase (A13) Interception storage (mm)where iLAI and ibase are parameters.

E∗ta = E∗

tp

∫ 0

zrf( (z)

)f (T(z)) r(z) (A14) Actual transpiration before

compensatory uptake (mm d−1)where r(z) is the relative root density distribution, z is root depth and f(((z)) and f(T(z)) are response functions

for soil water potential and soil temperature.Eta = E∗

ta + fumov · (E∗tp − E∗

ta) (A15) Actual transpiration (mm d−1)where fumov is the degree of compensation, Eta

* is the uptake without any account of compensatory uptake,and Etp

* is the potential transpiration with eventual reduction due to interception evaporation.

f ( (z)) = min((

c (z)

)p1Etp+p2, f�

)(A16) Response function for soil water

potential (–)where p1, p2 and c are parameters, and an additional response function, f� , corresponds to the normal need

of oxygen supply to fine roots.

f (T(z)) = 1 − e−tWA max(0,T(z)−Ttrig tWB Iday ≤ pdaycut1 Iday > pdaycut

(A17) Response function for soil temperature(–)

where tWA , pdaycut and tWB are parameters. Ttrig is the trigger temperature.

L�Etp = �Rn+acp((es−ea)/ra)�+(1+(rs/ra)) (A18) Potential transpiration (mm d−1)

where Rn is net radiation available for transpiration, es is the vapour pressure at saturation, ea is the actualvapour pressure, a is air density, cp is the specific heat of air at constant pressure, L� is the latent heat ofvapourisation, � is the slope of saturated vapour pressure versus temperature curve, is the psychrometer‘constant’, rs is ‘effective’ surface resistance and ra is the aerodynamic resistance.

rs = 1max(Algl ,0.001) (A19) Stomatal resistance (s m−1)

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60 J. Wu et al. / Ecological Modelling 260 (2013) 50– 61

(Continued)Equations No. Description

where gl is the leaf conductance.gl = Ris

Ris+grisgmax

1+((es−ea)/gvpd ) (A20) Stomatal conductance per leaf area(m s−1)

where gris , gmax and gvpd are parameter values.Soil carbon and nitrogen processesCDecompL = klf(T)f(�)CLitter (A21) Decomposition of litter (g C m−2 d−1)where kl is a parameter.CDecompH = khf(T)f(�)CHumus (A22) Decomposition of humus (g C m−2 d−1)where kh is a parameter.

f (T) =1 T > tmax(

T − tmin

tmax − tmin

)2

tmin ≤ T ≤ tmax

0 T < tmin

(A23) Response function for soil temperature(Ratkowsky function) (–)

where tmax and tmin are parameters and simultaneously optimized in Eq. (A7).

f (�) = min

p�satact � = �s(((�s − �)/p�Upp)

p�p (1 − p�satact) + p�satact ,((� − �wilt)/p�Low)p�p

)�wilt ≤ � ≤ �s

0 � < �wilt

(A24) Response function for soil moisture (–)

where p�Upp , p�Low , p�Satact , and p�p are parameters and the variables, �s , �wilt , and �, are the soil moisturecontent at saturation, the soil moisture content at the wilting point, and the actual soil moisture content,respectively.

Soil physical processes

qh(0)kho(Ts−T1)�z/2 + Cw(Ta − �TPa)qin + Lvqvo (A25) Soil surface heat flow (J m−2 d−1)

where kho is the conductivity of the organic material at the surface, Ts is the surface temperature, T1 is thetemperature in the uppermost soil layer, �TPa is a parameter that represents the temperature differencebetween the air and the precipitation, qin , is the water infiltration rate, qvo is the water vapour flow, and Lv isthe latent heat. The temperature difference, Ta − �TPa , can optionally be exchanged to surface temperature,Ts .

Se =( a

)−�(A26) The effective saturation (–)

where a is the air-entry tension, is the pressure head or actual water tension, and � is the pore sizedistribution index.

qwp =∫ zsat

zpks

(zsat−zp)dudp

dz (A27) Groundwater outflow (mm d−1)

where ksat is the saturated conductivity, du is the unit length of the horizontal element, zp is the lower depth ofthe drainage pipe, zsat is the simulated depth of the water table, and dp is a characteristic distance betweendrainage pipes.

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