Journal of Geophysical Research: Biogeosciences

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1 RESEARCH ARTICLE Key Points: Stomatal conductance models are evaluated against eddy covariance data Models give similar results across vegetation types Stomatal VPD response is important regardless of climatic conditions Supporting Information: Supporting Information S1 Correspondence to: J. Knauer, Citation: Knauer, J., C. Werner, and S. Zaehle (2015), Evaluating stomatal models and their atmospheric drought response in a land surface scheme: A multibiome analysis, J. Geophys. Res. Biogeosci., 120, , doi:. Received 19 JUN 2015 Accepted 3 SEP 2015 Accepted article online 8 SEP 2015 Published online 3 OCT American Geophysical Union. All Rights Reserved. Evaluating stomatal models and their atmospheric drought response in a land surface scheme: A multibiome analysis Jürgen Knauer 1, Christiane Werner 2,3, and Sönke Zaehle 1 1 Department of Biogeochemical Integration, Max Planck Institute for Biogeochemistry, Jena, Germany, 2 Department of Agroecosystem Research, BayCEER, University of Bayreuth, Bayreuth, Germany, 3 Ecosystem Physiology, University of Freiburg, Freiburg im Breisgau, Germany Abstract Stomatal conductance (g s ) is a key variable in Earth system models as it regulates the transfer of carbon and water between the terrestrial biosphere and the lower atmosphere. Various approaches have been developed that aim for a simple representation of stomatal regulation applicable at the global scale. These models differ, among others, in their response to atmospheric humidity, which induces stomatal closure in a dry atmosphere. In this study, we compared the widely used empirical Ball-Berry and Leuning stomatal conductance models to an alternative empirical approach, an optimization-based approach, and a semimechanistic hydraulic model. We evaluated these models using evapotranspiration (ET) and gross primary productivity (GPP) observations derived from eddy covariance measurements at 56 sites across multiple biomes and climatic conditions. The different models were embedded in the land surface model JSBACH. Differences in performance across plant functional types or climatic conditions were small, partly owing to the large variations in the observational data. The models yielded comparable results at low to moderate atmospheric drought but diverged under dry atmospheric conditions, where models with a low sensitivity to air humidity tended to overestimate g s. The Ball-Berry model gave the best fit to the data for most biomes and climatic conditions, but all evaluated approaches have proven adequate for use in land surface models. Our findings further encourage future efforts toward a vegetation-type-specific parameterization of g s to improve the modeling of coupled terrestrial carbon and water dynamics. 1. Introduction Stomata play a major regulating role in terrestrial water and carbon fluxes, as they control the exchange of both water vapor and carbon dioxide between the vegetated land surface and the atmosphere. High stomatal conductance (g s ) not only favors high photosynthetic rates and thus gross primary productivity (GPP) but also leads to higher transpirational water losses under otherwise equal atmospheric conditions. An amplified water flux toward the atmosphere affects the energy partitioning at the land surface as it increases the latent heat flux at the expense of the sensible heat flux. This effect lowers the Bowen ratio and surface temperature [Dirks and Hensen, 1999] with possible implications for mesoscale atmospheric circulation patterns and the climate system [Mascart et al., 1991; Berry et al., 2010]. Stomata respond to a multitude of environmental stimuli such as radiation, atmospheric CO 2, soil water, and vapor pressure deficit (VPD) [e.g., Jarvis, 1976; Schulze, 1986]. A decrease in atmospheric humidity induces stomatal closure to protect plants against excessive water losses but simultaneously exposes the plant to physiological stress by reducing carbon uptake [McDowell et al., 2008; Will et al., 2013]. Water availability is considered as one of the main limiting factors for global plant growth [Nemani et al., 2003], and projections of climate change suggest an aggravation of the limiting role of droughts, as changes in precipitation patterns as well as increases in air temperature and atmospheric demand are expected [Burke and Brown, 2008; Hartmann et al., 2013]. This emphasizes the need to better understand and predict plant physiological responses to atmospheric drought, which is further supported by the fact that ecosystem models have been found to perform comparatively poor in regions characterized by seasonal water scarcity [Morales et al., 2005; Jung et al., 2007]. The predicted changes in environmental factors governing g s in combination with the high sensitivity of global climate simulations to stomatal processes have emphasized the need to include accurate process representations of canopy conductance in state-of-the-art climate models [Berry et al., 2010]. The vast majority of these models use empirical representations of g s, which are based on the long-standing knowledge that g s KNAUER ET AL. MULTIBIOME STOMATAL MODEL EVALUATION 1894

2 correlates with photosynthesis [Wong et al., 1979]. One of the most frequently used representatives of those models is the Ball-Berry (BB) model [Ball et al., 1987], which has proven successful in large-scale modeling approaches due to its simplicity and its ability to give accurate predictions of g s at large spatial scales and under varying environmental conditions [Buckley and Mott, 2013]. The model relates g s to net assimilation rate (A n ), the CO 2 concentration at the leaf surface, and relative humidity. Several modifications have been proposed to the original Ball-Berry model, either based on leaf level data [Leuning, 1990; Collatz et al., 1991; Aphalo and Jarvis, 1993; Leuning, 1995], or ecosystem data [Friend and Kiang, 2005], all of which differ with regard to the measure of atmospheric humidity employed and the mathematical function describing stomatal closure in response to increasing atmospheric demand. One major drawback of empirical models is that their parameters have no theoretical foundation, which hinders their prediction and interpretation across vegetation types and restricts the model s predictive capability under changing environmental conditions [Gao et al., 2002; Medlyn et al., 2011]. In this respect, modeling approaches using process-based formulations would be desirable but remain unfeasible especially on regional and larger spatial scales due to an incomplete understanding of the underlying mechanisms [Damour et al., 2010; Buckley and Mott, 2013]. A promising alternative toward a more mechanistic representation of stomatal behavior is models which relate g s to water flow in the soil-plant-atmosphere continuum. Such models simulate water flow in dependence on the water potential difference between the soil and the leaf as well as the hydraulic resistance along this pathway [Damour et al., 2010]. The plant resistance to water flow is primarily a function of the path length and anatomical properties of water-conducting tissues, and therefore requires detailed knowledge about plant hydraulic traits [Zimmermann, 1978; Tyree and Ewers, 1991]. Models based on these principles use comparatively complex formulations and are difficult to parameterize [e.g., Williams et al., 1996; Tuzetetal., 2003; Hickler et al., 2006]. Therefore, a more simplified description of this concept is often applied [Federer, 1982; Knorr, 2000; Sitch et al., 2003], which represents plant hydraulic properties as a single parameter, the maximum transpiration rate. Plant water loss is then simulated as the lesser of a transpiration supply and demand rate [Federer, 1982]. This approach is simple, but still suffers from parameter uncertainties, since information on plant hydraulic properties is comparatively rare. A third major model family for g s goes back to the theory of optimal stomatal behavior by Cowan and Farquhar [1977], who hypothesized that plants regulate stomatal aperture in such a way as to minimize water loss and maximize carbon gain over a given time interval, i.e., minimize the expression T λa n, where A n is net assimilation, T is transpiration, and λ is the marginal water cost of carbon to the plant. Based on the optimization theory, Katul et al. [2009] and Medlyn et al. [2011] independently derived an expression of g s which depends on the inverse square root of VPD. Both approaches contain the marginal water cost of carbon (λ) as a parameter component. In contrast to the parameters in the Ball-Berry type models, λ is not an empirically fitted constant but a biologically meaningful quantity, which is assumed to vary across plant functional types and environmental conditions [Manzoni et al., 2011; Medlyn et al., 2011]. Since the derived equations remained simple and structurally similar to the BB-type models, stomatal models based on the optimization theory appear to be a promising alternative to well established and widely used empirical g s formulations for use in land surface models (LSMs). The objective of this study is to assess the aforementioned process representations of g s with regard to their capability of simulating the observed response of carbon and water fluxes to varying conditions of atmospheric drought across all major global biomes. For this purpose, we compared eddy covariance measurements of evapotranspiration (ET) and gross primary productivity (GPP) at 56 sites covering multiple climate zones and vegetation types with simulations obtained with the following g s models: (1) the Ball-Berry (BB) and (2) Leuning (LEU) model, both empirical and widely used coupled photosynthesis-stomatal conductance models, (3) an alternative empirical model proposed by Friend and Kiang [2005] (FRIEND), (4) a model combining empirical approaches with the stomatal optimization theory, the unified stomatal optimization (USO) model [Medlyn et al., 2011], and (5) a semimechanistic approach based on plant hydraulics and the concept of transpiration supply and demand [Knorr, 2000] (BETHY). All models were embedded into the JSBACH land surface scheme of the Max Planck Institute (MPI) Earth system model [Reick et al., 2013]. The original formulation of JSBACH lacks a stomatal response to VPD and thereby serves as a null hypothesis of no stomatal response to atmospheric drought at the ecosystem level. We finally outline the consequences of the stomatal response to atmospheric drought for seasonal vegetation dynamics and global simulations of ET and GPP. KNAUER ET AL. MULTIBIOME STOMATAL MODEL EVALUATION 1895

3 2. Methods 2.1. JSBACH Model Description JSBACH (Version 3.0) [Raddatz et al., 2007; Reick et al., 2013] is the land component of the Max Planck Institute Earth system model (MPI-ESM) [Giorgetta et al., 2013]. Land physics components (surface radiation, energy balance, and heat transport) are inherited from the atmosphere model ECHAM5 [Roeckner et al., 2003]. The biogeochemical components of JSBACH are in large parts based on the biosphere model BETHY [Knorr, 2000]. Soil hydrology is simulated with a five layer scheme [Hagemann and Stacke, 2014]. The spatial units in the model are grid cells, which are again split into tiles to account for subgrid-scale heterogeneity of vegetation cover [Reick et al., 2013]. Each tile is associated with one plant functional type (PFT). JSBACH distinguishes in total 20 PFTs, which differ in their biochemical (e.g., maximum carboxylation rate, maximum electron transport rate, and photosynthetic pathway), phenological (e.g., maximum leaf area index (LAI)), and biogeophysical (e.g., vegetation height, albedo, and surface roughness) attributes [Raddatz et al., 2007; Reick et al., 2013] (PFT-specific parameter values are provided in Table S1 in the supporting information). The initial global distribution of vegetation types is prescribed on the basis of global land cover maps but changes dynamically as vegetation in the model is subject to natural and anthropogenic land cover change [Reick et al., 2013]. LAI is calculated with the phenology model LoGro-P [Raddatz et al., 2007], in which temperature and moisture dependent growth and shedding rates determine the annual course of LAI, which is constrained by a PFT-specific maximum value. There is no direct link between productivity and LAI in the model. Net assimilation rate (A n ) for multiple canopy layers is based on the photosynthesis models of Farquhar et al. [1980] for C3 plants and Collatz et al. [1992] for C4 plants Stomatal Conductance Models Baseline Model In the original JSBACH version, hereinafter called the baseline model, A n and g s are first calculated for unstressed, i.e., nonwater-limited conditions. The unstressed net assimilation rate A n,pot (mol m 2 s 1 ) is calculated using a prescribed intercellular CO 2 concentration C i (mol mol 1 ), which is set to C i,pot = 0.87C a for C3 plants and C i,pot = 0.67C a for C4 plants [Knorr, 2000], where C a is the atmospheric CO 2 concentration (mol mol 1 ) and the subscript pot denotes unstressed conditions. The unstressed stomatal conductance to water vapor g s,pot (mol m 2 s 1 ) is determined by solving the diffusion equation: g s,pot = 1.6 A n,pot C a C i,pot (1) Under water-stressed conditions, stomatal conductance to water vapor g s is derived by scaling g s,pot from equation (1) with an empirical water stress factor β, which is a linear function of soil water content: g s = β g s,pot (2) where 1 θ θ crit θ θ β = wilt θ θ crit θ wilt <θ<θ crit (3) wilt 0 θ θ wilt where θ is volumetric soil water content (unitless), θ crit is the critical soil moisture content, above which plants are considered to be unaffected by water stress, and θ wilt represents the permanent wilting point, below which water stress is at its maximum. C i, and A n are then recomputed given g s. The canopy-scale equivalents of g s (canopy conductance, G c ), and A n are calculated as the integral over the leaf area. This approach does not account for the influence of atmospheric humidity on stomatal behavior Alternative Models The semimechanistic BETHY approach [Knorr, 2000; Federer, 1982] assumes that transpiration rate is either limited by atmospheric demand (demand function) or by the supply of water supported by the plant hydraulic system (supply function) [Cowan, 1965; Federer, 1982]. When the demand function exceeds the supply function, which occurs under conditions of soil water scarcity and/or in a dry atmosphere, G c is reduced according to the ratio of the two functions (Figure 1b). The demand function is represented by the potential KNAUER ET AL. MULTIBIOME STOMATAL MODEL EVALUATION 1896

4 Figure 1. (a) Functions describing the response of G c to an increase in VPD for the models evaluated in this study. Relative humidity h s in the Ball-Berry model and specific humidity q in the Friend model were converted to VPD for a temperature of 25 C. The BETHY function shown is calculated for a T max of 5 mm d 1,aG c,pot of 0.4 mol m 2 s 1,anda G a of 6 mol m 2 s 1. (b) Graphical representation of the BETHY model. G c is lowered according to the ratio T supply /T pot if transpiration is limited by T pot. T supply equals the maximum transpiration rate T max if no soil water stress occurs, otherwise it is lowered by a water stress factor (equation (5)). The situation as shown represents conditions of constant soil moisture throughout the day. transpiration rate T pot (kg m 2 s 1 ), which is here defined as the transpiration rate under given meteorological conditions, unlimited water supply, and maximum canopy conductance (G c,pot ) as calculated from equation (1): T pot = ρ q sat (T, p) q G a G c,pot (4) where ρ is air density (kg m 3 ), q is specific humidity (kg kg 1 ), q sat is saturation specific humidity (kg kg 1 ) at temperature T and pressure p, and G a is the aerodynamic conductance (m s 1 ). The supply function T supply depends on the available soil water content in the root zone and on the maximum transpiration rate (T max,kgm 2 s 1 ) of vegetation: G c is then given by T supply = β T max (5) { Gc,pot T G c = supply T pot 0 T supply T pot (6) G c,pot T supply > T pot where G c,pot is the unstressed canopy conductance as calculated in equation (1). A n and C i are then recalculated given g s as in the baseline model. In contrast to the baseline and BETHY model, no potential rates are calculated for the approaches described in the following. Instead, C i, A n, and g s are iteratively solved. The Ball-Berry (BB) model empirically relates A n and g s based on gas-exchange cuvette measurements [Ball et al., 1987]: g s = g 0 + g 1 β A n h s C a (7) where A n is net assimilation rate, h s is relative humidity at the leaf surface (unitless), and C a is the CO 2 concentration at the leaf surface. g 0 (mol m 2 s 1 ) and g 1 (unitless) are both fitted parameters and represent the residual conductance as A n approaches zero and the slope of the function, respectively. Leuning [1995] proposed a modified version of the BB model. He replaced C a with (C a Γ), where Γ is the CO 2 compensation point (mol mol 1 )[Leuning, 1990] and the relative humidity term with an inverse hyperbolic response function of the leaf-to-surface vapor pressure deficit (D s,kpa)[lohammar et al., 1980]. The revised model (LEU) is given by A n g s = g 0 + g 1 β (C a Γ)(1 + D s D 0 ) (8) where D 0 (kpa) is an empirically fitted parameter representing the sensitivity of stomata to changes in D s. KNAUER ET AL. MULTIBIOME STOMATAL MODEL EVALUATION 1897

5 For use in a general circulation model, Friend and Kiang [2005] parameterized the response of stomatal conductance to specific humidity deficit such that it yielded the commonly observed afternoon closure of stomata. For this study, the resulting function was incorporated into the common form of the BB model and is given by g s = g 0 + g 1 β A n a(b(q sat q)) C a (9) where a and b are empirically fitted constants. The unified stomatal optimization (USO) model developed by Medlyn et al. [2011] is a combination of the optimal stomatal conductance model developed by Cowan and Farquhar [1977] and the photosynthesis model of Farquhar et al. [1980]: ( g s = g g 1 β ) An (10) Ds C a where g 1 has units of kpa 0.5. Since the models were applied at the canopy scale in this study, all humidity measures at the leaf surface were replaced by their respective values measured in the near-surface atmosphere (e.g., D s was replaced by VPD measured at sensor height). Figure 1a shows the stomatal response functions to VPD for all models for a temperature of 25 C and nonlimiting soil moisture. The functions differ in their sensitivity to VPD. The BB model shows a linear VPD response, whereas all other approaches show a higher sensitivity at low-vpd ranges and a lower sensitivity at higher VPD (> 1.5 to 2 kpa). The USO model shows the strongest nonlinearity, followed by the LEU and FRIEND model. The BETHY model predicts constant g s at low VPD, while transpirational demand T pot is lower than the prescribed plant water transport capacity (T supply ), followed by a strong decline once T pot exceeds T supply and a moderate decline at higher VPD values Model Parameterization The g 1 parameter in the BB model is set to a common value of 9.3 for C3 plants as determined by Ball et al. [1987] and to 3.0 for C4 plants according to Collatz et al. [1992]. This is in accordance to the typical approach in state-of-the-art LSMs, such as the Community Land Model (CLM) [Oleson et al., 2013], the ORCHIDEE dynamic global vegetation model [Krinner et al., 2005],or the CABLE land surface model [Kowalczyk et al., 2006], where parameters are treated as global constants, which differ only with photosynthetic pathway. For the other models (LEU, FRIEND, and USO), the value of g 1 was calibrated using least squares against g s values predicted by the BB model over a relative humidity range of 30 95% (corresponding to a VPD range of approximately kpa at 25 C). The obtained g 1 values were 8.41 for the LEU, 9.85 for the FRIEND, and 3.4 kpa 0.5 for the USO model. The VPD-sensitivity parameter D 0 in the LEU model is set to 1.5 kpa according to Leuning [1995] and as commonly used in LSMs such as CABLE [De Kauwe et al., 2015]. The residual conductance parameter g 0 is kept constant at a value of 0.01 mol m 2 s 1 for C3 plants [Leuning, 1990] and 0.08 mol m 2 s 1 for C4 plants [Collatz et al., 1992]. The additional constants in the FRIEND model are set to a = 2.8 and b = 80 [Friend and Kiang, 2005]. The T max parameter in the BETHY model is constant for all PFTs and is set to a common value of 5mmd 1 as suggested by Haxeltine and Prentice [1996] based on data summarized in Kelliher et al. [1993] Flux Data and Data Processing Model results were evaluated against eddy covariance measurements of ecosystem carbon and water fluxes from the FLUXNET network [Baldocchi et al., 2001]. A tabular description of the 56 sites used in this study can be found in Table S2 in the supporting information. The sites are distributed around the globe covering a wide range of climatic conditions and biomes (Figure 2). Half-hourly measurements of carbon dioxide and water vapor fluxes were processed using standard procedures. Data treatment included the correction of the storage component of the carbon flux and the removal of spikes in the half-hourly data as documented by Papale et al. [2006]. Periods of low-turbulent mixing were discarded based on a site-specific friction velocity (u ) threshold according to Papale et al. [2006]. Missing or bad quality data were gap filled according to the methodology described in Reichstein et al. [2005]. For the analysis, only measured values or data gap filled with high confidence according to Reichstein et al. [2005] were used. GPP is derived from net ecosystem exchange (NEE) measurements via a flux partitioning algorithm, which serves to separate NEE into its two components GPP and ecosystem respiration (R eco ). In this study, the method described by Reichstein et al. [2005] is used, where nighttime ecosystem respiration is extrapolated to daytime using a temperature response function which takes the short-term temperature sensitivity of R eco KNAUER ET AL. MULTIBIOME STOMATAL MODEL EVALUATION 1898

6 Figure 2. Distribution of flux tower sites considered in this study (a) in the temperature-precipitation space and (b) geographically. Symbols represent PFTs (TrEF=Tropical evergreen forest, TeBEF=Temperate broadleaf evergreen forest, TeBDF=Temperate broadleaf deciduous forest, CEF=Coniferous evergreen forest, TrS=Savanna with C4 grass, TeS=Temperate open woodland with C3 grass, TeH=C3 grassland). into account. After the determination of R eco, GPP was calculated as the difference between NEE and R eco [Reichstein et al., 2005]. ET was inferred from the measured latent heat flux. Since the focus in this study was on transpirational (i.e., physiologically controlled) rather than nontranspirational water fluxes, days with rainfall and the two subsequent days were excluded if precipitation exceeded 0.2 mm (day with rainfall), 0.5 mm (day before), or 1 mm (2 days before). For the remaining days, transpiration was calculated as the average of ET values at daytime, under the assumption that interception storage is largely depleted 2 days after rain events [Grelle et al., 1997] and soil evaporation is either negligible on sites with a closed canopy or a minor constituent of the total water flux after two rain-free days. As a consequence, the total water flux (ET) in this study can be considered to be dominated by transpiration. Canopy conductance G c (m s 1 ) was derived by inverting the Penman-Monteith equation [Monteith, 1965]: γλet G G c = a (11) εr n + ρc p VPD G a λ(ε + γ)et where γ is the psychrometric constant (kpa K 1 ), λ is the latent heat of vaporization (J kg 1 ), ε is the change of latent heat content relative to the change of sensible heat content of saturated air (kpa K 1 ), R n is net radiation (W m 2 ), and C p is the specific heat of air (J kg 1 K 1 ). The soil heat flux and heat storage were neglected. Aerodynamic conductance G a (m s 1 ) was calculated based on the Monin-Obukhov similarity theory in dependence on wind speed, friction velocity, atmospheric stability, and surface roughness [Hansen et al., 1983; Bonan, 2008a]. Throughout the analysis, only values at full daylight (photosynthetic photon flux density (PPFD) > 600 μmol m 2 s 1 ) and within the growing season were used. To separate the effects of atmospheric drought on plant physiology from those of soil water scarcity, moderate and severe soil water stressed conditions were excluded. This was done by excluding data which fell below site-specific soil moisture thresholds based on modeled soil moisture. If applicable, time periods affected by disturbances such as mowing were removed JSBACH Model Runs Site level runs of JSBACH were forced with meteorological measurements from the flux towers. Vegetation at the site was assigned to one or several of the PFTs implemented in JSBACH based on ancillary data and site-specific information from the literature. The sites were distributed across the following PFTs: Tropical evergreen forest (TrEF), temperate broadleaf evergreen forest (TeBEF), temperate broadleaf deciduous forest (TeBDF), coniferous evergreen forest (CEF), and C3 grassland (TeH). Two new classes were formed to account for FLUXNET sites with a nonhomogenous vegetation cover: Temperate open woodland with C3 grass (TeS, consisting of temperate broadleaf evergreen forest and C3 grassland) and savanna with C4 grass (TrS, consisting of tropical deciduous forest (TrDF) or temperate broadleaf evergreen forest and C4 grassland). The PFT classes and their major attributes are shown in Table S1 in the supporting information. Prior to the model runs, modeled maximum LAI values as well as vegetation height were adjusted to the observed values as reported in the FLUXNET ancillary database or in the literature. If no values were reported, the default values of JSBACH were used. Photosynthetic capacity was adjusted to site conditions using derived GPP from the flux measurements under favorable atmospheric conditions for photosynthesis (VPD < 0.7 kpa, Temperature > 10 C, KNAUER ET AL. MULTIBIOME STOMATAL MODEL EVALUATION 1899

7 Figure 3. Relative deviation between the models and the observed flux data (dashed line) for ET. Values represent PFT medians based on half-hourly model outputs of ET under optimal conditions (values are based on half-hourly data at full daylight, within the growing season and in the absence of soil water stress). Error bars represent standard errors of the median. PFT abbreviations as in Figure 2. PPFD > 1200 μmol m 2 s 1, and no soil water stress). The PFT assignment, default as well as adjusted maximum carboxylation capacity (V cmax ), and LAI values for all sites are listed in Table S2 in the supporting information. Global offline JSBACH simulations were conducted for the 30 year time period for each model version at a spatial resolution of approximately The model was forced with the global atmospheric reanalysis ERA-Interim [Deeetal., 2011]. ERA-Interim provides a wide variety of gridded data products, of which precipitation, specific humidity, wind speed, air temperature, shortwave and longwave radiation were used at daily resolution and atmospheric CO 2 concentration at annual resolution to force the model. For the global simulations, PFT-specific vegetation properties were set to the default values as shown in Table S1 in the supporting information Model Evaluation For each FLUXNET site, filtered half-hourly model outputs of ET and GPP were split into VPD groups. For each VPD bin, medians of the variables were calculated, provided a sufficient number of data points (n 7) in the respective bin. Data were then aggregated into PFT groups, and medians and standard errors were calculated. Model performance was evaluated using the normalized root-mean-square error (NRMSE) [Janssen and Heuberger, 1995]: N (Sim i Obs i ) 2 NRMSE = 1 N i=1 where Obs are measured flux data, Sim are simulated values, and Obs denotes the mean of all flux data. The NRMSE was calculated using the medians of the VPD-binned data for the whole VPD range Obs (12) KNAUER ET AL. MULTIBIOME STOMATAL MODEL EVALUATION 1900

8 Figure 4. Normalized root-mean-square error calculated for (a) ET and (b) GPP based on half-hourly model outputs aggregated into bins of VPD (bin width = 0.1 kpa). Shown are PFT means (± standard errors). Letters indicate differences between means (normal font = Tukey HSD test, p <0.05; italic = Games-Howell test, p <0.05). PFT abbreviations are the same as in Figure 2. (bin width = 0.1 kpa). The results were used to compare models applying a one-way analysis of variance (ANOVA) and a Tukey honest significant difference (HSD) post hoc analysis in case of homoscedastic data. In case of a heteroscedastic data distribution within groups, a Welch-ANOVA and the Games-Howell post hoc test were applied. Two prerequisites for applying an ANOVA, homoscedasticity and normal distribution, were tested with the Bartlett test and the Shapiro-Wilk test, respectively. The significance level for all tests was p < To evaluate the overall model performance (i.e., using the complete modeled time period including soil water stressed periods), NRMSE was calculated for daily ET and GPP values for all sites. All statistical analyses were conducted in R (Version 3.1.0) [R Core Team, 2013]. Global model simulations were compared to upscaled FLUXNET observations from Jung et al. [2011], hereinafter named MTE (model tree ensembles) product. For this product, GPP and latent heat flux were predicted using a machine learning method based on remote sensing indices, climate and meteorological data, and land use information. Global sums of annual GPP and ET were compared to calculations by Beer et al. [2010] and the multidata set synthesis LandFlux-EVAL by Müller et al. [2013], respectively. 3. Results 3.1. Model Performance The implications of the alternative assumptions on the VPD response of G c for ET are shown in Figure 3. Model results of ET were split into classes of VPD and shown as relative bias (i.e., relative deviation) to the measured flux data (dashed line). Only data in the absence of moderate and severe soil water stress and under full daylight (PPFD > 600 μmol m 2 s 1 ) were considered. Since vegetation properties, such as LAI and photosynthetic capacity, were adjusted to site conditions for each site, deviations at low VPD are similar for all models. With increasing VPD, all alternative models give better results than the baseline model, which consistently overestimates ET particularly under conditions of high VPD. This is true for all PFTs, as transpiration closely follows the measured data over the entire VPD range. Differences between models are not obvious below a VPD of approximately 2 kpa, but some general patterns are visible under drier atmospheric conditions. The USO model usually shows the highest simulated ET at high VPD, which reflects the low stomatal sensitivity to VPD under dry conditions in this model (Figure 1a). To a lesser extent, the LEU model overestimates g s and thus ET in a dry atmosphere. In contrast, the BB and FRIEND models have the highest sensitivities even at lower atmospheric water contents, resulting in the best behavior under such circumstances. The BETHY approach showed medium performance in general and large KNAUER ET AL. MULTIBIOME STOMATAL MODEL EVALUATION 1901

9 Table 1. NRMSE for All Model Versions a PFT Baseline Ball-Berry Leuning Friend USO BETHY ET TrEF 0.33 (0.15) 0.35 (0.16) 0.37 (0.16) 0.38 (0.15) 0.37 (0.16) 0.35 (0.15) TeBEF 0.89 (0.18) 0.66 (0.13) 0.69 (0.15) 0.68 (0.15) 0.70 (0.16) 0.75 (0.18) TeBDF 1.15 (0.40) 1.00 (0.29) 1.02 (0.30) 1.02 (0.29) 1.03 (0.31) 1.06 (0.33) CEF 1.01 (0.41) 0.82 (0.33) 0.86 (0.35) 0.85 (0.35) 0.86 (0.36) 0.91 (0.41) TrS 0.93 (0.54) 0.95 (0.57) 0.95 (0.57) 0.97 (0.56) 0.97 (0.58) 0.92 (0.56) TeS 1.22 (1.05) 0.97 (0.78) 0.98 (0.81) 0.97 (0.77) 1.04 (0.86) 1.11 (0.97) TeH 0.65 (0.31) 0.59 (0.26) 0.60 (0.27) 0.59 (0.27) 0.61 (0.28) 0.61 (0.28) All sites 0.93 (0.46) 0.79 (0.37) 0.81 (0.39) 0.81 (0.38) 0.83 (0.40) 0.85 (0.43) GPP TrEF 0.27 (0.12) 0.26 (0.09) 0.26 (0.08) 0.26 (0.07) 0.26 (0.08) 0.30 (0.06) TeBEF 0.47 (0.10) 0.38 (0.08) 0.39 (0.08) 0.38 (0.08) 0.40 (0.09) 0.38 (0.10) TeBDF 0.53 (0.19) 0.49 (0.16) 0.49 (0.16) 0.49 (0.16) 0.50 (0.16) 0.53 (0.18) CEF 0.53 (0.14) 0.45 (0.11) 0.48 (0.12) 0.46 (0.11) 0.48 (0.12) 0.47 (0.12) TrS 0.97 (0.34) 1.12 (0.50) 1.09 (0.45) 1.15 (0.54) 1.07 (0.42) 1.04 (0.46) TeS 0.58 (0.09) 0.48 (0.08) 0.49 (0.07) 0.48 (0.08) 0.54 (0.07) 0.53 (0.08) TeH 1.11 (1.36) 1.08 (1.45) 1.08 (1.43) 1.07 (1.44) 1.10 (1.43) 1.08 (1.36) All sites 0.66 (0.65) 0.61 (0.70) 0.62 (0.69) 0.62 (0.70) 0.63 (0.69) 0.63 (0.66) a Values represent PFT means (± standard deviations). The NRMSE is calculated based on daily model outputs. The best model for each PFT is shown in bold. For PFT abbreviations, see Figure 2. differences between PFTs. The apparent overestimation for most PFTs indicates an inappropriate choice of the parameter value for T max, which is probably too high for most ecosystem types considered in this study. We repeated the analysis using simulated transpiration instead of filtered simulated ET. Modeled transpiration showed consistently lower values than their filtered ET counterpart but otherwise an equal behavior across PFTs (Figure S3 in the supporting information). This is an indication that our filtering procedure as outlined in section 2 does not completely exclude soil evaporation contributing to the ET flux which, however, has only minor effects on the results. In addition, lowering the radiation threshold to 80 μmol m 2 s 1 did not lead to notable differences in the results (not shown). The model misfit as shown in Figure 3 is further quantified as the NRMSE of relative model-observation differences for the whole VPD range (bin width = 0.1 kpa; Figure 4). Figure S4 in the supporting information shows the same information as Figure 4 for VPD values > 2 kpa. Again, the tested models show a clear improvement to the baseline model. This holds true for all PFTs, even though not statistically significant in most cases. Differences between the alternative models were generally low and statistically insignificant, but BB and FRIEND showed the best model results for most PFTs, both for ET and GPP. The higher NRMSE for the LEU and USO models reflects the overestimated fluxes under conditions of high atmospheric demand due to the lower stomatal sensitivity at high VPD (Figure 1a). We next evaluated the implications of the different simulated stomatal sensitivities to VPD for total ecosystem water and carbon fluxes. Table 1 shows model evaluation results for all time periods, i.e., including water stressed conditions. All models showed improvements to the baseline model for both ET and GPP for all PFTs except savanna ecosystems. Differences between the BB, LEU, FRIEND, and USO models were only minor, but the BB model performed slightly better than the other approaches across all PFTs (e.g., mean NRMSE over all sites for ET was 0.79 for the BB model and for the other alternative models) Figure 5 shows the difference in NRMSE between the baseline and the BB model as a metric for model improvement. The BB model showed considerably lower NRMSE values for both ET and GPP for most sites and only a minor decline in performance for a few sites. The improvement was in general more pronounced for ET than for GPP. All other models showed a very similar behavior (results not shown). Interestingly, model improvement was achieved regardless of daylight mean growing season VPD (nonsignificant slope for both ET KNAUER ET AL. MULTIBIOME STOMATAL MODEL EVALUATION 1902

10 Figure 5. (a) Normalized root-mean-square error (NRMSE) of the Ball-Berry (BB) model and (b) difference in NRMSE between the baseline and BB model for ET and GPP for all sites plotted against the mean growing season VPD at daylight. Negative values in Figure 5b indicate improved model performance compared to the baseline version. and GPP), which underlines the ecological significance of the stomatal response to atmospheric humidity in all ecosystems investigated. In addition to the differences in the magnitude of carbon and water fluxes, the different g s formulations further resulted in altered seasonal dynamics in interaction with soil moisture. Figure 6 shows the temporal dynamics of ET and GPP exemplary for the site FR-Pue (Puechabon). This temperate evergreen forest features a typical Mediterranean-type climate with warm and wet winters and hot and dry summers. Consequently, soil water content in summer falls regularly below the point at which water stress starts to negatively impact plant photosynthesis [Keenan et al., 2010; Piayda et al., 2014]. In the baseline model, the higher water use due to enhanced G c in the spring causes an earlier decline in transpiration and GPP in summer. Contrarily, the alternative models including an atmospheric drought response show a lower G c in the early growing season, which leads to a higher water availability in summer and a more gradual decline of GPP and ET at the onset of the drought period. Another striking feature of Figure 6 is the high-simulated springtime ET, which also indicates a large overestimation in simulated water use efficiency (WUE), and which may be partly explained by an inappropriate g 1 parameter value for this site. The g 1 parameter is a measure for plant intrinsic water use efficiency (iwue), as it represents the sensitivity of g s to A n. We used flux data to estimate the g 1 parameter at the ecosystem level, thereby assessing the potential of constraining model parameter values with eddy covariance based estimates of g 1 and improving the magnitude of simulated WUE. To achieve this, the ecosystem scale G c was derived from eddy covariance data by inverting the Penman-Monteith equation (equation (11)). The regression slope of G c against (GPP h) C a, taking the BB model, is an ecosystem-scale estimate of the g 1 parameter. Comparing these eddy covariance derived slopes with leaf level estimates as employed for our model runs showed that ecosystem scale g 1 estimates were usually higher than those used for the simulations for most PFTs (Figure S5 in the supporting information). As a consequence, a parameterization of JSBACH with the eddy covariance derived g 1 values leads to an overestimation of simulated photosynthesis and transpiration in the model, and a degradation of the model-data fit (results not shown). KNAUER ET AL. MULTIBIOME STOMATAL MODEL EVALUATION 1903

11 Figure 6. Mean annual course of (a) GPP and (b) ET for a Mediterranean site (FR-Pue), averaged over the time period Shown are daily means smoothed by a moving average filter (window width = 11 days) Global Simulations Global simulations showed similar spatial patterns for all approaches. Consequently, global results are only shown for the Ball-Berry (BB) model. Global predictions of GPP and ET by the BB model and the comparison to the baseline model and the MTE product are shown in Figure 7. The JSBACH-BB version showed considerable reductions in ET for most parts of the world. Only large scale elevated areas such as the Tibetan Plateau did not follow this pattern. GPP was substantially reduced in the BB model compared to the baseline model for almost the entire globe. Only smaller regions in higher latitudes showed a significant increase in GPP. Reductions were mostly in the magnitude of 5-10% for ET and 10-20% for GPP and sum up to km 3 yr 1 and 21 PgC yr 1 globally (Table 2). All other models show similar reductions for ET and GPP at the global scale. Despite these considerable reductions, GPP was still highly overestimated by the JSBACH-BB model compared to the MTE product (Figure 7f). This, and the fact that global sums of GPP were reduced for the alternative models imply a notable model improvement with regard to global terrestrial carbon uptake. Comparisons with the MTE product further reveal a major underprediction of ET for tropical regions and slightly higher values for North America and Australia. Globally, ET was reduced which results in a lower estimate of the land-atmosphere water flux than reported by Müller et al. [2013]. Table 2. Mean Annual Global Sums of ET ( ) and GPP ( ) for the Different Model Versions ET (10 3 km 3 yr 1 ) GPP (PgC yr 1 ) Baseline Ball-Berry Leuning Friend USO BETHY Reference 64.5 a 123 (8) b a Müller et al. [2013]. b Beer et al. [2010], standard deviation shown in brackets. KNAUER ET AL. MULTIBIOME STOMATAL MODEL EVALUATION 1904

12 Figure 7. Mean annual values of (a) ET and (b) GPP of the JSBACH-BB version and (c and d) absolute deviations to the baseline model and (e and f) to the MTE product, averaged over the time period Red colors indicate lower predictions by the BB model compared to the baseline model or the MTE product, respectively. 4. Discussion 4.1. Model Performance and Ecological Implications For all vegetation types considered, the inclusion of a stomatal response mechanism to atmospheric drought lead to significant improvements in model performance relative to the baseline JSBACH version, which assumes g s being insensitive to VPD. This improvement is not surprising considering the fact that stomatal closure as a response to rising VPD is long known [e.g., Jarvis, 1976]. The differences between the alternative response functions embedded in JSBACH, however, are more interesting and relevant to land surface models in general. These functions show different sensitivities of stomatal closure to an increase in VPD (Figure 1a). This caused a large difference in G c between the alternative models and the baseline model, while the differences among the alternative models were small over a wide range of VPD values. Interestingly, differences between the alternative models under particular conditions (e.g., low VPD) were often compensated by the opposite pattern under contrasting conditions (e.g., high VPD). The USO model, for instance, consistently predicted lower g s under low-vpd conditions and higher g s under high VPD compared to the other models. A similar behavior could also be observed for daily and annual time series. Since VPD varies significantly over the course of a day and between seasons, such compensating effects are likely to offset differences that exist at particular conditions. As a result, the overall performance of the alternative models was largely comparable. Our analysis supported approaches with a more linear response of g s to VPD (BB and FRIEND) better than KNAUER ET AL. MULTIBIOME STOMATAL MODEL EVALUATION 1905

13 highly nonlinear formulations (LEU and USO). However, the differences were too small to result in significant performance differences across models, partly owing to the large scatter in the observations, compared to the fairly similar functional responses (Figure 1a). Eddy covariance measurements are inherently noisy due to small-scale variability in ecosystem fluxes and subject to random as well as systematic errors, which cause considerable uncertainties in the data (see Richardson et al. [2012] for an overview). We attempted to reduce the influence of random errors by including a large number of values (half-hourly measurements) and a large number (56) of sites in our analysis. Energy balance nonclosure [Wilson et al., 2002] and GPP inference via a flux partitioning algorithm [Reichstein et al., 2005] are potential sources of systematic errors. Both might cause an unknown bias in the ET and GPP observations and consequently lead to an overestimation or underestimation of the model-data mismatch. While this introduces uncertainty in the absolute value of biases and errors presented here, it appears unlikely that this would systematically affect the relative changes of water and carbon fluxes with increasing VPD, and therefore our judgment on overall model performance. Significant variations in terms of predicted ET and GPP between the alternative model versions could not be detected if sites were aggregated into climate zones, whereas our results clearly indicated an improvement compared to the baseline results for all climate zones (results not shown). Furthermore, model performance improved regardless of the mean growing season VPD at the site (Figure 5). These results suggest that the effect of stomatal closure under conditions of high VPD is a critical physiological adaptation to high atmospheric demand in all of the ecosystems considered in this study. This mechanism thus plays a decisive role in the regulation of ecosystem carbon uptake and water loss even under conditions of low or intermediate atmospheric drought. These findings are in accordance with studies investigating the implications of increased VPD on vegetation [Eamus et al., 2013; Will et al., 2013]. Higher temperatures and associated increases in VPD can lead to partial hydraulic failure and carbon starvation which amplifies drought-associated vegetation mortality, a phenomenon that has been documented for most biomes across the Earth [Allen et al., 2010] What Is the Appropriate Model? LSMs usually include either the BB or the LEU model coupled to a photosynthesis model (see De Kauwe et al. [2013] for an overview). These two approaches are similar but represent the stomatal response to atmospheric humidity with a different degree of complexity. The Leuning model includes an additional parameter D 0, which adjusts the stomatal sensitivity to changes in VPD [Leuning, 1995]. The results presented in this study show that the benefit of this additional model complexity remains limited, as it does not lead to a superior model performance, if run with global parameter values. An additional, fundamental consideration is that the LEU model suffers from the strong correlation of its parameters g 1 and D 0 [Leuning, 1995]. As with g 1,itis known that D 0 varies largely even between related species and similar ecosystems [Leuning, 1995; Wang et al., 2001; Medlyn et al., 2011; Héroult et al., 2013], which will hamper a robust estimation of this parameter for use in global vegetation models. The FRIEND model provides a somewhat better representation of the response of G c to increasing atmospheric drought than the LEU model, but it is not superior in performance compared to the BB model. The model is based on a heuristic formulation, with little knowledge on its robustness and the species-specific variations of the two additional parameters needed to describe the atmospheric drought response. Given that the model does not lead to an improved simulation of the carbon and water fluxes, it appears overparameterized. The BB model has often been criticized for its assumption that stomata respond to relative humidity rather than VPD or transpiration [Mott and Parkhurst, 1991; Aphalo and Jarvis, 1991]. Notwithstanding, JSBACH using the BB model captured the observed VPD response of transpiration and GPP across a large set of different biomes and climates equally well or better than alternative, nonlinear models relating stomatal closure to VPD or specific air humidity. In the absence of a process-based model which explicitly simulates the physiological controls of stomatal aperture, the BB thus fulfills two major requirements for global models: (1) robustness (good model performance for all ecosystems considered) and (2) parsimony (simple model structure). This makes the BB model a valuable approach for modeling g s at the global scale, particularly if information on the spatial distribution of model parameters (e.g., D 0 in the LEU or T max in the BETHY model) is unavailable. The BETHY model appears to be suitable for use in LSMs due to its simplicity. Only one parameter (T max ), representing the maximum transpiration rate supported by the plant hydraulic system, is required. The approach further has a firm physiological basis, as numerous studies confirmed a close relationship between g s and plant hydraulic properties [e.g., Meinzer and Grantz, 1990; Saliendra et al., 1995; Manzoni et al., 2013]. However, the model is very sensitive to the exact value of T max, and detailed knowledge on its variation with KNAUER ET AL. MULTIBIOME STOMATAL MODEL EVALUATION 1906

14 plant hydraulic characteristics is thus a prerequisite for applying the model. This information is sparse, in particular at the PFT level [Hickler et al., 2006], which hampers the use of the BETHY model in LSMs. One possibility to overcome this limitation is to relate plant hydraulics to plant physiological properties such as photosynthetic capacity. Such a hydraulic-photosynthetic coordination was proposed by Katul et al. [2003] and further elaborated by other researchers [e.g., Santiago et al., 2004; Brodribb et al., 2005]. Making use of these relationships could help to bring stomatal modeling on a more mechanistic basis without adding excessive model complexity. Alternatives to the BETHY approach usually represent stomatal behavior based on plant hydraulics and are located at the mechanistic end of the stomatal model spectrum. The soil-plant-atmosphere model by Williams et al. [1996] for instance combines plant hydraulic constraints with the optimality criterion of maximizing resource use efficiency. A version of this model coupled to a land surface scheme has recently been applied at site level [Bonan et al., 2014], where it showed improved performance over the BB model in water stressed periods. Nonetheless, a global application of such models is currently limited by their extensive requirements on the parameterization of plant hydraulic properties Model Parameterization The results of this study showed that the alternative stomatal models significantly improved the simulated g s with respect to the null model (baseline) with on average similar performance. This was achieved with commonly employed parameter values. However, all models might further benefit from an improved model parameterization. The common parameter for photosynthesis-stomatal conductance models is the slope parameter g 1, which represents the sensitivity of g s to A n and which is therefore closely related to plant intrinsic water use efficiency (iwue). We found a clear discrepancy between iwue simulated by JSBACH and observed by the FLUXNET sites as well as differences in iwue across PFTs (Figure S5 in the supporting information). These differences contradict the usual approach implemented in most state-of-the-art LSMs, which treat g 1 as a global constant, neglecting possible differences with climatic conditions or vegetation type. In fact, variations in the slope parameter between species are known for a long time [Ball et al., 1987], and a recent compilation of g 1 estimates at the leaf level revealed significant differences between vegetation types [Lin et al., 2015]. A vegetation type-specific model parameterization, which is further reconcilable with the PFT concept employed in LSMs, therefore appears promising in improving model results. In this respect, the USO model has the merit of providing a theoretical explanation of the slope parameter g 1 [Medlyn et al., 2011]. Thus, instead of estimating the g 1 parameter based on statistical fits to data, this approach can be used to predict parameter values in dependence on environmental conditions and plant traits. Constraining g 1 in such a way has recently been tested by De Kauwe et al. [2015] for the CABLE LSM at the global scale. Due to its analogy to the empirical Ball-Berry type models [Medlyn et al., 2011], insights gained from the USO model parameterization may also be used to improve the spatial and temporal parameter variation in the widespread empirical stomatal models. Another possibility for parameterizing the model is the derivation of parameter values directly from FLUXNET data, as attempted in this study. The parameter estimates differed remarkably to those currently used in the model, which represent estimates derived at the leaf level [e.g., Ball et al., 1987; Leuning, 1995]. This discrepancy between leaf and ecosystem level parameter estimates as found for the g 1 parameter may be caused by a range of possible reasons. At the ecosystem level, leaf boundary and atmospheric resistances can be a considerable component in the overall vegetation-atmosphere resistance pathway and lead to a partial decoupling of the canopy from the atmosphere [e.g., Meinzer et al., 1997; Magnani et al., 1998]. This can lead to a significant deviation of the temperature and humidity conditions at the notional canopy surface from those in the free air stream [Grantz and Meinzer, 1990; McNaughton and Jarvis, 1991], which affects estimates of eddy covariance derived g 1 differently than leaf level estimates. Further possible reasons are related to uncertainties in the derivation of G c (equation (11)) and G a resulting from uncertainties in surface roughness estimation and energy balance nonclosure [Wilson et al., 2002]. Furthermore, eddy covariance derived G c is representative of canopy conductance only under conditions where soil water evaporation is negligible. While this may be the case for ecosystems with large LAI, the comparability of eddy covariance derived G c with the leaf area-weighted integral of a model s g s is limited, particularly under conditions of high soil conductance (i.e., wet soil) [Paw U and Meyers, 1989; Kelliher et al., 1995]. All alternative approaches except the BETHY model share a further parameter g 0, which represents the residual or minimum g s at nighttime [Leuning, 1995; Barnard and Bauerle, 2013]. This parameter is usually set to a constant low value in the order of 0.01 mol m 2 s 1 or less (see De Kauwe et al. [2013] for a compilation of values). These values, however, were found to be much lower than measurements of nighttime g s KNAUER ET AL. MULTIBIOME STOMATAL MODEL EVALUATION 1907