1. Introduction
In many places, the climate at the end of the century will be unlike any found on Earth today, and thus there exists no modern analog for either climate or ecosystems with which to compare (Williams et al. 2007). Observational evidence suggests that increasing atmospheric CO2 and the associated global warming has already led to changes in the biosphere and altered the carbon cycle (Zhu et al. 2016; De Kauwe et al. 2016; Piao et al. 2014; Wang et al. 2014). Because there is no analog ecological community to base predictions on, in order to project vegetation response to novel environments, process-based models must correctly reproduce ecosystem functioning: the sensitivity of vegetation to the physical environment. Observational constraints are critical for testing the fidelity of our ability to simulate ecosystem functioning in the present-day climate and to provide confidence in simulations under a changing climate. Here we evaluate the ecosystem functioning of process-based models by comparing the sensitivity of terrestrial vegetation leaf area to interannual variations of climate in simulations from phase 5 of the Coupled Model Intercomparison Project (CMIP5; Taylor et al. 2012) with observations of the sensitivity of leaf area to climate. The annual leaf area of the vegetation relates to many parts of ecosystem function. The amount of leaf area determines the potential for photosynthesis and transpiration and is the result of the partitioning of gross primary productivity to leaves (McCarthy et al. 2006; Bonan 2002). Long-term changes in leaf area also have effects on the albedo of Earth (and thus the energy balance) and the global circulation of the atmosphere (Zhu et al. 2016; Forzieri et al. 2017; Zeng et al. 2017).
We focus on Earth system model simulations from the CMIP5 archive, which simulate both physical and biological Earth processes for the whole globe, along with the interactions between them. We compare Earth system models and observations of the present-day sensitivity of ecosystems’ leaf area to climate as a functional constraint on the models that can help to reduce persistent spread in predictions and to improve our understanding of the underlying mechanisms.
Though there has been an expansion of the biological and physical processes represented in Earth system models over time, the uncertainty in future CO2 absorption by the terrestrial biosphere has stayed stubbornly consistent (Lovenduski and Bonan 2017; Friedlingstein et al. 2014, 2006). Earth system models show a significant spread in their predictions of future CO2 concentration and thus global temperature at the end of the century (Friedlingstein et al. 2014). In addition, the inclusion of an interactive carbon cycle increases the projected uncertainty and absolute value of global temperature, with most of the signal coming from uncertainties in land carbon uptake (Yu et al. 2016; Friedlingstein et al. 2014; Booth et al. 2012). A portion of this uncertainty is due to the terrestrial vegetation, which also plays a large role in absorbing CO2 added to the atmosphere through anthropogenic emissions of CO2—currently absorbing approximately a quarter of emissions (Le Quréré et al. 2015). Improving our representation of terrestrial vegetation in Earth system models will be critical in predicting future CO2 levels in the atmosphere.
To simulate vegetation, models must use a number of simplifications to represent real world processes. This includes simplified physiological processes, omission of relevant processes, and representation of complex ecosystems with only a few plant functional types—the simplified and static representations of the broad physiological characteristics of major plant groups. The realities of limited computational resources for numerical simulations also lead to calculations at coarse spatial resolution for both vegetation and climate processes in Earth system models. Simulation at coarse spatial scales will affect the climate that the biosphere is interacting with in addition to affecting the ecosystem functioning of the biosphere itself. Climates simulated by Earth system models can have biases in mean climate (e.g., mean annual precipitation) as well as biases in variation (e.g., high interannual variability in surface temperature; Merrifield and Xie 2016), which can have significant implications for the simulations of the ecosystems. This makes it difficult to separate the effects of biases in climate from the effects of a poor representation of vegetation processes. Our work specifically analyzes the sensitivity of vegetation to interannual variations in climate independent of spatial pattern to constrain and formulate hypotheses about the simulated ecosystem functioning compared to observations.
Prior studies have used satellite observations and upscaled flux tower observations to analyze the sensitivity of vegetation to climate (Quetin and Swann 2017; Green et al. 2017; De Kauwe et al. 2016; Chu et al. 2016; Rafique et al. 2016; Seddon et al. 2016; Wu et al. 2015; Piao et al. 2009; Jung et al. 2011; Beer et al. 2010; Xiao et al. 2011). Through these various analyses, it is clear that there is a strong sensitivity of vegetation to interannual climate variations, that the relationship changes across the globe, and that it varies with the mean annual climate of a place. Analyzing the sensitivity of vegetation on an annual basis does pose a challenge to interpretation where we expect there to be seasonal and time-lagged effects between seasons. Our analysis also builds on analyses of the carbon cycle in Earth system model simulations from the CMIP5 archive (Anav et al. 2013a,b; Mahowald et al. 2016; Shao et al. 2013) and simulated interactions between climate and the carbon cycle (Liu et al. 2017, 2016; Mahowald et al. 2016; Wang et al. 2014; Cox et al. 2013; Shao et al. 2013). For example, it has been observed that leaf area simulated by Earth system models from CMIP5 is consistently larger on average and has larger variability compared to observations (Merrifield and Xie 2016; Anav et al. 2013a,b). Additionally, there is a relatively large spread of leaf area across the models (Mahowald et al. 2016; Shao et al. 2013). Prior studies have also established that the observed interactions of climate and carbon cycle can be used to constrain carbon cycle forecasts (Cox et al. 2013).
a. Deriving ecosystem function from observations
In Quetin and Swann (2017), we calculated a metric for the sensitivity of ecosystems to climate that can be used to compare the behavior of modeled ecosystems against observations. The metric is calculated by fitting a multiple linear regression to the percent interannual variations in plant activity, predicted by the interannual variations in temperature and precipitation [see methods section, Eq. (1)]. Our coefficients of sensitivity are then the regression coefficients of this equation. The sensitivity of vegetation to temperature,
b. Proposed processes driving 
and 


We hypothesize the sign and magnitude of
Proposed mechanisms driving β.
From empirical and theoretical studies in the literature we can develop an expectation for how different processes would influence the sign of
Precipitation can fall either as snow or rain depending on the climate and season. In cold regions, where we expect that a large fraction of annual precipitation falls as snow, our previous research found negative
We hypothesize that the concomitant change of cloudiness with annual changes in temperature and precipitation would impact both
In our analysis, we use the values of
2. Methods
In this study, we chose to use LAI to represent vegetation activity as it relates to many ecosystem functions (e.g., gross primary productivity, transpiration) at the relatively long, annual time scales. Additionally, it can be derived from remote observations and is easily available as output from Earth system models (Bonan 2002, p. 256). We use an ensemble of different Earth system model simulations from the CMIP5 archive and choose a time interval that overlaps with observations.
a. Data
We use observationally based LAI estimates derived from a combination of optical observations from the Moderate Resolution Imaging Spectroradiometer (MODIS) and the Advanced Very High Resolution Radiometer [AVHRR; Zhu et al. 2013; Xiao et al. 2014; Liu et al. 2012; the LAI 3g (LAI3g), Global Land Surface Satellite (GLASS), and Global Mapping (GLOBMAP) datasets]. We use LAI from the LAI3g dataset in calculating our observed βs for comparison with Earth system models. We recognize that LAI estimates derived in this way are not direct observations of LAI and contain uncertainty in both the observations and statistical techniques used to derive LAI from optical observations. For observationally based estimates of temperature, we use 2-m air temperature and precipitation from CRU Time Series (TS) 4.01 (Harris and Jones 2017; Harris et al. 2014). In addition, we compare our results with the same analysis using 2-m air temperature from ERA-Interim and observations of precipitation from Global Precipitation Climatology Project (GPCP; Dee et al. 2011; Adler et al. 2003).
b. Earth system models from CMIP5
We use an ensemble of 10 fully coupled Earth system model simulations from the CMIP5 archive that have prognostic LAI (single realization r1i1p1). Included in each of these models is a terrestrial biosphere that models the flux of carbon, water, etc. from the land surface (Taylor et al. 2012). The Earth system model simulations that we analyze here are from fully coupled models, with the land and atmosphere (including atmospheric CO2 concentrations) interacting with each other. The models used are detailed in Table 2 (Taylor et al. 2012). Our analysis uses monthly mean model output of LAI, surface temperature, and precipitation (variable names lai, tas, and pr, respectively). We create a continuous dataset that includes recent years and has maximum overlap with observations by combining simulations of the historical period (simulation name esmHist) with the first six years of future simulations from the emissions scenario that best matches the actual carbon emissions for the time period 2006–11 (simulation name esmRCP8.5).
Summary of models.
c. Interpolation of data
Observations of temperature and precipitation from CRU TS 4.01 were both reported at the same spatial resolution of 0.5° × 0.5° latitude–longitude and were interpolated to a common 1° × 1° latitude–longitude grid. ERA-Interim and GPCP were both reported at 1° × 1° longitude–latitude. However, the two grids did not match, so we interpolated them both to a matching 1° × 1° latitude–longitude grid. In addition, we coarsened the high-resolution LAI data derived from observations to better match other observations and models by interpolating it to 1° × 1° grid and then reinterpolating to the midpoint of the coarser grid—essentially doing an averaging across grid points (McKinney 2010). All models were analyzed on their native spatial grid.
d. Multiple linear regression


To test for the impact of temporal trends, we performed the regression both on the raw data as well as the detrended data. We found that our analysis was not sensitive to the inclusion or omission of trends. We report the analysis on detrended time series to focus on the sensitivity of the ecosystem to interannual variation and to avoid interpreting trends from anthropogenic greening (Mao et al. 2016, 2013). We performed regressions for the longest time series available (1982–2011) with CRU TS 4.01 as limited by observations, and, as a check for robustness, on a shorter time period (1997–2011) with ERA-Interim and GPCP. The earliest LAI data we used are available in 1982, while the earliest available high-resolution precipitation data (at 1° × 1° latitude–longitude grid) are available starting in 1997, and our preferred LAI observation (LAI3g) is available for 2011. We compare our metrics of the sensitivity of the ecosystem to climate variation β across 10 Earth system models from the CMIP5 archive as well as a dataset of leaf area derived from observations. We focus on observed β derived from LAI3g due to the consistency of the data through time across the long time series. However, we note that distinguishing whether one LAI dataset is better than another is difficult (Jiang et al. 2017).
e. Aggregating across climate
We aggregate our results in climate space by assigning vegetated terrestrial grid points from observations and models into climate bins defined by mean annual temperature and precipitation, and we calculate the area-weighted average sensitivities for these climate bins assuming a spherical Earth. We found little difference between calculating the unweighted-bin average compared to the bin average weighted by area, as most points in each bin fall at similar latitudes and thus have roughly the same area. The climate space ranges from −20° to 30°C temperature, and 0 to 5000 mm yr−1 of precipitation, and each bin extends 2°C by 200 mm yr−1. We accounted for water and nonvegetative points by discarding spatial points where the mean value of LAI fell below a threshold indicating little vegetation (less than 0.2 LAI; Scurlock et al. 2001). Each model generates a unique climate relative to each other and the observations. In the case of our analysis, this means that not all climate bins represented in observations are represented by all of the models, and some models also create novel climates not seen in observations. We restrict our analysis of ecosystem functioning to climates common to both models and observations to avoid the confounding influence of ecosystem models operating in different mean annual climates. Each of the 10 Earth system models we analyzed simulates its own climate and therefore can differ from the others in the mean annual temperature and precipitation at each spatial point. We find that the climate simulated by the 10 Earth system models do not capture the full breadth of joint temperature and precipitation space found in observations. Though not all extreme environments are represented, the majority of observed vegetated land points fall within climate regions that are represented by all of the models. The large majority of models fail to simulate high-precipitation climate regions at all temperatures (Fig. 1). This systematically low bias in precipitation results in particularly poor model coverage over climates observed in the deep Amazon and the Maritime Continent (Fig. S1 in the online supplemental material). In addition, all of the models fail to simulate very cold vegetated land areas (Fig. 1). These vegetated places with low temperatures are primarily observed at high latitudes and along the Tibetan Plateau (Fig. S1).
Number of models, out of 10, that represent each binned space in mean annual temperature and mean annual precipitation space. Black contour shows the maximum extent of climate space in observations.
Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-17-0580.1
f. Uncertainty in value of β for each climate bin
Each climate bin represents a number of spatial locations on Earth that share the same mean annual temperature and mean annual precipitation. Each spatial point thus contributes an estimate of β to that climate bin from which we calculate the average value of β for that climate bin, as well as characterize the variability within a bin. The uncertainty in the value of β for each bin results from a combination of the uncertainty of the regression (temporal uncertainty) and the spread in β for each bin (spatial uncertainty). To account for both uncertainties, the standard errors of the regression coefficient for each spatial grid point and the standard errors of the distribution of regression coefficients from all spatial grid points in each bin were combined through a root-mean-square weighted by degree of freedom to create a standard error of the regression coefficient for each bin. We use this standard error to test if the values of β differ from zero using the Student’s t distribution. We report the p value of the Student t distribution and mark the bins that have field significance at 95% using the method from Wilks (2016).
g. Comparison across models
We compared the models to each other and to observations by analyzing the consensus as well as the outliers in the sign and value of β. For consensus in sign, the number of models that agreed in sign was counted in each climate bin. When at least eight models agreed in sign, we identified outliers as any model that did not agree with the rest. We tested the similarity in value by using the standard error, where outliers were identified as models that fell outside two standard errors of the mean across models in any bin.
h. Systematic change of β across climate gradients
To better quantify and compare consistent features of the systematic change in β across climate, we calculate fits to the mean β of each climate bin within a subset of climate space. We focus our analysis on two climate gradients: changes in
We fit a line to
Systematic variation across climate gradients.
For
i. Statistical methods
Analysis uses Python and particularly depends on modules from numpy, scipy, scikit-learn, matplotlib, and xarray (Hunter 2007; McKinney 2010; Pedregosa et al. 2011; van der Walt et al. 2011; Hoyer and Hamman 2017). The Python scipy interpolate interp2D function was used to interpolate the spatial grid. We compute the multiple linear regressions at each grid point using the Python function sklearn.linear_model.LinearRegression from the scikit-learn package (Pedregosa et al. 2011). For our uncertainty test, we use the Student’s t distribution from Python’s scipy package (McKinney 2010). Linear regression across mean annual temperature was calculated using sklearn.linear_model.LinearRegression() and sklear.linear_model.RANSACRegressor() when omitting outliers. To smooth, we used (scipy.interpolate.interp1d) in order, followed by a Butterworth filter (scipy.signal.butter, scipy.signal.filtfilt) to remove the higher-frequency noise. The Butterworth filter was set to
3. Results
In the following section, we present results comparing and contrasting
Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-17-0580.1
Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-17-0580.1
The number of models that agree in sign for (a)
Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-17-0580.1
a. Consensus in simulated ecosystem function across climate space: 

All of the models agree with observations that very cold regions (below 0°C) have positive
The number of models that agree in sign for (a)
Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-17-0580.1
The p value of mean
Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-17-0580.1
A strong consensus among models for a negative
Using a linear fit of the change of
(a) A linear fit of
Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-17-0580.1
b. Consensus in simulated ecosystem function across climate space: 

Models and observations show broad agreement on the sign of
Mean annual temperature and mean annual precipitation bins that are outliers in the sign (disagree with eight or more models in sign) and the standard deviation (outside two standard deviations of the mean) of
Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-17-0580.1
The p value of mean
Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-17-0580.1
The transition from strong positive
4. Discussion
We evaluate
a. Temperature-driven processes dominate increases in sunlight in hot, wet climates
The most prominent difference in ecosystem functioning between observations and models is a model consensus for a strong negative
In hot climates, increased temperature has three costs for plants: increased respiratory costs; reduced photosynthetic efficiency, since plants are likely to be living near or beyond the thermal optimum for photosynthesis; and increased stress from high atmospheric water demand. In previous work we hypothesized that an increase in sunlight during warmer years in these very hot and wet climates offsets these three factors by increasing photosynthesis (Quetin and Swann 2017). In wet climates, there is a large enough supply of water so that energy from the sun incident on the surface is largely dissipated through latent heat, rather than sensible heat or longwave radiation that requires the surface to heat up. In this way, ample water in the environment from precipitation allows for smaller increases in the cost to vegetation from temperature resulting in an overall benefit from increased sunlight.
In hot, wet places, models show a consensus on the sign of simulated
Though the weak
These hot, wet regions of the globe still have a seasonal dry season, so it is still possible that there is a seasonal water deficit that does not show up in our annual analysis. The timing of the seasonality of increased rainfall compared with the seasonality of increased temperature may affect the interannual ecosystem functioning observed through β. For example, warming during the dry season in the tropics would likely lead to negative
b. Lack of adaptation and acclimation in models amplifies the gradient in ecosystem function
Adaptation and acclimation allow for physiological characteristics of plants (e.g., photosynthetic performance) to adjust to best match the environment in which the plant is growing. Adaptation operates through evolutionary changes of species over multiple generations. Acclimation happens within a single individual and can operate on a range of time scales, from minutes to the plant’s lifetime. Conceptually, adaptation and acclimation both provide vegetation with flexibility in responding to environmental change, though on different time scales. We hypothesize that the generally high magnitudes of simulated
While it is possible to represent acclimation in models (e.g., Lombardozzi et al. 2015; Smith et al. 2017), it requires defining how the processes occur, and observations are generally lacking to constrain the problem at global scales across many ecosystems (Lombardozzi et al. 2015; Smith et al. 2017). Models generally represent species with only a few plant functional types with fixed physiological characteristics (Box 1996). These plant functional types are generally located in the model empirically and not allowed to adapt individually or as a community to change physiological or community assembly characteristics in response to the climate. This is a particular issue if the model-simulated climate is significantly different than the real world where the ecosystem was adapted to a different climate. One way to change the physiological characteristics of an ecosystem is to change what plant functional types occur there. While dynamic global vegetation models can move plant functional types around the globe spatially, these changes occur slowly (i.e., generations of plants), and there is evidence of acclimation on short time scales (i.e., in a single plant down to minutes) in the real world (Berry and Bjorkman 1980; Smith and Dukes 2013; Way and Yamori 2014; Yamori et al. 2014; Atkin and Tjoelker 2003; Atkin et al. 2005).
Given that these Earth system models do not adjust the performance of simulated vegetation as a function of mean climate, we expect to see higher simulated
We can use the temperature at which the transition from positive
Without the flexibility of adaption and acclimation, the ecosystem functioning simulated by Earth system models changes more from climate to climate compared with observations. This lack of flexibility may have consequences for predicting the response of vegetation to global warming. If ecosystem functioning changes too strongly across climate gradients, it follows that the ecosystem functioning may be too sensitive to changes in the global climate. In this case, our predictions of vegetation changes in response to a warmer future using Earth system models would be too large. Indeed, in global warming experiments, adding temperature acclimation of photosynthesis and respiration to one Earth system model alters the carbon cycle and the biophysical response of the vegetation (Booth et al. 2012; Lombardozzi et al. 2015; Smith et al. 2017). Without the addition of adaptation and acclimation, our results suggest the ecosystems simulated in these Earth system models will respond too strongly to changes in physical climate due to global warming.
c. Highly consistent precipitation threshold for ecosystem functioning
The rapid transition from strong positive
5. Conclusions
The majority of the 10 Earth system models we analyze here reproduce the broad pattern of ecosystem functioning—both the sensitivity of vegetation to temperature
Though the broad patterns are similar between models and observations, our analysis shows an amplified change of ecosystem functioning across mean annual temperature. We hypothesize that not representing adaptation and acclimation of vegetation to climate in models is driving the amplified change in ecosystem functioning. Our analysis suggests that simulated photosynthetic performance curves are too steep, and thus simulated plants benefit too much from warmer years in cold climates and lose too much productivity in warmer years in hot climates. Finally, we find a strong agreement across models and observations for a threshold between water-limited ecosystems and energy-limited ecosystems at an annual precipitation of 1000 mm yr−1, as observed in
A stronger response of simulated ecosystem functioning to interannual variations of climate compared to observations leads us to suggest that estimates of the response of vegetation to physical climate changes due to increased atmospheric CO2 may be too large. In particular, we have identified that additional research is needed to determine which process—high respiration costs, decreases in photosynthetic efficiency at high temperatures that are too large, high carbon costs of atmospheric water demand, or too little increased sunlight during warmer years—results in fewer leaves during warmer years in hot, wet climates.
We have demonstrated the utility of comparing the broad empirical patterns of the sensitivity of ecosystems to climate that can be observed remotely. By analyzing these interactions across a climate space, we propose areas of the Earth system models with deficient representations of processes that will result in poor simulation of ecosystem functioning. These patterns can serve as a functional constraint while incorporating and improving process details (i.e., acclimation and adaptation) into Earth system models, which are critical for predicting the carbon cycle, hydrological cycle, and terrestrial surface energy balance in the sparsely observed regions of the globe and novel climates we expect from global warming.
Acknowledgments
We acknowledge support from the National Science Foundation Grant AGS-1553715. We acknowledge the organizations and groups responsible for CMIP, including the World Climate Research Programme, the climate modeling groups, and the U.S. Department of Energy’s Program for Climate Model Diagnosis and Intercomparison.
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