Editorial Type:
Article
Article Type:
Research Article

Sensitivity of Leaf Area to Interannual Climate Variation as a Diagnostic of Ecosystem Function in CMIP5 Carbon Cycle Models

Gregory R. Quetin Department of Atmospheric Sciences, University of Washington, Seattle, Washington

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Abigail L. S. Swann Department of Atmospheric Sciences, University of Washington, Seattle, Washington

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Print Publication:
15 Oct 2018
DOI:
https://doi.org/10.1175/JCLI-D-17-0580.1
Page(s):
8607–8625
Open access

Abstract

The response of the biosphere to variation in climate plays a key role in predicting the carbon cycle, hydrological cycle, terrestrial surface energy balance, and the feedbacks in the climate system. Predicting the response of Earth’s biosphere to global warming requires the ability to mechanistically represent the processes controlling photosynthesis, respiration, and water use. This study uses observations of the sensitivity of leaf area to the physical environment to identify where ecosystem functioning is well simulated in an ensemble of Earth system models. These patterns and data–model comparisons are leveraged to hypothesize which physiological mechanisms—photosynthetic efficiency, respiration, water supply, atmospheric water demand, and sunlight availability—dominate the ecosystem response in places with different climates. The models are generally successful in reproducing the broad sign and shape of the sensitivity of leaf area to interannual variations in climate, except for simulating generally decreased leaf area during warmer years in places with hot, wet climates. In addition, simulated sensitivity of the leaf area to temperature is generally larger and changes more rapidly across a gradient of temperature than is observed. We hypothesize that the amplified sensitivity and change are both due to a lack of adaptation and acclimation in simulations. This discrepancy with observations suggests that the simulated sensitivities of vegetation climate are too strong in the models. Finally, models and observations share an abrupt threshold between dry regions and wet regions around 1000 mm yr−1.

Denotes content that is immediately available upon publication as open access.

Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JCLI-D-17-0580.s1.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Gregory R. Quetin, gquetin@washington.edu

Abstract

The response of the biosphere to variation in climate plays a key role in predicting the carbon cycle, hydrological cycle, terrestrial surface energy balance, and the feedbacks in the climate system. Predicting the response of Earth’s biosphere to global warming requires the ability to mechanistically represent the processes controlling photosynthesis, respiration, and water use. This study uses observations of the sensitivity of leaf area to the physical environment to identify where ecosystem functioning is well simulated in an ensemble of Earth system models. These patterns and data–model comparisons are leveraged to hypothesize which physiological mechanisms—photosynthetic efficiency, respiration, water supply, atmospheric water demand, and sunlight availability—dominate the ecosystem response in places with different climates. The models are generally successful in reproducing the broad sign and shape of the sensitivity of leaf area to interannual variations in climate, except for simulating generally decreased leaf area during warmer years in places with hot, wet climates. In addition, simulated sensitivity of the leaf area to temperature is generally larger and changes more rapidly across a gradient of temperature than is observed. We hypothesize that the amplified sensitivity and change are both due to a lack of adaptation and acclimation in simulations. This discrepancy with observations suggests that the simulated sensitivities of vegetation climate are too strong in the models. Finally, models and observations share an abrupt threshold between dry regions and wet regions around 1000 mm yr−1.

Denotes content that is immediately available upon publication as open access.

Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JCLI-D-17-0580.s1.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Gregory R. Quetin, gquetin@washington.edu
Keywords: Atmosphere-land interaction; Biosphere-atmosphere interaction; Ecosystem effects; Climate models; Land surface model; Model comparison

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, , is positive when there are more leaves in a warmer year; , the sensitivity of vegetation to precipitation, is positive when there are more leaves during a wetter year. Though we interpret these coefficients as the sensitivity of vegetation to climate, regression does not prove causation. Indeed, studies have shown the reverse causation, such that the climate is sensitive to long-term global trends of increased leaf area index (LAI) in vegetation (Zhu et al. 2016; Forzieri et al. 2017; Zeng et al. 2017). It is likely that a small amount of the sensitivity of climate to vegetation is captured by the multilinear coefficients from our analysis. However, at the scale of interannual variation at a grid point, we expect the sensitivity of vegetation to climate to be dominant because of the lack of correlation across the globe. For this analysis, we calculate and for observations of LAI derived from satellite and gridded datasets of observed 2-m air temperature and precipitation (see methods section). We then compare these observed values with and calculated from LAI and climate variables simulated by Earth system models with active carbon cycles and prognostic leaf area.

b. Proposed processes driving and

We hypothesize the sign and magnitude of and that would result if a particular process that occurs in nature were isolated (Table 1). The observed and are combinations of these processes, with the relative influence of each process varying with the climate being observed and the model simulating these processes. We expect that the primary drivers of (the change of leaves in response to warmer/cooler years) will be photosynthetic performance, respiration, and the response of stomata to the dryness of the atmosphere through the temperature-driven vapor pressure deficit. In contrast, we expect that the primary drivers of (the change of leaves in response to wetter or snowier/drier years) will be the effects of snow in colder climates and how well the water supply matches the water demand of the environment in other climates. In addition to these direct drivers of and , we note that both temperature and precipitation correlate with sunlight in different ways across the globe (e.g., increased sunlight in the tropics generally comes with lower rainfall and higher temperatures). These additional concomitant changes in sunlight with temperature or precipitation suggest other potential drivers of and because of increases of sunlight driving more overall photosynthesis.

Table 1.

Proposed mechanisms driving β.

Table 1.

From empirical and theoretical studies in the literature we can develop an expectation for how different processes would influence the sign of independent of one another. The dependence of photosynthetic efficiency on temperature is often measured as a concave curve, increasing with temperature to some optimum and then decreasing for hotter temperatures beyond the optimum (Berry and Bjorkman 1980; Day 2000; Smith and Dukes 2013; Way and Yamori 2014; Yamori et al. 2014). Given this shape, a plant living in an environment colder than the optimum temperature would have increased photosynthesis in warmer years and thus positive . Similarly, plants living in environments warmer than the optimum would have decreased photosynthesis in warmer years and thus a negative , while plants living near the optimum temperature would have only a weak response and a near zero. In contrast to photosynthesis, the metabolic costs of respiration generally increase with temperature so that a warmer year would lead to a negative across all temperatures. Finally, warmer years increase the vapor pressure deficit (assuming relative humidity is about the same), which increases the atmospheric demand for water from the vegetation. We expect this increased atmospheric demand for water to lead to a negative as the strategies that plants invoke to avoid hydraulic damage reduce carbon uptake.

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 , with most of the variation in vegetation driving the occurring at the beginning of the growing season (Quetin and Swann 2017). In these cold and highly seasonal climates, the mean annual leaf area is partly controlled by the length of the growing season. Thus increased precipitation is realized as increased snowfall that melts out later and can lead to a reduction in the length of the growing season. Without a large increase in maximum LAI during the summer, we expect the shorter growing season during a heavy snow year to have lower annual LAI and thus a negative (more leaves during drier years). Conversely, where precipitation falls as rain it serves as the main water supply for most vegetation. We expect having less water available from rainfall would induce water limitation and lead to less photosynthesis, thus a positive (more leaves during a wetter year).

We hypothesize that the concomitant change of cloudiness with annual changes in temperature and precipitation would impact both and . Warmer years can be accompanied by more sunlight due to fewer clouds. We expect increases in sunlight to benefit vegetation and lead to a positive through the positive correlation between sunlight and mean annual temperature. Sunlight is also correlated with rainfall such that rainier years can be correlated with less sunlight due to increased clouds. We expect a reduction in sunlight to reduce photosynthesis and lead to fewer leaves and thus through the negative correlation with precipitation lead to a negative .

In our analysis, we use the values of and to hypothesize which processes dominate in different climates. In addition, we quantify how and change across climate in both observations and models. By comparing across models and observations we are able to hypothesize which processes lead to disagreements among models and observations.

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).

Table 2.

Summary of models.

Table 2.

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

We create a metric of the sensitivity of the ecosystem to climate variation (both observed and simulated) by performing a multilinear regression of the percent change in LAI (%LAI) interannual variation with the interannual variation of temperature T and precipitation P [Eq. (1)].
e1
The regression coefficients are metrics of the sensitivity of vegetation showing how the percent leaf area generally changes in warmer/cooler, wetter/drier years; has units of percent LAI per degree Celsius (%LAI °C−1) and has units of percent LAI per millimeter (%LAI mm−1).

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).

Fig. 1.
Fig. 1.

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 across temperature for places with precipitation between 100 and 1000 mm yr−1, and changes in across precipitation for places with mean annual temperature between 20° and 30°C. We characterize the change in β in these domains using a linear fit where applicable and a smoothing technique where a predetermined function like a linear fit is less useful.

We fit a line to to quantify the slope of change and the temperature of transition from positive to negative . We test both an ordinary least squares linear fit and a random sample consensus (RANSAC) linear fit, which omits outlying points. Where the two solutions resulted in dramatically different answers is noted in Table 3. We report the slope and intercept from the RANSAC fit, as well as the variance explained (r2) of the RANSAC fit calculated for all the points, including the outliers.

Table 3.

Systematic variation across climate gradients.

Table 3.

For , we interpolated between binned values of and then smoothed the resulting transition across mean annual precipitation to highlight the general shape of the systematic change. We interpolated the data in order to use a Butterworth filter to remove the higher-frequency noise. The smoothed change across the gradient of mean annual precipitation is more representative of the systematic change to be quantified and compared across Earth system models and observations. We used the similarity of shape of the systematic change between Earth system models and observations to quantify a maximum value of and the mean annual precipitation at which approached zero. We defined the approach to zero as the point where drops below 0.01%LAI mm−1 yr−1 divided by the maximum we calculated above.

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 and applied through (McKinney 2010).

3. Results

In the following section, we present results comparing and contrasting and derived from Earth system models and observations. For use in calculating βs from observations, there are three derived observations of LAI available. We found that the mean LAI was broadly similar between these datasets, but that the derived and appeared most reasonable for LAI3g (and most similar to our previous analysis; Quetin and Swann 2017). In particular, derived from both GLOBMAP and GLASS LAI was positive in some of the hottest and driest environments (Fig. S2). Additionally, calculated from both GLOBMAP and GLASS LAI, with ERA-Interim temperature and GPCP precipitation, have intense positive values in the hottest climates outside of the driest areas, and in the midlatitudes (approximately 2000 mm yr−1 of rainfall and between 0° and 5°C). For these reasons, we focus our analysis on results using LAI from LAI3g for our observed βs when comparing with models (Figs. 2–4; Zhu et al. 2013). Additionally, we focused on the longer time series using βs calculated with CRU TS 4.01 as the βs calculated with ERA-Interim temperature and GPCP precipitation were broadly the same (Fig. S2).

Fig. 2.
Fig. 2.

aggregated in climate space for (a)–(j) CMIP5 models, (k) the mean of those models, and (l) LAI3g observations. Contours represent the extent of climate space represented in all models (black line).

Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-17-0580.1

Fig. 3.
Fig. 3.

aggregated in climate space for (a)–(j) CMIP5 models, (k) the mean of those models, and (l) LAI3g observations. Contours represent the extent of climate space represented in all models (black line).

Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-17-0580.1

Fig. 4.
Fig. 4.

The number of models that agree in sign for (a) and (b) . The standard deviation across models for (c) and (d) . Where the majority of models have a negative β, colors are brown; where positive, β colors are purple [in (a), (b)]. Dots indicate majority of models agree in sign with observations in (a) and (b), and that the observations are included within two standard errors of the models in (c) and (d).

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 (more leaves when warmer; Figs. 2, 4a). Above mean annual temperatures of 0°C, the consensus among models for a positive is dependent on mean annual precipitation. In places with more precipitation, regions of complete agreement among models on positive (more leaves when warmer) extend up to temperatures of 10°C (Figs. 2, 4a). However, at lower precipitation, about half the models show disagreement on the sign of starting at 0°C. This transition from complete agreement among models on the sign of to an even split between the models demarks the cold end of a climate region with little agreement among the models. The uncertainty of the sign of simulated occurs in climates where observations show a very weak positive changing to negative in warmer climates. When projected on to a map, this region of uncertainty in models primarily consists of the northern midlatitudes (Fig. 5a). The climates that are uncertain across models also includes areas of high uncertainty in each bin for many models and observations (Fig. 6a). Where there is strong agreement in simulated sign of in cooler climates, there is also a strong agreement in the simulated value of across models, with a standard deviation across the ensemble of less than 2%LAI °C−1 for most of the climate space below 10°C (Fig. 4c).

Fig. 5.
Fig. 5.

The number of models that agree in sign for (a) and (b) . Where the majority of models have a negative β, colors are brown; where positive, β colors are purple. Projected onto a spatial map using observed values of mean annual temperature and mean annual precipitation.

Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-17-0580.1

Fig. 6.
Fig. 6.

The p value of mean of each bin in climate space for (a)–(j) CMIP5 models, (k) the mean of those models, and (l) LAI3g observations. White dots with black outline signify field significance per Wilks (2016).

Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-17-0580.1

A strong consensus among models for a negative is evident at temperatures warmer than 10°C in dry climates and warmer than 18°C in the wettest climates analyzed. In these warmer climates, the consensus is shared primarily between 8 and 9 models, sometimes reaching all 10 models (Figs. 2, 4a). Two models (MIROC-ESM and BNU-ESM) display the most climates with a disagreement in with other models compared with the overall model consensus on the sign of (see Fig. 8). These warmer climates also show a much larger spread across models of the value of , generally having an across-model standard deviation greater than 10%LAI °C−1 and above 16+%LAI °C−1 in the driest/hottest climates (Fig. 4c). Although the majority of models agree with one another in simulating negative in hot climates, observations only concur with the model consensus of a negative in dry climates with precipitation below 1000 mm yr−1 (Fig. 2). In climates wetter than 1000 mm yr−1, there is model consensus, but it disagrees with observations that show generally positive (more leaves when warmer) in all but a few climate bins above 1000 mm yr−1 (Fig. 2). In these wet climates, most models and observations show large uncertainty in (Fig. 6).

Using a linear fit of the change of across climate space, we estimate the slope of change of across mean annual temperature to be −0.08%LAI °C−1 °C−1 in observations and −0.41%LAI to −0.09%LAI °C−1 °C−1 in models. We estimate that the temperature of the transition from positive to negative is +14.1°C in observations and −8.5° to +22.2°C in models (see methods section; Fig. 7a; Table 3). The modeled slopes of the change of simulated across mean annual temperature (units: %LAI °C−1 °C−1), from positive (at cooler temperatures) to negative (at relatively dry high temperature), are more than 2 times stronger than the observed slope (Table 3). In addition, the majority of models transition from positive to negative at cooler temperatures, +5.6°C, compared to the transition in observations at +14.1°C (Table 3). Note that these linear fits are not a strong representation for all models (Fig. S3).

Fig. 7.
Fig. 7.

(a) A linear fit of for the climate bins bounded by 100 and 1000 mm yr−1 across the global gradient of mean annual temperature (1997–2011). (b) An interpolated and smoothed line of for the climate bins bounded by 20° and 30°C across the global gradient of mean annual precipitation (1997–2011). Each line is a different model (see legend). Black line is LAI3g observation.

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 across climate space (Figs. 3, 4b). In hot and dry climates (greater than 0°C and less than 1000 mm yr−1), there is a consensus across models for strong positive (more leaves when wetter; Fig. 4b). A relatively high spread in the value of model-derived occurs in the driest climates (below 500 mm yr−1, above 0°C; Figs. 3, 4d). In contrast to observations and other models, only one model (BNU-ESM) shows a large number of negative bins in the hottest and driest climates (Figs. 3 and 8). The consensus across models is that the value of sharply decreases below 0°C and above 1000 mm yr−1, becoming negative in the majority of models (seven) below 0°C (Fig. 4). This simulated consensus of a decrease in concurs with an observed transition from positive to negative (below 0°C) and relatively weak (above 1000 mm yr−1). Above 1000 mm yr−1 of precipitation, and across a wide range of temperatures (0°–30°C), there is only a weak consensus among models that is positive, but all of the models concur with observations that the strength of is relatively weak in these wetter climates (Fig. 3). These regions of weak are primarily in the tropics and savannahs of the Amazon and Africa (Fig. 5b). The uncertainty in in both models and observations is broadly similar to the value of , with low uncertainty where is large (Fig. 9).

Fig. 8.
Fig. 8.

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 and for (a)–(j) CMIP5 models and (k) summary of number of bins outliers. Colors per the legend. Points jittered for clarity.

Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-17-0580.1

Fig. 9.
Fig. 9.

The p value of mean of each bin in climate space for (a)–(j) CMIP5 models, (k) the mean of those models, and (l) LAI3g observations. White dots with black outline signify field significance per Wilks (2016).

Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-17-0580.1

The transition from strong positive in dry climates to weak values in wet climates has a similar shape across most models (nine) and observations for relatively warm climates above 20°C (see methods section; Fig. 7b; S4). The magnitude of maximum positive in dry climates is highly variable (observations: 0.037%LAI mm−1, model mean ± standard deviation: 0.21%LAI ± 0.26%LAI mm−1). In contrast, the mean annual precipitation of the transition from strong to relatively weak is consistent across observations and models (observations: 1059 mm yr−1, model mean ± standard deviation: 1020 ± 207 mm yr−1; Fig. 7b; Table 3).

4. Discussion

We evaluate and across climate space, defined by mean annual temperature and precipitation in order to compare like climates in observations with like climates in models. In contrast to analyses that depend on the spatial location for comparison, our approach puts the Earth system models on a more equal climate footing and more specifically targets the modeling of the ecosystem climate interactions through the sensitivity of vegetation to interannual climate variation as opposed to the spatial patterns. Discrepancies between observations and models and between models in particular climates can suggest which process may be in error and provides a functional constraint that can be used in efforts to model the ecosystem climate interactions. This approach is limited to partially controlling for mean annual temperature and precipitation. Beyond mean climates, there are noted differences in the amplitude of interannual variations in climate models compared to observations (Anav et al. 2013b). In addition, because of both differences in the spatial distribution of climates and differences in the specified maps of vegetation, plant functional types in the models may occur in climates that are not natural to the particular plant functional type. We propose future work detailing the differences between models and observations due to the effects of different climate variability and the mismatch between climate and plant functional type.

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 (more leaves when cooler) in wet climates where only a weak positive is observed (Figs. 2, 4). Similar disagreements between observations and models have been shown in prior research with sensitivity of net biosphere productivity and net primary productivity to temperature (Liu et al. 2017, 2016). These hot, wet climate regions where models and observations disagree in the sign of encompass tropical forests and represent a large amount of global above-ground carbon (Saatchi et al. 2011). This climate region also shows high uncertainty in the mean value of in the bins for both models and observations, even though models have a strong . The simulated strong negative suggests that simulated tropical forests may be too sensitive to increases in temperature, and Earth system models are thus prone to predict worse outcomes for tropical forests in a warming climate than observations would suggest. These results are suggestive, but it should be noted that interannual variations in temperature occur with many other concomitant changes in environmental conditions, and the same correlations may not hold under greenhouse gas–driven warming. Therefore interannual variations are a limited indicator of how vegetation will respond to the longer-term changes under climate change.

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 , but disagree with observed . For the models to consistently disagree with observations, one of the three processes that we expect to cause a negative on its own—photosynthetic efficiency, respiration, or stomatal response to atmospheric water demand—must be stronger in the models compared with observations or the observed increase in sunlight during warmer years must be weaker. Simulating the wrong amplitude for any one, or combination, of these processes could result in an amplified negative even if some of the processes were correctly simulated. It is notable that despite disagreeing about the sign of , the models and observations all agree that is relatively weak in these hot, wet climates (Fig. 3). Weak in this wet climate suggests that the simulated vegetation is not water-supply limited.

Though the weak is suggestive of a lack of water-supply limitation, we cannot rule out that atmospheric water demand is causing intermittent stress, leading to negative . Even though plants may have ample soil water, atmospheric water demand during a warmer year could still cause hydraulic stress or stomatal closure without exhausting the water supply. Plants should have reduced carbon uptake in warmer years independent of their strategy to either endure or avoid stress during high atmospheric water demand (anisohydric, isohydric), creating another potential mechanism for negative in these hot, wet climates. In addition, vapor pressure deficit increases exponentially with temperature due to the Clausius–Clapeyron relationship for saturation pressure. Because of this exponential increase, we expect that a warmer year in warm to hot climates will have a much bigger negative influence on the vegetation than warm years occurring in cooler climates. Thus it is possible that the vegetation in hot, wet climates is not experiencing any limitation from water supply, but is experiencing limitations during years of high water demand that the physiology of the vegetation cannot keep up with, leading to negative .

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 (lack of water supply and increased atmospheric water demand), whereas warming during the wet season could be simultaneously associated with reduced cloudiness and increased sunlight allowing for higher rates of photosynthesis and a positive . Other work suggests that there is more seasonality to the sensitivity of vegetation to precipitation rather than the sensitivity of vegetation to temperature (Liu et al. 2017).

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 (both negative and positive) and the amplified change of across mean annual temperature is due to models not simulating the ability of vegetation photosynthesis (or carbon allotment between different pools, including leaf area) to adapt or acclimate to local climate conditions. Without the ability to adapt or acclimate, variation in temperature will more strongly reduce (or increase) the amount of carbon available for growing leaf area and thus increase the variation of leaf area with variation of temperature. Leaf area simulated with fixed responses to environmental factors will have larger that change more from climate to climate.

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 compared with observations. For example, vegetation of the same species grown in a colder climate compared to a warmer climate has been observed to flatten and shift the optimum of its photosynthetic performance curve to colder temperatures (Berry and Bjorkman 1980; Smith and Dukes 2013; Way and Yamori 2014; Yamori et al. 2014). In this example, a warmer year would increase the performance less, and thus lead to a lower overall , because the performance curve is flatter. Though operating through different mechanisms, any ability plants have to adjust physiology to match the environment should dampen the response of vegetation to changing climates.

We can use the temperature at which the transition from positive in colder climates to negative in warmer climates occurs to help identify which processes drive the amplified change of ecosystem function across climate. The transition of in sign demarks the temperature at which benefits of a warmer year for improved photosynthetic performance are outweighed by the costs of increased respiration during a warmer year and water stress from a drier atmosphere. Models represent this transition at cooler temperatures than observations [+14.1°C in observations and +5.6° to ± 8.2°C (mean ± standard deviation) in models]. Either the positive benefits in models of a warmer year are too small for photosynthesis or the costs are too high for respiration and water stress. We hypothesize that the majority of the cause of the cooler transition is due to simulating too steep an increase in the cost of respiration due to a lack of simulated adaptation and acclimation, leading to a stronger-than-observed cost in warmer years. Alternatively, a too-steep photosynthetic curve would lead to a stronger-than-observed benefit in warmer years leading to an overly strong at colder temperatures due to the lack of flattening of the photosynthetic performance curve through adaptation and acclimation, while a too-low optimum of the performance curve could change the intercept (Berry and Bjorkman 1980; Smith and Dukes 2013; Way and Yamori 2014; Yamori et al. 2014). It is also possible that the adaptation and acclimation of photosynthesis plays a role in the sensitivity of vegetation to interannual variation in temperature separate from adaptation and acclimation to temperature. Photosynthesis adapts and acclimates to the light environment, adjusting photosynthetic rates and sensitivity to both shade and high-light environments (Peguero-Pina et al. 2016; Niinemets et al. 2015; Givnish 1988). Temperature and the light environment often correlate, with sunnier climates and years often being warmer. The lack of photosynthetic adaptation and acclimation in response to the light environment could be an additional mechanism driving stronger-than-observed in models. We propose future work calculating the sensitivity of vegetation to both sunlight and temperature. Datasets with longer time series of both temperature and sunlight would help distinguish between temperature acclimation and light acclimation in observations and models.

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 to very weak occurs at nearly the same annual precipitation in all models and observations. The uniformity of the precipitation level at which the transition occurs appears to demark a sharp threshold separating water-limited ecosystems (strong positive : more leaves in a wetter year) from ecosystems with little response to interannual variation in precipitation (relatively weak ). The concept of a water-limited (not enough water) and energy-limited (more water than surface-incident energy) region is common in literature (Budyko 1961). However, we do not have a strong hypothesis for the consistency across multiple models and observations in the value of mean annual precipitation for this threshold. Our estimated threshold of approximately 1000 mm yr−1 of precipitation separating water-limited from energy-limited regimes is similar to thresholds in previous studies (Swann et al. 2016; Guan et al. 2015; Malhi et al. 2009). In addition, we note that the extent of these water-limited and energy-limited regions approximates the region described in Nemani et al. (2003) as light limited. In climates with temperatures above 20°C, precipitation correlates strongly with an aridity index derived from dividing precipitation by the potential evaporation from the shortwave energy incident on the surface (Quetin and Swann 2017). Though not explanatory, the threshold of 1000 mm yr−1 concurs with an aridity index of approximately 0.5 (2 times the potential energy to evaporate water as there is water from precipitation for evaporation). We note that the threshold in precipitation extends down to temperatures of 0°C for most models and observations. We lack an explanation at this time for the consistency of value for this threshold and suggest it as an avenue for future study.

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 and precipitation —across climate space. An exception to this general agreement is that the majority of models produce negative (more leaves when cooler) in hot, wet climates, where observations show a mild positive . This disagreement is not observed in .

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 . Because of the strong agreement between observations and models on this threshold, more detailed analysis of the simulated mechanisms that control this threshold could help determine the real-world mechanisms behind it.

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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  • <sc>Fig.</sc> 1.
    View in gallery
    Fig. 1.

    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.

  • <sc>Fig.</sc> 2.
    View in gallery
    Fig. 2.

    aggregated in climate space for (a)–(j) CMIP5 models, (k) the mean of those models, and (l) LAI3g observations. Contours represent the extent of climate space represented in all models (black line).

  • <sc>Fig.</sc> 3.
    View in gallery
    Fig. 3.

    aggregated in climate space for (a)–(j) CMIP5 models, (k) the mean of those models, and (l) LAI3g observations. Contours represent the extent of climate space represented in all models (black line).

  • <sc>Fig.</sc> 4.
    View in gallery
    Fig. 4.

    The number of models that agree in sign for (a) and (b) . The standard deviation across models for (c) and (d) . Where the majority of models have a negative β, colors are brown; where positive, β colors are purple [in (a), (b)]. Dots indicate majority of models agree in sign with observations in (a) and (b), and that the observations are included within two standard errors of the models in (c) and (d).

  • <sc>Fig.</sc> 5.
    View in gallery
    Fig. 5.

    The number of models that agree in sign for (a) and (b) . Where the majority of models have a negative β, colors are brown; where positive, β colors are purple. Projected onto a spatial map using observed values of mean annual temperature and mean annual precipitation.

  • <sc>Fig.</sc> 6.
    View in gallery
    Fig. 6.

    The p value of mean of each bin in climate space for (a)–(j) CMIP5 models, (k) the mean of those models, and (l) LAI3g observations. White dots with black outline signify field significance per Wilks (2016).

  • <sc>Fig.</sc> 7.
    View in gallery
    Fig. 7.

    (a) A linear fit of for the climate bins bounded by 100 and 1000 mm yr−1 across the global gradient of mean annual temperature (1997–2011). (b) An interpolated and smoothed line of for the climate bins bounded by 20° and 30°C across the global gradient of mean annual precipitation (1997–2011). Each line is a different model (see legend). Black line is LAI3g observation.

  • <sc>Fig.</sc> 8.
    View in gallery
    Fig. 8.

    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 and for (a)–(j) CMIP5 models and (k) summary of number of bins outliers. Colors per the legend. Points jittered for clarity.

  • <sc>Fig.</sc> 9.
    View in gallery
    Fig. 9.

    The p value of mean of each bin in climate space for (a)–(j) CMIP5 models, (k) the mean of those models, and (l) LAI3g observations. White dots with black outline signify field significance per Wilks (2016).

Fig. 1.

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.
Fig. 2.

aggregated in climate space for (a)–(j) CMIP5 models, (k) the mean of those models, and (l) LAI3g observations. Contours represent the extent of climate space represented in all models (black line).
Fig. 3.

aggregated in climate space for (a)–(j) CMIP5 models, (k) the mean of those models, and (l) LAI3g observations. Contours represent the extent of climate space represented in all models (black line).
Fig. 4.

The number of models that agree in sign for (a) and (b) . The standard deviation across models for (c) and (d) . Where the majority of models have a negative β, colors are brown; where positive, β colors are purple [in (a), (b)]. Dots indicate majority of models agree in sign with observations in (a) and (b), and that the observations are included within two standard errors of the models in (c) and (d).
Fig. 5.

The number of models that agree in sign for (a) and (b) . Where the majority of models have a negative β, colors are brown; where positive, β colors are purple. Projected onto a spatial map using observed values of mean annual temperature and mean annual precipitation.
Fig. 6.

The p value of mean of each bin in climate space for (a)–(j) CMIP5 models, (k) the mean of those models, and (l) LAI3g observations. White dots with black outline signify field significance per Wilks (2016).
Fig. 7.

(a) A linear fit of for the climate bins bounded by 100 and 1000 mm yr−1 across the global gradient of mean annual temperature (1997–2011). (b) An interpolated and smoothed line of for the climate bins bounded by 20° and 30°C across the global gradient of mean annual precipitation (1997–2011). Each line is a different model (see legend). Black line is LAI3g observation.
Fig. 8.

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 and for (a)–(j) CMIP5 models and (k) summary of number of bins outliers. Colors per the legend. Points jittered for clarity.
Fig. 9.

The p value of mean of each bin in climate space for (a)–(j) CMIP5 models, (k) the mean of those models, and (l) LAI3g observations. White dots with black outline signify field significance per Wilks (2016).
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