1. Introduction
The structure and productivity of vegetation across the world is coupled to climate through environmental variables such as light, water, and temperature. Structure and productivity of vegetation are also controls on the terrestrial carbon cycle (Friedlingstein et al. 2006), the terrestrial hydrological cycle (Schlesinger and Jasechko 2014; Jasechko et al. 2013), and the surface energy budget (Ghimire et al. 2014). To understand how global vegetation will be altered under climate change, we must understand how ecological–climate interaction operates at large spatial scales and thus across global climate gradients. In our work we have chosen mean annual temperature and precipitation as climate gradients with historical context in studying vegetation (e.g., Whittaker 1970), related to environmental resources important for vegetation function and with strong variation across the globe (Whittaker 1962; Kottek et al. 2006; Metzger et al. 2013). There is evidence that an important part of the way that vegetation and climate interact is through changes in phenology (Richardson et al. 2010, 2013). Though our analysis aggregates across the seasonal cycle of vegetation and climate, we still observe these changes as interannual variation in the annual means (e.g., a longer growing season is a greener year).
Three common approaches have previously been used to study how vegetation is controlled by the climate of a region and to predict how it will change in the future: 1) climate-biome classification—treating the current boundaries between biomes as determined by climate (Peel et al. 2007; Kottek et al. 2006; Smith et al. 2002; Metzger et al. 2013); 2) simplified models of climate constraint—based on physiological constraints on net primary productivity (Churkina and Running 1998; Nemani et al. 2003; Jolly et al. 2005; Running et al. 2004); and 3) global process-based models—extending plant- or plot-scale research to global scales through process-based numerical global models (Oleson et al. 2010; Boisvenue and Running 2006; Levis 2010).
Our analysis serves to bridge the static geographical observational (approach 1) and modeling approaches (approaches 2 and 3) by empirically quantifying the sensitivity of vegetation to interannual variations in environmental variables across the globe. By analyzing these sensitivities across climate space we can diagnose how ecosystem function varies across annual climate and hypothesize mechanisms that could explain the observed pattern. We define ecosystem function here as the integrated environmental modulation of both plant-scale physiological (photosynthesis, respiration, transpiration, and hydraulic stress) and population-scale ecological (demography, disturbance, and competition) processes measured at a coarse spatial scale (100 km × 100 km). We do not discriminate grid points based on plant type or human influence. Differences in the growth cycle of vegetation that extend into the interannual variations of the vegetation are treated as additional error in our analysis. Our study captures broad patterns of ecosystem functioning across the global range of two environmental conditions (mean annual temperature and precipitation) and allows us to identify major climate constraints on remotely sensed vegetation.
The effect of climate on vegetation is evident from observations of how vegetation is distributed across the globe and is explicit in efforts to classify biomes and the use of climate envelopes to predict the movement of biomes due to climate change (Koven 2013; Rubel and Kottek 2010). However, the way that ecosystem function varies across climate, rather than just vegetation distribution, has not been empirically investigated at a global scale. In this study we combine the concept from climate classification that climate shapes vegetation with our calculation of the interannual sensitivity of vegetation to climate from remotely sensed vegetation and observations and reanalysis of climate data. This allows us to identify emergent functional constraints measured at the scales and resolutions required to make global predictions about vegetation. Analyzing the sensitivity of vegetation across climate space expands on other work and enables us to find the underlying pattern of ecosystem function across global climate gradients (Seddon et al. 2016; Wu et al. 2015). Here our concept of binning across climate space is similar to the common practice in climate science of calculating the zonal mean of a variable, with latitude replaced with temperature and precipitation (see methods) (see Figs. 1 and 4 ).
2. Methods
a. Empirical sensitivity of vegetation to climate
We create an empirical estimate of the sensitivity of vegetation to climate at global scales by combining the satellite record of the normalized difference vegetation index (NDVI) with globally gridded estimates of temperature and precipitation. NDVI represents the longest global time series available to study vegetation response at a scale commensurate with global carbon cycling and ecological–climate feedbacks (Pinzon and Tucker 2014). NDVI has frequently been used to study temporal trends in vegetated land cover (e.g., Chen et al. 2014) and has been correlated with environmental variables across biomes and regions to demonstrate the connection between the physical environment and surface greenness (Wu et al. 2015; Zhou et al. 2003, 2001; Goward et al. 1991; Asner et al. 2000; Xu et al. 2014; Myneni et al. 2002). Though a simple metric of vegetation, observations of NDVI have the longest continuous global time series and relates strongly to leaf area, fraction of absorbed photosynthetically available radiation, plant fluorescence, gross primary productivity, and more advanced vegetation indices (Myneni et al. 2002; Frankenberg et al. 2011; Guanter et al. 2012; Glenn et al. 2008; Huete et al. 2002). As the time series of MODIS enhanced vegetation index (less saturation in dense vegetation) and targeted measurements of solar-induced fluorescence (a remote observation thought to be proportional to GPP) concurrent with climate observations grow longer we hope to be able to further test many of the hypotheses presented in this paper (Huete et al. 2002; Frankenberg et al. 2014, 2013, 2011; Guanter et al. 2012). In addition to remote sensing, individual flux tower locations can make more direct measurements of carbon and water fluxes (Baldocchi 2014). However, global products derived from these site-level observations (e.g., Jung et al. 2011; Beer et al. 2010; Xiao et al. 2011) also depend heavily on similar satellite observations.
We interpret the resulting 
We chose a simple linear model with two predictors in order to learn about ecosystem–climate interactions from the variation of a metric that reflects ecosystem–climate interactions across climate space. Rather than attempt to create the best linear model for NDVI at each pixel on the map, our regression model serves to linearize the effect of both temperature and precipitation consistently across the globe and simplify interpretation of the results.
Collinearity between the predictor variables of the linear regression (temperature and precipitation) is present at various levels across the globe. However, levels of correlation were not found to exceed commonly cited thresholds that would damage a linear regression at most grid points, and experiments that excluded high correlation values (
To examine the aggregated structure of 
Sensitivity of vegetation to interannual variation in (a) temperature 
Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0829.1
Sensitivity of vegetation to interannual variation in (a) temperature
Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0829.1
Sensitivity of vegetation to interannual variation in (a) temperature
Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0829.1
Spatial points plotted in climate space of mean annual temperature and mean annual precipitation. Nonvegetated grid points (gray), vegetated grid points used in analysis (green), and vegetated grid points where there were fewer than 10 in a bin (brown).
Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0829.1
Spatial points plotted in climate space of mean annual temperature and mean annual precipitation. Nonvegetated grid points (gray), vegetated grid points used in analysis (green), and vegetated grid points where there were fewer than 10 in a bin (brown).
Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0829.1
Spatial points plotted in climate space of mean annual temperature and mean annual precipitation. Nonvegetated grid points (gray), vegetated grid points used in analysis (green), and vegetated grid points where there were fewer than 10 in a bin (brown).
Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0829.1
b. Uncertainty
To quantify the uncertainty in the aggregate bins of 
Combined temporal and spatial uncertainty for bins of (a) 
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Combined temporal and spatial uncertainty for bins of (a)
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Combined temporal and spatial uncertainty for bins of (a)
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c. Environmental data
We perform the analysis on the 16-yr time series (1997–2012) of 1° × 1°latitude–longitude resolution observations where complete years of global observations of NDVI from the third generation index NDVI3g (Pinzon and Tucker 2014), near-surface air temperature from the 2-m ERA-Interim (Dee et al. 2011), and precipitation from the Global Precipitation Climatology Project (GPCP) (Adler et al. 2003) are concurrently available. We used the monthly surface temperature estimates from the 2-m ERA-Interim to represent the environmental temperature experienced by vegetation (Dee et al. 2011). We calculated a monthly precipitation dataset by summing daily precipitation from the GPCP 1° × 1°latitude–longitude resolution global dataset (Adler et al. 2003). The GPCP dataset is a combination of satellite and gauge data interpolated across the globe available at 1° × 1° from 1996 to 2012, with data for a complete year starting in 1997. Gridded datasets were interpolated to a common spatial grid with the MATLAB function interp2.m.
To calculate the regression of shortwave radiation and temperature we use shortwave downward surface radiation from the Surface Radiation Budget 3.1 (SRB 3.1) a 1° × 1°latitude–longitude monthly dataset (see Fig. 7) (Zhang et al. 2013). To create a radiatively based potential evapotranspiration (PET) estimate we use surface net downward shortwave radiation from Clouds and the Earth’s Radiant Energy System–Synoptic Radiative Fluxes and Clouds (CERES-SYN) from 2001 to 2012 (Smith et al. 2011) [in appendix, see section b, Eq. (A1), and Fig. A2b). Additional interannual environmental data for temperature, precipitation, and PET from CRU TS3.21 were used to ascertain the robustness of the analysis to choice of environmental data (Jones and Harris 2013). Additional datasets of PET from MODIS and Global Land Data Assimilation System (GLDAS) were compared to ascertain the certainty of the P/PET estimate (Fig. A2a) (Mu et al. 2007; Feng and Fu 2013).
d. Remotely sensed vegetation
We chose NDVI as an observation of vegetation because of its global coverage and the availability of relatively long time series. The NDVI3g time series is an improved global NDVI dataset from the Advanced Very High Resolution Radiometer (AVHRR) (Pinzon and Tucker 2014). The dataset has a ½° latitude–longitude resolution and global coverage of 15-day global maximum composites. Processing the datasets into maximum composites reduces the effects from clouds and the satellite viewing angle (Holben 1986). To create a common time step we created monthly maximum composites from the NDVI 15-day composites before calculating an annual mean time series from 1983 to 2012. We interpolated the data to 1° by 1° spatial resolution prior to analysis and shortened the NDVI time series to 1997–2012 to match the spatial scale and temporal range of the environmental data.
In this study we will interpret NDVI as a proxy for the surface greenness and chloroplast density and use it to calculate the interannual variation of vegetation. NDVI is calculated by normalizing the difference between the visible channel and near-infrared channel from the AVHRR instruments by the sum of the channels. Vegetation absorbs strongly in the visible band, distinguishing it from soils and other nonvegetated surfaces. Though not directly used here, NDVI also relates to leaf area index and fraction of absorbed photosynthetically active radiation (Myneni et al. 2002); thus we consider the signal from NDVI as primarily related to the leaves of vegetation and their potential to fix sunlight into sugars. We assume here that the greening of an ecosystem relative to the climatological mean signals that it is advantageous for the plants to deploy more chloroplasts in an attempt to fix more carbon. On an annual basis, we use an increase in greenness as a metric for a positive sensitivity of vegetation to climate that correlates with increased net primary production (Myneni et al. 1995).
The launch of satellites with instruments that measure additional spectral bands has allowed for the creation of new vegetation indices and remote observations of vegetation. For example, observations from the Moderate Resolution Imaging Spectroradiometer (launched in 1999) are used to generate an improved NDVI product with less interference from water vapor as well as the enhanced vegetation index (EVI), which uses a blue measurement channel to reduce the effects of aerosols (Solano et al. 2010). In general, both NDVI and EVI from MODIS have been shown to have larger seasonal amplitudes than NDVI from AVHRR, and EVI in particular does not saturate over high biomass areas as much as NDVI has been shown to (Huete et al. 2002). There is also the exciting new development of solar-induced fluorescence as a more direct observation of the photosynthetic activity, and thus gross primary productivity (GPP) (Frankenberg et al. 2014). Though NDVI has been shown to relate to GPP, it is not completely proportional and can show markedly different relationships between different vegetation types (Frankenberg et al. 2011; Guanter et al. 2012). Exploration of the measurement of solar-induced fluorescence is just getting under way using observations from Greenhouse Gases Observing Satellite (GOSAT) and Orbiting Carbon Observatory 2 (OCO-2) and do not yet have long enough time series to investigate the interannual ecological–climate interactions.
e. Standardization
f. Removing nonvegetated terrestrial grid points
Our analysis considers only vegetated terrestrial grid points by removing ocean and nonvegetated land grid points (Fig. 1). We removed ocean grid points using the water mask included in the NDVI3g data files. We determined a grid point to have a nonvegetated year when the three months with maximum NDVI values either had a minimum monthly value less than 0.1 or a mean of the three months that was less than 0.3, as adapted from Zhou et al. (2001) (Fig. 1). If a pixel was nonvegetated in any of the 30 years between 1983 and 2012 it was removed from further analysis. This filtering results in the removal of 3726 points of the possible 14 693 land points (25%) and can be visualized in Fig. 2. Defining vegetated points in this way likely removes some points that are vegetated at some point during the time series. For example, removing points with vegetation recovering from bare ground (e.g., afforestation) or where vegetation has been removed to bare ground (e.g., deforestation, fire). Removing nonvegetated grid points with this threshold also removes particularly low 
3. Results and discussion
a. Broad pattern of 
Aggregated 
Sensitivity of vegetation to interannual variation from 1997–2012 in (a) temperature 
Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0829.1
Sensitivity of vegetation to interannual variation from 1997–2012 in (a) temperature
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Sensitivity of vegetation to interannual variation from 1997–2012 in (a) temperature
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We observe inflections between positive and negative 
We hypothesize that the proportional relationship between T and P is operating through the water balance of the vegetation. The evidence for the relation of the proportionality of T and P to water balance comes from three arguments: dependence of atmospheric water demand being a function of temperature, the presence of the proportionality across multiple datasets (see appendix), and the presence of the mechanism in previous work on plant hydraulics (McDowell 2011; Grier and Running 1977). As temperature increases, the temperature-driven increase in atmospheric demand for water increases PET, causing hydrologic stress. Hydrologic stress can then be offset for plants if more water is supplied through precipitation. Other aspects of the environment that we do not account for have the potential to exacerbate the annual imbalance (seasonality of water demand and supply leading to runoff) and soil water storage (helping balance offset of supply and demand) and matric water potential of soils (resisting vegetation in meeting the atmospheric demand) (Borchert 1994). With these additional mechanisms in consideration it is notable that though the proportional relationship between T and P spans a large range of climates, it is only observed as a proportional in a relatively narrow transition zone. A similarly sloped line between the max correlation of temperature and precipitation with gross primary productivity derived from flux towers is evident (but not discussed) in a paper from Jung et al. (2011, their Figs. 8c,f). Physiological experiments also provide evidence of temperature influencing plants through atmospheric water demand. When the direct effects of temperature increases on vegetation are isolated from the temperature-driven increase in vapor pressure deficit, the vapor pressure effects are large relative to the direct temperature effects at warmer temperatures (Day 2000). From this we expect increases in atmospheric water demand, in the form of vapor pressure deficit, to be the dominant constraint on vegetation in places with relatively warm temperatures (above 16°C).
These observations of proportionality between temperature and precipitation also qualitatively agree with arguments that aridity (precipitation divided by potential evapotranspiration P/PET) is a critical climate variable in shaping ecosystems (e.g., Budyko 1961; Lugo et al. 1999). However, though contours of P/PET plotted across mean annual temperature and precipitation share the sign of the inflection contours, they have a slope (
Comparison of the sign of 
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Comparison of the sign of
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Comparison of the sign of
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In the following sections we further discuss hypotheses for the mechanisms governing the climate–vegetation interactions consistent with the observed pattern of 
b. Growing season limited: Temperature and snow cover
Vegetation is greener during both warmer and drier years in the coldest, driest vegetated areas of the globe, as well as places with annual mean temperatures up to relatively warm values of 15°C where precipitation is also high (1500 mm yr−1) (Fig. 5a). Places with these climates are primarily spatially located at high latitudes and experience a large seasonality in temperature and sunlight. These climate conditions lead to a growing season duration constrained by low temperatures and late snow cover melt (Takala et al. 2011) (Figs. 4c,d and 5b). We hypothesize that the main driver of variability on annual greenness is the duration of the growing season. Thus, we expect to see this mechanism acting mainly in the months at either end of the growing season rather than during months of peak greenness. In addition, these months are favored by atmospheric patterns of blocking and ENSO variation that might suggest that the climate in these months is also critical to setting the length of the growing season (Lejenäs and Økland 1983). Indeed, the months with the most variance in NDVI in cold (
The variance for each month in NDVI divided by the annual sum of monthly variance, shown across a range of annual mean temperatures in the Northern Hemisphere. Months with higher percent variance (dark green colors) contribute more strongly to the annual mean variance. Contours show mean monthly NDVI values.
Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0829.1
The variance for each month in NDVI divided by the annual sum of monthly variance, shown across a range of annual mean temperatures in the Northern Hemisphere. Months with higher percent variance (dark green colors) contribute more strongly to the annual mean variance. Contours show mean monthly NDVI values.
Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0829.1
The variance for each month in NDVI divided by the annual sum of monthly variance, shown across a range of annual mean temperatures in the Northern Hemisphere. Months with higher percent variance (dark green colors) contribute more strongly to the annual mean variance. Contours show mean monthly NDVI values.
Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0829.1
We hypothesize that the mechanism limiting vegetation greenness in these areas characterized by cold temperatures with both positive 
c. Water limited: Hot and dry
Nearly all of the negative values of 
Locations falling in the hot dry region are primarily clustered along the edges of nonvegetated deserts of the North American Southwest, the Sahel, South Africa, and Australia as well as northeast Brazil and the rain shadow of the Chilean coastal range (Figs. 4c and 5d). Nonvegetated points in deserts have been explicitly eliminated from this analysis, but plants living in these places are presumably limited by water availability as well. Because of the extensive spatial extent of the hot dry region and deserts we hypothesize that low precipitation is the most common limitation on global vegetation. In climate regions with 0.2 to 0.5 P/PET, 
d. Energy limited: Interaction of clouds and sunlight
Areas with positive 
One pathway that could explain generally increased greenness in warm years for these locations is for light limitation on photosynthesis to be relieved by additional insolation. Along a gradient of increasing P/PET, 
Variation of 
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Variation of
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Variation of
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We also note that interannual increases in temperature are concomitant with greater increases in insolation in wetter climate regions (sunnier, less clouds when warmer) (Fig. 7). We observe approximately a factor-of-2 change in the concomitant change of insolation with temperature (W m−2 °C−1) between P/PET values of 0.2 and 0.8 (Fig. 7). Increased water availability changes the relationship of sunlight and temperature, diverting more of the surface energy flux through latent heat rather than sensible heat. Thus, the same increase in photosynthetically active radiation does not lead to the same increase in air temperature as in drier regions. With a positive 
The response of ecosystem function in hot, wet regions to a changing climate may have strong implications for the terrestrial carbon cycle feedback on climate change. These hot, wet climate regions tend to have very large pools of aboveground carbon storage (Simard et al. 2011; Saatchi et al. 2011) and encompass the tropical rain forests in South America, Africa, and Indonesia, as well as southeast China (Figs. 4c,d and 5b). Our results suggest that concomitant increases in shortwave radiation act as a mediator on the effect of warming on greening in these hot, wet regions. We hypothesize that these ecosystems would have a different sensitivity to warming if it occurred without increases in solar radiation (i.e., from greenhouse gasses). Ecosystems would also likely have different sensitivity to a multiyear decline in rainfall such as from an extended drought as opposed to interannual variability. These long-term changes would instead drive the whole ecosystem down the precipitation gradient out of the hot, wet region toward positive 
e. Climate change implications
Observations of β derived from greenness suggest that ecosystem functioning depends on multiple physical aspects of climate, as well as the coordinated changes among them. Predicting the future changes of some of aspects of climate is much more difficult (i.e., rainfall), which helps explain the uncertainty in current predictions of the carbon cycle (Friedlingstein et al. 2006). In addition, climate change may not maintain the same concomitant changes that we can observe in interannual climate variations (e.g., temperature’s damped response to sunlight in wetter climates). Predictions based on any one variable alone (e.g., temperature) will not do as well where these concomitant changes are strong drivers, with ramifications for predictions ranging from global climate sensitivity to food supply (Friedlingstein et al. 2006; Battisti and Naylor 2009). In particular, temperature is likely to increase as a result of greenhouse gasses without an associated change in shortwave radiation. The strong implied effects of covariation of temperature with shortwave radiation should motivate future research to investigate the interconnections between climate variables under climate change and take into account their location in climate space.
To aid in predictions of new climate regimes our empirical characterization of present-day relationships between ecosystem functioning and climate can also serve as an observationally based constraints to improve process-based models (Luo et al. 2012). Comparing our linear metrics of the sensitivity of vegetation to climate with model output probes the veracity of ecosystem–climate interactions directly rather than the final results of these interactions (e.g., sensitivity of vegetation to temperature, rather than solely the temperature or greenness of a particular region). This added constraint complements and could possibly enhance other efforts to improve the representation of processes within global vegetation models. These observational constraints will improve simulations not only under current conditions but also under novel conditions by improving the functional fidelity of the global vegetation model. Improved models can then make better predictions despite the differences between present-day observed variability and anthropogenic-driven global warming of the next century.
Acknowledgments
We would like to acknowledge Leander Love-Anderegg, Robin Ross, Langdon Quetin, Marysa Lague, Elizabeth Garcia, and Marlies Kovenock for providing comments on the paper. The work was partially conducted while GRQ was supported by the University of Washington Program on Climate Change Fellowship. We would also like to acknowledge the Keck Institute for Space Studies at the California Institute of Technology who hosted GRQ during part of this work. We acknowledge National Science Foundation Grants AGS-1321745 and AGS-1553715.
All the original data used in our analysis are listed in the references.
APPENDIX
Uncertainty Analysis in Linear Regression, Binning, and Datasets
To establish the uncertainty and robustness of the analysis of ecological climate interaction across climate space we performed four experiments: a Monte Carlo bootstrap uncertainty estimate (section a), an experiment using the shorter time series available from MODIS NDVI (section b), an experiment with the CRU TS3.21 dataset representing statistically upscaled station observations of the environment (section c), and an experiment omitting grid points with strong interannual correlation between precipitation and temperature (section d) (Figs. 3 and A1). Results generally show low uncertainty in the sign of β outside of the transition area and the hot, wet region, and they are qualitatively consistent using MODIS NDVI and CRU TS3.21 in place of NDVI3g and the combination of ERA-Interim and GPCP, as well as when points of high correlation are omitted. Methodology and specific differences are discussed below.
Binned sensitivity of vegetation to annually averaged (row 1),(a), (b),(c) temperature 
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Binned sensitivity of vegetation to annually averaged (row 1),(a), (b),(c) temperature
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Binned sensitivity of vegetation to annually averaged (row 1),(a), (b),(c) temperature
Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0829.1
a. Estimating uncertainty of β in time and climate space
To estimate the uncertainty in the regression coefficient values β, we used a bootstrap Monte Carlo technique, similar to method 2 discussed in Efron (1979), in combination with the regression at each grid point (Fig. 1). We performed 10 000 regressions by randomly drawing 8-yr time series from the total 16-yr dataset. The mean of these 10 000 β values is reported as the sensitivity of vegetation (Fig. 4). The resulting distributions of sensitivity are combined with the uncertainties from the bins to determine 95% bounds on the uncertainty (Fig. 3).
To aggregate patterns of the β across climate space, each geospatial point was assigned a bin dictated by its climatological mean annual temperature and precipitation. There are 178 bins, each 1.8°C by 186.5 mm yr−1; bins with fewer than 10 points were ignored (Figs. 2 and 1a,b). We include all 10 000 vegetation sensitivities calculated as part of the temporal Monte Carlo for all spatial points falling in a given bin. We do a further Monte Carlo sampling of this set by selecting randomly from the 10 000-point temporal distribution of β for half of the spatial points in each bin. From this selection we calculate an area-weighted mean for that bin 10 000 times resulting in a distribution of bin-mean β. The area-weighted mean of the distribution of β within a bin is then reported as the β for that bin, and the range is used to determine the 95% bounds as the error bars (Fig. 3).
The uncertainty analysis includes the contributions of both the uncertainty in the regression (i.e., the consistency of the ecological climate interaction across time) and the uncertainty in each bin (i.e., the consistency in the ecological–climate interaction in any particular climate bin). The uncertainty in sign for 
b. Analysis with MODIS NDVI
As noted above there are multiple other remotely sensed vegetation indices, as well as multiple corrections to the NDVI vegetation index (Hilker et al. 2014; Solano et al. 2010; Holben 1986). To test the robustness of the observed patterns to our choice in NDVI product, we compared the newer MODIS NDVI observations that are available from 2003 to 2015 with the overlapping portion (2003–11) of NDVI3g with complete years. Qualitatively these analyses are very similar to those of the original analysis using NDVI3g from 1997 to 2012 (Fig. A1, right two columns). Hot, dry climates have negative 
c. Analysis with other environmental data
To ascertain the robustness of the analysis to choice of environmental datasets we used alternate environmental data from CRU TS3.21. We performed the regressions over the same time period 1997–2012 with CRU TS3.21 temperature and precipitation and NDVI3g vegetation index (Figs. A1a,d,g). CRU TS3.21 was chosen because it uses a different method to derive global gridded datasets of temperature and precipitation. Rather than a reanalysis product (such as ERA-Interim) or a combination of gauge and remote sensing observations (such as GPCP), CRU TS3.21 is a statistically upscaled gridded product based on station data. Station coverage is relatively dense over North America and Europe and particularly sparse over tropical South America and Africa. Our results using CRU TS3.21 show that the analysis using a different environmental dataset is qualitatively similar and continues to support our results and discussion (cf. Figs. 4a,b and 5a with Figs. A1a,d,g).
d. Temperature and precipitation correlation
The predictor variables of interannual temperature and precipitation used in the linear regression are often collinear in nature. Where there is particularly strong correlation, there is the possibility that a multilinear regression will not do a good job of separating the variation explained by each predictor variable. To address this concern we ran a test by omitting points from our analysis that have higher correlation coefficients (
Our omission of pixels with correlations above 0.6 (36% shared variance) is conservative per the statistical literature where it is suggested that correlation coefficients of up to 0.77 (60% shared variance) can be linearly separated and even some suggestion that values as high as a correlation coefficient of 0.89 (80% shared variance) are acceptable (O’Brien 2007). Only a small portion of the global area analyzed exceeds a correlation coefficient between precipitation and temperature of 0.6.
e. Variability across aridity datasets
(a) Contours of binned long-term means of multiple datasets of potential evapotranspiration. Binned values are contoured at values as in the Holdridge life zones chart and displayed in temperature and precipitation climate space. (b) map of mean PET from 2001 to 2012 created from CERES-SYN net shortwave downward surface radiation. Colors are in mm yr−1 of potential evapotranspiration.
Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0829.1
(a) Contours of binned long-term means of multiple datasets of potential evapotranspiration. Binned values are contoured at values as in the Holdridge life zones chart and displayed in temperature and precipitation climate space. (b) map of mean PET from 2001 to 2012 created from CERES-SYN net shortwave downward surface radiation. Colors are in mm yr−1 of potential evapotranspiration.
Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0829.1
(a) Contours of binned long-term means of multiple datasets of potential evapotranspiration. Binned values are contoured at values as in the Holdridge life zones chart and displayed in temperature and precipitation climate space. (b) map of mean PET from 2001 to 2012 created from CERES-SYN net shortwave downward surface radiation. Colors are in mm yr−1 of potential evapotranspiration.
Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0829.1
REFERENCES
Adler, R. F., and Coauthors, 2003: The Version-2 Global Precipitation Climatology Project (GPCP) monthly precipitation analysis (1979–present). J. Hydrometeor., 4, 1147–1167, doi:10.1175/1525-7541(2003)004<1147:TVGPCP>2.0.CO;2.
Asner, G. P., A. R. Townsend, and B. H. Braswell, 2000: Satellite observation of El Niño effects on Amazon forest phenology and productivity. Geophys. Res. Lett., 27, 981–984, doi:10.1029/1999GL011113.
Baldocchi, D., 2014: Measuring fluxes of trace gases and energy between ecosystems and the atmosphere—The state and future of the eddy covariance method. Global Change Biol., 20, 3600–3609, doi:10.1111/gcb.12649.
Battisti, D. S., and R. L. Naylor, 2009: Historical warnings of future food insecurity with unprecedented seasonal heat. Science, 323, 240–244, doi:10.1126/science.1164363.
Beer, C., and Coauthors, 2010: Terrestrial gross carbon dioxide uptake: Global distribution and covariation with climate. Science, 329, 834–838, doi:10.1126/science.1184984.
Berry, J., and O. Bjorkman, 1980: Photosynthetic response and adaptation to temperature in higher plants. Annu. Rev. Plant Physiol., 31, 491–543, doi:10.1146/annurev.pp.31.060180.002423.
Boisvenue, C., and S. W. Running, 2006: Impacts of climate change on natural forest productivity evidence since the middle of the 20th century. Global Change Biol., 12, 862–882, doi:10.1111/j.1365-2486.2006.01134.x.
Borchert, R., 1994: Soil and stem water storage determine phenology and distribution of tropical dry forest trees. Ecology, 75, 1437–1449, doi:10.2307/1937467.
Budyko, M. I., 1961: The heat balance of the Earth’s surface. Sov. Geogr., 2, 3–13, doi:10.1080/00385417.1961.10770761.
Chen, B., and Coauthors, 2014: Changes in vegetation photosynthetic activity trends across the Asia–Pacific region over the last three decades. Remote Sens. Environ., 144, 28–41, doi:10.1016/j.rse.2013.12.018.
Churkina, G., and S. W. Running, 1998: Contrasting climatic controls on the estimated productivity of global terrestrial biomes. Ecosystems, 1, 206–215, doi:10.1007/s100219900016.
Day, M. E., 2000: Influence of temperature and leaf-to-air vapor pressure deficit on net photosynthesis and stomatal conductance in red spruce (Picea rubens). Tree Physiol., 20, 57–63, doi:10.1093/treephys/20.1.57.
Dee, D. P., and Coauthors, 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553–597, doi:10.1002/qj.828.
Efron, B., 1979: Bootstrap methods: Another look at the jackknife. Ann. Stat., 7, 1–26, doi:10.1214/aos/1176344552.
Feng, S., and Q. Fu, 2013: Expansion of global drylands under a warming climate. Atmos. Chem. Phys., 13, 10 081–10 094, doi:10.5194/acp-13-10081-2013.
Frankenberg, C., and Coauthors, 2011: New global observations of the terrestrial carbon cycle from GOSAT: Patterns of plant fluorescence with gross primary productivity. Geophys. Res. Lett., 38, doi:10.1029/2011GL048738.
Frankenberg, C., J. Berry, L. Guanter, and J. Joiner, 2013: Remote sensing of terrestrial chlorophyll fluorescence from space. SPIE Newsroom, doi:10.1117/2.1201302.004725.
Frankenberg, C., C. O’Dell, J. Berry, L. Guanter, J. Joiner, P. Khler, R. Pollock, and T. E. Taylor, 2014: Prospects for chlorophyll fluorescence remote sensing from the Orbiting Carbon Observatory-2. Remote Sens. Environ., 147, 1–12, doi:10.1016/j.rse.2014.02.007.
Friedlingstein, P., and Coauthors, 2006: Climate–carbon cycle feedback analysis: Results from the C4MIP model intercomparison. J. Climate, 19, 3337–3353, doi:10.1175/JCLI3800.1.
Ghimire, B., C. A. Williams, J. Masek, F. Gao, Z. Wang, C. Schaaf, and T. He, 2014: Global albedo change and radiative cooling from anthropogenic land-cover change, 1700 to 2005 based on MODIS, land-use harmonization, radiative kernels, and reanalysis. Geophys. Res. Lett., 41, 9087–9096, doi:10.1002/2014GL061671.
Glenn, P. E., R. A. Huete, L. P. Nagler, and G. S. Nelson, 2008: Relationship between remotely-sensed vegetation indices, canopy attributes and plant physiological processes: What vegetation indices can and cannot tell us about the landscape. Sensors, 8, 2136–2160, doi:10.3390/s8042136.
Goward, S. N., B. Markham, D. G. Dye, W. Dulaney, and J. Yang, 1991: Normalized difference vegetation index measurements from the advanced very high resolution radiometer. Remote Sens. Environ., 35, 257–277, doi:10.1016/0034-4257(91)90017-Z.
Grier, C. G., and S. W. Running, 1977: Leaf area of mature northwestern coniferous forests: Relation to site water balance. Ecology, 58, 893–899, doi:10.2307/1936225.
Guanter, L., C. Frankenberg, A. Dudhia, P. E. Lewis, J. Gómez-Dans, A. Kuze, H. Suto, and R. G. Grainger, 2012: Retrieval and global assessment of terrestrial chlorophyll fluorescence from GOSAT space measurements. Remote Sens. Environ., 121, 236–251, doi:10.1016/j.rse.2012.02.006.
Hilker, T., and Coauthors, 2014: Vegetation dynamics and rainfall sensitivity of the Amazon. Proc. Natl. Acad. Sci. USA, 111, 16 041–16 046, doi:10.1073/pnas.1404870111.
Holben, B. N., 1986: Characteristics of maximum-value composite images from temporal AVHRR data. Int. J. Remote Sens., 7, 1417–1434, doi:10.1080/01431168608948945.
Huete, A., K. Didan, T. Miura, E. Rodriguez, X. Gao, and L. Ferreira, 2002: Overview of the radiometric and biophysical performance of the MODIS vegetation indices. Remote Sens. Environ., 83, 195–213, doi:10.1016/S0034-4257(02)00096-2.
Jasechko, S., Z. D. Sharp, J. J. Gibson, S. J. Birks, Y. Yi, and P. J. Fawcett, 2013: Terrestrial water fluxes dominated by transpiration. Nature, 496, 347–350, doi:10.1038/nature11983.
Jolly, W. M., R. Nemani, and S. W. Running, 2005: A generalized, bioclimatic index to predict foliar phenology in response to climate. Global Change Biol., 11, 619–632, doi:10.1111/j.1365-2486.2005.00930.x.
Jones, P., and I. Harris, 2013: CRU TS3.21: Climatic Research Unit (CRU) Time Series (TS) version 3.21 of high resolution gridded data of month-by-month variation in climate (Jan. 1901–Dec. 2012). NCAS British Atmospheric Data Centre, accessed 15 July 2016, doi:10.5285/D0E1585D-3417-485F-87AE-4FCECF10A992.
Jung, M., and Coauthors, 2011: Global patterns of land-atmosphere fluxes of carbon dioxide, latent heat, and sensible heat derived from eddy covariance, satellite, and meteorological observations. J. Geophys. Res., 116, G00J07, doi:10.1029/2010JG001566.
Kottek, M., J. Grieser, C. Beck, B. Rudolf, and F. Rubel, 2006: World map of the Koppen-Geiger climate classification updated. Meteor. Z., 15, 259–264, doi:10.1127/0941-2948/2006/0130.
Koven, C. D., 2013: Boreal carbon loss due to poleward shift in low-carbon ecosystems. Nat. Geosci., 6, 452–456, doi:10.1038/ngeo1801.
Lejenäs, H., and H. Økland, 1983: Characteristics of northern hemisphere blocking as determined from a long time series of observational data. Tellus, 35A, 350–362, doi:10.3402/tellusa.v35i5.11446.
Levis, S., 2010: Modeling vegetation and land use in models of the Earth system. Wiley Interdiscip. Rev.: Climate Change, 1, 840–856, doi:10.1002/wcc.83.
Lugo, A. E., S. L. Brown, R. Dodson, T. S. Smith, and H. H. Shugart, 1999: The Holdridge life zones of the conterminous United States in relation to ecosystem mapping. J. Biogeogr., 26, 1025–1038, doi:10.1046/j.1365-2699.1999.00329.x.
Luo, Y. Q., and Coauthors, 2012: A framework for benchmarking land models. Biogeosciences, 9, 3857–3874, doi:10.5194/bg-9-3857-2012.
McDowell, N. G., 2011: Mechanisms linking drought, hydraulics, carbon metabolism, and vegetation mortality. Plant Physiol., 155, 1051–1059, doi:10.1104/pp.110.170704.
Metzger, M. J., R. G. H. Bunce, R. H. G. Jongman, R. Sayre, A. Trabucco, and R. Zomer, 2013: A high-resolution bioclimate map of the world: A unifying framework for global biodiversity research and monitoring. Global Ecol. Biogeogr., 22, 630–638, doi:10.1111/geb.12022.
Mu, Q., F. A. Heinsch, M. Zhao, and S. W. Running, 2007: Development of a global evapotranspiration algorithm based on MODIS and global meteorology data. Remote Sens. Environ., 111, 519–536, doi:10.1016/j.rse.2007.04.015.
Myneni, R., F. Hall, P. Sellers, and A. Marshak, 1995: The interpretation of spectral vegetation indexes. IEEE Trans. Geosci. Remote Sens., 33, 481–486.
Myneni, R., and Coauthors, 2002: Global products of vegetation leaf area and fraction absorbed PAR from year one of MODIS data. Remote Sens. Environ., 83, 214–231.
Nemani, R. R., C. D. Keeling, H. Hashimoto, W. M. Jolly, S. C. Piper, C. J. Tucker, R. B. Myneni, and S. W. Running, 2003: Climate-driven increases in global terrestrial net primary production from 1982 to 1999. Science, 300, 1560–1563, doi:10.1126/science.1082750.
O’Brien, R. M., 2007: A caution regarding rules of thumb for variance inflation factors. Qual. Quant., 41, 673–690, doi:10.1007/s11135-006-9018-6.
Oleson, K. W., and Coauthors, 2010: Technical description of version 4.0 of the Community Land Model (CLM). NCAR Tech. Note NCAR/TN-478+STR, 266 pp. [Available online at http://www.cesm.ucar.edu/models/ccsm4.0/clm/CLM4_Tech_Note.pdf.]
Peel, M. C., B. L. Finlayson, and T. A. McMahon, 2007: Updated world map of the Köppen-Geiger climate classification. Hydrol. Earth Syst. Sci., 11, 1633–1644, doi:10.5194/hessd-4-439-2007.
Pinzon, J. E., and C. J. Tucker, 2014: A non-stationary 1981–2012 AVHRR NDVI3g time series. Remote Sens., 6, 6929–6960, doi:10.3390/rs6086929.
Richardson, A. D., and Coauthors, 2010: Influence of spring and autumn phenological transitions on forest ecosystem productivity. Philos. Trans. Roy. Soc. London, 365B, 3227–3246, doi:10.1098/rstb.2010.0102.
Richardson, A. D., T. F. Keenan, M. Migliavacca, Y. Ryu, O. Sonnentag, and M. Toomey, 2013: Climate change, phenology, and phenological control of vegetation feedbacks to the climate system. Agric. For. Meteor., 169, 156–173, doi:10.1016/j.agrformet.2012.09.012.
Rubel, F., and M. Kottek, 2010: Observed and projected climate shifts 1901–2100 depicted by world maps of the Köppen-Geiger climate classification. Meteor. Z., 19, 135–141, doi:10.1127/0941-2948/2010/0430.
Running, S. W., R. R. Nemani, F. A. Heinsch, M. Zhao, M. Reeves, and H. Hashimoto, 2004: A continuous satellite-derived measure of global terrestrial primary production. BioScience, 54, 547–560, doi:10.1641/0006-3568(2004)054[0547:ACSMOG]2.0.CO;2.
Saatchi, S. S., and Coauthors, 2011: Benchmark map of forest carbon stocks in tropical regions across three continents. Proc. Natl. Acad. Sci. USA, 108, 9899–9904, doi:10.1073/pnas.1019576108.
Schlesinger, W. H., and S. Jasechko, 2014: Transpiration in the global water cycle. Agric. For. Meteor., 189–190, 115–117, doi:10.1016/j.agrformet.2014.01.011.
Seddon, A. W. R., M. Macias-Fauria, P. R. Long, D. Benz, and K. J. Willis, 2016: Sensitivity of global terrestrial ecosystems to climate variability. Nature, 531, 229–232, doi:10.1038/nature16986.
Simard, M., N. Pinto, J. B. Fisher, and A. Baccini, 2011: Mapping forest canopy height globally with spaceborne lidar. J. Geophys. Res., 116, G04021, doi:10.1029/2011JG001708.
Smith, G., A. C. Wilber, S. K. Gupta, and P. W. Stackhouse, 2002: Surface radiation budget and climate classification. J. Climate, 15, 1175–1188, doi:10.1175/1520-0442(2002)015<1175:SRBACC>2.0.CO;2.
Smith, G., K. Priestley, N. Loeb, B. Wielicki, T. Charlock, P. Minnis, D. Doelling, and D. Rutan, 2011: Clouds and Earth Radiant Energy System (CERES), a review: Past, present and future. Adv. Space Res., 48, 254–263, doi:10.1016/j.asr.2011.03.009.
Solano, R., K. Didan, A. Jacobson, and A. Huete, 2010: MODIS vegetation indices (MOD13) C5 user’s guide. The University of Arizona Terrestrial Biophysics and Remote Sensing Laboratory Rep., 42 pp. [Available online at https://www.ctahr.hawaii.edu/grem/modis-ug.pdf.]
Sprugel, D. G., M. G. Ryan, J. Brooks, K. Vogt, and T. A. Martin, 1995: Respiration from the organ level to the stand. Resource Physiology of Conifers, W. Smith and T. Hinckley, Eds., Academic Press, 255–299.
Takala, M., K. Luojus, J. Pulliainen, C. Derksen, J. Lemmetyinen, J.-P. Kärnä, J. Koskinen, and B. Bojkov, 2011: Estimating Northern Hemisphere snow water equivalent for climate research through assimilation of space-borne radiometer data and ground-based measurements. Remote Sens. Environ., 115, 3517–3529, doi:10.1016/j.rse.2011.08.014.
Whittaker, R. H., 1962: Classification of natural communities. Bot. Rev., 28, 1–239, doi:10.1007/BF02860872.
Whittaker, R. H., 1970: Communities and Ecosystems. Macmillan, 162 pp.
Wu, D., X. Zhao, S. Liang, T. Zhou, K. Huang, B. Tang, and W. Zhao, 2015: Time-lag effects of global vegetation responses to climate change. Global Change Biol., 21, 3520–3531, doi:10.1111/gcb.12945.
Xiao, J., and Coauthors, 2011: Assessing net ecosystem carbon exchange of U.S. terrestrial ecosystems by integrating eddy covariance flux measurements and satellite observations. Agric. For. Meteor., 151, 60–69, doi:10.1016/j.agrformet.2010.09.002.
Xu, G., and Coauthors, 2014: Changes in vegetation growth dynamics and relations with climate over China’s landmass from 1982 to 2011. Remote Sens., 6, 3263–3283, doi:10.3390/rs6043263.
Zhang, T., P. W. Stackhouse, S. K. Gupta, S. J. Cox, J. C. Mikovitz, and L. M. Hinkelman, 2013: The validation of the GEWEX SRB surface shortwave flux data products using BSRN measurements: A systematic quality control, production and application approach. J. Quant. Spectrosc. Radiat. Transfer, 122, 127–140, doi:10.1016/j.jqsrt.2012.10.004.
Zhou, L., C. J. Tucker, R. K. Kaufmann, D. Slayback, N. V. Shabanov, and R. B. Myneni, 2001: Variations in northern vegetation activity inferred from satellite data of vegetation index during 1981 to 1999. J. Geophys. Res., 106, 20 069–20 083, doi:10.1029/2000JD000115.
Zhou, L., R. K. Kaufmann, Y. Tian, R. B. Myneni, and C. J. Tucker, 2003: Relation between interannual variations in satellite measures of northern forest greenness and climate between 1982 and 1999. J. Geophys. Res., 108, 4004, doi:10.1029/2002JD002510.
