Global patterns, trends, and drivers of water use efficiency from 2000 to 2013

Water use efficiency (WUE; gross primary production [GPP]/evapotranspiration [ET]) estimates the tradeoff between carbon gain and water loss during photosynthesis and is an important link of the carbon and water cycles. Understanding the spatiotemporal patterns and drivers of WUE is helpful for projecting the responses of ecosystems to climate change. Here we examine the spatiotemporal patterns, trends, and drivers of WUE at the global scale from 2000 to 2013 using the gridded GPP and ET data derived from the Moderate Resolution Imaging Spectroradiometer (MODIS). Our results show that the global WUE has an average value of 1.70 g C/kg H2O with large spatial variability during the 14-year period. WUE exhibits large variability with latitude. WUE also varies much with elevation: it first remains relatively constant as the elevation varies from 0 to 1000 m and then decreases dramatically. WUE generally increases as precipitation and specific humidity increase; whereas it decreases after reaching maxima as temperature and solar radiation increases. In most land areas, the temporal trend of WUE is positively correlated with precipitation and specific humidity over the 14-year period; while it has a negative relationship with temperature and solar radiation related to global warming and dimming. On average, WUE shows an increasing trend of 0.0025 g C kg 1 H2O yr 1 globally. Our global-scale assessment of WUE has implications for improving our understanding of the linkages between the water and carbon cycles and for better projecting the responses of ecosystems to climate change.


INTRODUCTION
Water use efficiency (WUE) is the carbon uptake per unit water consumed by vegetation (g C/kg H 2 O). It is an integrated physiological indicator and measures the tradeoff between carbon gain and water loss during photosynthesis (Farquhar et al. 1989, Cowan 2002. WUE is an important link of the carbon and water cycles, and improved understanding of its patterns and drivers is essential for the prediction of ecosystem responses to future climate change. For example, as a useful tool for water and carbon cycle simulation and prediction, WUE is used as an parameter in land surface or ecosystem models for the calculation of carbon assimilation in cases where evapotranspiration (ET) is known (Morén et al. 2001, Van Wijk and Bouten 2002, Tang et al. 2006, Wang et al. 2014).
Theoretically, WUE should be the ratio of plant productivity to transpiration rather than to ET (the sum of evaporation from ground and canopy intercepted water and canopy transpiration). However, it remains a challenge to partition ET observations to plant transpiration and evaporation from soils and canopies (Baldocchi 2003(Baldocchi , 2008. Therefore, the ratio of GPP to ET has been widely used to measure WUE , Xiao et al. 2013. Thus, WUE is typically calculated as the ratio of gross primary production (GPP) to ET, i.e., WUE ¼ GPP/ET (e.g., Reichstein et al. 2007, Lu and Zhuang 2010, Mu et al. 2011a, Brü mmer et al. 2012). An alternative definition of WUE is the ratio of net primary productivity (NPP) to ET (e.g., Dan andJi 2007, Tian et al. 2011). The eddy covariance (EC) technique provides continuous measurements of net ecosystem exchange (NEE) and latent heat flux (or ET). NEE is routinely partitioned into GPP and ecosystem respiration. Therefore WUE, the ratio of GPP to ET, can be directly calculated from EC GPP and ET data.
Although a number of studies have assessed the patterns of WUE and its responses to climate (Niu et al. 2011, Linderson et al. 2012, Xiao et al. 2013, broad-scale research on WUE is limited mainly because of the lack of data (i.e., GPP and ET) at regional to global scales (Law et al. 2002, Reichstein et al. 2007, Beer et al. 2009, Keenan et al. 2013. Several studies examined the spatial patterns and controlling factors of WUE at regional or national scales using GPP and ET derived from EC flux towers (e.g., Beer et al. 2009, Keenan et al. 2013, Xiao et al. 2013 or process-based ecosystem models (e.g., Tian et al. 2010). Relatively few studies have assessed the magnitude, patterns, and trends of WUE at the global scale (Ito and Inatomi 2012).
Numerous studies have been conducted to investigate the influences of meteorological and morphological variables on WUE. Previous studies have examined the controlling effects of precipitation, temperature, solar radiation, and specific humidity (or vapor pressure deficit; Scanlon and Albertson 2004, Hu et al. 2008, Yang et al. 2010, Mu et al. 2011a. Several studies also examined the morphological effects of leaf area index (LAI) on WUE (Beer et al. 2009, Keenan et al. 2013).
However, the relative effects of these factors on WUE are not well understood. For example, Yu et al. (2008) found that WUE decreased with increasing precipitation for three forest sites in eastern China, whereas the opposite phenomenon was observed by Niu et al. (2011). A synthesis study by Keenan et al. (2013) showed that the meteorological variables had little effect on the increase in WUE at forest sites, and the main factor was increasing atmospheric CO 2 concentrations. The differences in these findings can be partly attributed to the different spatiotemporal scales, biomes, and locations of these studies.
Here we used a global GPP and ET dataset derived from MODIS over the period from 2000 to 2013 to assess the spatial patterns, trends, and drivers of WUE at the global scale. Specifically, we first examined the magnitude and spatial patterns of WUE. We then assessed the effects of morphological (LAI) and meteorological (precipitation, temperature, solar radiation, and specific humidity) drivers on WUE. We also assessed the interannual variability and trends of WUE over the 14-year period.

GPP and ET data
We used the global GPP (Running et al. 2004, Zhao et al. 2005 and ET (Mu et al. 2007(Mu et al. , 2011b datasets derived from MODIS. The global GPP and ET datasets are both freely available on the Numerical Terradynamic Simulation Group website (http://www.ntsg.umt.edu). The MODIS GPP data (MOD17) are calculated as a multi-product function (Heinsch et al. 2003) where e max is the maximum light use efficiency; SWrad is the short-wave downward solar radiation, of which 45% is photosynthetically active radiation (PAR); FPAR is the fraction of PAR absorbed by plants, which can be derived from MODIS products (MOD15A2, see below); fVPD and fT min are the reduction scalars from water stresses (high daily vapor pressure deficit, VPD) and low temperature (low daily minimum temperature T min ), respectively. The MOD17 GPP data were calculated globally at a 1-km resolution at 8-day, monthly (MOD17A2), and v www.esajournals.org annual (MOD17A3) intervals. A detailed description of the calculation of the MOD17 GPP can be found in Heinsch et al. (2003).
The MODIS ET product (MOD16) was produced by Mu et al. (2007Mu et al. ( , 2011b) based on the Penman-Monteith equation (Monteith 1964). At the global scale, MODIS land cover (MOD12Q1; Friedl et al. 2010), MODIS Collection 5 FPAR/LAI (MOD15A2; Myneni et al. 1997) and Collection 4 0.05-degree CMG MODIS albedo (Jin et al. 2003, Salomon et al. 2006 are used as the model inputs. The MODIS ET product is available globally at a resolution of 1 km. The improved version of annual MODIS ET products (MOD16A3) was used in this study and was downloaded from the Numerical Terradynamic Simulation Group website (ftp://ftp.ntsg.umt. edu/). The improved ET product is driven by a consistent version of meteorological variables from the GMAO (Global Modeling and Assimilation Office), and the ET was estimated with reasonable accuracy (Mu et al. 2011b).

In situ WUE database
We obtained in situ WUE values from the literature in order to evaluate the accuracy of the global WUE calculated from MODIS GPP and ET. Only sites with at least two years of data were selected because sites with one year of data generally did not cover the whole year. We obtained a total of 141 site years of WUE data from 34 flux tower stations (Appendix : Table A1). These sites encompass a range of ecosystems and climate types.
We obtained elevation data from the NASA  (Kanamitsu et al. 2002;http://www.esrl.noaa.gov/). The meteorological variables are available four times daily, and can be aggregated to daily, monthly, and annual time scales. These variables are in a Gaussian grid (T62, 192 3 94) projection and have a spatial resolution of 1.8888 3 1.8888 after spline interpolation. We resampled the NCEP data to 1-km resolution to match the spatial resolution of the GPP and ET data.

Data analysis
We used the MODIS GPP and ET to calculate WUE. For each 1-km grid cell, we calculated annual WUE from annual GPP and ET for each year over the period from 2000 to 2013; annual WUE values were then averaged over the 14 years to calculate mean annual WUE. Values above 1000 g C/kg H 2 O were treated as abnormal and neglected throughout our research. We used the in situ WUE database to evaluate the accuracy of the global WUE dataset. It should be noted that there is scale mismatch for the comparison of in-situ and MODIS WUE values.
The interannual variability for the average 14year WUE of each pixel was calculated using the bootstrap method (e.g., Zhang et al. 2013). The WUEs from the 14 observations were resampled 1000 times, and then the corresponding mean of each set of resampled data was calculated. Then, the 95% confidence limits for the resulting resampled data were calculated, and the width of the interval between the upper and lower limits was treated as the uncertainty level (at a 95% confidence level).
Regression analysis was conducted between WUE and different geographical (latitude and elevation), morphological (LAI), and meteoro-logical variables (precipitation, near surface air temperature [air temperature afterwards], downward short-wave solar radiation [solar radiation afterwards], and specific humidity). A specific analysis of the WUE according to different biomes was also conducted. The WUE trend was investigated by linear regression analysis. For each 1-km grid cell, we calculated the linear trend of WUE by regressing WUE against time.

Comparison of in situ and MODIS WUE data
We compared our global WUE dataset derived from MODIS GPP and ET data products against the eddy covariance (EC)-derived WUE database (Fig. 1a). There is a moderately strong relationship between the global WUE and EC-WUE (R 2 ¼ 0.55, p , 0.001). Compared with EC values, the MODIS WUE slightly underestimated WUE for WUE values above 2 g C/kg H 2 O and slightly overestimated WUE for WUE values below 2 g C/kg H 2 O. This systematic error may be caused by the difference between the flux tower fetch and the MODIS resolution (Kim et al. 2012). Another reason may be that flux towers generally focus on high production ecosystems (Turner et al. 2006). It should also be noted that ECcalculated GPP is derived from the partitioning of net ecosystem exchange that often uses empirical or process-based modeling (Desai et al. 2008). And therefore, Fig. 1 is not strictly a comparison of remote sensing to direct in situ observations.
The regression relationship much improves when we further compared at the biome level (R 2 ¼ 0.66, p , 0.001). All of the biomes are scattered around the 1:1 line, except a relatively underestimated value for DBF (2.41 and 1.80 g C/kg H 2 O for observed and MODIS estimated, respectively). Though observed WUE for CRO is larger than that for GRA, this value is also underestimated and is found be the least among all MODIS biomes (Fig. 1b).

Global patterns of WUE
Over the 14 years analyzed, the global average GPP and ET were 879.48 g CÁm À2 Áyr À1 and 518.83 mm/yr and this results in an average WUE of 1.70 g C/kg H 2 O. WUE shows a large spatial variability at the global scale (Fig. 2). Large WUE values are found in humid and semi-humid areas of the northern hemisphere, such as Europe, central North America, and central and eastern Siberia, with relatively small interannual variations (Fig. 2b). WUE also shows large values in semi-arid areas, such as in the northern African savannas and open shrublands in southern South America and central Australia; however, WUE in these areas are with large interannual variations WUE is significantly different among biomes (one-way ANOVA, a ¼ 0.05; Fig. 3). In general, forests have the largest WUE among all biomes; closed shrublands also have relatively large WUE values but with large uncertainty; Croplands   WUE is relatively stable as the elevation increases from 0 to 1100 m, and then rapidly decreases at higher elevations (Fig. 4). A maximum of 1.97 g C/kg H 2 O is found at an elevation of 1105 m. WUE has a strong, negative relationship with elevation for elevation between 1105 and 5000 m (WUE ¼ À0.0004 [elevation] þ 2.34, R 2 ¼ 0.94, p , 0.001). Above 5000 m, the WUE is close to zero.
Globally, WUE varies much with latitude, especially for the southern hemisphere (Fig. 4). WUE begins to increase at ;À50.58 S and reaches a maximum of 3.21 g C/kg H 2 O at ;À26.58 S. After a sharp decrease, the WUE is relatively stable between À17.58 S and 608 N except extreme large values are found between 8.58 N and 18.58 N. The particularly high WUE values (above 3 g C/kg H 2 O) found at around À26.58 S and 16.58 N are caused by the large values in parts of Africa, Australia, and New Zealand (Fig. 2). The WUE values around these two latitudes are with large uncertainty due to sparse vegetation. Above 608 N, the WUE decreases sharply with latitude The morphological effects of vegetation on WUE were assessed using the LAI. The global average LAI varies from 0 to 8.7 m 2 /m 2 at the annual scale over the study period (Fig. 5). The WUE first linearly increases sharply when the LAI is smaller than 1.5 m 2 /m 2 (WUE ¼ 0.172 [LAI] À0.281, R 2 ¼ 0.98, p , 0.001) with a maximum of 2.26 g C/kg H 2 O. After decreases through 2.1 m 2 /m 2 , WUE starts to increase from 1.75 to 2.14 g C/kg H 2 O when LAI reaches 4.8 m 2 /m 2 (WUE ¼ 0.014 [LAI] þ 1.43, R 2 ¼ 0.97, p , 0.001). When LAI is above 4.8 m 2 /m 2 , WUE does not fluctuate much.
The WUE increases as the solar radiation increases in regions where solar radiation is less than 242.2 W/m 2 (WUE ¼À0.009 [solar radiation] þ 0.023, R 2 ¼ 0.83, p , 0.001; Fig. 6c). The WUE reaches a maximum of 2.65 g C/kg H 2 O at ;242.2 W/m 2 and tends to decrease as solar radiation increases (WUE ¼ À0.032 [solar radiation] þ10.193, R 2 ¼ 0.85, p , 0.001). Since the solar radiation for most land areas (90%) is below 242.2 W/m 2 , this indicates a large solar radiation would introduce a large WUE in most land areas. WUE also changes with specific humidity (Fig.  6d). In relatively dry regions where specific humidity is less than 0.0072 kg/kg, WUE is larger when the specific humidity is large (WUE ¼ 392.92 [specific humidity] À0.3, R 2 ¼ 0.99, p , 0.001). WUE reaches its maximum of 2.24 g C/kg H 2 O around 0.0092 kg/kg and then becomes stable when specific humidity is above 0.01 kg/ kg.  v www.esajournals.org 0.71, p , 0.01), but no significant trend is observed for ET ( p ¼ 0.12). This results in an increasing trend in WUE ( p ¼ 0.12). Therefore, WUE is more influenced by GPP than by ET over the study period.

Trends in WUE
Overall, WUE increases by 0.0025 g CÁkg À1 H 2 OÁyr À1 at the global scale (Fig. 7a). Areas with a positive trend in WUE account for 58% of the global land area. WUE increases rapidly in almost the entire North America and a highly significant increase is observed in Alaska (Fig.  7b). Positive trends are also found in the Amazonian Plain, central Africa, India, and eastern China. These areas show relatively large WUE values and large positive trends. In contrast, in Eastern Europe, northern Africa, and southern South America, where large WUE values are found (Fig. 2), large deceasing trends are observed (Fig. 7b).

Effects of meteorological drivers on temporal trends in WUE
On average, precipitation increased by 6.44 mm yr/yr over the 14 years. In total, around 55% of the land surface experienced a positive trend (Appendix: Fig. A1). A positive linear relation- Fig. 7. Spatial patterns of (a) WUE trends (g CÁkg À1 H 2 OÁyr À1 ) from 2000 to 2013 and (b) significance of the trends. Highly significant (þ), significant (þ), non-significant, significant (À), and highly significant (À) show positive trend with p , 0.05, positive trend with p , 0.1, non-significant trend, negative trend with p , 0.1, and negative trend with p , 0.05 (t test).
v www.esajournals.org ship is found between WUE and precipitation for 44% of the land surface, with an average slope of 0.0002 g CÁkg À1 H 2 OÁmm À1 Áyr (Fig. 9a). The positive relationship is found in areas with relatively dense vegetation (e.g., forests) and high precipitation; while the sparsely vegetated areas such as Northern Africa and northern Asia experience a negative relationship. Most of these sparsely vegetated areas have relative low precipitation (Appendix: Fig. A1). This indicates that WUE increases as precipitation increases in relatively wet areas and increases as precipitation decreases in relatively dry areas.
Temperature increased over most parts of the global land surface (around 64%) during the study period with an average slope of 0.0238 C/yr (Appendix: Fig. A2). Forty percent of the land area shows a negative relationship between WUE and temperature, with an average slope of À0.026 g CÁkg À1 H 2 OÁ8C À1 (Fig. 9b). The negative relationship is even more apparent for the southern hemisphere (SH), with high signifi- v www.esajournals.org cance. In the northern hemisphere, India and southern North America also show a negative relationship between WUE and temperature. However, for cold areas, such as the northern high latitudes and the Tibetan Plateau, a positive relationship is observed between WUE and temperature.
Over the 14 years, the global land surface experienced a dimming phase, with solar radiation decreasing by 0.15 WÁm À2 Áyr À1 on average. Areas with decreasing trends occupy 57% of the total land surface (Appendix: Fig. A3). These areas are the same as those with increasing trends in precipitation, such as the Amazonian Plain, central and North Africa, and Southeast Asia, with high significance. Overall, solar radiation has a negative relationship with WUE trend for the global dimming, with an average slope of À0.005 g CÁkg À1 H 2 OÁm 2 ÁW À1 (Fig. 9c). This indicates that for most areas (around 67%), WUE increases as solar radiation decreases (Appendix: Fig. A3).
Not surprisingly, the specific humidity shows an increasing trend because of increasing precipitation at the global scale (0.00002 kgÁkg À1 Áyr À1 ; Appendix: Fig. A4). Areas with a positive trend account for 69% of the total land surface and the total area is a little larger than that for precipitation (Appendix: Fig. A4). WUE shows a positive relationship with specific humidity for 69% of the total land surface, and the average slope is 17.36 g CÁkg À1 H 2 OÁkgÁkg À1 (Fig. 9d). In contrast, a significant negative relationship between WUE and specific humidity is observed in Southeast Asia, northern and southern Africa, and patchy areas in South America.

Global patterns and trends of WUE
WUE values generally show large spatial variability at the global scale. Generally, biomes with high productivity have large WUE values (Fig. 2a). In areas with sparse vegetation, a large WUE has also been observed but with large interannual variation (Fig. 2b). This is obvious for the WUE of CSH, which has a larger standard deviation compared with other biomes (Fig. 3). The negative relationship between WUE and elevation may also be caused by frequent ice and v www.esajournals.org snow cover and thus sparse vegetation associated with low temperature and precipitation in high-elevation areas (Fig. 4). The latitudinal WUE pattern clearly shows the influence of interannual variability induced by the sparse vegetation (Fig. 4).
The temporal trend over the 14 years studied varies greatly in magnitude and also differs in direction (increasing or decreasing). Few studies have examined global WUE (Dan and Ji 2007, Mu et al. 2011a, Ito and Inatomi 2012. Ito and Inatomi (2012) calculated WUE as NPP/ET or GPP/ET ratios using a global terrestrial model. They found that for the period 1995-2004, the global average WUE, calculated as GPP/ET, was 1.92 g C/kg H 2 O, which is slightly higher than our value (1.70 g C/kg H 2 O). This might be caused by the markedly larger WUE values for croplands and savannas in their results, and the different time period used. However, the spatial patterns obtained by Ito and Inatomi (2012) and by us are similar (Fig. 4 in Ito and Inatomi 2012). We further compare the WUE in the year of 2010 from our study with global WUE (Xiao et al., unpublished manuscript) calculated using a datadriven approach (Xiao et al. 2008) and WUE from Jung et al. (2011;Fig . 10a). WUE from Jung et al. (2011) is calculated as the ratio of GPP to ET and is scaled up from flux tower values by a machine learning technique for 2000-2011 at 0.58 3 0.58 grid resolution. We compare the biome-averaged WUE from the two studies. All the biomes are scattered around the 1:1 line except for closed shrublands (CSH) for both cases. WUE for CSH from our study (2.79 g C/kg H 2 O) is much larger than those from Xiao et al. (unpublished manuscript) and Jung et al. (2011;1.31 and 1.21 g C/kg H 2 O, respectively). Since CSH occupies 0.5% of the global land area according to the MODIS land cover with the UMD classification scheme, we thus removed it from our figure. The regression relationship is much improved when CSH is removed (Fig. 10a). Note that WUE from our study is comparable with Xiao et al. (unpublished manuscript) for low productivity biomes and is smaller for high productivity biomes; while it is opposite when compared with Jung et al. (2011). At the global scale, the WUE patterns are similar among the three studies (Appendix: Fig. A5). WUE from Xiao et al. (unpublished manuscript) is largest for forests in North America and Northern Asia (most above 2.5). Our estimates are between the estimates of the two datasets for these areas. However, WUE in Amazonia tropical forest from our results are systematically smaller than those of the other two studies (Appendix: Fig. A5). This might be caused by the smaller GPP from this area as MODIS GPP tends to be underestimated for the high-productivity ecosystems (Turner et al. 2006). A large positive bias is also observed for southern Arica and wet Australia, indicating large uncertainties for these areas (Fig. 2b). These results indicate necessity of validation of MODIS products of GPP and ET in more areas besides North America and Europe (Zhao et al. 2005, Mu et al. 2007. Overall, an increasing trend is found during the research period on the global scale. These results are consistent with those of Ito and Inatomi (2012) and Dan and Ji (2007). Similarly, Tian et al. (2010) investigated WUE values (calculated as NPP/ET), using a process-based model, for the southern USA during 1895-2007. They found that WUE increased by 25% over the period for their study area. In contrast, our results show that several areas such as southern South America, Eastern Europe, and southern China show strong decreasing trends, which may be caused by climatic variables (Fig. 9).
Since the time period of our analysis based on the MODIS data is relatively short, we further compare the MODIS-derived WUE with that from the Integrated Biosphere Model (IBIS, Kucharik et al. 2000) and that from Jung et al. (2011;Fig. 10b). IBIS is run for the period 1948-2010 to calculate the global GPP and ET at 0.58 3 0.58 latitude-longitude grid resolution. Temporal trend of Jung et al. (2011) is for the period of 1982-2011 based on the available satellite data. WUE from IBIS shows a significant increasing trend for its analyzed period ( p , 0.001); while it is not the case for Jung et al. (2011;p ¼ 0.19). However, when evaluated for the period of -2010-2011for IBIS and Jung et al. (2011, both of the two studies show significant increasing trends ( p ¼ 0.009 and p ¼ 0.045 for IBIS and Jung et al. [2011], respectively). These results indicate that MODIS products can detect the disturbances and thus variations of WUE over the global scale. On the other hand, the absolute values of IBIS derived WUE are signifv www.esajournals.org icantly larger than those from Jung et al. (2011) and MODIS products (one-way ANOVA, p , 0.001). This necessitates further work on the MODIS products validation or model calibration for GPP or ET accuracy assessments.

Influences of meteorological and morphological variables on WUE
The influences of meteorological and morphological variables on the patterns and trends of WUE, and the responses of WUE to these variables, may be different, or even opposite, at different spatial (leaf, canopy, ecosystem, regional, or global) and temporal scales (half-hourly, seasonal, and interannual; Scanlon and Albertson 2004, Krishnan et al. 2006, Hu et al. 2008, Tian et al. 2010, Yang et al. 2010, Mu et al. 2011a, Niu et al. 2011, Keenan et al. 2013. We investigated the effects of four meteorological variables (precipitation, temperature, solar radiation, and specific humidity) and one morphological variable (LAI) on WUE. Global studies of the effects of meteorological variables on WUE are rare (Mu et al. 2011b, Ito and Inatomi 2012, Keenan et al. 2013 and there is no consensus on the subject. In a synthetic analysis, Keenan et al. (2013) investigated the inherent WUE (WUEi, WUE multiplied by VPD) using observed GPP and ET data from forest sites in northeast US and Western Europe. They observed an increase in forest WUEi over a period from around the mid-1990s to the present. Despite the slightly different time period, this is consistent with our result for the increasing trend in those areas (Fig. 7a). Keenan et al. (2013) attributed the increases in the WUEi for these forest sites to increasing atmospheric CO 2 concentrations, with a small fraction explained by meteorological or morphological variables. However, Figs. A1-A4 show that the sites Keenan et al. (2013) selected are mainly located within areas where meteorological variables are not changing significantly, i.e., in regions in northeast US and Western Europe.
To further explore how meteorological vari-  Jung et al. (2011;right panel) with that from our study; (b) comparison of time series of WUE from Jung et al. (2011), our study (MODIS) and that from the Integrated Biosphere Model (IBIS, right bar). The time period for Jung et al. (2011) and IBIS is 1982-2011and 1948-2010. The abbreviations for the different biomes are the same as those in Fig. 3.
v www.esajournals.org ables influence WUE, we assessed how WUE responds to extreme weather events by taking the European droughts during 2000-2010 as an example. Three droughts occurred during this period, i.e., in 2003period, i.e., in , 2008period, i.e., in and 2010period, i.e., in (Ivits et al. 2014. We compared WUE in 2010 and that for the averaged values during 2000-2013 (DWUE) for the region. During the 2010 European drought, 71% of the area shows a decreased WUE (DWUE , 0; Fig. 11a). The averaged WUE was observed to drop for all the three droughts and was most obvious in 2010 (Fig. 11b). All of the biomes show decreased WUE except for OSH in Norway and grasslands of the Alps during this drought (data not shown).
Few studies have examined the effects of LAI on WUE (Hu et al. 2008, Keenan et al. 2013, since most of the studies on WUE have focused on short time periods (usually half an hour or several weeks). However, over longer periods (e.g., seasonal and interannual), LAI could be important in WUE because it can substantially influence WUE by affecting the ratio of transpiration to ET (Hu et al. 2008). WUE increases almost linearly as LAI increases for regions where the LAI is smaller than 1.5 m 2 /m 2 , whereas WUE does not fluctuate much for regions with LAI larger than 2 m 2 /m 2 (Fig. 5). The saturation of WUE with LAI is in agreement with Beer et al. (2009), who calculated WUEi using observed flux datasets. The LAI affects WUE by regulating the ratio of plant transpiration to ET (Hu et al. 2008. It should be noted that the positive relationship between WUE and LAI may also be partly due to the inherent relationship among the MODIS GPP, ET and LAI datasets, which are derived from the same MODIS reflectance data and ancillary land classification data.

Uncertainty and limitations
Our WUE values are calculated from the MODIS GPP and ET. The MODIS GPP and ET products have significant uncertainty , Mu et al. 2011b). MODIS GPP is calculated using a simple multi-product formula (Eq. 1), and the GPP estimates highly depend on the input parameters, especially e max (maximum light use efficiency). For example, e max is held constant for each vegetation type in the MODIS GPP algorithm although this parameter is in fact highly variable (Turner et al. 2006). Other uncertainties may arise from the meteorological inputs from coarser resolutions (Global T62 Gaussian grid, ;1.888 3 1.888 for WGS-84 projection) compared with other MODIS products . Similarly, uncertainties of MODIS ET products may arise from the corresponding meteorological inputs, the ET algorithm and other MODIS inputs such as LAI and land cover (Kim et al. 2012, Xue et al. 2013). These uncertainties are indicated in our comparison results (Fig. 1), which show a systematic error of WUE with moderate R 2 (0.55) at the site level. Therefore, this necessitates validation of MODIS products by more measured data and improvement of the algorithm.
Our results show that future work should be conducted to improve the accuracy of MODIS GPP and ET particularly in sparsely vegetated areas. The MODIS GPP and ET products have several sources of uncertainty: model inputs, model structure, and model parameters. For example, the uncertainty in model inputs including meteorological data and the land cover map can lead to significant uncertainty in model simulations , Xiao et al. 2011. The uncertainty in model parameters can also lead to significant uncertainty in modeled fluxes (Xiao et al. 2011. Moreover, the MODIS algorithms for GPP and ET use a single set of parameters to represent each biome and do not consider the spatial heterogeneity within each biome (Eq. 1). In reality, the different physiological parameters may vary even within a given vegetation type because of the variability in soil types, climate and vegetation (Quesada et al. 2010), leading to biases in GPP and ET estimates at the global scale (Castanho et al. 2013). Parameter variability within a vegetation type can lead to large variability in flux estimates (Xiao et al. 2011).
Furthermore, because of the limited data available from the MODIS products, we investigated the temporal trends in WUE for only 14 years. An inter-comparison with WUE from other sources (i.e., IBIS model results and Jung et al. [2011]) show that the MODIS products can detect the disturbances and general trends over the global scale; whereas, absolute values of WUE do not have a consensus among the three datasets. Therefore, a longer time series of WUE values would be even more helpful for understanding vegetation adaption to climate change.
Finally, in this study, we focus on the influences of latitude, altitude, LAI, and four meteorological variables, but WUE could be influenced by other factors such as nutrient cycling (e.g., Keenan et al. 2013), CO 2 concentration (e.g., Saurer et al. 2004, Keenan et al. 2013, and land use change (e.g., Tian et al. 2011), especially over longer time periods. These factors should be considered in future studies when longer time series of WUE and spatially explicit information on these variables become available.

CONCLUSIONS
WUE is an essential parameter that characterizes the coupling of vegetation carbon and water cycles. As a first thorough investigation, this research maps the spatiotemporal patterns of WUE on the global scale. WUE shows large spatial variability globally and is influenced by various meteorological and morphological variables. The WUE also shows a significant increasing trend for most vegetated areas over the study period. The meteorological variables play an important role in temporal variations in WUE. Despite the limitations of the MODIS products, they are perhaps the best gridded data products available for calculating WUE at the global scale. Our results can improve our understanding of the linkages between the global water and carbon cycles by assessing the responses of WUE to climate; and therefore have implications such as future response projection and ecosystem management.

ACKNOWLEDGMENTS
This study was financially supported by the National Key Basic Research Program of China (2013CB956604) and the National Science Foundation of China (Grants No. 41301020 and 31270563). J. Xiao v www.esajournals.org was supported by the National Aeronautics and Space Administration through the Carbon Cycle Science Program (award number NNX14AJ18G) and the Terrestrial Ecology Program (award number NNX12AK56G). The authors express their sincere thanks to graduate students from the Digital Ecosystem Lab of IBCAS for assistance with the data analysis and to the anonymous reviewers and the Editor Dr. Howard Epstein for constructive comments on the manuscript.