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Multi-decadal trends in global terrestrial evapotranspiration and its components

Evapotranspiration (ET) is the process by which liquid water becomes water vapor and energetically this accounts for much of incoming solar radiation. If this ET did not occur temperatures would be higher, so understanding ET trends is crucial to predict future temperatures. Recent studies have reported prolonged declines in ET in recent decades, although these declines may relate to climate variability. Here, we used a well-validated diagnostic model to estimate daily ET during 1981–2012, and its three components: transpiration from vegetation (Et), direct evaporation from the soil (Es) and vaporization of intercepted rainfall from vegetation (Ei). During this period, ET over land has increased significantly (p < 0.01), caused by increases in Et and Ei, which are partially counteracted by Es decreasing. These contrasting trends are primarily driven by increases in vegetation leaf area index, dominated by greening. The overall increase in Et over land is about twofold of the decrease in Es. These opposing trends are not simulated by most Coupled Model Intercomparison Project phase 5 (CMIP5) models, and highlight the importance of realistically representing vegetation changes in earth system models for predicting future changes in the energy and water cycle.


Results
Model validations. The PML estimated ET and its partitioning are comprehensively assessed from point to global scale, including: (i) catchment precipitation (P) and streamflow (Q) data; (ii) eddy-covariance flux tower data; (iii) satellite-derived soil moisture; (iv) field experiments of ET partitioning; (v) comparing annual E i /P ratio in homogeneous forests; (vi) evaluation of E s in extreme climates; and (vii) model inter-comparison. This assessment includes five validations, being (i) to (v), and two evaluations, (vi) to (vii); all are outlined below in-turn.
First, over a long-term catchment water balance, 'observed' mean annual ET is the difference between the observed catchment mean annual P-Q. The PML estimated ET compares well with long-term water-balance ET observations from 643 largely unregulated large (> 2000 km 2 ) catchments across the world (Fig. 1a), with coefficient of determination R 2 = 0.87 and Bias = − 1.4%. The time-series of aggregated estimated annual ET from the 643 catchments also show good correspondence to the annual P-Q aggregated series (Fig. 1d, R 2 = 0.65). This indicates a good performance of the annual ET simulations. In addition, PML-estimated ET trend compares reasonably well to the catchment annual P-Q trend for 46 large unregulated catchments (> 10,000 km 2 ) distributed across North America, Europe, South America and Australia (Fig. 1b, R 2 = 0.40). It is noted that the catchment annual P-Q trend may have noticeable errors in some catchments due to the influence of catchment storage changes.
Second, at monthly scale, the estimated ET is compared to eddy-covariance flux measurements in 95 flux towers widely spread (Fig. 1c), yielding a good agreement indicated by R 2 = 0.77 and Bias = − 6.0% (Fig. 1c). To test the robustness of the PML model for simulating ET in various climatic conditions, we split the 95 flux towers into two groups: dry and wet. The 16 sites with aridity index (the ratio of potential evapotranspiration to precipitation) more than 1.5 are deemed as 'dry'; and the 79 sites with aridity index less than 1.5 classified as 'wet' . Monthly estimated ET corresponds well to the measured in both dry (R 2 = 0.77 and Bias = − 9.7%) and wet (R 2 = 0.77 and Bias = − 5.3%) climatic conditions, demonstrating that the PML model performs equally well in both dry and wet conditions. Third, the ET partitioning into its respective components is also independently evaluated. The annual E s series estimated by the PML model shows good agreement with the TRMM (Tropical Rainfall Measuring Mission) (b) Comparison of estimated annual ET trend (mm year −2 ) to catchment annual ET (P-Q) for 46 large catchments (> 10, 000 km 2 ) with less than 3-year missing data. (c) Comparison of the estimated ET (mm month −1 ) to the measured ET at 95 flux sites (red dots in the global map). (d) Annual anomalies of the estimated ET, ET components, and catchment observed ET (P-Q), all aggregated from catchments (number of catchments per year provided using grey bars) with annual Q observations. (e) Annual anomalies of the estimated ET, ET components, and the observed microwave soil moisture, all aggregated between 40 °N and 40 °S (area covered by the microwave soil moisture data). Error bars for ET and its components are s.d. obtained from the two PML simulations. Error bars for P-Q are s.d. obtained from the two precipitation datasets. R 2 in Fig. 1(a-d) is obtained from comparing measured ET and estimated ET. R 2 in Fig. 1(e) is obtained from comparing soil moisture and estimated E s . The maps were generated using a commercial software MATLAB.
Fourth, the ET partitioning is also checked against 12 field experiments covering various ecosystems for which the E s /ET percentage ratio is obtained ( Table 1). The E s /ET percentage ratio estimated by the PML model corresponds well to the results obtained by the field experiments, with R 2 = 0.79.
Fifth, the annual E i /P percentage is also compared to measurements in 11 largely homogeneous inland forest sites (Table 2). Most sites are in humid tropical forests where E i likely accounts for a significant proportion of ET. Both measurements and estimates show narrow ranges of E i /P percentage ratios. The measurements show that about 8-14% of annual P is partitioned to E i for the selected forests, which are similar to the PML estimates that vary from 5% to 11%.
Sixth, the ET partitioning can be qualitatively evaluated in extreme climates, such as deserts in Sahara, central Asia, Arabian Peninsula, and central Australia where mean annual potential ET is more than 10 times of mean annual P (Fig. 2a). In these areas, most of precipitation is used for E s , as estimated by the PML model (Figs 2c and 2d).  Seventh, the ET estimates from the PML model are also compared to other two diagnostic models (MTE 1 and GLEAM 6 ), 9 land surface models 1 and 39 Coupled Model Intercomparison Project Phase 5 (CMIP5) climate models 18 (Fig. 3). The PML model shows reasonable agreement to the median of the nine land surface models, MTE and GLEAM in the annual global average ET estimates: R 2 of 0.69, 0.52 and 0.31, respectively, and shows the least agreement to the median of 39 CMIP5 models: R 2 of 0.14. All the three diagnostic models show significantly increasing ET trend over 1982-2011, being 0.68, 0.32 and 0.38 mm year −2 for PML (p < 0.01), MTE (p < 0.01) and GLEAM (p < 0.1) models, respectively.
Overall, these seven assessments, including five point to regional validations and two global evaluations, give confidence on the ET components used in our analysis.
Global and continental summary. The spatial distribution of PML mean annual ET is shown in Fig. 2b.
The 1981-2012 mean ET across the global land surface (not considering water bodies and permanent ice surfaces) is 538.1 ± 56.5 mm year −1 (i.e., 63.2 × 10 3 km 3 year −1 ) (Fig. 4a) or ~67% of mean annual P (805.6 ± 41.7 mm year −1 ); in good agreement with previous estimates based on similar study periods 1,2,3,6 . PML E t accounts for ~65% of ET (350.4 ± 54.7 mm year −1 ), E s for ~25% (133.9 ± 15.0 mm year −1 ) and E i for ~10% (53.7 ± 5.5 mm year −1 ). These estimates fall within the broad range of variability reported by studies based on isotopes 8,9 , and satellite observations and modelling [19][20][21] . The relative contribution of the different ET components varies per continent (Fig. 2c,d), reflecting water availability, energy constraints and land cover heterogeneity. Continents containing vast tracts of tropical forests, like South America, evaporate more and the relative contributions from E t and E i are larger (Fig. 2b,c); whereas in largely arid continents, such as Australia, E s is a substantial contributor (Fig. 2d).
Averaged across the global land surface, the inter-annual variance of ET is 1907 ± 147 mm 2 year −2 , representing only ~6.2% of the P variance (Fig. 4b). The greater than ten-fold difference between P and ET variances is because vegetation and soil serve as 'storage' buffers. The E s variance of 967 ± 28 mm 2 year −2 is similar to the E t variance globally (958 ± 94 mm 2 year −2 ), despite the E t being more than double E s . This is because some vegetation, especially trees, has access to deep soil water for E t , and have developed deep roots in response to  P variability 22,23 . Compared to that, shallow soil water is a more immediate buffer for E s responding directly to the P variability. As a result, global variance in E s is comparable to that in E t , as E s is a larger component of ET in regions with a high inter-annual variability in P, like Australia or South Africa 6 .
The global multi-decadal trend  in ET is positive (p < 0.01), i.e. in the same direction as previous estimates 1,6 ( Fig. 3). This is caused by significant positive trends in E t (0.72 ± 0.23 mm year −2 ) and in E i (0.14 ± 0.07 mm year −2 ), which are partly counter-balanced by a significant but smaller negative trend in E s (-0.32 ± 0.07 mm year −2 ) (Fig. 4c). Strong positive ET trends are observed in northern and eastern Asia, India, eastern North America, Europe, northern Sub-Saharan Africa and northern and eastern Amazonia (Fig. 5a), mainly as a result of increased E t (Fig. 5b). Negative ET trends are observed over parts of subtropical and temperate South America, the Middle East and western United States, and are mainly explained by reductions in E s (Fig. 5a,c). Decreases in E s in the Sahel 24 , Indian Subcontinent and southern China are also accompanied by increases in E t (Fig. 5b,c). Causality analysis. The contrasting positive trend in E t and negative trend in E s is mostly explained by the increase in leaf area index (LAI) (Fig. 5d). This increasing trend in LAI has been attributed to CO 2 fertilization 25 , global warming 26 , increased productivity in croplands 27 , afforestation and forest protection 27,28 . The increase in LAI also means more shading of the soil surface and less coupling between the atmosphere and the soil surface, and these are likely to be the main reasons for the decreasing trend in E s 29,30 . The trends in ET and its components due to the observed increase in LAI are further explored as the difference between PML-ET simulations obtained using the observed LAI time series and PML-ET results obtained using detrended LAI time series. The spatial distribution of the trend difference is shown in Fig. 6 and the continental summary of the trend difference is summarised in Table 3. The LAI increase causes noticeable increase in ET (Fig. 6a) in Europe, India, eastern China, eastern and northern Australia, Sahel, and eastern Amazon, which is accompanied by an increase in E t (Fig. 6b) and decrease in E s (Fig. 6c). The trend difference in E i is much smaller compared to that in E t or in E s (Fig. 6d).
The contrasting trends between E s and E t occur mainly in croplands, grasslands, mixed forests and shrublands (see Supplementary Information Figs S1 and S2). Furthermore, the contrasting trends are confirmed when they are stratified using the LAI trend ranging from − 0.025 to 0.035 m 2 m −2 year −1 (see Supplementary Information  Fig. S3).
Globally, the increase in LAI causes an increase in E t and E i trends by 0.71 and 0.08 mm year −2 , and a decrease in E s trend by 0.30 mm year −2 ( Table 3). The increase in LAI causes an increase in E t trend for all continents, ranging from 0.57 mm year −2 in Africa to 1.16 mm year −2 in Europe, and also causes a slight increase in E i trend, ranging from 0.04 mm year −2 in Australia to 0.19 mm year −2 in Europe. In contrast, the increase in LAI reduces E s trend for all continents; ranging from − 0.18 mm year −2 in North America to − 0.56 mm year −2 in South America. These impacts on E t , E s and E i cause noticeable ET trends increasing in all continents, ranging from 0.30 mm year −2 in North America to 0.84 mm year −2 in Europe.
While the trend in ET is influenced by vegetation change, the ET (and its components) variability is dominated by inter-annual climate variability 31 . Globally, this is demonstrated by Fig. 7a showing similar variance estimates in annual ET, E t and E s from PML using observed LAI time series and using detrended LAI time series. There is a strong correlation between P and E s (and ET) (Fig. 5e) and the P trend influences E s and ET trends in the southern mid-latitudes, such as the increasing trend in northern Australia and southern Africa and the decreasing trend in southern South America (Fig. 5a,c,f). In these regions, the dynamics of the EI Niño/Southern Oscillation 6,32 dominate the multi-decadal P and ET variability. When stratified using the P trend, the ET trend gradually rises with increasing P trend (see Supplementary Information Fig. S4). Furthermore, a decrease in E s trend and E i trend occurs when the P trend decreases; a strong increase in E i trend accompanies the strong increase in P trend. . Trends in ET, E t , and E s are obtained from the average of the two PML simulations. Trends in LAI are obtained from the AVHRR based LAI product, and P trends are averaged from the two P products (i.e., PGF and WFDEI). The maps were generated using MATLAB.

Discussion
Using the well-validated diagnostic PML model, we estimated that global ET is comprised of 65% E t , 25% E s and 10% E i . Although E t is larger than E s , their inter-annual variability is similar, because the variability in E t is buffered by vegetation and soil moisture storage. The E s has high inter-annual variability reflecting the high inter-annual variability of P. Regionally, the ET variability is dominated by E t and E i in densely vegetated and wet regions, and by E s in sparsely vegetated and arid regions.
The PML model showed positive trend in ET consistent with, and close to, the median (+ 0.63 mm year −2 ) of the trends in four other global ET products 1,6,33,34 . PML and these other four products all show slightly positive ET trends globally of similar magnitude in the last three decades. Over 1981-2012, the PML model estimates positive  Table 3. Trends (mm year −2 ) in ET and its components (average from simulations 1 and 2) obtained using observed LAI time series and those obtained (average from simulations 3 and 4) using the detrended LAI across globe and each continent. The symbols ** , * and n denote significance level 1-α = 99% (p < 0.01), 1-α = 95% (p < 0.05), and not significant (p > 0.05), respectively. The "Difference" is calculated as "Trended" minus "Detrended".  Table S1. Green dots are variance or trend estimated by PML using observed LAI time series (Fig. 7a,c), and are variance and trend in LAI time series (Fig. 7b,d); black dots are variance or trend estimated by PML using detrended LAI time series (Fig. 7a,c), and are variance and trend in detrended LAI time series (Fig. 7b,d) E t trend of 0.72 mm year −2 , which is partially counteracted by a negative E s trend of 0.32 mm year −2 . These contrasting trends are primarily driven by the increasing trend in vegetation LAI. There is a limitation in the PML model in that it does not directly account for the impact of enhanced CO 2 concentration on vegetation water use efficiency. To quantify this potential impact, we used the CABLE 35 global land surface model which simulates changes in water use efficiency. The experiment was performed using the same forcing data, but with two CO 2 concentration forcings: fixed CO 2 concentration set at 1981 level, and annual CO 2 concentration time series from 1981 to 2012. The CABLE simulations show that the change in vegetation water use efficiency due to increasing CO 2 concentrations from 1981 to 2012 reduces E t by 0.17 mm year −2 and increases E s by 0.04 mm year −2 , hence reducing ET by 0.13 mm year −2 . The positive E t trend estimated by the PML model will therefore be smaller (by 20-30%) if the CO 2 influence on vegetation water use efficiency is taken into account, but the PML result will still show the strong opposing trends in E t and E s .

LAI inputs
We further explore the trends in PML ET components with simulations from the eight CMIP5 models that archive outputs of ET, E t and E s (Fig. 7c) over a common 1981-2005 period. All eight models show positive ET trend, with the PML estimate close to the median of the trend from the eight models. However, the CMIP5 models do not show the contrasting E t and E s trends, and generally simulate higher positive trend in E s than in E t . Possible reasons for this may include: (i) a more direct ET response to P in the CMIP5 models thereby implying an insufficient accounting of the vegetation and soil moisture buffering on ET in the CMIP5 models (as seen in the higher variance in ET and its components in the models (Fig. 7a)); and (ii) the limited number of CMIP5 models used here (not all models archive all ET components, and there is possible inconsistency in the definition of ET components between models). Also for 1981-2005, we compare observed LAI with simulations from the five CMIP5 models that archived LAI. Results show that the five CMIP5 models overestimate inter-annual LAI variability (Fig. 7b) and do not optimally incorporate LAI to simulate ET components (Fig. 7c) though these five CMIP5 models simulate global LAI greening reasonably (Fig. 7d). Both these findings (i.e., assessing CMIP5 ET and LAI characteristics) suggest the need for better incorporating vegetation dynamics for land-atmospheric interactions in global earth system models to adequately predict future changes in the energy and water fluxes.

Methods
The PML model. At each grid cell, daily ET is the sum of E s , E t and E i . The PML model estimates E s and E t according to 10 where ε = s/γ, in which γ is the psychrometric constant and s = de * /dT is the slope of the curve relating saturation water vapour pressure to temperature; ρis the density of air and c p is the specific heat of air at constant pressure; a a a is the water vapour pressure deficit of the air (humidity deficit), in which ( ) ⁎ e T a is the saturation water vapour pressure at air temperature and e a is the actual water vapour pressure; G a is the aerodynamic conductance; G c is the canopy conductance for transpiration; and f is the fraction of P to equilibrium soil evaporation εA s /(1+ ε), estimated from the accumulated precipitation over the previous month 11 . A, the available energy absorbed by the surface (net absorbed radiation minus soil heat flux), is partitioned using LAI into canopy absorption (A c ) and soil absorption (A s ). E i is modelled using an adapted version of the widely adopted Gash rainfall interception model, and assumes that the ratio between the wet canopy evaporation rate and the rainfall rate does not vary between storms 36 . ET estimated at a land grid cell is aggregated from ET estimated from each land cover type within the grid cell.
There is only one-free parameter, the maximum stomatal conductance ( g sx ) to calculate E t in PML. The g sx was estimated for each land cover type using the trial-and-error method by comparing (1) modelled mean annual ET with water balance ET observations (mean annual P minus mean annual Q), and (2) modelled monthly ET with in situ flux tower ET measurements.
At the mean annual scale (1981-2012), the PML model is further constrained by the classic Budyko framework, the Fu hydroclimatic model 37 at each grid cell since PML is not constrained by mean annual water balances. The Fu model ensures that mean annual ET is always less than mean annual P for grid cells covered by non-crop vegetation. For cropland, mean annual ET can be larger than mean annual precipitation if irrigation uses groundwater or water transferred from other basins. Therefore, in only those grid cells covered by non-crop vegetation, the three ET components were equally scaled to match the mean annual ET (1981-2012) estimated from the Fu model. There is one parameter β in the Fu model, which was calibrated against catchment ET observations. Data. Meteorological forcings from 1981 to 2012 used to drive the PML model include daily precipitation, air temperature, vapour pressure, shortwave downward radiation, longwave downward radiation and wind speed. The forcings were obtained from two widely used datasets: the Princeton Global Forcing (PGF) data 14,15 and the WATCH Forcing Data ERA-Interim (WFDEI) meteorological forcing data 13 .
Vegetation forcing data were obtained as follows. LAI data from 1981 to 2011 were obtained from Boston University (BU) dataset 16 . It was derived from the Advanced Very High Resolution Radiometer (AVHRR)-NDVI data. The temporal resolution for the BU dataset is half-monthly and its spatial resolution is 0.0833°. The LAI time series data in 2011 was used for 2012. Emissivity and albedo at 0.05° spatial resolution and 8-day resolution from 1981to 2012 were obtained from the Global Land Surface Satellite (GLASS) dataset 38 . The GLASS albedo product was produced from both AVHRR (1981)(1982)(1983)(1984)(1985)(1986)(1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)  to 2012. The surface emissivity and mean daily air temperature, was used to estimate daily outgoing longwave radiation, R lo . Static land cover for 16 land cover types based on the International Geosphere-Biosphere Program (IGBP) Data, generated using 2000-2001 MODIS data, were obtained from the Oak Ridge National Laboratory Distributed Active Archive Center 39 .
Validation datasets include catchment streamflow, fluxnet eddy covariance ET and over land microwave soil moisture. A total of 643 largely unregulated catchments with a widespread geographic distribution were selected to evaluate model performance at the mean annual scale. To exclude regulated catchments, major dam locations were obtained from three sources: (i) International Commission of Large Dams 40 ; (ii) Meridian World Data (http://www.meridianworlddata.com/) and (iii) National Land and Water Resources Audit of Australia (http://www.nlwra.gov.au/). Daily streamflow data for the selected catchments was obtained from four sources: (i) the Global Runoff Data Centre (located in Germany, http://www.bafg.de/GRDC/EN/Home/homepage_node. html); (ii) the Water Information Research and Development Alliance between CSIRO and Australian Bureau of Meteorology 41 ; (iii) the Model Parameter Estimation Experiment (MOPEX) 42 and (iv) the Chinese Academy of Sciences. Each catchment had at least 5 years of observations. Catchment mean annual ET values were estimated as mean annual P minus mean annual runoff (Q), assuming that changes in soil water storage are negligible in the long term 43 .
A total of 95 fluxnet towers were selected to evaluate model performance at monthly scale. Data for the 93 towers were obtained from the LaThuile FLUXNET dataset. An additional two sites were obtained, one from the OzFlux and another from AmeriFlux. The selected sites span a wide range of climate regimes, covering a total of 11 vegetation types 39  Each flux site meets the following criteria: (1) mostly homogeneous land cover at 1 km radius from the flux tower (checked with Google Earth); (2) daily energy balance closure of more than 75%; and (3) more than 2 years of daily data (during days with no precipitation) available. Note here that our evaluation compares the ET PML at 0.50° spatial resolution (i.e., the resolution of the global forcing data) against ET flux representing ET from a radius of tens to hundreds of metres (depending on biophysical, atmospheric and instrumental characteristics).
Annual variation of ET and its components was validated against that of observed soil moisture in sparsely-vegetated regions. The observed soil moisture data were obtained from the radiometer Microwave Instrument on board NASA's Tropical Rainfall Measuring Mission (TRMM) that started providing passive microwave observations at 10.7 GHz (X-band) and eight higher frequencies including the 37 GHz (Ka) band from December 1997. The observations can be assimilated in a microwave radiation transfer model to infer soil moisture, soil and canopy temperature and vegetation optical depth. We used the top soil moisture retrieved from the Land Parameter Retrieval Model 44 based on L-and Ka-band brightness temperatures. The retrieved soil moisture represents the top few centimeters corresponding to 10.7 GHz (X-band). The platform TRMM covers regions between 40 °N and 40 °S. Due to the influence of dense vegetation, reasonable soil moisture retrievals over tropical forests are not available and thus masked out 45 . The dataset used in this study was resampled to 0.50° spatial resolution and aggregated to monthly average for January 1998 to December 2012.
Simulations 1-2 were carried out using observed LAI time series, and simulations 3-4 were carried out by repeating the simulations 1-2 but using detrended LAI (i.e. removing the long-term trend, but allowing for sub-annual variation related to seasonal cycles). The difference between simulations 1-2 and simulations 3-4 is used to quantify the impacts of LAI change on trends and variability in ET and its components.
Statistical analysis. Annual 46 was used for trend analysis and significance testing.