Satellite and gridded meteorological data can be used to estimate evaporation (E) from land surfaces using simple diagnostic models. Two satellite datasets indicate a positive trend (first time derivative) in global available energy from 1983 to 2006, suggesting that positive trends in evaporation may occur in “wet” regions where energy supply limits evaporation. However, decadal trends in evaporation estimated from water balances of 110 wet catchments do not match trends in evaporation estimated using three alternative methods: 1) , a model-tree ensemble approach that uses statistical relationships between E measured across the global network of flux stations, meteorological drivers, and remotely sensed fraction of absorbed photosynthetically active radiation; 2) , a Budyko-style hydrometeorological model; and 3) , the Penman–Monteith energy-balance equation coupled with a simple biophysical model for surface conductance. Key model inputs for the estimation of and are remotely sensed radiation and gridded meteorological fields and it is concluded that these data are, as yet, not sufficiently accurate to explain trends in E for wet regions. This provides a significant challenge for satellite-based energy-balance methods. Trends in for 87 “dry” catchments are strongly correlated to trends in precipitation (R2 = 0.85). These trends were best captured by , which explicitly includes precipitation and available energy as model inputs.
The quantity of water available for runoff (Q) and changing the amount of moisture stored in catchments is the difference between precipitation (P) and evaporation (E). Runoff from river basins is substantial in humid regions where P exceeds E, but there is little or no runoff in arid regions where E ≈ P. Between these extremes, runoff is often the small residual between P and E and subtle changes in either can strongly affect water yields. Global warming associated with rising atmospheric CO2 concentrations is expected to substantially modify the global hydrological cycle (Huntington 2006; Milly et al. 2005) and thus change the balance between P, E, and Q by differing amounts in various regions across the globe. Evaporation from land surfaces is fundamentally determined by the availability of water and energy, and understanding the contributions of trends and changing patterns in water and energy supply to changing evaporation is an important issue for earth system science. Suggested reasons for variations in E and Q include changes in precipitation (Zhang et al. 2007), the impact of global brightening/dimming on available energy (Roderick and Farquhar 2002; Wild et al. 2008, 2005), the coupled changes in photosynthesis and surface conductance due to enhanced greenhouse gas concentrations (Gedney et al. 2006), decreases in soil moisture content (Jung et al. 2010), and changes in land use or land cover (Piao et al. 2007). To identify possible causes for changes in E, Jung et al. (2010) used the model-tree ensemble (MTE) algorithm of Jung et al. (2009) to calculate monthly evaporation rates (EMTE) for the global land surface from 1982 to 2008. The MTE is a machine-learning algorithm trained using evaporation measurements from the global Flux Network (FLUXNET) database, gridded global meteorological data, and remotely sensed fraction of absorbed photosynthetically active radiation. According to this algorithm, global average EMTE increased by 0.71 ± 0.1 mm yr−2 from 1982 to 1997, but with a slight decreasing trend in EMTE in the following decade. An ensemble of outputs from nine independent models gave similar results, and Jung et al. (2010) attributed the reduction in EMTE in the past decade to declining soil water availability (i.e., precipitation), particularly across Africa and Australia where microwave remote sensing–based soil moisture data showed negative trends. This paper complements the work of Jung et al. (2010) by comparing four different approaches to estimating global and regional trends in evaporation from 1983 to 2006: 1) using the water balances of large, unregulated catchments ; 2) through the model-tree ensemble approach of Jung et al. (2010) (EMTE); 3) application of a classical “Budyko” hydrometeorological model (Fu 1981); and 4) through an energy-balance model that utilizes gridded meteorological data and remotely sensed radiation and leaf area index data (Leuning et al. 2008). The energy-balance approach is particularly useful for assessing whether trends in E can be explained by key biological and meteorological variables other than precipitation.
2. Modeling and estimation approaches
We first clarify our notation before introducing the estimation approaches used. Variables EMTE, EPML, P, and Q represent monthly or annual values, while , , , , , and indicate 5- or 23-yr (1983–2006) averages. Trends in all of the variables are for 5-yr running averages or 3-yr block averages.
a. Catchment water balances
Annual evaporation rates were calculated from the water balances of unregulated catchments using
Over the long term, the change in water storage is assumed to be negligible in unregulated catchments, allowing this term to be neglected when estimating (Zhang et al. 2001). Use of Eq. (1) also assumes precipitation is the only source of water in the catchment and evaporation the only loss; that is, no water is gained or lost via interbasin transfers (a leaky catchment; Le Moine et al. 2007) or via deep groundwater.
b. “Budyko-curve” hydrometeorological model
In this paper we use the form of the Budyko model given by Fu (1981):
in which ω is a parameter and is the mean annual potential evaporation calculated by summing daily potential evaporation:
and where αPT = 1.26 (Priestley and Taylor 1972). Here Ai is the available energy for each 24-h day, λ is the latent heat of evaporation, and ɛ = s/γ, in which γ is the psychrometric constant and s = de*/dT—the slope of the curve relating saturation water vapor pressure to temperature. A single value, ω = 2.48, was used in Eq. (2) for all catchments globally. Its value was calibrated using water balances of gauged, unregulated catchments, averaged over the period 1983–2006 (Zhang et al. 2010).
c. Penman–Monteith combination equation
where As = τAi and Ac = (1 − τ)Ai are the flux density of available energy absorbed each day by the soil and canopy, respectively; τ = exp(−kALai); Lai is leaf area index; kA is the extinction coefficient for net radiation; ρ the density of air; and cp the specific heat of air at constant pressure.
Term 1 on the right is used to estimate evaporation from the soil by multiplying the equilibrium evaporation rate at the soil surface, ɛAs/(1 + ɛ), by a coefficient f that varies from f = 1 when the soil surface is wet to f = 0 when it is dry. In this paper we follow Zhang et al. (2010) in calculating the temporal variation of f as a function of precipitation and equilibrium evaporation rates for one month before and after the current 1-month time step.
Term 2 describes evaporation from the plant canopy. It is a function of Ac; Da, the water vapor pressure deficit of the air at a reference height above the canopy; and Ga, the aerodynamic conductance. In addition to these meteorological variables, calculation of canopy evaporation requires knowledge of the canopy conductance Gc. This biophysical variable was estimated using the following simple model (Isaac et al. 2004; Leuning et al. 2008):
where gsx is the apparent maximum stomatal conductance of leaves at the top of the canopy, kQ is the extinction coefficient for visible radiation, and Qh is the average flux density of visible radiation at the top of the canopy. The parameters Q50 and D50 are the values of Qh and Da, respectively, at which stomatal conductance is half its maximum value. The canopy conductance Gc varies with Qh and Da on all time scales and with Lai at seasonal time scales. Equation (5) contains no explicit dependence of Gc on soil moisture because we wish to apply Eqs. (4) and (5) using remotely sensed and gridded meteorological data only. While this is a deficiency in the model, Gc does depend indirectly on long-term variation in soil water availability through the landscape-scale adjustment of Da and Lai—the so-called “ecological equilibrium” concept.
Four of the five parameters in Eqs. (4) and (5) [called the Penman-Monteith-Leuning (PML) model] were assigned constant values (kQ = kA = 0.6, Q50 = 30 W m−2, and D50 = 0.7 kPa; Leuning et al. 2008). Following Zhang et al. (2010), the magnitude of the fifth parameter gsx was estimated separately for each 0.5° land surface pixel used in our analysis by adjusting gsx to force agreement between the 23-yr averages of and for that pixel. Note, this does not force the trends (first time derivative) in and to be the same over the averaging period. An advantage of EPML is that it can be evaluated at fine temporal resolution and it allows us to examine the relative importance of key variables other than A that control evaporation, namely Da, Ga, Lai, and f. The advantage of is that it explicitly includes precipitation as an input variable, whereas only uses P in calculating the soil wetness variable f.
We used the above equations to estimate and gsx and, thence, monthly EPML of land surfaces at a 0.5° resolution globally for the period 1983–2006. The results were used to assess whether trends in calculated from catchment water balances are consistent with 1) trends in due to variation in A and P; 2) with trends in resulting from those in A, Da, Ga, Lai, and f; or 3) with trends in derived by Jung et al. (2010).
3. Data and methods
To calculate monthly EPML we used monthly meteorological fields of daytime average air temperature and humidity to calculate Da and Ga, while Ac, As, and Qh were calculated using average incoming solar radiation, combined with remotely sensed estimates of Lai and surface albedo.
Global data fields of vapor pressure and temperature [time series (TS) 3.0] at 0.5° resolution came from the Climate Research Unit (New et al. 2000). Leaf area index and land cover type data at ~8-km resolution were obtained from Boston University (Ganguly et al. 2008a,b). Two precipitation datasets were examined—one from the Global Precipitation Climatology Project (GPCP, version 2; Adler et al. 2003) at 2.5° resolution, the other from the Global Precipitation Climatology Centre (GPCC, version 4; Rudolf and Schneider 2004) at 0.5° resolution. There was little difference between the two datasets at a common resolution of 2.5° (not shown), so the 0.5° GPCC dataset was used in the subsequent analyses.
Three global radiation products were used to calculate and EPML: 1) net short- and longwave radiation from the International Satellite Cloud Climatology Project (ISCCP) dataset (2.5° resolution; Zhang et al. 2004), 2) the Global Energy and Water Cycle Experiment Surface Radiation Budget products (SRB) at a 1.0° resolution (Gupta et al. 2006), and 3) the National Centers for Environmental Prediction (NCEP) and the National Center for Atmospheric Research (NCAR) reanalysis data (referred to as NCEP data) (Kalnay et al. 1996). All datasets were resampled to 0.5° spatial resolution. There are considerable differences in the annual global means and trends in available energy derived from the three datasets and we examine later the consequences of these differences for EFu and EPML (in Fig. 7 and Table 3).
Catchment water balances were calculated for 197 unregulated catchments over the hydrological year, defined as October–September to minimize effects of snowfall on yearly water balances (Dai et al. 2009). Selected catchments have an area >500 km2 and missing daily streamflow data are less than 5% of the total. Streamflow data were from several sources: 1) 55 monthly series from the 925 gauges of Dai et al. (2009), 2) 53 daily series from the Global Runoff Data Centre streamflow database (http://www.bafg.de/GRDC/EN/Home/homepage__node.html), and 3) 88 daily series from Australia. Catchment boundaries were respectively delineated by 1) the Simulated Topological Network (STP-30p; Vorosmarty et al. 2000), 2) the HYDRO1k digital elevation model (DEM; Peel et al. 2010), and 3) the Australian GEODATA 9-s digital elevation model (Hutchinson 2002). Regulated catchments were identified from the 1) International Commission of Large Dams (Vorosmarty et al. 2003), 2) Meridian World Data (http://www.meridianworlddata.com/), and 3) National Land and Water Resources Audit of Australia (http://www.nlwra.gov.au/). It is noted that even in unregulated catchments, there may be changes in streamflow because the land is experiencing change draws of water for irrigation, flood control engineering, land use change, wetlands loss, etc. Such changes do not affect our analysis provided precipitation, evaporation, and runoff occur within the same catchment.
Trends in , , EMTE (or ), EPML (or ), and their inputs were calculated using the Mann–Kendall tau-b nonparametric technique including Sen’s slope method (Sen 1968). This trend test is widely used in hydrology (Burn and Hag Elnur 2002). To minimize the effect of changes in interannual water storage on , the trend test was applied to 5-yr moving averages for P and Q (Teuling et al. 2009). We recognize that a moving average increases the serial correlation (autocorrelation) of a data series. A prewhitening procedure, developed by Yue et al. (2002), was applied to each moving average series to eliminate the effect of serial correlation prior to applying the Mann–Kendall trend test in order to satisfy the test assumption of data independence. In addition, the data were also analyzed using 3-yr block averages (there are eight points for 23-yr time series) to check the consistency of the conclusions from the trends obtained using the 5-yr moving averages.
Before examining trends in evaporation rates predicted by the methods described above, we first compare mean annual evaporation for 1983–2006 for the global land surface for “wet” pixels, where the aridity index , and “dry” pixels, where AI > 1.5 (Table 1 and Fig. 1). Average global land surface evaporation estimated using the MTE approach of Jung et al. (2010) is , while Mueller et al. (2011) reported a value of 45.3 ± 5.7 W m−2 (572.4 ± 68.4 mm yr−1) from an analysis of 40 global evaporation datasets. Using the ISCCP radiation data, we estimated , which is a difference of ±4% relative to the mean of the two, and and differ by ±6% for wet pixels and only ±2% for dry pixels. The two approaches give similar values for the annual average volume of water evaporated globally, and both are in excellent agreement with estimates given by Oki and Kanae (2006). The average of these three estimates is 11% less than that of Trenberth et al. (2007).
Time series of anomalies in annual EMTE and EPML relative to their respective means are shown in Fig. 2 for the global land surface and for wet and dry pixels. We see that interannual variation in EPML is greater than for EMTE in all three panels and that the variation in EPML is greatest for wet pixels. There is a statistically significant increasing trend in the evaporation anomalies for all three classes (p < 0.01), but the slope of 1.088 mm yr−1 in the global trend for annual EPML is almost double that of 0.528 mm yr−1 for EMTE. Trends predicted using annual EPML are also double those from EMTE for wet and dry catchments.
Patterns of 23-yr average evaporation rates across the global land surface are very similar to those for (Fig. 3), with both models giving high rates in tropical and wet regions such as in the Amazon and Congo basins and low evaporation rates in arid and high-latitude regions, such as in central Australia and Siberia. We note that is not available for the Sahara Desert and Greenland. There is a high degree of spatial correlation between and : r = 0.90 for wet pixels and r = 0.81 for dry pixels. Note that the average patterns of and are identical for reasons explained in section 2c.
While there is good agreement between the global patterns in and averaged over the 23-yr study period, this is not the case for the trends in evaporation from wet catchments as calculated using the two approaches (Table 2). There is essentially no correlation between trends in and those in and a correlation coefficient of only 0.32 for versus (Table 2). A better relationship amongst the three is found for dry catchments, where the correlation coefficient is ~0.5 for versus or , and ~0.6 for versus .
Figures 4a–d show global maps of average trends in , , and for each 0.5° land surface pixel and Figs. 4e–h show maps of the corresponding probability (p) values for statistical significance. Estimated trends in are a positive 2–6 mm yr−1 across equatorial Africa, India, and northwest Australia with p < 0.05, but they are quite small across the rest of the globe. In contrast, and show increasing and decreasing trends across different regions. Both suggest significant (p = 0.05) decreasing trends in the southwestern United States, the Himalayas, and parts of Africa and South America, with increasing trends for equatorial Africa, northwest Australia, and the northeastern United States. It is very difficult to validate these trend estimates using because of the small number of unregulated catchments that still remain across the globe. Trends indicated by and in northern Australia, northwestern Canada, and eastern Siberia are similar to trends in for those regions, but catchment water balances indicate negative trends in for subequatorial Africa and northeastern Brazil, opposite to those in and . The trend in is not significant (p > 0.1) in the Amazon basin, whereas shows a mixture of positive and negative trends and suggests positive trends (Fig. 4).
Global maps of trends in the key drivers of evaporation—precipitation , available energy A, humidity deficit D, and leaf area index Lai—are shown in Fig. 5. Most striking is the strong positive trend in remotely sensed available energy (ISCCP forcing) in the central United States and in much of the Southern Hemisphere, especially in Brazil and central Africa. These are generally accompanied by strong negative trends in , small decreasing trends in D, and increasing Lai, whereas the positive trend in A for the northwest of Australia is associated with an increase in and a decrease in D. Sensitivity analyses showed that trends in D and Lai observed in Fig. 5 do not explain the trends in seen in Fig. 4 (data not shown). Instead, precipitation mainly controls evaporation in dry catchments , whereas evaporation from wet catchments (AI ≤ 1.5) is largely determined by available energy. This is consistent with (Fisher et al. 2009), who found that A accounts for 87% of the variance in E measured at 31 flux stations in Amazonia.
Values of and EPML (or ) presented thus far were calculated using ISCCP radiation data, but the SRB and NCEP global radiation datasets were also available for analysis (section 3). We note that radiation data are not used to calculate EMTE, which is estimated using evaporation measurements from the global FLUXNET database, gridded global meteorological data, and remotely sensed fraction of absorbed photosynthetically active radiation (Jung et al. 2010). In Fig. 6 we compare maps of trends in available energy constructed using the three datasets and in Fig. 7 we examine the effects of alternative estimates of available energy on the calculated trends in annual EPML (note that is only available at a mean annual scale). Figure 6 shows that there are clear differences in the magnitudes, sign, and patterns between the three datasets, with ISCCP and SRB showing positive trends in A over South America and Africa that are not apparent in the NCEP dataset. The SRB dataset shows strong negative trends in A over Asia but such trends are not seen in the other two radiation products. These differences can be seen more quantitatively when the radiation data are applied to the 110 wet catchments used in this study. Substantial differences in mean trends in annual available energy are calculated using the ISCCP, SRB, and NCEP data: 8.95, 4.74, and −3.11 MJ m−2 yr−2, respectively (Fig. 7a). When these radiation datasets are used with the PML model, the corresponding mean trends in annual EPML are 1.65, 1.52, and 0.28 mm yr−1 (Fig. 7b). Note that the offset in A between the ISCCP and SRB datasets does not appear in the trends in EPML because annual EPML is constrained by the Fu (1981) hydrometeorological model using each radiation dataset independently (section 2). The negative trend in A seen in the NCEP dataset is not apparent in the trend in EPML because of compensating trends in the other variables affecting EPML.
The results presented in Figs. 1–7 are for pixels across the global land surface. In Figs. 8 and 9, trend analysis is conducted for 110 unregulated wet and 87 dry catchments for which we calculated . Figure 8 shows there is no correlation between trends in and and weak but significant correlation between and or at p = 0.1 for wet catchments. Correlations between and , , and are all significant at p = 0.001 for dry catchments but the regression slope for the MTE method and the PML model are much less than unity. Only the Fu model results in a desired linear regression slope close to one and a high R2 value. This is because precipitation appears explicitly in the Fu model [Eq. (2)] and because in dry catchments trends in are highly correlated to those in P (Fig. 9b). The inclusion of P in the Fu model clearly improves predictions of trends in E for dry catchments where , but not for wet catchments where there is only a weak correlation between trends in and (Fig. 9a).
Trends in and for the 197 catchments were also calculated using the SRB and NCEP available energy data. Table 3 shows statistics comparing trends in and with those in . Although the ISCCP product has the coarsest spatial resolution (2.5°) amongst the three, the trends in and estimated by the ISCCP product have the best linear correlation to those in (Table 3). This is highlighted in wet catchments where both trends in and forced by the ISCCP data are significantly correlated (p = 0.053) to those in , but not for the trends obtained from the other two. In dry catchments, trends in forced by the ISCCP data have the highest R2 values while those for trends in forced by the three radiation products are almost the same.
The results shown in Figs. 8 and 9 may be biased because they were obtained from 5-yr moving averages, which can increase the serial correlation in the data. However, recalculation of the trends in , , , and using 3-yr block averages yielded similar results (data not shown); that is, weak but significant correlation between and and but not between and in wet catchments, and strong correlation in dry catchments.
The values of used above rely on data from a range of catchment sizes. Small-area catchments typically cover one to several of the 0.5° pixels of the GPCC precipitation data, and combining these with local runoff measurements could inflate trends in (i.e., ) compared to larger catchments. To examine whether this adversely affects the results shown in Fig. 8, we identified 107 small-area catchments (500–5000 km2) and 90 large-area catchments (>5000 km2). Results from the two groups (not shown) are similar to those shown in Fig. 8—that is, trends in compare well to those in , , and in dry catchments, but not in wet catchments. Yang et al. (2007) also found that catchment area did not change the relationship between and for 108 catchments in China with areas varying from 200 to 100 000 km2.
Our analysis has shown that decadal trends in evaporation calculated using water balances, of 110 wet catchments are not matched by trends in . This model-tree ensemble approach of Jung et al. (2010) uses statistical relationships between evaporation rates measured at 253 globally distributed flux stations and meteorological drivers, including remotely sensed fraction of photosynthetically active radiation. Similarly in wet catchments there are only weak correlation between trends in and , a hydrometeorological model, and between and , which is calculated using the Penman–Monteith energy-balance equation coupled with a simple biophysical model for surface conductance. The lack of correlation between and any of , , or may be due to uncertainties in caused by errors in runoff and precipitation data for the selected catchments. Catchment runoff data are measured directly and hence are considered the most reliable in this study. Errors in precipitation can be quite large in regions where spatial interpolation is based on a sparse network of rain gauges (Oki et al. 1999). Such uncertainties are unlikely to explain the lack of correlation because identical conclusions are reached using two global precipitation datasets [GPCC: 0.5° grid cells (Rudolf and Schneider 2004) or GPCP: 2.5° resolution (Adler et al. 2003)]. A mismatch in scale between runoff and precipitation data may contribute to large trend values in (>±10 mm yr−1) in relatively small catchments (<50 000 km2).
We note that remotely sensed radiation is a key input to the two structurally different diagnostic models (EPML and EFu) and thus the lack of correlation between trends in these quantities and for wet catchments seen in Fig. 8 may result from uncertainties in magnitudes and trends in available energy. Evidence for this is seen in Fig. 6 where trends in A calculated using two remotely sensed radiation (ISCCP and SRB) datasets and one global forecast model data product (NCEP) result in quite different patterns globally and for the catchments analyzed in this paper (Fig. 7). These results suggest that radiation data derived from satellites may not yet be sufficiently accurate to explain trends in evaporation at global and regional scales over the past quarter century.
Model structural limitations as well as errors in input data may be responsible for the discrepancies in trends in compared to those in , , or . In a multimodel comparison study, Mueller et al. (2011) found that simple diagnostic models as used in this study provided means and standard deviations of E in global datasets that were similar to estimates from more complex land surface models and reanalysis datasets. All models yielded uncertainties that exceeded 20% of mean evaporation fluxes in most regions of the globe, and Mueller et al. (2011) concluded that further collections of “ground truth” observations are needed to constrain model estimates of evaporation. Given such uncertainties in the fluxes themselves, it is perhaps not surprising that we are unable to reconcile trends in land surface evaporation from water balance studies with those from models using the currently available forcing data.
Improvements are needed in global datasets of precipitation, runoff, radiation, and meteorological forcing before we can be confident in model estimates of the magnitude and sign of trends in evaporation from land surfaces. Effective combination of precipitation and soil moisture information with satellite radiation and vegetation data will undoubtedly improve estimation of trends in global E by hydrological models in the future.
Aiguo Dai provided monthly streamflow data for the 925 global river basins, and the Global Runoff Data Centre, Koblen, Germany provided daily streamflow data for 107 gauges. We thank Dr. Chris Smith, Dr. Michael Roderick, and two anonymous reviewers for their helpful comments.