We developed a new method to estimate terrestrial evapotranspiration (ET) from satellite data without using meteorological inputs. By analyzing observations from 20 eddy covariance tower sites across continental North America, we found a strong relationship between monthly gross primary production (GPP) and ET (R2 = 0.72–0.97), implying the potential of using the remotely sensed GPP to invert ET. We therefore adopted the Temperature-Greenness model which calculates 16 day GPP using MODIS EVI and LST products to estimate GPP and then to calculate ET by dividing GPP with ecosystem water use efficiency (the ratio of GPP to ET). The proposed method estimated 16 day ET very well by comparison with tower-based measurements (R2 = 0.84, p < 0.001, n = 1290) and provided better ET estimates than the MODIS ET product. This suggests that routine estimation of ET from satellite remote sensing without using fine-resolution meteorological fields is possible and can be very useful for studying water and carbon cycles.
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 Land surface evapotranspiration (ET) is a key component of the water and energy balance over terrestrial ecosystems [Oki and Kanae, 2006]. Among many methods of ET quantification, satellite remote sensing has been shown to be one of the most promising ways of mapping ET over larger areas [e.g., Bastiaanssen et al., 1998; Norman et al., 1995]. Numerous models with varying structure and complexities have been developed to derive ET from remotely sensed variables (e.g., land surface temperature, LST, and vegetation index, VI) in combination with concurrent meteorological measurements (e.g., near surface air temperature and vapor pressure) [e.g., Bastiaanssen et al., 1998; Long and Singh, 2012; Lu and Zhuang, 2010; Norman et al., 1995; Su, 2002; Yang and Shang, 2013]. With increasing spatial and temporal resolutions of satellite images, meteorological inputs at sufficient temporal and spatial scales corresponding to those of satellite images are required but infrequently available. For example, the Moderate Resolution Imaging Spectroradiometer (MODIS) Global Terrestrial Evapotranspiration Product (MOD16) adopts Global Modeling and Assimilation Office meteorological data at 1° latitude × 1.25° longitude resolution and uses the version 4 0.05° Climate Modeling Grid albedo as a major model input [Mu et al., 2011]. This is much too coarse with respect to 1 km × 1 km MODIS pixel, and the mismatch in spatial resolution among the three input data sets is a key limitation of MOD16, especially for regions with strong climatic gradients.
 Although it would be possible to improve the spatial resolution of meteorological fields, it is worthwhile exploring methods to estimate ET only from remotely sensed information. This would substantially reduce the input effort and therefore increase the robustness of satellite-based ET models. The idea lies in use of some variables which are highly correlated with ET and have the potential to be estimated based entirely on remote sensing.
 ET consists of two components, evaporation (E) from the soil and transpiration (T) from the vegetation canopy. Because photosynthesis and transpiration are both biologically regulated by plant stomata and T generally dominates ET over vegetated surfaces, gross primary production (GPP) is considered valuable to infer ET over large areas only using satellite data [Beer et al., 2009; Zhang et al., 2009]. Existing studies have shown that use of remote sensing data solely can provide reasonable GPP estimates across a wide range of vegetation types [Rahman et al., 2005; Sims et al., 2008; Peng et al., 2013]. Moreover, the ratio of GPP to ET, known as the ecosystem water use efficiency (WUE), was found to be fairly constant over time for certain ecosystems [Beer et al., 2007; Beer et al., 2009; Law et al., 2002]. Therefore, once the among-site variability of WUE is well assessed, ET can be estimated from remotely sensed GPP. The objective of this study is to develop a method to estimate ET using remotely sensed GPP. ET estimates from the developed method were evaluated with eddy covariance measurements within the Ameriflux network.
2 Site, Data, and Methods
2.1 Flux Site Data
 Data from 20 sites within the Ameriflux network (http://public.ornl.gov/ameriflux) were used to develop and evaluate the new method (Table 1 and also see auxiliary material). These sites represent a wide diversity of bioclimate across North America. For each site, daily values of GPP and ET accumulated from half-hourly measurements of net ecosystem exchange and latent heat by eddy covariance systems were used. Data quantity control was described in publications listed in Table 1. Daily data were further summed up to obtain monthly GPP and ET values. Months with data gap longer than 3 days were discarded from this analysis. In addition to flux data, biological and ancillary data, such as leaf area index and soil texture, were also acquired.
Table 1. Descriptions of the Flux Sites in This Study, Including Site Identifier (Site ID), Plant Functional Type (PFT), Latitude (Lat, °N), Longitude (Lon,°oW), Data Period, Observed Water Use Efficiency (WUE) , Coefficient of Determination Between Observed Monthly GPP and Monthly ET (R2), and Reference
 To estimate GPP, two MODIS land surface products were used in this study (from the Oak Ridge National Laboratory's Distributed Active Archive Center, http://www.modis.ornl.gov/modis/), including Enhanced Vegetation Index (EVI) and LST. EVI was obtained from the 16 day Terra MODIS vegetation index product (MOD13Q1, 250 m), and LST was acquired from the 8 day LST and Emissivity product (MOD11A2, 1000 m). The LST data were averaged with two consecutive periods of the data in order to conform to the 16 day MODIS EVI data. Only EVI data with aerosol values listed as “low” and the “usefulness” values greater than 8 (on a scale of 0–10) and LST data marked as cloud free were used. Following Sims et al. , all data were extracted from 3 km × 3 km area centered on the flux tower.
2.3 Ecosystem Water Use Efficiency
 The coefficient of determination (R2) between monthly GPP and ET for the 20 sites ranges from 0.72 to 0.97 (Table 1 and also see auxiliary material), demonstrating that WUE of the ecosystem remains generally invariant at the monthly scale. Then, WUE for each site was calculated from
where n is the number of months with available data.
 Ecosystem WUE varies by a factor of ~3 among sites (Figure 1), which is mainly attributed to environmental gradients. Following Beer et al. , we regressed WUE to two stable environment properties (R2 = 0.82, p < 0.001, n = 20),
where a1 and a2 are regression coefficients (see auxiliary material), θF is volumetric soil water content at field capacity, and LAImax is the maximum leaf area index during the data period. In this study, θF was estimated to be the water content retained in the soil at −0.02 MPa of suction pressure, which is midway of most reported θF values (−0.01 to −0.033 MPa) [Haise et al., 1954; Lei et al., 1988]. The VG-M model [Van Genuchten, 1980] was adopted to describe the soil water retention curve, and the parameters of the VG-M model for each site were estimated from measured soil texture and bulk density using the method given by Schaap et al . The exponential function of LAImax in equation (2) corresponds to the fraction of absorbed sunlight in the photosynthetic active radiation (PAR) domain. kc is the extinction coefficient of radiation attenuation and is set to be 0.6.
 The leave-one-out cross validation is performed to test equation (2) (Figure 1). The estimated WUE agrees fairly well with observed ones (R2 = 0.80, p < 0.001, n = 20; see auxiliary material). These estimated WUE values were later used to invert ET in combination with remotely sensed GPP.
2.4 ET Estimation
 Since ecosystem WUE remains fairly invariant at the monthly scale, monthly ET can be calculated by dividing monthly GPP with WUE (i.e., ET = GPP/WUE). However, to be consistent with the temporal scale of the MODIS data, we calculated ET at a 16 day interval here by assuming that the 16 day WUE is also relatively constant. It is assumed that short-term (e.g., days and subdays) fluctuations in WUE can be effectively eliminated at the 16 day time scale.
 We chose the Temperature-Greenness (TG) model proposed by Sims et al.  to estimate 16 day GPP. It was successfully applied to estimate 16 day GPP for evergreen and deciduous forests in North America [Sims et al., 2008]. The TG model estimates GPP using a combination of MODIS LST and EVI products at the 16 day interval as
where m_TG is the coefficient which can be estimated as a function of annual mean nighttime LST [Sims et al., 2008]. Equation (4) indicates a zero GPP when EVI is smaller than 0.1, and equation (5) indicates that the value of R_LST changes linearly between 1 when LST is 30°C and 0 when LST is 0 °C or 50 °C.
3 Results and Discussion
 Overall, the proposed approach estimated 16 day ET reasonably well with reference to tower-based measurements (R2 = 0.84, p < 0.001, n = 1290). The root-mean-square error (RMSE) ranges from 0.16 to 0.72 mm/d and the mean relative error (MRE) are found between 0.6% and 38.6% (Table 1). The bias in ET estimation results mostly from errors in modeled WUE from equation (2). For example, at US_WCr, equation (2) underestimates WUE by 19.3%, which results in a 15.8% overestimation of ET. The residual bias may be explained by error in m_TG estimates.
 Larger scatters of the relationship between observed and estimated ET are found at the US_Me2 (R2 = 0.64, p = 0.001, n = 57) and US_Fuf sites (R2 = 0.68, p < 0.001, n = 44), which could be ascribed to the weaker relationship between GPP and ET (Table 2 and also see auxiliary material) and lower accuracy of the TG model in estimating GPP (Table 2). Because of the strong correlation between GPP and ET, the accuracy of ET estimates depends highly on that of GPP estimates. For the remaining sites, R2 between observed and estimated GPP by the TG model ranges from 0.74 to 0.96 and R2 between observed and estimated ET are all larger than 0.75 (p < 0.001). Besides the TG model, other remote sensing-based GPP models could also be used, e.g., the chlorophyll content model [Gitelson et al., 2006; Peng et al., 2013]. Wu et al.  evaluated the chlorophyll content model over 15 North American flux sites and reported that the model could provide good estimates of monthly GPP for both deciduous forest sites and nonforest sites with moderate results for evergreen forest sites.
Table 2. Summary of Statistics of Model Performance at Each Site
RMSE is the root mean square error (g C/m2/d for GPP and mm/d for ET); MRE is the mean relative error (%). Statistics of MOD16 are given in Mu et al. . Hyphen (–) denotes null value.
 Despite the overall good performance, the proposed method tends to underestimate ET at the lower end in all sites except for the grassland site (Figure 2 and also see auxiliary material). This is mainly due to the underestimation of soil evaporation (E) during nongrowing seasons. Theoretically GPP should be a better indicator of plant transpiration (T) than total ET [Beer et al., 2009]. However, T usually dominates ET, and the partitioning between E and T changes proportionally (depends mostly on surface vegetation conditions) during growing seasons, which may still result in a good GPP-ET relationship. Nevertheless, GPP and T decline toward zeros during nongrowing season, while E may still occur if temperature and water conditions permit. Although the nongrowing season is mainly defined by either low temperature or low soil moisture in natural ecosystems which implies only small E values, cautions should be paid when applying the method to cropland ecosystems where plant phenology and soil moisture conditions are profoundly impacted by human activities, e.g., irrigation.
 It is more encouraging to see that nearly all statistics at all sites for the proposed method show better performance than the MOD16 product (Table 2). In addition to MODIS 1 km land surface products, MOD16 uses other coarse resolution meteorological inputs and is essentially an interpolated and “pseudocontinuous” product, i.e., not truly per pixel [Rahman et al., 2005]. Performance of the MODIS ET algorithm could be largely improved when in situ meteorological measurements are used [Mu et al., 2011]. Another limitation in MOD16 is that the effects of soil moisture restriction on evaporation are generally reflected by meteorological forcing based on the complementary relationship, resulting in slower response of variations in energy and heat fluxes than the thermal infrared remote sensing-based ET models [Long and Singh, 2010]. If estimating integrated ET over longer time scales (e.g., half a month) is the main focus of studies and the MODIS ET algorithm underperforms in most cases, reliable estimates of ET based purely on satellite remote sensing demonstrated in this study should have greater robustness.
 In addition to the advantages in fewer inputs, the developed method circumvents up-scaling instantaneous ET estimates at satellite overpass time to daily values or longer time scales and therefore reduces possible uncertainties in extrapolating ET under clear-sky days over days without quality satellite images [Ryu et al., 2012]. MODIS 16 day EVI and 8 day LST data are used in the TG model to estimate GPP and subsequently ET. These multiday composite products are more routinely available than daily MODIS data (e.g., MODIS swath LST). Effects of cloud on ET estimation have been largely reduced because the composite 8 day LST product is mainly used to capture low temperatures (e.g., nongrowing season) and drought information over a half-month period in the TG model, and these phenomena do not change substantially between clear and cloudy days. This is an advantage over those models that incorporate instantaneous remotely sensed LST.
 However, there are also some limitations in the study: (1) only 20 sites were used to develop the method, which may be not sufficient to come to a robust relationship to map WUE at regional scales; (2) all sites used are located on continental North America, with most regions subject to temperate or boreal climate. To make the method an option for global ET estimation, more efforts will be needed to parameterize and validate the model over different bio-climates around the world; (3) validation of the developed method was performed only at tower scales. Validation of large-scale ET estimates from this approach can also be performed using water balance closure (e.g., Yang et al., 2012), and it is our ongoing work.
 This study developed a method to estimate terrestrial ecosystem ET from remote sensing by exploiting the linkage between water and carbon cycles. The major strength of this method is that it does not require meteorological input as used by other satellite-based ET models. This method is easy to apply, requiring only routinely available EVI and LST data at longer time scales (e.g., 16 days in MODIS products) to calculate GPP as well as the remotely sensed leaf area index and regional soil texture data set to estimate WUE. ET estimates from the proposed method compare reasonably well with flux tower measurements at all validation sites. Comparison with the MOD16 ET product shows that the developed method generally outperforms the MOD16 algorithm. Additional efforts will be made to improve the method under lower evaporation conditions (e.g., nongrowing season).
 We are grateful to the Oak Ridge National Laboratory for providing the tower flux data from AmeriFlux Network sites; all people involved in the field work are greatly appreciated. This work is financially supported by the National Natural Science Foundation of China (Grant Nos. 51279077 and 50939004) and the National Key Technology R&D Program of China (Grant No. 2011BAD25B05).