Evapotranspiration (ET) is highly variable in space and time and plays a fundamental role in hydrology and land–atmosphere interactions. Over the past few decades, the use of satellite data to map regional-scale ET has advanced considerably. This is due to the advancements in ET modeling as well as progress in thermal remote sensing satellite missions, and our ability to retrieve the land surface temperature (LST) or radiometric surface temperature (TR) that is highly sensitive to evaporative cooling and surface moisture variations. Because LST governs the land surface energy budget (Kustas and Norman, 1996; Kustas and Anderson, 2009), thermal ET models principally focus on the surface energy balance (SEB) approach in which TR represents the lower boundary condition to constrain energy–water fluxes (Anderson et al., 2012). Contemporary SEB models emphasize estimating aerodynamic conductance (gA) and sensible heat flux (H) while solving ET (i.e., latent heat flux, λE) as a residual SEB component. Despite many advancements in mapping spatially distributed ET, some fundamental challenges remain in existing SEB algorithms including (a) the inequality between TR and the aerodynamic temperature (T0), which is essentially responsible for the exchanges of H and λE (Chávez et al., 2010; Boulet et al., 2012); (b) a non-unique relationship between T0 and TR due to differences between the roughness lengths (i.e., effective source/sink heights) for momentum (z0M) and heat (z0H) within vegetation canopy and substrate complex (Troufleau et al., 1997; Paul et al., 2014; van Dijk et al., 2015b); (c) the unavailability of a universally agreed model to estimate T0 (Colaizzi et al., 2004); and (d) the lack of a physically based or analytical gA model. To overcome these challenges, we implement the current version of a recently developed analytical ET model, the Surface Temperature Initiated Closure (STIC, version 1.2; Mallick et al., 2014, 2015, 2016), using the Moderate Resolution Imaging Spectroradiometer (MODIS) data to develop spatially distributed ET maps.

In state-of-the-art SEB models, an emphasis on estimating gA and H is laid due to the perception of the broad applicability of the Monin–Obukhov similarity theory (MOST) or Richardson number (Ri) criteria, and the requirement of minimum inputs for determining these variables. However, these approaches created additional uncertainties, particularly in accommodating T0 vs. TR inequalities, as well as adapting the differences between z0M and z0H (Paul et al., 2014). Compensating these temperature and roughness length disparities consequently led to the inception of the kB-1 term as a fitting parameter (Verhoef et al., 1997a), and later the progress of the two-source ET model (Kustas and Norman, 1997; Norman et al., 1995; Anderson et al., 2011). Although useful, the above approaches still rely on empirical response functions of roughness components to characterize gA that has an uncertain transferability in space and time (Holwerda et al., 2012; van Dijk et al., 2015b). In contemporary SEB modeling, gA sub-models are stand-alone and lack the necessary physical feedbacks between the conductances, T0, and vapor pressure deficit surrounding the evaporating surface (D0). The feedback of gA on gC and D0 is critical in semiarid and arid ecosystems (Kustas et al., 2016), where soil moisture stress and sparse vegetation can cause substantial disparities between TR and T0 (Kustas et al., 2016; Paul et al., 2014; Timmermans et al., 2013; Gokmen et al., 2012). Therefore, thermal-based ET modeling needs explicit consideration of these important biophysical feedbacks to overcome the existing gA and T0 uncertainties in regional-scale ET mapping (Kustas et al., 2016). Hence, a genuine question in regional ET mapping is the following: how can state-of-the-art SEB models overcome the existing challenges in regional evapotranspiration mapping that arise due to uncertain conductance parameterizations, and can analytical models help this verification process?

The STIC formulation provides analytical solutions to gA, T0, and canopy (or surface) conductance (gC), and simultaneously captures the critical feedbacks between gA,gC, T0, and vapor pressure deficit surrounding the evaporating surface (D0) thereby obtaining a “closure” of the SEB . The prime focus of STIC (Mallick et al., 2014, 2015, 2016) is based on physical integration of TR into the Penman–Monteith (PM) equation, which is fundamentally constrained to account for the necessary feedbacks between ET, TR, DA, gA, and gC (Monteith, 1965). Monteith (1981) highlighted the fact that the biophysical conductances (i.e., gA and gC) regulating ET are heavily temperature dependent, after which a stream of research demonstrated the dominant control of TR on gC and associated canopy-scale aerodynamics (Moffett and Gorelick, 2012; Blonquist et al., 2009). Somewhat surprisingly, the idea of integrating TR into the PM model was never attempted because of complexities associated with gC parameterization (Bell et al., 2015; Matheny et al., 2014), until the concept of STIC was formulated (Mallick et al., 2014, 2015). The recent version of STIC, STIC1.2, combines PM with the Shuttleworth–Wallace (SW) model (Shuttleworth and Wallace, 1985) to estimate the source/sink height temperature and vapor pressure (T0 and e0; Mallick et al., 2016). By algebraic reorganization of aerodynamic equations of H and λE, Bowen ratio evaporative fraction hypothesis (Bowen, 1926) and modified advection-aridity hypothesis (Brutsaert and Stricker, 1979), STIC1.2 formulates multiple state equations where the state equations were constrained with an aggregated moisture availability factor (M). Through physically linking M with TR and the source/sink height dew point temperature (TSD), STIC1.2 established a direct feedback between TR and ET, while simultaneously overcoming the empirical uncertainties in conductances and T0 estimations.

Despite providing analytical solutions for the key conductances in PM-based ET modeling, the STIC1.2 model has yet to gain a profound interest among the thermal remote sensing community and those interested in regional-scale ET modeling. This could largely be attributed to the fact that the model is only used for understanding ecosystem-scale ET partitioning and their biophysical controls at the eddy covariance (EC) footprints (Mallick et al., 2015, 2016), where all the necessary forcing variables were measured at the flux tower sites. In this paper, we present the first ever implementation of the STIC1.2 model using MODIS LST and associated land surface products, and its validation in 13 core AmeriFlux sites across an aridity gradient in the conterminous US in three different precipitation conditions representing dry, normal, and wet years. ET estimates from STIC1.2 are also compared against two parametric ET models, namely SEBS (Surface Energy Balance System; Su, 2002) and MOD16 (Mu et al., 2007, 2011). Through the implementation and validation of the STIC1.2 model at a regional-scale, the current study addresses the following research questions:

What is the performance of STIC1.2 when applied at the regional-scale across an aridity gradient and during contrasting rainfall years in the conterminous US?

Overall, STIC1.2 performed reasonably well across an aridity gradient and a wide range of biomes in the conterminous US. One noticeable weakness of STIC1.2 appears to be its tendency to underestimate ET in grassland and cropland land cover types (Figs. 4 and 5). These biases could be attributed to the nature of the MODIS LST product that aggregates sub-grid heterogeneity in TR, vegetation cover, and radiation at 1 km  × 1 km area. Due to the relatively low tower heights in CRO and GRA sites (3–10 m), the EC towers aggregate fluxes at scales of approximately 0.009–0.10 km2. Such a critical mismatch of the scales between MODIS pixels and the flux tower footprint could be a potential source of disagreement between STIC1.2 and tower-observed ET (Stoy et al., 2013). Another source of error could be the presence of widely varied dry and wet patches within one MODIS 1 km × 1 km pixel as well as around the flux towers. For example, if more than 50 % of the area falling within a 1 km × 1 km MODIS pixel is predominantly dry, the lumped TR signal in MODIS LST product will be biased due to the dryness of the landscape (Stoy et al., 2013; Mallick et al., 2014, 2015) and the resultant ET will be underestimated. The overestimation tendency in WSA is mainly due to the poor performance of STIC1.2 in the Tonzi Ranch site (US-Ton), which could be associated with the uncertainties in surface emissivity correction and systematic underestimation of MODIS LST in arid and semiarid ecosystems (Wan and Li, 2008; Jin and Liang, 2006; Hulley et al., 2012). Since TR plays an important role in constraining the conductances in STIC1.2, an underestimation of TR would result in an overestimation of gC and underestimation of gA, which would result in overestimation of ET. The differences between STIC1.2 vs. observed ET in WSA may also largely be attributed to the Bowen ratio energy balance closure correction of EC λE observations (Chávez et al., 2005; Twine et al., 2000). Although the Bowen ratio correction forces SEB closure, in arid and semiarid ecosystems major corrections are generally observed in sensible heat flux, whereas λE is negligibly corrected (Chávez et al., 2005; Mallick et al., 2018). Besides, direct water vapor adsorption on the land surface occurs in arid and semiarid ecosystems when air close to the surface is drier than the overlying air (McHugh et al., 2015; Agam and Berliner, 2006), and this source of moisture is unaccounted for in the EC measurements. This will automatically result in a disagreement between STIC1.2 and observed ET. Nevertheless, the performance of STIC1.2 in forest ecosystems is encouraging, given the uncertainties associated with more complex SEB models that use MOST to parameterize the turbulent mixing in tall canopies (Finnigan et al., 2009; Garratt, 1978; Harman and Finnigan, 2007) that could induce substantial biases in estimated fluxes (Wagle et al., 2017; Numata et al., 2017; Bhattarai et al., 2016).

The overall performance metrics from the three models may be slightly biased due to their strikingly poor performances at some specific sites (Table S1). For example, although SEBS overestimated ET by over 64 % in the two semiarid WSA (US-Ton, US-SRM) and GRA (US-SRG and US-Wkg) sites (Table S1), its performance in US-Ne1 (CRO), two wet grasslands (US-Kon and US-KFS), and US-NR1 (ENF) were better or comparable than the other two models. This could be due to the inability of the kB-1 parameterization scheme in SEBS to account for the substantial differences between TR and T0 due to strong soil water limitations. MOD16 underestimated ET from all but three sites (US-Ton, US-MMS, US-NC1) and underestimated mean ET by over 50 % in US-Ne1 (CRO), US-SRM (WSA), US-SRG (GRA), and US-Wkg (GRA) sites. STIC1.2 appears to be relatively consistent among the three models, as the mean bias errors were within 20 % for all but three sites (US-Ton, US-Kon, US-Ne1).

Performance intercomparison of STIC1.2 with SEBS and MOD16 indicated overall low statistical errors for STIC1.2, and better agreement than SEBS and MOD16 with observed ET values. The principal differences between STIC1.2 and SEBS (as evident from Figs. 7a and 8–13), in particular the overestimation of ET through SEBS, is in cases of high TR and DA with low vegetation cover (i.e., low NDVI), a characteristic feature of arid and semiarid ecosystems. In these water-limited ecosystems, TR induced water stress and the diminishing ET rate leads to high atmospheric dryness (i.e., high DA), increased evaporative potential, and very high sensible heat flux. This leads to substantial differences between TR and T0, and the role of radiometric roughness length (z0H) becomes critical, which is estimated empirically through the adjustment factor kB-1 (Paul et al., 2014). Although there is a first order dependence of kB-1 on TR, radiation, and meteorological variables (Verhoef et al., 1997a), no physical model of kB-1 is available (Paul et al., 2014). Therefore, uncertainties in kB-1 estimation are propagated into z0H. Overestimation (or underestimation) of z0H would lead to underestimation (overestimation) of gA in SEBS, which is mirrored in ET differences between SEBS vs. observations (dETSEBS-obs; Zhou et al., 2012). This is also evident when a logarithmic pattern was found between dETSEBS-obs and kB-1, with a correlation of 0.39 (p-value < 0.005; Fig. 13a). Major ET differences were found (±20 mm) within a kB-1 range of 2–6 (arid, semiarid, heterogeneous vegetation), whereas ET differences were diminished within ±10 mm above kB-1 of 6 (subhumid, humid, homogeneous vegetation). Apart from z0H, empirical parameterization of z0M and a resultant ±50 % uncertainties in z0M can also lead to 25 % errors in gA estimation (Liu et al., 2007; Verhoef et al., 1997a), which will lead to more than 30 % uncertainty in ET estimates. This is also evident from the exponential scatter between z0M and dETSEBS-obs (Fig. 13b) that showed a significant negative correlation between z0M and the residual ET error (r = -0.40, p-value < 0.005).

It is important to emphasize that the momentum transfer equation for estimating gA in SEBS is based on the semi-empirical MOST approach that mainly holds for extended, uniform, and flat surfaces (Foken, 2006; Verhoef et al., 1997b). MOST tends to become uncertain on rough surfaces due to a breakdown of the similarity relationships for heat and water vapor transfer in the roughness sub-layer, which results in an underestimation of the “true” gA by a factor of 1–3 (Holwerda et al., 2012; van Dijk et al., 2015a; Simpson et al., 1998). Since gA is the main anchor in SEBS, an underestimation of gA would lead to an underestimation of sensible heat flux and an overestimation of ET (Gokmen et al., 2012; Paul et al., 2014). Also, due to the priority of estimating gA and H, SEBS appears to ignore the important feedbacks between gC, DA, ϕ, and transpiration (which are included in STIC1.2), which consequently led to differences between STIC1.2 and SEBS. Relatively better performance of SEBS at croplands, as well as in wet years could be attributed to the ability of the model to perform well in predominantly homogeneous vegetation and under wet conditions where the differences between TR and T0 are not critical. The overestimation tendency of ET by SEBS was predominant during the dry year (Figs. 4 and S2). Notably, SEBS ET estimates were within 3, 8, and 17 % of observed ET in the CRO, ENF, and DBF sites, respectively, which were comparable or sometimes better than the other two models (Fig. 5 and Table S1). In addition, the performance of SEBS was relatively good in cropland (Fig. 5). Overestimation of ET from SEBS is mostly associated with the underestimation of sensible heat flux (H) in the arid and semiarid sites (nearly 41 % underestimation in this study). Such underestimation of H by SEBS is highlighted by Chen et al. (2013), who proposed an improved way of estimating roughness length for heat transfer through a new parameterization of kB-1 adopted from Yang et al. (2002) for bare soil and snow surfaces. This could be the main reason for the better performance of SEBSChen ET product (Fig. 12) than the other models. STIC1.2 ET estimates compared well against those from SEBSChen (R2 = 0.81 and 0.58, at monthly and annual scales) than the version of SEBS used in this study (Fig. 14). This comparison and better performance of SEBSChen demonstrated that improved kB-1 parameterization and better characterization of surface roughness are key to improve SEBS accuracies, typically in the arid and semiarid ecosystems. However, it is also important to emphasize that different meteorological forcing was used to generate annual ET in SEBSChen and an explicit comparison of STIC1.2 with SEBSChen with same meteorological forcing is beyond the scope of this study.

The wide use of the global MOD16 ET product for calculating regional water and energy balances should be evaluated on a case-by-case basis as one could come to different conclusions using ET outputs from the other two models considered in this study. A significant underestimation of actual ET by the MOD16 ET products, particularly in arid and semiarid conditions has already been reported (Hu et al., 2015; Ramoelo et al., 2014; Feng et al., 2012). Conversely, others have reported better performance of MOD16 ET products in humid climates (Hu et al., 2015) and forest ecosystems (Kim et al., 2012), consistent with the performance of the model in the two flux sites in North Carolina in our study (Table S1). Underestimation of ET by the MOD16 ET products in croplands has also been reported (Velpuri et al., 2013; Kim et al., 2012; Yang et al., 2015; Biggs et al., 2016), though not to the same extent as found in this study. Yang et al. (2015) highlighted four key uncertainties associated with the MOD16 algorithm (Mu et al., 2011), which could explain the relatively poor performance of MOD16 in this study. First, the dependency of the MOD16 algorithm on meteorological forcing (and not the TR) to account for the soil moisture restriction on evaporation and transpiration results in a slow response of variations in energy and heat fluxes (Long and Singh, 2010). Second, underestimation of transpiration in MOD16 could occur due to overestimation of environmental stresses on canopy conductance that is expressed as the potential canopy conductance multiplied by two empirical scaling factors that represent influences from TA and DA (Yang et al., 2013) Third, the empirical nature of the soil moisture constraint function (Fisher et al., 2008) based on the complementary hypothesis (Bouchet, 1963) using DA and RH leads to large uncertainties in evaporation from the unsaturated soil. Finally, the coarse resolution meteorological data (1∘ × 1.25∘) used in MOD16 may not be well representative of surfaces with high moisture variability. Additionally, the empirical scaling functions used for constraining the conductances and the spatial-scale mismatch between MODIS and flux towers could also introduce additional uncertainties in MOD16 ET. Similarly, our results suggest that caution should be taken when applying SEBS under the extreme dry condition, and also for grasslands, savannas, and deciduous broadleaf forests. The overestimation of grassland ET from SEBS is consistent with a recent study (Bhattarai et al., 2016), which could be attributed to the uncertain characterization of zOH (Gokmen et al., 2012). However, the performance of SEBS was relatively better under wet conditions, and in homogeneous croplands and evergreen needleleaf forests (Fig. 5, Table S1).

Apart from the simple parameterization of zOM and canopy heights using NDVI, another source of uncertainty in the implementation of STIC1.2 and SEBS at the 8-day timescale (using MOD11A2) could be the use of average 8-day daily time meteorological inputs that may not well correspond with LST observation days within each MODIS 8-day cycle. We found all 8-day daytime-averaged meteorological variables (those used in STIC1.2 and SEBS) except wind speed to be good representative of instantaneous measurements within the 8-day period (Table S2). This could be a source of additional uncertainty in SEBS since it uses wind speed to parameterize the aerodynamic conductance using MOST. Model implementation at an instantaneous timescale (i.e., MODIS overpass time and using daily MODIS products including MOD11A1 datasets) showed that the performance of STIC1.2 (R2 = 0.61, PBIAS = -5 %) was similar to its performance at the 8-day timescale. However, for SEBS (R2 = 0.53) the performance was marginally better with a PBIAS of 17 % (Table S3). In addition to the wind speed, the slight overestimation of 8-day average ϕ (PBIAS = 9 %), and variations in TR, TA, TR - TA, and other meteorological variables during days within the corresponding 8-day period could have added positive biases to SEBS (increase from 17 to 28 %), when evaluated at the 8-day timescale. Conversely, the overestimation in ϕ could have slightly reduced STIC1.2 biases (increase from -5 to -3 %). SEBS is sensitive to the meteorological input, especially the temperature gradient, and its performance is expected to degrade with the use of gridded forcing data (Ershadi et al., 2013; McCabe et al., 2016; van der Kwast et al., 2009; Vinukollu et al., 2011). Lewis et al. (2014) suggested that wind speed from NLDAS-2 may not be as reliable as other meteorological variables (TA and RH) in the western US. Overall, the application of STIC1.2 and SEBS at the instantaneous timescale showed similar predictive capacity and potential model strengths and weaknesses. STIC1.2 appears to be consistent through time, which could be due to the analytical nature, and STIC1.2 does not rely on wind speed to solve for gA and gC. Results also suggest that biases from SEBS could be within 20% if uncertainties associated with meteorological and radiative forcing are reduced.

This paper establishes the first ever regional-scale implementation of a simplified thermal remote-sensing-based model, Surface Temperature Initiated Closure (STIC1.2) for spatially explicit ET mapping, which is independent of any empirical parameterization of aerodynamic/surface conductances and aerodynamic temperature. By combining MODIS land surface temperature, surface reflectances, and gridded weather data, we demonstrate the promise of STIC1.2 to generate regional ET at 1 km × 1 km spatial resolution in the conterminous US. Independent validation of STIC1.2 using observed flux data from dry, wet, and normal precipitation years at 13 core AmeriFlux sites covering a wide range of climatic, biome, and aridity gradients in the US led us to the following conclusions. i.

Overall, STIC1.2 explained significant variability in the observed 8-day cumulative ET with a root mean square error (RMSE) of less than 1 mm day-1 and was robust throughout dry, wet, and normal years. Biome-wise evaluation of STIC1.2 suggests the smallest errors in forest ecosystems, followed by grassland, cropland, and woody savannas. Underestimation of ET in croplands is mainly attributed to the spatial-scale mismatch between a MODIS pixel and the flux tower footprint in croplands, and an overestimation of ET in woody savannas is mainly attributed to the large uncertainties in the MODIS LST product in savannas, and SEB closure correction of EC ET observations.