Thermal infrared (TIR) remote sensing of land surface temperature enables spatially distributed evapotranspiration rates to be calculated across vegetation canopies at various scales, according to the extent of the remote sensing data. Combination evapotranspiration models in the tradition of Penman–Monteith [Monteith, 1965] and two-source models after Shuttleworth and Wallace  are some of the most prevalent approaches to do so. Applied to remote sensing data, these models solve the surface energy balance and turbulent heat transport equations for each pixel in the TIR image. The TIR pixels often range from submeter scale [Jones et al., 2002; Loheide and Gorelick, 2005; Shimoda and Oikawa, 2008; this study] to subfield scale [e.g., Blonquist et al., 2009] to 60 m for Landsat-7 data [e.g., Anderson et al., 2004], and even larger for other satellite platforms [e.g., Kustas et al., 2004]. Although TIR-based evapotranspiration models are often applied to coarse scale, low-resolution satellite data, the model adjustments proposed by this study will be demonstrated using submeter, high-resolution TIR data. The rationale for examining this fine scale and the potential applicability to coarser scales of general interest are described in due course.
 Because one generally cannot measure all evapotranspiration model parameters at the same resolution as the TIR imagery, one typically assumes coarse scale homogeneity in many parameters (e.g., total radiation, ground heat flux, humidity, wind speed, canopy height, and stomatal resistance). Unfortunately, this assumed homogeneity may be contrary to real and important land surface heterogeneity in one or more of these parameters. For example, if TIR data reveal substantial heterogeneity in canopy surface temperature, it is then desirable to account for the likely concurrent heterogeneity in temperature-related components of the surface energy balance.
 In practice, spatially distributed TIR-based evapotranspiration estimates are usually based on only one value of stomatal resistance for all TIR pixels in a canopy, regardless of pixel temperature variations. This practice results in local evapotranspiration rates that vary monotonically with temperature. In some combination models, such as the Penman-Monteith model (Figure 1a [Monteith, 1965]) and the Jarvis-McNaughton/Priestley-Taylor combined model (introduced presently [Priestley and Taylor, 1972; Jarvis and McNaughton, 1986]), evapotranspiration increases monotonically with increasing temperature, all else being equal. This model behavior contrasts with one's generally correct intuition that higher-surface temperatures should result in higher sensible heat flux and lower evapotranspiration. In other models, such as the Shuttleworth and Wallace  model (also introduced presently), evapotranspiration decreases monotonically with increasing temperature, sometimes achieving anomalously negative evapotranspiration values at high temperatures. In either case, the combination models fail to capture the nonlinear relationship between evapotranspiration and temperature expected from plant biophysics when they are evaluated using one value of stomatal resistance to calculate surface evapotranspiration across a range of surface temperatures.
 Plant biophysics indicates that stomatal conductance (the inverse of stomatal resistance) and temperature covary in a predictably nonlinear, concave-down manner, with lower stomatal conductance values occurring at high- and low-canopy temperatures (Figure 1c) [Jarvis, 1976; Armond et al., 1978]. Because canopy temperature is significantly easier to measure than stomatal conductance, determining the shape of this concave-down biophysical relationship from the TIR data alone would usefully inform spatially distributed evapotranspiration calculations: this is the aim of this study. If one accounts for this nonlinearity, leaf temperature and modeled evapotranspiration should covary in a more biophysically realistic manner (Figure 1d).
 Conventional evapotranspiration models are highly sensitive to the canopy stomatal resistance parameter [Beven, 1979; Raupach, 1998]. This sensitivity is especially pronounced for the low resistance, moderate leaf temperature conditions characteristic of efficiently functioning leaves (Figure 1b) and when the other resistances to vapor transport, the aerodynamic and boundary layer resistances, are low [Jarvis and McNaughton, 1986]. Under these conditions, given observed spatial variation in canopy temperature, it is especially desirable to account for concurrent spatial variations in stomatal resistance. Unfortunately, stomatal resistance measurement methods are labor-intensive and limited to leaf scale, typically environmentally controlled conditions [LI-COR, 2005; Leinonen et al., 2006; Guilioni et al., 2008], so it is impractical to measure the stomatal resistance of every pixel location using current technology.
 Stomatal conductance may covary with many other environmental variables besides leaf temperature and evapotranspiration rate, such as total incident radiation, vapor pressure deficit, soil moisture, ambient CO2 concentration, leaf age and nutrient status, and plant acclimation history. Yet, nonlinear coupling among stomatal resistance, leaf temperature, evapotranspiration, and canopy energy balance is an intrinsic aspect of canopy physiological function [Jarvis, 1976; Farquhar and Sharkey, 1982; Collatz et al., 1991]. Leaf temperature observations integrate all the contributing variables into one final symptom of the local canopy energy balance. For example, low midday soil moisture may hydraulically limit the supply of water for transpiration, induce stomatal closure, or both. Such limitations will prevent efficient canopy cooling via transpiration, so leaf temperatures will rise. However, if we know that leaf temperatures are elevated, we know that the leaves are not being adequately cooled, and so we do not need to know precisely how much soil moisture is available to understand that transpiration is reduced. It is in this sense that leaf temperature is a symptom of the surface energy balance that integrates over other contributing factors. Other causes of high apparent leaf temperatures include partial leaf senescence, standing dead plant matter, and elevated canopy positions incurring high radiation loads. However, leaf temperature is known to be more sensitive to conductance than to other variables such as leaf size or absorptivity for both sunlit and shaded leaves [Smith and Nobel, 1977].
 The severity of the discrepancies in pixel-level evapotranspiration estimates caused by not accounting for the nonlinear stomatal conductance-temperature relationship are schematically represented at different temperatures by the vertical distance between the solid curve and dashed line in Figure 1d. To reduce these discrepancies, in this study we impose two new constraints on some existing evapotranspiration models. First, stomatal conductance and temperature should vary in a biophysically realistic manner, as in Figure 1c. Second, total evapotranspiration flux (energy) should be conserved across scales: this would be schematically represented by the area under one of the curves in Figure 1f matching the total evapotranspiration calculated by an unmodified, conventional evapotranspiration model for the same canopy area.
 A heterogeneous TIR image, containing thousands to millions of pixels, will exhibit some variance among its temperature values (e.g., Figure 1e). Because variance naturally increases as resolution increases and more extreme values are resolved rather than averaged out [Journel and Huijbregts, 1978; Isaaks and Srivastava, 1989], we should particularly seek to account for spatial variations in surface conditions when studying the surface energy balance at fine spatial scales. Hence, as a first step in this direction, this study develops a modeling methodology incorporating the above constraints using example data collected at 1-cm pixel resolution over small, 1.5 m2 canopy patches of two vegetation types. This demonstration scale also permitted verification of the stomatal conductance-temperature relationships derived by the new method against laboratory data collected at a comparable (cm) scale.
 We acknowledge that the coupling of evapotranspiration, stomatal conductance, and leaf temperature can be simulated in great detail by biochemical photosynthetic assimilation-stomatal conductance models [e.g., Farquhar et al., 1980; Collatz et al., 1991]. However, applying biochemical models over large land areas still requires assuming homogeneity in the many parameters used to characterize photosynthetic assimilation rates, many more parameters than are required by combination models or by our method. In this study, our intention is only to improve upon the erroneous assumption of homogenous canopy stomatal resistance in the face of observed canopy temperature variations. Our method provides a hybrid approach between complex biochemical canopy models and more approximate, but generally useful, homogenous-canopy combination models [Raupach and Finnigan, 1988].