A modified surface energy balance algorithm for land (M-SEBAL) based on a trapezoidal framework
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The surface energy balance algorithm for land (SEBAL) has been designed and widely used (and misused) worldwide to estimate evapotranspiration across varying spatial and temporal scales using satellite remote sensing over the past 15 yr. It is, however, beset by visual identification of a hot and cold pixel to determine the temperature difference (dT) between the surface and the lower atmosphere, which is assumed to be linearly correlated with surface radiative temperature (Trad) throughout a scene. To reduce ambiguity in flux estimation by SEBAL due to the subjectivity in extreme pixel selection, this study first demonstrates that SEBAL is of a rectangular framework of the contextual relationship between vegetation fraction (fc) and Trad, which can distort the spatial distribution of heat flux retrievals to varying degrees. End members of SEBAL were replaced by a trapezoidal framework of the fc-Trad space in the modified surface energy balance algorithm for land (M-SEBAL). The warm edge of the trapezoidal framework is determined by analytically deriving temperatures of the bare surface with the largest water stress and the fully vegetated surface with the largest water stress implicit in both energy balance and radiation budget equations. Areally averaged air temperature (Ta) across a study site is taken to be the cold edge of the trapezoidal framework. Coefficients of the linear relationship between dT and Trad can vary with fc but are assumed essentially invariant for the same fc or within the same fc class in M-SEBAL. SEBAL and M-SEBAL are applied to the soil moisture-atmosphere coupling experiment (SMACEX) site in central Iowa, U.S. Results show that M-SEBAL is capable of reproducing latent heat flux in terms of an overall root-mean-square difference of 41.1 W m 2 and mean absolute percentage difference of 8.9% with reference to eddy covariance tower-based measurements for three landsat thematic mapper/enhanced thematic mapper plus imagery acquisition dates in 2002. The retrieval accuracy of SEBAL is generally lower than M-SEBAL, depending largely on the elected extremes. Spatial distributions of heat flux retrievals from SEBAL are distorted to a certain degree due to its intrinsic rectangular framework.