Spatial-scale effect on the SEBAL model for evapotranspiration estimation using remote sensing data

Abstract The Surface Energy Balance Algorithm for Land (SEBAL) has been successfully applied to remote sensing data to estimate surface evapotranspiration (ET) at different spatial and temporal resolutions in more than 30 countries. However, the selection of dry and wet pixels over the area of interest (AOI) makes the SEBAL-estimated ET subject to the sizes of the AOI and the satellite pixels. This paper investigates the effect of the sizes of the AOI and satellite pixels on SEBAL-derived surface energy components by proposing generalized analytical equations. These equations demonstrate how the variations in the intermediate variables, the AOI, and the pixel size affect the resulting surface energy components and under which circumstances the sensible heat flux will be misestimated, without needing to run the SEBAL model. These analytical equations were verified through application to 23 clear-sky MODIS overpasses that cover different soil water contents and crop growth stages from January 2010 to late October 2011. The spatial effects of increasing the size of the AOI for SEBAL can be summarized as follows: (1) if the locations of dry and wet pixels do not vary, the pixel-by-pixel sensible heat flux ( H LA ) calculated using the larger AOI is equal to that of the smaller AOI ( H SA , with H LA / H SA  = 1), (2) if only the surface temperatures of wet pixels do not vary, the relative variation in H is equal to the relative variation of the slope ( a ) of the linear equation between the near-surface air temperature difference and the surface temperature ( H LA / H SA  = 1 +  δH SA / H SA  = 1 +  δa / a ), and (3) under other circumstances, H LA / H SA decreases with surface temperatures at a slowing pace from ∼∞ at the temperature of the wet pixel ( T s,wet ) to a certain value at the temperature of the dry pixel ( T s,dry ) (both temperatures are for the small AOI). Analogously, a general analytical equation—a function of the coefficients of the linear equation between the near-surface air temperature difference and surface temperature at the high-resolution, the effective temperature, and the effective momentum roughness length—could be used to quantify the spatial-scale effect of the satellite pixel size. The findings from this study may help determine suitable sizes of the AOIs and the satellite pixels and aid in quantifying uncertainties in the SEBAL-derived surface energy components.