According to Norman and Becker,38 there are two types of emissivity for each nonisothermal pixel, i.e., -emissivity and -emissivity. Centered on the geographical locations of the validation sites, we calculated -emissivity and -emissivity for the subregions of , , ASTER pixels (, , MODIS pixels) using Eqs. (1) and (2). The -emissivity can be used to express the area weighting of the component emissivity, which has no relationship with the component temperature. If a pixel has components, then Display Formula
(1)where represents the band, is the normalized-area proportion of component , and is the emissivity of each component in the direction of . The -emissivity is defined as the ratio of the total radiation of a natural object surface to the blackbody radiation with an identical temperature distribution. When the pixel has components, Display Formula
(2)where is the approximation to the exponential function of blackbody radiation. Thus, the -emissivity is a function of an object’s component temperatures. Figures 5 and 6 show the calculated -emissivity and -emissivity using ASTER TIR emissivity on June 3 and June 10, 2011, for the three subregions. For site 1, the absolute difference between -emissivity and -emissivity for each TIR band is on June 3, 2011, and the value of the difference is on June 10, 2011. The corresponding difference values for site 2 on June 3 and June 10, 2011, are 0.0005 and 0.0009, respectively. Thus, the definition of emissivity will not affect the validation results in this study. Hereafter, we will use -emissivity in the comparison. Because the size (area ratio) of each ASTER pixel within the subregion is the same, the -emissivity equals the average emissivity. We also calculated the standard deviation of the ASTER emissivity for each subregion.