A conceptual model for effective directional emissivity from nonisothermal surfaces

The conventional definition of emissivity requires the source of radiation to be isothermal in order to compare its thermal emission to that of a blackbody at the same temperature. This requirement is not met for most land surfaces considered in thermal infrared remote sensing, Thus, the effective or equivalent emissivity of nonisothermal surfaces has been a poorly defined but widely used concept for years. Recently, several authors have attempted to define this concept more clearly. Unfortunately, definitions such as ensemble emissivity (e-emissivity) and emissivity derived from the surface bidirectional reflectance distribution function (r-emissivity) [27] do not fully satisfy current needs for estimating true land surface temperature (LST), We suggest the use of an additional term, the "apparent emissivity increment," which considers the effects of geometric optics to explain the directional and spectral dependence in LST caused by the three-dimensional (3-D) structure and subpixel temperature distribution of the surface, We define this quantity based upon the emissivity derived from the bidirectional reflectance distribution function (epsilon(BRDF)) for isothermal surfaces and present a conceptual model of thermal emission from nonisothermal land surfaces. Our study also indicates that an average LST corresponding to the hemispherical wideband epsilon(BRDF) will be useful in remote sensing-based LST modeling and inversion.