Simulation of scaling effects of thermal emission from non-isothermal pixels with the typical three-dimensional structure

This paper suggests approaches to simulate scaling effects of thermal emission from non-isothermal pixels with a typical three-dimensional structure. We simulate effective emissivities of various V-shaped valleys by using our Monte Carlo method under the isothermal assumption. An analytical formula of the effective emissivities is derived based on photon rebounding between surfaces in the valleys. The comparison between the simulated and the analytically modelled effective emissivities shows that the analytical formula is highly accurate. After simulating effective emissivities of the V-shaped valley under several non-isothermal conditions, we find that the structure and component temperature difference of a pixel cause the scaling effects of thermal emission of the pixel. The results, therefore, prove that Planck's law has to be corrected for remote sensing to estimate land surface temperature with high accuracy.