Influence of Temperature Inertia on Thermal Radiation Directionality Modeling Based on Geometric Optical Model

Different from bidirectional reflectance, temperature variation takes some time with the change of illumination. However, previous thermal radiation directionality (TRD) models have less considered the influence of this temperature inertia (TI) effect. By using the concept of conversion component, this article proposed an improved geometric optical (GO) model, called MGP_TI model. This model considers the TI effect by further dividing the background component into the continuously sunlit, continuously shaded, converted from sunlit to shaded, and converted from shaded to sunlit backgrounds. Upon combining with in situ measurements and a comprehensive simulated data set of component temperatures and prescribing three levels of TI and six observation times, the TI influence on TRD modeling was comprehensively analyzed. Results indicated that: 1) the overall absolute and relative greatest influence were 0.34 °C and 6.9%, respectively, suggesting that the TI influence on the value of TRD was less significant compared with the land surface temperature (LST) retrieval accuracy and the TRD extent; 2) the TI would weaken TRD on the direction of sun motion, whereas it enhanced the TRD on the opposition direction, and the primary influence was enhancing first and then weakening during the period from 10:30 to 15:30, which were determined by the differences in conversion component fractions; and 3) the TI effect could also result in the delay of the hotspot, and the occurrence and degree of the delay were influenced by the TI strength, local solar time and temperature differences of sunlit/shaded components.