A New Directional Canopy Emissivity Model Based on Spectral Invariants

A new directional canopy emissivity model (CE-P) based on spectral invariants is proposed in this paper. First, we prove the existence of the spectral invariant properties in the thermal infrared (TIR) band using a Monte Carlo model. Based on it, the equation of the new model is derived from the perspective of absorption. In this expression, single-scattering and multiscattering effects are separated analytically in the TIR band. We find that the overall contribution of multiple scatterings is less than 0.005 when the component emissivities are over 0.90, and the overall contribution decreases with increasing leaf or soil emissivity. Furthermore, the new model can avoid the logical difficulty encountered when using the traditional cavity effect factor to simulate the emissivity of a sparse vegetation canopy. The results of 4SAIL and Discrete Anisotropic Radiative Transfer (DART) are selected to do cross validation. The CE-P can achieve a high accuracy compared with 4SAIL and DART, with an absolute bias less than 0.002 when the leaf (soil) emissivity is equal to 0.98 (0.94). Four widely used analytical models are selected for comparison. The resulting accuracies of these models are ordered from CE-P to REN15, FR97, FR02, and VALOR96 with the most serious error up to 0.002, 0.002, 0.007, 0.013, and 0.014, respectively. Three main conclusions are obtained through the sensitivity analysis: the multiscattering between vegetation and the background can be ignored when the leaf (soil) emissivity is no less than 0.94 (0.90), the second and higher order scattering within the vegetation can also be ignored when the leaf (soil) emissivity is no less than 0.94 (0.90), and the single-scattering effect within the canopy should be considered which can be calculated using three view factors.