Assessment of Five Thermal Infrared Kernel-Driven Models Using Limited Multiangle Observations

There are five widely used kernel-driven models in the thermal infrared domain designed for the angular correction of land surface temperature (LST), including three-parameter Roujean Lagouarde (RL), Vinnikov, RossThick-LiSparseR (Ross–Li), LiStrahlerFriedl-LiDenseR (LSF-Li), and four-parameter Vinnikov-RoujeanLagouarde (Vinnikov-RL). Their fitting accuracies with hundreds of observation angles (i.e., sufficient angle) were studied; however, the fitting ability of these five models with limited observation angles is unknown, which makes it difficult to choose the appropriate one in applications. To solve this problem, 30 600 groups of multiangle directional brightness temperature (DBT) datasets were simulated by the unified optical-thermal 4-stream model considering scattering by arbitrary inclined leaves (4SAIL) model considering ten different leaf area index values, three leaf inclination distribution functions, two hotspot factors, 17 different component temperatures, five solar zenith angles, and six solar azimuth angles. Each group contains DBT values in 21 960 viewing directions [i.e., 61 viewing zenith angle (VZA) $\times $ 360 viewing azimuth angle (VAA)]. We assume that all limited observations are in the plane with VAA = 180°/0° and VZA changing from −60° to 60° with a step of 10°. There are 13 candidate angles to be selected. Five, seven, nine, and 11 angle sampling schemes include 225, 400, 225, and 36 limited multiangle combinations, respectively. Each combination was used to drive these five kernel-driven models to fit 21 960 DBTs for 30 600 groups of 4SAIL simulations. The root-mean-square error (RMSE) of each combination and mean RMSE of all 886 combinations were used to assess the overall fitting ability of five kernel-driven models. In addition, 1 k errors were added to the driven DBTs to evaluate the models’ robustness. Four groups of airborne measured DBTs were adopted to validate the assessment conclusions. Results show that the recommended order of these five models driven by 5–11 multiangle DBTs is Vinnikov-RL, LSF-Li, Vinnikov, Ross–Li, and RL when the driven DBTs do not contain errors; Vinnikov-RL, Vinnikov, LSF-Li, Ross–Li, and RL when the driven DBTs contain 1k errors; and Vinnikov-RL, LSF-Li, Ross–Li, RL, and Vinnikov for four groups of airborne measured datasets.