Surface upward longwave radiation (SULR) is an important component of the surface energy balance and is closely related to land surface temperature and emissivity. The estimation of SULR plays an important role in the study of surface energy circulation and climate change. State-of-the-art methods to estimate SULR, including the physical method and the hybrid method, are conducted without considering directional thermal radiation (DTR), which may induce a large error in the estimation, particularly over sparsely vegetated surfaces. In this paper, we modified the physical temperature–emissivity algorithm by combining a directional emissivity model (FRA97) and a kernel-driven DTR model to estimate the SULR of vegetated surfaces while considering the thermal directionality of the land surface. The most suitable kernel-driven model and an angle combination of the DTR were selected from six kernel-driven models and five angular combinations. The sensitivity of the proposed algorithm to the input parameters was also analyzed. The proposed algorithm was then validated with the Wide-angle infrared Dual-mode line/area Array Scanner (WiDAS) data set and longwave radiation data of automatic meteorological stations from the Heihe Watershed Allied Telemetry Experimental Research experiment. The results showed that the five-angle combination with large-angle intervals performs the best. When the leaf area index (LAI) is less than 1.2, the RossThick-LiSparseR model performs the best; when LAI is larger than 1.2, the RossThick-LiDenseR model is the most accurate. The SULR is not sensitive to surface downward longwave radiation and LAI, is slightly sensitive to leaf and soil emissivity at certain LAIs, and is highly sensitive to DTR, which may greatly affect the accuracy of the estimated SULR. The root-mean-square error (RMSE) and the mean bias error (MBE) of the SULR estimated using the WiDAS data and the proposed algorithm are 5.618 and −1.642 W/m 2 , respectively, thereby improving the estimation accuracy by as much as 7.479 and 10.511 W/m 2  at most in terms of RMSE and MBE, respectively, compared with the results calculated without considering the DTR.
['Tian Hu', 'Yongming Du', 'Biao Cao', 'Hua Li', 'Zunjian Bian', 'Donglian Sun', 'Qinhuo Liu']
Estimation of Upward Longwave Radiation From Vegetated Surfaces Considering Thermal Directionality