Estimation of Surface Upward Longwave Radiation Using a Direct Physical Algorithm

Surface upward longwave radiation (SULR) is a significant component of the surface radiation budget and is closely linked with evapotranspiration, soil moisture, and surface cooling on clear nights. Therefore, accurately estimating SULR is essential to better understand its spatiotemporal dynamics or to characterize the thermal environment of a given land surface. Currently, most methods for estimating SULR (including the physical and hybrid methods) fail to account for the thermal anisotropy, which can introduce significant errors into the calculation. We previously proposed the combined algorithm that considers the thermal anisotropy to more accurately estimate the SULR. However, this proposed method has several shortcomings. For example, it considers the directionality of the emissivity and the effective temperature separately under the support of a parametric directional emissivity model. However, the directional emissivity model is not maturely developed for different land surface types, especially on non-vegetated surfaces. And the separation of land surface temperature and emissivity may undermine the estimation accuracy. Furthermore, this proposed method requires a series of input parameters that is not always available, limiting its applicability. In this paper, we present a refined algorithm that uses a kernel-driven model and the technique of band conversion to calculate the SULR directly based on surface-leaving radiances. This direct physical algorithm is then applied to the Wide-angle infrared Dual-mode line/area Array Scanner data set and validated using longwave radiation data collected by automatic meteorological stations from the Heihe Watershed Allied Telemetry Experimental Research experiment. The results of these tests suggest that the direct algorithm works effectively. The root-mean-square error (RMSE) and mean bias error (MBE) of the direct algorithm on maize surfaces are 4.417 and 0.474 W · m
^-2
, respectively. When the thermal anisotropy is incorporated, the RMSE and absolute MBE decrease by a maximum of 4.734 and 7.414 W·m
^-2
, respectively. Different land types yield different results: for vegetable surfaces, the estimation biases of the direct model are approximately -2 W · m
^-2
, whereas orchard surfaces yield biases are between -2 and -3.5 W · m
^-2
, and village surfaces yield biases exceeding -10 W · m
^-2
. These differences can be attributed to the varying effects of the kernel-driven model across different types of land surfaces. The RMSE and absolute MBE obtained using the direct algorithm are slightly smaller (0.587 and 1.685 W·m
^-2
, respectively) than those obtained using the combined algorithm; they are also smaller than the results of the traditional temperature-emissivity algorithm (by 8.7 and 11.7 W · m
^-2
, respectively).