Determination of the Hemispherical Equivalent Angle for Surface Upward Longwave Radiation

Surface upward longwave radiation (SULR) is an indicator reflecting the thermal condition of the Earth’s surface and a key variable in the surface radiation budget. It is widely employed in hydrology, ecology, meteorology, and environmental fields. Current SULR remote sensing retrieval methods assume the Earth’s surface is Lambertian, i.e., the surface thermal radiation is isotropic. However, ground, airborne, and satellite-scale studies show the brightness temperature differences are up to 10 K in different directions for complex land surfaces. The ignorance of thermal anisotropy limits the accuracy of current SULR products. Therefore, it is essential to perform hemispherical integration of SULR under conditions of thermal anisotropy. The hemispherical integrated SULR can be approximated by a directional SULR at hemispherical equivalent angle (HEA). However, the current HEA for SULR is between 44.0° and 55.0°. To make it clearer, the Vinnikov-Chen kernel-driven model (KDM) is extensively adopted to simulate 3645600 samples for HEA determination. Results show that the range of HEA is 46.6°–47.8° (with an average HEA equal to 47.0°). The HEA is independent of the KDM coefficients and solar azimuth angle (SAA), but slightly changes with solar zenith angle (SZA) and hotspot width. Furthermore, the validation of HEA using a series of 3-D radiative transfer simulations shows the mean absolute error (MAE) is 0.00–1.36 W/m2. This study provides a new insight to the HEA, which will benefit to SULR estimation.