Because of its clear physical meaning, physical methods are more often used for space-borne microwave radiometers to retrieve the rain rate, but they are rarely used for ground-based microwave radiometers that are very sensitive to rainfall. In this article, an opacity physical retrieval method is implemented to retrieve the rain rate (denoted as Opa-RR) using ground-based microwave radiometer data (21.4 and 31.5 GHz) of the tropospheric water radiometer (TROWARA) at Bern, Switzerland from 2005 to 2019. The Opa-RR firstly establishes a direct connection between the rain rate and the enhanced atmospheric opacity during rain, then iteratively adjusts the rain effective temperature to determine the rain opacity, based on the radiative transfer equation, and finally estimates the rain rate. These estimations are compared with the available simultaneous rain rate derived from rain gauge data and reanalysis data (ERA5). The results and the intercomparison demonstrate that during moderate rains and at the 31 GHz channel, the Opa-RR method was close to the actual situation and capable of the rain rate estimation. In addition, the Opa-RR method can well derive the changes in cumulative rain over time (day, month, and year), and the monthly rain rate estimation is superior, with the rain gauge validated R2 and the root-mean-square error value of 0.77 and 22.46 mm/month, respectively. Compared with ERA5, Opa-RR at 31GHz achieves a competitive performance.
Machine learning moment closure models for the radiative transfer equation I: directly learning a gradient based closure
