Metric Learning for Approximation of Microwave Channel Error Covariance: Application for Satellite Retrieval of Drizzle and Light Snowfall

Improved microwave retrieval of land and atmospheric state variables requires proper weighting of the information content of radiometric channels through their error covariance matrix. Inspired by recent advances in metric learning techniques, a new framework is proposed for a formal approximation of the channel error covariance. The idea is tested for the detection of precipitation and its phase over oceans, using coincidences of passive/active data from the Global Precipitation Measurement (GPM) and CloudSat satellites. The initial results demonstrate that the presented approach cannot only capture the known laws of radiative transfer equations, but also the surrogate signatures that can arise due to the co-occurrence of precipitation and other radiometrically active land-atmospheric state variables. In particular, the results demonstrate high precision (low error) for the low-frequency channels of 10-37 GHz in the detection of both rain and snowfall over oceans. Using the optimal estimate of the channel error covariance through the multi-frequency {k} -nearest neighbor (kNN) classification approach, without any ancillary data, it is demonstrated that the probability of passive microwave detection of snowfall (0.97) can be higher than that of the rainfall (0.88), when drizzle and light snowfall are the dominant form of precipitation. This improvement is hypothesized to be largely related to the information content of the low-frequency channels of 10-37 GHz that can capture the co-occurrence of snowfall with an increased cloud liquid water content, sea ice, and wind-induced changes of surface emissivity.