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The attenuation-based rainfall estimator is less sensitive to the variability of raindrop size distributions (DSDs) than conventional radar rainfall estimators. For the attenuation-based quantitative precipitation estimation (QPE), the key is to accurately estimate the horizontal specific attenuation  A   H  , which requires a good estimate of the ray-averaged ratio between  A   H   and specific differential phase  K  DP , also known as the coefficient  α . In this study, a variational approach is proposed to optimize the coefficient  α  for better estimates of  A   H   and rainfall. The performance of the variational approach is illustrated using observations from an S-band operational weather radar with rigorous quality control in south China, by comparing against the  α  optimization approach using a slope of differential reflectivity  Z  DR  dependence on horizontal reflectivity factor  Z   H  . Similar to the  Z  DR -slope approach, the variational approach can obtain the optimized  α  consistent with the DSD properties of precipitation on a sweep-to-sweep basis. The attenuation-based hourly rainfall estimates using the sweep-averaged  α  values from these two approaches show comparable accuracy when verified against the gauge measurements. One advantage of the variational approach is its feasibility to optimize  α  for each radar ray, which mitigates the impact of the azimuthal DSD variabilities on rainfall estimation. It is found that, based on the optimized  α  for radar rays, the hourly rainfall amounts derived from the variational approach are consistent with gauge measurements, showing lower bias (1.0%), higher correlation coefficient (0.92), and lower root-mean-square error (2.35 mm) than the results based on the sweep-averaged  α .

Improved Attenuation-Based Radar Precipitation Estimation Considering the Azimuthal Variabilities of Microphysical Properties