Improving the Gaussianity of radar reflectivity departures between observations and simulations using symmetric rain rates

Abstract. Given that the Gaussianity of the observation error distribution is the fundamental principle of some data assimilation and machine learning algorithms, the error structure of radar reflectivity has become increasingly important with the development of high-resolution forecasts and nowcasts of convective systems. This study examines the error distribution of radar reflectivity and discusses what causes the non-Gaussian error distribution using 6-month observations minus backgrounds (OmBs) of composites of vertical maximum reflectivity (CVMRs) in mountainous and hilly areas. By following the symmetric error model in all-sky satellite radiance assimilation, we reveal the error structure of CVMRs as a function of symmetric rain rates, which is the average of the observed and simulated rain rates. Unlike satellite radiance, the error structure of CVMRs shows a sharper slope for light precipitation than for moderate precipitation. Thus, a three-piecewise fitting function is more suitable for CVMRs. The probability density functions of OmBs normalized by symmetric rain rates become more Gaussian than the probability density functions normalized by all samples. Moreover, the possibility of using a third-party predictor to construct the symmetric error model is also discussed in this study. The result shows that the Gaussian distribution of OmBs can be further improved via more accurate precipitation observations. According to the Jensen–Shannon divergence, a more linear predictor, the logarithmic transformation of the rain rate, can provide the most Gaussian error distribution in comparison with other predictors.