Search

Given that the Gaussianity of observation error distribution is the fundamental principle of some data assimilation and machine learning algorithms, the error structure of radar reflectivity becomes 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 give rise to the non-Gaussian error distribution by 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 unveil the error structure of CVMRs as a function of symmetric rain rates, which is the average of observed and simulated rain rates. Unlike satellite radiance, the error structure of CVMRs shows a sharper slope in light precipitations than moderate precipitations. 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 in comparison with the probability density function normalized by the whole samples. Moreover, the possibility of using third-party predictor to construct the symmetric error model are also discussed in this study. The Gaussianity of OmBs can be further improved by using a more accurate precipitation observations. According to the Jensen-Shannon divergence, a more linear predictor, the logarithmic transformation of rain rate, can provide the most Gaussian error 20 distribution in comparison with other predictors. [ABSTRACT FROM AUTHOR]

This study presents the first-ever complete characterization of random errors in dual-polarimetric spectral observations of meteorological targets by cloud radars. The characterization is given by means of mathematical equations for joint probability density functions (PDF) and error covariance matrices. The derived equations are checked for consistency using real radar measurements. One of the main conclusions of the study is that the convenient representation of spectral polarimetric measurements including differential reflectivity ZDR, correlation coefficient pHV, and differential phase ΦDP is not suited for the proper characterization of the error covariance matrix. This is because the aforementioned quantities are complex, non-linear functions of the radar raw data and thus their error covariance matrix is commonly derived using simplified linear relations and by neglecting the correlation of errors. This study formulates the spectral polarimetric measurements in terms of a different set of quantities that allows for a proper analytic treatment of their error covariance matrix. The results given in this study allow for utilization of spectral polarimetric measurements for advanced meteorological applications, among which are variational retrieval techniques, data assimilation, and sensitivity analysis. [ABSTRACT FROM AUTHOR]