Statistical Characteristics of Radar Heavy Precipitation Data in the Wavelet Domain and Its Relationship with Environmental Parameters

To obtain the best estimation of heavy precipitation, a priori model based on the multi-scale statistical characteristics of radar heavy precipitation data is very important. Based on the data of 180 independent precipitation events of the Nanjing S-band Doppler weather radar from 2013 to 2016, this paper performs a wavelet decomposition to study the non-Gaussian edge distribution characteristics of the wavelet coefficients in the wavelet domain of heavy precipitation radar echoes and the fractal characteristics between scales. Moreover, a corresponding mathematical model was established based on the prior statistical characteristics of heavy precipitation. Research results show that for radar echoes with different precipitation structures exhibiting different shapes, the fractal parameters are not very different and the directivity is not obvious, implying that the wavelet coefficients of heavy precipitation can be uniformly modeled. Non-Gaussian features within the intrascale can be represented by a generalized Gaussian distribution, and fractal features between scales can be represented by an exponential form. To further explain the relationship between the statistical characteristics of heavy precipitation in the wavelet domain and the physical parameters of precipitation, the relationship between the fractal parameters of wavelet coefficients in the wavelet domain of heavy precipitation and environmental parameters is discussed. It is found that the correlation coefficient between the convective available potential energy and the fractal parameters in the environmental parameters ( \tau _H : first-order horizontal direction) is 0.5535, and the correlation coefficient between the precipitation per hour and the fractal parameters (\bar\tau _2: the mean of the second-order wavelet coefficients and fractal parameters in each direction) is 0.3848, while the correlations between other environmental parameters and fractal parameters are lower than 0.28. Statistical characteristics of heavy precipitation in the wavelet domain and the prior information with environmental parameters can be used for parametric modeling of heavy precipitation data. It has an important reference value for subsequent applications such as the optimal estimation of heavy precipitation, data assimilation, data downscaling, and multi-source data fusion.