Modeling the Interdependence Structure between Rain and Radar Variables Using Copulas: Applications to Heavy Rainfall Estimation by Weather Radar

Abstract

In radar quantitative precipitation estimates (QPE), the progressive evolution of rainfall algorithms has been guided by attempts to reduce the uncertainties in rainfall retrieval. However, because most of the algorithms are based on the linear dependence between radar and rain variables and designed for rain rates ranging from light to moderate rainfall, they result in misleading estimations of intense or strong rainfall rates. In this paper, based on extensive data gathered during the AMMA and Megha-Tropiques data campaigns, we provided a way to improve the estimation of intense rainfall rates from radar measurements. To this end, we designed a formulation of the QPE algorithm that accounts for the co-dependency between radar observables and rainfall rate using copula simulation synthetic datasets and using the quantile regression features for a more complete picture of covariate effects. The results show a clear improvement in heavy rainfall retrieval from radar data using copula-based R(KDP) algorithms derived from a realistic simulated dataset. For a better performance, Gaussian copula-derived algorithms require a 0.8 percentile distribution to be considered. Conversely, lower percentiles are better for Student’s, Gumbel and HRT copula estimators when retrieving heavy rainfall rates (R > 30). This highlights the need to investigate the entire conditional distribution to determine the performance of radar rainfall estimators.