Copula-based assimilation of radar and gauge information to derive bias-corrected precipitation fields

Abstract. This study addresses the problem of combining radar information and gauge measurements. Gauge measurements are the best available source of absolute rainfall intensity albeit their spatial availability is limited. Precipitation information obtained by radar mimics well the spatial patterns but is biased for their absolute values.

In this study copula models are used to describe the dependence structure between gauge observations and rainfall derived from radar reflectivity at the corresponding grid cells. After appropriate time series transformation to generate "iid" variates, only the positive pairs (radar >0, gauge >0) of the residuals are considered. As not each grid cell can be assigned to one gauge, the integration of point information, i.e. gauge rainfall intensities, is achieved by considering the structure and the strength of dependence between the radar pixels and all the gauges within the radar image. Two different approaches, namely Maximum Theta and Multiple Theta, are presented. They finally allow for generating precipitation fields that mimic the spatial patterns of the radar fields and correct them for biases in their absolute rainfall intensities. The performance of the approach, which can be seen as a bias-correction for radar fields, is demonstrated for the Bavarian Alps. The bias-corrected rainfall fields are compared to a field of interpolated gauge values (ordinary kriging) and are validated with available gauge measurements. The simulated precipitation fields are compared to an operationally corrected radar precipitation field (RADOLAN). The copula-based approach performs similarly well as indicated by different validation measures and successfully corrects for errors in the radar precipitation.