Spatiotemporal Precipitation Estimation from Rain Gauges and Meteorological Radar Using Geostatistics

Automatic interpolation of precipitation maps combining rain gauge and radar data has been done in the past but considering only the data collected at a given time interval. Since radar and rain gauge data are collected at short intervals, a natural extension of previous works is to account for temporal correlations and to include time into the interpolation process. In this work, rainfall is interpolated using data from the current time interval and the previous one. Interpolation is carried out using kriging with external drift, in which the radar rainfall estimate is the drift, and the mean precipitation is set to zero at the locations where the radar estimate is zero. The rainfall covariance is modeled as non-stationary in time, and the space system of reference moves with the storm. This movement serves to maximize the collocated correlation between consecutive time intervals. The proposed approach is analyzed for four episodes that took place in Catalonia (Spain). It is compared with three other approaches: (i) radar estimation, (ii) kriging with external drift using only the data from the same time interval, and (iii) kriging with external drift using data from two consecutive time intervals but not accounting for the displacement of the storm. The comparisons are performed using cross-validation. In all four episodes, the proposed approach outperforms the other three approaches. It is important to account for temporal correlation and use a Lagrangian system of coordinates that tracks the rainfall movement.