Time-dependent Z-R relationships for estimating rainfall fields from radar measurements

The operational use of weather radars has become a widespread and useful tool for estimating rainfall fields. The radar-gauge adjustment is a commonly adopted technique which allows one to reduce bias and dispersion between radar rainfall estimates and the corresponding ground measurements provided by rain gauges. This paper investigates a new methodology for estimating radar-based rainfall fields by recalibrating at each time step the reflectivity-rainfall rate (Z-R) relationship on the basis of ground measurements provided by a rain gauge network. The power-law equation for converting reflectivity measurements into rainfall rates is readjusted at each time step, by calibrating its parameters using hourly Z-R pairs collected in the proximity of the considered time step. Calibration windows with duration between 1 and 24 h are used for estimating the parameters of the Z-R relationship. A case study pertaining to 19 rainfall events occurred in the north-western Italy is considered, in an area located within 25 km from the radar site, with available measurements of rainfall rate at the ground and radar reflectivity aloft. Results obtained with the proposed method are compared to those of three other literature methods. Applications are described for a posteriori evaluation of rainfall fields and for real-time estimation. Results suggest that the use of a calibration window of 2-5 h yields the best performances, with improvements that reach the 28% of the standard error obtained by using the most accurate fixed (climatological) Z-R relationship.