Correcting of real-time radar rainfall bias using a Kalman filtering approach

This paper presents a method to adjust the mean field bias of radar rainfall estimates in real time. The underlying philosophy for estimation of radar rainfall in real-time used in this study is that the estimated radar rainfall must first be corrected for the reflectivity measurement errors and the Z–R conversion errors based on the physical methods, and thereafter a statistical method is used to remove the average difference (mean field bias) between radar estimates at the rain gauge locations and the corresponding gauge rainfall amounts. Kalman filtering techniques are used as the basis for correcting the mean filed bias in real time. The logarithmic mean field radar rainfall bias is modelled as an Autoregressive order 1 process having a stationary variance. The observation error variance is estimated from a difference between a variance of the observed mean field bias and the stationary variance of the logarithmic bias process. The variance of the observed mean field bias is estimated using a radar rainfall error variance model which depends on (a) the number of rain gauges that measure non-zero rainfall at that hour; (b) the location of these rain gauges; (c) the conditional mean of rain gauge rainfall; and (d) the number of pulses used for reflectivity measurements. A 7-month radar and rain gauge data record from the Kurnell radar in Sydney, Australia are used to test the efficiency of the proposed method. The results shown that the Kalman filtering approach outperforms the use of sample bias correction method when rain gauge density is less than about 1 gauge per 90 km2 for both climatological and stratiform rainfall, and has a higher accuracy compared to the case where no bias correction is performed, irrespective of the number of rain gauges used in the calibration.