Analysis of conditional bias in radar rainfall products

The goal of this study is to improve understanding of the optimization criteria in estimation of remote sensing precipitation. Conditional bias (CB) in radar rainfall (RR) products is formally defined and its significance as an important RR performance criterion is discussed. The CB is a statistic describing differences between given true rainfall values and conditional expectations of the corresponding rainfall estimates conditioned on the truth. An analytical model is used to study the behavior of the CB and its impact on the relationship between the estimated and the true rainfall. We show that large values of the CB result in significant and systematic underestimation of heavy rainfalls, even if the overall bias in the RR products is removed. Among the factors that affect the CB are the optimization method of the RR products, the measurement errors of near-surface radar reflectivity and the natural Z-R variability. Experimental evidence of the CB and its effects are also demonstrated based on NEXRAD data compared with accurate rain gauge measurements of area-averaged rainfall. The new characteristic of the RR uncertainties is compared with the commonly-used mean square error (MSE). The following dilemma between these two performance criteria is demonstrated: removing the CB from the estimates significantly increases the MSE, but minimizing the MSE results in large CB values. Since one cannot simultaneously minimize both of the two errors, the choice of the primary performance criterion must depend on the specific application of the optimized RR product. We argue that there are many applications in which the CB-free rainfall estimates might perform better than the products minimizing the MSE. We also discuss connotations of the CB studied here with the conditional biases considered in the verifications of weather forecasts.