Joint distribution of multiplicative errors in radar and satellite QPEs and its use in estimating the conditional exceedance probability

This paper characterizes the joint distribution of multiplicative errors (ME) in radar (R) and satellite (S) quantitative precipitation estimates (QPEs). A semi-parametric framework is established on the basis of this joint distribution to describe the probability of rainfall exceeding a particular threshold given concurrent R and S-based estimates (referred to as conditional exceedance probability, or CEP). This framework entails integrating copula-based joint distributions of MEs over a range of rainfall amounts to yield the joint probability of exceedance, which forms the basis for estimating CEP. In demonstrating this approach, MEs were computed for R (Weather Surveillance Radar-1988 Doppler) and S (Self-calibrating Multivariate Precipitation Retrieval) for central Texas over 2000–2007 using gauge records as the reference. Analysis of the MEs in R and S reveals a substantial correlation between the two, and it also shows that the interdependence is complex as a considerable portion of S QPEs are negatively biased while their concurrent R values are bias-neutral. CEP values from the semi-parametric approach is found to be generally superior to those empirically derived based on rainfall estimates: it yields values for a wide range of rainfall thresholds and suffers much fewer discontinuities and artifacts that the empirical results exhibit. For the lower range of S and R thresholds where sample size is relatively large (i.e., <20 mm h⁻¹ for the summer), the two sets of CEPs bear close resemblance, with both showing a relatively weak, but nevertheless substantial dependence on the threshold value for S. These findings confirm the plausibility of the semi-parametric CEP values, and demonstrate the utility of S QPEs in improving the confidence in rainfall exceedance under this framework.