Improving analysis of heavy to extreme precipitation with conditional bias-penalized optimal estimation

Techniques commonly used for precipitation analysis are based on minimizing mean squared error of the predictand. Because the distribution of positive precipitation is extremely median-heavy, such techniques tend to work poorly over the tail ends of the distribution. In this work, we present an extension of conditional bias-penalized kriging (CBPK) that specifically improves analysis of heavy to extreme precipitation. CBPK adds penalty for Type-II conditional bias to the usual kriging formulation to improve performance over tails. The extension, referred to herein as extended CBPK (ECBPK), addresses the issue with the original formulation of CBPK that it can produce significantly negative estimates for nonnegative predictands such as precipitation. For comparative evaluation of ECBPK, we carry out synthetic and real-world experiments of rain gauge-only precipitation analysis. The real-world experiments include multi-year reanalysis of hourly precipitation over the service areas of the National Weather Service (NWS) Arkansas Red-Basin River Forecast Center in Oklahoma, and the Lower Colorado River Authority in Texas. The cross validation results are compared with those of the Single Optimal Estimator used in the NWS's Multisensor Precipitation Estimator. The synthetic experiments use synthetic random fields as the truth, and include analysis and validation of point and mean areal precipitation as a function of the rain gauge network density and the spatial correlation scale.