Evaluation of heterogeneity statistics as reasonable proxies of the error of precipitation quantile estimation in the Minneapolis-St. Paul region

摘要

Estimating precipitation frequency is important in engineering, agriculture, land use planning, and many other disciplines. The index flood method alleviates small sample size issues due to short record length by calculating normalized quantile estimates for averaged data from a "region" of gauges. For a perfectly homogeneous region this adds no error; heterogeneity statistics seek to quantify a real-world region's deviation from this assumption. Hosking and Wallis (1997) introduced a Monte Carlo heterogeneity statistic called here H_1 and used a simulation study to assess its utility while rejecting two similar statistics called here H_2 and H_3. A nearly linear relationship was found between H_1 and the percentage root mean square error (RMSE) increase due to heterogeneity, establishing H_1 as a "reasonable proxy" of quantile error. The H_1-percent RMSE added relationship found in the simulation experiment was used to find equivalent RMSEs for heterogeneity thresholds against which all three H statistics were tested. In this study the "reasonable proxy" relationship is evaluated across a highly skewed daily precipitation dataset in Minnesota for H_1, H_2 and H_3. Simulated regions used in quantile error estimation are generated using at-site L-moment ratios scaled toward the regional mean with a shrinkage multiplier. A linear relationship is found between Monte Carlo estimates of quantile RMSE and both H_1 and H_2 across all possible regionalizations of twelve gauges. H_2's relationship is less linear than H_1's as quantified by Pearson's r. A synthetic study is also undertaken using the same sample sizes, regional L-moment averages, and between-site variations as the Hosking and Wallis (1997) simulation. The H_2-percent RMSE added relationship is found to be nearly as linear as for H_1, complementing the enumeration study's findings. Because H_2's linear relationship with percent RMSE added has approximately one-fourth the slope of theH_1-RMSE relationship, heterogeneity thresholds calculated with reference to H_1 should not be applied to H_2. H_2 thresholds can be derived from the H_2-percent RMSE added relationship in analogous fashion to the method used in Hosking and Wallis (1997) for H_1. The resulting thresholds are one-fourth the magnitude of the H_1 thresholds.