The relationship between Monte Carlo estimators of heterogeneity and error for daily to monthly time steps in a small Minnesota precipitation gauge network

• Published in: Water resources research 2015-07, Vol.51 (7), p.5161-5176
• Main Authors: Wright, Michael, Ferreira, Celso, Houck, Mark, Giovannettone, Jason
• Format: Article
• Language: English
• Subjects: Agricultural engineering; Agriculture; Coefficient of variation; Error analysis; Estimates; Estimation errors; Estimators; Frequency analysis; Gauges; Heterogeneity; Homogeneity; linear moments; Permissible error; Precipitation; Precipitation gauges; Quantiles; Regional analysis; regionalization; Skewness; Statistical analysis; Statistical methods; Statistics
• ISSN: 0043-1397; 1944-7973
• DOI: 10.1002/2014WR015399

Precipitation quantile estimates are used in engineering, agriculture, and a variety of other disciplines. Index flood regional frequency methods pool normalized gauge data in the case of homogeneity among the constituent gauges of the region. Unitless regional quantile estimates are outputted and rescaled at each gauge. Because violation of the homogeneity hypothesis is a major component of quantile estimation error in regional frequency analysis, heterogeneity estimators should be “reasonable proxies” of the error of quantile estimation. In this study, three Monte Carlo heterogeneity statistics tested in Hosking and Wallis (1997) are plotted against Monte Carlo estimates of quantile error for all five‐or‐more‐gauge regionalizations in a 12 gauge network in the Twin Cities region of Minnesota. Upper‐tail quantiles with nonexceedance probabilities of 0.75 and above are examined at time steps ranging from daily to monthly. A linear relationship between heterogeneity and error estimates is found and quantified using Pearson's r score. Two of Hosking and Wallis's (1997) heterogeneity measures, incorporating the coefficient of variation in one case and additionally the skewness in the other, are found to be reasonable proxies for quantile error at the L‐moment ratio values characterizing these data. This result, in addition to confirming the utility of a commonly used coefficient of variation‐based heterogeneity statistic, provides evidence for the utility of a heterogeneity measure that incorporates skewness information. Key Points: Two commonly used heterogeneity statistics based on linear moment ratios are validated Linearity with respect to quantile error of estimation is shown for both statistics A method for evaluating all regionalizations of a gauge data set is presented