Abstract:
When an engineering firm designs a dam, a government assesses its readiness for flood or famine, or a municipal water supply company invests in new infrastructure, lives and major financial investments are at stake. To design a sturdy dam, prepare a sufficient emergency response, size a water treatment plant, or answer many other important questions, estimates of the magnitude and frequency of future precipitation events are often needed. Because the societal and financial costs of erroneous estimates can be extremely high, mechanisms exist to quantify and minimize the error of estimation. Precipitation gauge records are often pooled to reduce the error of quantile estimates by increasing sample size. This introduces a new error component proportional to heterogeneity, the degree to which the constituent gauges diverge from the regional average. Precipitation frequency analysts, especially in data-poor regions, use heterogeneity statistics to evaluate whether a candidate regionalization adds more error through heterogeneity than it reduces through increased sample size. This dissertation assesses the relationship between error in quantile estimates and five heterogeneity statistics proposed in the literature, offering precipitation analysts quantifications of these statistics' efficacy and making recommendations for their use. All five-or-more-site regionalizations of a twelve-gauge Minnesota dataset are enumerated and Monte Carlo simulation is used to estimate quantile error and the heterogeneity statistics. Linear relationships found between heterogeneity estimators and quantile error are compared to those found in simulation experiments isolating the heterogeneity-related component of quantile error. Two statistics have highly linear relationships to error in both the simulation and enumeration studies. The less linear statistic is more robust to deviation from the hypothesis that regional coefficient of variation and skewness ranges increase in tandem as heterogeneity rises. Novel heterogeneity thresholds are defined for this statistic. This research offers context and validation for a family of popular heterogeneity statistics whose relative utility has previously been unclear. Precipitation analysts using the regional frequency analysis framework to answer questions about precipitation magnitude now have a full reckoning of the utility of these statistics, increasing the level of confidence they can have in the accuracy of their results.
