When Heavy Tails Disrupt Hydrologic Modeling and Design

Código

I-EBHE0013

Autores

Richard Vogel

Tema

WG 1.10: Hydrologic Design - Solutions & Communication

Resumo

Heavy tails (HT) appear in a myriad of hydrologic applications, and their presence can disrupt hydrologic modeling as well as common statistical and machine learning methods. HT distributions can be surprising, as hydrologic processes governing such distributions often produce unexpectedly large values that significantly exceed the process?s expected value. This contrasts with light-tailed distributions (i.e., exponential or normal), where extremely large values are highly unlikely. Most prior hydrologic literature on HT distributions focused on their impact on the estimation of extremes (i.e., floods and droughts), whereas we discuss their impact on the performance of common hydrologic modeling methods. Examples of very HT distributions reviewed here include daily series of rainfall-runoff model residuals, river discharge, suspended sediment, phosphorus, total nitrogen loads, residential water use, and saturated hydraulic conductivity of soils. Importantly, the impact of HT distributions on hydrologic methods cannot be understood by letting the "data speak for itself" because even with sample sizes in the hundreds of thousands, we will never know, for example, if a sample from a HT distribution exhibits infinite moments and thus may produce erratic behavior in a myriad of hydrological and statistical methods applied to such data. Instead, the impact of HT distributions can only be understood using the theory of data (i.e., probability). Yet, HT literature requires an advanced theoretical background in probability, which most hydrologists lack. We review known impacts of HT populations on the instability and bias in the performance of the commonly used bootstrap method as well as a wide class of common hydrologic statistics, including the Nash?Sutcliffe efficiency, coefficients of variation, skewness and kurtosis, correlations, and even the ubiquitous sample mean. Product moments (i.e. variance, skew, etc) can be infinite for some HT populations, yet analogous upper L-moments always exist. The theory of L-moments is uniquely suited to HT applications. The value of L-moments is documented to provide a practical heaviness index, L-kurtosis, which can alert us to HT conditions when disruption to hydrologic modeling can be expected. Very simple measures for avoiding such disruption, including aggregation, transformations, and robust statistics, are suggested.