On the distributions of seasonal river flows: Lognormal or power law?

Abstract

[1] Distributional analysis of river discharge time series is an important task in many areas of hydrological engineering, including optimal design of water storage and drainage networks, management of extreme events, risk assessment for water supply, and environmental flow management, among many others. Having diverging moments, heavy-tailed power law distributions have attracted widespread attention, especially for the modeling of the likelihood of extreme events such as floods and droughts. However, straightforward distributional analysis does not connect well with the complicated dynamics of river flows, including fractal and multifractal behavior, chaos-like dynamics, and seasonality. To better reflect river flow dynamics, we propose to carry out distributional analysis of river flow time series according to three ''flow seasons'': dry, wet, and transitional. We present a concrete statistical procedure to partition river flow data into three such seasons and fit data in these seasons using two types of distributions, power law and lognormal. The latter distribution is a salient property of the cascade multiplicative multifractal model, which is among the best models for turbulence and rainfall. We show that while both power law and lognormal distributions are relevant to dry seasons, river flow data in wet seasons are typically better fitted by lognormal distributions than by power law distributions.

On the emergence of heavy-tailed streamflow distributions

“…Daily river flows have been previously recognized as a heavy-tail distributed variable [9,24]. Several statistical and physically-based models have been developed to characterize runoff dynamics and estimate streamflow distributions (e.g.…”

Estimating the flood frequency distribution at seasonal and annual time scales

“…Similarly, Kochanek et al (2012) and focused on the upper quantiles of the annual peak flows by fitting data collected in two seasons. Other analogous contributions were provided by Buishand and Demarè (1990), who refer to rainfall depths, and Singh et al (2005).…”

“…Allamano et al (2011) analyse the magnitude of under-(or over-) estimation of design events in the presence of seasonality by using the POT or AM approach. Bowers et al (2012) presents a statistical procedure to partition river flow data into three seasons and focuses on two particular distributions to describe the constructed seasonal river flows: power law and lognormal. Fang et al (2007) proposed an approach based on the peaks-over-threshold sampling method and a nonidentical Poisson distribution to model the flood occurrence within each season.…”

A Cautionary Note on the Reproduction of Dependencies through Linear Stochastic Models with Non-Gaussian White Noise

“…Apparently, both Nataf-and copula-based approaches can provide a remedy to the limitations of the TF approach, as well as explicitly account for non-Gaussianity, which is omnipresent within hydrometeorological processes (e.g., [79][80][81][82][83][84][85]). We deem that Nataf-based models provide a convenient and more precise alternative given that they utilize (in an auxiliary or parent role) existing and well-known stochastic models which provide the basis for a straightforward and operational efficient generation scheme.…”