A comparison of methods for modeling marginal non-zero daily rainfall across the Australian continent

TL;DR

This study compares EVT-based methods and gamma mixture models for accurately estimating non-zero daily rainfall across Australia, finding gamma mixtures often outperform EVT methods for low and moderate rainfall.

Contribution

It evaluates and compares the performance of Naveau et al.'s EVT-based methods with gamma mixture models on a large Australian rainfall dataset.

Findings

Gamma mixtures outperform EVT methods for small and moderate rainfall.

Gamma mixtures provide equivalent fits to EVT methods for heavy rainfall.

The analysis covers 16,968 sites across Australia.

Abstract

Naveau et al. (2016) have recently developed a class of methods, based on extreme-value theory (EVT), for capturing low, moderate, and heavy rainfall simultaneously, without the need to choose a threshold typical to EVT methods. We analyse the performance of Naveau et al.'s methods, along with mixtures of gamma distributions, by fitting them to marginal non-zero rainfall from 16,968 sites spanning the Australian continent and which represent a wide variety of rainfall patterns. Performance is assessed by the distribution across sites of the log ratios of each method's estimated quantiles and the empirical quantiles. We do so for quantiles corresponding to low, moderate, and heavy rainfall. Under this metric, mixtures of three and four gamma distributions outperform Naveau et al's methods for small and moderate rainfall, and provide equivalent fits for heavy rainfall.