Using Mixed Probability Distribution Functions for Modelling Non-Zero Sub-Daily Rainfall in Australia

Abstract

Probabilistic models for sub-daily rainfall predictions are important tools for understanding catchment hydrology and estimating essential rainfall inputs for agricultural and ecological studies. This research aimed at achieving theoretical probability distribution to non-zero, sub-daily rainfall using data from 1467 rain gauges across the Australian continent. A framework was developed for estimating rainfall data at ungauged locations using the fitted model parameters from neighbouring gauges. The Lognormal, Gamma and Weibull distributions, as well as their mixed distributions were fitted to non-zero six-minutes rainfall data. The root mean square error was used to evaluate the goodness of fit for each of these distributions. To generate data at ungauged locations, parameters of well-fit models were interpolated from the four closest neighbours using inverse weighting distance method. Results show that the Gamma and Weibull distributions underestimate and lognormal distributions overestimate the high rainfall events. In general, a mixed model of two distributions was found better compared to the results of an individual model. Among the five models studied, the mixed Gamma and Lognormal (G-L) distribution produced the minimum root mean square error. The G-L model produced the best match to observed data for high rainfall events (e.g., 90th, 95th, 99th, 99.9th and 99.99th percentiles).

Keywords

• sub-daily rainfall
• ungauged catchment
• statistical modelling
• probability distribution