Abstract
Probabilistic models are useful tools in understanding rainfall characteristics, generating synthetic data and predicting future events. This study describes the results from an analysis on comparing the probabilistic nature of daily, monthly and seasonal rainfall totals using data from 1327 rainfall stations across Australia. The main objective of this research is to develop a relationship between parameters obtained from models fitted to daily, monthly and seasonal rainfall totals. The study also examined the possibility of estimating the parameters for daily data using fitted parameters to monthly rainfall. Three distributions within the Exponential Dispersion Model (EDM) family (Normal, Gamma and Poisson-Gamma) were found to be optimal for modelling the daily, monthly and seasonal rainfall total. Within the EDM family, Poisson-Gamma distributions were found optimal in most cases, whereas the normal distribution was rarely optimal except for the stations from the wet region. Results showed large differences between regional and seasonal ϕ-index values (dispersion parameter), indicating the necessity of fitting separate models for each season. However, strong correlations were found between the parameters of combined data and those derived from individual seasons (0.70–0.81). This indicates the possibility of estimating parameters of individual season from the parameters of combined data. Such relationship has also been noticed for the parameters obtained through monthly and daily models. Findings of this research could be useful in understanding the probabilistic features of daily, monthly and seasonal rainfall and generating daily rainfall from monthly data for rainfall stations elsewhere.
Highlights
Probabilistic models have extensive applications in understanding rainfall characteristics, generating synthetic data and predicting future events [1,2]
The models slightly overestimate the 95th percentiles of daily rainfall and underestimate the 99th percentiles of daily and overestimate the 95th percentiles of daily rainfall and underestimate the 99th percentiles of daily and
Advanced statistical models have been fitted to data from 1327 gauging stations with reasonably long continuous rainfall records to test the applicability of different probability distribution functions
Summary
Probabilistic models have extensive applications in understanding rainfall characteristics, generating synthetic data and predicting future events [1,2]. Model based prediction has been used in ecology, hydrology, water resources management and agricultural planning [3,4,5,6]. Synthetic data obtained through models are useful when observed rainfall record is inadequate in length, completeness, or spatial coverage [7,8,9]. Determining theoretical probability distributions for modelling rainfall at various timescales has gained interest in contemporary literature. Either Markov chain [10,11] or logistic regression models [12] have been used to model occurrence of daily rainfall.
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