Evaluation of Stochastic Daily Rainfall Data Generation Models

Abstract

In developing countries, data is usually a scarce resource as data collection is an expensive exercise. Therefore, analytical method is required to simulate the actual situations and provide synthetic data for forecasting purposes. This paper will compare several methods of synthetically generating rainfall data based on available data. Several models will be used, including lag-one Markov chain model, two-step model, and transition probability model to generate stochastic daily rainfall data of long-term duration, using data from a catchment in Australia. Three variations of lag-one Markov chain models were used: untransformed, logarithmic transformation, and square root transformation. Two-step model uses Markov chain to model rainfall occurrences and gamma distribution to model rainfall depths. Six variations of the Transition Probability Matrices were used, 3 using Shifted Exponential Distribution and 3 using Box-Cox Power Transformation was adopted to predict the high rainfall depths, and the parameters are determined using maximum-likelihood method on the available rainfall data. The models' results were tested by comparing the statistics of the generated data against those of the available data. Direct comparisons of the means, standard deviations, and skews show satisfactory results. Further comparisons of monthly means, standard deviations, skews, maxima and minima, as well as the lengths of wet and dry spells had also shown satisfactory results. In conclusion, all the models have produced synthetic rainfall data, which are statistically similar to those of the available data. In comparison, the TPM model gave the most accurate results. Therefore, this model may be utilised for synthetic rainfall data generations, which can then be used for forecasting.