A parametric daily precipitation model application in Botswana

Abstract

A parametric precipitation model is developed for generation of daily rainfall time series based on historic data. The precipitation model is a composite model of Markov-chain (MC) and probability distribution (PD). Thirty nine rain gauge stations in Botswana that have daily rainfall record length in the range of 11 to 83 years have been considered to test the applicability of the model. Results show that Markov-chain (MC) model can be used to model the persistence behaviour of the transition probability matrix (TPM) of dry and wet day rainfall sequences. With the MC model, the two-parameter gamma distribution is found to be most robust and suitable model to describe the magnitude of rainfall depths in wet days. The performance of the gamma distribution was evaluated among other three candidate distributions we considered, namely the lognormal, the exponential and weibull distributions. We have conducted model performance tests of the proposed precipitation model and its MC and PD components with the historical records. Both the sequence of wet-dry day sequences and rain day rainfall magnitudes were simulated with the seasonally varying parameter sets we have developed. Simulated rainfall, both its dry-wet day sequence and rainy day rainfall depths were closely comparable with the historical records with reasonably success rates. Regression coefficient between the simulated and observed annual rainfall at the 39 stations is 66%.

Key Words: Markov Chain, Transition Probability Matrix, Gamma distribution, Parameter, Descriptive ability test