Stochastic modelling of daily rainfall in Nigeria: intra-annual variation of model parameters

Abstract

A Markov model of order 1 may be used to describe the occurrence of wet and dry days in Nigeria. Such models feature two parameter sets; P01 to characterise the probability of a wet day following a dry day and P11 to characterise the probability of a wet day following a wet day. The model parameter sets, when estimated from historical records, are characterised by a distinctive seasonal behaviour. However, the comparison of this seasonal behaviour between rainfall stations is hampered by the noise reflecting the high variability of parameters on successive days. The first part of this article is concerned with methods for smoothing these inherently noisy parameter sets. Smoothing has been approached using Fourier series, averaging techniques, or a combination thereof. It has been found that different methods generally perform well with respect to estimation of the average number of wet events and the frequency duration curves of wet and dry events. Parameterisation of the P01 parameter set is more successful than the P11 in view of the relatively small number of wet events lasting two or more days. The second part of the article is concerned with describing the regional variation in smoothed parameter sets. There is a systematic variation in the P01 parameter set as one moves northwards. In contrast, there is limited regional variation in the P11 set. Although this regional variation in P01 appears to be related to the gradual movement of the Inter Tropical Convergence Zone, the contrasting behaviour of the two parameter sets is difficult to explain on physical grounds.q1999 Elsevier Science B.V. All rights reserved