A multi-period Markov model for monthly rainfall in Lagos, Nigeria

Abstract

Long periods of historical hydrological data such as rainfall and streamflow which are necessary for planning and design of water resources projects, are often not available and have to be forecasted. Many models available for this were developed and tested in developed countries in temperate climates and so their application in tropical climates is questionable. A twelve-period Markov model has been developed for the monthly rainfall data for Lagos, along the coast of South Western Nigeria. The goodness of fit of the model was assessed by estimating the autocorrelations of the residuals of the historical data (from January 1924 to December 1983) for lags one to sixty. A 95% confidence band was also established for the autocorrelations. The results show that all but two of the autocorrelations fall within the 95% confidence band confirming that the residuals are indeed white noise. This indicates that the model is very adequate.

Multi-scale invariant fields: estimation and prediction

“…Examples of this can be described as the sub-sequences of PC processes. For instance, Tthe accumulated precipitation on the same month of successive years for a specific place, or the traffic volume of a highway at some specific hour of each working can be considered in this way (see [2,11,32]). One may term such Markov properties as periodic Markov properties, in that subsequences are obtained at points {t + nτ , n ∈ N} for any fixed t, where τ is the period of the main PC sequences.…”

“…Therefore, at a level of 95% certainty, the first component scale Markov property for the precipitation is accepted. Using the same method, the sample partial auto-correlation α Y 2 (2) of Y 2 at lag 2 is evaluated by estimating R X * 2 (2) and R X * 2 (1); these estimates are performed using the accumulated precipitation data for the pair of sub-rectangles (A i1,k , A i3,k ), and the pair of sub-rectangles (A i1,k , A i2,k ) or (A i2,k , A i3,k ) for i = 1, 2, 3 and k = 1, 2, 3, 4 which cause the sample partial auto-correlation at lag 2, of, say α Y 2 (2), to be evaluated as 0.3242…”