THE EFFECT OF SERIAL-CORRELATION ON RESERVOIR CAPACITY USING THE MODIFIED GOULDS PROBABILITY MATRIX-METHOD (MGPM)

The effects of serial correlation of inflows on estimating the reservo ir capacity using the modified Gould's probability matrix method was i nvestigated using the historical monthly streamflow sequences of 6 pot ential reservoir sites in Kenya. The ratios of the capacities determin ed using the starting months of analysis, giving the maximum to those determined using the starting month of analysis and giving the minimum lag 1 annual serial correlation coefficient for each flow sequence, w ere used as the indicators of this effect. This approach was adapted a fter it was observed that the correlation coefficients varied highly w ith the starting month of analysis. Average ratios of 1.02, 0.91, 0.85 and 0.76 were obtained at the 30, 50, 70 and 90% draft levels respect ively. Serial correlation therefore had an effect for drafts greater t han 30% of the means flow and this effect increased with the draft. It has therefore been recommended that the starting month of analysis gi ving the minimum annual serial correlation coefficient should be appli ed when using the modified Gould's probability matrix (MGPM) method if the demand is greater than 30% of the mean flow. It is likely that th e same recommendation could be as valid for other capacity determinati on methods that assume independence of annual flows. The minimum seria l correlation coefficients for 5 of the 6 sites were however still con siderable with 4 of them being greater than 0.1 and the maximum being 0.349. Using the starting month of analysis giving the minimum annual serial correlation coefficient may therefore not adequately prevent th e risk of an underdesign of reservoir capacity. It has been proposed t hat a method similar to the MGPM method but which routes the reservoir contents for periods longer than the one year used in the MGPM method has the potential to adequately check the serial correlation problem. The requirement is that the period should be long enough to give an i nsignificant correlation coefficient with one of the starting months o f analysis that could be applied with that period. A 2-year period has been found to give practically insignificant correlation coefficients with 5 of the 6 streamflow sequences.