Comparison of the modified gould's probability matrix and the behaviour analysis method of reservoir capacity determination

Abstract

This study mainly consisted of a quantitative comparison of the Behavior Analysis (BA) and the Modified Gould's Probability Matrix (MGPM) method of reservoir capacity determination. By a qualitative analysis that evaluated tht'capability of sixteen methods to model the reservoir capacity d termination problem, the two were found to be superior to the rest The effects of the main shortcomings of the two procedures; the assumption of an initial storage state (ISS) in using the BA and the assumption that annual flows are independent (zero annual serial correlation (ASC)) in using the MGPM method were studied, minimised and the methods then compared. Historical monthly streamflow sequences from six potential reservoir sites within Kenya were used. Draft levels of 30, 50, 70 and 90% of the mean flow and probabilities of failures of 2, 4, 6, 8, 10, 12, 14 and 16% were applied. The effect of ISS was investigated by comparing capacities determined assuming an ISS of 100% with those determined. assuming ISSs of 75, 50, 25 and 0%. It was observed that ISS was highly significant at the 90% draft and only slightly significant for two sequences at the 70% 1eve 1 . At the 30 and 50% 1eve 1, it was insignificant. The effect of ISS was minimised by computing the averages of the capacities determined assuming all the five or"the three ISSs of 25, 50 and 75%. As the lag 1 annual se ri a lvco rre lat t on coefficient (ASCC) varied highly with the starting month of analysis (SMA), it was decided that the effect of ASC be studied using the SMAs giving the least and those giving the highest ASCC. ASC was found to be significant for draft levels greater than 30% with this effect increasing wit~ draft. It was thus recommended that to minimise the effect of ASC, the SMA giving the least ASCC should be used if the draft level is greater than 30%. As the minimum ASCC could still be significant, applying the SMA giving the least ASCC may not eliminate the effect of ASC. Procedu res that app 1y du rat ions 1onge r than 1 year but otherwi~e similar to the MGPM were proposed as potentially better in eliminating the effect of serial correlation. The development and testing of such procedures was thus recommended. The comparison of the BA and the MGPM method revealed that the two gave capacities comparing reasonable well at the 30% draft. At higher/drafts, the BA gave capacities greater than the MGPM with the variation increasing with draft. From a further analysis, it was observed that for three of the sequences at the 90% draft, the BA method assuming an initially full reservoir (ISS of 100%) gave capacities considerably greater than the MGPM method using the SMAs giving the 1east ASCC. These obse rvat ions ind icat e t hat for drafts greater than 30% of the mean flow, the BA method is a better procedure to use than the MGPM in order to avoid underdesign.