Stochastic model of flow duration curves for selected rivers in north-western Bangladesh

Abstract

This study describes and demonstrates the use of a probability model for representing stochastic flow duration curves for selected rivers in the north-western region of Bangladesh. Empirical flow duration curves are also generated, compared with the stochastic flow duration curves, and finally regional flow duration curves are generated. The daily discharge records of 18 discharge gauging stations in the north-western region of Bangladesh are used in this study. The analysis involves estimation of mean daily discharge and their variance by rank, selection of homogeneous sites and a suitable probability distribution for obtaining the stochastic flow duration curve by combining the principle of order statistics. Based on homogeneity test using discordancy measures all of the above selected stations were found to be homogeneous. Four probability distributions: lognormal, gamma, generalized extreme value (GEV) and mixture lognormal, which possess the ability to match the combination of skewness and peakedness, were tested for modeling the stochastic flow duration curve. Based on X2 and K-S goodness-of-fit tests five parameter mixture lognormal distribution was found to be suitable for modeling the stochastic flow duration curve. The stochastic flow duration curves were derived applying five parameter mixture lognormal distribution for the selected gauging stations. Following this, such curves were separately obtained using observed flows and a comparison of the two showed that the mixture lognormal distribution is adequate for modeling the flow duration curve. Empirical flow duration curves for the selected stations were also generated and compared with the stochastic flow duration curves. For a given station, discharge obtained from the stochastic flow duration curve for a given rank compared reasonably well with those obtained from the empirical flow duration curve at corresponding exceedence probability. Finally, regional flow duration curves are constructed using both stochastic and empirical approaches and their comparison showed that these two regional curves also follow the similar relationship.