Tsallis Entropy-Based Flow Duration Curve

The flow duration curve (FDC) is employed for addressing a multitude of problems in water resources engineering, such as prediction of the distribution of future flows, forecasting of future recurrence frequencies, comparison of watersheds, construction of load duration curves, and determination of low flow thresholds. Usually, the FDC is constructed empirically for a given set of flow data, and the FDC so constructed is found to vary from one year to another and from one gauging station to another within the same watershed. This article attempts to analytically derive the FDC by maximizing the Tsallis entropy based on the knowledge that the mean discharge is known, thus obviating the need for any fitting. The mean discharge is found to be strongly related to the drainage area. The Tsallis entropy-based FDC is tested using field data and is found to be in agreement with the observed curve. The entropy method permits a probabilistic characterization of the FDC and hence a quantitative assessment of its uncertainty. With this method, the flow duration curve can also be forecasted for different recurrence intervals. The entropy is found to monotonically increase with the increase in time interval, indicating that the flow system becomes more complex but the degree of complexity decreases with increasing time interval after a certain time, eventually reaching a constant value, reflecting a reduced influence of land use change and other human influences on the flow regime.