Flow Duration Curve Using Entropy Theory

Using the entropy theory, this study derives a function for modeling the flow duration curve (FDC) based on two equations that form simple constraints: (1) the total probability of all flow discharges, and (2) the mean discharge. Parameters of the derived curve are determined from the entropy theory with the use of these two constraints. For deriving the flow duration curve by the entropy theory, a nonlinear cumulative distribution function is assumed, which is tested using observed flow data. The derived flow duration curves are tested using field data and are found to be in agreement with observed curves. With the entropy parameter determined for each station, the flow duration curve can also be forecasted for different recurrence intervals. The main advantage of the use of the entropy theory-based FDCs is that the parameters are based on observations, and hence no fitting is needed. Second, the theory permits a probabilistic characterization of the flow duration curve and hence the probability density function underlying the curve. It also permits a quantitative assessment of the uncertainty of the flow duration curve. Additional work is needed to regionalize the FDC parameters. (C) 2014 American Society of Civil Engineers.