Chance-Constrained Optimization-Based Parameter Estimation for Muskingum Models

Abstract

The development of a chance-constrained optimization-based model for Muskingum model parameter estimation is presented. The desired Muskingum model parameters are to be useful to give the flood forecast in terms of expected flood for given limits of tolerance and probability of occurrence. When errors of observation occur, an error term is added to a mean flow to give the actual flow. The developed model minimizes the sum of squares of difference between the actual observed and computed outflows in order to determine the Muskingum model parameters. The constraints are the chance-constrained Muskingum flow routing equations. The first-order second moment method of chance-constrained optimization is used to develop the optimization model. The developed model is demonstrated for four scenarios of Muskingum model parameter estimation. The results show that, given the allowable limits of error in Muskingum model parameters, the developed model has a capability to give expected values of Muskingum model parameters when the historic data that are used for the parameter estimation process contain a specified amount of observation errors and obey a specified probability distribution. The chance-constrained optimization-based model for Muskingum model parameter estimation results into Muskingum model parameters that can give flood forecasts such that the forecasted flood allows the provision of better flood damage mitigation facilities.