UNIVARLATE LEAST SQUARES MUSKINGUM FLOOD ROUTING1

ABSTRACT: The Muskingum method of hydrologic flood routing is based on a graphical bivariate curve fitting procedure. The subjectivity of this procedure may lead to problems of reproducibility and provides no guarantee of model coefficients which minimize the error of estimation. A transformation is developed to express the Muskingum method as a univariate transcendental function suitable for numeric solution. Solution of this function minimizes the sum of the squared deviations between estimated and measured rates of discharge. Five textbook examples of the Muskingum method are evaluated by the univariate transformation. Error reductions range from negligible to tenfold. While the univariate transformation may not improve upon graphically-based results in every case, in no instances are the univariate results inferior; in many cases they are superior.