Variable parameter McCarthy–Muskingum routing method considering lateral flow

Abstract

Summary The fully mass conservative variable parameter McCarthy–Muskingum (VPMM) method recently proposed by Perumal and Price (2013) for routing floods in channels and rivers without considering lateral flow is extended herein for accounting uniformly distributed lateral flow contribution along the reach. The proposed procedure is applied for studying flood wave movement in a 24.2 km river stretch between Rottweil and Oberndorf gauging stations of Neckar River in Germany wherein significant lateral flow contribution by intermediate catchment rainfall prevails during flood wave movement. The geometrical elements of the cross-sectional information of the considered routing river stretch without considering lateral flow are estimated using the Robust Parameter Estimation (ROPE) algorithm that allows for arriving at the best performing set of bed width and side slope of a trapezoidal section. The performance of the VPMM method is evaluated using the Nash–Sutcliffe model efficiency criterion as the objective function to be maximized using the ROPE algorithm. The twenty-seven flood events in the calibration set are considered to identify the relationship between ‘total rainfall’ and ‘total losses’ as well as to optimize the geometric characteristics of the prismatic channel (width and slope of the trapezoidal section). Based on this analysis, a relationship between total rainfall and total loss of the intermediate catchment is obtained and then used to estimate the lateral flow in the reach. Assuming the lateral flow hydrograph is of the form of inflow hydrograph and using the total intervening catchment runoff estimated from the relationship, the uniformly distributed lateral flow rate q L at any instant of time is estimated for its use in the VPMM routing method. All the 27 flood events are simulated using this routing approach considering lateral flow along the reach. Many of these simulations are able to simulate the observed hydrographs very closely. The proposed approach of accounting lateral flow using the VPMM method is independently verified by routing flood hydrograph of 6 flood events which are not used in the total rainfall vs total loss relationship established for the intervening catchment of the studied river reach. Close reproduction of the outflow hydrographs of these independent events using the proposed VPMM method accounting for lateral flow demonstrate the practical utility of the method.