Multi-criteria optimisation of the Muskingum flood model: a new approach

Abstract

Existing Muskingum hydrological routing models adopt a single criterion in the calibration process. Some models minimise the sum of the squared deviations between estimated and observed outflows (outflow criterion), while others minimise the sum of the squared deviations between the estimated and observed storages (storage criterion). However, models that adopt the outflow (storage) criterion result in a poor fit to the observed storages (outflows). This paper presents a new approach that incorporates both criteria in the calibration process and aids trade-off analysis. The multi-criteria function is expressed as a weighted function of normalised outflow and storage criteria, representing the deviations from ideal outflow and storage values. The routing procedure is based on the author's four-parameter Muskingum model with constant parameters and the fourth-order Runge–Kutta method. The proposed model was applied to three examples. A criterion weight of 0·4–0·6 was found to produce an excellent trade-off between outflow and storage criteria. The results show that the model substantially improves on both criteria compared with single-criterion models. The proposed model, which properly captures the entire flood propagating characteristics in calibration, should be of interest to hydrological engineers and practitioners.