Fuzzy multi-objective function for rainfall-runoff model calibration

Continuous rainfall-runoff modeling is essential to simulate the rainfall-runoff relationship in water resource projects. The performance of a rainfall-runoff model heavily depends on suitable choice of model parameters, which are normally calibrated by using an objective function. This study presents a fuzzy multi-objective function (FMOF) to improve the performance of conventional objective functions, such as the root mean square error (RMSE) and the mean absolute percent error (MPE). Daily rainfall and flow discharge measurements, as well as monthly evaporation estimates are used to calibrate and verify a rainfall-runoff model, over a 9-year and a 4-year period, respectively. The model calibrated with RMSE and MPE as objective functions tends to match high and low flow periods, respectively. The FMOF leads to improved simulation of a wide range of flow stages as it can combine various objective functions with different acceptable levels. The method suggested herein is shown to be more appropriate for basins with extremely heterogeneous temporal flow distribution.