Estimation of a Unique Pair of Nash Model Parameters: An Optimization Approach

Water resources planning and management requires hydrologic models to estimate runoff from a catchment. For catchments with limited data, the choice of model and identification of its parameters is very important for development of a direct runoff hydrograph. A method is presented to determine a unique pair of hydrologic parameters of the Nash Model, number of linear cascade (n) and storage coefficient (k), using optimization based on Downhill Simplex technique. In this study physical parameters of the catchment are derived from (SPOT) satellite imageries of the basin using ERDAS software. Four different objective functions of varying complexity are tested to find the best solution. Weighted root mean square error (RMSE) and Model Efficiency (Nash-Sutcliffe coefficient) are used to evaluate the model performance. Using the NASH model, a direct surface runoff hydrograph (DSRH) is developed. Kaha catchment is part of Indus river system and is located in the semi-arid region of Pakistan. This catchment is dominated by hill torrent flows and is used in this work to demonstrate the applicability of the proposed method. Ten randomly selected rainfall-runoff events are used for calibration and five events are used for validation. Model results during validation are very promising with model efficiency exceeding 93% and error in peak discharge under 8%. The sensitivity of the Nash model output in response to variation in hydrologic parameters n and k is also investigated. When evaluating the hydrologic response of large catchments, model output is more sensitive to n as compared to k indicating that the runoff diffusion phenomenon is dominant compared to translation flow effects