Evaluation of the accuracy of HMS-SMA and bilinear time series models in predicting daily runoff (Case study: Idenak station at Maroun basin)

Abstract
Background and Objective: Prediction of runoff in order to effective operation of flood control reservoirs and earth flood walls is essential. Predictions also make possible emergency operation of reservoirs by estimating time of floods occurrence and expected damages. Predictions are based on recent meteorological and hydrological conditions of the basin and may include future conditions. Although, most of applications are for flood prediction, these may support water supply, hydroelectric requirements, environmental needs and other requirements for operation. Thus, various complex relations and models such as conceptual rainfall-runoff, linear time series, and hybrid models are developed, but in most cases the calculated values obtained by the models are significantly different. The objective of this research is assessment of precision of HMS-SMA conceptual model and bilinear model in prediction of daily runoff of Maroun basin located in Khouzestan province of Iran. The distinction between the current study and previous studies is that the comparison of the HEC-HMS and bilinear time series models has not been considered so far to predict daily runoff in Iran.
Materials and Methods: In the current study, daily discharge data of Maroun river within 17 years (1995-2011) at Idenak hydrometric station located in Maroun basin were analyzed. Maroun basin to upstream of Maroun dam according to topography and location of hydrometric stations was divided to four sub-basins and each of the sub-basins were introduced to HMS-SMA conceptual model independently. Amongst different rainfall-runoff models in HEC-HMS conceptual model, Clark’s unit hydrograph was used because of its applicability and acceptable performance in large basins. Furthermore, according to literature review and suggestions, SMA model of linear reservoir base flow was used for estimating of base flow. Flood routing in various reaches were performed by Muskingum method. Additionally, due to possibility of snowfall in the basin, for modeling of snow melt, index temperature method was used. Bilinear models were introduced by Granger and Anderson. In fact, bilinear models are extension of second order Taylor series. Considering to non-persistence of mean and variance of time series of discharge of Idenak station, the time series transformed to a persistent one by differencing, Box-Cox and square root transformation.
Results: Considering to various hydrograph shapes in verification and calibration processes, it is evident that HMS-SMA model has a good precision in estimating low flows compare to high flows. The mean and variance of the time series transformed to a persistent one by second order differencing. Then various bilinear models with various orders were fitted to time series data. Verification of the fitted bilinear models to daily discharges of Idenak station was achieved by portemanteau statistic. Finally, bilinear model in the form of BL(2,2,1,1) with the least Akaike criterion was selected as the best model and was applied for comparing to the predicted daily discharges by the HMS-SMA model.
Conclusion: Summing up assessment criteria of the HMS-SMA and bilinear models show that bilinear model in the form of BL(2,2,1,1) with a coefficient of determination, sum of residual errors and mean square root of errors equal to 0.91, 8.9, and 17.8 respectively, is the best model with high precision in modeling and prediction of daily discharges of Maroun basin compare to HMS-SMA model. Furthermore, it is concluded that by increasing order of moving average in bilinear models, their ability for predicting daily discharges decreases.