Evaluation of the Combined AR-ARCH and GAR-ARCH Models in Modeling Rivers Flow Rate (Case Study: Zarineh River in West Azerbaijan)

Many of processes related to water resources systems are non-linear over time. Although certain aspects of these systems may be closer than other aspects of the linear process. However, the nature of the non-linearity is not obvious for us. For this reason, it seems that by combination of linear and nonlinear models can be increased the hydrological modeling results. Using time series models is one of the applied methods to simulate and predict the hydrological data. One of the main problems in using time series models to modeling and prediction the hydrologic data is a kind of generate random data series. In this process the generated data will be changed with changing random series. In this study, the first, time series of Zarineh rood river discharge data were evaluated of initial analysis such as trend, stationary and independent and homogeneous. The results showed that the evaluated data in annual scale and in 5 percentage confidence level are without trend and the homogeneity and stationary of data were confirmed. Finally the data that were evaluated with the initial tests were investigated with the AR (Autoregressive) and GAR (Gamma Autoregressive) models and the AR(1) and GAR(1) models were selected as the best models with attention to the AICC test’s results. After the comparing the mentioned (AR & GAR) models, extracted the residual time series of these models and were fitted by ARCH (Autoregressive Conditional Heteroscedastic) models. Then combined two autoregressive and gamma autoregressive models, two AR-ARCH and GAR-ARCH models were obtained. The results of modeling the discharge of Zarineh-rood river showed that with combined two GAR-ARCH and AR-ARCH models, the model validation accurate was increased 12 percentage and 11 percentage in scale of cubic meters per second respectively and the model errors were decreased about 40 and 50 percentages in scale of cubic meters per second respectively. The results of evaluation and comparing the accuracy and amount error of two AR (Autoregressive) and GAR (Gamma autoregressive) models showed that the GAR (Gamma autoregressive) model has better results in modeling the Zarineh-rood flow discharge data. The GAR model has a lower error and upper accuracy than AR model. Also the results showed that the combined models have better results than traditional models in modeling the peak flow discharge of Zarineh-rood River in comparing the AR (Autoregressive) models. Using the nonlinear models and combine of these models with linear models greatly increases the modeling and forecasting results.