Rainfall-runoff process modeling using time series transfer function

Extended Abstract 1- Introduction Nowadays, forecasting and modeling the rainfall-runoff process is essential for planning and managing water resources. Rainfall-Runoff hydrologic models provide simplified characterizations of the real-world system. A wide range of rainfall-runoff models is currently used by researchers and experts. These models are mainly developed and applied for simulation and prediction. They allow decision-makers to make the most effective decision for planning and operation. Rainfall-runoff modeling is essential in flood routing, flood prediction, flood frequency estimation, real-time flood forecasting, warning climate changes, and other cases. Time series analysis includes methods for analyzing and modeling time-series data to extract forecasts and other characteristics of the time-series data. Time series forecasting is using a model to predict future values based on previously observed values. The transfer function is an advanced and multivariate time series model that enables us to utilize other time series to produce response time-series forecasts. Although the rainfall-runoff process has been modeled by various methods so far, less attention has been paid to the transfer function model. The primary purpose of this study is to introduce the transfer function to model the rainfall-runoff process and compare its results to the common time series model (SAIRMA) in Ramian and Galikesh watersheds.   2- Methodology In this research, to model the rainfall-runoff process, the monthly averages of rainfall and discharge time series of Ramian and Galikesh watersheds were used for a period of 36 years (1981-2017). These two watersheds are branches of the Gorganroud River which has an essential role in providing water resources required in Golestan province. The time series homogeneity was examined using Chow`s method. The existence of trends in time series was investigated based on the moving average time series plot, and the existence of seasonal trends was explored using autocorrelation charts. The cross-correlation diagram was used to investigate the relationship between rainfall and runoff time series. The SARIMA and transfer function models were used to predict monthly runoff. Without considering the rainfall time series, the runoff time series was modeled by a SARIMA model. Also, considering the precipitation time series as an input time series, a transfer function is used to model runoff time series as a response time series. The transfer function modeling was performed in three steps, pre-whitening, selecting the appropriate parameters of the transfer function model, and finally fitting a SARIMA model to the residual values. For the SARIMA model, the goodness of fit test was evaluated based on the Box Pierce statistic. For the transfer function model, two indices were computed. The first index investigated the relationship between runoff and rainfall, and the second index performed the goodness of fit test for residual time series. Then, based on the forecasted and fitted values and using MAD, RMSE, MAPE, and E indices, the accuracy, and precision of SARIMA and transfer function models were compared.   3- Results  According to the autocorrelation diagrams, the results showed that the all-time series has a seasonal trend over 12 months. Also, according to the moving average time series, there was no significant shift in rainfall time series, but there was a decreasing trend in the runoff time series. The transformation log(1+Yt)   was used to the monthly average discharges time series. Then, the transfer function and SARIMA models were used to forecast the monthly average discharges for the next 12 months by using Minitab and SAS software. In the next step, the validation of the predicted data and the fitted data of monthly average discharges of two models were evaluated using MAD, RMSE, MAPE, and E indices. The results showed that the transfer function model in both Galikesh and Ramian watersheds has higher precision from the two perspectives of forecasting and model fitting than the Box and Jenkins (SARIMA) model.   4- Discussion & Conclusions  In this research, to model the rainfall-runoff process, the monthly average of rainfall and runoff were used in Ramian and Galikesh watersheds. Then SARIMA and transfer function models were used to predict monthly runoff. The results showed that the transfer function model in both Galikesh and Ramian watersheds has higher precision than the SARIMA model from the two forecasting and model fitting perspectives. Changes in rainfall, directly and indirectly, cause changes in runoff, and this effect might be happened either at the same time or with a time lag. The transfer function model can consider the time lags of both time series in forecasting runoff time series. The SARIMA models lack the information of other environmental parameters and apply just the runoff in the present and past times to predict future values. Since the pattern of these parameters changes annually, not considering these changes leads to unreliable forecasts from SARIMA models. However, in transfer function models, it is possible to investigate the effect of more than one environmental parameter on the runoff changes, increasing the accuracy of model fitting and forecasting.