Long-term runoff study using SARIMA and ARIMA models in the United States

In this study, the ability of the seasonal autoregressive integrated moving average (SARIMA) and autoregressive integrated moving average (ARIMA) models was investigated for long-term runoff forecasting in the United States. In the first stage, the amount of runoff is forecasted for 2011 in each US state using the data from 1901 to 2010 (mean of all stations in each state). The results show that the accuracy of the SARIMA model is better than that of the ARIMA model. The relative error of the SARIMA model for all states is <5%. In the second stage, the runoff is forecasted for 2001 to 2011 by using the average annual runoff data from 1901 to 2000. The SARIMA model with periodic term equal to 20, R2 = 0.91, and mean bias error (MBE) = 1.29 mm is the best model in this stage. According to the obtained results, a trend is observed between annual runoff data in the United States every 20 years or almost a quarter century.