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

Abstract

ABSTRACT: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, R 2 = 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.KEY WORDS ARIMA; hydrological processes; periodic term; runoff forecasting; seasonal trend Schar et al. (2004) forecasted a seasonal runoff using precipitation from meteorological data assimilation systems. The high correlations suggest that a reliable seasonal runoff forecasting system can be constructed from the statistical relationship between the model-assimilated precipitation and subsequent runoff. Artificial neural network is one of the other approaches for runoff forecasting. In addition, seasonal runoff was simulated using Hydrologic Engineering Center (HEC) models (Anderson et al., 2002). Patry and Marino (1984c) presented a two-stage urban runoff forecast model. This approach was found to be particularly useful for lead times of up to 30 min. Wang et al. (2011) developed a modified rational equation for arid-region runoff estimation successfully. Habib et al. (2007) investigated the effect of local systematic and random errors of the commonly used tipping-bucket (TB) rain gauges on the accuracy of runoff predictions. The computed runoff differences caused by the TB random errors were dependent on the magnitude of the runoff discharge, and on the temporal resolution of the rainfall input. In recent decades, radar information helps researchers in accurate forecasting of runoff data (Rahimi et al., 2014). Marino (1984a, 1984b) investigated the sensitivity and application of different equation models to real-time urban runoff forecasting. Runoff forecasting history SARIMA and ARIMA applications in hydrological forecastingAmong the many methods and models available for investigating long-term forecasts, such as stochastic models, fuzzy theory, artificial neural network (Banihabib et al., 2012;Valipour et al., * Correspondence: M. Valipour, Young Researchers and Elite Club, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran. E-mail: vali-pour@hotmail.com 2012a), and rough theory, autoregressive integrated moving average (ARIMA) and seasonal autoregressive integrated moving average (SARIMA) models have been applied based on stochastic theory; considering the serial correl...

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