AR-GARCH with Exogenous Variables as a Postprocessing Model for Improving Streamflow Forecasts

Abstract

The common strategy for real-time streamflow forecasting involves a precalibrated rainfall-runoff model for streamflow simulation together with a statistical postprocessing model of simulation errors for updating simulated streamflow. Recognizing both autocorrelation and heteroscedasticity inherent in the simulation errors of rainfall-runoff models, the autoregressive-generalized autoregressive conditional heteroscedasticity (AR-GARCH) model is introduced as a statistical postprocessing model of simulation errors in this study, in which the AR model is used to forecast the mean process of simulation errors, and the GARCH model to forecast the variance process of simulation errors. For investigating how well incorporating exogenous variables that contribute to heteroscedasticity improves update accuracy by comparing the GARCH model with and without exogenous variable, in this study, two rainfall-runoff models (one lumped and one distributed) have been chosen to simulate streamflow in three basins. Case studies show that (1) the AR-GARCH model with an exogenous variable showed advantages over AR-GARCH without exogenous variables through both increased forecast accuracy and reduced uncertainty during the validation period, and (2) more than 90% of error heteroscedasticity is due to the internal variable and less than 10% is due to the exogenous variable in this study. Only one exogenous variable was considered in this study, so further research is necessary to identify more exogenous variables which may have a greater contribution to simulate error heteroscedasticity. In conclusion, the developed AR-GARCH model with exogenous variables has the flexibility to deal with the characteristics of error series including autocorrelation and heteroscedasticity. Although the application of this study focused on streamflow forecasting, the developed methodology may be generalized and implemented in other applications to time-series data with complex errors.