AR-GARCH with Exogenous Variables as a Postprocessing Model for Improving Streamflow Forecasts
Publication: Journal of Hydrologic Engineering
Volume 25, Issue 8
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.
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Data Availability Statement
Except the daily inflow and outflow data of reservoirs which are obtained under nondisclosure agreement, other data, models, or code used in this study are available from the corresponding author by request.
Acknowledgments
This study was supported by the National Key R&D Program of China (2017YFC0405901), the National Natural Science Foundation of China (Grant Nos. 41890822 and 51525902), the Research Council of Norway (FRINATEK Project 274310), and the Ministry of Education “Plan 111” Fund of China (B18037), all of which are greatly appreciated. We greatly appreciate the editor and the three reviewers for their insightful comments and constructive suggestions for improving the manuscript.
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Journal of Hydrologic Engineering
Volume 25 • Issue 8 • August 2020
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©2020 American Society of Civil Engineers.
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Received: Aug 15, 2019
Accepted: Feb 21, 2020
Published online: May 31, 2020
Published in print: Aug 1, 2020
Discussion open until: Oct 31, 2020
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