Young-Oh Kim 1 , Dae-Il Jeong 2 , Seung-Oh Yu 3 , and Ick-Hwan Ko 4
1 School of Civil, Urban & Geosystems Engineering, Seoul National University, San 56-1, Shillim-Dong, Kwanak- Ku, Seoul, 151-742, Korea (tel: +82 2 880-8916, email: yokim@snu.ac.kr )
2 School of Civil, Urban & Geosystems Engineering, Seoul National University (tel: +822 880-8354, email:jung922@snu.ac.kr )
3 School of Civil, Urban & Geosystems Engineering, Seoul National University (tel: +82 2 880-8354, email:skull1@snu.ac.kr )
4 Water Resources Research Institute, Korea Water Resources Corporation, 462-1, Jonmin-dong, Yusung-Gu, Daejeon, 305-790, Korea (tel: +82 42 860-0311, email:ihko@kowaco.or.kr )
Introduced in 1970’s, ESP (Ensemble Streamflow Prediction) became a key part of the advanced hydrologic prediction system for the National Weather Service in the United State. In Korea, Kim et al. (2001) introduced ESP as an alternative probabilistic forecasting technique for improving the water supply outlook. More recently, Jeong and Kim (2002) successfully applied the same technique to a one-month ahead inflow forecasting for Chungju multipurpose dam in Korea. In their study, it was emphasized that systematic (or modeling) error dominates in the winter and spring (i.e. dry seasons) while random (or meteorologic) error dominates in the summer (i.e. wet season). They suggested that the rainfall-runoff used model used in their ESP study should be improved to obtain more accurate probabilistic inflow forecasts, which is the objective of the present study.
To improve the output series of a rainfall-runoff model, one generally has to analyze all the model components and to devise better alternatives for some components that may degrade the model performance. This type of improvement strategy, however, requires considerable effort and time. The present study proposed an alternative way to improve the model performance: Rather than modifying the model itself, the model output (i.e. the simulated runoff series) is adjusted by using the exogenous information. In this study, we assumed another rainfall-runoff model so that another series of the simulated runoff would be available as the exogenous information. This study then attempted to improve the simulated runoff series of the first model by “combining” with the simulated runoff series of the second model. In other words, two (or more) independently calibrated rainfall-runoff models were combined to improve their simulation accuracy.
Since first introduced by Bates and Granger (1969), combining methods have been studied and applied for economic forecasting. In hydrologic forecasting or simulation studies, however, few paid attention to this topic. McLeod et al. (1987) reported the first experiments dealing with the combination of river flow forecasts, but no further significant study has been made since then. McLeod et al. (1987) made several forecasts of a monthly river flow from time series and conceptual rainfall-runoff models and combined the forecasts based on the forecast error covariance. They found significant improvements in forecast performance when forecasts from different models were combined.
In this study, we attempted to make a broader review of combining methods that have been commonly used in economic forecasting than McLeod et al. (1987) did and compared performance of the combining methods though a hydrologic example. Note that the combining theory described in the following section can be applied to both cases of forecasting and simulating hydrologic time series.