Probabilistic Prediction for Monthly Streamflow through Coupling Stepwise Cluster Analysis and Quantile Regression Methods

In this study, a stepwise cluster forecasting (SCF) framework is proposed for probabilistic prediction for monthly streamflow through integrating stepwise cluster analysis and quantile regression methods. The developed SCF method can capture discrete and nonlinear relationships between explanatory and response variables. A cluster tree was generated through the SCF method for reflecting complex relationships between independent (i.e. explanatory) and dependent (i.e. response) variables in the hydrologic system. Quantile regression approach was employed to construct probabilistic relationships between inputs and outputs in each leaf of the cluster tree. The developed SCF method was applied for monthly streamflow prediction in Xiangxi River based on the gauged records at Xingshan gauging station and related meteorological data. The performance of the SCF method was evaluated through indices of percent bias (PBIAS), RMSE-observations standard deviation ratio (RSR), and Nash-Sutcliffe efficiency coefficient (NSE). Two new indices, the relative distance to the bounds (RDB) and the degree of uncertainty (DOU) were proposed to reflect the uncertainty of the predictions from SCF model. The results showed that the uncertainty of the predictions was acceptable and would not change significantly in calibration and validation periods. Quantile regression was integrated into prediction process of the SCF approach to provide probabilistic forecasts. The 90 % confidence intervals could well bracket the observations in both calibration and validation periods. Comparison among different forecasting techniques showed the effectiveness of the proposed method.