Development of PCA-based cluster quantile regression (PCA-CQR) framework for streamflow prediction: Application to the Xiangxi river watershed, China

In this study, a PCA-based cluster quantile regression (PCA-CQR) method was proposed through integrating principal component analysis and quantile regression approaches into a stepwise cluster analysis framework. In detail, the principal component analysis was adopted to overcome the multicollinearity among the explanatory variables, while the quantile regression approach was used to provide probabilistic information in prediction. The proposed PCA-CQR method can effectively capture discrete and nonlinear relationships between explanatory and response variables. The applicability of PCA-CQR was demonstrated by a case study of monthly streamflow prediction in the Xiangxi River, China. The nonlinearity between the hydro-meteorological variables and the streamflow measurements was characterized through the measure of maximal information coefficient (MIC), which demonstrated the need of the proposed PCA-CQR method. The results showed that the previous monthly streamflow and precipitation, as well as potential evapotranspiration in current month posed significant nonlinear impacts on the streamflow in current month. Three components could well reflect the total variance of the input variables. Comparison between traditional SCA and PCA-CQR showed that the proposed approach could provide more accurate predictions than traditional SCA methods. Moreover, probabilistic forecasts could be provided by PCA-CQR, and the 90% predictive intervals could well bracket the observations in both calibration and validation periods. Also, sensitivity analysis was performed to identify the impacts of the control parameters in PCA-CQR on the performance of the proposed model. The results showed the proposed PCA-CQR improved the robustness of traditional SCA. Finally, comparison among PCA-CQR, GRNN and MLR also showed the effectiveness of the proposed method.