Middle and Long-Term Runoff Probabilistic Forecasting Based on Gaussian Mixture Regression

Reliable forecasts of middle and long-term runoff can be highly valuable for water resources planning and management. The uncertainty of runoff forecasting is also essential for water resource managers. However, deterministic models only provide single prediction values without uncertainty attached. In this study, Gaussian Mixture Regression (GMR) approach is applied for probabilistic middle and long-term runoff forecasting, which can quantify the predictive uncertainty directly. GMR consists two parts, optimizing the model parameters and hyperparameters of Gaussian Mixture Model (GMM) and forecasting the posterior conditional probability density. GMR is applied to a real-world runoff forecasting case study at Xiangjiaba Station and Panzhihua Station on the Jinsha River. And it is compared with Support Vector Machines and Artificial Neural Network. The experimental results show its excellent performance both on accuracy and reliability. Uncertainty estimation for the probabilistic forecast is also shown, the results demonstrate that GMR is able to handle the heteroscedastic data like runoff and can provide an effective uncertainty estimation.