Real-time probabilistic forecasting of river water quality under data missing situation: Deep learning plus post-processing techniques

Abstract Quantifying the uncertainty of probabilistic water quality forecasting induced by missing input data is fundamentally challenging. This study introduced a novel methodology for probabilistic water quality forecasting conditional on point forecasts. A Multivariate Bayesian Uncertainty Processor (MBUP) was adopted to probabilistically model the relationship between the point forecasts made by a deep learning artificial neural network (ANN) and their corresponding observed water quality. The methodology was tested using hourly water quality series at an island of Shanghai City in China. The novelties relied upon: firstly, the use of a transfer learning algorithm to overcome flatten- and under-prediction bottlenecks of river water quality raised in artificial neural networks, and secondly, the use of the MBUP to capture the dependence structure between observations and forecasts. Two deep learning ANNs were used to make the point forecasts. Then the MBUP approach driven by the point forecasts demonstrated its competency in improving the accuracy of probabilistic water quality forecasts significantly, where predictive distributions encountered in multi-step-ahead water quality forecasts were effectively reduced to small ranges. The results demonstrated that the deep learning plus the post-processing approach suitably extracted the complex dependence structure between the model’s output and observed water quality so that model reliability (Containing Ratio > 85% and average Relative Band-width   0.8 and Root-Mean-Square-Error