Single-Objective and Multi-Objective Flood Interval Forecasting Considering Interval Fitting Coefficients

Human activities and climate change have exacerbated the frequency of extreme weather events such as rainstorms and floods, which makes it difficult to accurately quantify the uncertainty characteristics in runoff prediction. Therefore, the lower and upper boundary estimation method (LUBE) has become an important means to quantify uncertainty and has been widely used. However, the traditional interval prediction evaluation system only relies on coverage and width indicators, and performs poorly in single-objective optimization methods, which limits the large-scale application of the LUBE method. Based on this, this study innovatively proposes the prediction interval fitting coefficient (PIFC), and combines the prediction interval coverage probability (PICP) and normalized average width index (PINAW) to construct the coverage width fitting-based criterion (CWFC) for the first time, which broadens and improves the interval prediction evaluation dimension system. Further, the single-objective and multi-objective LUBE interval forecasting models based on the randomized weighted particle swarm algorithm (RWPSO) and the non-dominated sorting genetic algorithms III (NSGA-III) are constructed in this study. The verification results of cascade hydropower stations in the Yalong river basin show that the calculation efficiency and prediction effect of the single target interval prediction model are both improved after the introduction of PIFC. Under the CWFC objective function, the PINAW and PIFC indexes in the prediction interval are significantly better, and the PICP gap is smaller. Under multi-objective conditions (PICP, PINAW and PIFC), the Pareto non-inferior solution set can provide more choices for decision makers. During the flood season, PICP can reach more than 93%, PINAW is controlled below 10%, and PIFC can reach more than 0.95. This fully proves that the performance of interval prediction has been significantly improved after the introduction of PIFC, and the research results can provide a new way for basin interval prediction.