Calibration and prediction uncertainty analysis of a hydraulic-water quality coupling model using a modified moth-flame optimizer

There is a lag between the latest development of the heuristic algorithm and its application in environmental model calibration. Besides, heuristic algorithms are usually thought to be deterministic and can hardly account for the equifinality of different parameters. To fix these limitations, we proposed a novel elite opposition-modified moth-flame optimizer (EOMFO) and presented a scheme combining it with the frequency statistical method for auto-calibration and prediction uncertainty estimation. A case study of a hydraulic-water quality coupling model was provided, in which the urban non-point source ammonia nitrogen (NH3-N) and total phosphorus (TP) were simulated. Compared with the benchmark particle swarm optimizer (PSO) and MFO, EOMFO has better global optimization ability and can obtain behavioral samples with higher quality for sensitive parameters. Regarding the calibration performance, EOMFO performed well in both the NH3-N and TP simulations (Nash–Sutcliffe efficiency around or greater than 0.5 and R greater than 0.7) and outperformed benchmark algorithms for both the deterministic prediction and uncertainty band prediction. The generated uncertainty band bracketed the majority of TP observation points, although it is not in good agreement with NH3-N observations due to several potential reasons. With this scheme, a more efficient and robust calibration process is expected.