A balanced calibration of water quantity and quality by multi-objective optimization for integrated water system model

Due to the high interactions among multiple processes in integrated water system models, it is extremely difficult, if not impossible, to achieve reasonable solutions for all objectives by using the traditional step-by-step calibration. In many cases, water quantity and quality are equally important but their objectives in model calibration usually conflict with each other, so it is not a good practice to calibrate one after another. In this study, a combined auto-calibration multi-process approach was proposed for the integrated water system model (HEQM) using a multi-objective evolutionary algorithm. This ensures that the model performance among inseparable or interactive processes could be balanced by users based on the Pareto front. The Huai River Basin, a highly regulated and heavily polluted region of China, was selected as a case study. The hydrological and water quality parameters of HEQM were calibrated simultaneously based on the observed series of runoff and ammonia-nitrogen (NH₄-N) concentrations. The results were compared with those of the step-by-step calibration to demonstrate the rationality and feasibility of the multi-objective approach. The results showed that a Pareto optimal front was formed and could be divided into three clear sections based on the elastic coefficient of model performance between NH₄-N and runoff, i.e., the dominated section for NH₄-N improvement, the trade-off section between NH₄-N and runoff, and the dominated section for runoff improvement. The trade-off of model performance between runoff and NH₄-N concentration was clear. The results of the step-by-step calibration fell in the dominated section for NH₄-N improvement, where just the optimum of the runoff simulation was achieved with a large potential to improve NH₄-N simulation without a significant degradation of the runoff simulation. The overall optimal solutions for all the simulations appeared in the trade-off section. Therefore, the Pareto front provided different satisfactory solutions for users to choose according to their specific objectives. This study is expected to promote the application of multi-objective calibration in water system modeling, and provide scientific and technological supports for the implementation of integrated river basin management.