为评估不同优化方法在分布式水文模型参数率定中的效率和效果，分别使用基于代理模型的多目标优化方 法 (multi-objective?adaptive?surrogate?modeling-based?optimization，MO-ASMO)、NSGA-Ⅱ和 SCE-UA 对 SWAT 模型 进行参数率定。基于四湖流域 2008—2021 年的实测流量数据以及高程、土地利用、土壤类型等数据，构建 SWAT 模型，并针对 3 种不同优化方法的参数率定结果，采用相对误差百分比（PBIAS）、Nash-Sutcliffe 效率系数 （ENS）、均方根误差（ERMS）和 Kling-Gupta 效率指标（EKG）4 种评价指标对比不同优化算法的优化效果，此外还创新 性地量化不同统计指标的不确定性，以更全面地评估不同算法优化结果的稳健性与可靠性。结果表明，与单目标 优化方法 SCE-UA 相比，多目标优化方法的参数率定结果表现出更好的可靠性和稳健性，在多目标优化方法中， MO-ASMO 方法能以显著更少的模型运行次数达到与 NSGA-Ⅱ相似的优化效果。

The traditional automatic calibration of hydrological model parameters are mainly focusing on single-objective optimization, but the optimization based on a single objective can not capture and utilize all the characteristic information of hydrological observations. Several studies have shown that the single- objective calibration of hydrological models can not reproduce all the characteristics of hydrological factors (such as runoff) well, so it is necessary to constrain multiple features of hydrological factors by multiple objective functions. At present, many studies apply classical multi-objective optimization algorithms to calibrating hydrological models. Compared with the single-objective optimization methods, the classical multi-objective optimization algorithms need to run the model tens of thousands of times to find the optimal solutions. Despite the rapid development of computer technology in the past decades, the use of multi-objective optimization algorithms in hydrological models (especially complex physical distributed hydrological models) still causes a large computational burden. Therefore, the study of efficient and reliable multi-objective optimization methods has important engineering application value. In 2016, Professor Duan's group proposed MO-ASMO, a multi-objective optimization method based on a surrogate model. The core of MO-ASMO is to use cheap statistical surrogate models to replace the original computationally expensive physical models in the optimization process, aiming to significantly reduce the computational burden while maintaining the optimization effect. Clark et al pointed out that it is necessary to quantify the uncertainty of statistical performance metrics in the process of parameter calibration of hydrological models. This is because when the Nash-Sutcliffe efficiency coefficient (ENS) and Kling-Gupta efficiency coefficient (EKG) are used as objective functions for parameter calibration, the optimization results may be seriously affected by a small number of data points. It leads to great uncertainty in the statistical metrics, which will affect the simulation effect after the model parameters are calibrated. The distributed hydrological model SWAT model was constructed in the Sihu basin. The MO-ASMO method was used to calibrate the parameters of SWAT model. The results were compared with the classical multi-objective optimization method NSGA-Ⅱ and the single-objective optimization method SCE-UA. At the same time, to further evaluate the reliability and robustness of the parameter optimization results, Bootstrap and Jackknife methods were used to quantify the uncertainty of the statistical metrics. The following conclusions were obtained: (1) According to the Pareto front and evaluation metrics of the multi-objective optimization, MO-ASMO and NSGA-Ⅱ were close to convergence when the number of runs are 2 300 and 10 000, respectively. The two methods can achieve similar optimization results after convergence, but MO-ASMO can greatly reduce the running time of the model in the process of multi-objective optimization. The optimization results of the single-objective optimization method were good during the calibration period, but the simulation effect degraded significantly during the validation period, indicating that there is a situation of overfitting and the optimization results are unstable. (2) The uncertainty of statistics metrics ENS and EKG of optimization results of different algorithms was quantified by Bootstrap and Jackknife methods. The uncertainty order of the optimization results of the three optimization methods is NSGA-Ⅱ (10 000) ≈ MO-ASMO(2 300) < NSGA-Ⅱ (2 300) < SCE-UA.The optimization results of MO-ASMO (2 300) and NSGA-Ⅱ (10 000) have the best robustness and less uncertainty. The results of NSGA-Ⅱ (2 300) are the second, and the optimization results of model parameters under single-objective optimization are less robust. The results of multi-objective optimization have less uncertainty than those of single-objective optimization, which indicates that it is necessary to use multiple objective functions in the process of hydrological model parameter optimization to avoid problems of compensatory parameters caused by traditional single-objective optimization, to reduce the uncertainty of parameter optimization.