基于代理模型的水文模型参数多目标优化

针对传统多目标优化算法存在计算复杂且效率偏低的问题，提出了一种基于代理模型的多目标优化方案。以淮河大坡岭水文站以上流域为例，采用多元自适应回归样条方法构建新安江模型参数与不同目标的响应曲面关系，进而估计参数的近似Pareto解集。采用4种目标函数（总水量误差系数，均方根误差，高水流量误差系数和低水流量误差系数）和4种模型精度评价指标（Nash-Sutcliffe效率系数，洪峰流量相对误差，径流深相对误差和峰现时间误差）评定模型优化结果，选择10场洪水过程和4种不确定性评价指标估计Pareto解集的模型预测区间特征。结果表明代理模型可有效降低模型评估与优化过程中的计算消耗，为实现多目标优化的高效性奠定了基础。此外，不确定性分析结果也进一步验证了方法的有效性和结果的可靠性，为复杂模型参数优化与不确定性评估提供了参考。

Multi-objective Optimization for Hydrological Models Using Surrogate Modeling

Generally, multi-objective optimization requires running original simulation models thousands of times and as such demand prohibitively large computational budgets. Recently, surrogate models have been used in combination with a variety of multi-objective optimization algorithms to approximate the true Pareto-front within limited original model evaluations. In this study, the multi-objective optimization based on surrogate modeling (multivariate adaptive regression splines, MARS) for conceptual rainfall-runoff model (Xinanjiang model, XAJ) was proposed, using streamflow data of Dapoling catchment in the upper stream of Huaihe River in China. Four objective functions were used to optimize model parameters, i.e. overall water balance error (F1), root mean square error (F2), relative error of peak flows (F3) and low flows (F4), and four evaluation criteria were selected to quantify the goodness-of-fit of observations against simulation model calculated values, i.e. Nash-Sutcliffe efficiency coefficient (NSE), relative error of peak flow and runoff volume (REPF and RERV), and time error of peak flow (TEPF). Results demonstrate that the surrogate-modeling based method method increased the feasibility of applying parameter optimization to computationally intensive simulation models via reducing the number of simulation runs. Compared to the single objective optimization results, it indicates that the multi-objective optimization method can infer the most probable parameter set and furnish useful information about the nature of the response surface in the vicinity of the optimum. In addition, uncertainty analysis results also reveal that the proposed method based on surrogate modeling is high efficiency because the uncertainty ranges based on the Pareto sets cover most of the observed hydrograph. The method is easy to operate and thereby feasible for practical operations for complex simulation models