二维水动力模型参数和边界条件不确定性分析

模型不确定性一直是数学模型研究的重要课题。以Toce河上游约5 km的物理模型为案例，分别采用拉丁超立方体抽样-广义似然不确定性估计（LHS-GLUE）和SCEM-UA方法分析了二维水动力学模型参数、边界条件及两者共同作用导致模型模拟水位的不确定性，并利用偏秩相关分析方法分析了模型参数和边界条件对模拟水位的敏感性。结果表明，水动力模型参数Manning系数对模拟水位的敏感性要大于边界条件对模拟水位的敏感性，且Manning系数对模拟水位的敏感性具有时空变异性；两种方法均可以准确获取模型参数Manning系数和边界条件的不确定性区间，但相比于LHS-GLUE方法，SCEM-UA可以更加准确地推求参数Manning系数和边界条件的后验分布，更适用于二维水动力模型不确定分析。

Uncertainty analysis of two-dimensional hydrodynamic model parameters and boundary conditions

Model uncertainty has always been considered as an important issue in the study of mathematical models. In this study, a physical model of the upper Toce River section of 5 km long is used to investigate the uncertainty in two-dimensional hydrodynamic model parameters, boundary conditions, and their interaction, by using the Latin hypercube sampling-generalized likelihood uncertainty estimation (LHS-GLUE) and the shuffled complex evolution metropolis-UA (SCEM-UA) methods. Sensitivities of model parameters and boundary conditions to water level are analyzed using partial rank correlation analysis. The results indicate that the sensitivity of Manning’s roughness coefficient of the hydrodynamic model to water level is greater than that of the boundary conditions and it has spatial-temporal variability. Either of these two methods could give a reasonable uncertainty interval in water level simulations, but compared with GLUE, SCEM-UA could better estimate the posterior distribution of model parameters and boundary conditions, thus more suitable for analysis of model uncertainty.