构建无导数最优化方法的简化模式的反问题研究

项目名称： 构建无导数最优化方法的简化模式的反问题研究

项目编号： No.41475068

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 天文学、地球科学

项目作者： 胡淑娟

作者单位： 兰州大学

项目金额： 85万元

中文摘要： 初始误差和模式误差是制约数值预报准确率的主要因素。在用资料同化技术、集合预报手段以及条件非线性最优扰动法等减小初始误差对预报结果影响的过程中，发现模式误差的作用不可忽略。模式误差估计问题因成为改进数值预报效果的关键技术而备受关注。基于对模式误差统计特征的分析，本课题拟将模式误差综合考虑成为一项丢失了的外强迫项，把历史资料看作是准确模式的一系列特解，构造模式误差项所满足的微分方程反问题，使模式误差的动力学特征由历史资料所表示的实际大气来确定。本项目构建无导数最优化的新方法求解微分方程反问题所对应的最优控制问题，克服以往梯度类的下降法需要运行原数值模式的切线性模式或伴随模式的缺陷；通过划分区域的方式把模式误差的近期信息随时空客观地、连续地演变至预报时间段，克服以往方法中时间无关型模式误差简单外推的不足，为复杂业务模式实现时空演变的模式误差估计（显著改进预报效果）提供可行的数值方法与理论依据。

中文关键词： 无导数最优化；非线性扰动；反问题；历史资料

英文摘要： Initial error and model error are key factors restricting the accuracy of numerical weather prediction (NWP). Many studies have focused on the errors of initial conditions including variational data assimilation, ensemble forecasting techniques and conditional nonlinear optimal perturbation (CNOP). Crucial to improving the accuracy of NWP, the model error estimation has received intensive attentions. The purpose of this study is to estimate the time-varying and spatial-varying model errors by using historical observations. Based on the statistic characteristics, the model errors can be assumed as a missing forcing term of the accurate model governing the actual atmosphere. The observed data (ignoring the measurement error) can then be viewed as a series of solutions of the accurate model. Therefore, NWP can be considered as an inverse problem to uncover the unknown model error term by using long periods of observed data. This study firstly constructs a derivative-free optimization (DFO) method to find the minimum solution of the inverse problem for the original numerical model with an external forcing term, where computing the gradient of the objective functional and solving the tangent linear model or adjoint model of the original numerical model are not required. Secondly, this study uncovers the time-varying and spatial-varying model errors in the forecast periods using the historical data to overcome the limitations of the traditional time-independent extrapolation. The proposed theories and methods for suppressing NWP errors will be useful in future applications of high accuracy NWP.

英文关键词： derivative-free optimization method;nonlinear perturbation;inverse problem;past data