Collaborative Research: Improved Minimization Techniques in Meteorological Data Assimilation

该项目的目标是开发改进的优化技术，用于气象学中的三维和四维数据同化，既减少同化过程所需的计算机时间，又提高结果的可靠性。 这项研究将包括现有的同化代码的实验工作，结合优化算法和物理模型的理论研究。 该项目代表了豪尔赫·诺塞达尔博士（西北大学），斯蒂芬赖特博士（芝加哥大学）和国家环境预测中心（NCEP）的研究人员。新的优化技术包括用于最小化非线性成本函数的丰富的有限内存拟牛顿方法，用于加速共轭梯度方法的自动预处理器，和非线性最小二乘问题的结构拟牛顿方法。 新技术将被设计用于背景协方差矩阵不具有简单稀疏结构的情况。 当在计算过程中在模型中使用不同级别的分辨率时，这些技术也必须是鲁棒的，这是气象模型的常见情况。 因此，必须建立一个理论框架，量化这些不准确性对算法性能的影响。大气科学和数学科学司共同支持这一项目。

The goal of this project is to develop improved optimization techniques for use in three- and four-dimensional data assimilation in meteorology that will both reduce the computer time required in the assimilation process and increase the reliability of the results. The research will consist of experimental work with existing assimilation codes, in conjunction with a theoretical study of both the optimization algorithms and the physical models. The project represents a collaborative effort among Dr. Jorge Nocedal (Northwestern University), Dr. Stephen Wright (University of Chicago), and researchers at the National Centers for Environmental Prediction (NCEP).The new optimization techniques include enriched limited memory quasi-Newton methods for minimizing the nonlinear cost functions, automatic preconditioners to accelerate the conjugate gradient method, and structured quasi-Newton methods of nonlinear least squares problems. The new techniques will be designed for the case in which the background covariance matrix does not have a simple sparsity structure. The techniques must also be robust when varying levels of resolution are used in the model during computation, a common situation with meteorological models. Thus, a theoretical framework that quantifies the effects of these inaccuracies on the performance of the algorithms will have to be developed.The Divisions of Atmospheric Sciences and Mathematical Sciences jointly support this project.