A Computational Study of the Nudging Approach to Data Assimilation

这项工作开发和测试了将数据同化到数学模型中以实现更准确预测的新方法，例如在天气预报中。其新奇之处在于考虑了以下数据：(A)集中在一个小区域(如大都市地区)，(B)移动(如卫星、商用飞机、汽车，甚至手机)，以及(C)来自容易测量的量，如大气压力。数值实验将得到严格的数学分析的支持。这项工作涉及将数据同化、确定形式和湍流联系在一起的计算项目。数据同化是通过轻推进行的，这种方法已被证明有助于进行严格的数学分析，但与卡尔曼滤波器相比，经过的计算测试要少得多。轻推与确定形式密切相关，即轨迹空间中的常微分方程组，它捕捉系统的全局吸引子，如流体流动的纳维尔-斯托克斯方程。这类系统预计将表现出混乱的行为，这引发了本研究解决的一组特定的计算问题。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This work develops and tests new approaches to assimilating data into mathematical models to achieve more accurate prediction, for example in weather forecasts. The novelty is to consider data that is (a) concentrated in a small region (as over a metropolitan area), (b) moving (as from satellites, commercial airplanes, cars, even cell phones), and (c) from easily-measured quantities, such as atmospheric pressure. Numerical experiments will be supported by rigorous mathematical analysis.This work involves computational projects that tie together data assimilation, determining forms, and turbulence. The data assimilation is by nudging, an approach that has proven to be conducive to rigorous mathematical analysis but has undergone much less computational testing than have Kalman filters. Nudging is closely related to determining forms, ordinary differential equations in trajectory spaces that capture the global attractors of systems such as the Navier-Stokes equations of fluid flow. Such systems are expected to display turbulent behavior, which raises a particular set of computational issues addressed by this research.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.