Collaborative Research: Determining Forms and Data Assimilation with Stochastic Data

协作研究：利用随机数据确定形式和数据同化

• 批准号: 1418838
• 负责人: Hakima Bessaih
• 金额: $ 13.96万
• 依托单位: University of Wyoming
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-15 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1418838&HistoricalAwards=false
• 关键词: Collaborative; Research; Determining; Forms; Data

Among the numerous factors that make accurate weather forecasting a challenge is initialization. The finite number of data collecting instruments distributed about the globe and atmosphere give only an incomplete description of the state of the weather at any instant. Yet there is a wealth of such data over an extended time period in the past, which when combined with certain mathematical models can provide a more complete description. The general procedure for this is called data assimilation. It provides more accurate starting values for computer simulations of the weather going into the future. This award funds research into a new method of data assimilation that is flexible enough to be combined with a variety of simulation techniques. The work will concern both the implementation of this method, and the effect of measurement errors in the data, which inevitably occur. The assimilation process leads to another mathematical model that can be used to cleanse the past data of such noise. In this second direction, the goal is not to obtain a higher resolution condition for starting a simulation for the future, but to reconstruct a highly resolved version over the time period of the original data. This has natural applications in voice and pattern recognition. The research team will implement a recent data assimilation algorithm based on feedback control for several important physical systems. The approach can be applied with a variety of determining parameters, such as nodal values, and finite volume elements. The team will also carry out computations with a new determining form based on feedback control. The steady states of this ordinary differential equation are precisely the finite-dimensional projections of trajectories in the global attractor. The team will study both computationally and analytically the effects of stochastic perturbations in the data. In the case of the data assimilation algorithm, the plan is to quantify and control the effect of the noise on the highly resolved state to be used in a subsequent direct numerical simulation. In the case of the determining form, the idea is to use its evolutionary process to remove the noise from the data itself.

初始化是对准确天气预报造成挑战的众多因素之一。分布在全球和大气中的有限数量的数据收集仪器只能对任何时刻的天气状态进行不完整的描述。然而，过去很长一段时间内有大量此类数据，当与某些数学模型相结合时，可以提供更完整的描述。这样做的一般过程称为数据同化。它为计算机模拟未来的天气提供更准确的起始值。 该奖项资助一种新的数据同化方法的研究，该方法足够灵活，可以与各种模拟技术相结合。这项工作将涉及该方法的实施以及不可避免地发生的数据测量误差的影响。同化过程产生了另一个数学模型，可以用来清除过去数据中的此类噪音。在第二个方向中，目标不是获得更高分辨率的条件来开始未来的模拟，而是在原始数据的时间段内重建高分辨率版本。这在语音和模式识别中有天然的应用。研究团队将为几个重要的物理系统实施一种基于反馈控制的最新数据同化算法。该方法可以应用于各种确定参数，例如节点值和有限体积单元。该团队还将采用基于反馈控制的新确定形式进行计算。这个常微分方程的稳态正是全局吸引子轨迹的有限维投影。该团队将通过计算和分析研究数据中随机扰动的影响。就数据同化算法而言，计划是量化和控制噪声对高分辨率状态的影响，以用于后续的直接数值模拟。在确定形式的情况下，其想法是利用其进化过程来消除数据本身的噪声。