Practical Filtering Methods with Model Errors

具有模型误差的实用过滤方法

• 批准号: 1317919
• 负责人: John Harlim
• 金额: $ 24.94万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-12-15 至 2017-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1317919&HistoricalAwards=false
• 关键词: Practical; Filtering; Methods; Model; Errors

The projects in this proposal are part of the PI's long-term career goal to deliver a class of practically scalable data assimilation (or filtering) schemes with solid theoretical foundations for state estimation of geophysical fluid dynamics. This proposal is an outgrowth of the PI's recent successful effort in designing accurate, reduced filtering methods with cheap stochastic models as alternatives to expensive models. Four projects are proposed: 1. Design computationally faster stochastic filters to assimilate atmospheric infrared sounder (AIRS) in the presence of multiple cloud types in the tropics. 2. Develop stable linear autoregressive (AR) filters for nonlinear, weakly chaotic dynamical systems. This project involves designing a novel parameterization scheme for AR models that avoids utilizing a long time series as in classical regression strategy, yet respects the sufficient conditions for optimal AR filtering, established in the PI's recent work. 3. Study the role of higher order terms of the singular perturbation expansion when a reduced model from classical averaging theory is used in filtering multi-scale interaction between modes of turbulent signals with moderate separation of scales. This study involves formal asymptotic expansion and rigorous error estimation. The PI will show that the higher order terms are important to avoid covariance underestimation in the presence of model errors. 4. Develop a fast filtering framework to assimilate multi-scale dynamical systems with "superparameterization", a fast numerical scheme to resolve interaction of cloud-scale dynamics and large-scale tropical convecting atmosphere. The new algorithm will include an online small-scale estimation scheme that imposes statistical consistency between the large and small-scale variables. Fundamental issues in real-time weather prediction are model errors. This problem is attributed to incomplete understanding of the physics and our lack of computational resources to resolve physical processes in various time and length scales. Modern operational weather models poorly reproduce the tropical observational records even after resolving 10 billion variables. This long-standing issue prevents the global weather model forecasting skill to improve from weekly to monthly, as reported in a recent article in the World Meteorological Organization bulletin. The results from this proposal will transform the future design of computational methods for various prediction related problems in the presence of model errors, in particular numerical weather prediction. This proposal supports an interdisciplinary research training environment for a graduate student, involving mathematical analysis, statistical modeling, and scientific computing. The PI, who is jointly appointed as a faculty in the mathematics and meteorology departments at PSU, will develop an interdisciplinary graduate course with emphasis on PDE and waves for atmospheric and ocean modeling.

该提案中的项目是PI长期职业目标的一部分，即提供一类可扩展的数据同化（或过滤）方案，并具有稳固的理论基础，以进行状态估算地球物理流体动力学的估计。该提案是PI最近成功地使用廉价随机模型来设计准确，减少过滤方法的成功努力的产物。提出了四个项目：1。在热带地区存在多种云类型的情况下，在计算上设计更快的随机过滤器，以吸收大气红外声音（AIRS）。 2。为非线性，弱混沌动力学系统开发稳定的线性自回旋（AR）过滤器。该项目涉及为AR模型设计一种新型参数化方案，该方案避免使用长期序列，如经典的回归策略，但尊重PI最近工作中确定的最佳AR过滤条件。 3。研究奇异扰动扩展的高阶项的作用，当使用经典平均理论的减少模型用于过滤尺度中等分离的湍流信号模式之间的多尺度相互作用。这项研究涉及正式的渐近扩张和严格的误差估计。 PI将表明，高阶项对于避免在存在模型误差的情况下低估协方差很重要。 4。开发一个快速过滤框架，以“超级参数”吸收多尺度动力学系统，这是一种快速的数值方案，以解决云规模动力学和大规模热带对流气氛的相互作用。新算法将包括一个在线小规模估计方案，该方案在大型和小型变量之间施加统计一致性。实时天气预测中的基本问题是模型错误。这个问题归因于对物理学的不完全理解以及我们缺乏在各个时间和长度尺度上解决物理过程的计算资源。现代操作天气模型即使解决了100亿个变量，也可以繁殖热带观察记录。如今，这个长期存在的问题阻止了全球天气模型的预测技能，从每周到每月都有改善，正如世界气象组织公告最近的一篇文章所报道的那样。该提案的结果将在存在模型误差的情况下，特别是数值天气预测的情况下，转化各种与预测相关问题的计算方法的未来设计。该建议支持研究生的跨学科研究培训环境，涉及数学分析，统计建模和科学计算。 PI被任命为PSU数学和气象部门的教职员工，将开发跨学科的研究生课程，重点是PDE和波浪，以进行大气和海洋建模。