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Data assimilation in highly nonlinear geophysical systems: particle filters with localization

高度非线性地球物理系统中的数据同化：具有定位功能的粒子滤波器

基本信息

批准号：
NE/H008853/1
负责人：
Peter Jan Van Leeuwen
金额：
$ 32.66万
依托单位：
University of Reading
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2010
资助国家：
英国
起止时间：
2010 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=NE%2FH008853%2F1
关键词：
Data assimilation highly nonlinear geophysical

项目摘要

Data assimilation is at the heart of many activities in geophysical sciences, being it meteorology, oceanography, hydrology, seismology etc. In data assimilation numerical models of a certain (geophysical) system are combined with observations from that system. The purpose of doing this can either be forecasting, model improvement or trying to understand the system under study better. To start with forecasting of e.g. weather, the present-day state-of-the-art models would not do a very good job without the continuous feeding of observations into them. The these models are quite good in representing the physical and chemical processes in the atmosphere, but need information on the actual state of the atmosphere before a good forecast can be made. The same is true for all geophysical fields. With regard to model improvement and system understanding data assimilation can also play a very important role. The models contain several processes that are not well described due to either resolution problems or poorly known physics. This results in several (sometimes hundreds) of poorly known parameters, which can be estimated by data assimilation. Finally, by using a model in which observations have been assimilated the real atmospheric (oceanic etc.) can be studied, instead of the model representation. Several methods to perform data assimilation have been implemented in large-scale geophysical systems. All of them are based on linearisations of some kind. Examples are the Ensemble Kalman Filter and the 4-Dimensional Variational method (4D-Var). Due to increasing model resolution more and more processes are being resolved in the models, and these processes tend to be more and more nonlinear. An example is cloud formation and precipitation in the atmosphere. The data-assimilation community is looking hard for methods that can handle these nonlinearities. It has been argued for a long time now that particle filters good do the job. In principle, these methods are fully nonlinear. However, applications of particle filters in meteorology and oceanography are limited to small dimensional systems due to the enormous number of particles that have to be used. On way to solve this problem is by trying to increase the effective size of the ensemble of particles. This can be done by so-called localization. This technique is used extensively in the Ensemble Kalman Filter, without which that method would not work on operational numerical weather prediction or large-scale ocean models. In localization one allows observations to have only influence on a limited area of the domain, only on the area close to the observation. This results in a local estimation problem, and the number of ensemble members compared to the number of unknowns (only those in that area) increases considerable. If one divides the whole model domain up into 1000 of those smaller areas, the effective ensemble size increases with a factor 1000. One cannot use localization directly in a particle filter, and in this proposal three new ways of doing it are investigated in a suite of geophysical models, running from very simple to close to operational. The objectives of this proposal are: - Generate a data-assimilation method for highly nonlinear large-dimensional geophysical systems. Since the models and observation operators are becoming more and more nonlinear, this objective is highly relevant to NERC. The methods developed will be applicable to all NERC-related research fields. - Make the field of particle filtering accessible for geophysics. Particle filters are one of the few methods that are fully nonlinear and have strong potential to be applicable in large-scale systems. - Investigate the use of localization for particle filtering to achieve the above mentioned goals. - Demonstrate the use of localization in a large-scale application in meteorology.

数据同化是地球物理科学中许多活动的核心，如气象学、海洋学、水文学、地震学等。在数据同化中，某一（地球物理）系统的数值模型与该系统的观测相结合。这样做的目的可以是预测，模型改进或试图更好地理解所研究的系统。从天气预报开始，如果没有观测数据的持续输入，当今最先进的模型就不能很好地完成任务。这些模式能很好地反映大气中的物理和化学过程，但在作出良好的预报之前，需要有关大气实际状况的资料。所有的地球物理场也是如此。在模型改进和系统理解方面，数据同化也可发挥非常重要的作用。这些模型包含了几个过程，由于分辨率问题或物理学知之甚少，这些过程没有得到很好的描述。这导致几个（有时数百个）不太了解的参数，可以通过数据同化来估计。最后，利用同化了观测资料的模式，模拟了真实的大气（海洋等）可以研究，而不是模型表示。在大型地球物理系统中，已经实施了几种进行数据同化的方法。所有这些都是基于某种线性化。例如，Enhancement卡尔曼滤波器和四维变分方法（4D-Var）。由于模型分辨率的提高，越来越多的过程在模型中被解析，并且这些过程趋向于越来越非线性。一个例子是云的形成和大气中的降水。数据同化社区正在努力寻找能够处理这些非线性的方法。很长一段时间以来，人们一直认为粒子过滤器可以很好地完成这项工作。原则上，这些方法是完全非线性的。然而，粒子滤波器在气象学和海洋学中的应用仅限于小维系统，因为必须使用大量的粒子。解决这个问题的方法是试图增加粒子系综的有效尺寸。这可以通过所谓的本地化来实现。这一技术广泛用于包围卡尔曼滤波器，如果没有它，该方法将无法用于业务数值天气预报或大规模海洋模型。在局部化中，允许观察仅对域的有限区域产生影响，仅对靠近观察的区域产生影响。这导致了局部估计问题，并且与未知数（仅在该区域中的那些）的数量相比，系综成员的数量显著增加。如果将整个模型域划分为1000个较小的区域，则有效的总体大小以因子1000增加。人们不能直接在粒子滤波器中使用本地化，在该提案中，在一套地球物理模型中研究了三种新的方法，从非常简单到接近操作。该提案的目标是：-生成高度非线性的大尺寸地球物理系统的数据同化方法。由于模型和观测算子变得越来越非线性，因此这一目标与NERC高度相关。所开发的方法将适用于所有与NERC相关的研究领域。- 使粒子滤波领域成为物理学的一部分。粒子滤波器是少数几种完全非线性的方法之一，在大规模系统中具有很强的应用潜力。- 研究使用粒子滤波的定位，以实现上述目标。- 演示本地化在气象学中的大规模应用。