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

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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.