Abstract
This paper compares several commonly used state-of-the-art ensemble-based data assimilation methods in a coherent mathematical notation. The study encompasses different methods that are applicable to high-dimensional geophysical systems, like ocean and atmosphere and provide an uncertainty estimate. Most variants of Ensemble Kalman Filters, Particle Filters and second-order exact methods are discussed, including Gaussian Mixture Filters, while methods that require an adjoint model or a tangent linear formulation of the model are excluded. The detailed description of all the methods in a mathematically coherent way provides both novices and experienced researchers with a unique overview and new insight in the workings and relative advantages of each method, theoretically and algorithmically, even leading to new filters. Furthermore, the practical implementation details of all ensemble and particle filter methods are discussed to show similarities and differences in the filters aiding the users in what to use when. Finally, pseudo-codes are provided for all of the methods presented in this paper.
Highlights
Data assimilation (DA) is the science of combining observations of a system, including their uncertainty, with estimates of that system from a dynamical model, including its uncertainty, to obtain a new and more accurate description of the system including an uncertainty estimate of that description
Before we precede to the main point of our paper – describing in unified notation current state-of-the-art ensemble and particle filter methods for non-linear and non-Gaussian applications, their implementation, and practical application, a short summary is in order on the historical development in both ensemble Kalman filter and particle filter areas
We have described ten most popular ensemble Kalman filter methods that are applicable to high-dimensional non-Gaussian problems
Summary
Data assimilation (DA) is the science of combining observations of a system, including their uncertainty, with estimates of that system from a dynamical model, including its uncertainty, to obtain a new and more accurate description of the system including an uncertainty estimate of that description. Ensemble Kalman filters are currently highly popular DA methods that are applied to a wide range of dynamical models including oceanic, atmospheric, and land surface models. The increasing popularity of Kalman-Filter-based ensemble (EnKF) methods in these fields is due to the relative ease of the filter implementation, increasing computational power and the natural forecast error evolution in EnKF schemes with the dynamical. We note that many of the filters discussed in this paper are available freely from Sangoma project website along with many other tools valuable and/or necessary for data assimilation systems
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