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# Data Assimilation and Inverse Problems

## Data assimilation (DA) is a term used in weather, ocean, and climate science that refers to the following problem: given a dynamical model (e.g. a model simulating atmospheric motion) and a series of observations (e.g. wind measurements from the real weather), find a trajectory of the model that matches the observed data.

The illustration gives a rough idea of the concept.

Very similar problems appear in other fields of science and engineering, and one might even say that DA simply goes by other names there. In any event, there is a strong relationship between data assimilation and nonlinear smoothing and filtering (probability theory), nonlinear observers (control theory and engineering), and inverse problems (applied and numerical mathematics).

What is particular about data assimilation in weather, ocean, and climate science is that one has to deal with very large dimensional (strictly speaking, infinite dimensional) systems, since atmosphere and ocean are described by partial differential equations.

The Data Assimilation research group at the Department of Mathematics and Statistics is part of the Data Assimilation Research Centre (DARC), which involves researchers across the entire School. Go to the DARC website for general information on the research activities on data assimilation in Reading.

Our group is also closely linked to the Numerical Analysis and Computational Modelling group.

### Research

#### Coupled atmosphere-ocean data assimilation (Amos Lawless, Nancy Nichols)

A fully dynamical representation of the oceans is indispensable in order to obtain climate simulations which have at least something to do with reality. The same is true if we ever expect to gain any forecasting skill beyond the medium range (i.e. seasonal to decadal timescales). The different timescales displayed by the ocean as compared to the atmosphere render coupled atmosphere-ocean data assimilation a particularly challenging problem.

#### Particle filtering and Monte-Carlo Methods (Richard Everitt)

The primary research interests here are in methodological work in Bayesian statistics, in both inference and modelling. The majority of our work on inference is in Markov chain Monte Carlo, sequential Monte Carlo and approximate Bayesian computation, with modelling interests focussing on graphical models. There is ongoing interest in the use of computers in computational statistics. The use of advanced Bayesian methodology for solving problems in statistical genetics, genomics, epidemiology and network analysis is another area of current research.

#### Robustness and error estimation of data assimilation (Jochen Broecker)

The robustness of data assimilation methods with respect to variations in the dynamic model (or model assumptions) and the observations is investigated - that is, we ask the question whether a small change in these data will entail only a small change in the solution. This is of practical relevance for a number of reasons. In addition to theoretical results about data assimilation performance, we work on methods which enable the practitioner to perform ex-post error analysis of data assimilation results. Simply comparing the output with the observations is dangerous, since the observations have already been used to find the solution, so this approach might give overly optimistic results.

### People

Name Position Telephone
+44 (0) 118 378
Email
Dr Amos Lawless Lecturer 5018 a.s.lawless
Dr Jochen Broecker Associate Professor 8578 j.broecker
Professor Nancy Nichols Professor of Applied Mathematics 8988 n.k.nichols
Dr Roland Potthast Professor of Applied Mathematics 7614 r.w.e.potthast
Dr Sarah Dance Associate Professor of Data Assimilation 6452 s.l.dance
Professor Sebastian Reich Professor of Numerical Analysis and Scientific Computing s.reich

### Publications

Publications of the members of the research group, available at Reading Publications Database Centaur, can by found by clicking the link below.

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