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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.

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 we have to deal with very large dimensional (strictly speaking, infinite dimensional) systems, since atmosphere and ocean are described by partial differential equations.

The Data Assimilation and Inverse Problems 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 of Mathematical, Physical and Computational Sciences. Go to the DARC website for general information on the research activities on data assimilation at Reading.

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


One part of our research in this area includes the application of numerical analysis techniques to analyse and improve the performance of data assimilation algorithms. More information about this work can be found on the Numerical Analysis and Computational Modelling research group page

Other data assimilation research includes:

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

The improvement of weather forecasts on timescales of days to weeks and beyond relies on capturing the interactions between the atmosphere and the ocean, and many operational forecasting centres are now moving to the use of coupled atmosphere-ocean models for their routine forecasts.

The atmosphere-ocean system can be considered as a coupled dynamical system with very different spatial and temporal scales in the different components, which makes the data assimilation problem particularly challenging. We are developing new data assimilation methods for coupled dynamical systems and working with the Met Office to test them in an operational weather forecasting system.

Robustness and error estimation of data assimilation (Dr 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.

Data assimilation for applications in hazardous weather and flood prediction (Professor Sarah L Dance)

Urban areas often suffer from increased vulnerability to natural hazards, including extreme weather and other environmental factors, due to dense populations and infrastructure.

Our ability to manage these hazards is limited, in large part, by the accuracy of computational model predictions that we use for long-term planning (e.g., designing flood defences) and the production of timely forecasts (e.g., guiding emergency responders and the deployment of flood alleviation measures).

However, urban areas also present rich sources of data, that to date have not been fully explored or exploited (e.g., citizen science, smartphones, internet of things etc.). Our vision is to use dynamic data assimilation (DA) to promote a revolution in the skill of computational model predictions by combining them with new sources of observational data, and to ensure the impact of these developments.