Hybrid data assimilation for coupled atmosphere-ocean models

Lead Research Organisation: University of Reading
Department Name: Mathematics and Statistics


The monitoring of the climate of planet Earth and the possibility to predict environmental changes on time-scales of weeks to months, and even on decadal time-scales, is becoming of increasing importance to society. Changes in phenomena such as floods, droughts and sea-level rise are expected to have a large societal impact, affecting many aspects of human life, including agriculture, provision of flood defences and human health. For policymakers there is a need to understand more accurately how the planet is changing and to have improved predictions of future changes.

As part of this goal to increase our knowledge of the Earth, space agencies have invested heavily in Earth observation programmes over recent years, with continued investment planned over the coming decade (for example, the European Space Agency Sentinel satellites, which are being developed as part of the European Earth Observation programme Copernicus). This has led to a huge rise in the number of measurements available from satellites covering many different components of the Earth system, including the atmosphere, ocean, land and cryosphere. The synergistic use of these measurements provides the possibility of an increased understanding of the workings of the whole Earth system and an improved predictive capability.

Data assimilation is the science of combining observations from different data sources with a computer model forecast in order to extract the most information from the available measurements. In order to improve the capability of environmental monitoring and prediction, and to make better use of new satellite data, many operational centres, such as the Met Office, are now developing assimilation techniques that use observations of the atmosphere and ocean together in order to estimate the state of the combined system. In order to obtain optimal impact from the measurements it is important to characterize the statistics of the errors in the computer model forecast. In particular, when treating the coupled atmosphere-ocean system, a proper representation of the relationship between the errors in the atmosphere and ocean model forecasts is needed. In this project we will develop new methods for estimating these error statistics and for including this information within data assimilation schemes. The involvement of the Met Office and the European Centre for Medium-range Weather Forecasts in the project will allow rapid transfer of knowledge to operational practice.

Planned Impact

The science developed in this project will be of direct benefit to operational weather forecasting agencies such as the Met Office and the European Centre for Medium-range Weather Forecasts (ECMWF), who are currently developing data assimilation schemes for coupled atmosphere-ocean models. The idealised experiments used in this project will be developed in discussion with scientists from these centres, so that the results of the project may have a direct impact on the current and future development of operational systems.

A successful development and implementation of this science into operational practice has the potential to improve environmental prediction on time scales of weeks to months, and even decadal prediction. Improving such predictions will allow more detailed guidance to be given to policymakers who must invest in projects over these time scales, thus allowing more cost-effective planning in mitigating against climate change. Improved predictions will also be of great benefit to wider society, especially industrial sectors affected by the weather, such as agriculture, flood defence and public health.


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Description Using a simplified atmosphere-ocean model and data assimilation system, we have examined the structure of error covariances across the air-sea interface. These structures have been shown to vary with season and with time of day. The structure of these covariances has been explained according to the physics of atmosphere-ocean interactions.
Usually such covariance are estimated from a sample of forecasts, but sampling error must be removed. New methods have been developed to remove sampling error while still retaining the important atmosphere-ocean cross-covariance information.
The benefit of using atmosphere-ocean cross-correlations within a coupled data assimilation system has been demonstrated, with identification of the circumstances as to when this benefit is most likely to be significant. We have shown that the explicit representation of these correlations can result in a more consistent coupled atmosphere-ocean state than when relying solely on the information being implicitly generated by the assimilation system
Exploitation Route The understanding of the structure atmosphere-ocean error covariances is a fundamental part of developing data assimilation methods for future prediction with coupled models. Such data assimilation systems are currently being developed at the Met Office and the European Centre for Medium-range Weather Forecasts. The new methods developed for treating sample covariances may be applied not only to atmosphere-ocean systems, but to other environmental systems where sample covariance information is used. The results concerning the effect of using these covariances in the assimilation system indicates that operational forecasting centres may have benefit from designing explicit atmosphere-ocean cross-covariance representation for their coupled models.
Sectors Environment

Description Data assimilation training course for early career researchers
Geographic Reach National 
Policy Influence Type Influenced training of practitioners or researchers
Impact A 4-day advanced level course on data assimilation theory and practice was delivered to 23 early career researchers.
Description Novel Assimilation Methods for Coupled Atmosphere-ocean Prediction (NAMCAP)
Amount £191,588 (GBP)
Funding ID P107915 
Organisation Newton Fund 
Sector Public
Country United Kingdom
Start 04/2020 
End 03/2021
Title Ensemble covariances 
Description Building on a previous single-column atmosphere-ocean data assimilation system, we have developed software to estimate ensemble covariances for this system and to run coupled atmosphere-ocean data assimilation experiments in a basis defined by the eigenvectors of the covariance matrix. 
Type Of Material Computer model/algorithm 
Year Produced 2017 
Provided To Others? No  
Impact This development has led to a greater understanding of the nature of the error correlations between the atmosphere and the ocean, including their physical origins, as well as new methods to treat sampling error in ensemble covariance estimates. These have been reported in two publications. 
Description Met Office coupled DA 
Organisation Meteorological Office UK
Country United Kingdom 
Sector Academic/University 
PI Contribution Visits to Met Office to present results from project.
Collaborator Contribution Met Office provided staff time to comment on results and proposed experiments.
Impact 4 publications. Further grant application for funding
Start Year 2012
Title Single-column coupled atmosphere-ocean assimilation system 
Description Starting from model code developed by ECMWF, we have developed a variational data assimilation system for a single-column coupled atmosphere-ocean model. This includes strongly and weakly coupled assimilation systems, plus the ability to calculate covariance information from ensembles. 
Type Of Technology Software 
Year Produced 2015 
Impact This software has been used in the group to allow fundamental research on coupled atmosphere-ocean data assimilation. This research has been communicated to operational users through conference presentations and peer-reviewed papers, and results are being taken account of in their systems. 
Description Blog entry on DARE data assimilation blog 
Form Of Engagement Activity Engagement focused website, blog or social media channel
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Public/other audiences
Results and Impact Two blog entries concerning data assimilation
Year(s) Of Engagement Activity 2017
URL http://blogs.reading.ac.uk/dare/blog/
Description NCOF working group on data assimilation 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact Working group on data assimilation of the National Centre for Ocean Forecasting. This involved discussions with practioners (especially Met Office) about how our research results could help them to interpret their own results in a full atmosphere-ocean model and how our results could guide their developments.
Year(s) Of Engagement Activity 2014,2015,2016
Description School Big Bang Careers Fair 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Schools
Results and Impact Display at school Big Bang Careers' Fair and talk on the science of weather modelling and use of observations.
Year(s) Of Engagement Activity 2017