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On optimal solution error covariances in variational data assimilation problems

This paper determines the relationship between the optimal solution error covariance matrix and the Hessian of the cost function in different control problems. The body of work in Gejadze's REF papers underpinned his NERC Advanced Fellowship (NE/J018201/1) where the research will be applied within the framework of the NEMO ocean model, with the UK Met Office, to improve global predictions of ocean flow, temperature, salinity. This will "give insights into how to construct and make best use of ensembles of model forecasts and, therefore, considerably improve the quality of the forecasts." (Mike Bell, National Centre for Ocean Forecasting, mike.bell@metoffice.gov.uk)