A hybrid variational-ensemble data assimilation scheme with systematic error correction for limited-area ocean models

A hybrid variational-ensemble data assimilation scheme to estimate the vertical and horizontal parts of the background error covariance matrix for an ocean variational data assimilation system is presented and tested in a limited-area ocean model implemented in the western Mediterranean Sea. An extensive data set collected during the Recognized Environmental Picture Experiments conducted in June 2014 by the Centre for Maritime Research and Experimentation has been used for assimilation and validation. The hybrid scheme is used to both correct the systematic error introduced in the system from the external forcing (initialisation, lateral and surface open boundary conditions) and model parameterisation, and improve the representation of small-scale errors in the background error covariance matrix. An ensemble system is run offline for further use in the hybrid scheme, generated through perturbation of assimilated observations. Results of four different experiments have been compared. The reference experiment uses the classical stationary formulation of the background error covariance matrix and has no systematic error correction. The other three experiments account for, or not, systematic error correction and hybrid background error covariance matrix combining the static and the ensemble-derived errors of the day. Results show that the hybrid scheme when used in conjunction with the systematic error correction reduces the mean absolute error of temperature and salinity misfit by 55 and 42 % respectively, versus statistics arising from standard climatological covariances without systematic error correction.