Covariance modelling

Variational data assimilation (VAR) relies heavily on the specification of error covariance matrices which describe how well background and observational data are known. The optimality of the assimilation is strongly related to the accuracy of these matrices. VAR was originally developed for synoptic and global scale assimilation problems, and there are many challenges that need to be addressed to allow VAR to be applied to high-resolution systems. Two challenging areas are concerned with modelling the 'B' and 'R' matrices, which are being investigated by HRAA members.

The 'B-matrix' is meant to account for the size of - and correlations between - random errors in the background state. Until now, efforts in modelling the B-matrix have focused on its properties at synoptic scales where familiar meteorological balances, and other simple ideas (e.g. assuming isotropy of error correlations) guide how the B-matrix is formulated. At high-resolution (of order 1km grid length) these existing methods for modelling the B-matrix are less appropriate, and the B-matrix is expected to become flow-dependent. The B-matrix should also have an additonal role at high resolution to allowing meteorological features that are wrongly placed in the background to be 'moved' by the assimilation.

The 'R-matrix' is similarly meant to account for random errors in the way the observations are used by VAR. The relative sparsity of observations used for synoptic-scale data assimilation allows the R-matrix to be assumed diagonal (ie correlations between errors in different observations are assumed negliglble). In contrast high-density observations are required for high-resolution data assimilation and the diagonal R assumption is expected to be invalid.


Forecast errors for convective scale variational data assimilation R. Bannister, M. Dixon
Adaptive boundary layer data assimilation A. Fowler, R. Bannister, S. Migliorini
DIAMET ensemble covariance statistics (internal only) file:///home/hraa/public_html/cov/DIAMETCovStats/html/

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