A demonstration of cycled 4D-Var in the presence of model error
Article first published online: 27 AUG 2010
© Crown Copyright 2010. Published by John Wiley & Sons, Ltd.
Quarterly Journal of the Royal Meteorological Society
Volume 136, Issue 651, pages 1379–1395, July 2010 Part B
How to Cite
Cullen, M. J. P. (2010), A demonstration of cycled 4D-Var in the presence of model error. Q.J.R. Meteorol. Soc., 136: 1379–1395. doi: 10.1002/qj.653
- Issue published online: 10 SEP 2010
- Article first published online: 27 AUG 2010
- Manuscript Accepted: 13 MAY 2010
- Manuscript Revised: 7 MAY 2010
- Manuscript Received: 21 JUL 2009
- Gordon Inverarity
- data assimilation;
- error growth
The justification for the standard four-dimensional variational data assimilation (4D-Var) method used at several major operational centres assumes a perfect forecast model, which is clearly unrealistic. However, the method has been very successful in practice. We investigate the reasons for this using a toy model with fast and slow time-scales and with non-random model error. The model error is chosen so that the solution remains predictable on both time-scales. The fast modes are much less well observed than the slow modes. We show that poorly observed modes can be best forecast by using a regularization matrix in place of the background-error covariance matrix, and using it to give a much stronger constraint than that implied by the true background error for these modes. The effect is that use can be made of observations over a longer time period. This allows the resulting forecast-error growth to be reduced to much less than that of random perturbations generated using the analysis-error covariance matrix and even less than the model error growth given sufficiently accurate observations. © Crown Copyright 2010. Published by John Wiley & Sons, Ltd.