• 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.