# Mohamed Jardak, Met Office

## The Met Office "Mean Pert" Scheme

##### Coauthors

A. Lorenc, M. Wlasak, N. Bowler and T. Payne #### Abstract:

Most global numerical weather prediction (NWP) centres use variational data assimilation (DA) since they are able to run efficiently with large models and many observations. Recently the Met Office has been working on the use of an ensemble of variational data assimilations EDA to replace the current ensemble transform Kalman filter (ETKF) scheme. However, the computational cost of this EDA scheme proved to be high, especially for large ensemble sizes.

To reduce the cost we have developed a mean-perturbation DA scheme. This re-formulates the EDA problem into finding an analysis for the ensemble mean, and then calculating perturbations to this analysis, rather than directly calculating an analysis state for each member. More resources are then deployed to the ensemble mean variational analysis by allowing for nonlinearities in the observation operator and by using more iterations for the minimisation. On the other hand perturbations minimisations assume the observation operator to be linear; so fewer iterations are needed. This is justified by the fact that the variational analyses of the perturbations are estimating the uncertainty which is often poorly represented. As a consequence there is substantial computational cost saving since the calculation of the perturbations dominates the total cost.

In experiments with an ensemble of four-dimensional ensemble-variational
assimilations (En-4DEnVar) it was found that many fewer iterations could be used
for the perturbations than for the update of the ensemble mean. Although this
greatly reduced the computational cost of the scheme it did not adversely affect
the results.