*Ross Bannister*

*Data Assimilation Research Centre*

Collaborators: Theory Applications Group, Met Office (JCMM)

Mathematics Dept., Reading Univ.

It is crucial to know (and its inverse).

Most basically ...

- Too big to store
- Too big to calculate
- Too big to use ...

... (and we need to know its inverse!)

__Presently ...__

Make assumptions about the nature of the error correlations

(ie compact the information needed to approximate and ).

One important stage in completing this process is the

* parameter transform, *.

Meteorological variables Parameters

Parameters are assumed to be uncorrelated ...

There are no good theoretical reasons to suppose that these variables are uncorrelated (and they are not uncorrelated).

__New parameters ...__

There are better reasons to suppose that a new set of (PV based) parameters are more uncorrelated.

Meteorological variables New parameters

To implement this new scheme in the Met Office 3d Var system, we need to know:

- the transformation, (new parameters to met. variables),
- the inverse transformation, ,
- the adjoint transformation, ,
- and vertical statistics for each parameter.