THEORETICAL ASPECTS OF VARIATIONAL DATA ASSIMILATION

Ross Bannister

Data Assimilation Research Centre

Collaborators: Theory Applications Group, Met Office (JCMM)

Mathematics Dept., Reading Univ.

The Cost Function

The background error covariance matrix

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.