# STATISTICAL CONSIDERATIONS IN ATMOSPHERIC DATA ASSIMILATION

Ross Bannister, Stefano Migliorini
Alan O'Neill, William Lahoz, Roger Brugge

In data assimilation we must:
• Reproduce accurately observations via the observation operators.
• Represent realistically the error statistics of all information.

Some of DARC's activities:
1. How can we best assimilate data from ENVISAT?
2. How can we use physics to better estimate uncertainties in the background fields?

# 1. How can we best assimilate data from ENVISAT?

## Existing approach at Met Office (obsolete)

Assimilate by interpolation and with fixed and diagonal .
 PROBLEMS: Retrieved profile does not represent point values of . Errors are correlated and profile dependent.

## DARC approach #1 (implemented)

Assimilate by layer averaging and with fixed and diagonal .
 PROBLEMS: Retrieved profile does not represent simple layer averaged . Errors are correlated and profile dependent. Difficult to implement for humidity (R.H.).

## DARC approach #2 (planned) - S.Migliorini, C.Rodgers

Assimilate by averaging kernels and with full error statistics.

Retrieved state and 'truth'

 Modification #1, assimilate: with error covariance:

 Modification #2, assimilate prewhitened profiles: ENVISAT contribution to :

## Example Averaging Kernels for MIPAS Ozone

IFAC-CNR, University of Bologna

# 2. How can we use physics to better estimate uncertainties in the background fields?

R.Bannister, I.Roulstone, M.Cullen, N.Nichols
Pressure-Pressure & Pressure-Theta

Theta-Pressure Covariances

Horizontal wind-Pressure Covariances

Var. uses control variables, , prewhitened according to B.

Part of the transformation between and spaces is to choose alternative parameters.
 Pragmatic approach (engineering) - capture most of flow - . - capture most of remaining part of flow - . - capture most of remaining part of flow - . etc. Theoretical approach (physics) Choose parameters that are uncorrelated, spanned by mutually exclusive normal modes. - 'balanced' streamfunction - slow manifold - . - unbalanced part of vortical flow . - divergent part of flow .

Statistics are accumulated for each parameter