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?






Observational data:


equation
equation

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'
equation
equation

Modification #1, assimilate:
equation

with error covariance:
equation
equation
equation
equation
equation



Modification #2, assimilate prewhitened profiles:
equation
equation

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.
equation
equation
equation

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