Assimilation of the information content of Envisat MIPAS data Stefano MiglioriniData Assimilation Research Centre, University of ReadingThanks to: R. Bannister, R. Brugge, A. Geer, W. Lahoz, A. O’Neill, C. Piccolo, C. Rodgers:

Assimilation of the information content of Envisat MIPAS data Stefano Migliorini Data Assimilation Research Centre, University of Reading Thanks to: R. Bannister, R. Brugge, A. Geer, W. Lahoz, A. O’Neill, C. Piccolo, C. Rodgers

Outline:

Outline
Discussion of the C. Rodgers’ theoretical framework on how to assimilate the information content of retrievals without any a priori contamination
Our work in DARC for its application to the assimilation of MIPAS ozone data
Conclusions

3DVar cost function: observation term:

3DVar cost function: observation term Assimilation of radiances:
Y is a vector of radiances, H is the jacobian of the forward model
Problems with hyperspectral sensors: too much information
Assimilation of retrievals:
y is a vector of e.g. mass mixing ratios, H is an interpolation or a layer averaging operator
The a priori information used in the retrieval process can lead to correlation with background errors covariances are generally neglected

Characterisation of retrievals:

When the forward model is linear within one standard deviation from the solution, the retrieval can be expressed as
zr is the retrieved atmospheric profile
zr0 is the simulated retrieval from a simulated noise-free measurement using the forward model
A is the averaging kernel matrix
x0 is the a priori information used in the retrieval
Ge is the retrieval error
Characterisation of retrievals

Assimilation of retrievals(removing the a priori!):

Assimilation of retrievals (removing the a priori!) Expressing the retrieval as
The relationship between the measurement and the state vector is now
and the observation term can be written as

‘Optimal’ assimilation of retrievals:

‘Optimal’ assimilation of retrievals Errors on y are uncorrelated with background (a-priori) errors used in the retrieval
As a consequence, errors on y are uncorrelated with background errors in the background term of the cost function
Assimilation of y instead of zr leads to a more consistent estimate of the real atmospheric state.

The model grid:

The model grid The full state vector grid must be defined on a grid fine enough to capture the internal variability of the atmosphere
The model grid used in data assimilation is generally on a coarser grid
To minimise the cost function we need to interpolate the model fields to the state vector (“fine”) grid
The true state will in general be different from the result of an interpolation from the model grid to the state vector grid:

Fine grid vs. coarse grid:

Fine grid vs. coarse grid xm x xw = W xm fine grid coarse grid

Contribution of different grids:

Contribution of different grids We can express the retrieval as true state on the model grid ‘residual’ due to the interpolation on the fine grid where

Representation error:

Representation error Defining
we can write

How do we estimate Sb ?:

How do we estimate Sb ? To calculate the state vector covariance matrix Sb it is possible to use a lower-dimensional covariance matrix, B
We can choose B as the background error covariance matrix estimated via the NMC method
Then
But Sb is now singular: we need to make it meaningful by e.g. extrapolating from its non-zero eigenvalues

Ozone state vector covariance matrix :

Ozone state vector covariance matrix ECMWF ozone background error covariance matrix covariance matrix on the forward model grid

Ozone state vector covariance matrix :

Ozone state vector covariance matrix ECMWF ozone background error covariance matrix covariance matrix on the forward model grid

Ozone state vector covariance matrix :

Ozone state vector covariance matrix

Systematic errors:

Systematic errors Forward model errors
Spectroscopic database errors
Horizontal homogeneity error
Non-LTE errors
Instrumental errors
Spectral calibration errors
Radiometric calibration errors
Instrument line shape and field of view errors
If each retrieval is considered on its own, systematic errors can be treated as random errors

MIPAS ozone error budget:

MIPAS ozone error budget random, p and T propagation on ozone, systematic and total errors

Pre-whitening:

Pre-whitening Adding each error contribution
and setting
The 3DVar cost function for satellite retrievals is
where the noise in the observation term is now “white”
(observation error covariance is a unit matrix)

Summary:

Summary To perform an “optimal” assimilation (e.g. in a minimum variance sense) of satellite retrievals IS POSSIBLE.
The information needed is
The a priori on the state vector grid
The averaging kernel matrix
The covariance matrix of the retrieval noise, both random and systematic
The covariance matrix of an ensemble of state vectors, interpolated from the vertical background error covariance matrix on the model grid

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