MORSE .avk File

14APR24

Description

Averaging Kernel Matrix for each retrieval.

This is a square matrix of dimensions the same as the retrieval state vector.

The Averaging Kernel Matrix A represents the expected contribution of the real atmospheric profile x^t to the retrieved profile x^r, allowing for influences of the a priori estimate a on the retrieved values and vertical resolution.

x^r = A x^t + (I − A) a where I is the Identity Matrix.

Elements of A are defined as

A(i,j) = dx^r(i) / dx^t(j)

The matrix itself is computed from

A = I − S_x S_a⁻¹ where S_x is the random (noise) error covariance matrix of the retrieval and S_a is the error covariance matrix of the a priori estimate.

Thus, for an ideal retrieval, the averaging kernel matrix approaches the identity matrix and, for a least squares fit (i.e. S_a ∼ ∞ ) it is the identity matrix.

Structure

The .avk file follows the Common File Format except that the Common_Pixel_Data section is replaced by a Matrix Data section containing just the averaging kernel matrix.

The size of the matrix, NX × NX is computed from

NX = ∑_i NLVPRF(i)

where NLVPRF(i), listed in the File Header section, are the sizes of the state vector component profiles for each retrieved species i.

Matrix Data
A(1,1) A(2,1) ...	Averaging Kernel Matrix elements
... A(NX,1) A(1,2) ...
... A(NX,NX)

Fields

Field	Type	Definition	Range
A(:,:)	R	(NX,NX) Averaging kernel matrix	0 ≤ A ≤ 1 (generally)

• MORSE Index