AVK File Structure

19NOV22 - Add IDL code to Read and Plot data
Contents

Overview

An optional MORSE output is the Averaging Kernel Matrix (.avk file) 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 xt to the retrieved profile xr, allowing for influences of the a priori estimate a on the retrieved values and vertical resolution.

xr = A xt + (I - A ) a
where I is the Identity Matrix.

Elements of A are defined as

A(i,j) = dxr(i) / dxt(j)

The matrix itself is computed from

A = I - Sx Sa-1
where Sx is the random (noise) error covariance matrix of the retrieval and Sa 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. Sa ∼ ∞ ) it is the identity matrix.

Example: hiros_ch4.avk which can be read with read_avk.pro

Also, plot_avk.pro plots the AVK data creating an Encapsulated PostScript file, which has been converted to avk.pdf

File Structure

The .avk file follows the same structure as the .rtv file except that the Profile Data section is replaced by a Matrix Data section containing just the averaging kernel matrix.

The File Header section contains just the elements of the retrieval state vector, which map directly to the elements of the averaging kernel matrix in the order listed.

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

NX = ∑i NLevP(i)
where NLevP(i), listed in the File Header section, are the sizes of the state vector component profiles.

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

Data Dictionary
Field Type Definition Range
A Float(NX,NX) Averaging kernel matrix 0 ≤ A ≤ 1 (generally)

Document Updates

19NOV22 Add IDL code to Read and Plot data
21SEP22 Original