Procedure for the calculation of the MSS
In this section we summarize the steps necessary to calculate the MSS.
1. To define the vertical grid on which to calculate the MSS.
2. To calculate the linearization point x0 on the grid defined in step 1. The linearization point can be calculated using a standard retrieval technique (that uses a priori information or regularization techniques) and then interpolating the retrieved profile onto the vertical grid defined in step 1.
3. To calculate the Jacobian matrix K of the forward model in the linearization point onto the vertical grid defined in step 1.
4. To perform the SVD of the matrix Sy-1/2K and to determine the matrices U, Λ and V by Eq. (3.9):
Sy-1/2K = U Λ VT , (3.9)
As output of the SVD calculation it is possible also to obtain the matrix W that contains the orthonormal basis of the null space.
5. To calculate the components â of the MSS by using Eq. (3.10):
The MSS is given by V and â . The elements of â are uncorrelated with each other and their errors are given by the diagonal elements of the matrix Λ-1 (see Eq. (3.12)).
