9.7 Practice 8
9.7.1 Objectives
To study specific features of methods applied for regularizing the solution of the
inverse ill-posed problem of remote temperature sounding.
To obtain the optimal solution by choosing input parameters.
9.7.2 Software and Set of Input Parameters
1. The method of statistical regularization supposes analyzing matrices S и K TT
influence on the desired result. There are two computer programs in the directory
Lab4:
The program “RADNIMB6.exe” solves the direct problem, and calculates the
outgoing intensity from input temperature profile “aer.dat” that contains transmission function and average temperature profile T(z).
The program “DZ_T_SR5.exe”, solves the inverse problem for choused
matrices S and K TT elements . All elements at principal diagonal are taken
equal each other (only one value is taken) and correlation coefficients are zeroth.
Variants of input data
There are two temperature profiles: mean and aerologic (true) T aer . The
transmission function P is calculated at corresponding spectral channels. For
example:
n ij, sm
À1
P
669.8
0.001 strong absorption
676.7
0.8 weak absorption
. . .
. . .
746.7
0.22
Four variants of input parameters are to be considered:
(a) variant: All diagonal elements of the temperature correlation matrix K TT
are equal to 0.1
Values of diagonal elements of the errors matrix S are equal to 1.0
The program calculates the vector
^
~ f (retrieved temperature deviations
profile), then calculates temperature values ^
T, and at last the difference
^
T À T aer . Result is saved in the file “dz.dat” In the first variant the solution
coincides with the mean profile. The mean deviation from true values
appears around 8
C because there is no new information.
(b) variant: diagonal elements of the temperature correlation matrix K TT are
equal to 10 (i.e. average deviations from the mean profile are Æ3
)
Values of diagonal elements of the errors matrix S are equal to 0.1.
94
9 The Thermal Remote Sounding of the Atmosphere
9.7.1 Objectives
To study specific features of methods applied for regularizing the solution of the
inverse ill-posed problem of remote temperature sounding.
To obtain the optimal solution by choosing input parameters.
9.7.2 Software and Set of Input Parameters
1. The method of statistical regularization supposes analyzing matrices S и K TT
influence on the desired result. There are two computer programs in the directory
Lab4:
The program “RADNIMB6.exe” solves the direct problem, and calculates the
outgoing intensity from input temperature profile “aer.dat” that contains transmission function and average temperature profile T(z).
The program “DZ_T_SR5.exe”, solves the inverse problem for choused
matrices S and K TT elements . All elements at principal diagonal are taken
equal each other (only one value is taken) and correlation coefficients are zeroth.
Variants of input data
There are two temperature profiles: mean and aerologic (true) T aer . The
transmission function P is calculated at corresponding spectral channels. For
example:
n ij, sm
À1
P
669.8
0.001 strong absorption
676.7
0.8 weak absorption
. . .
. . .
746.7
0.22
Four variants of input parameters are to be considered:
(a) variant: All diagonal elements of the temperature correlation matrix K TT
are equal to 0.1
Values of diagonal elements of the errors matrix S are equal to 1.0
The program calculates the vector
^
~ f (retrieved temperature deviations
profile), then calculates temperature values ^
T, and at last the difference
^
T À T aer . Result is saved in the file “dz.dat” In the first variant the solution
coincides with the mean profile. The mean deviation from true values
appears around 8
C because there is no new information.
(b) variant: diagonal elements of the temperature correlation matrix K TT are
equal to 10 (i.e. average deviations from the mean profile are Æ3
)
Values of diagonal elements of the errors matrix S are equal to 0.1.
94
9 The Thermal Remote Sounding of the Atmosphere