Feng Xu, Anthony B. Davis, Suniti V. Sanghavi, John V. Martonchik, and David J. Diner, "Linearization of Markov chain formalism for vector radiative transfer in a plane-parallel atmosphere/surface system," Appl. Opt. 51, 3491-3507 (2012)
The Markov chain formalism for polarized radiative transfer through a vertically inhomogeneous atmosphere is linearized comprehensively with respect to the aerosol and polarizing surface properties. For verification, numerical results are compared to those obtained by the finite difference method. We demonstrate the use of the linearized code as part of a retrieval of aerosol and surface properties for an atmosphere overlying a black and Fresnel-reflecting ocean surface.
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Mean Percentage Error of the Derivatives of Intensity Calculated for the Viewing Angles Varying between 0° and 90° in the Principal Plane by FD Approach as a Function of a
1.902
The aerosol/surface medium state vector (, , , , , , , , , , ) is set to be (1.38, , 0.1, 2.718, 1.0, 0.10, , 1.5, 1.0, 1.34, 5.0). The values in bold indicate the smallest error of FD approach.
Table 2.
Aerosol Retrieval from Synthetic Data for Cases 6–8 and 10 [16], Using Both BRF and Polarizationa
Parameter
Case 6
Case 7
Case 8
Case 10
1.380
1.380
1.380
1.380
0.000
0.000
0.000
0.000
(μm)
0.099
0.100
0.100
0.099
2.725
2.718
2.717
2.728
0.050
0.100
0.200
0.400
17
22
20
19
The true values of aerosol properties are , , , , and , 0.10, 0.20, and 0.40 for Cases 6–8 and 10, respectively.
Aerosol and Surface Retrieval from Synthetic Data for the Atmospheres in Cases 6–8 and 10 [16] Overlying an Ocean Surface of Wind Speed , Using Both BRF and Polarization
Mean Percentage Error of the Derivatives of Intensity Calculated for the Viewing Angles Varying between 0° and 90° in the Principal Plane by FD Approach as a Function of a
1.902
The aerosol/surface medium state vector (, , , , , , , , , , ) is set to be (1.38, , 0.1, 2.718, 1.0, 0.10, , 1.5, 1.0, 1.34, 5.0). The values in bold indicate the smallest error of FD approach.
Table 2.
Aerosol Retrieval from Synthetic Data for Cases 6–8 and 10 [16], Using Both BRF and Polarizationa
Parameter
Case 6
Case 7
Case 8
Case 10
1.380
1.380
1.380
1.380
0.000
0.000
0.000
0.000
(μm)
0.099
0.100
0.100
0.099
2.725
2.718
2.717
2.728
0.050
0.100
0.200
0.400
17
22
20
19
The true values of aerosol properties are , , , , and , 0.10, 0.20, and 0.40 for Cases 6–8 and 10, respectively.
Aerosol and Surface Retrieval from Synthetic Data for the Atmospheres in Cases 6–8 and 10 [16] Overlying an Ocean Surface of Wind Speed , Using Both BRF and Polarization