Analytical Jacobian Calculation in RT Model Including Polarization Effect

Abstract:

The greenhouse gas observing satellite “GOSAT” launched in January 2009 has been observing global distribution of CO₂ and CH₄. The TANSO-FTS mounted on GOSAT measures the two polarized components (called “P” and “S”) of short wavelength infrared (SWIR) spectrum reflected from the earth’s surface. In NIES, column-averaged dry air mole fraction of CO₂ and CH₄ (XCO₂ and XCH₄) are retrieved from SWIR spectra. However, the observed polarization information is not effectively utilized in the retrieval process due to the large computational cost of a vector RT model, instead the polarization synthesized spectra and a scalar RT model are used in the operational processing. An optical path length modification due to aerosol scattering is known as the major error source for XCO₂ and XCH₄ retrieval from SWIR spectra. Because the aerosol scattering changes polarization state of light, more accurate or additional aerosol information is expected by using the observed polarization spectra effectively in the retrieval process, which improves the retrieval accuracy of XCO₂ and XCH₄. In addition, for information content analysis, sensitivity analysis and error analysis, Jacobian matrix is important onto retrieval algorithm design before analyses for actual observed data. However, in the case of using RT model including polarization effect in retrieval process, the computational cost of Jacobian matrix calculations in maximum a posteriori retrieval is significantly large. Efficient calculation of analytical Jacobian is necessary.

As a first step, we are implementing an analytical Jacobian calculation function to the vector RT model “Pstar”. RT scheme of Pstar is based on hybrid method comprising the discrete ordinate and matrix operator methods. The reflection/transmission matrices and source vectors are obtained for each vertical layer through the discrete ordinate solution, and the vertically inhomogeneous system is constructed using the matrix operator method. Because the delta-M truncation method is used in the Pstar to reduce the computational cost, single scattering component correction called TMS method is implemented. Calculation of analytical Jacobian has to be constructed above the RT scheme. We will show the formulation and some results of the analytical Jacobian implementation at the presentation.