LIM: Forschung: Strahlung/Stoerungstheorie

Investigator: Prof. Dr. Thomas Trautmann

The Essence of Radiative Perturbation Theory

Radiative perturbation theory is a computational technique which can greatly reduce the computational effort to repeatedly solve the radiative transfer equation (RTE) for planetary atmospheres which differ from each other by relatively small or modererate changes of their optical parameters. As in the usual radiative transfer theory, perturbation theory requires the solution of the RTE plus the solution of its adjoint, the latter of which representing the importance function of the particular radiative quantity of interest. As soon as these solutions, forward and adjoint, are available, the radiative effect for a perturbed model atmosphere can be obtained via simple integrations. This is much faster than solving the RTE for each perturbed atmospheric state separately.

The Project

Linear perturbation theory allows a fast computation of radiative effects, such as upward and downward radiative flux densities, radiative heating rates, the spherical radiative flux (c.f. actinic flux), or radiances at the top of the atmosphere.

The following scientific issues are investigated:

The so-called pseudo-spherical treatment of the radiative transfer eqaution in a spherical shell atmosphere is investigated. Pseudo-spherical treatment means that both the direct solar beam as well as the single-scattered diffuse radiation is computed by taking the sphericity of the Earth's atmosphere into account. The multiple-scattered diffuse light is still treated as in a horizontally homogeneous plane-parallel medium.
In terms of radiative perturbation theory the term describing the extinction of the direct and single-scattered radiation can be formulated as a perturbation with respect to the standard RTE (plane-parallel).
Nadir radiances at the location of a satellite's detector can be employed to retrieve the total column content of atmospheric absorber gases such as ozone. The spectral absorption features of a particular gas can be exploited to obtain information on the vertical profile of the molecule concentration of the absorber. To this end the RTE has to be solved for the same atmospheric state for a set of different wavelengths. In addition to that, the solar illumination of an atmospheric column should be treated for many solar zenith angles (SZAs) simultaneously. Moreover, since the local surface albedo at the bottom of an atmospheric column is not known precisley, the functional dependency of the nadir radiance on surface albedo needs to be determined.
This big advantage of radiative perturbation theory is that such functional dependencies can be obtained in a rigorous analytic manner. For example, from a single adjoint computation, which involves the solution of the adjoint RTE, the nadir radiance at the satellite's position can be obtained for arbitrary SZA. Contrary to that, one is required to solve the (forward) RTE for each SZA separately.
Recently, a linearized radiative transfer model system for the forward and adjoint radiation field has been developed on the basis of the so-called Gauss-Seidel method for solving the RTE. It has been demonstrated that linear radiative perturbation theory requires by far less CPU time to retrieve the ozone profile than a retrieval method based on the widely employed discrete ordinate method of radiative transfer.
A further potential for CPU time saving is to speed up radiative transfer computations, at the bottom (BOA) or the top of the atmosphere (TOA), for high spectral resolution via (0.1 nm or so) linear perturbation theory. The recipe for this is to solve the RTE exactly at a coarser wavelength grid which is able to capture the main features of the atmospheric absorber in question. For the wavelengths on the finer grid the exact computations may serve as a reference case. The vertical profile of the deviations of the absorption coefficient from it reference profile can then be employed to obtain to first-order accuracy the radiation field at BOA or TOA, again for arbitrary SZA.
It is also possible to compute higher-order corrections to linear perturbation theory. In principle this requires that the Greens function of the forward and adjoint RTE can be constructed. First results have proven that this approach is feasible and that it yields results for the radiation field of a perturbed atmosphere which are indistinguishable from corresponding exact radiative transfer computations.

Cooperation

The development of radiative perturbation theory and its application to radiative transfer and remote sensing problems is carried aout in cooperations with Dr. Jochen Landgraf, and Holger Walter, Space Research Organization Netherlands (SRON), Utrecht, The Netherlands.

Dr. Michael A. Box, School Of Physics, University of New South Wales, Sydney Australia.

Recent Publications and References

1: Trautmann, T., H. Walter, and J. Landgraf, 2001: Actinic Fluxes and photodissociation frequencies of NO₂ (J_NO2) for very large solar zenith angles: Comparison of two radiative transfer codes. In: IRS 2000: Current Problems in Atmospheric Radiation. Proceedings of International Radiation Symposium, St. Petersburg, Russia, July 24-29 2000, edited by W. L. Smith and Y. M. Timofeyev, p. 397-400.
2: Landgraf, J., O. P. Hasekamp, M. A. Box, and T. Trautmann, 2001: A linearized radiative transfer model for ozone profile retrieval using the analytical forward-adjoint perturbation theory approach. Journal of Geophysical Research, 106, 27291-27305, 2001.
3: Bösch, H., C. Camy-Peyret, M. Chipperfield, R. Fitzenberger, H. Harder, C. Schiller, M. Schneider, T. Trautmann, and K. Pfeilsticker, 2001: Comparison of measured and modeled stratospheric UV/visible actinic fluxes at large solar zenith angles. Geophys. Res. Lett., 28, 1179-1182.
4: Landgraf, J., O. P. Hasekamp, and T. Trautmann, 2002: Linearization of radiative transfer with respect to surface properties. J. Quant. Spectrosc. Radiat. Transfer, 72, 327-339.
5: Box, M. A., 2002: Radiative perturbation theory: a review. Environmental Modelling & Software , 17, 95-106.

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