References

ACP

Atmospheric Chemistry and Physics

ACP

1680-7324

Copernicus GmbH

Göttingen, Germany

10.5194/acp-6-4823-2006

McSCIA: application of the Equivalence Theorem in a Monte Carlo radiative transfer model for spherical shell atmospheres

Spada

¹ Krol

M. C.

¹ ² ³ Stammes

⁴

Institute for Marine and Atmospheric research Utrecht (IMAU), Utrecht, The Netherlands

Netherlands Institute for Space Research (SRON), Utrecht, The Netherlands

Meteorology and Air Quality, Wageningen University, The Netherlands

Koninklijk Nederlands Meteorologisch Instituut (KNMI), De Bilt, The Netherlands

25 10 2006

6 12 4823 4842

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A new multiple-scattering Monte Carlo 3-D radiative transfer model named McSCIA (Monte Carlo for SCIAmachy) is presented. The backward technique is used to efficiently simulate narrow field of view instruments. The McSCIA algorithm has been formulated as a function of the Earth's radius, and can thus perform simulations for both plane-parallel and spherical atmospheres. The latter geometry is essential for the interpretation of limb satellite measurements, as performed by SCIAMACHY on board of ESA's Envisat. The model can simulate UV-vis-NIR radiation. First the ray-tracing algorithm is presented in detail, and then successfully validated against literature references, both in plane-parallel and in spherical geometry. A simple 1-D model is used to explain two different ways of treating absorption. One method uses the single scattering albedo while the other uses the equivalence theorem. The equivalence theorem is based on a separation of absorption and scattering. It is shown that both methods give, in a statistical way, identical results for a wide variety of scenarios. Both absorption methods are included in McSCIA, and it is shown that also for a 3-D case both formulations give identical results. McSCIA limb profiles for atmospheres with and without absorption compare well with the one of the state of the art Monte Carlo radiative transfer model MCC++. A simplification of the photon statistics may lead to very fast calculations of absorption features in the atmosphere. However, these simplifications potentially introduce biases in the results. McSCIA does not use simplifications and is therefore a relatively slow implementation of the equivalence theorem.

References 1

Adams, C. N. and Kattawar, G. W.: Radiative transfer in spherical shell atmospheres 1. Rayleigh Scattering, Icarus, 35, 139–151, 1978.

Berk, A., Bernstein, L. S., and Robertson, D. C.: MODTRAN: A moderate resolution model for LOWTRAN-7, GL-TR-89-0122, Geophysics Laboratory, Hanscom AFB, MA 01732, 1989.

Bovensmann, H., Burrows, J. P., Buchwitz, M., Frerick, J., Noel, S., Rozanov, V. V., Chance, K. V., and Goede, A. P. H.: SCIAMACHY: Mission Objectives and Measurement Modes, J. Atmos. Sci., 56, 127–150, 1999.

Burrows, J. P., Weber, M., Buchwitz, M., Rozanov, V., Ladstatter-Weissenmayer, A., Richter, A., de Beek, R., Hoogen, R., Bramstedt, K., Eichmann, K., Eisinger, M., and Perner, D.: The Global Ozone Monitoring Experiment (GOME): Mission concept and first scientific results, J. Atmos Sci., 56, 151–175, 1999.

Cahalan, R. and Davies, R.: Intercomparison of three-dimensional radiation codes (I3RC): Proceedings of the first and second international workshops., University of Arizona Press, 2000.

Cahalan, R., Ridgway, W., Wiscombe, W., Gollmer, S., and Harshvardhan: Independent pixel and Monte Carlo estimates of stratocumulus albedo, J. Atmos. Sci., 51, 3776–3790, 1994.

Cashwell, E. D. and Everett, C. J.: Monte Carlo Method for random walk problems, Pergamon Press, 1959.

Collins, D. G., Blattner, W. G., Wells, M. B., and Horak, H. G.: Backward Monte Carlo calculations of the polarization characteristics of the radiation emerging from spherical shell atmospheres, Appl. Opt., 11, 2684–2696, 1972.

Davis, J., McKee, T., and Cox, S.: Application of the Monte Carlo method to problems in visibility using a local estimate: an investigation, Appl. Opt., 24, 3193–3205, 1985.

de Haan, J., Bosma, P., and Hovenier, J.: The adding method for multiple scattering calculations of polarized light, Astron. Astrophys., 183, 371–391, 1987.

Feigelson, E. (Ed.): Radiation in a cloudy atmosphere, Kluwer, p. 308, 1984.

Flittner, D. E., Bhartia, P. K., and Herman, B. M.: O3 profiles retrieved from limb scatter measurements: Theory, Geophys. Res. Lett., 27, 2601–2604, 2000.

Heidinger, A. and Stephens, G. L.: Molecular Line Absorption in a Scattering Atmosphere. Part II: Application to remote Sensing in the O2 A band, J. Atmos. Sci., 57, 1615–1634, 2000.

Heidinger, A. and Stephens, G. L.: Molecular Line Absorption in a Scattering Atmosphere. Part III: Pathlength Characteristics and Effects of Spatially Heterogeneous Clouds, J. Atmos. Sci., 59, 1641–1654, 2002.

Irvine, W.: The formation of absorption bands and the distribution of photon optical paths in a scattering atmosphere, Bulletin of the Astronomical Institutes of The Netherlands, 17, 266–279, 1964.

Jacob, D. J.: Introduction to Atmospheric Chemistry, Princeton University Press, 1999.

Kaiser, J.: Atmospheric Parameter Retrieval from UV-vis-NIR Limb Scattering Measurements, Logos Verlag, Berlin, Germany, 2002.

Kaiser, J., von Savigny, C., Eichmann, K.-U., No�l, S., Bovensmann, H., Frerick, J., and Burrows, J.: Satellite Pointing Retrieval from Atmospheric Limb Scattering of Solar UV-B Radiation, Can. J. Phys., 82, 1041–1052, 2004.

Kattawar, G. W. and Adams, C. N.: Radiative transfer in spherical shell atmospheres, II, asymmetric phase function, Icarus, pp. 436–449, 1978.

Lenoble, J.: Radiative transfer in scattering and absorbing atmospheres: Standard computational procedures, A. Deepak Publishing, Hampton, Virginia, 1985.

Lenoble, J.: Atmospheric Radiative Transfer, A. Deepak Publishing, Hampton, Virginia, 1993.

Levelt, P. F., van den Oord, G. H. J., Dobber, M. R., Malkki, A., Visser, H., de Vries, J., Stammes, P., Lundell, J., and Saari, H.: The Ozone Monitoring Instrument, IEEE Trans. Geo. Rem. Sens., Special Issue on the EOS-Aura mission, 44(5), 1199–1208, 2006.

Liou, K.-N.: An introduction to atmospheric radiation, Academic Press Inc., 1980.

Loughman, R., Griffioen, E., Oikarinen, L., Postylyakov, O., Rozanov, A., Flittner, D., and Rault, D.: Comparison of radiative transfer models for limb-viewing scattered sunlight measurements, J. Geophys. Res., D, Atmos., 109(D18), 6303, doi:10.1029/2003JD003854, 2004.

Marchuk, G. I., Mikhailov, G. A., Nazaraliev, M. A., Dearbinjan, R. A., Kargin, B. A., and Elepov, B. S.: The Monte Carlo methods in atmospheric optics, vol. 12 of Springer ser. in Opt. Sci., Springer Verlag, 1980.

Marshak, A. and Davis, A.: 3D radiative transfer in cloudy atmospheres, Springer Berlin, Heidelberg, New York, 2005.

Mount, G. H., Rusch, D. W., Noxon, J. F., Zawodny, J. M., and Barth, C. A.: Measurements of stratospheric NO2 from the SME satellite, J. Geophys. Res., 89, 1327–1340, 1984.

O'Hirok, W. and Gautier, C.: A three-dimensional radiative transfer model to investigate the solar radiation within a cloudy atmosphere. Part I: Spatial effects., J. Atmos. Sci., 55, 2162–2179, 1998.

Oikarinen, L., Sihvola, E., and Kyrola, E.: Multiple scattering radiance in limb-viewing geometry, J. Geophys. Res., 104, 31 261–31 274, 1999.

Partain, P. T., Heidinger, A. K., and Stephens, G. L.: High spectral resolution atmospheric radiative transfer: Application of the equivalence theorem, J. Geophys. Res., 105, 2163–2177, 2000.

Postylyakov, O. V.: Linearized vector radiative transfer model MCC++ for a spherical atmosphere, J. Quant. Spectr. Radiat. Trans., 88, 297–317, 2004.

Postylyakov, O. V., Kyrola, E., and Oikarinen, L.: Fine comparison of radiative transfer models for scattering limb simulation, EGS – AGU – EUG Joint Assembly, Abstracts from the meeting held in Nice, France, 6–11 April 2003, abstract #5566, pp. 5566–5567, 2003.

Rozanov, A., Bovensmann, H., Bracher, A., Hrechany, S., Rozanov, V., Sinnhuber, M., Stroh, F., and Burrows, J.: NO2 and BrO vertical profile retrieval from SCIAMACHY limb measurements: Sensitivity studies, Adv. Space Res., 2005.

Rusch, D. W., Mount, G. H., Barth, C. A., Thomas, R. J., and Callan, M. T.: Solar mesosphere explorer ultraviolet spectrometer: measurements of ozone in the 1.0–0.1 mb region, J. Geophys. Res., 89, 11 677–11 678, 1984.

Segers, A. J., von Savigny, C., Brinksma, E. J., and Piters, A. J. M.: Validation of IFE-1.6 SCIAMACHY limb ozone profiles, Atmos. Chem. Phys., 5, 3045–3052, 2005.

Sioris, C., Kurosu, T., Martin, R., and Chance, K.: Stratospheric and tropospheric NO2 observed by SCIAMACHY: first results, Adv. Space Res., 34, 780–785, 2004.

Spada, F. and Krol, M. C.: McSCIA: a Monte Carlo model for analysis of 3D features in a spherical atmosphere, in IRS 2004: Current Problems in Atmospheric Radiation, A. Deepak Publishing, Hampton, Virginia, 2005.

Spanier, J. and Gelbard, E. M.: Monte Carlo principles and Neutron Transport Problems, Addison Wesley, 1969.

Stammes, P.: Spectral radiance modelling in the UV-Visible range, in IRS 2000: Current problems in Atmospheric Radiation, pp. 385–388, A. Deepak Publ., Hampton, VA, 2001.

Stammes, P., Levelt, P., de Vries, J., Visser, H., Kruizinga, B., Smorenburg, C., Leppelmeier, G., and Hilsenrath, E.: Scientific requirements and optical design of the Ozone Monitoring Instrument on EOS-CHEM, in: Proceedings of SPIE Conference on Earth Observing Systems IV, vol. 3750, p. 221–232, SPIE, 1999.

Stephens, G. L. and Heidinger, A.: Molecular Line Absorption in a Scattering Atmosphere. Part I: Theory, J. Atmos. Sci., 57, 1599–1614, 2000.

van de Hulst, H. C.: Multiple light scattering, Academic press, 1980.

von Savigny, C., Haley, C. S., Sioris, C. E., McDade, I. C., Llewellyn, E. J., Degenstein, D., Evans, W. F. J., Gattinger, R. L., Griffioen, E., Kyrölä, E., Lloyd, N. D., McConnell, J. C., McLinden, C. A., Mégie, G., Murtagh, D. P., Solheim, B., and Strong, K.: Stratospheric ozone profiles retrieved from limb scattered sunlight radiance spectra measured by the OSIRIS instrument on the Odin satellite, Geophys. Res. Lett., 30, 1755–1758, 2003.

Walter, H. and Landgraf, J.: Towards Linearization of Atmospheric Radiative Transfer in Spherical Geometry, J. Quant. Spectr. Radiat. Trans., 95, 175–200, 2005.

Walter, H. H., Landgraf, J., Spada, F., and Doicu, A.: Linearization of a radiative transfer model in spherical geometry, J. Geophys. Res., in press, 2006.