Fast Stochastic Radiative Transfer Models for Trace Gas and Cloud Property Retrievals Under Cloudy Conditions

Part of the Springer Series in Light Scattering book series (SSLS)


The stochastic radiative transfer models based on the analytical procedure of statistical averaging of the radiative transfer equation are reviewed. For broken clouds , the first-order stochastic model for a two-dimensional radiance vector , whose entries are the mean radiance field and the covariance of the radiance and the indicator fields, is derived. An algorithm for accurate retrieving ozone and clouds parameters under broken cloud conditions is designed. Because the independent pixel approximation fails to predict accurate radiances, the retrieval algorithm uses a stochastic radiative transfer model. The accuracy of the stochastic model in forward models and retrieval algorithms is analyzed.


  1. Adams ML, Larsen EW, Pomraning GC (1989) Benchmark results for particle transport in a binary Markov statistical medium. J Quant Spectrosc Radiat Transf 42(4):253–266CrossRefADSGoogle Scholar
  2. Afanas’ev VP, Golovina OY, Gryazev AS, Efremenko DS, Kaplya PS (2015) Photoelectron spectra of finite-thickness layers. J Vac Sci Technol B 33(3):03D101CrossRefGoogle Scholar
  3. Afanas’ev VP, Efremenko DS, Kaplya PS (2016) Analytical and numerical methods for computing electron partial intensities in the case of multilayer systems. J Electron Spectrosc Relat Phenom 210:16–29CrossRefGoogle Scholar
  4. Afanas’ev VP, Gryazev AS, Efremenko DS, Kaplya PS (2017) Differential inverse inelastic mean free path and differential surface excitation probability retrieval from electron energy loss spectra. Vacuum 136:146–155CrossRefADSGoogle Scholar
  5. Ahmad Z (2004) Spectral properties of backscattered UV radiation in cloudy atmospheres. J Geophys Res 109(D1)Google Scholar
  6. Alexandrov MD, Marshak A, Ackerman AS (2010) Cellular statistical models of broken cloud fields. Part I: theory. J Atmos Sci 67(7):2125–2151CrossRefADSGoogle Scholar
  7. Anisimov O, Fukshansky L (1992) Stochastic radiation in macroheterogeneous random optical media. J Quant Spectrosc Radiat Transf 48(2):169–186CrossRefADSGoogle Scholar
  8. Barker HW (1996) A parametrization for computing grid-averaged solar fluxes for inhomogeneous marine boundary layer clouds: I. Methodology and homogeneous biases. J Atmos Sci 53(16):2289–2303CrossRefADSGoogle Scholar
  9. Barker HW, Davis AB (2005) Approximation methods in atmospheric 3D radiative transfer. Part 2: unresolved variability and climate applications. In: Marshak A, Davis AB (eds) 3d radiative transfer in cloudy atmospheres, vol 6. Springer, Berlin, pp 343–383Google Scholar
  10. Barker HW, Wielicki BA, Parker L (1996) A parametrization for computing grid-averaged solar fluxes for inhomogeneous marine boundary layer clouds: II. Validation using satellite data. J Atmos Sci 53(16):2304–2316CrossRefADSGoogle Scholar
  11. Berg LK, Kassianov EI (2008) Temporal variability of fair-weather cumulus statistics at the ACRF SGP site. J Clim 21(13):3344–3358CrossRefADSGoogle Scholar
  12. Boersma KF (2004) Error analysis for tropospheric NO 2 retrieval from space. J Geophys Res 109(D4)Google Scholar
  13. Budak VP, Korkin SV (2008) On the solution of a vectorial radiative transfer equation in an arbitrary three-dimensional turbid medium with anisotropic scattering. J Quant Spectrosc Radiat Transfr 109(2):220–234CrossRefADSGoogle Scholar
  14. Budak VP, Klyuykov DA, Korkin SV (2010) Convergence acceleration of radiative transfer equation solution at strongly anisotropic scattering. In: Kokhanovsky AA (ed) Light scattering reviews, vol 5. Springer, Berlin, pp 147–203Google Scholar
  15. Budak VP, Kaloshin GA, Shagalov OV, Zheltov VS (2015) Numerical modeling of the radiative transfer in a turbid medium using the synthetic iteration. Opt Express 23(15):A829CrossRefADSGoogle Scholar
  16. Byrne RN, Somerville RCJ, Subasilar B (1996) Broken-cloud enhancement of solar radiation absorption. J Atmos Sci 53(6):878–886CrossRefADSGoogle Scholar
  17. Cahalan RF, Ridgway W, Wiscombe WJ, Bell TL, Snider JB (1994a) The albedo of fractal stratocumulus clouds. J Atmos Sci 51(16):2434–2455Google Scholar
  18. Cahalan RF, Ridgway W, Wiscombe WJ, Gollmer S, Harshvardhan S, Gollmer S (1994b) Independent pixel and Monte Carlo estimates of stratocumulus albedo. J Atmos Sci 51(51):3776–3790Google Scholar
  19. Cairns B, Lacis AA, Carlson BE (2000) Absorption within inhomogeneous clouds and its parameterization in general circulation models. J Atmos Sci 57:700–714CrossRefADSGoogle Scholar
  20. Davis A, Gabriel PM, Lovejoy SM, Schertzer D, Austin GL (1990) Discrete angle radiative transfer III: numerical results and meteorological applications. J Geophys Res: Atmos 95(D8):11729–11742CrossRefADSGoogle Scholar
  21. Davis AB, Marshak A (2010) Solar radiation transport in the cloudy atmosphere: a 3D perspective on observations and climate impacts. Rep Prog Phys 73(2):026801CrossRefADSGoogle Scholar
  22. Doicu A, Trautmann T (2009a) Discrete-ordinate method with matrix exponential for a pseudo-spherical atmosphere: scalar case. J Quant Spectrosc Radiat Transf 110(1–2):146–158Google Scholar
  23. Doicu A, Trautmann T (2009b) Discrete-ordinate method with matrix exponential for a pseudo-spherical atmosphere: vector case. J Quant Spectrosc Radiat Transf 110(1–2):159–172Google Scholar
  24. Doicu A, Trautmann T, Schreier F (2010) Numerical regularization for atmospheric inverse problems. Springer, BerlinCrossRefzbMATHGoogle Scholar
  25. Doicu A, Efremenko DS, Loyola D, Trautmann T (2014a) Approximate models for broken clouds in stochastic radiative transfer theory. J Quant Spectrosc Radiat Transf 145:74–87Google Scholar
  26. Doicu A, Efremenko DS, Loyola D, Trautmann T (2014b) Discrete ordinate method with matrix exponential for stochastic radiative transfer in broken clouds. J Quant Spectrosc Radiat Transf 138:1–16Google Scholar
  27. Efremenko DS, Loyola D, Spurr RJD, Doicu A (2014) Acceleration of radiative transfer model calculations for the retrieval of trace gases under cloudy conditions. J Quant Spectrosc Radiat Transf 135:58–65CrossRefADSGoogle Scholar
  28. Efremenko DS, Schüssler O, Doicu A, Loyola D (2016) A stochastic cloud model for cloud and ozone retrievals from UV measurements. J Quant Spectrosc Radiat Transf 184:167–179CrossRefADSGoogle Scholar
  29. Evans KF (1998) The spherical harmonic discrete ordinate method for three-dimensional atmospheric radiative transfer. J Atmos Sci 55(3):429–446CrossRefADSGoogle Scholar
  30. Farman JC, Gardiner BG, Shanklin JD (1985) Large losses of total ozone in Antarctica reveal seasonal ClOx/NOx interaction. Nature 315(6016):207–210CrossRefADSGoogle Scholar
  31. Gabriel PM, Evans KF (1996) Simple radiative transfer methods for calculating domain-averaged solar fluxes in inhomogeneous clouds. J Atmos Sci 53(6):858–877CrossRefADSGoogle Scholar
  32. Gabriel PM, Lovejoy SM, Davis A, Schertzer D, Austin GL (1990) Discrete angle radiative transfer II: renormalization approach for homogeneous and fractal clouds. J Geophys Res: Atmos 95(D8):11717–11728CrossRefADSGoogle Scholar
  33. Hu Y-X, Wielicki B, Lin B, Gibson G, Tsay S-C, Stamnes K, Wong T (2000) \(\delta \)-fit: a fast and accurate treatment of particle scattering phase functions with weighted singular-value decomposition least-squares fitting. J Quant Spectrosc Radiat Transf 65(4):681–690Google Scholar
  34. Ingmann P, Veihelmann B, Langen J, Lamarre D, Stark H, Bazalgette Courreges-Lacoste G (2012) Requirements for the GMES atmosphere service and ESA’s implementation concept: Sentinels-4/-5 and -5p. Remote Sens Environ 120:58–69CrossRefADSGoogle Scholar
  35. Kargin BA (2000) Statistical modeling of stochastic problems of the atmosphere and ocean optics. In: Matvienko GG, Panchenko MV (eds) Seventh international symposium on atmospheric and ocean optics. SPIE-International society for optical engineeringGoogle Scholar
  36. Kassianov E (2003) Stochastic radiative transfer in multilayer broken clouds. Part I: Markovian approach. J Quant Spectrosc Radiat Transf 77(4):373–393CrossRefADSGoogle Scholar
  37. Kassianov E, Lane-Veron DE, Berg LK, Ovchinnikov M, Kollias P (2012) Markovian approach and its applications in a cloudy atmosphere, vol 7. Light scattering reviews. Springer Science + Business Media, New York, pp 69–107Google Scholar
  38. Kokhanovsky AA (2003) The influence of horizontal inhomogeneity on radiative characteristics of clouds: an asymptotic case study. IEEE Trans Geosci Remote Sens 41(4):817–825CrossRefADSGoogle Scholar
  39. Lane DE, Goris K, Somerville RCJ (2002) Radiative transfer through broken clouds: observations and model validation. J Clim 15(20):2921–2933CrossRefADSGoogle Scholar
  40. Levermore CD, Pomraning GC, Sanzo DL, Wong J (1986) Linear transport theory in a random medium. J Math Phys 27(10):2526–2536Google Scholar
  41. Levermore CD, Wong J, Pomraning GC (1988) Renewal theory for transport processes in binary statistical mixtures. J Math Phys 29:995–1004MathSciNetCrossRefzbMATHADSGoogle Scholar
  42. Loyola D, Thomas W, Livschitz Y, Ruppert T, Albert P, Hollmann R (2007) Cloud properties derived from GOME/ERS-2 backscatter data for trace gas retrieval. IEEE Trans Geosci Remote Sens 45(9):2747–2758CrossRefADSGoogle Scholar
  43. Lubenchenko AV, Batrakov AA, Pavolotsky AB, Lubenchenko OI, Ivanov DA (2018) XPS study of multilayer multicomponent films. Appl Surf Sci 427(Part A):711–721Google Scholar
  44. Malvagi F, Byrne N, Pomraning GC, Somerville RCJ (1993) Stochastic radiative transfer in a partially cloudy atmosphere. J Atmos Sci 50(14):2146–2158CrossRefADSGoogle Scholar
  45. Marchuk GI, Mikhailov GA, Nazaraliev MA, Darbinjan RA, Kargin BA, Elepov BS (1980) The Monte Carlo methods in atmospheric optics, vol 12. Springer series in optical sciences. Springer, BerlinGoogle Scholar
  46. McLinden CA, McConnell JC, Griffioen E, McElroy CT (2002) A vector radiative-transfer model for the Odin/OSIRIS project. Can J Phys 80:375–393CrossRefADSGoogle Scholar
  47. Plank VG (1969) The size distribution of cumulus clouds in representative Florida populations. J Appl Meteorol 8(1):46–67CrossRefGoogle Scholar
  48. Platt U, Stutz J (2008) Differential optical absorption spectroscopy: principles and applications. Springer, BerlinGoogle Scholar
  49. Pomraning GC (1989) Statistics, renewal theory and particle transport. J Quant Spectrosc Radiat Transf 42(4):279–293CrossRefADSGoogle Scholar
  50. Pomraning GC (1991) A model for interface intensities in stochastic particle transport. J Quant Spectrosc Radiat Transf 46:221–236CrossRefADSGoogle Scholar
  51. Prigarin SM, Kargin BA, Oppel UG (1998) Random fields of broken clouds and their associated direct solar radiation, scattered transmission and albedo. Pure Appl Opt 7(6):1389–1402CrossRefADSGoogle Scholar
  52. Roozendael VM, Loyola D, Spurr R, Balis D, Lambert J-C, Livschitz Y, Valks P, Ruppert T, Kenter P, Fayt C, Zehner C (2006) Ten years of GOME/ERS-2 total ozone data: the new GOME data processor (GDP) version 4: I. Algorithm description. J Geophys Res: Atmos 111(D14311(1–21))Google Scholar
  53. Sahini DC (1989a) An application of reactor noise techniques to neutron transport problems in a random medium. Ann Nucl Energy 16:397–408Google Scholar
  54. Sahini DC (1989b) Equivalence of generic equation method and the phenomeno-logical model for linear transport problem in a two-state random scattering medium. J Math Phys 30:1554–1559Google Scholar
  55. Seah MP, Gilmore IS, Spencer SJ (2000) Background subtraction: II. General behaviour of REELS and the Tougaard universal cross section in the removal of backgrounds in AES and XPS. Surf Sci 461(1–3):1–15CrossRefADSGoogle Scholar
  56. Smirnov BM (1975) Ekologicheskie problemy atmosfery zemli. Uspekhi Fizicheskikh Nauk 117(10):313–332 (in Russian)Google Scholar
  57. Stephens GL (1988) Radiative transfer through arbitrarily shaped optical media. Part II: group theory and simple closures. J Atmos Sci 45(12):1818–1848CrossRefADSGoogle Scholar
  58. Szczap F, Isaka H, Saute M, Guillemet B, Iotukhovski A (2000a) Effective radiative properties of bounded cascade absorbing clouds: definition of an effective single-scattering albedo. J Geophys Res: Atmos 105(D16):20635–20648Google Scholar
  59. Szczap F, Isaka H, Saute M, Guillemet B, Iotukhovski A (2000b) Effective radiative properties of bounded cascade absorbing clouds: definition of the equivalent homogeneous cloud approximation. J Geophys Res: Atmos 105(D16):20617–20633Google Scholar
  60. Titov GA (1990) Statistical description of radiative transfer in clouds. J Atmos Sci 47(1):24–38CrossRefADSGoogle Scholar
  61. Titov GA, Zhuravleva TB, Zuev VE (1997) Mean radiation fluxes in the near-IR spectral range: algorithms for calculation. J Geophys Res: Atmos 102(D2):1819–1832CrossRefADSGoogle Scholar
  62. Vainikko GM (1973a) Correlation of direct solar radiance in the broken cloudiness. Statistical investigations of broken cloudiness. Meteorological investigations. Trudy MGK SSSR, pp 65–74 (in Russian)Google Scholar
  63. Vainikko GM (1973b) The equations for mean radiance in the broken clouds. Statistical investigations of broken cloudiness. Meteorological investigations. Trudy MGK SSSR, pp 28–37 (in Russian)Google Scholar
  64. Vanderhaegen D (1986) Radiative transfer in statistically heterogeneous mixtures. J Quant Spectrosc Radiat Transf 36(6):557–561CrossRefADSGoogle Scholar
  65. Wiscombe WJ (1977) The delta-M method: rapid yet accurate radiative flux calculations for strongly asymmetric phase functions. J Atmos Sci 34(9):1408–1422CrossRefADSGoogle Scholar
  66. Zhuravleva TB (2008) Simulation of solar radiative transfer under different atmospheric conditions. Part I. The deterministic atmosphere. Atmos Ocean Opt 21(2):81–95Google Scholar
  67. Zuev VE, Titov GA (1995) Radiative transfer in cloud fields with random geometry. J Atmos Sci 52(2):176–190CrossRefADSGoogle Scholar
  68. Zuev VE, Titov GA (1996) Atmosphere optics and climate. Institute of Atmospheric Optics, Tomsk (in Russian)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Institut für Methodik der Fernerkundung (IMF)Deutsches Zentrum für Luft- und Raumfahrt (DLR)Weßling, OberpfaffenhofenGermany

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