Skip to main content
SpringerLink
Log in

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

  • Chapter
  • First Online:
Springer Series in Light Scattering

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

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • 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):253–266

    Article  ADS  Google Scholar 

  • 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):03D101

    Article  Google Scholar 

  • 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 210:16–29

    Article  Google Scholar 

  • 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 136:146–155

    Article  ADS  Google Scholar 

  • Ahmad Z (2004) Spectral properties of backscattered UV radiation in cloudy atmospheres. J Geophys Res 109(D1)

    Google Scholar 

  • Alexandrov MD, Marshak A, Ackerman AS (2010) Cellular statistical models of broken cloud fields. Part I: theory. J Atmos Sci 67(7):2125–2151

    Article  ADS  Google Scholar 

  • Anisimov O, Fukshansky L (1992) Stochastic radiation in macroheterogeneous random optical media. J Quant Spectrosc Radiat Transf 48(2):169–186

    Article  ADS  Google Scholar 

  • 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):2289–2303

    Article  ADS  Google Scholar 

  • 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 343–383

    Google Scholar 

  • 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):2304–2316

    Article  ADS  Google Scholar 

  • Berg LK, Kassianov EI (2008) Temporal variability of fair-weather cumulus statistics at the ACRF SGP site. J Clim 21(13):3344–3358

    Article  ADS  Google Scholar 

  • Boersma KF (2004) Error analysis for tropospheric NO 2 retrieval from space. J Geophys Res 109(D4)

    Google Scholar 

  • 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):220–234

    Article  ADS  Google Scholar 

  • 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 147–203

    Google Scholar 

  • 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):A829

    Article  ADS  Google Scholar 

  • Byrne RN, Somerville RCJ, Subasilar B (1996) Broken-cloud enhancement of solar radiation absorption. J Atmos Sci 53(6):878–886

    Article  ADS  Google Scholar 

  • Cahalan RF, Ridgway W, Wiscombe WJ, Bell TL, Snider JB (1994a) The albedo of fractal stratocumulus clouds. J Atmos Sci 51(16):2434–2455

    Google Scholar 

  • 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):3776–3790

    Google Scholar 

  • Cairns B, Lacis AA, Carlson BE (2000) Absorption within inhomogeneous clouds and its parameterization in general circulation models. J Atmos Sci 57:700–714

    Article  ADS  Google Scholar 

  • 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):11729–11742

    Article  ADS  Google Scholar 

  • 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):026801

    Article  ADS  Google Scholar 

  • 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):146–158

    Google Scholar 

  • 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):159–172

    Google Scholar 

  • Doicu A, Trautmann T, Schreier F (2010) Numerical regularization for atmospheric inverse problems. Springer, Berlin

    Book  MATH  Google Scholar 

  • Doicu A, Efremenko DS, Loyola D, Trautmann T (2014a) Approximate models for broken clouds in stochastic radiative transfer theory. J Quant Spectrosc Radiat Transf 145:74–87

    Google Scholar 

  • 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 138:1–16

    Google Scholar 

  • 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 135:58–65

    Article  ADS  Google Scholar 

  • 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 184:167–179

    Article  ADS  Google Scholar 

  • Evans KF (1998) The spherical harmonic discrete ordinate method for three-dimensional atmospheric radiative transfer. J Atmos Sci 55(3):429–446

    Article  ADS  Google Scholar 

  • Farman JC, Gardiner BG, Shanklin JD (1985) Large losses of total ozone in Antarctica reveal seasonal ClOx/NOx interaction. Nature 315(6016):207–210

    Article  ADS  Google Scholar 

  • Gabriel PM, Evans KF (1996) Simple radiative transfer methods for calculating domain-averaged solar fluxes in inhomogeneous clouds. J Atmos Sci 53(6):858–877

    Article  ADS  Google Scholar 

  • 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):11717–11728

    Article  ADS  Google Scholar 

  • 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):681–690

    Google Scholar 

  • 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 120:58–69

    Article  ADS  Google Scholar 

  • 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 engineering

    Google Scholar 

  • Kassianov E (2003) Stochastic radiative transfer in multilayer broken clouds. Part I: Markovian approach. J Quant Spectrosc Radiat Transf 77(4):373–393

    Article  ADS  Google Scholar 

  • 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 69–107

    Google Scholar 

  • Kokhanovsky AA (2003) The influence of horizontal inhomogeneity on radiative characteristics of clouds: an asymptotic case study. IEEE Trans Geosci Remote Sens 41(4):817–825

    Article  ADS  Google Scholar 

  • Lane DE, Goris K, Somerville RCJ (2002) Radiative transfer through broken clouds: observations and model validation. J Clim 15(20):2921–2933

    Article  ADS  Google Scholar 

  • Levermore CD, Pomraning GC, Sanzo DL, Wong J (1986) Linear transport theory in a random medium. J Math Phys 27(10):2526–2536

    Google Scholar 

  • Levermore CD, Wong J, Pomraning GC (1988) Renewal theory for transport processes in binary statistical mixtures. J Math Phys 29:995–1004

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • 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):2747–2758

    Article  ADS  Google Scholar 

  • Lubenchenko AV, Batrakov AA, Pavolotsky AB, Lubenchenko OI, Ivanov DA (2018) XPS study of multilayer multicomponent films. Appl Surf Sci 427(Part A):711–721

    Google Scholar 

  • Malvagi F, Byrne N, Pomraning GC, Somerville RCJ (1993) Stochastic radiative transfer in a partially cloudy atmosphere. J Atmos Sci 50(14):2146–2158

    Article  ADS  Google Scholar 

  • 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, Berlin

    Google Scholar 

  • McLinden CA, McConnell JC, Griffioen E, McElroy CT (2002) A vector radiative-transfer model for the Odin/OSIRIS project. Can J Phys 80:375–393

    Article  ADS  Google Scholar 

  • Plank VG (1969) The size distribution of cumulus clouds in representative Florida populations. J Appl Meteorol 8(1):46–67

    Article  Google Scholar 

  • Platt U, Stutz J (2008) Differential optical absorption spectroscopy: principles and applications. Springer, Berlin

    Google Scholar 

  • Pomraning GC (1989) Statistics, renewal theory and particle transport. J Quant Spectrosc Radiat Transf 42(4):279–293

    Article  ADS  Google Scholar 

  • Pomraning GC (1991) A model for interface intensities in stochastic particle transport. J Quant Spectrosc Radiat Transf 46:221–236

    Article  ADS  Google Scholar 

  • 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):1389–1402

    Article  ADS  Google Scholar 

  • 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 

  • Sahini DC (1989a) An application of reactor noise techniques to neutron transport problems in a random medium. Ann Nucl Energy 16:397–408

    Google Scholar 

  • 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 30:1554–1559

    Google Scholar 

  • 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):1–15

    Article  ADS  Google Scholar 

  • Smirnov BM (1975) Ekologicheskie problemy atmosfery zemli. Uspekhi Fizicheskikh Nauk 117(10):313–332 (in Russian)

    Google Scholar 

  • Stephens GL (1988) Radiative transfer through arbitrarily shaped optical media. Part II: group theory and simple closures. J Atmos Sci 45(12):1818–1848

    Article  ADS  Google Scholar 

  • 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):20635–20648

    Google Scholar 

  • 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):20617–20633

    Google Scholar 

  • Titov GA (1990) Statistical description of radiative transfer in clouds. J Atmos Sci 47(1):24–38

    Article  ADS  Google Scholar 

  • 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):1819–1832

    Article  ADS  Google Scholar 

  • 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 

  • 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 

  • Vanderhaegen D (1986) Radiative transfer in statistically heterogeneous mixtures. J Quant Spectrosc Radiat Transf 36(6):557–561

    Article  ADS  Google Scholar 

  • Wiscombe WJ (1977) The delta-M method: rapid yet accurate radiative flux calculations for strongly asymmetric phase functions. J Atmos Sci 34(9):1408–1422

    Article  ADS  Google Scholar 

  • Zhuravleva TB (2008) Simulation of solar radiative transfer under different atmospheric conditions. Part I. The deterministic atmosphere. Atmos Ocean Opt 21(2):81–95

    Google Scholar 

  • Zuev VE, Titov GA (1995) Radiative transfer in cloud fields with random geometry. J Atmos Sci 52(2):176–190

    Article  ADS  Google Scholar 

  • Zuev VE, Titov GA (1996) Atmosphere optics and climate. Institute of Atmospheric Optics, Tomsk (in Russian)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Methodik der Fernerkundung (IMF), Deutsches Zentrum für Luft- und Raumfahrt (DLR), Münchener Straße 20, 82234, Weßling, Oberpfaffenhofen, Germany

    Dmitry S. Efremenko, Adrian Doicu, Diego Loyola & Thomas Trautmann

Authors
  1. Dmitry S. Efremenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Adrian Doicu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Diego Loyola
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Thomas Trautmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dmitry S. Efremenko .

Editor information

Editors and Affiliations

  1. Vitrociset Belgium, Darmstadt, Germany

    Alexander Kokhanovsky

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Efremenko, D.S., Doicu, A., Loyola, D., Trautmann, T. (2018). Fast Stochastic Radiative Transfer Models for Trace Gas and Cloud Property Retrievals Under Cloudy Conditions. In: Kokhanovsky, A. (eds) Springer Series in Light Scattering. Springer Series in Light Scattering. Springer, Cham. https://doi.org/10.1007/978-3-319-70796-9_3

Download citation

Publish with us

Policies and ethics

Search

Navigation