Approximation Methods in Atmospheric 3D Radiative Transfer Part 2: Unresolved Variability and Climate Applications

  • H.W. Barker
  • A.B. Davis
Part of the Physics of Earth and Space Environments book series (EARTH)


Radiative Transfer Optical Depth Cloud Fraction Radiative Transfer Equation Liquid Water Path 
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  1. Avaste, O.A. and G.M. Vainikko (1974). Solar radiative transfer in broken clouds. Izv. Acad. Sci. USSR Atmos. Oceanic Phys., 10, 1054–1061.Google Scholar
  2. Barker, H.W. (1992). Solar radiative transfer for clouds possessing isotropic variable extinction coefficient. Quart. J. Roy. Meteor. Soc., 118, 1145–1162.CrossRefGoogle Scholar
  3. Barker, H.W. and B.A. Wielicki (1997). Parameterizing grid-averaged longwave fluxes for inhomogenous marine boundary layer clouds. J. Atmos. Sci., 54, 2785–2798.CrossRefGoogle Scholar
  4. Barker, H.W., B.A. Wielicki, and L. Parker (1996). A parameterization for computing grid-averaged solar fluxes for inhomogeneous marine boundary layer clouds — Part 2, Validation using satellite data. J. Atmos. Sci., 53, 2304–2316.CrossRefGoogle Scholar
  5. Barker, H.W., G.L. Stephens, and Q. Fu (1999). The sensitivity of domain-averaged solar fluxes to assumptions about cloud geometry. Quart. J. Roy. Meteor. Soc., 125, 2127–2152.CrossRefGoogle Scholar
  6. Barker, H.W., R. Pincus, and J.-J. Morcrette (2002). The Monte Carlo independent column approximation: Application within large-scale models. In Proceedings from the GCSS Workshop. Kananaskis, Alberta, Canada.Google Scholar
  7. Barker, H.W., and Räisänen, P., (2004). Radiative sensitivities for cloud geometric properties that are unresolved by conventional GCMs. Quart. J. Roy. Meteor. Soc., 130, 2069–2086.CrossRefGoogle Scholar
  8. Barker, H.W., G.L. Stephens, P.T. Partain, J.W. Bergman, B. Bonnel, K. Campana, E.E. Clothiaux, S. Clough, S. Cusack, J. Delamere, J. Edwards, K.F. Evans, Y. Fouquart, S. Freidenreich, V. Galin, Y. Hou, S. Kato, J. Li, E. Mlawer, J.-J. Morcrette, W. O’Hirok, P. Räisänen, V. Ramaswamy, B. Ritter, E. Rozanov, M. Schlesinger, K. Shibata, P. Sporyshev, Z. Sun, M. Wendisch, N. Wood, and F. Yang (2003). Assessing 1D atmospheric solar radiative transfer models: Interpretation and handling of unresolved clouds. J. Climate, 16, 2676–2699.CrossRefGoogle Scholar
  9. Benner, T.C. and K.F. Evans (2001). Three-dimensional solar radiative transfer in small tropical cumulus field derived from high-resolution imagery. J. Geophys. Res., 106, 14,975–14,984.Google Scholar
  10. Borde, R. and H. Isaka (1996). Radiative transfer in multifractal clouds. J. Geophys. Res., 101, 29,461–29,478.CrossRefGoogle Scholar
  11. Buldyrev, S.V., M. Gitterman, S. Havlin, A.Ya. Kazakov, M.G.E. da Luz, E.P. Raposo, H.E. Stanley, and G.M. Viswanathan (2001). Properties of Lévy flights on an interval with absorbing boundaries. Physica A, 302, 148–161.CrossRefGoogle Scholar
  12. Cahalan, R.F. (1989). Overview of fractal clouds. In Advances in Remote Sensing. A. Deepak Publishing, Hampton, VA, pp. 371–388.Google Scholar
  13. Cahalan, R.F. and J.B. Snider (1989). Marine stratocumulus structure during FIRE. Remote Sens. Environ., 28, 95–107.CrossRefGoogle Scholar
  14. Cahalan, R.F., W. Ridgway, W.J. Wiscombe, S. Gollmer, and Harshvardhan (1994a). Independent pixel and Monte Carlo estimates of stratocumulus albedo. J. Atmos. Sci., 51, 3776–3790.CrossRefGoogle Scholar
  15. Cahalan, R.F., W. Ridgway, W.J. Wiscombe, T.L. Bell, and J.B. Snider (1994b). The albedo of fractal stratocumulus clouds. J. Atmos. Sci., 51, 2434–2455.CrossRefGoogle Scholar
  16. Cahalan, R.F., D. Silberstein, and J. Snider (1995). Liquid water path and planeparallel albedo bias during ASTEX. J. Atmos. Sci., 52, 3002–3012.CrossRefGoogle Scholar
  17. Cairns, B., A.A. Lacis, and B.E. Carlson (2000). Absorption within inhomogeneous clouds and its parameterization in general circulation models. J. Atmos. Sci., 57, 700–714.CrossRefGoogle Scholar
  18. Chambers, L.H., B.A. Wielicki, and K.F. Evans (1997). On the accuracy of the independent pixel approximation for satellite estimates of oceanic boundary layer cloud optical depth. J. Geophys. Res., 102, 1779–1794.CrossRefGoogle Scholar
  19. Charlock, T. and B.M. Herman (1976). Discussion of the Elsasser formulation for infrared fluxes. J. Appl. Meteor., 15, 657–661.CrossRefGoogle Scholar
  20. Coakley, J.A. and P. Chýlek (1975). The two-stream approximation in radiative transfer: Including the angle of the incident radiation. J. Atmos. Sci., 32, 409–418.CrossRefGoogle Scholar
  21. Davis, A. and A. Marshak (1997). Lévy kinetics in slab geometry: Scaling of transmission probability. In Fractal Frontiers. M.M. Novak and T.G. Dewey (eds.). World Scientific, Singapore, pp. 63–72.Google Scholar
  22. Davis, A.B. and A. Marshak (2001). Multiple scattering in clouds: Insights from three-dimensional diffusion/P1 theory. Nuclear Sci. and Engin., 137, 251–280.Google Scholar
  23. Davis, A.B. and A. Marshak (2004). Photon propagation in heterogeneous optical media with spatial correlations: Enhanced mean-free-paths and wider-than-exponential free-path distributions. J. Quant. Spectrosc. Radiat. Transfer, 84, 3–34.CrossRefGoogle Scholar
  24. Davis, A., P.M. Gabriel, S.M. Lovejoy, D. Schertzer, and G.L. Austin (1990). Discrete angle radiative transfer III: Numerical results and meteorological applications. J. Geophys. Res., 95, 11,729–11,742.Google Scholar
  25. Dirac, P.A.M. (1977). In History of Twentieth Century Physics. C. Weiner (ed.). Academic Press, New York (NY).Google Scholar
  26. Evans, K.F. (1993). A general solution for stochastic radiative transfer. Geoph. Res. Lett., 20, 2075–2078.Google Scholar
  27. Fu, Q. and K.-N. Liou (1992). On the correlated-k distribution method for radiative transfer in inhomogeneous atmospheres. J. Atmos. Sci., 49, 2139–2156.CrossRefGoogle Scholar
  28. Gabriel, P.M. and K.F. Evans (1996). Simple radiative transfer methods for calculating domain-averaged solar fluxes in inhomogeneous clouds. J. Atmos. Sci., 53, 858–877.CrossRefGoogle Scholar
  29. Gabriel, P.M., S.M. Lovejoy, A. Davis, D. Schertzer, and G.L. Austin (1990). Discrete angle radiative transfer II: Renormalization approach for homogeneous and fractal clouds. J. Geophys. Res., 95, 11,717–11,728.Google Scholar
  30. Joseph, J.H., W.J. Wiscombe, and J.A. Weinman (1976). The delta-Eddington approximation for radiative flux transfer. J. Atmos. Sci., 33, 2452–2459.CrossRefGoogle Scholar
  31. Kassianov, E. (2003). Stochastic radiative transfer in multilayer broken clouds — Part I: Markovian approach. J. Quant. Spectrosc. Radiat. Transfer, 77, 373–393.CrossRefGoogle Scholar
  32. Kassianov, E., T.P. Ackerman, R. Marchand, and M. Ovtchinnikov (2003). Stochastic radiative transfer in multilayer broken clouds — Part II: Validation tests. J. Quant. Spectrosc. Radiat. Transfer, 77, 395–416.CrossRefGoogle Scholar
  33. Khairoutdinov, M.F. and D.A. Randall (2001). A cloud-resolving model as a cloud parameterization in the NCAR Community Climate System Model: Preliminary results. Geophys. Res. Lett., 28, 3617–3620.CrossRefGoogle Scholar
  34. Lacis, A.A. and V. Oinas (1991). A description of the correlated-k method for modeling nongrey gaseous absorption, thermal emission, and multiple scattering in vertically inhomogeneous atmospheres. J. Geophys. Res., 96, 9027–9063.Google Scholar
  35. Lane, D.E., K. Goris, and R.C.J. Somerville (2002). Radiative transfer through broken cloud fields: Observations and model validation. J. Climate, 15, 2921–2933.CrossRefGoogle Scholar
  36. Li, J. (2002). Accounting for unresolved clouds in a 1D infrared radiative transfer model. Part I: Solution for radiative transfer, scattering, and cloud overlap. J. Atmos. Sci., 59, 3302–3320.CrossRefGoogle Scholar
  37. Li, J. and H.W. Barker (2002). Accounting for unresolved clouds in a 1D infrared radiative transfer model. Part II: Horizontal variability of cloud water path. J. Atmos. Sci., 59, 3321–3339.CrossRefGoogle Scholar
  38. Li, J. and Q. Fu (2000). Absorption approximation with scattering effect for infrared radiation. J. Atmos. Sci., 57, 2905–2914.CrossRefGoogle Scholar
  39. Lohmann, U. and J. Feichter (1997). Impact of sulfate aerosols on albedo and lifetime of clouds: A sensitivity study with the ECHAM4 GCM. J. Geophys. Res., 102, 13,685–13,700.CrossRefGoogle Scholar
  40. McFarlane, N.A., G.J. Boer, J.-P. Blanchet, and M. Lazare (1992). The Canadian Climate Centre second-generation general circulation model and its equilibrium climate. J. Climate, 5, 1013–1044.CrossRefGoogle Scholar
  41. Meador, W.E. and W.R. Weaver (1980). Two-stream approximations to radiative transfer in planetary atmospheres: A unified description of existing methods and a new improvement. J. Atmos. Sci., 37, 630–643.CrossRefGoogle Scholar
  42. Min, Q.-L. and L.C. Harrison (1999). Joint statistics of photon pathlength and cloud optical depth. Geophys. Res. Lett., 26, 1425–1428.CrossRefGoogle Scholar
  43. Newman W.I., J.K. Lew, G.L. Siscoe, and R.G. Fovell (1995). Systematic effects of randomness in radiative transfer. J. Atmos. Sci., 52, 427–435.CrossRefGoogle Scholar
  44. Oreopoulos, L. and H.W. Barker (1999). Accounting for subgrid-scale cloud variability in a multi-layer, 1D solar radiative transfer algorithm. Quart. J. Roy. Meteor. Soc., 125, 301–330.CrossRefGoogle Scholar
  45. Petty, G.W. (2002). Area-average solar radiative transfer in three-dimensionally inhomogeneous clouds: The independently scattering cloudlets model. J. Atmos. Sci., 59, 2910–2929.CrossRefGoogle Scholar
  46. Pfeilsticker, K. (1999). First geometrical pathlengths probability density function derivation of the skylight from spectroscopically highly resolving oxygen A-band observations. 2. Derivation of the Lévy-index for the skylight transmitted by midlatitude clouds. J. Geophys. Res., 104, 4101–4116.CrossRefGoogle Scholar
  47. Pincus, R., S.A. MacFarlane, and S.A. Klein (1999). Albedo bias and the horizontal variability of clouds in subtropical marine boundary layers: Observations from ships and satellites. J. Geophys. Res., 104, 6183–6191.CrossRefGoogle Scholar
  48. Pincus, R., H.W. Barker, and J.-J. Morcrette (2003). A new radiative transfer model for use in GCMs. J. Geophys. Res., 108, 4376–4379.CrossRefGoogle Scholar
  49. Räisänen, P. and H.W. Barker (2005). Evaluation and optimization of sampling errors for the Monte Carlo independent column approximation. Quart. J. Roy. Meteor. Soc., in press.Google Scholar
  50. Räisänen, P., G.A. Isaac, H.W. Barker, and I. Gultepe (2003). Solar radiative transfer for stratiform clouds with horizontal variations in liquid water path and droplet effective radius. Quart. J. Roy. Meteor. Soc., 129, 2135–2149.CrossRefGoogle Scholar
  51. Räisänen, P., H.W. Barker, M.F. Khairoutdinov, and D.A. Randall (2005a). Stochastic generation of subgrid-scale cloudy columns for large-scale models. Quart. J. Roy. Meteor. Soc., 130, 2047–2067.CrossRefGoogle Scholar
  52. Räisänen, P., H.W. Barker, and J.N.S. Cole (2005b). The Monte Carlo independent column approximation’s conditional random noise: Impact on simulated climate. J. Climate, in press.Google Scholar
  53. Randall, D., M. Khairoutdinov, A. Arakawa, and W. Grabowski (2003). Breaking the cloud parameterization deadlock. Bull. Amer. Meteor. Soc., 84, 1547–1564.CrossRefGoogle Scholar
  54. Ronnholm, K., M.B. Baker, and H. Harrison (1980). Radiation transfer through media with uncertain or random parameters. J. Atmos. Sci., 37, 1279–1290.CrossRefGoogle Scholar
  55. Rosenbaum, S. (1971). The mean Green’s function: A nonlinear approximation. Radio Sci., 6, 379–386.Google Scholar
  56. Rossow, W.B., C. Delo, and B. Cairns (2002). Implications of the observed mesoscale variations of clouds for the earth’s radiation budget. J. Climate, 15, 557–585.CrossRefGoogle Scholar
  57. Samorodnitsky, G. and M.S. Taqqu (1994). Stable Non-Gaussian Random Processes. Chapman and Hall, New York (NY).Google Scholar
  58. Schertzer, D. and S. Lovejoy (1987). Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes. J. Geophys. Res., 92, 9693–9714.CrossRefGoogle Scholar
  59. Schuster, A. (1905). Radiation through a foggy atmosphere. Astrophys. J., 21, 1–22.CrossRefGoogle Scholar
  60. Smith, R.N.B. (1990). A scheme for predicting layer clouds and their water content in a GCM. Quart. J. Roy. Meteor. Soc., 116, 435–460.CrossRefGoogle Scholar
  61. Stephens, G.L. (1988a). Radiative transfer through arbitrary shaped optical media, I: A general method of solution. J. Atmos. Sci., 45, 1818–1836.CrossRefGoogle Scholar
  62. Stephens, G.L. (1988b). Radiative transfer through arbitrary shaped optical media, II: Group theory and simple closures. J. Atmos. Sci., 45, 1837–1848.CrossRefGoogle Scholar
  63. Stephens, G.L., P.M. Gabriel, and S.-C. Tsay (1991). Statistical radiative transfer in one-dimensional media and its application to the terrestrial atmosphere. Transp. Theory and Stat. Phys., 20, 139–175.Google Scholar
  64. Szczap, F., H. Isaka, M. Saute, B. Guillemet, and A. Iotukhovski (2000a). Effective radiative properties of bounded cascade absorbing clouds: Definition of the equivalent homogeneous cloud approximation. J. Geophys. Res., 105, 20,617–20,634.Google Scholar
  65. Szczap, F., H. Isaka, M. Saute, B. Guillemet, and A. Iotukhovski (2000b). Effective radiative properties of bounded cascade nonabsorbing clouds: Definition of an effective single-scattering albedo. J. Geophys. Res., 105, 20,635–20,638.Google Scholar
  66. Tiedtke, M. (1996). An extension of cloud-radiation parameterization in the ECMWF model: The representation of subgridscale variations in optical depth. Mon. Wea. Rev., 124, 745–750.CrossRefGoogle Scholar
  67. Tompkins, A.M. (2002). A prognostic parameterization for the subgrid-scale variability of water vapor and clouds in large-scale models and its use to diagnose cloud cover. J. Atmos. Sci., 59, 1917–1942.CrossRefGoogle Scholar
  68. Wiscombe, W.J. and G.W. Grams (1976). The backscattered fraction in two-stream approximations. J. Atmos. Sci., 33, 2440–2451.CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • H.W. Barker
  • A.B. Davis

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