Slide 1

Effective Transport Kernels for Spatially Correlated Media, Application to Cloudy Atmospheres Anthony B. Davis Los Alamos National Laboratory Space & Remote Sensing Sciences Group (ISR-2) with help from many others LA-UR-04-6228 Slide 2 Key References 1.Davis, A., and A. Marshak, L vy 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 (1997). 2.Pfeilsticker, K., First geometrical pathlength distribution measurements of skylight using the oxygen A-band absorption technique - II, Derivation of the L vy-index for skylight transmitted by mid-latitude clouds, J. Geophys. Res., 104, 4101-4116 (1999). 3.Buldyrev, S. V., S. Havlin, A. Ya. Kazakov, M. G. E. da Luz, E. P. Raposo, H. E. Stanley, and G. M. Viswanathan, Average time spent by L vy flights and walks on an interval with absorbing boundaries, Phys. Rev. E, 64, 41108-41118 (2001). 4.Kostinski, A. B., On the extinction of radiation by a homogeneous but spatially correlated random medium, J. Opt. Soc. Am. A, 18, 1929-1933 (2001). 5.Davis, A. B., and A. Marshak, Photon propagation in heterogeneous optical media with spatial correlations: Enhanced mean-free-paths and wider-than-exponential free-path distributions, J. Quant. Spectrosc. Rad. Transf., 84, 3-34 (2004). 6.Davis, A. B., and H. W. Barker, Approximation methods in three-dimensional radiative transfer, in Three-Dimensional Radiative Transfer for Cloudy Atmospheres, A. Marshak and A. B. Davis (eds.), Springer-Verlag, Heidelberg (Germany), to appear (2004). and others, as we proceed Slide 3 Outline Motivation & Background (atmospheric radiation science only) Mean-field transport kernels Heuristic scattering-translation factorization Directional diffusion: Transport MFP revisited Spatial impact: Non-exponential tails Implications for effective medium theories (homogenization) Anomalous photon diffusion: The basic boundary-value problem Time-dependent (first, then ) Steady-state Observational corroborations Time-domain lightning observations Fine spectroscopy in oxygen absorption lines/bands Summary & Outlook Slide 4 Ren Magritte, 1929 Motivation, 1: Surrealism Slide 5 Motivation, 2: State-of-the-Art Conceptual Models inside operational cloud remote sensing schemes (chez NASA et Co.), and inside any Global Climate Models radiation module This is a cloud. Slide 6 Motivation, 3: Reality! from Space Shuttle archive (courtesy Bob Cahalan) Slide 7 Approximation theory in atmospheric radiative transfer: Needs assessment Variability: Resolved or not? in computational grid in observations (pixels) Slide 8 Large-scale radiation budget estimation: Unresolved variability effects Clear-cloudy separation (70s - 80s) The cloud fraction enters A correlation scale enters: Stochastic RT in Markovian binary media The Independent-Column Approximation (ICA) limit for very large aspect ratios Cloudy part gets variable Stephens closure-based effective medium theory (1988) Davis et al.s parameterization with power-law rescaling (1991) Cahalans ICA-based effective medium theory (1994) Barkers Gamma-weighted/2-stream ICA (1996) More effective medium theories Cairns et al.s renormalization theory (2000) Pettys cloudets (2002): large clumps as scattering entities Recent numerical solutions for GCM consumption And what about cloud overlap (vertical correlation)? The McICA Project (2003-) Slide 9 Some definitions in 3D Radiative Transfer Slide 10 Directional diffusion Slide 11 Directional diffusion: Spatial impact After n* (1g) 1 scatterings, directional memory is lost. Slide 12 Directional diffusion and its spatial impact illustrated in 2D Slide 13 Effective (i.e., mean) transport kernels: the actual photon free-path distributions Slide 14 Need for long-range spatial correlations! Slide 15 Synthetic scale-invariant media that are turbulence-like Slide 16 Three remarkable properties of effective free-path distributions For 2.-3., using a very different approach, see: Kostinski, A. B., 2001: On the extinction of radiation by a homogeneous but spatially correlated random medium, J. Opt. Soc. Am. A, 18, 1929-1933. Slide 17 Variability scales of 3D-transport interest? Consider extinction (x) or local (pseudo-)MFP 1/ (x). How much does it typically change, on a relative scale, between two discrete transport events (emission or injection, scattering, absorption or escape)? N.B. Extreme cases are well-known in stochastic RT theory for binary Markovian media, respectively, the limits of: a. atomistic mixing (i.e. optical homogeneity using mean values); c. linear mixing by volume fraction (a.k.a. the ICA/IPA in atmospheric work). Slide 18 An illustration with binary media: Implications for effective medium theories: * will all fail at large-enough scales; * watch for correlations over the (actual) MFP. Slide 19 Expectations for Earths cloudy atmosphere, 1: Barker et al.s (1996) LandSat Analysis From: Gamma distributions capture many cloud optical depth scenarios. Slide 20 Expectations for Earths cloudy atmosphere, 2: Effective transport kernels are power-law Assuming s = H (thickness) in previous slide: Slide 21 Solar photons multiply scattering in the cloudy atmosphere Slide 22 Anomalous diffusion through a finite medium: Time-dependence for transmission from free space to a finite slab (thickness H): Slide 23 Anomalous diffusion through a finite medium: Steady-state transmission from a half-space to a finite slab (thickness H): For a more rigorous approach: Slide 24 Observations, 1a: Differential absorption spectroscopy at very high resolution From: Min Q.-L., L. C. Harrison, P. Kiedron, J. Berndt, and E. Joseph, 2004: A high-resolution oxygen A-band and water vapor band spectrometer, J. Geophys. Res., 109, D02202, doi:10.1029/2003JD003540. x-section density pathlength Slide 25 Observations, 1b: Ground-based Oxygen Spectroscopy Cases near the =2 line are very overcast, and those near =1 are for sparse clouds, as expected from model. A single cloud layer ( =2) with variable thickness H the slope of the linear path vs optical depth plot. A complex cloud situation (1<