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Original Articles

Mathematical aspects of BRDF modeling: Adjoint problem and green's function

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Pages 263-280 | Published online: 19 Oct 2009

References

  • Bass , L. P. , Volocsvhenko , A. M. and Germogenova , T. A. 1986 . Methods of Discrete Ordinates in Radiation Transport Problems (in Russian, with English abstract) . Inst. Appl. Math., Russ. Acad. of Sci., Moscow , : 231
  • Bell , G. I. and Glasstone . 1970 . Nuclear Reactor Theory , 619 New York : Van Nostrand Reinholt .
  • Box , M. A. , Gerstl , S. A. W. and Simmer , C. 1988 . Application of the adjoint formulation of the calculation of atmospheric radiative effects. . Beitr. Phys. Almosph. , 61 : 303 – 311 .
  • Cahalan , R. F. 1994 . Bounded cascade clouds: Albedo and effective thickness. . Nonlinear Processes in Geoph. , 1 : 156 – 167 .
  • Cahalan , R. F. and Snider , J. B. 1989 . Marine stratocumulus structure during FIRE. . Remote Sens. Environ. , 28 : 95 – 107 .
  • Chandrasekhar , S. 1950 . Radiative Transfer , 393 Oxford University Press . reprinted by Dover, 1960, New York (NY)
  • Choulli , M. and Stefanov , P. 1996 . Reconstruction of the coefficient of the stationary transport equation from boundary measurements . Inverse Problems , 12 : L19 – L23 .
  • Davis , A. , Marshak , A. , Cahalan , R. and Wiscombe , W. 1997 . The LANDSAT scale‐break in stratocumulus as a three‐dimensional radiative transfer effect, implications for cloud remote sensing . J. Atmos. Sci. , 54 : 241 – 260 .
  • Davis , A. , Marshak , A. , Wiscombe , W. and Cahalan , R. 1996 . Scale‐invariance in liquid water distributions in marine stratocumulus, Part I, Spectral properties and stationarity issues. . J. Atmos. Sci. , 53 : 1538 – 1558 .
  • Kimes , D. , Knyazikhin , Y. , Privette , J. , Abuelgasim , A. and Gao , F. 2000 . Inversion methods for physically‐based models . Remote Sensing Reviews , this issue
  • Knyazikhin , Y. , Martonchik , J. V. , Myneni , R. B. , Diner , D. J. and Running , S. W. 1998a . Synergistic algorithm for estimating vegetation canopy leaf area index and fraction of absorbed photosynthetically active radiation from MODIS and MISR data. . J. Geophys. Res. , 103 : 32257 – 32275 .
  • Knyazikhin , Y. , Martonchik , J. V. , Diner , D. J. , Myneni , R. B. , Verstraete , M. M. , Pinty , B. and Gobron , N. 1998b . Estimation of vegetation canopy leaf area index and fraction of absorbed photosynthetically active radiation from atmosphere‐corrected MISR data. . J. Geophys. Res. , 103 : 32239 – 32256 .
  • Mandelbrot , B. B. 1977 . Fractals: Form, Chance, and Dimension , 365 San Francisco : W. H. Freeman . (Ca)
  • Marshak , A. , Davis , A. , Cahalan , R. F. and Wiscombe , W. J. 1994 . Bounded cascade models as non‐stationary multifractals. . Phys. Rev. E , 49 : 55 – 69 .
  • Marshak , A. , Davis , A. , Wiscombe , W. J. , Ridgway , W. and Cahalan , R. F. 1998 . Biases in shortwave column absorption in the presence of fractal clouds. . J. Climate , 11 : 431 – 446 .
  • Marshak , A. , Davis , A. , Wiscombe , W. and Cahalan , R. 1995 . Radiative smoothing in fractal clouds . J. Geophys. Res. , 100 : 26,247 – 26,261 .
  • Marshak , A. , Davis , A. , Wiscombe , W. and Cahalan , R. 1997 . Scale‐invariance of liquid water distributions in marine stratocumulus, Part 2 ‐ Multifractal properties and intermittency issues. . J. Atmos. Sci. , 54 : 1423 – 1444 .
  • Myneni , R. B. , Ross , J. and Asrar , G. 1989 . A review on the theory of photon transport in leaf canopies in slab geometry. . Agric. For. Meleoroh , 45 : 1 – 165 .
  • Panferov , O. , Knyazikhin , Y. , Myneni , R. B. , Szarzynski , J. , Engwald , S. , Schnitzler , K. G. and Gravenhorst , G. 1999 . The role of canopy structure in the spectral variation of transmission and absorption of solar radiation in vegetation canopies . IEEE Trans. Geosci. Remote Sens , (submitted for publication)
  • Papoulis , A. 1965 . Probability, Random Variables, and Stochastic Processes , xi + 583 New York, NY : McGraw‐Hill .
  • Rahman , H. , Pinty , B. and Verstraete , M. M. 1993 . Coupled surface‐atmosphere model reflectance model (CSAR) model 2. Semiempirical surface model usable with NOAA Advance Very High Resolution Radiometer data. . J. Geophys. Res. , 98 : 20791 – 20801 .
  • Ross , J. 1981 . The Radiation Regime and Architecture of Plant Stands , 391 Norwell, Mass. : Dr. W. Junk .
  • Schertzer , D. and Lovejoy , S. 1987 . Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes. . J. Geophys. Res. , 92 : 9693 – 9714 .
  • Stamnes , K. 1982 . Reflection and transmission by a vertically inhomogeneous planetary atmosphere. . Planet. Space Sci. , 30 : 727 – 732 .
  • Tucker , C. J. 1979 . Red and photographic infrared linear combination for monitoring vegetation. . Remote Sens. Environ. , 8 : 127 – 150 .
  • van de Hulst , H. C. 1980 . Multiple Light Scattering: Tables, Formulas, and Applications , Vol. 1 , San Diego, Ca : Academic Press .
  • Verstraete , M. M. and Pinty , B. 1996 . Designing optical spectral indexes for remote sensing applications. . IEEE Trans. Geoscience Rem. Sensing , 34 : 1254 – 1265 .
  • Walter‐Shea , E. A. and Norman , J. M. 1991 . “ Leaf Optical Properties ” . In Photon‐ Vegetation Interactions: Applications in Plant Physiology and Optical Remote Sensing , Edited by: Myneni , R. B. and Ross , J. 229 – 251 . New York : Springer‐Verlag .
  • Corresponding author. Tel.: (617) 353 8843, Fax: (617) 353 8399, e‐mail: jknjazi@cr sa.bu.edu
  • Tel.: (301) 614–6122, Fax: (301) 614–6307, e‐mail: [email protected]

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