BRDF/albedo

  • spectral bidirectional reflectance function - :
  • ratio of measured spectral radiance to perfect Lambertian surface under same illumination contions
  • BRF here assumed corrected for atmospheric effects

include. diffuse sky, multiple scattering ground-atmos.

  • spectral directional-hemispherical reflectance -
  • integral over viewing (illumination) hemisphere of BRF (reciprocitous)
  • reflectance over all angles from direct illumin. source (sun)
  • or ... reflectance in given direction from diffuse illumin. source (sky)

  • spectral bi-hemispherical reflectance -
  • angular integral of sDHR over illumination hemisphere
  • reflectance in all directions from (isotropic) diffuse source (sky?)
  • spectral albedo -
  • total (in all directions) reflected radiation at given wavelength
  • can be approximated for direct and diffuse illumination sources (sun/sky) -
  • dept. on atmos. state

  • albedo -
  • total incident SW radn / total reflected
  • is proportion of absorbed SW radiation (photosyn, heat)
  • can be approximated as:
  • for proportion of illumin. in solar spectrum (dept. on atmos. state; )
  • approximate integral by summation over bands available

data sources and models

  • require angular samples of
  • require model to interpolate / integrate
  • fit BRDF model
  • model needs to be fast, robust, deal with heterogeneity
  • select linear kernel-driven models (Wanner et al., 1995)
  • essentially angular ‘shapes’ of BRF
  • derived from volume-scattering and GO shadowing theory
  • with linear approximations
  • defined to be nadir refl. at nadir illumin.
  • used to normalise for angular effects
  • similar to BRF model used in MODIS VI for norm.
  • spectral model parameters (weightings)
  • may have some physical meaning, but obscured by linearisation


model inversion

  • linear model has analytical solution to inversion
  • involves forming 3x3 matrix & finding inverse
  • simple, fast, robust
  • linear model implictly deal with heterogeneity
  • angular integrals of kernels precalculated for albedo

practical considerations

  • cloud cover reduces no. of samples for model fit
  • in MODIS/MISR algorithm, use 16 days sampling
  • angular sampling
  • global 1km product
  • accuracy ~ 10% relative

spectral albedo (blue, green, red, nir) at TM resolution

HAPEX-sahel, S. supersite, Niger, W. Africa
references:

  • Justice et al. (1998) The Moderate Resolution Imaging Spectrometer (MODIS): Land Remote Sensing for Global Change Research. IEEE Trans. geosci. RS 36(4) 1228-1249
  • Wanner, W., Strahler, A.H., Hu, B., Lewis, P., Muller, J-P., Li, X., Barker Schaaf, C.L., and Barnsley, M.J. (1997), Global retrieval of bidirectional reflectance and albedo over land from EOS MODIS and MISR data: theory and algorithm. J. Geophys. Res. 102(D14) 17143-17161
  • Wanner, W., Li, X., and A.H. Strahler (1995) On the derivation of kernels for kernel-driven models of bidirectional reflectance, J. Geophys. Res. 100, 21077-21090.