Abstract

Bidirectional reflection distribution functions (BRDFs) of inhomogeneous land surfaces that consist of protruding structures on a flat suface are modeled. The components are allowed to have individual reflection properties. Modeling the BRDFs takes into account the simultaneous influence of vertical structure and of different anisotropic BRDFs assigned to the components. A realistic simulation of bare soil and partly or fully vegetated surfaces with a pronounced 3-D structure is possible. A sensitivity study shows to what extent surface reflection is affected by vertical structure and zenith angle of incidence when different BRDFs are assigned to both surface components. The results can be used to decide for which conditions area weighted adding of BRDFs from homogeneous surfaces is sufficient to get an average BRDF for an inhomogeneous surface. It tends to be insufficient when vertical structure, zenith angle of incidence, and the albedo of the ground increase in relation to the albedo of the protrusions.

© 1990 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. T. Kriebel, “Measured Spectral Bidirectional Reflection Properties of Four Vegetated Surfaces,” Appl. Opt. 17, 253–259 (1978).
    [CrossRef] [PubMed]
  2. D. S. Kimes, J. A. Kirchner, “Radiative Transfer Model for Heterogeneous 3-D Scenes,” Appl. Opt. 21, 4119–4129 (1982).
    [CrossRef] [PubMed]
  3. G. H. Suits, “The Calculation of the Directional Reflectance of a Vegetative Canopy,” Remote Sensing Environ. 2, 117–125 (1972).
    [CrossRef]
  4. C. Simmer, S. A. W. Gerstl, “Remote Sensing of Angular Characteristics of Canopy Reflectances,” IEEE Trans. Geosci. Remote Sensing, GE-23, 648–658 (1985).
    [CrossRef]
  5. B. Pinty, D. Ramond, “A Simple Bidirectional Reflectance Model for Terrestrial Surfaces,” J. Geophys. Res. 91, 7803–7808 (1986).
    [CrossRef]
  6. N. S. Goel, T. Grier, “Estimation of Canopy Parameter for Inhomogeneous Vegetation Canopies from Reflectance Data: III. TRIM: A Model for Radiative Transfer in Heterogeneous Three-Dimensional Canopies,” Remote Sensing Environ. 25, 255–293 (1988).
    [CrossRef]
  7. D. S. Kimes, P. J. Sellers, “Inferring Hemispherical Reflectance of the Earth’s Surface for Global Energy Budget from Remotely Sensed Nadir or Directional Radiance Values, Remote Sensing Environ. 18, 205–223 (1985).
    [CrossRef]
  8. D. S. Kimes et al., “Directional Reflectance Distributions of a Hardwood and Pine Forest Canopy,” IEEE Trans. Geosci. Remote Sensing, GE-24, 281–293 (1986).
    [CrossRef]
  9. E. M. Middleton, D. W. Deering, “Surface Anisotropy and Hemispheric Reflectance for a Semiarid Ecosystem,” Remote Sensing Environ. 23, 193–212 (1987).
    [CrossRef]
  10. F. E. Nicodemus, “Reflectance Nomenclature and Directional Reflectance and Emissivity,” Appl. Opt. 9, 1474–1475 (1970).
    [CrossRef] [PubMed]
  11. K. T. Kriebel, P. Koepke, “Improvements in the Shortwave Cloud-Free Radiation Budget Accuracy. Part II: Experimental Study Including Mixed Surface Albedos,” J. Climate Appl. Meteorol. 26, 396–409 (1987).
    [CrossRef]
  12. R. Meerkoetter, “Ein Modell zur Simulation von Reflexionsfunktionen heterogen zusammengesetzter Landoberflachen,” Universitat Munchen-Meteorologisches Institut, Wissenschaftliche Mitteilung Nr.62, (1989). Available from Meteorologisches Institut der Universität, Theresienstrasse 37,8000 Munchen 2, Federal Republic of Germany.
  13. J. M. Norman, J. M. Welles, E. A. Walter, “Contrasts Among Bidirectional Reflectance of Leaves, Canopies, and Soils,” IEEE Trans. Geosci. Remote Sensing, GE-23, 659–667 (1985).
    [CrossRef]
  14. X. Li, A. H. Strahler, “Geometric-Optical Bidirectional Reflectance Modeling of a Conifer Forest Canopy,” IEEE Trans. Geosci. Remote Sensing GE-24, 906–919 (1986).
    [CrossRef]
  15. J. Otterman, G. H. Weiss, “Reflection from a Field of Randomy Located Vertical Protrusions,” Appl. Opt. 23, 1931–1936 (1984).
    [CrossRef] [PubMed]
  16. F. D. Eaton, I. Dirmhirn, “Reflected Irradiance Indicatrices of Natural Surfaces and Their Effect on Albedo,” Appl. Opt. 18, 994–1008 (1979).
    [CrossRef] [PubMed]

1988 (1)

N. S. Goel, T. Grier, “Estimation of Canopy Parameter for Inhomogeneous Vegetation Canopies from Reflectance Data: III. TRIM: A Model for Radiative Transfer in Heterogeneous Three-Dimensional Canopies,” Remote Sensing Environ. 25, 255–293 (1988).
[CrossRef]

1987 (2)

E. M. Middleton, D. W. Deering, “Surface Anisotropy and Hemispheric Reflectance for a Semiarid Ecosystem,” Remote Sensing Environ. 23, 193–212 (1987).
[CrossRef]

K. T. Kriebel, P. Koepke, “Improvements in the Shortwave Cloud-Free Radiation Budget Accuracy. Part II: Experimental Study Including Mixed Surface Albedos,” J. Climate Appl. Meteorol. 26, 396–409 (1987).
[CrossRef]

1986 (3)

B. Pinty, D. Ramond, “A Simple Bidirectional Reflectance Model for Terrestrial Surfaces,” J. Geophys. Res. 91, 7803–7808 (1986).
[CrossRef]

D. S. Kimes et al., “Directional Reflectance Distributions of a Hardwood and Pine Forest Canopy,” IEEE Trans. Geosci. Remote Sensing, GE-24, 281–293 (1986).
[CrossRef]

X. Li, A. H. Strahler, “Geometric-Optical Bidirectional Reflectance Modeling of a Conifer Forest Canopy,” IEEE Trans. Geosci. Remote Sensing GE-24, 906–919 (1986).
[CrossRef]

1985 (3)

J. M. Norman, J. M. Welles, E. A. Walter, “Contrasts Among Bidirectional Reflectance of Leaves, Canopies, and Soils,” IEEE Trans. Geosci. Remote Sensing, GE-23, 659–667 (1985).
[CrossRef]

D. S. Kimes, P. J. Sellers, “Inferring Hemispherical Reflectance of the Earth’s Surface for Global Energy Budget from Remotely Sensed Nadir or Directional Radiance Values, Remote Sensing Environ. 18, 205–223 (1985).
[CrossRef]

C. Simmer, S. A. W. Gerstl, “Remote Sensing of Angular Characteristics of Canopy Reflectances,” IEEE Trans. Geosci. Remote Sensing, GE-23, 648–658 (1985).
[CrossRef]

1984 (1)

1982 (1)

1979 (1)

1978 (1)

1972 (1)

G. H. Suits, “The Calculation of the Directional Reflectance of a Vegetative Canopy,” Remote Sensing Environ. 2, 117–125 (1972).
[CrossRef]

1970 (1)

Deering, D. W.

E. M. Middleton, D. W. Deering, “Surface Anisotropy and Hemispheric Reflectance for a Semiarid Ecosystem,” Remote Sensing Environ. 23, 193–212 (1987).
[CrossRef]

Dirmhirn, I.

Eaton, F. D.

Gerstl, S. A. W.

C. Simmer, S. A. W. Gerstl, “Remote Sensing of Angular Characteristics of Canopy Reflectances,” IEEE Trans. Geosci. Remote Sensing, GE-23, 648–658 (1985).
[CrossRef]

Goel, N. S.

N. S. Goel, T. Grier, “Estimation of Canopy Parameter for Inhomogeneous Vegetation Canopies from Reflectance Data: III. TRIM: A Model for Radiative Transfer in Heterogeneous Three-Dimensional Canopies,” Remote Sensing Environ. 25, 255–293 (1988).
[CrossRef]

Grier, T.

N. S. Goel, T. Grier, “Estimation of Canopy Parameter for Inhomogeneous Vegetation Canopies from Reflectance Data: III. TRIM: A Model for Radiative Transfer in Heterogeneous Three-Dimensional Canopies,” Remote Sensing Environ. 25, 255–293 (1988).
[CrossRef]

Kimes, D. S.

D. S. Kimes et al., “Directional Reflectance Distributions of a Hardwood and Pine Forest Canopy,” IEEE Trans. Geosci. Remote Sensing, GE-24, 281–293 (1986).
[CrossRef]

D. S. Kimes, P. J. Sellers, “Inferring Hemispherical Reflectance of the Earth’s Surface for Global Energy Budget from Remotely Sensed Nadir or Directional Radiance Values, Remote Sensing Environ. 18, 205–223 (1985).
[CrossRef]

D. S. Kimes, J. A. Kirchner, “Radiative Transfer Model for Heterogeneous 3-D Scenes,” Appl. Opt. 21, 4119–4129 (1982).
[CrossRef] [PubMed]

Kirchner, J. A.

Koepke, P.

K. T. Kriebel, P. Koepke, “Improvements in the Shortwave Cloud-Free Radiation Budget Accuracy. Part II: Experimental Study Including Mixed Surface Albedos,” J. Climate Appl. Meteorol. 26, 396–409 (1987).
[CrossRef]

Kriebel, K. T.

K. T. Kriebel, P. Koepke, “Improvements in the Shortwave Cloud-Free Radiation Budget Accuracy. Part II: Experimental Study Including Mixed Surface Albedos,” J. Climate Appl. Meteorol. 26, 396–409 (1987).
[CrossRef]

K. T. Kriebel, “Measured Spectral Bidirectional Reflection Properties of Four Vegetated Surfaces,” Appl. Opt. 17, 253–259 (1978).
[CrossRef] [PubMed]

Li, X.

X. Li, A. H. Strahler, “Geometric-Optical Bidirectional Reflectance Modeling of a Conifer Forest Canopy,” IEEE Trans. Geosci. Remote Sensing GE-24, 906–919 (1986).
[CrossRef]

Meerkoetter, R.

R. Meerkoetter, “Ein Modell zur Simulation von Reflexionsfunktionen heterogen zusammengesetzter Landoberflachen,” Universitat Munchen-Meteorologisches Institut, Wissenschaftliche Mitteilung Nr.62, (1989). Available from Meteorologisches Institut der Universität, Theresienstrasse 37,8000 Munchen 2, Federal Republic of Germany.

Middleton, E. M.

E. M. Middleton, D. W. Deering, “Surface Anisotropy and Hemispheric Reflectance for a Semiarid Ecosystem,” Remote Sensing Environ. 23, 193–212 (1987).
[CrossRef]

Nicodemus, F. E.

Norman, J. M.

J. M. Norman, J. M. Welles, E. A. Walter, “Contrasts Among Bidirectional Reflectance of Leaves, Canopies, and Soils,” IEEE Trans. Geosci. Remote Sensing, GE-23, 659–667 (1985).
[CrossRef]

Otterman, J.

Pinty, B.

B. Pinty, D. Ramond, “A Simple Bidirectional Reflectance Model for Terrestrial Surfaces,” J. Geophys. Res. 91, 7803–7808 (1986).
[CrossRef]

Ramond, D.

B. Pinty, D. Ramond, “A Simple Bidirectional Reflectance Model for Terrestrial Surfaces,” J. Geophys. Res. 91, 7803–7808 (1986).
[CrossRef]

Sellers, P. J.

D. S. Kimes, P. J. Sellers, “Inferring Hemispherical Reflectance of the Earth’s Surface for Global Energy Budget from Remotely Sensed Nadir or Directional Radiance Values, Remote Sensing Environ. 18, 205–223 (1985).
[CrossRef]

Simmer, C.

C. Simmer, S. A. W. Gerstl, “Remote Sensing of Angular Characteristics of Canopy Reflectances,” IEEE Trans. Geosci. Remote Sensing, GE-23, 648–658 (1985).
[CrossRef]

Strahler, A. H.

X. Li, A. H. Strahler, “Geometric-Optical Bidirectional Reflectance Modeling of a Conifer Forest Canopy,” IEEE Trans. Geosci. Remote Sensing GE-24, 906–919 (1986).
[CrossRef]

Suits, G. H.

G. H. Suits, “The Calculation of the Directional Reflectance of a Vegetative Canopy,” Remote Sensing Environ. 2, 117–125 (1972).
[CrossRef]

Walter, E. A.

J. M. Norman, J. M. Welles, E. A. Walter, “Contrasts Among Bidirectional Reflectance of Leaves, Canopies, and Soils,” IEEE Trans. Geosci. Remote Sensing, GE-23, 659–667 (1985).
[CrossRef]

Weiss, G. H.

Welles, J. M.

J. M. Norman, J. M. Welles, E. A. Walter, “Contrasts Among Bidirectional Reflectance of Leaves, Canopies, and Soils,” IEEE Trans. Geosci. Remote Sensing, GE-23, 659–667 (1985).
[CrossRef]

Appl. Opt. (5)

IEEE Trans. Geosci. Remote Sensing (4)

J. M. Norman, J. M. Welles, E. A. Walter, “Contrasts Among Bidirectional Reflectance of Leaves, Canopies, and Soils,” IEEE Trans. Geosci. Remote Sensing, GE-23, 659–667 (1985).
[CrossRef]

X. Li, A. H. Strahler, “Geometric-Optical Bidirectional Reflectance Modeling of a Conifer Forest Canopy,” IEEE Trans. Geosci. Remote Sensing GE-24, 906–919 (1986).
[CrossRef]

C. Simmer, S. A. W. Gerstl, “Remote Sensing of Angular Characteristics of Canopy Reflectances,” IEEE Trans. Geosci. Remote Sensing, GE-23, 648–658 (1985).
[CrossRef]

D. S. Kimes et al., “Directional Reflectance Distributions of a Hardwood and Pine Forest Canopy,” IEEE Trans. Geosci. Remote Sensing, GE-24, 281–293 (1986).
[CrossRef]

J. Climate Appl. Meteorol. (1)

K. T. Kriebel, P. Koepke, “Improvements in the Shortwave Cloud-Free Radiation Budget Accuracy. Part II: Experimental Study Including Mixed Surface Albedos,” J. Climate Appl. Meteorol. 26, 396–409 (1987).
[CrossRef]

J. Geophys. Res. (1)

B. Pinty, D. Ramond, “A Simple Bidirectional Reflectance Model for Terrestrial Surfaces,” J. Geophys. Res. 91, 7803–7808 (1986).
[CrossRef]

Remote Sensing Environ. (4)

N. S. Goel, T. Grier, “Estimation of Canopy Parameter for Inhomogeneous Vegetation Canopies from Reflectance Data: III. TRIM: A Model for Radiative Transfer in Heterogeneous Three-Dimensional Canopies,” Remote Sensing Environ. 25, 255–293 (1988).
[CrossRef]

D. S. Kimes, P. J. Sellers, “Inferring Hemispherical Reflectance of the Earth’s Surface for Global Energy Budget from Remotely Sensed Nadir or Directional Radiance Values, Remote Sensing Environ. 18, 205–223 (1985).
[CrossRef]

E. M. Middleton, D. W. Deering, “Surface Anisotropy and Hemispheric Reflectance for a Semiarid Ecosystem,” Remote Sensing Environ. 23, 193–212 (1987).
[CrossRef]

G. H. Suits, “The Calculation of the Directional Reflectance of a Vegetative Canopy,” Remote Sensing Environ. 2, 117–125 (1972).
[CrossRef]

Other (1)

R. Meerkoetter, “Ein Modell zur Simulation von Reflexionsfunktionen heterogen zusammengesetzter Landoberflachen,” Universitat Munchen-Meteorologisches Institut, Wissenschaftliche Mitteilung Nr.62, (1989). Available from Meteorologisches Institut der Universität, Theresienstrasse 37,8000 Munchen 2, Federal Republic of Germany.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Example of a model surface. Shown are 2 × 2 periods of an arbitrary surface structure.

Fig. 2
Fig. 2

Photographic view of a land surface mainly composed of grassland and sections of coniferous forest. Freigegeben Reg. v. Obb., Luftamt Süd GS300/128/88.

Fig. 3
Fig. 3

Model surfaces with different structure parameters V = 3 × 10−1 (upper model surface) and V = 100; the ground cover parameter is B = 25% in both cases.

Fig. 4
Fig. 4

Spectral characteristics of some natural surface materials: (a) fresh fallen snow; (b) old snow; (c) lime stone; (d) sand; and (e) green plants (from Eaton and Dirmhirn16).

Fig. 5
Fig. 5

Albedo deviation ΔA as a function of structure parameter V for the zenith angle of incidence Θ = 25° and different ground cover parameters B. The curve parameter is the albedo quotient Q.

Fig. 6
Fig. 6

Same as Fig. 5, except for Θ = 45°.

Fig. 7
Fig. 7

Same as Fig. 5, except for Θ = 65°.

Fig. 8
Fig. 8

Same as Fig. 5, except for Θ = 85°.

Fig. 9
Fig. 9

Albedo deviation ΔA as a function of structure parameter V. The curves for Q = 0.5 and Q = 1 correspond to model surfaces with isotropic BRDFs assigned to the components; the curve for Q = 0.32 results from a simulation of protrusions of coniferous forest on a pasture land. Corresponding anisotropic BRDFs are measured at λ = 0.87 μm.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

BRDF λ ( Θ , ϕ ; θ , φ ) = d L λ r ( Θ , ϕ ; θ , φ ) L λ i ( Θ , ϕ ) cos Θ sin Θ d Θ d ϕ ,
V = H 2 F ,
B = Σ F i A ,
Q = A p A s ,
A = 1 π Ω o 0 2 π 0 π / 2 BRDF cos θ sin θ d θ d φ ,
Δ A = A t - A f A f × 100 % ,

Metrics