Abstract

The directional-reflectance distributions of radiant flux from homogeneous vegetation canopies with greater than 90% ground cover are analyzed with a radiative-transfer model. The model assumes that the leaves consist of small finite planes with Lambertian properties. Four theoretical canopies with different leaf-orientation distributions were studied: erectophile, spherical, planophile, and heliotropic canopies. The directional-reflectance distributions from the model closely resemble reflectance distributions measured in the field. The physical scattering mechanisms operating in the model explain the variations observed in the reflectance distributions as a function of leaf-orientation distribution, solar zenith angle, and leaf transmittance and reflectance. The simulated reflectance distributions show unique characteristics for each canopy. The basic understanding of the physical scattering properties of the different canopy geometries gained in this study provide a basis for developing techniques to infer leaf-orientation distributions of vegetation canopies from directional remote-sensing measurements.

© 1984 Optical Society of America

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References

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  1. D. S. Kimes, “Dynamics of directional reflectance factor distributions for vegetation canopies,” Appl. Opt. 22, 1364–1372 (1983).
    [CrossRef] [PubMed]
  2. J. A. Smith, R. E. Oliver, “Effects of changing canopy directional reflectance on feature selection,” Appl. Opt. 13, 1599–1604 (1974); R. E. Oliver, J. A. Smith, “A stochastic canopy model of diurnal reflectance. Final report,” DAH CO4-74-60001 (U.S. Army Research Office, Durham, N.C., 1974).
    [CrossRef] [PubMed]
  3. K. Cooper, J. A. Smith, D. Pitts, “Reflectance of a vegetation canopy using the adding method,” Appl. Opt. 21, 4112–4117 (1982); J. Goudriaan, “Crop meteorology: a simulation study,” Thesis (Centre for Agricultural Publishing and Documentation, Wageningen, The Netherlands, 1977); G. H. Suits, “The calculation of the directional reflectance of a vegetative canopy,” Remote Sensing Environ. 2, 117–125 (1972); J. Ross, The Radiation and Architecture of Plant Stands (Dr. W. Junk, The Hague, 1981); W. Verhoef, J. J. J. Bunnik, “Influence of crop geometry on multispectral reflectance determined by the use of canopy reflectance models,” NLR MP 81042 U (National Aerospace Laboratory NLR, Amsterdam, The Netherlands, 1981), pp. 273–290; N. J. J. Bunnik, “The multispectral reflectance of shortwave radiation by agricultural crops in relation with their morphological and optical properties,” Thesis (Veenman and Zonen, Wageningen, The Netherlands, 1978).
    [CrossRef] [PubMed]
  4. D. S. Kimes, J. A. Kirchner, “Radiative transfer model for heterogeneous 3D scenes,” Appl. Opt. 21, 4119–4129 (1982).
    [CrossRef] [PubMed]
  5. J. M. Norman, J. M. Welles, “Radiative transfer in an array of canopies,” Agron. J. 75, 481–488 (1983).
    [CrossRef]
  6. D. S. Kimes, J. A. Kirchner, “Diurnal variations of vegetation canopy structure,” Int. J. Remote Sensing 4, 257–271 (1983).
    [CrossRef]
  7. T. Nilson, “A theoretical analysis of the frequency of gaps in plant stands,” Agric. Meteorol. 8, 25–38 (1971).
    [CrossRef]
  8. C. T. deWit, “Photosynthesis of leaf canopies,” (Center for Agricultural Publications and Documentation, Wageningen, The Netherlands, 1965), Chap. 4.
  9. J. Ehleringer, I. Forseth, “Solar tracking by plants,” Science 210, 1094–1098 (1980).
    [CrossRef] [PubMed]
  10. J. A. Kirchner, D. S. Kimes, J. E. McMurtrey, “Variation of directional reflectance factors with structural changes of a developing alfalfa canopy,” Appl. Opt. 21, 3766–3774 (1982).
    [CrossRef] [PubMed]
  11. D. S. Kimes, W. W. Newcomb, J. B. Schutt, P. J. Pinter, R. D. Jackson, “Directional reflectance factor distributions of a cotton row crop,” Int. J. Remote Sensing (to be published).
  12. H. T. Breece, R. T. Holmes, “Bidirectional scattering characteristics of health green soybean and corn leaves in vivo,” Appl. Opt. 10, 119–127 (1971).
    [CrossRef]
  13. V. C. Vanderbilt, C. Grant, L. L. Beihl, B. F. Robinson, “Specular, diffuse, and polarized light scattered by two wheat canopies,” Appl. Opt. (to be published).
  14. D. S. Kimes, B. N. Holben, C. J. Tucker, W. W. Newcomb, “Optimal directional view angles for remote sensing missions,” Int. J. Remote Sensing (to be published).

1983 (3)

J. M. Norman, J. M. Welles, “Radiative transfer in an array of canopies,” Agron. J. 75, 481–488 (1983).
[CrossRef]

D. S. Kimes, J. A. Kirchner, “Diurnal variations of vegetation canopy structure,” Int. J. Remote Sensing 4, 257–271 (1983).
[CrossRef]

D. S. Kimes, “Dynamics of directional reflectance factor distributions for vegetation canopies,” Appl. Opt. 22, 1364–1372 (1983).
[CrossRef] [PubMed]

1982 (3)

1980 (1)

J. Ehleringer, I. Forseth, “Solar tracking by plants,” Science 210, 1094–1098 (1980).
[CrossRef] [PubMed]

1974 (1)

1971 (2)

H. T. Breece, R. T. Holmes, “Bidirectional scattering characteristics of health green soybean and corn leaves in vivo,” Appl. Opt. 10, 119–127 (1971).
[CrossRef]

T. Nilson, “A theoretical analysis of the frequency of gaps in plant stands,” Agric. Meteorol. 8, 25–38 (1971).
[CrossRef]

Beihl, L. L.

V. C. Vanderbilt, C. Grant, L. L. Beihl, B. F. Robinson, “Specular, diffuse, and polarized light scattered by two wheat canopies,” Appl. Opt. (to be published).

Breece, H. T.

Cooper, K.

deWit, C. T.

C. T. deWit, “Photosynthesis of leaf canopies,” (Center for Agricultural Publications and Documentation, Wageningen, The Netherlands, 1965), Chap. 4.

Ehleringer, J.

J. Ehleringer, I. Forseth, “Solar tracking by plants,” Science 210, 1094–1098 (1980).
[CrossRef] [PubMed]

Forseth, I.

J. Ehleringer, I. Forseth, “Solar tracking by plants,” Science 210, 1094–1098 (1980).
[CrossRef] [PubMed]

Grant, C.

V. C. Vanderbilt, C. Grant, L. L. Beihl, B. F. Robinson, “Specular, diffuse, and polarized light scattered by two wheat canopies,” Appl. Opt. (to be published).

Holben, B. N.

D. S. Kimes, B. N. Holben, C. J. Tucker, W. W. Newcomb, “Optimal directional view angles for remote sensing missions,” Int. J. Remote Sensing (to be published).

Holmes, R. T.

Jackson, R. D.

D. S. Kimes, W. W. Newcomb, J. B. Schutt, P. J. Pinter, R. D. Jackson, “Directional reflectance factor distributions of a cotton row crop,” Int. J. Remote Sensing (to be published).

Kimes, D. S.

D. S. Kimes, J. A. Kirchner, “Diurnal variations of vegetation canopy structure,” Int. J. Remote Sensing 4, 257–271 (1983).
[CrossRef]

D. S. Kimes, “Dynamics of directional reflectance factor distributions for vegetation canopies,” Appl. Opt. 22, 1364–1372 (1983).
[CrossRef] [PubMed]

D. S. Kimes, J. A. Kirchner, “Radiative transfer model for heterogeneous 3D scenes,” Appl. Opt. 21, 4119–4129 (1982).
[CrossRef] [PubMed]

J. A. Kirchner, D. S. Kimes, J. E. McMurtrey, “Variation of directional reflectance factors with structural changes of a developing alfalfa canopy,” Appl. Opt. 21, 3766–3774 (1982).
[CrossRef] [PubMed]

D. S. Kimes, B. N. Holben, C. J. Tucker, W. W. Newcomb, “Optimal directional view angles for remote sensing missions,” Int. J. Remote Sensing (to be published).

D. S. Kimes, W. W. Newcomb, J. B. Schutt, P. J. Pinter, R. D. Jackson, “Directional reflectance factor distributions of a cotton row crop,” Int. J. Remote Sensing (to be published).

Kirchner, J. A.

McMurtrey, J. E.

Newcomb, W. W.

D. S. Kimes, B. N. Holben, C. J. Tucker, W. W. Newcomb, “Optimal directional view angles for remote sensing missions,” Int. J. Remote Sensing (to be published).

D. S. Kimes, W. W. Newcomb, J. B. Schutt, P. J. Pinter, R. D. Jackson, “Directional reflectance factor distributions of a cotton row crop,” Int. J. Remote Sensing (to be published).

Nilson, T.

T. Nilson, “A theoretical analysis of the frequency of gaps in plant stands,” Agric. Meteorol. 8, 25–38 (1971).
[CrossRef]

Norman, J. M.

J. M. Norman, J. M. Welles, “Radiative transfer in an array of canopies,” Agron. J. 75, 481–488 (1983).
[CrossRef]

Oliver, R. E.

Pinter, P. J.

D. S. Kimes, W. W. Newcomb, J. B. Schutt, P. J. Pinter, R. D. Jackson, “Directional reflectance factor distributions of a cotton row crop,” Int. J. Remote Sensing (to be published).

Pitts, D.

Robinson, B. F.

V. C. Vanderbilt, C. Grant, L. L. Beihl, B. F. Robinson, “Specular, diffuse, and polarized light scattered by two wheat canopies,” Appl. Opt. (to be published).

Schutt, J. B.

D. S. Kimes, W. W. Newcomb, J. B. Schutt, P. J. Pinter, R. D. Jackson, “Directional reflectance factor distributions of a cotton row crop,” Int. J. Remote Sensing (to be published).

Smith, J. A.

Tucker, C. J.

D. S. Kimes, B. N. Holben, C. J. Tucker, W. W. Newcomb, “Optimal directional view angles for remote sensing missions,” Int. J. Remote Sensing (to be published).

Vanderbilt, V. C.

V. C. Vanderbilt, C. Grant, L. L. Beihl, B. F. Robinson, “Specular, diffuse, and polarized light scattered by two wheat canopies,” Appl. Opt. (to be published).

Welles, J. M.

J. M. Norman, J. M. Welles, “Radiative transfer in an array of canopies,” Agron. J. 75, 481–488 (1983).
[CrossRef]

Agric. Meteorol. (1)

T. Nilson, “A theoretical analysis of the frequency of gaps in plant stands,” Agric. Meteorol. 8, 25–38 (1971).
[CrossRef]

Agron. J. (1)

J. M. Norman, J. M. Welles, “Radiative transfer in an array of canopies,” Agron. J. 75, 481–488 (1983).
[CrossRef]

Appl. Opt. (6)

H. T. Breece, R. T. Holmes, “Bidirectional scattering characteristics of health green soybean and corn leaves in vivo,” Appl. Opt. 10, 119–127 (1971).
[CrossRef]

J. A. Smith, R. E. Oliver, “Effects of changing canopy directional reflectance on feature selection,” Appl. Opt. 13, 1599–1604 (1974); R. E. Oliver, J. A. Smith, “A stochastic canopy model of diurnal reflectance. Final report,” DAH CO4-74-60001 (U.S. Army Research Office, Durham, N.C., 1974).
[CrossRef] [PubMed]

J. A. Kirchner, D. S. Kimes, J. E. McMurtrey, “Variation of directional reflectance factors with structural changes of a developing alfalfa canopy,” Appl. Opt. 21, 3766–3774 (1982).
[CrossRef] [PubMed]

K. Cooper, J. A. Smith, D. Pitts, “Reflectance of a vegetation canopy using the adding method,” Appl. Opt. 21, 4112–4117 (1982); J. Goudriaan, “Crop meteorology: a simulation study,” Thesis (Centre for Agricultural Publishing and Documentation, Wageningen, The Netherlands, 1977); G. H. Suits, “The calculation of the directional reflectance of a vegetative canopy,” Remote Sensing Environ. 2, 117–125 (1972); J. Ross, The Radiation and Architecture of Plant Stands (Dr. W. Junk, The Hague, 1981); W. Verhoef, J. J. J. Bunnik, “Influence of crop geometry on multispectral reflectance determined by the use of canopy reflectance models,” NLR MP 81042 U (National Aerospace Laboratory NLR, Amsterdam, The Netherlands, 1981), pp. 273–290; N. J. J. Bunnik, “The multispectral reflectance of shortwave radiation by agricultural crops in relation with their morphological and optical properties,” Thesis (Veenman and Zonen, Wageningen, The Netherlands, 1978).
[CrossRef] [PubMed]

D. S. Kimes, J. A. Kirchner, “Radiative transfer model for heterogeneous 3D scenes,” Appl. Opt. 21, 4119–4129 (1982).
[CrossRef] [PubMed]

D. S. Kimes, “Dynamics of directional reflectance factor distributions for vegetation canopies,” Appl. Opt. 22, 1364–1372 (1983).
[CrossRef] [PubMed]

Int. J. Remote Sensing (1)

D. S. Kimes, J. A. Kirchner, “Diurnal variations of vegetation canopy structure,” Int. J. Remote Sensing 4, 257–271 (1983).
[CrossRef]

Science (1)

J. Ehleringer, I. Forseth, “Solar tracking by plants,” Science 210, 1094–1098 (1980).
[CrossRef] [PubMed]

Other (4)

D. S. Kimes, W. W. Newcomb, J. B. Schutt, P. J. Pinter, R. D. Jackson, “Directional reflectance factor distributions of a cotton row crop,” Int. J. Remote Sensing (to be published).

V. C. Vanderbilt, C. Grant, L. L. Beihl, B. F. Robinson, “Specular, diffuse, and polarized light scattered by two wheat canopies,” Appl. Opt. (to be published).

D. S. Kimes, B. N. Holben, C. J. Tucker, W. W. Newcomb, “Optimal directional view angles for remote sensing missions,” Int. J. Remote Sensing (to be published).

C. T. deWit, “Photosynthesis of leaf canopies,” (Center for Agricultural Publications and Documentation, Wageningen, The Netherlands, 1965), Chap. 4.

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Figures (11)

Fig. 1
Fig. 1

Three-dimensional framework of the model showing the rectangular cell matrix, the cell coordinate system, diffuse solar sources (only one is illustrated), and the direct solar source. The diffuse and direct solar sources are extended down to the surface of each cell on the top surface of the cell matrix.

Fig. 2
Fig. 2

View of the solid angle of a particular sector with its corresponding midvector. The entire 4π sr sphere is subdivided into contiguous sectors defined by an azimuth (Δϕ) and an off-nadir (Δϕ) interval.

Fig. 3
Fig. 3

Leaf-angle distribution functions for several types of canopies: a, planophile; b, spherical; c, erectophile.

Fig. 4
Fig. 4

A, coordinate system defining solar and sensor angles; B, polar plot showing scheme for plotting directional-reflectance factors. The solar azimuth is always 180°. The sensor’s azimuth and off-nadir angles are shown as ϕ and θ, respectively. A sensor with a 0° azimuth looks into the sun. Thus azimuths of 0 and 180° represent forward scattering and backscattering, respectively. The spectral directional-reflectance factors were plotted in the polar plot, in which the distance from the origin represents the off-nadir view angle of the sensor and the angle from ϕ = 0° represents the sensor’s azimuth. The cross points show the directions of simulated data. Lines of equal reflectance were contoured using linear interpretation, as presented in Fig. 5.

Fig. 5
Fig. 5

Simulated directional-reflectance-factor distributions for the A, erectophile; B, spherical; C, planophile; and D, heliotropic canopies for the red band. Four different solar directions are shown for each canopy. The solar position is indicated by the star on each distribution. Equal lines of percent reflectance are contoured. The polar coordinate system used for plotting is described in detail in Fig. 4. Decimal numbers show the maximum and/or minimum reflectance values of each distribution.

Fig. 6
Fig. 6

Fundamental scattering distribution L(θr, ϕr; θs, ϕs), or phase function, of an isolated conglomerate of leaves for the A, erectophile; B, spherical; C, planophile; and D, heliotropic leaf geometries for the red band. Four different source directions are shown for each canopy. The source position is indicated by the bold filled circle on each distribution. Equal lines of radiance ×1000 are contoured. The polar coordinate system used for plotting is described in detail in Fig. 4. Decimal numbers show the maximum and/or minimum radiance values of each distribution. Only the updwelling radiances are shown in these distributions; however, the downdwelling-radiance distribution is completely predictable from its updwelling-radiance distribution, as shown and explained in Fig. 7.

Fig. 7
Fig. 7

The L distribution for both the A, updwelling and B, downdwelling quarter spheres are shown for spherical leaf distribution and a source at an off-nadir view angle of 77.1°. Both leaf reflectance and transmittance are 0.05. The radiance values ×1000 for each scattering direction are plotted. Notice that all view directions that lie in the same line of sight but have opposite directions have the same radiance value. For example, the value at 180° azimuth and 51.4° off-nadir is equal to the value at 0° azimuth and 128.6° off-nadir because these directions lie in the same line of sight and have the same leaf geometry and because the leaf transmittance is equal to leaf reflectance. Similarly, the value at 150° azimuth and 77.1° off-nadir has the same value as 330° azimuth and 102.9° off-nadir. However, the 330° azimuth and 102.9° off-nadir direction is equivalent to 30° azimuth and 102.9° off-nadir direction because of the symmetry about the principal plane of the source. Thus the same symmetry seen in the updwelling and downdwelling distribution holds for the erectophile, spherical, planophile, and heliotropic distributions for all source angles when leaf reflectance equals leaf transmittance.

Fig. 8
Fig. 8

Measured directional-reflectance-factor distributions of grass lawn canopy in NOAA Satellite AVHRR band 1 (0.58–0.68 μm) for three solar zenith angles: A, 42°; B, 56°; and C, 70°. The percent cover of the canopy is 97%. The leaf-orientation distribution is between an erectophile and a spherical canopy. Measurements were taken at 15° and 45° increments of off-nadir and azimuth angles, respectively. The solar position is indicated by the star on each distribution. Equal lines of percent reflectance are contoured. The decimal numbers on each distribution show the maximum and/or minimum reflectance values.

Fig. 9
Fig. 9

Measured directional-reflectance-factor distributions of an alfalfa canopy in TM band 3 (0.63–0.69 μm) for three solar zenith angles: A, 21°; B, 47°; and C, 57°. The cover of the canopy is 92%. The leaf-orientation distribution is between a planophile and a spherical canopy. Measurements were taken at 15° and 45° increments of off-nadir and azimuth angles, respectively. The solar position is indicated by the star on each distribution. Equal lines of percent reflectance are contoured. The decimal numbers on each distribution show the maximum and/or minimum reflectance values.

Fig. 10
Fig. 10

Directional-reflectance-factor distributions for the planophile canopy for the NIR band. Four different solar directions are shown. The solar position is indicated by the star on each distribution. Equal lines of percent reflectance are contoured. The polar coordinate system used for plotting is described in detail in Fig. 4. Decimal numbers show the maximum and/or minimum reflectance values of each distribution.

Fig. 11
Fig. 11

Reflectance/transmittance sensitivity for the spherical canopy in the red band and at a solar zenith angle of 51.4°. Three reflectance-factor distributions are shown for different leaf reflectance (ρ) and transmittance (τ) values as shown in plots A–C.

Tables (1)

Tables Icon

Table 1 Probability of Gap (in percent) through the Entire Canopy as a Function of View Angle for Each Canopy Geometrya

Equations (5)

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Ω = sin θ d θ d ϕ .
g ( θ , ϕ ) = ( θ a , ϕ a ) a · r f ( θ a , ϕ a ) ,
Z ( θ r , ϕ r ; θ s , ϕ s ) = ( α a , ϕ a ) S A ( θ s , ϕ s ; θ a , ϕ a ) × [ Ω ( θ s , ϕ s ) / π ] w ( θ r , ϕ r ; θ a , ϕ a ) ρ τ ,
w ( θ r , ϕ r ; θ a , ϕ a ) = a · r f ( θ a , ϕ a ) g ( θ a , ϕ a ) .
L ( θ r , ϕ r ; θ s , ϕ s ) = Z ( θ r , ϕ r ; θ s , ϕ s ) / Ω ( θ s , ϕ s ) .

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