Abstract

A simple equation has been developed for describing the bidirectional reflectance of some vegetative canopies and bare soil surfaces. The equation describes directional reflectance as a function of zenith and azimuth view angles and solar azimuth angle. The equation works for simulated and field measured red and IR reflectance under clear sky conditions. Hemispherical reflectance can be calculated as a function of the simple equation coefficients by integrating the equation over the hemisphere of view angles. A single equation for estimating soil bidirectional reflectance was obtained using the relationships between solar zenith angles and the simple equation coefficients for medium and rough soil distributions. The equation has many useful applications such as providing a lower level boundary condition in complex plant canopy models and providing an additional tool for studying bidirectional effects on pointable sensors.

© 1985 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. E. Nicodemus, Ed., Self Study Manual on Optical Radiation Measurements: Part 1—Concepts, Chapters 1 to 3, Natl. Bur. Stand. U.S. NBS Tech. Memo. 910-1 (National Bureau of Standards, Gaithersburg, Md., 1976).
  2. G. H. Suits, “The Cause of Azimuthal Variations in Directional Reflectance of Vegetation Canopies,” Remote Sensing Environ. 2, 175 (1972).
    [CrossRef]
  3. J. Smith, K. Ranson, MRS. Bidirectional Reflectance Literature Survey (ORI, Silver Spring, Md., 1979).
  4. J. M. Norman, J. M. Welles, “Radiative Transfer in an Array of Canopies,” Argon. J. 75, 481 (1983).
  5. J. E. Colwell, “Vegetation Canopy Reflectance,” in Proceedings, Tenth International Symposium on Remote Sensing of Environment (Environmental Research Institute of Michigan, Ann Arbor, 1974).
  6. D. Kimes, J. Smith, “Simulation of Solar Radiation Absorption in Vegetation Canopies,” Appl. Opt. 19, 2801 (1980).
    [CrossRef] [PubMed]
  7. J. M. Norman, “Modeling the Complete Crop Canopy,” in Modification of the Aerial Environment of Plants, B. J. Barfield, J. F. Gerber, Eds. (American Society of Agricultural Engineers, St. Joseph, Mich.1979), Chap. 3.6.
  8. K. J. Ranson, V. C. Vanderbilt, L. L. Biehl, B. F. Robinson, M. E. Bauer, Soybean Canopy Reflectance as a Function of View and Illumination geometry, Agristars Tech. Report (Laboratory for Applications of Remote Sensing, Purdue U., West Lafayette, Ind., 1982).
  9. V. V. Salmonson, W. E. Marlatt, “Airborne Measurements of Reflected Solar Radiation,” Remote Sensing Environ. 2, 1 (1971).
    [CrossRef]

1983

J. M. Norman, J. M. Welles, “Radiative Transfer in an Array of Canopies,” Argon. J. 75, 481 (1983).

1980

1972

G. H. Suits, “The Cause of Azimuthal Variations in Directional Reflectance of Vegetation Canopies,” Remote Sensing Environ. 2, 175 (1972).
[CrossRef]

1971

V. V. Salmonson, W. E. Marlatt, “Airborne Measurements of Reflected Solar Radiation,” Remote Sensing Environ. 2, 1 (1971).
[CrossRef]

Bauer, M. E.

K. J. Ranson, V. C. Vanderbilt, L. L. Biehl, B. F. Robinson, M. E. Bauer, Soybean Canopy Reflectance as a Function of View and Illumination geometry, Agristars Tech. Report (Laboratory for Applications of Remote Sensing, Purdue U., West Lafayette, Ind., 1982).

Biehl, L. L.

K. J. Ranson, V. C. Vanderbilt, L. L. Biehl, B. F. Robinson, M. E. Bauer, Soybean Canopy Reflectance as a Function of View and Illumination geometry, Agristars Tech. Report (Laboratory for Applications of Remote Sensing, Purdue U., West Lafayette, Ind., 1982).

Colwell, J. E.

J. E. Colwell, “Vegetation Canopy Reflectance,” in Proceedings, Tenth International Symposium on Remote Sensing of Environment (Environmental Research Institute of Michigan, Ann Arbor, 1974).

Kimes, D.

Marlatt, W. E.

V. V. Salmonson, W. E. Marlatt, “Airborne Measurements of Reflected Solar Radiation,” Remote Sensing Environ. 2, 1 (1971).
[CrossRef]

Norman, J. M.

J. M. Norman, J. M. Welles, “Radiative Transfer in an Array of Canopies,” Argon. J. 75, 481 (1983).

J. M. Norman, “Modeling the Complete Crop Canopy,” in Modification of the Aerial Environment of Plants, B. J. Barfield, J. F. Gerber, Eds. (American Society of Agricultural Engineers, St. Joseph, Mich.1979), Chap. 3.6.

Ranson, K.

J. Smith, K. Ranson, MRS. Bidirectional Reflectance Literature Survey (ORI, Silver Spring, Md., 1979).

Ranson, K. J.

K. J. Ranson, V. C. Vanderbilt, L. L. Biehl, B. F. Robinson, M. E. Bauer, Soybean Canopy Reflectance as a Function of View and Illumination geometry, Agristars Tech. Report (Laboratory for Applications of Remote Sensing, Purdue U., West Lafayette, Ind., 1982).

Robinson, B. F.

K. J. Ranson, V. C. Vanderbilt, L. L. Biehl, B. F. Robinson, M. E. Bauer, Soybean Canopy Reflectance as a Function of View and Illumination geometry, Agristars Tech. Report (Laboratory for Applications of Remote Sensing, Purdue U., West Lafayette, Ind., 1982).

Salmonson, V. V.

V. V. Salmonson, W. E. Marlatt, “Airborne Measurements of Reflected Solar Radiation,” Remote Sensing Environ. 2, 1 (1971).
[CrossRef]

Smith, J.

D. Kimes, J. Smith, “Simulation of Solar Radiation Absorption in Vegetation Canopies,” Appl. Opt. 19, 2801 (1980).
[CrossRef] [PubMed]

J. Smith, K. Ranson, MRS. Bidirectional Reflectance Literature Survey (ORI, Silver Spring, Md., 1979).

Suits, G. H.

G. H. Suits, “The Cause of Azimuthal Variations in Directional Reflectance of Vegetation Canopies,” Remote Sensing Environ. 2, 175 (1972).
[CrossRef]

Vanderbilt, V. C.

K. J. Ranson, V. C. Vanderbilt, L. L. Biehl, B. F. Robinson, M. E. Bauer, Soybean Canopy Reflectance as a Function of View and Illumination geometry, Agristars Tech. Report (Laboratory for Applications of Remote Sensing, Purdue U., West Lafayette, Ind., 1982).

Welles, J. M.

J. M. Norman, J. M. Welles, “Radiative Transfer in an Array of Canopies,” Argon. J. 75, 481 (1983).

Appl. Opt.

Argon. J.

J. M. Norman, J. M. Welles, “Radiative Transfer in an Array of Canopies,” Argon. J. 75, 481 (1983).

Remote Sensing Environ.

G. H. Suits, “The Cause of Azimuthal Variations in Directional Reflectance of Vegetation Canopies,” Remote Sensing Environ. 2, 175 (1972).
[CrossRef]

V. V. Salmonson, W. E. Marlatt, “Airborne Measurements of Reflected Solar Radiation,” Remote Sensing Environ. 2, 1 (1971).
[CrossRef]

Other

F. E. Nicodemus, Ed., Self Study Manual on Optical Radiation Measurements: Part 1—Concepts, Chapters 1 to 3, Natl. Bur. Stand. U.S. NBS Tech. Memo. 910-1 (National Bureau of Standards, Gaithersburg, Md., 1976).

J. M. Norman, “Modeling the Complete Crop Canopy,” in Modification of the Aerial Environment of Plants, B. J. Barfield, J. F. Gerber, Eds. (American Society of Agricultural Engineers, St. Joseph, Mich.1979), Chap. 3.6.

K. J. Ranson, V. C. Vanderbilt, L. L. Biehl, B. F. Robinson, M. E. Bauer, Soybean Canopy Reflectance as a Function of View and Illumination geometry, Agristars Tech. Report (Laboratory for Applications of Remote Sensing, Purdue U., West Lafayette, Ind., 1982).

J. Smith, K. Ranson, MRS. Bidirectional Reflectance Literature Survey (ORI, Silver Spring, Md., 1979).

J. E. Colwell, “Vegetation Canopy Reflectance,” in Proceedings, Tenth International Symposium on Remote Sensing of Environment (Environmental Research Institute of Michigan, Ann Arbor, 1974).

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 (3)

Fig. 1
Fig. 1

Polar contour plot of vegetative canopy visible reflectance predictions from Cupid for a solar zenith angle θs of 79° and a leaf area index of 4. The distance from the origin represents the view zenith angle indicated by the dotted grids at 15, 30, 45, and 60°. The angle from 0° represents the view azimuth angle. Solar azimuth is at 0°. The isolines represent contours of percent reflectance. Visible leaf reflectance and transmittance used in Cupid were 8 and 7%. Near-IR leaf reflectance and transmittance were 46 and 52%. Soil visible reflectance was 14%, and soil near-IR reflectance was 23%.

Fig. 2
Fig. 2

A perspective 3-D plot of LAI = 2.87 soybean field data for θs = 39° (dashed lines) and θs = 61° (solid lines). The center of the plot represents nadir with the distance from it representing view zenith in lines of 10° increments. View azimuth is represented by the angle from 0°. The reflectance at a given view zenith and azimuth is represented by the height of the surface at that point. The scale is in percent reflectance. The third quadrant has been removed for ease of viewing. Solar azimuth is 0°. This plot illustrates the increased reflectance resulting from an increase in solar zenith angle and the increase in reflectance with increased view zenith angle.

Fig. 3
Fig. 3

Perspective 3-D plot for the θs = 43° medium soil data (solid lines) with an overlay of the Eq. (4) fit surface (dotted lines). The distance from nadir is given in 10° increments. Vertical scale is in percent reflectance. The third quadrant has been removed for ease of viewing. Solar azimuth is 0°. This figure illustrates how well the equation fits the bidirectional reflectance distribution surface. Note how the equation surface generally approximates the data surface except for the hot spot reflectance peak (where the view zenith equals the solar zenith). Also note how the equation surface increases with the data surface in the solar azimuth direction.

Tables (3)

Tables Icon

Table I Results of Least-Squares Fitting of Eq. (2) on Simulated Canopy Data

Tables Icon

Table II Results of Least-Squares Fitting of Eq. (2) on Soybean and Soil Field Data

Tables Icon

Table III Ratio of Nadir Reflectance RN to Hemispherical Reflectance RH for Simulated Vegetation Canopy Data, Soybean, and Soil Field Data

Equations (6)

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

r = a + b cos ( ϕ )
r = a θ υ 2 + b θ υ cos ( ϕ υ ϕ s ) + c ,
R H = 2.305 a π + c .
r soil = R H , soil 0.13 [ A θ υ 2 + B θ υ cos ( ϕ υ ϕ s ) + C ] , A = 4.988 × 10 4 2.953 × 10 5 θ s + 8.920 × 10 7 θ s 2 , B = 6.988 × 10 4 + 2.243 × 10 3 θ s , C = 14.46 + 3.216 × 10 2 θ s 1.7373 × 10 3 θ s 2 ,
r ( θ v , ϕ v ) cos ( θ v ) Sin ( θ v ) d θ d v ϕ v cos ( θ v ) Sin ( θ v ) d θ d v ϕ v
r ( θ v , ϕ v ) cos ( θ v ) Sin ( θ v ) d θ d v ϕ v cos ( θ v ) Sin ( θ v ) d θ d v ϕ v

Metrics