Abstract

The Duntley equations for propagation of unidirectionally incident light through a diffusing medium have been generalized and interpreted to account for the diurnal nature of near-infrared radiation measured in an Ithaca, N. Y. corn canopy. The Duntley optical coefficients associated with the specular component of light were assumed to vary as the secant of the sun’s zenith angle. Generalization of the Duntley relations was required in order to predict values of irradiance within the canopy and to account for the effect of background reflectance from the soil. Five independent measurements of canopy irradiance suffice to determine the Duntley parameters. Twenty-four measurements of transmittance within the canopy were used, however, in a least-squares calculation to obtain the best fit of the Duntley equations to irradiance within the corn canopy. The Duntley equations fit the experimental results within a standard deviation of 3.2% for a period from noon to sundown. If the laboratory measurements of optical constants for a single corn leaf are used as constraints, the Duntley equations fit the data to within 3.7%. The best fit to near-ir-transmittance measurements occurs when zero absorptance is assumed for the canopy. The Duntley equations reduce to a three-parameter representation for the special case of no absorptance.

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  1. W. A. Allen and A. J. Richardson, J. Opt. Soc. Am. 58, 1023 (1968).
  2. J. H. Allen, Jr. and K. W. Brown, Agron. J. 57, 575 (1965).
  3. W. A. Allen, H. W. Gausman, A. J. Richardson, and J. R. Thomas, J. Opt. Soc. Am. 59, 1376 (1969).
  4. P. Kubelka and F. Munk, Z. Tech. Physik 12, 593 (1931).
  5. Beckman Instruments, Inc., Fullerton, Calif. Trade names are included for information only and do not constitute endorsement by the U. S. Department of Agriculture.
  6. R. A. Holmes and R. B. MacDonald, Proc. IEEE 57, 629 (1969).
  7. D. M. Gates, H. J. Keegan, J. S. Schleter, and V. R. Weidner, Appl. Opt. 4, 11 (1965).
  8. Seishi Isobe, Bull. Nat. Inst. Agricultural Sci. (Japan), Ser. A, No. 9, 29 (March, 1962).
  9. The leaf-area index is defined as the cumulative one-sided leaf area per unit ground area measured from the canopy top to a plane a given distance above the ground. The total LAI is the value determined at the plane of the soil. See D. J. Watson, Ann. Bot. Lond., N. S. 11, 41 (1947).
  10. S. Q. Duntley, J. Opt. Soc. Am. 32, 61 (1942).
  11. J. L. Monteith and G. Szeicz, Quart. J. Roy. Meteorol. Soc. 87, 159 (1961).
  12. W. G. Graham and K. M. King, Quart. J. Roy. Meteorol. Soc. 87, 425 (1961).
  13. Jen-Hu Chang, The Hawaiian Planters Record 56, 195 (1961).
  14. Lin-Sen Chia, Quart. J. Roy. Meteorol. Soc. 93, 116 (1967).
  15. The infinite reflectance R is the reflectance attained by leaves stacked to an infinite depth. In practice, a maximum value of reflectance is achieved at all wavelengths when the number of leaves exceeds eight.

Allen, W. A.

W. A. Allen, H. W. Gausman, A. J. Richardson, and J. R. Thomas, J. Opt. Soc. Am. 59, 1376 (1969).

W. A. Allen and A. J. Richardson, J. Opt. Soc. Am. 58, 1023 (1968).

Allen, Jr., J. H.

J. H. Allen, Jr. and K. W. Brown, Agron. J. 57, 575 (1965).

Brown, K. W.

J. H. Allen, Jr. and K. W. Brown, Agron. J. 57, 575 (1965).

Chang, Jen-Hu

Jen-Hu Chang, The Hawaiian Planters Record 56, 195 (1961).

Chia, Lin-Sen

Lin-Sen Chia, Quart. J. Roy. Meteorol. Soc. 93, 116 (1967).

Duntley, S. Q.

S. Q. Duntley, J. Opt. Soc. Am. 32, 61 (1942).

Gates, D. M.

D. M. Gates, H. J. Keegan, J. S. Schleter, and V. R. Weidner, Appl. Opt. 4, 11 (1965).

Gausman, H. W.

W. A. Allen, H. W. Gausman, A. J. Richardson, and J. R. Thomas, J. Opt. Soc. Am. 59, 1376 (1969).

Graham, W. G.

W. G. Graham and K. M. King, Quart. J. Roy. Meteorol. Soc. 87, 425 (1961).

Holmes, R. A.

R. A. Holmes and R. B. MacDonald, Proc. IEEE 57, 629 (1969).

Isobe, Seishi

Seishi Isobe, Bull. Nat. Inst. Agricultural Sci. (Japan), Ser. A, No. 9, 29 (March, 1962).

Keegan, H. J.

D. M. Gates, H. J. Keegan, J. S. Schleter, and V. R. Weidner, Appl. Opt. 4, 11 (1965).

King, K. M.

W. G. Graham and K. M. King, Quart. J. Roy. Meteorol. Soc. 87, 425 (1961).

Kubelka, P.

P. Kubelka and F. Munk, Z. Tech. Physik 12, 593 (1931).

MacDonald, R. B.

R. A. Holmes and R. B. MacDonald, Proc. IEEE 57, 629 (1969).

Monteith, J. L.

J. L. Monteith and G. Szeicz, Quart. J. Roy. Meteorol. Soc. 87, 159 (1961).

Munk, F.

P. Kubelka and F. Munk, Z. Tech. Physik 12, 593 (1931).

Richardson, A. J.

W. A. Allen, H. W. Gausman, A. J. Richardson, and J. R. Thomas, J. Opt. Soc. Am. 59, 1376 (1969).

W. A. Allen and A. J. Richardson, J. Opt. Soc. Am. 58, 1023 (1968).

Schleter, J. S.

D. M. Gates, H. J. Keegan, J. S. Schleter, and V. R. Weidner, Appl. Opt. 4, 11 (1965).

Szeicz, G.

J. L. Monteith and G. Szeicz, Quart. J. Roy. Meteorol. Soc. 87, 159 (1961).

Thomas, J. R.

W. A. Allen, H. W. Gausman, A. J. Richardson, and J. R. Thomas, J. Opt. Soc. Am. 59, 1376 (1969).

Weidner, V. R.

D. M. Gates, H. J. Keegan, J. S. Schleter, and V. R. Weidner, Appl. Opt. 4, 11 (1965).

Other

W. A. Allen and A. J. Richardson, J. Opt. Soc. Am. 58, 1023 (1968).

J. H. Allen, Jr. and K. W. Brown, Agron. J. 57, 575 (1965).

W. A. Allen, H. W. Gausman, A. J. Richardson, and J. R. Thomas, J. Opt. Soc. Am. 59, 1376 (1969).

P. Kubelka and F. Munk, Z. Tech. Physik 12, 593 (1931).

Beckman Instruments, Inc., Fullerton, Calif. Trade names are included for information only and do not constitute endorsement by the U. S. Department of Agriculture.

R. A. Holmes and R. B. MacDonald, Proc. IEEE 57, 629 (1969).

D. M. Gates, H. J. Keegan, J. S. Schleter, and V. R. Weidner, Appl. Opt. 4, 11 (1965).

Seishi Isobe, Bull. Nat. Inst. Agricultural Sci. (Japan), Ser. A, No. 9, 29 (March, 1962).

The leaf-area index is defined as the cumulative one-sided leaf area per unit ground area measured from the canopy top to a plane a given distance above the ground. The total LAI is the value determined at the plane of the soil. See D. J. Watson, Ann. Bot. Lond., N. S. 11, 41 (1947).

S. Q. Duntley, J. Opt. Soc. Am. 32, 61 (1942).

J. L. Monteith and G. Szeicz, Quart. J. Roy. Meteorol. Soc. 87, 159 (1961).

W. G. Graham and K. M. King, Quart. J. Roy. Meteorol. Soc. 87, 425 (1961).

Jen-Hu Chang, The Hawaiian Planters Record 56, 195 (1961).

Lin-Sen Chia, Quart. J. Roy. Meteorol. Soc. 93, 116 (1967).

The infinite reflectance R is the reflectance attained by leaves stacked to an infinite depth. In practice, a maximum value of reflectance is achieved at all wavelengths when the number of leaves exceeds eight.

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