Abstract

A stochastic leaf radiation model based upon physical and physiological properties of dicot leaves has been developed. The model accurately predicts the absorbed, reflected, and transmitted radiation of normal incidence as a function of wavelength resulting from the leaf–irradiance interaction over the spectral interval of 0.40–2.50 μm. The leaf optical system has been represented as Markov process with a unique transition matrix at each 0.01-μm increment between 0.40 μm and 2.50 μm. Probabilities are calculated at every wavelength interval from leaf thickness, structure, pigment composition, and water content. Simulation results indicate that this approach gives accurate estimations of actual measured values for dicot leaf absorption, reflection, and transmission as a function of wavelength.

© 1977 Optical Society of America

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References

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  1. A. Willstaetter, K. Stoll, Untersuchungen über die Assimilation der Kohlensäure (Verlag-Springer, Berlin, 1918), pp. 122–127.
  2. D. M. Gates, H. J. Keegan, J. C. Schleter, V. R. Weider, Appl. Opt. 4, 11 (1965).
    [Crossref]
  3. W. A. Allen, H. W. Gausman, A. J. Richardson, J. R. Thomas, J. Opt. Soc. Am. 59, 1376 (1969).
    [Crossref]
  4. H. W. Gausman, W. A. Allen, R. Cardenas, A. J. Richardson, Appl. Opt. 9, 545 (1970).
    [Crossref] [PubMed]
  5. E. B. Knipling, Remote Sensing Environ. 1, 155 (1970).
    [Crossref]
  6. J. T. Woolley, Plant Physiol. 47, 656 (1971).
    [Crossref] [PubMed]
  7. T. R. Sinclair, R. M. Hoffer, M. M. Schreiber, Agron. J. 63, 864 (1971).
    [Crossref]
  8. T. R. Sinclair, M. M. Schreiber, R. M. Hoffer, Agron. J. 65, 276 (1973).
    [Crossref]
  9. F. B. Salisbury, C. Ross, Plant Physiology (Wadsworth, Belmont, California, 1969), 765 pp.
  10. D. M. Gates, “Physical and Physiological Properties of Plants,” in Remote Sensing: With Special Reference to Agriculture and Forestry (National Academy of Sciences, Washington, D.C., 1970), pp. 224–252.
  11. H. E. Bennett, J. O. Porteus, J. Opt. Soc. Am. 51, 123 (1961).
    [Crossref]
  12. C. J. Tucker, unpublished research data.
  13. J. H. Troughton, F. B. Sampson, Plants: A Scanning Electron Microscope Survey (Wiley, New York, 1973), 120 pp.
  14. Paraphrased from Ref. 1, pp. 122–127.
  15. R. Kumar, L. Silva, Appl. Opt. 12, 2950 (1973).
    [Crossref] [PubMed]
  16. J. T. Woolley, Plant physiologist, USDA Agricultural Research Service; personal communication (1976).
  17. H. W. Gausman, W. A. Allen, D. E. Escobar, Appl. Opt. 13, 109 (1974).
    [Crossref] [PubMed]
  18. H. W. Gausman, Agron. J. 65, 504 (1973).
    [Crossref]
  19. M. C. Anderson, Ecology 48, 1050 (1967).
    [Crossref]
  20. M. B. Allen, Photophysiology (1) (Academic, New York, 1964). pp. 83–110.
  21. J. A. Curcio, C. C. Petty, J. Opt. Soc. Am. 41, 302 (1951).
    [Crossref]
  22. W. A. Allen, H. W. Gausman, A. J. Richardson, Appl. Opt. 12, 2448 (1973).
    [Crossref] [PubMed]
  23. R. W. Preisendorfer, Radiative Transfer on Discrete Spaces (Pergamon, New York, 1965), 495 pp.
  24. R. M. Devlin, A. V. Barker, Photosynthesis (Van Nostrand Reinhold, New York, 1971), 304 pp.
  25. K. Esau, Plant Anatomy (Wiley, New York, 1965), 767 pp.
  26. E. Parzen, Stochastic Processes (Holden-Day, San Francisco, 1962), pp. 187–275.

1974 (1)

1973 (4)

1971 (2)

J. T. Woolley, Plant Physiol. 47, 656 (1971).
[Crossref] [PubMed]

T. R. Sinclair, R. M. Hoffer, M. M. Schreiber, Agron. J. 63, 864 (1971).
[Crossref]

1970 (2)

1969 (1)

1967 (1)

M. C. Anderson, Ecology 48, 1050 (1967).
[Crossref]

1965 (1)

1961 (1)

1951 (1)

Allen, M. B.

M. B. Allen, Photophysiology (1) (Academic, New York, 1964). pp. 83–110.

Allen, W. A.

Anderson, M. C.

M. C. Anderson, Ecology 48, 1050 (1967).
[Crossref]

Barker, A. V.

R. M. Devlin, A. V. Barker, Photosynthesis (Van Nostrand Reinhold, New York, 1971), 304 pp.

Bennett, H. E.

Cardenas, R.

Curcio, J. A.

Devlin, R. M.

R. M. Devlin, A. V. Barker, Photosynthesis (Van Nostrand Reinhold, New York, 1971), 304 pp.

Esau, K.

K. Esau, Plant Anatomy (Wiley, New York, 1965), 767 pp.

Escobar, D. E.

Gates, D. M.

D. M. Gates, H. J. Keegan, J. C. Schleter, V. R. Weider, Appl. Opt. 4, 11 (1965).
[Crossref]

D. M. Gates, “Physical and Physiological Properties of Plants,” in Remote Sensing: With Special Reference to Agriculture and Forestry (National Academy of Sciences, Washington, D.C., 1970), pp. 224–252.

Gausman, H. W.

Hoffer, R. M.

T. R. Sinclair, M. M. Schreiber, R. M. Hoffer, Agron. J. 65, 276 (1973).
[Crossref]

T. R. Sinclair, R. M. Hoffer, M. M. Schreiber, Agron. J. 63, 864 (1971).
[Crossref]

Keegan, H. J.

Knipling, E. B.

E. B. Knipling, Remote Sensing Environ. 1, 155 (1970).
[Crossref]

Kumar, R.

Parzen, E.

E. Parzen, Stochastic Processes (Holden-Day, San Francisco, 1962), pp. 187–275.

Petty, C. C.

Porteus, J. O.

Preisendorfer, R. W.

R. W. Preisendorfer, Radiative Transfer on Discrete Spaces (Pergamon, New York, 1965), 495 pp.

Richardson, A. J.

Ross, C.

F. B. Salisbury, C. Ross, Plant Physiology (Wadsworth, Belmont, California, 1969), 765 pp.

Salisbury, F. B.

F. B. Salisbury, C. Ross, Plant Physiology (Wadsworth, Belmont, California, 1969), 765 pp.

Sampson, F. B.

J. H. Troughton, F. B. Sampson, Plants: A Scanning Electron Microscope Survey (Wiley, New York, 1973), 120 pp.

Schleter, J. C.

Schreiber, M. M.

T. R. Sinclair, M. M. Schreiber, R. M. Hoffer, Agron. J. 65, 276 (1973).
[Crossref]

T. R. Sinclair, R. M. Hoffer, M. M. Schreiber, Agron. J. 63, 864 (1971).
[Crossref]

Silva, L.

Sinclair, T. R.

T. R. Sinclair, M. M. Schreiber, R. M. Hoffer, Agron. J. 65, 276 (1973).
[Crossref]

T. R. Sinclair, R. M. Hoffer, M. M. Schreiber, Agron. J. 63, 864 (1971).
[Crossref]

Stoll, K.

A. Willstaetter, K. Stoll, Untersuchungen über die Assimilation der Kohlensäure (Verlag-Springer, Berlin, 1918), pp. 122–127.

Thomas, J. R.

Troughton, J. H.

J. H. Troughton, F. B. Sampson, Plants: A Scanning Electron Microscope Survey (Wiley, New York, 1973), 120 pp.

Tucker, C. J.

C. J. Tucker, unpublished research data.

Weider, V. R.

Willstaetter, A.

A. Willstaetter, K. Stoll, Untersuchungen über die Assimilation der Kohlensäure (Verlag-Springer, Berlin, 1918), pp. 122–127.

Woolley, J. T.

J. T. Woolley, Plant Physiol. 47, 656 (1971).
[Crossref] [PubMed]

J. T. Woolley, Plant physiologist, USDA Agricultural Research Service; personal communication (1976).

Agron. J. (3)

T. R. Sinclair, R. M. Hoffer, M. M. Schreiber, Agron. J. 63, 864 (1971).
[Crossref]

T. R. Sinclair, M. M. Schreiber, R. M. Hoffer, Agron. J. 65, 276 (1973).
[Crossref]

H. W. Gausman, Agron. J. 65, 504 (1973).
[Crossref]

Appl. Opt. (5)

Ecology (1)

M. C. Anderson, Ecology 48, 1050 (1967).
[Crossref]

J. Opt. Soc. Am. (3)

Plant Physiol. (1)

J. T. Woolley, Plant Physiol. 47, 656 (1971).
[Crossref] [PubMed]

Remote Sensing Environ. (1)

E. B. Knipling, Remote Sensing Environ. 1, 155 (1970).
[Crossref]

Other (12)

M. B. Allen, Photophysiology (1) (Academic, New York, 1964). pp. 83–110.

R. W. Preisendorfer, Radiative Transfer on Discrete Spaces (Pergamon, New York, 1965), 495 pp.

R. M. Devlin, A. V. Barker, Photosynthesis (Van Nostrand Reinhold, New York, 1971), 304 pp.

K. Esau, Plant Anatomy (Wiley, New York, 1965), 767 pp.

E. Parzen, Stochastic Processes (Holden-Day, San Francisco, 1962), pp. 187–275.

F. B. Salisbury, C. Ross, Plant Physiology (Wadsworth, Belmont, California, 1969), 765 pp.

D. M. Gates, “Physical and Physiological Properties of Plants,” in Remote Sensing: With Special Reference to Agriculture and Forestry (National Academy of Sciences, Washington, D.C., 1970), pp. 224–252.

C. J. Tucker, unpublished research data.

J. H. Troughton, F. B. Sampson, Plants: A Scanning Electron Microscope Survey (Wiley, New York, 1973), 120 pp.

Paraphrased from Ref. 1, pp. 122–127.

A. Willstaetter, K. Stoll, Untersuchungen über die Assimilation der Kohlensäure (Verlag-Springer, Berlin, 1918), pp. 122–127.

J. T. Woolley, Plant physiologist, USDA Agricultural Research Service; personal communication (1976).

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Figures (8)

Fig. 1
Fig. 1

Transverse view of a broad bean leaf. Beneath the upper epidermis is a layer of elongated palisade parenchyma (P) cells. The lower half of the leaf contains the spongy mesophyll. A small vein (V) is at center left. Also note the labyrinth of the intercellular air spaces (used by permission from Troughton and Sampson13).

Fig. 2
Fig. 2

Typical spectral absorptance, reflectance, and transmittance of a plant leaf. Note the high absorptance due to plant pigments (predominantly the chlorophylls) in the visible region, the lack of absorptance, and resulting high values of reflectance and transmittance in the 0.8–1.3-μm region (extracted from Knipling5).

Fig. 3
Fig. 3

Coefficients of absorptance for chlorophyll a and b (a) and lutein (b). These in vitro absorptance curves have been shifted 0.01 μm to longer wavelengths as suggested in the literature.9

Fig. 4
Fig. 4

Coefficients of absorptance for pure liquid water at 20°C (extracted from Curcio and Petty21).

Fig. 5
Fig. 5

Compartment model of a leaf optical system. The arrows between compartments represent the flow rates and the direction of flow. The processes or leaf cellular aggregates are indicated within the compartments.

Fig. 6
Fig. 6

Iterative response of stochastic model to incident radiation. Radiative flux plots at two wavelengths showing the interactions occurring as the predictions proceed to a steady state: (a) the intraleaf radiative flux at 0.50 μm and (b) the intraleaf radiative flux at 0.80 μm.

Fig. 7
Fig. 7

Predicted spectrooptical functions output from LFMOD1. Model predictions of the spectrooptical characteristics of a black maple leaf from 0.40 μm to 2.50 μm based upon leaf structure; chlorophyll, carotenoid, and leaf water content; and specular properties of the cuticle.

Fig. 8
Fig. 8

Comparison of the spectral reflectance modeled for black maple and measured values for silver maple (Acer sacchrarum). Note the close similarity between the two spectral reflectance curves.

Tables (2)

Tables Icon

Table I Table of Probabilities Used in LFMODI

Tables Icon

Table II Assumptions Used in Calculating the Various Probabilities

Equations (12)

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T λ = H λ exp ( - α λ x ) ,
p k , j ( n ) = Prob ( X t + n = k X t = j ) ,
R k , j = p k , j ( 1 ) ,
P = [ R 11 R 21 R n 1 R 12 R 22 R n 2 R 1 n R 2 n R n n ]
P = [ 0 R 21 R 31 0 0 0 0 0 0 0 0 R 22 0 0 0 0 0 0 0 0 0 0 0 R 43 R 53 0 R 73 0 0 0 0 0 0 R 44 0 0 0 0 0 0 0 0 0 R 45 R 55 R 65 R 75 0 0 0 0 0 0 0 0 R 66 0 0 0 0 0 0 0 0 0 0 0 R 87 R 97 R 10 , 7 0 0 0 0 0 0 0 R 88 0 0 0 0 R 39 0 0 0 0 R 89 R 99 R 10 , 9 0 0 0 0 0 0 0 0 0 R 10 , 10 ]
p o T = [ 1 0 0 0 0 0 0 0 0 0 ] ,
P n = P n p o ,
lim n P n p 0 = p .
n = 1 p k , k ( n )
p 1 , 1 ( n ) = 0
p k , k ( n ) = 1 for every n
p k , k ( n ) < 1

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