Abstract

A light absorption model (LAM) for vegetative plant canopies has been derived from the Suits reflectance model. From the LAM the absorption of light in the photosynthetically active region of the spectrum (400–700 nm) has been calculated for a Penjamo wheat crop for several situations including (a) the percent absorption of the incident radiation by a canopy of LAI 3.1 having a four-layer structure, (b) the percent absorption of light by the individual layers within a four-layer canopy and by the underlying soil, (c) the percent absorption of light by each vegetative canopy layer for variable sun angle, and (d) the cumulative solar energy absorbed by the developing wheat canopy as it progresses from a single layer through its growth stages to a three-layer canopy. This calculation is also presented as a function of the leaf area index and is shown to be in agreement with experimental data reported by Kanemasu on Plainsman V wheat.

© 1978 Optical Society of America

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References

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  1. E. Kanemasu, “Estimated Winter Wheat Yield from Crop Growth Predicted by LANDSAT,” Final Report, NASA, Johnson Space Center, NAS9-14899 (1977).
  2. W. Duncan, R. Loomis, W. Williams, R. Hanau, Hilgardia 38, 181 (1967).
  3. G. Arkin, R. Vanderlip, J. Ritchie, Trans. ASAE 19, 622 (1976).
  4. G. Suits, Remote Sensing Environ. 2, 117 (1972).
    [CrossRef]
  5. D. Gates, Science 151, 523 (1966).
    [CrossRef] [PubMed]
  6. J. Bassham, Science 197, 630 (1977).
    [CrossRef] [PubMed]
  7. J. Chance, E. LeMaster, Appl. Opt. 16, 407 (1977).
    [CrossRef] [PubMed]
  8. G. Suits, G. Safir, Remote Sensing Environ. 2, 183 (1972).
    [CrossRef]
  9. W. Allen, T. Gayle, A. Richardson, J. Opt. Soc. Am. 60, 372 (1970).
    [CrossRef]
  10. W. Wendlandt, H. Hecht, Reflectance Spectroscopy (Wiley, New York, 1966).
  11. J. Chance, J. Cantu, “A Study of Plant Canopy Reflectance Models,” Final Report on Faculty Research Grant, Pan American U. (1975).
  12. K. Leith, “Functioning of Terrestrial Ecosystem at the Primary Production Level,” F. Edcardt, Ed. (UNESCO, Paris, 1968), p. 233–243.
  13. W. Allen, J. Richardson, J. Opt. Soc. Am. 58, 1023 (1968).
    [CrossRef]
  14. C. L. Wiegand, USDA, SEA, Weslaco, TX, private communication.

1977 (2)

1976 (1)

G. Arkin, R. Vanderlip, J. Ritchie, Trans. ASAE 19, 622 (1976).

1972 (2)

G. Suits, Remote Sensing Environ. 2, 117 (1972).
[CrossRef]

G. Suits, G. Safir, Remote Sensing Environ. 2, 183 (1972).
[CrossRef]

1970 (1)

1968 (1)

1967 (1)

W. Duncan, R. Loomis, W. Williams, R. Hanau, Hilgardia 38, 181 (1967).

1966 (1)

D. Gates, Science 151, 523 (1966).
[CrossRef] [PubMed]

Allen, W.

Arkin, G.

G. Arkin, R. Vanderlip, J. Ritchie, Trans. ASAE 19, 622 (1976).

Bassham, J.

J. Bassham, Science 197, 630 (1977).
[CrossRef] [PubMed]

Cantu, J.

J. Chance, J. Cantu, “A Study of Plant Canopy Reflectance Models,” Final Report on Faculty Research Grant, Pan American U. (1975).

Chance, J.

J. Chance, E. LeMaster, Appl. Opt. 16, 407 (1977).
[CrossRef] [PubMed]

J. Chance, J. Cantu, “A Study of Plant Canopy Reflectance Models,” Final Report on Faculty Research Grant, Pan American U. (1975).

Duncan, W.

W. Duncan, R. Loomis, W. Williams, R. Hanau, Hilgardia 38, 181 (1967).

Gates, D.

D. Gates, Science 151, 523 (1966).
[CrossRef] [PubMed]

Gayle, T.

Hanau, R.

W. Duncan, R. Loomis, W. Williams, R. Hanau, Hilgardia 38, 181 (1967).

Hecht, H.

W. Wendlandt, H. Hecht, Reflectance Spectroscopy (Wiley, New York, 1966).

Kanemasu, E.

E. Kanemasu, “Estimated Winter Wheat Yield from Crop Growth Predicted by LANDSAT,” Final Report, NASA, Johnson Space Center, NAS9-14899 (1977).

Leith, K.

K. Leith, “Functioning of Terrestrial Ecosystem at the Primary Production Level,” F. Edcardt, Ed. (UNESCO, Paris, 1968), p. 233–243.

LeMaster, E.

Loomis, R.

W. Duncan, R. Loomis, W. Williams, R. Hanau, Hilgardia 38, 181 (1967).

Richardson, A.

Richardson, J.

Ritchie, J.

G. Arkin, R. Vanderlip, J. Ritchie, Trans. ASAE 19, 622 (1976).

Safir, G.

G. Suits, G. Safir, Remote Sensing Environ. 2, 183 (1972).
[CrossRef]

Suits, G.

G. Suits, G. Safir, Remote Sensing Environ. 2, 183 (1972).
[CrossRef]

G. Suits, Remote Sensing Environ. 2, 117 (1972).
[CrossRef]

Vanderlip, R.

G. Arkin, R. Vanderlip, J. Ritchie, Trans. ASAE 19, 622 (1976).

Wendlandt, W.

W. Wendlandt, H. Hecht, Reflectance Spectroscopy (Wiley, New York, 1966).

Wiegand, C. L.

C. L. Wiegand, USDA, SEA, Weslaco, TX, private communication.

Williams, W.

W. Duncan, R. Loomis, W. Williams, R. Hanau, Hilgardia 38, 181 (1967).

Appl. Opt. (1)

Hilgardia (1)

W. Duncan, R. Loomis, W. Williams, R. Hanau, Hilgardia 38, 181 (1967).

J. Opt. Soc. Am. (2)

Remote Sensing Environ. (2)

G. Suits, G. Safir, Remote Sensing Environ. 2, 183 (1972).
[CrossRef]

G. Suits, Remote Sensing Environ. 2, 117 (1972).
[CrossRef]

Science (2)

D. Gates, Science 151, 523 (1966).
[CrossRef] [PubMed]

J. Bassham, Science 197, 630 (1977).
[CrossRef] [PubMed]

Trans. ASAE (1)

G. Arkin, R. Vanderlip, J. Ritchie, Trans. ASAE 19, 622 (1976).

Other (5)

C. L. Wiegand, USDA, SEA, Weslaco, TX, private communication.

W. Wendlandt, H. Hecht, Reflectance Spectroscopy (Wiley, New York, 1966).

J. Chance, J. Cantu, “A Study of Plant Canopy Reflectance Models,” Final Report on Faculty Research Grant, Pan American U. (1975).

K. Leith, “Functioning of Terrestrial Ecosystem at the Primary Production Level,” F. Edcardt, Ed. (UNESCO, Paris, 1968), p. 233–243.

E. Kanemasu, “Estimated Winter Wheat Yield from Crop Growth Predicted by LANDSAT,” Final Report, NASA, Johnson Space Center, NAS9-14899 (1977).

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Figures (10)

Fig. 1
Fig. 1

A comparison of the Suits three-layer reflectance model with experimental data for Penjamo wheat in the soft dough stage 98 days from emergence with an LAI of 3.5. Soil reflectance is shown for comparison.

Fig. 2
Fig. 2

LAM calculations for a four-layer Penjamo wheat canopy of LAI 3.1 as a function of the wavelength of incident light. The absorption of each canopy layer is shown as well as the total canopy absorption.

Fig. 3
Fig. 3

LAM calculations for percentage absorption of light by the underlying soil beneath the four-layer canopy. Also shown is the percentage of incident light exiting the top surface of the canopy.

Fig. 4
Fig. 4

The percent absorbed energy of 650-nm incident light calculated by the LAM for a four-layer Penjamo wheat canopy as a function of the sun zenith angle. The absorption of each canopy layer is shown as well as the total canopy absorption.

Fig. 5
Fig. 5

The underlying soil absorption and exiting upward flux calculations are shown for variable sun zenith angle.

Fig. 6
Fig. 6

Cumulative energy absorbed in the PAR by a wheat canopy throughout the growing season.

Fig. 7
Fig. 7

The reflectance of vegetative components in a well developed Penjamo wheat canopy measured 98 days from emergence.

Fig. 8
Fig. 8

The transmittance of green and brown leaves taken from the same Penjamo wheat canopy.

Fig. 9
Fig. 9

The absorptance of vegetative components throughout most of the growing season.

Fig. 10
Fig. 10

A comparison of LAM absorption calculations with the experimental results of Kanemasu for varying LAI.

Tables (1)

Tables Icon

Table I Results of the LAM for Solar Energy Absorbed by Wheat in the PAR Calculated on a Daily Basis with Wheat Parameters Updated Weekly

Equations (20)

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d E λ ( + d , i , x ) / d x = a ( i ) E λ ( + d , i , x ) + b ( i ) E λ ( d , i , x ) + c ( i ) E λ ( s , i , x ) , d E λ ( d , i , x ) / d x = a ( i ) E λ ( d , i , x ) + b ( i ) E λ ( + d , i , x ) c ( i ) E λ ( s , i , x ) , d E λ ( s , i , x ) / d x = k ( i ) E λ ( s , i , x ) .
a ( i ) = m a ( i , m ) , b ( i ) = m b ( i , m ) , c ( i ) = m c ( i , m ) , c ( i ) = m c ( i , m ) , k ( i ) = m k ( i , m ) ,
a ( i , m ) = { σ h ( i , m ) n ( i , m ) [ 1 T ( i , m ) ] + σ υ ( i , m ) n ( i , m ) [ 1 R ( i , m ) + T ( i , m ) 2 ] } ,
b ( i , m ) = { σ h ( i , m ) n ( i , m ) R ( i , m ) + σ υ ( i , m ) n ( i , m ) [ R ( i , m ) + T ( i , m ) 2 ] } ,
c ( i , m ) = { σ h ( i , m ) n ( i , m ) R ( i , m ) + ( 2 / π ) σ υ ( i , m ) n ( i , m ) [ R ( i , m ) + T ( i , m ) 2 ] tan θ } , c ( i , m ) = { σ h ( i , m ) n ( i , m ) T ( i , m ) + ( 2 / π ) σ υ ( i , m ) n ( i , m ) [ R ( i , m ) + T ( i , m ) 2 ] tan θ } , k ( i , m ) = [ σ h ( i , m ) n ( i , m ) + ( 2 / π ) σ υ ( i , m ) n ( i , m ) tan θ ] ,
E λ ( + d , N , Z ) = ρ s [ E λ ( d , N , Z ) + E λ ( s , N , Z ) ] .
E λ ( s , i , x ) + E λ ( d , i , x ) + E λ ( + d , i , x + Δ x ) ,
E λ ( + d , i , x ) + E λ ( d , i , x + Δ x ) + E λ ( s , i , x + Δ x ) .
A ( x + Δ x ) A ( x ) Δ x = E λ ( + d , i , x + Δ x ) E λ ( + d , i , x ) Δ x E λ ( d , i , x + Δ x ) E λ ( d , i , x ) Δ x E λ ( s , i , x + Δ x ) E λ ( s , i , x ) Δ x ,
d A ( x ) d x = d E λ ( + d , i , x ) d x d E λ ( d , i , x ) d x d E λ ( s , i , x ) d x .
lim x + x i A ( x ) = A ( x i ) .
A ( x ) = E λ ( + d , i , x ) E λ ( d , i , x ) E λ ( s , i , x ) [ E λ ( + d , 1,0 ) E λ ( d , 1,0 ) E λ ( s , 1,0 ) ] .
A ( x ) = ( 1 1 / ρ s ) E λ ( + d , i , x ) [ E λ ( + d , 1,0 ) E λ ( d , 1,0 ) E λ ( s , 1,0 ) ] .
lim x E λ ( + d , i , x ) = 0 ;
lim x A ( x ) = A = ( E λ ( d , 1,0 ) + E λ ( s , 1,0 ) ) [ E λ ( + d , 1,0 ) ] .
A = 1 [ ( a + k ) b c + b 2 c ( b 2 + k 2 a 2 ) ( a + g ) + ( a k ) + c b a 2 k 2 b 2 ] ,
TDE = 2 0.4 0.7 t n t s A [ λ , θ ( t ) ] E [ λ , θ ( t ) ] d t d λ ,
TDE = ( 2 ) ( 0.3 ) ( 3600 ) i A ( 0.6 , θ i ) E ( 0.6 , θ i ) ,
n ( i , m ) = N ( i , m ) ( X i X i 1 ) L W .
σ h ( i , m ) = Area ( i , m ) N ( i , m ) · cos θ , σ υ ( i , m ) = Area ( i , m ) N ( i , m ) · sin θ .

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