Abstract

Optical instruments currently available for measuring the leaf-area index (LAI) of a plant canopy all utilize only the canopy gap-fraction information. These instruments include the Li-Cor LAI-2000 Plant Canopy Analyzer, Decagon, and Demon. The advantages of utilizing both the canopy gap-fraction and gap-size information are shown. For the purpose of measuring the canopy gap size, a prototype sunfleck–LAI instrument named Tracing Radiation and Architecture of Canopies (TRAC), has been developed and tested in two pure conifer plantations, red pine (Pinus resinosa Ait.) and jack pine (Pinus banksiana Lamb). A new gap-size-analysis theory is presented to quantify the effect of canopy architecture on optical measurements of LAI based on the gap-fraction principle. The theory is an improvement on that of Lang and Xiang [Agric. For. Meteorol. 37, 229 (1986)]. In principle, this theory can be used for any heterogeneous canopies.

© 1995 Optical Society of America

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References

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  1. J. M. Chen, T. A. Black, “Defining leaf area index for non-flat leaves,” Plant Cell Environ. 15, 421–429 (1992).
    [CrossRef]
  2. M. A. Spanner, L. L. Pierce, D. L. Peterson, S. W. Running, “Remote sensing temperate coniferous forest leaf area index: the influence of canopy closure, understory and background reflectance,” Int. J. Remote Sensing 11, 95–111 (1990).
    [CrossRef]
  3. M. A. Spanner, L. L. Pierce, S. W. Running, D. L. Peterson, “The seasonal trends of AVHRR data of temperate coniferous forests: relationship with leaf area index,” Remote Sensing Environ. 33, 97–112 (1990).
    [CrossRef]
  4. B. Leblon, H. Granberg, C. Ansseau, A. Royer, “A semi-empirical model to estimate the biomass production of forest canopies from spectral variables part 1: relationship between spectral variables and light interception efficiency,” Remote Sensing Rev. 7, 109–125 (1993).
    [CrossRef]
  5. H. L. Gholz, F. K. Fitz, R. H. Waring, “Leaf area differences associated with old-growth forest communities in the western Oregon Cascades,” Can. J. For. Res. 6, 49–57 (1976).
    [CrossRef]
  6. N. J. Smith, “Estimating leaf area index and light extinction coefficients in stands of Douglas-fir,” Can. J. For. Res. 30, 317–321 (1993).
    [CrossRef]
  7. J. Welles, “Some indirect methods of estimating canopy structure,” in Instrumentation for Studying Vegetation Canopies for Remote Sensing in Optical and Thermal Infrared Regions, J. Norman, N. Geol, eds. (Harwood, London, 1990), pp. 31–43.
  8. A. R. G. Lang, Y. Xiang, “Estimation of leaf area index from transmission of direct sunlight in discontinuous canopies,” Agric. For. Meteorol. 37, 229–243 (1986).
    [CrossRef]
  9. S. T. Gower, J. M. Norman, “Rapid estimation of leaf area index in forests using the LI-COR LAI-2000,” Ecology 72, 1896–1900 (1991).
    [CrossRef]
  10. J. M. Chen, T. A. Black, “Foliage area and architecture of plant canopies from sunfleck size distributions,” Agric. For. Meteorol. 60, 249–266 (1992).
    [CrossRef]
  11. H. H. Neumann, G. den Hartog, R. H. Shaw, “Leaf area measurements based on hemispheric photographs and leaf-litter collection in a deciduous forest during autumn leaf-fall,” Agric. For. Meteorol. 45, 325–345 (1989).
    [CrossRef]
  12. E. E. Miller, J. M. Norman, “A sunfleck theory for plant canopies. I: Lengths of sunlit segments along a transect,” Agron. J. 63, 735–738 (1971).
    [CrossRef]
  13. M. Monsi, T. Saeki, “Uber den Lichtfaktor in den Pflanzeng-esellschaften und Seine Bedeutung fur die Stoffproduktion,” Jpn. J. Bot. 14, 22–52 (1953).
  14. K. Fassnacht, S. T. Gower, J. M. Norman, R. M. McMurtrie, “A comparison of optical and direct methods for estimating foliage surface area index in forests,” Agric. For. Meteorol. 71, 183–207 (1994).
    [CrossRef]
  15. G. Deblonde, M. Penner, A. Royer, “Measuring leaf area index with the LI-COR LAI-2000 in pine stands,” Ecology 75, 1507–1511 (1994).
    [CrossRef]
  16. T. Nilson, “A theoretical analysis of the frequency of gaps in plant stands,” Agric. Meteorol. 8, 25–38 (1971).
    [CrossRef]
  17. J. M. Chen, T. A. Black, R. S. Adams, “Evaluation of hemispherical photography for determining plant area index and geometry of a forest stand,” Agric. For. Meteorol. 56, 129–143 (1991).
    [CrossRef]
  18. LAI-2000 PCA Operating Manual (Li-Cor, Inc., Lincoln, Neb., 1991).
  19. A. R. G. Lang, “Application of some of Cauchy’s theorems to estimation of surface areas of leaves, needles and branches of plants, and light transmittance,” Agric. For. Meterol. 55, 191–212 (1991).
    [CrossRef]
  20. J. B. Miller, “A formula for average foliage density,” Aust. J. Bot. 15, 141–144 (1967).
    [CrossRef]
  21. A. R. G. Lang, “Simplified estimate of leaf area index from transmittance of the Sun’s beam,” Agric. For. Meteorol. 41, 179–186 (1987).
    [CrossRef]
  22. A. R. G. Lang, R. E. McMurtrie, M. L. Benson, “Validity of surface area indices of Pinus radiata estimated from transmittance of the Sun’s beam,” Agric. For. Meteorol. 57, 157–170 (1991).
    [CrossRef]

1994

K. Fassnacht, S. T. Gower, J. M. Norman, R. M. McMurtrie, “A comparison of optical and direct methods for estimating foliage surface area index in forests,” Agric. For. Meteorol. 71, 183–207 (1994).
[CrossRef]

G. Deblonde, M. Penner, A. Royer, “Measuring leaf area index with the LI-COR LAI-2000 in pine stands,” Ecology 75, 1507–1511 (1994).
[CrossRef]

1993

N. J. Smith, “Estimating leaf area index and light extinction coefficients in stands of Douglas-fir,” Can. J. For. Res. 30, 317–321 (1993).
[CrossRef]

B. Leblon, H. Granberg, C. Ansseau, A. Royer, “A semi-empirical model to estimate the biomass production of forest canopies from spectral variables part 1: relationship between spectral variables and light interception efficiency,” Remote Sensing Rev. 7, 109–125 (1993).
[CrossRef]

1992

J. M. Chen, T. A. Black, “Defining leaf area index for non-flat leaves,” Plant Cell Environ. 15, 421–429 (1992).
[CrossRef]

J. M. Chen, T. A. Black, “Foliage area and architecture of plant canopies from sunfleck size distributions,” Agric. For. Meteorol. 60, 249–266 (1992).
[CrossRef]

1991

J. M. Chen, T. A. Black, R. S. Adams, “Evaluation of hemispherical photography for determining plant area index and geometry of a forest stand,” Agric. For. Meteorol. 56, 129–143 (1991).
[CrossRef]

A. R. G. Lang, “Application of some of Cauchy’s theorems to estimation of surface areas of leaves, needles and branches of plants, and light transmittance,” Agric. For. Meterol. 55, 191–212 (1991).
[CrossRef]

S. T. Gower, J. M. Norman, “Rapid estimation of leaf area index in forests using the LI-COR LAI-2000,” Ecology 72, 1896–1900 (1991).
[CrossRef]

A. R. G. Lang, R. E. McMurtrie, M. L. Benson, “Validity of surface area indices of Pinus radiata estimated from transmittance of the Sun’s beam,” Agric. For. Meteorol. 57, 157–170 (1991).
[CrossRef]

1990

M. A. Spanner, L. L. Pierce, D. L. Peterson, S. W. Running, “Remote sensing temperate coniferous forest leaf area index: the influence of canopy closure, understory and background reflectance,” Int. J. Remote Sensing 11, 95–111 (1990).
[CrossRef]

M. A. Spanner, L. L. Pierce, S. W. Running, D. L. Peterson, “The seasonal trends of AVHRR data of temperate coniferous forests: relationship with leaf area index,” Remote Sensing Environ. 33, 97–112 (1990).
[CrossRef]

1989

H. H. Neumann, G. den Hartog, R. H. Shaw, “Leaf area measurements based on hemispheric photographs and leaf-litter collection in a deciduous forest during autumn leaf-fall,” Agric. For. Meteorol. 45, 325–345 (1989).
[CrossRef]

1987

A. R. G. Lang, “Simplified estimate of leaf area index from transmittance of the Sun’s beam,” Agric. For. Meteorol. 41, 179–186 (1987).
[CrossRef]

1986

A. R. G. Lang, Y. Xiang, “Estimation of leaf area index from transmission of direct sunlight in discontinuous canopies,” Agric. For. Meteorol. 37, 229–243 (1986).
[CrossRef]

1976

H. L. Gholz, F. K. Fitz, R. H. Waring, “Leaf area differences associated with old-growth forest communities in the western Oregon Cascades,” Can. J. For. Res. 6, 49–57 (1976).
[CrossRef]

1971

E. E. Miller, J. M. Norman, “A sunfleck theory for plant canopies. I: Lengths of sunlit segments along a transect,” Agron. J. 63, 735–738 (1971).
[CrossRef]

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

1967

J. B. Miller, “A formula for average foliage density,” Aust. J. Bot. 15, 141–144 (1967).
[CrossRef]

1953

M. Monsi, T. Saeki, “Uber den Lichtfaktor in den Pflanzeng-esellschaften und Seine Bedeutung fur die Stoffproduktion,” Jpn. J. Bot. 14, 22–52 (1953).

Adams, R. S.

J. M. Chen, T. A. Black, R. S. Adams, “Evaluation of hemispherical photography for determining plant area index and geometry of a forest stand,” Agric. For. Meteorol. 56, 129–143 (1991).
[CrossRef]

Ansseau, C.

B. Leblon, H. Granberg, C. Ansseau, A. Royer, “A semi-empirical model to estimate the biomass production of forest canopies from spectral variables part 1: relationship between spectral variables and light interception efficiency,” Remote Sensing Rev. 7, 109–125 (1993).
[CrossRef]

Benson, M. L.

A. R. G. Lang, R. E. McMurtrie, M. L. Benson, “Validity of surface area indices of Pinus radiata estimated from transmittance of the Sun’s beam,” Agric. For. Meteorol. 57, 157–170 (1991).
[CrossRef]

Black, T. A.

J. M. Chen, T. A. Black, “Defining leaf area index for non-flat leaves,” Plant Cell Environ. 15, 421–429 (1992).
[CrossRef]

J. M. Chen, T. A. Black, “Foliage area and architecture of plant canopies from sunfleck size distributions,” Agric. For. Meteorol. 60, 249–266 (1992).
[CrossRef]

J. M. Chen, T. A. Black, R. S. Adams, “Evaluation of hemispherical photography for determining plant area index and geometry of a forest stand,” Agric. For. Meteorol. 56, 129–143 (1991).
[CrossRef]

Chen, J. M.

J. M. Chen, T. A. Black, “Foliage area and architecture of plant canopies from sunfleck size distributions,” Agric. For. Meteorol. 60, 249–266 (1992).
[CrossRef]

J. M. Chen, T. A. Black, “Defining leaf area index for non-flat leaves,” Plant Cell Environ. 15, 421–429 (1992).
[CrossRef]

J. M. Chen, T. A. Black, R. S. Adams, “Evaluation of hemispherical photography for determining plant area index and geometry of a forest stand,” Agric. For. Meteorol. 56, 129–143 (1991).
[CrossRef]

Deblonde, G.

G. Deblonde, M. Penner, A. Royer, “Measuring leaf area index with the LI-COR LAI-2000 in pine stands,” Ecology 75, 1507–1511 (1994).
[CrossRef]

den Hartog, G.

H. H. Neumann, G. den Hartog, R. H. Shaw, “Leaf area measurements based on hemispheric photographs and leaf-litter collection in a deciduous forest during autumn leaf-fall,” Agric. For. Meteorol. 45, 325–345 (1989).
[CrossRef]

Fassnacht, K.

K. Fassnacht, S. T. Gower, J. M. Norman, R. M. McMurtrie, “A comparison of optical and direct methods for estimating foliage surface area index in forests,” Agric. For. Meteorol. 71, 183–207 (1994).
[CrossRef]

Fitz, F. K.

H. L. Gholz, F. K. Fitz, R. H. Waring, “Leaf area differences associated with old-growth forest communities in the western Oregon Cascades,” Can. J. For. Res. 6, 49–57 (1976).
[CrossRef]

Gholz, H. L.

H. L. Gholz, F. K. Fitz, R. H. Waring, “Leaf area differences associated with old-growth forest communities in the western Oregon Cascades,” Can. J. For. Res. 6, 49–57 (1976).
[CrossRef]

Gower, S. T.

K. Fassnacht, S. T. Gower, J. M. Norman, R. M. McMurtrie, “A comparison of optical and direct methods for estimating foliage surface area index in forests,” Agric. For. Meteorol. 71, 183–207 (1994).
[CrossRef]

S. T. Gower, J. M. Norman, “Rapid estimation of leaf area index in forests using the LI-COR LAI-2000,” Ecology 72, 1896–1900 (1991).
[CrossRef]

Granberg, H.

B. Leblon, H. Granberg, C. Ansseau, A. Royer, “A semi-empirical model to estimate the biomass production of forest canopies from spectral variables part 1: relationship between spectral variables and light interception efficiency,” Remote Sensing Rev. 7, 109–125 (1993).
[CrossRef]

Lang, A. R. G.

A. R. G. Lang, “Application of some of Cauchy’s theorems to estimation of surface areas of leaves, needles and branches of plants, and light transmittance,” Agric. For. Meterol. 55, 191–212 (1991).
[CrossRef]

A. R. G. Lang, R. E. McMurtrie, M. L. Benson, “Validity of surface area indices of Pinus radiata estimated from transmittance of the Sun’s beam,” Agric. For. Meteorol. 57, 157–170 (1991).
[CrossRef]

A. R. G. Lang, “Simplified estimate of leaf area index from transmittance of the Sun’s beam,” Agric. For. Meteorol. 41, 179–186 (1987).
[CrossRef]

A. R. G. Lang, Y. Xiang, “Estimation of leaf area index from transmission of direct sunlight in discontinuous canopies,” Agric. For. Meteorol. 37, 229–243 (1986).
[CrossRef]

Leblon, B.

B. Leblon, H. Granberg, C. Ansseau, A. Royer, “A semi-empirical model to estimate the biomass production of forest canopies from spectral variables part 1: relationship between spectral variables and light interception efficiency,” Remote Sensing Rev. 7, 109–125 (1993).
[CrossRef]

McMurtrie, R. E.

A. R. G. Lang, R. E. McMurtrie, M. L. Benson, “Validity of surface area indices of Pinus radiata estimated from transmittance of the Sun’s beam,” Agric. For. Meteorol. 57, 157–170 (1991).
[CrossRef]

McMurtrie, R. M.

K. Fassnacht, S. T. Gower, J. M. Norman, R. M. McMurtrie, “A comparison of optical and direct methods for estimating foliage surface area index in forests,” Agric. For. Meteorol. 71, 183–207 (1994).
[CrossRef]

Miller, E. E.

E. E. Miller, J. M. Norman, “A sunfleck theory for plant canopies. I: Lengths of sunlit segments along a transect,” Agron. J. 63, 735–738 (1971).
[CrossRef]

Miller, J. B.

J. B. Miller, “A formula for average foliage density,” Aust. J. Bot. 15, 141–144 (1967).
[CrossRef]

Monsi, M.

M. Monsi, T. Saeki, “Uber den Lichtfaktor in den Pflanzeng-esellschaften und Seine Bedeutung fur die Stoffproduktion,” Jpn. J. Bot. 14, 22–52 (1953).

Neumann, H. H.

H. H. Neumann, G. den Hartog, R. H. Shaw, “Leaf area measurements based on hemispheric photographs and leaf-litter collection in a deciduous forest during autumn leaf-fall,” Agric. For. Meteorol. 45, 325–345 (1989).
[CrossRef]

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.

K. Fassnacht, S. T. Gower, J. M. Norman, R. M. McMurtrie, “A comparison of optical and direct methods for estimating foliage surface area index in forests,” Agric. For. Meteorol. 71, 183–207 (1994).
[CrossRef]

S. T. Gower, J. M. Norman, “Rapid estimation of leaf area index in forests using the LI-COR LAI-2000,” Ecology 72, 1896–1900 (1991).
[CrossRef]

E. E. Miller, J. M. Norman, “A sunfleck theory for plant canopies. I: Lengths of sunlit segments along a transect,” Agron. J. 63, 735–738 (1971).
[CrossRef]

Penner, M.

G. Deblonde, M. Penner, A. Royer, “Measuring leaf area index with the LI-COR LAI-2000 in pine stands,” Ecology 75, 1507–1511 (1994).
[CrossRef]

Peterson, D. L.

M. A. Spanner, L. L. Pierce, D. L. Peterson, S. W. Running, “Remote sensing temperate coniferous forest leaf area index: the influence of canopy closure, understory and background reflectance,” Int. J. Remote Sensing 11, 95–111 (1990).
[CrossRef]

M. A. Spanner, L. L. Pierce, S. W. Running, D. L. Peterson, “The seasonal trends of AVHRR data of temperate coniferous forests: relationship with leaf area index,” Remote Sensing Environ. 33, 97–112 (1990).
[CrossRef]

Pierce, L. L.

M. A. Spanner, L. L. Pierce, S. W. Running, D. L. Peterson, “The seasonal trends of AVHRR data of temperate coniferous forests: relationship with leaf area index,” Remote Sensing Environ. 33, 97–112 (1990).
[CrossRef]

M. A. Spanner, L. L. Pierce, D. L. Peterson, S. W. Running, “Remote sensing temperate coniferous forest leaf area index: the influence of canopy closure, understory and background reflectance,” Int. J. Remote Sensing 11, 95–111 (1990).
[CrossRef]

Royer, A.

G. Deblonde, M. Penner, A. Royer, “Measuring leaf area index with the LI-COR LAI-2000 in pine stands,” Ecology 75, 1507–1511 (1994).
[CrossRef]

B. Leblon, H. Granberg, C. Ansseau, A. Royer, “A semi-empirical model to estimate the biomass production of forest canopies from spectral variables part 1: relationship between spectral variables and light interception efficiency,” Remote Sensing Rev. 7, 109–125 (1993).
[CrossRef]

Running, S. W.

M. A. Spanner, L. L. Pierce, D. L. Peterson, S. W. Running, “Remote sensing temperate coniferous forest leaf area index: the influence of canopy closure, understory and background reflectance,” Int. J. Remote Sensing 11, 95–111 (1990).
[CrossRef]

M. A. Spanner, L. L. Pierce, S. W. Running, D. L. Peterson, “The seasonal trends of AVHRR data of temperate coniferous forests: relationship with leaf area index,” Remote Sensing Environ. 33, 97–112 (1990).
[CrossRef]

Saeki, T.

M. Monsi, T. Saeki, “Uber den Lichtfaktor in den Pflanzeng-esellschaften und Seine Bedeutung fur die Stoffproduktion,” Jpn. J. Bot. 14, 22–52 (1953).

Shaw, R. H.

H. H. Neumann, G. den Hartog, R. H. Shaw, “Leaf area measurements based on hemispheric photographs and leaf-litter collection in a deciduous forest during autumn leaf-fall,” Agric. For. Meteorol. 45, 325–345 (1989).
[CrossRef]

Smith, N. J.

N. J. Smith, “Estimating leaf area index and light extinction coefficients in stands of Douglas-fir,” Can. J. For. Res. 30, 317–321 (1993).
[CrossRef]

Spanner, M. A.

M. A. Spanner, L. L. Pierce, D. L. Peterson, S. W. Running, “Remote sensing temperate coniferous forest leaf area index: the influence of canopy closure, understory and background reflectance,” Int. J. Remote Sensing 11, 95–111 (1990).
[CrossRef]

M. A. Spanner, L. L. Pierce, S. W. Running, D. L. Peterson, “The seasonal trends of AVHRR data of temperate coniferous forests: relationship with leaf area index,” Remote Sensing Environ. 33, 97–112 (1990).
[CrossRef]

Waring, R. H.

H. L. Gholz, F. K. Fitz, R. H. Waring, “Leaf area differences associated with old-growth forest communities in the western Oregon Cascades,” Can. J. For. Res. 6, 49–57 (1976).
[CrossRef]

Welles, J.

J. Welles, “Some indirect methods of estimating canopy structure,” in Instrumentation for Studying Vegetation Canopies for Remote Sensing in Optical and Thermal Infrared Regions, J. Norman, N. Geol, eds. (Harwood, London, 1990), pp. 31–43.

Xiang, Y.

A. R. G. Lang, Y. Xiang, “Estimation of leaf area index from transmission of direct sunlight in discontinuous canopies,” Agric. For. Meteorol. 37, 229–243 (1986).
[CrossRef]

Agric. For. Meteorol.

J. M. Chen, T. A. Black, “Foliage area and architecture of plant canopies from sunfleck size distributions,” Agric. For. Meteorol. 60, 249–266 (1992).
[CrossRef]

H. H. Neumann, G. den Hartog, R. H. Shaw, “Leaf area measurements based on hemispheric photographs and leaf-litter collection in a deciduous forest during autumn leaf-fall,” Agric. For. Meteorol. 45, 325–345 (1989).
[CrossRef]

A. R. G. Lang, Y. Xiang, “Estimation of leaf area index from transmission of direct sunlight in discontinuous canopies,” Agric. For. Meteorol. 37, 229–243 (1986).
[CrossRef]

K. Fassnacht, S. T. Gower, J. M. Norman, R. M. McMurtrie, “A comparison of optical and direct methods for estimating foliage surface area index in forests,” Agric. For. Meteorol. 71, 183–207 (1994).
[CrossRef]

J. M. Chen, T. A. Black, R. S. Adams, “Evaluation of hemispherical photography for determining plant area index and geometry of a forest stand,” Agric. For. Meteorol. 56, 129–143 (1991).
[CrossRef]

A. R. G. Lang, “Simplified estimate of leaf area index from transmittance of the Sun’s beam,” Agric. For. Meteorol. 41, 179–186 (1987).
[CrossRef]

A. R. G. Lang, R. E. McMurtrie, M. L. Benson, “Validity of surface area indices of Pinus radiata estimated from transmittance of the Sun’s beam,” Agric. For. Meteorol. 57, 157–170 (1991).
[CrossRef]

Agric. For. Meterol.

A. R. G. Lang, “Application of some of Cauchy’s theorems to estimation of surface areas of leaves, needles and branches of plants, and light transmittance,” Agric. For. Meterol. 55, 191–212 (1991).
[CrossRef]

Agric. Meteorol.

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

Agron. J.

E. E. Miller, J. M. Norman, “A sunfleck theory for plant canopies. I: Lengths of sunlit segments along a transect,” Agron. J. 63, 735–738 (1971).
[CrossRef]

Aust. J. Bot.

J. B. Miller, “A formula for average foliage density,” Aust. J. Bot. 15, 141–144 (1967).
[CrossRef]

Can. J. For. Res.

H. L. Gholz, F. K. Fitz, R. H. Waring, “Leaf area differences associated with old-growth forest communities in the western Oregon Cascades,” Can. J. For. Res. 6, 49–57 (1976).
[CrossRef]

N. J. Smith, “Estimating leaf area index and light extinction coefficients in stands of Douglas-fir,” Can. J. For. Res. 30, 317–321 (1993).
[CrossRef]

Ecology

G. Deblonde, M. Penner, A. Royer, “Measuring leaf area index with the LI-COR LAI-2000 in pine stands,” Ecology 75, 1507–1511 (1994).
[CrossRef]

S. T. Gower, J. M. Norman, “Rapid estimation of leaf area index in forests using the LI-COR LAI-2000,” Ecology 72, 1896–1900 (1991).
[CrossRef]

Int. J. Remote Sensing

M. A. Spanner, L. L. Pierce, D. L. Peterson, S. W. Running, “Remote sensing temperate coniferous forest leaf area index: the influence of canopy closure, understory and background reflectance,” Int. J. Remote Sensing 11, 95–111 (1990).
[CrossRef]

Jpn. J. Bot.

M. Monsi, T. Saeki, “Uber den Lichtfaktor in den Pflanzeng-esellschaften und Seine Bedeutung fur die Stoffproduktion,” Jpn. J. Bot. 14, 22–52 (1953).

Plant Cell Environ.

J. M. Chen, T. A. Black, “Defining leaf area index for non-flat leaves,” Plant Cell Environ. 15, 421–429 (1992).
[CrossRef]

Remote Sensing Environ.

M. A. Spanner, L. L. Pierce, S. W. Running, D. L. Peterson, “The seasonal trends of AVHRR data of temperate coniferous forests: relationship with leaf area index,” Remote Sensing Environ. 33, 97–112 (1990).
[CrossRef]

Remote Sensing Rev.

B. Leblon, H. Granberg, C. Ansseau, A. Royer, “A semi-empirical model to estimate the biomass production of forest canopies from spectral variables part 1: relationship between spectral variables and light interception efficiency,” Remote Sensing Rev. 7, 109–125 (1993).
[CrossRef]

Other

J. Welles, “Some indirect methods of estimating canopy structure,” in Instrumentation for Studying Vegetation Canopies for Remote Sensing in Optical and Thermal Infrared Regions, J. Norman, N. Geol, eds. (Harwood, London, 1990), pp. 31–43.

LAI-2000 PCA Operating Manual (Li-Cor, Inc., Lincoln, Neb., 1991).

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Figures (11)

Fig. 1
Fig. 1

Schematic canopy gap-size distribution measured on a transect beneath the canopy, where F(λ) is the fraction of the transect that is occupied by gaps larger than λ. Gaps λi are sorted in a descending order from left to right (top), and F(λ) is formed as the accumulated gap fraction starting from the largest gap λ1.

Fig. 2
Fig. 2

Gap-size distribution and redistribution after a gap-removal process, where a1 is a measured gap-size distribution Fm(λ), b1 is the first estimate of F(λ) for a random canopy, a2 is the redistribution [Fmr(λ)] after two large gaps are removed, and b2 is the second estimate of F(λ). In finding the final Fmr(λ) for the calculation in Eq. (16), the removal of gaps appearing at probabilities in excess of F(λ) is repeated until Fmr(λ) is brought to the closest agreement with F(λ).

Fig. 3
Fig. 3

Imaginary plant canopy with gaps inserted in a random canopy. These inserted gaps mixing with gaps in the original canopy can be found through gap-size analysis.

Fig. 4
Fig. 4

Portion of instantaneous PPFD measured near noon on 16 September 1993 on a transect in a red pine stand. The measurement interval is 10.3 mm.

Fig. 5
Fig. 5

Two gap-size distributions measured in a red pine stand (a) at a solar zenith angle θ = 44.0°, (b) at θ = 58.4°. A measured distribution Fm(λ) is denoted by ■, the final distribution of Fmr(λ) is denoted by ●, and F(λ) is shown as a smooth curve.

Fig. 6
Fig. 6

Gap-size distributions measured in a jack pine stand at θ = 67.6°. A measured distribution Fm(λ) is denoted by ■, the final distribution of Fmr(λ) is denoted by ●, and F(λ) is shown as a smooth curve.

Fig. 7
Fig. 7

Element-clumping index becomes asymptotic at large input element widths for both jack pine and red pine stands. The destructively measured widths were 59 mm and 130 mm for jack pine and red pine shoots, respectively.

Fig. 8
Fig. 8

Effective LAI (Le) measured on transects in a jack pine and a red pine stand with the Li-Cor LAI-2000 Plant Canopy Analyzer.

Fig. 9
Fig. 9

Comparisons of indirect and direct measurements of plant-area index. The indirect measurements were obtained with the LAI-2000 Plant Canopy Analyzer and the Portram, and the direct measurements were obtained through destructive sampling.

Fig. 10
Fig. 10

Sunlight distribution in a sunfleck resulting from a canopy gap of size λ, where PD is the level of direct PPFD above the canopy.

Fig. 11
Fig. 11

Projection of a sphere representing a conifer shoot on a horizontal surface.

Tables (1)

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Table 1 Summary of TRAC Measurements

Equations (30)

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F ( λ ) = ( 1 + ρ w λ ) exp [ ρ ( σ + w λ ) ] ,
F ( λ ) = ( 1 + L λ W ) exp [ L ( 1 + λ W ) ] ,
W = σ / w .
W = c w ,
L p = G ( θ ) L E cos θ ,
W p = W ¯ cos θ p ,
cos θ p = ( cos 2 θ + tan 2 Δ β 1 + tan 2 Δ β ) 1 / 2 ,
F ( λ ) = ( 1 + L p λ W p ) exp [ L p ( 1 + λ W p ) ] .
P ( θ ) = exp [ G ( θ ) Ω E L E / cos θ ] ,
Ω E L E = cos θ G ( θ ) ln [ F m ( 0 ) ] .
L E = cos θ G ( θ ) ln [ F ( 0 ) ] ,
Ω E = ln [ F m ( 0 ) ] ln [ F ( 0 ) ] .
Δ g = F m ( 0 ) F mr ( 0 ) .
L Ec = cos θ G ( θ ) ln [ F mr ( 0 ) ] .
L E = cos θ ( 1 + Δ g ) G ( θ ) ln [ F mr ( 0 ) ] .
Ω E = ( 1 + Δ g ) ln [ F m ( 0 ) ] ln [ F mr ( 0 ) ] .
Ω = Ω E / γ E .
P ( θ ) = exp [ G ( θ ) Ω L / cos θ ] ,
γ E = L / L E ,
L e = Ω L .
γ E = A L / A s ,
S 1 = λ P D ,
S 2 = 0 λ s P ( x ) d x
λ = 1 P D 0 λ s P ( x ) d x .
A B ¯ = 2 ( x 1 2 + y 1 2 ) 1 / 2 ,
x 2 ( D 2 cos θ ) 2 + y 2 ( D 2 ) 2 = 1 ,
y = x tan Δ β .
A B ¯ = D ( 1 + tan 2 Δ β cos 2 θ + tan 2 Δ β ) 1 / 2 .
cos θ p = ( cos 2 θ + tan 2 Δ β 1 + tan 2 Δ β ) 1 / 2 .
W p = W sin Δ β .

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