Problems
277
Irons, J., G.S. Campbell, J.M. Norman, D.W. Graham, and W.K. Kovalick
(1 992) Prediction and measurement of soil bidirectional reflectance.
IEEE Transactions of Geoscience and Remote Sensing. 30:249-260.
Kuusk, A. (1991) The hot spot effect in plant canopy reflectance.
In Photon-Vegetation Interactions: Applications in Optical Remote Sensing and Plant Ecology. Eds. R.B. Myneni and J. Ross.
Springer-Verlag, Berlin. pp. 13 9-1 59.
Kuusk, A. (1995) A fast, invertible canopy reflectance model. Remote
Sensing of Environment. 5 1 :342-350.
Monteith, J.L. and M.H. Unsworth. (1990) Principles of Environmental
Physics. Edward Arnold Publishers, London. 29 1 pp.
Myneni, R.B. and J. Ross. (eds.) (1991) Photon-Vegetation Interactions: Applications in Optical Remote Sensing and Plant Ecology.
Springer-Verlag, Berlin. 565 pp.
Norman, J.M. (1992) Scaling processes between leaf and canopy levels. In
Scaling Physiological Processes: Leaf to Globe. Eds. J.R. Ehleringer
and C.B. Field. Academic Press, Inc. San Diego, CA pp. 41-76.
Norman, J.M. and G.S. Campbell (1989) Canopy structure. In Plant Physiological Ecology: Field Methods and Instrumentation. Eds. R.W.
Pearcy, J. Ehleringer, H.A. Mooney, and P.W. Rundel. Chapman
and Hall, N.Y. pp. 301-325.
Norman, J.M. and J.M. Welles (1983) Radiative transfer in an array of
canopies. Agronomy Journal 75:48 1-488.
Walthall, C.L., J.M. Norman, J.M. Welles, G.S. Campbell, and B.L. Blad
(1985) Simple equation to approximate the bidirectional reflectance
from vegetative canopies and bare soil surfaces. Applied Optics.
24:383-387.
Welles, J.M. (1990) Some indirect methods for determining canopy
structure. Remote Sensing Reviews. 5:3 1 4 3 .
Problems
15.1. A canopy with a spherical leaf angle distribution has a total leaf
area index of three. Find the flux density of PAR on sunlit and on
shaded leaves at the bottom of the canopy, and the fraction of the
leaves which are sunlit and shaded. Assume a clear sky with a solar
zenith angle of 30".
15.2. Find the daily fractional transmission of PAR, NIR, and total solar
radiation by a canopy with leaf area index, L, = 2. Assume that
the leaf angle distribution is approximated by an ellipsoidal angle
distribution with x = 2.
15.3. If the ratio of red to far red radiation at the top of the canopy in
problem 15.1 is 1, what is the ratio at the bottom of the canopy.
Assume
= 0.8 and c q , , , d = 0.2.
277
Irons, J., G.S. Campbell, J.M. Norman, D.W. Graham, and W.K. Kovalick
(1 992) Prediction and measurement of soil bidirectional reflectance.
IEEE Transactions of Geoscience and Remote Sensing. 30:249-260.
Kuusk, A. (1991) The hot spot effect in plant canopy reflectance.
In Photon-Vegetation Interactions: Applications in Optical Remote Sensing and Plant Ecology. Eds. R.B. Myneni and J. Ross.
Springer-Verlag, Berlin. pp. 13 9-1 59.
Kuusk, A. (1995) A fast, invertible canopy reflectance model. Remote
Sensing of Environment. 5 1 :342-350.
Monteith, J.L. and M.H. Unsworth. (1990) Principles of Environmental
Physics. Edward Arnold Publishers, London. 29 1 pp.
Myneni, R.B. and J. Ross. (eds.) (1991) Photon-Vegetation Interactions: Applications in Optical Remote Sensing and Plant Ecology.
Springer-Verlag, Berlin. 565 pp.
Norman, J.M. (1992) Scaling processes between leaf and canopy levels. In
Scaling Physiological Processes: Leaf to Globe. Eds. J.R. Ehleringer
and C.B. Field. Academic Press, Inc. San Diego, CA pp. 41-76.
Norman, J.M. and G.S. Campbell (1989) Canopy structure. In Plant Physiological Ecology: Field Methods and Instrumentation. Eds. R.W.
Pearcy, J. Ehleringer, H.A. Mooney, and P.W. Rundel. Chapman
and Hall, N.Y. pp. 301-325.
Norman, J.M. and J.M. Welles (1983) Radiative transfer in an array of
canopies. Agronomy Journal 75:48 1-488.
Walthall, C.L., J.M. Norman, J.M. Welles, G.S. Campbell, and B.L. Blad
(1985) Simple equation to approximate the bidirectional reflectance
from vegetative canopies and bare soil surfaces. Applied Optics.
24:383-387.
Welles, J.M. (1990) Some indirect methods for determining canopy
structure. Remote Sensing Reviews. 5:3 1 4 3 .
Problems
15.1. A canopy with a spherical leaf angle distribution has a total leaf
area index of three. Find the flux density of PAR on sunlit and on
shaded leaves at the bottom of the canopy, and the fraction of the
leaves which are sunlit and shaded. Assume a clear sky with a solar
zenith angle of 30".
15.2. Find the daily fractional transmission of PAR, NIR, and total solar
radiation by a canopy with leaf area index, L, = 2. Assume that
the leaf angle distribution is approximated by an ellipsoidal angle
distribution with x = 2.
15.3. If the ratio of red to far red radiation at the top of the canopy in
problem 15.1 is 1, what is the ratio at the bottom of the canopy.
Assume
= 0.8 and c q , , , d = 0.2.