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Photon Transport in Discontinuous Canopies: A Weighted Random Approach

  • Chapter
Photon-Vegetation Interactions

Abstract

In its most general sense, remote sensing is the science of deducing information about a surface or medium by measuring radiation that has been emitted or scattered by that surface or medium. Specifically, remote sensing usually implies measurements of the earth. With the advent of sensors aboard aircraft and satellites, the potential to acquire information about the earth’s surface and resources increased on an unprecedented scale. The realization of that potential involves building the necessary links between surface characteristics and emanating radiation. This chapter contains a discussion of the relationship between the structure of vegetation and the measured brightness of that vegetation as viewed from above. In particular, how does the angle of view and the angle of illumination affect the brightness of a vegetative canopy?

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Abbreviations

Aj :

albedo of the jth layer in the random model

As :

soil reflectance

Ci :

fraction of leaves that are sunlit at ith grid point

Dj :

downward diffuse irradiance above the jth layer in the random model

Fd(r⃗i):

downward diffuse irradiance at the ith grid point

Ft :

total incident irradiance on the horizontal at the top of the canopy

Fu(r⃗i):

upward diffuse irradiance at the ith grid point

G(Ω̱):

canopy extinction coefficient: the fraction of area projected toward (Ω̱)

Hmt, Hmb :

fraction of mth ellipsoid chopped in the top or bottom half

I(r⃗i,Ω̱):

scene radiance from the ith grid point. Scene radiance is either from soil or foliage

I(r⃗i,Ω̱, θL):

total radiance of the foliage in angle class (α, β) at the ith grid point

I(Ω̱):

radiance leaving the canopy in direction (θV, ϕv)

Ib(r⃗i,Ω̱, θL):

Radiance from foliage at ith point due to direct beam

Id(r⃗i,Ω̱, θL):

radiance from foliage in angle class α at ith point due to diffuse irradiance

L:

leaf area index

ΔL:

layer LAI for random model

M:

path length through the canopy

ΔM:

grid point spacing

Nb :

number of replicated boxes involved in a particular ray’s path

Ns :

number of subcanopies in one box

Ng :

number of grid points that lie within any subcanopy

T:

diffuse noninterceptance for a random model layer

T̛:

beam noninterceptance for a random model layer

Tu(r⃗i):

diffuse noninterceptance, upper hemisphere, for the ith grid point

Tl(r⃗i):

diffuse noninterceptance, lower hemisphere, for the ith grid point

Uj :

upward diffuse irradiance above the jth layer in the random model

fb :

fraction of incident total irradiance that is direct beam

gL(θL):

fraction of leaf area at leaf angle class (θL)

p(r⃗i,Ω̱):

probability of a ray from direction (Ω̱) reaching point (r⃗) without being intercepted

r⃗1, r⃗2 :

entry and exit points for a box

r⃗3, r⃗4 :

entry and exit points for a ellipsoid

r̄L :

weighted leaf reflectance for a layer of leaves

r:

random model layer reflectance

rx, ry, rz :

radii in the x, y, and z directions of an ellipsoid

rL :

leaf reflectance

Sj, S̛j :

source terms up and down for the random model above the jth layer

t̄L :

weighted leaf transmittance for a layer of leaves

t:

random model layer transmittance

tL :

leaf transmittance

uL :

foliage area density (m-1): leaf area per canopy volume

ϕO :

solar azimuth angle

ϕL :

leaf azimuth angle

ϕ:

view azimuth angle

ω̛L :

leaf transmittance or reflectance, depending on view and sun angles

ρ(θ — ϕO :

soil bidirectional reflectance function for view angle θ and azimuth angle ϕ

ρ (Ω̱, θO):

bidirectional reflectance distribution function

θO :

solar zenith angle

θL :

leaf tilt angle

θ:

view zenith angle

Ω̱L · Ω̱:

cosine of the angle between the leaf normal and the viewer

Ω̱L · Ω̱O :

cosine of the angle between the leaf normal and the sun

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Authors
  1. J. M. Welles
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  2. J. M. Norman
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Editor information

Editors and Affiliations

  1. Hydrological Sciences Branch, NASA-Goddard Space Flight Center, Mail Code 974, 20771, Greenbelt, MD, USA

    Ranga B. Myneni

  2. Institute of Astrophysics and Atmospheric Physics, Estonian Academy of Sciences, Tartu, 202444, Tõravere, Estonia

    Juhan Ross

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© 1991 Springer-Verlag Berlin Heidelberg

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Welles, J.M., Norman, J.M. (1991). Photon Transport in Discontinuous Canopies: A Weighted Random Approach. In: Myneni, R.B., Ross, J. (eds) Photon-Vegetation Interactions. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75389-3_12

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  • DOI: https://doi.org/10.1007/978-3-642-75389-3_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-75391-6

  • Online ISBN: 978-3-642-75389-3

  • eBook Packages: Springer Book Archive

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