Photon-Vegetation Interactions pp 139-159 | Cite as

# The Hot Spot Effect in Plant Canopy Reflectance

## Abstract

The diffuse reflection of radiation from different media has a sharp maximum in the backward direction. This phenomenon is known as heiligenschein in meteorology, the opposition effect in astronomy, and the hot spot effect in aerial photography and optical remote sensing. These three effects are caused by the same physical mechanisms, and hence are essentially equivalent. If the particles of the reflecting/scattering medium cast shadows, then the shadows cannot be seen looking along the incident rays since they are screened by the particles themselves. With a change in the view direction we can see some of the shadows. Therefore, the mean radiance of reflection decreases. Generally, the radiance of the reflecting medium will decrease with increasing angle α between the view direction and incident rays because of the decreased probability of seeing illuminated particles.

### Keywords

Covariance Photosynthesis Autocorrelation Refraction Azimuth### Symbols

- a(z, Ω̱)
gap probability (penetration function)

- BDGP
BiDirectional Gap Probability

- I(Ω̱)
radiance in the direction Ω̱

- C
_{HS}(z, α) hot spot factor

- d
_{L} leaf diameter

- g
_{L}(θ_{L})/2π distribution density of leaf normals

- G(Ω̱)
Ross-Nilson G-function (the mean projection of a unit foliage area)

- H
canopy height

- F
_{0} flux density of direct solar radiation

- k
leaf hair index

- LAI
Leaf Area Index

- L
_{0} leaf area index (LAI)

- n
refraction index

- p(z, Ω̱
_{0}, Ω̱) bidirectional gap probability (BDGP)

- r
aureole radius

- r
_{LD} reflection coefficient of leaves

- R(θ, φ)
canopy bidirectional reflectance factor

- s
_{L} mean chord length of leaves

- t
_{LD} transmission coefficient of leaves

- u
_{L}(z) leaf area density

- α
angle between vectors − Ω̱

_{0}and Ω̱- Γ(Ω̱
_{0}→ Ω̱) area scattering phase function

- ξ(x, y, z)
leaf indicator function

- Ω̱(θ, φ)
unit vector directed to the observer

- Ω̱
_{0}(θ_{0,}0) unit vector directed to the Sun

- θ
polar angle of the observation direction

- θ
_{0} polar angle of the Sun

- φ
azimuth angle relative to the Sun’s azimuth

- Y
_{ξ(Ω̱0), ξ(Ω̱)}(S) cross-correlation coefficient of ξ(Ω̱

_{0}) and ξ(Ω̱)

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