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

Plant Canopy Vegetation Canopy Principal Plane Leaf Canopy Canopy Reflectance## 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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## References

- Bobrov MS (1940) On the physical interpretation of the phase curves of Saturn’s rings. Astron J 17(6): 1–8 (in Russian)Google Scholar
- Bobrov MS (1961) Generalization of the theory of the shadowing effect on Saturn’s rings for unequal dimensions. Astron J 38(4): 669–680 (in Russian)Google Scholar
- Campbell GS (1986) Extinction coefficients for radiation in plant canopies calculated using an ellipsoidal inclination angle distribution. Agric For Meteorol 36:317–321CrossRefGoogle Scholar
- De Wit CT (1965) Photosynthesis of leaf canopies. Agric Res Rep 663:57, WageningenGoogle Scholar
- Durnin J, Miceli JJJr, Eberly JH (1987) Diffraction-free beams. Phys Rev Lett 58:1499–1501PubMedCrossRefGoogle Scholar
- Franklin FA, Cook AF (1965) Optical properties of Saturn’s rings. II. Two-color phase curves of the two bright rings. Astron J 70:704–720CrossRefGoogle Scholar
- Gerstl SAW, Simmer C, Powers BJ (1986) The canopy hot spot as crop identifier. In: Damen MCJ et al. (eds) Remote Sens Res Dev Environ Mgmt Proc 7th Int Symp Enschede, The Netherlands, ISPRS, 26(1):261–263Google Scholar
- Goel NS, Strebel DE (1983) Inversion of vegetation canopy reflectance models for estimating agronomic variables, I. Problem definition and initial results using the Suits model. Remote Sens Environ 13:487–507CrossRefGoogle Scholar
- Hapke BW (1963) A theoretical photometric function for the lunar surface. J Geophys Res 68:4571–4586Google Scholar
- Irvine WM (1966) The shadowing effect in diffuse reflection. J Geophys Res 71:2931–2937Google Scholar
- Kanevskii VA, Ross JK (1983) Effect of the architecture of a conifer on directional distribution of its reflectance: A Monte-Carlo simulation. Earth Res Space 4:100–102 (in Russian, English translation in Sov J Remote Sens 1985, 3(4):659–663)Google Scholar
- Kanevskii VA, Ryazantsev VF, Movchan YaI et al. (1986) Laser systems with diversity receivers for remote sensing of phytometric vegetation parameters. Earth Res Space 1:84–87 (in Russian, to be translated in Sov J Remote Sens)Google Scholar
- Kuusk A (1983) The hot spot effect of a uniform vegetative cover. Earth Res Space 4:90–9.Google Scholar
- Kuusk A The hot spot effect of a uniform vegetative cover (in Russian, English translation in Sov J Remote Sens 1985, 3(4):645–658)Google Scholar
- Kuusk A (1986) Photographic methods for studying the reflectance of vegetation cover. Earth Res Space 4:113–118.Google Scholar
- Kuusk A (1986) Photographic methods for studying the reflectance of vegetation cover. (in Russian, English translation in Sov J Remote Sens 1990, 6(4):672–681)Google Scholar
- Kuusk A (1987) Direct sunlight scattering by the crown of a tree. Earth Res Space 2:106–111 (in Russian, to be translated in Sov J Remote Sens)Google Scholar
- Kuusk A (1988) Brightness of the aureole around the laser beam in the vegetable cover. Earth Res Space 5:87–93 (in Russian, to be translated in Sov J Remote Sens)Google Scholar
- Levin BR (1969) The theoretical basis for statistical radiotechnique. Vol. 1. Sov Radio, Moscow 748 (in Russian)Google Scholar
- Lumme K, Bowell E (1981) Radiative transfer in the surfaces of atmosphereless bodies. I. Theory. Astron J 86:1694–1704Google Scholar
- Nilson T (1971) A theoretical analysis of the frequency of gaps in plant stands. Agric Meteorol 8:25–38CrossRefGoogle Scholar
- Nilson T (1977) A theory of radiation penetration into non-homogeneous plant canopies. The penetration of solar radiation into plant canopies. Acad Sci ESSR Rep, Tartu, pp 5–70 (in Russian)Google Scholar
- Nilson T (1990) A timber reflectance model. Earth Res Space 3:63–72 (in Russian, to be translated in Sov J Remote Sens)Google Scholar
- Nilson T, Kuusk A (1989) A reflectance model for the homogeneous plant canopy and its inversion. Remote Sens Environ 27:157–167CrossRefGoogle Scholar
- Ross J (1975) The radiation regime and architecture of plant stands. Gidrometeoizdat. Leningrad, 342 pp (in Russian, English translation 1981, Junk Publ, The Hague)Google Scholar
- Ross JK, Marshak AL (1987) Monte-Carlo determination of spectral radiance of the vegetative cover as a function of illumination conditions. Earth Res 2:96–105 (in Russian, to be translated in Sov J Remote Sens)Google Scholar
- Ross JK, Nilson TA (1968) A mathematical model of radiation regime of the plant cover. Actinometry and atmospheric optics. Tallinn, Valgus, pp 263–281 (in Russian)Google Scholar
- Roumjantsev VA (ed) (1987) Laser remote sensing of vegetation. Leningrad, Acad Sci USSR, The Main Astronomical Observatory, 168 pp (in Russian)Google Scholar
- Seeliger H (1887) Zur Theorie der Beleuchtung der grossen Planeten insbesondere des Saturn. Abh Bayer Akad Wiss Math-Phys Kl II, 16:403–516Google Scholar
- Seeliger H (1895) Theorie der Beleuchtung staubförmiger kosmischer Massen insbesondere des Saturnringes. Abh Bayer Akad Wiss Math-Naturwiss Kl II, 18:1–72Google Scholar
- Strahler AH, Li X (1985) Geometric-optical bidirectional reflectance modeling. Int Geosci Remote Sens Symp IGARSS’ 85 Amherst, Mass, Oct 7–9, 2:882–883Google Scholar
- Vanderbilt VC, Bauer ME, Silva LF (1979) Prediction of solar irradiance distribution in a wheat canopy using a laser technique. Agric Meteorol 20:147–160CrossRefGoogle Scholar