Graziani F. (editor) Computational Methods in Transport

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Reﬂectance Modeling with Turbid Medium Radiative Transfer 203

Fig. 24. Predicted green/yellow/red cherry distributions. (Field 408 Block 4)

204 Barry D. Ganapol

550nm

1234

0.025

0.026

0.027

0.028

0.029

0.030

0.031

0.032

680nm

1234

0.045

0.050

0.055

0.060

800nm

1234567

0.0115

0.0120

0.0125

0.0130

Degree of Linear

Polarization (Dp0)

at TOC

LAI = 2

Fig. 25. Canopy reﬂectance for scene with a random LAD

Reﬂectance Modeling with Turbid Medium Radiative Transfer 205

12345

1234

1234567

= 0.1 Soil

= 0.3 T-72

= 1

Reflectance/I

Fig. 26. T-72 tank in the clear

206 Barry D. Ganapol

1234567

Reflectance/I

1234567

Dp0

Contour Graph 3

X Data

Y Data

Contour Graph 4

Y Data

X Data

Y Data

Contour Graph 2

Contour Graph 7

Contour Graph 6

Contour Graph 5

Fig. 27a. T-72 under foiliage of LAI = 4

Reﬂectance Modeling with Turbid Medium Radiative Transfer 207

1234567

Contour Graph 3

X Data

Y Data

X Data

Contour Graph 10

X Data

Y Data

X Data

Contour Graph 9

Y Data

Contour Graph 2

X Data

Y Data

Contour Graph 1

X Data

Y Data

Contour Graph 8

Reflectance/I Dp0

Fig. 27b. T-72 under foiliage of LAI = 6

208 Barry D. Ganapol

0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48

0.040 0.041 0.042 0.043 0.044 0.045 0.046 0.047

0.086 0.088 0.090 0.090 0.094 0.096 0.098 0.100 0.102 0.104

Dp0

0.024

0.026

0.028

0.030

0.032

0.034

0.040

0.045

0.050

0.055

0.060

0.065

0.0105

0.0110

0.0115

0.0120

0.0125

0.0130

0.0135

Fig. 28a. Dp0 versus R

for original scene

Reﬂectance Modeling with Turbid Medium Radiative Transfer 209

0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50

0.00

0.02

0.04

0.06

0.08

0.10

0.032 0.034 0.036 0.038 0.040 0.042 0.044 0.046 0.048 0.050 0.052

0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110

T-72

Dp0

0.12

0.0

0.1

0.2

0.3

0.4

0.5

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.6

Fig. 28b. Dp0 versus R

for with T-72 in an LAI = 6 canopy

210 Barry D. Ganapol

References

1. B. Hapke and E. Wells, J. Geophys Res., 86(B4), 3055–3060, (1981).

2. M. Minnaert, Astrophys. Jour., 93, 403–410 (1941).

3. C. Walthal, et. al., Appl. Opt., 24(4), 383–387 (1985).

4. J. Ross, The Radiation Regime and Architecture of Plant Stands, W. Junk, The

Hague, Netherlands (1981).

5. B. Ganapol ,et. al., Rem. Sens. Environ. 70:153–166 (1999).

6. B. Ganapol, et. al., Rem. Sens. Environ. 63:182–193 (1998).

7. C. Siewert, Nucl. Sci. & Eng., 69, 156–160 (1979).

8. B. Hosgood, et. al. European Commission, Joint Research Centre, Institute for

Remote Sensing Applications, Report EUR 16095 EN (1995).

9. L. Grant, C. Daughtry., and V. Vanderbilt., Envir. Exp. Bot. 27,139–145

(1987).

10. E. Larsen and W.F. Miller, Nucl. Sci. & Eng., 73, 76–83 (1980).

11. F. Press, Numerical Recipes, Cambridge Press, (2001).

12. W. Abbott and E. Allen, Nucl. Sci. & Eng., 108, 278–288 (1991).

Rayspread: A Virtual Laboratory for Rapid

BRF Simulations Over 3-D Plant Canopies

Jean-Luc Widlowski, Thomas Lavergne, Bernard Pinty, Michel Verstraete

and Nadine Gobron

Institute for Environment and Sustainability, Joint Research Centre, TP. 440, Via

E. Fermi 1, 21020 Ispra (VA), Italy

Jean-Luc.Widlowski@jrc.it

Accurate knowledge of the spatial (and temporal) variability of the biosphere’s

characteristics is useful not only to address critical scientiﬁc issues (climate

change, environmental degradation, biodiversity preservation, etc.) but also

to provide appropriate initial state and boundary conditions for general cir-

culation or landscape succession models. In particular, the 3-D structure of

vegetation emerged as a crucial player in processes aﬀecting carbon seques-

tration, landscape dynamics and the exchanges of energy, water and trace

gases with the atmosphere e.g., [BWG04]. The growth and development of

plant architecture, in turn, are primarily conditioned by eﬀective interception

of solar radiation that provides the necessary energy for photosynthesis and

other physiological processes [VB86].

In this context, space borne, optical remote sensing provides a conve-

nient, eﬃcient and cost-eﬀective way to acquire information on the state of

terrestrial vegetation, over large areas and at spatial resolutions adequate

to address many key ecological and climate change related issues. The physi-

cal interpretation of such remote sensing measurements, however, can provide

reliable quantitative information only on the relevant state variables that con-

trol the interactions of the radiation ﬁeld with all intervening media from the

light source to the detector e.g., [VPM96]. The simulation of such processes,

using physically based radiative transfer (RT) models, thus allows to esti-

mate the most probable value of a remote sensing measurement, given that

the values of all state variables in the model, the conditions of observation

and the nature and role of all relevant radiative processes in the system are

speciﬁed in advance. This modeling approach is known as the direct or for-

ward mode, and can be used, for example, to determine which state variable

in a given model is primarily responsible for the observed signal variabil-

ity under speciﬁc condition of observation and illumination. It also provides

ample testing ground for the intercomparison of diﬀerent radiation transfer

models [PWT04].

The interpretation of remote sensing data requires applying the same

model in inverse mode, or more speciﬁcally inverting the model against the

data set, in order to retrieve the state variables of interest [GS83, KKP00].

At the Earth’s surface, the spectral, directional and polarization signatures

212 J.-L. Widlowski et al.

of the various scattering elements, together with their number, geometry and

spatial distribution, are responsible for the radiative characteristics of the re-

ﬂected electromagnetic signal in the optical part of the solar spectrum. Fur-

thermore, the conditions of observation and illumination, as well as the state

of the atmosphere at the time of measurement, may signiﬁcantly alter the

reﬂectance values of terrestrial surfaces. State of the art inversion techniques

involve the pre-computing of reﬂectance ﬁelds (and/or related quantities) for

a pre-selected ensemble of likely canopy structures and under a wide vari-

ety of possible scenarios of illumination and observation geometries. These

look-up-tables (LUT) can then be searched to identify the best-matching

candidate capable of explaining the entire string of available (multi-spectral

and/or -directional) remote sensing data. Such approaches reduce the amount

of retrievable solutions to the inversion but require (1) the availability of de-

tailed knowledge regarding typical canopy architectures (in particular the

size, shape, and number of leaves, branches and crowns) as well as their tem-

poral evolutions, (2) a RT model capable to actually represent such complex

3-D structures, and (3) the accurate and reliable simulation of the reﬂectance

ﬁelds for these canopy representations under all envisaged spectral, viewing

and illumination conditions.

This contribution will provide a concise description of the major RT char-

acteristics in plant canopies. Following this, the Rayspread model will be pre-

sented, which addresses the need for rapid, yet accurate, simulations of the

reﬂectance ﬁeld over arbitrarily complex plant environments. Validation and

veriﬁcation of this model are followed by a small case study on the impact of

woody structures on the directional signatures of vegetation canopies.

1 Canopy Radiation Transfer Fundamentals

The radiative transfer equation is a statement of the law of energy conser-

vation [Cha60]. Under steady state conditions and neglecting any polariza-

tion, diﬀraction and emission eﬀects, its integro-diﬀerential form describes the

change in the intensity I [W m

−2

−1

] of monochromatic radiation travelling

in direction Ω at some location r:

Ω •∇I(r, Ω)+˜σ

(r, Ω, Ω

) I(r, Ω)=



4π

˜σ

(r, Ω



→ Ω) I(r, Ω



) dΩ



(1)

Variations in intensity are thus either due to radiation – originally travelling

in direction Ω – being intercepted by the foliage (second left hand term),

or else, due to radiation being scattered from some direction Ω



into the

direction of interest Ω at location r (right hand term). More speciﬁcally, ˜σ

−1

] is the extinction coeﬃcient, which indicates the loss in intensity due

to absorption and scattering of radiation away from Ω,and˜σ

[sr

−1

]isthe

diﬀerential scattering coeﬃcient for photons scattered from some direction

Ω



into a unit solid angle about direction Ω at point r. For the purpose of