Objectives

The objectives of the workshop are to stimulate discussions around the use The objectives of the workshop are to stimulate discussions around the use of of 3D (and probably 4D = 3D+time) realistic modeling of canopy structure 3D (and probably 4D = 3D+time) realistic modeling of canopy structure to be used in remote sensing applicationsto be used in remote sensing applications. .

On what basis is it possible to derive simpler RT representations for On what basis is it possible to derive simpler RT representations for operational applications?operational applications?

WORKSHOP ON THE USE OF 3D REALISTIC CANOPY ARCHITECTURE MODELING FOR REMOTE SENSING APPLICATIONS

Avignon, France, March-9, 2005

Y. Knyazikhin1, D. Huang1, N. Shabanov1, W. Yang1,

M. Rautiainen2, R.B. Myneni1

1Department of Geography, Boston University2Department of Forest Ecology, University of Helsinki

jknjazi@bu.edu

Stochastic Radiative Transfer for Remote Sensing of Vegetation

INTERPRETATION OF SATELLITE DATAINTERPRETATION OF SATELLITE DATA

• Satellite-borne sensors measure mean intensities of canopy-leaving radiance averaged over the three-dimensional canopy radiation field

• Three-dimensional radiation models can simulate 3D radiation field. However, they require 3D input and are time consuming

• Operational data processing requires fast retrieval algorithms. One – dimensional model is the desirable option.

Problem: To develop a radiative transfer approach for modeling the radiation regime of natural vegetation which is

1. as realistic as 3D model

2. as simple as 1D model

3D TRANSPORT EQUATION AS A BASIS FOR REMOTE 3D TRANSPORT EQUATION AS A BASIS FOR REMOTE SENSING OF VEGETATIONSENSING OF VEGETATION

To estimate the canopy radiation regime, three important features must be carefully formulated.

(1) architecture of individual plant and the entire canopy

0

2

4

6

8

10

12

14

16

400 500 600 700

Wavelength, nanometer

Lea

f al

bedo

, %

Current yearSecond yearThird year

0%

10%

20%

30%

40%

50%

400 900 1400 1900 2400

Wavelength, nanometer

Soil

refl

ecta

nce

Silicia Fine SandClayey SoilPeat

(2) optical properties of vegetation elements and soil

Solar zenith angle

Azi

mu

th

ANGULAR DISTRIBUTION OF INCIDENT RADIATION

(3) incident radiation field3D DISTRIBUTION OF

SCATTERED RADIATION

MEAN CHARACTERISTICS OF 3D FIELDMEAN CHARACTERISTICS OF 3D FIELD

0 1 2 3 4 5 6 7 80.000

0.005

0.010

0.015

0.020

0.025

3D, =1 3D, =2 1D

Ref

lect

ance

LAI

0 1 2 3 4 5 6 7 80.0

0.2

0.4

0.6

0.8

1.0

3D, =1 3D, =2 1D

Ab

sorp

tan

ce

LAI

• 3D APPROACH

one first solves the 3D radiative transfer equation for each realization of canopy structure and then averages the solutions over all possible realizations

•1D APPROACH

one first averages the extinction coefficient and scattering phase function over space and then solves the 1D radiative transfer equation with average characteristics

STOCHASTIC APPROACH

to obtain closed 1D equations whose solutions are mean characteristics of the 3D radiation field

“The problem of obtaining closed equations for probabilistic characteristics of the radiation field was first formulated and solved by G.M. Vainikko (1973) where the equations for the mean radiance … were derived through spatial averaging of the stochastic transfer equation in the model of broken cloudiness, sampling realization of which cannot be constructed. The method of G.M. Vainikko has limited efficiency. …. These disadvantages were avoided in later papers… .” (Titov, G., Statistical description of radiation transfer in clouds, J. Atmos. Sci., 47, p.29, 1990)

Vainikko, G. (1973). Transfer approach to the mean intensity of radiation in noncontinuous clouds. Trudy MGK SSSR, Meteorological Investigations, 21, 28–37.

Pomraning, G.C. (1991). Linear kinetic theory and particle transport in stochastic mixtures. World Scientific Publishing Co. Pte. Ltd., Singapore.

HISTORYHISTORY

Shabanov, N. V., Y. Knyazikhin, F. Baret, and R. B. Myneni, Stochastic modeling of radiation regime in discontinuous vegetation canopy, Remote Sens. Environ, 74, 125-144, 2000.

George Titov and Jerry Pomraning.

From A. Marshak and A.Davis (Eds), Three-Dimensional Radiative Transfer in Cloudy Atmospheres. Springer Verlag.

PARAMETERIZATIONPARAMETERIZATION

g(z)the probability of finding foliage elements at depth z.

GROUND COVER = max {g(z)}

Horizontal plane at depth z

q(z,,)

the probability of finding simultaneously vegetation elements on horizontal planes at depths z and

along the direction .

0

z

1

CORRELATION OF FOLIAGE ELEMENTS AT TWO LEVELSCORRELATION OF FOLIAGE ELEMENTS AT TWO LEVELS

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

K

(degree)

5 25 45 65 80

z/D

CONDITIONAL PROBABILITYK(z,,)=q(z,,)/g(z) Clustering (clumping) of foliage elements arises

naturally in the framework of the stochastic approach:

DETECTING A LEAF MAKES IT MORE LIKELY THAT THE NEXT LEAF WILL BE DETECTED NEARBY

0

z

1

0.0 0.5 1.0 1.5 2.0 2.5 3.00.0

0.2

0.4

0.6

0.8

1.0

Monte Carlo simulation analytical equation

K

tan||

D

z

1D approach: K=g()

3D EFFECTS3D EFFECTS

Stochastic approach reproduces 3D effects reported in literature

0 1 2 3 4 5 6 7 80.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

3D, =1 3D, =2 1D

ND

VI

LAI

0.0 0.2 0.4 0.6 0.8 1.00.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

3D, =1 3D, =2 1D

ND

VI

FPAR

0 1 2 3 4 5 6 7 80.000

0.005

0.010

0.015

0.020

0.025

3D, =1 3D, =2 1D

Ref

lect

ance

LAI

saturation

Ignoring 3D effects can result Ignoring 3D effects can result in reflectance saturation at in reflectance saturation at low LAIlow LAI

CANOPY SPECTRAL INVARIANT - 1CANOPY SPECTRAL INVARIANT - 1

i() mean number of photon interactions with leaves before either being absorbed or exiting the canopy (measurable)

0.0 0.2 0.4 0.6 0.8 1.00.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

y=1.28-1.04x

y=1.67-1.38x

A

B

inve

rse

rati

o

leaf albedo ()

qi portion of shaded area

leaf albedo (measurable)

i()[1p] =qi0

p recollision probability - the probability that a photon scattered from a leaf in the canopy will interact within the canopy again

NIR

RED 0

1

)(

1

ii q

p

qi

CONCLUSIONSCONCLUSIONS

The objectives of the workshop are to stimulate discussions around the use The objectives of the workshop are to stimulate discussions around the use of of 3D (and probably 4D = 3D+time) realistic modeling of canopy structure 3D (and probably 4D = 3D+time) realistic modeling of canopy structure to be used in remote sensing applicationsto be used in remote sensing applications. .

Realistic models of canopy structure are required to derive and Realistic models of canopy structure are required to derive and parameterize the “q-function” which describes the correlation of foliage parameterize the “q-function” which describes the correlation of foliage elements in vegetation canopieselements in vegetation canopies

On what basis is it possible to derive simpler RT representations for On what basis is it possible to derive simpler RT representations for operational applications?operational applications?

Stochastic Transfer Equation becauseStochastic Transfer Equation because

Its solution coincides exactly with what satellite-borne sensors Its solution coincides exactly with what satellite-borne sensors measure; that is, the mean field emanating from the smallest area to be measure; that is, the mean field emanating from the smallest area to be resolved, from a pixelresolved, from a pixel

It reproduces 3D effectsIt reproduces 3D effects

It provides a powerful tool to parameterize 3D effectsIt provides a powerful tool to parameterize 3D effects

It is as simple as 1D Radiative Transfer EquationIt is as simple as 1D Radiative Transfer Equation