CANOPY SPECTRAL INVARIANTS FOR REMOTE SENSING OF CANOPY STRUCTURE

Yuri Knyazikhin1, Mitchell Schull

1, Liang Hu

1, Ranga Myneni

1 and Pedro Latorre Carmona

2

1Boston University, Boston, USA

2Universidad Jaume I, Castellón de la Plana, Spain

ABSTRACT

The concept of canopy spectral invariants expresses the

observation that simple algebraic combinations of leaf and

canopy spectral reflectances become wavelength

independent and determine two canopy structure specific

variables – the recollision and escape probabilities. The

recollision probability (probability that a photon scattered

from a phytoelement will interact within the canopy again) is

a measure of the multi-level hierarchical structure in a

vegetated pixel and can be obtained from hyperspectral data.

The escape probability (probability that a scattered photon

will escape the vegetation in a given direction) is sensitive to

canopy geometrical properties and can be derived from

multi-angle spectral data. The escape and recollision

probabilities have the potential to separate forest types based

on crown shape and the number of hierarchical levels within

the landscape. This paper introduces the concept and

demonstrates how this approach can be used to monitor

forest structural parameters with multi-angle and

hyperspectral data.

Index Terms— MODIS, MISR, AVIRIS,

PROBA/CHRIS, canopy spectral invariants, canopy

structure

1. INTRODUCTION

Interaction of solar radiation with the vegetation canopy is

described by the three-dimensional radiative transfer

equation [1]-[2]. The interaction cross-section that appears

in this equation is treated as wavelength independent

considering the size of the scattering elements (leaves,

branches, twigs, etc.) relative to the wavelength of solar

radiation [1]. Although the scattering and absorption

processes are different at different wavelengths, the

interaction probabilities for photons in vegetation media are

determined by the structure of the canopy rather than photon

frequency or the optics of the canopy. This feature results in

canopy spectrally invariant behavior for a vegetation canopy

bounded from below by a non-reflecting surface: some

simple algebraic combinations of the single-scattering

albedo and canopy spectral transmittances and reflectances

eliminate their dependencies on wavelength through the

specification of two canopy structure specific spectrally

invariant variables – the recollision and escape probabilities.

These variables specify an accurate relationship

between the spectral response of a vegetation canopy to the

incident solar radiation at the leaf and the canopy scale and

allows for a simple and accurate parameterization for the

partitioning of the incoming radiation into canopy

transmission, reflection and absorption at any wavelength in

the solar spectrum. This result is essential to both modeling

and remote sensing communities as it allows for the

separation of the structural and radiometric components of

the measured and/or modeled signal. The former is a

function of canopy age, density and arrangement while the

latter is a function of canopy biochemical behavior.

Consequently, the canopy spectral invariants offer a simple

and accurate parameterization for the shortwave radiation

block in many global models of climate, hydrology,

biogeochemistry, and ecology [3]-[4].

In remote sensing applications, the information content

of spectral data can be fully exploited if the wavelength

independent variables can be retrieved, for they can be more

directly related to structural characteristics of the vegetation

canopy. This concept underlies the operational algorithm of

global leaf area index, and the fraction of photosynthetically

active radiation absorbed by vegetation developed for the

moderate resolution imaging spectroradiometer (MODIS)

and multiangle imaging spectroradiometer (MISR)

instruments of the Earth Observing System (EOS) Terra

mission [5]-[6]. The canopy spectral invariants have also

been exploited in developing a 26 year leaf area index data

record from multiple sensors [7]-[8]. Here we will introduce

the concept and its application for investigating the three-

dimensional canopy structure from space measurements.

2. CANOPY SPECTRAL INVARIANTS

Figure 1 (left panel) demonstrates the spectral invariant

phenomenon. By plotting values of the ratio between the

surface reflectance and leaf albedo versus reflectance values

for a vegetated pixel, a linear relationship is obtained, where

the slope and intercept give the recollision and directional

escape probabilities, respectively [9], [10].

The wavelength independent recollision probability is

the probability that a photon scattered from a phytoelement

will interact within the canopy again [11]. This parameter

accounts for a cumulative effect of the canopy structure over

a wide range of scales [9], [12]. For example, if a vegetation

canopy is treated as a big leaf, i.e., no structure, Leaf Area

Index (LAI) is, the recollision probability is zero because a

photon reflected or transmitted by one “big” leaf will not

encounter another leaf. If one cuts the leaf into “small

pieces” and uniformly distributes the pieces in a canopy

layer (the structure has changed with LAI unaltered), the

recollision probability changes its value from zero to about

Figure 1. Left Panel: By plotting values of the surface reflectance to leaf albedo ratio versus reflectance

values for a vegetated pixel, a linear relationship is obtained, where the slope and intercept give the

recollision and directional escape probabilities, respectively. PROBA/CHRIS data acquired over Harvard

Forest, Massachusetts, are used in this example. The CHRIS sensor on ESA’s PROBA platform provides

multi-angular imagery for up to 62 spectral bands in the range 415–1050 nm with a spectral resolution of 5–

12 nm at 5 nominal angles (55, 36, 0,-36,-55), at a spatial resolution of 20 m. Data from the interval between

720nm and 900nm are used. Right Panel: The directional escape probability as a function of the scattering

angle. Surface reflectances at blue (band L1), green (band L4), red (band L7) and near infrared (band L15)

are added for comparison. The angular signatures are normalized by corresponding maximum values.

Figure 2. Left and Middle Panels: Recollision probability and LAI at the Bartlett Experimental Forest, New

Hampshire, derived from Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) data. The AVIRIS

sensor provides calibrated images of the up-welling spectral radiance in 224 contiguous spectral channels with

wavelengths from 400 to 2500 nanometers at a spatial resolution of 3.3 m. Right Panel: By plotting the

recollision probability versus LAI, two curves are obtained. The upper and lower curves corresponds to

needle leaf and broadleaf pixels, respectively. Rautiainen et al. derived similar relationships using forest

inventory data from 1032 plots in Finland [13].

0.3 [11]. At a given LAI, the recollision probability

increases with the number of hierarchical levels present in

the landscape (e.g., the clumping of needles into shoots,

shoots and leaves into crowns, etc). This property can be

used to discriminate between broadleaf and coniferous

canopies as illustrated in Fig. 2.

The wavelength independent directional escape

probability (Fig. 1, right panel) is the probability that a

scattered photon will escape the vegetation in a given

direction. Its angular variation is related to forest cover,

plant LAI and crown shape. Disney et al. documented the

sensitivity of the escape and recollision probabilities to the

stand age [14].

Figure 3 (upper panel) illustrates the separation of forest

classes in the spectral invariant space. The location of a

point in this space depends on properties of the canopy

structure at both microscale (e.g., leaf vs. shoot) and

macroscale (e.g., dimensions of trees and their spatial

distribution). The ratio of the angular escape probability, R,

to the total escape, 1-p, (horizontal axis) vary with tree

shape and stand geometry, while |ln(1-p)| (vertical axis) is

related to the number of hierarchical levels within the pixel

(e.g., the clumping of needles into shoots, shoots and leaves

into crowns, etc). In this example, the Spruce/Fir and

Hemlock classes have approximately the same LAI. Because

Hemlock shoots are “flatter” and therefore less complex

compared to their Spruce/Fir counterparts, the recollision

probability of a “Hemlock shoot” is smaller than that of the

Spruce/Fir class. This results in a lower location of the

Hemlock pixels on the plane with respect to the Spruce/Fir

class. The horizontal shift is determined by stand (tree

density, stem distribution) and crown geometry (crown

shape and its internal structure). On the left there are

Spruce/Fir which are very conical in shape. However, as the

points move toward the right, crowns become more

spherical in shape as in the case of Hemlocks and become

even more spherical as seen in Beech/Oak. The mixed forest

class occupies a space between needle leaf and broadleaf

forests. In this example the broadleaf class has a higher LAI

(higher p value) and a “simpler” microscale structure (flat

leaf) compared to its needle leaf counterpart (low LAI,

shoot-like leaf scale complexity). The LAI and stand

geometry are a dominant factors that determine the location

of the broadleaf class in the spectral invariant space.

A simple threshold approach has been applied to maps

of the recollision and escape probabilities. Results shown in

Figure 3 (lower panel) suggest that the canopy spectral

invariants convey information needed to discriminate

between forest types.

3. CONCLUSIONS

The wavelength independent canopy interceptance,

recollision and directional escape probabilities specify an

accurate relationship between the spectral response of a

vegetation canopy with non-reflecting background to

incident radiation at the leaf and canopy scales. The

recollision probability is the probability that a photon

scattered from a phytoelement will interact within the

canopy again and is equal to the maximum eigenvalue of the

radiative transfer equation [4]. The directional escape

probability is the probability that a scattered photon will

escape the vegetation in a given direction. This result was

Figure 3. Upper Panel: Spectral invariant space. The

rescollision and escape probabilities were derived

from AVIRIS data acquired over Bartlett

Experimental Forest in nadir direction. Shown are

high density points. Lower Panel: Distribution of

forest types at the Bartlett Experimental Forest site

derived from spectral invariants by applying a

threshold approach (right bars). Left bars represent

the ground truth data.

obtained by the expansion of the solution of 3D radiative

transfer equation in eigenvectors [4]. The independency of

the interaction cross-section on wavelength was critical to

relate canopy absorptive and reflective properties to the

maximum eigenvalue. The canopy spectral invariants can be

considered fundamental descriptors of the impact of canopy

structure on canopy scattering where the scattering objects

are large compared with the wavelength of radiation.

4. ACKNOWLEDGMENTS

This research was funded by the Jet Propulsion

Laboratory, California Institute of Technology under MISR

contract 1259071, by the National Aeronautics and Space

Administration (NASA) under Grants NNX08AE81G,

NNX08AL55G, NNX08AE89A, NNX09AI30G and by

NASA Headquarters under the NASA Earth and Space

Science Fellowship Program under Grant NNX07AO41H.

Pedro Latorre Carmona’s work was partially funded by the

“Advanced ground segment methodologies in Earth

Observation: optical Data calibration and Information

eXtraction” (EODIX) project (AYA2008-05965-C04-

04/ESP).

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