LIBERTY—Modeling the Effects
of Leaf Biochemical Concentration
on Reflectance Spectra
Terence P. Dawson,* Paul J. Curran,* and Stephen E. Plummer†
T
he conifer leaf model LIBERTY (Leaf Incorporating
Biochemistry Exhibiting Ref lectance and Transmittance
Yields) is an adaptation of radiative transfer theory for determining the optical properties of powders. LIBERTY
provides a simulation, at a fine spectral resolution, of
quasiinfinite leaf ref lectance (as represented by stacked
leaves) and single leaf reflectance. Single leaf ref lectance
and transmittance are important input variables to vegetation canopy reflectance models. A prototype parameterization of LIBERTY was based upon measurements of pine
needles and known absorption coefficients of pure component leaf biochemicals. The estimated infinite-reflectance
output was compared with the spectra of both dried and
fresh pine needles with root mean square errors (RMSE)
of 2.87% and 1.73%, respectively. The comparisons between measured and estimated ref lectance and transmittance values for single needles were also very accurate
with RSME of 1.84% and 1.12%, respectively. Initial inversion studies have demonstrated that significant improvements can be made to LIBERTY by utilizing in vivo
absorption coefficients which have been determined by
the inversion process. These results demonstrate the capability of LIBERTY to model accurately the spectral response of pine needles. Elsevier Science Inc., 1998
INTRODUCTION
Understanding the interaction of radiation with vegetation canopies requires a knowledge of the spectral prop* Department of Geography, University of Southampton, Highfield, Southampton, United Kingdom
† Section for Earth Observation, Institute of Terrestrial Ecology,
Monks Wood, Abbots Ripton, Cambridgeshire, United Kingdom
Address correspondence to Terence P. Dawson, Univ. of Oxford,
Environmental Change Unit, 1a Mansfield Rd., Oxford OX1 3TB, UK.
E-mail: [email protected]
Received 22 October 1996; revised 13 December 1997.
REMOTE SENS. ENVIRON. 65:50–60 (1998)
Elsevier Science Inc., 1998
655 Avenue of the Americas, New York, NY 10010
erties of individual leaves (Aber, 1994). Leaves are an
important component of forest canopies, and it is the
concentration of their biochemical constituents, namely,
pigments, water, nitrogen, cellulose, and lignin, together
with canopy structure that shapes the absorption features
of remotely sensed ref lectance spectra. Absorption features in the near infrared region of the spectrum (1000–
2500 nm) are a function of the bending and stretching
vibrations of biochemical bonds (between, for example,
hydrogen–carbon and nitrogen–oxygen atoms) together
with their harmonics and overtones (Kemp, 1987). In the
visible region, chlorophyll and carotenoid pigments have
strong absorption due to electron energy transitions
(Lichtenhaler, 1987; Mackinney, 1941). Fine spectral
resolution remotely sensed data can be statistically analyzed to estimate the concentration of biochemicals in
forest canopies. Such information has been used to drive
ecosystem simulation models and estimate photosynthetic efficiency, the rate of nutrient cycling, and the degree of vegetation stress (Curran, 1994). Strong correlations between leaf biochemical concentrations and
specific wavebands of measured spectra have now been
reported by Wessman et al. (1988), Martin and Aber
(1990), Curran and Kupiec (1995), and Zagolski et al.
(1996). However, wavebands selected by multiple linear
regression using biochemical assay data are often not
consistent with the absorption features of the biochemicals within the leaves. Even when known causal wavebands are selected in the regression equation, spectral
correlation with biochemical concentrations are not always strong (Dawson et al., 1995a). To investigate this
further, a physical modeling approach is required to describe and quantify the ref lectance, scattering, and absorption of canopy leaves as a function of their biochemical and physical properties.
Some of the earliest research on leaf reflectance mod0034-4257/98/$19.00
PII S0034-4257(98)00007-8
LIBERTY—Conifer Leaf Model
eling was based upon the Kubelka–Munk (K–M) radiative transfer theory (Allen and Richardson, 1968), and
this theory has since been used by others (Yamada and
Fujimura, 1988; Conel et al., 1993). The K–M approach
is a two-stream approximation to the radiative-transfer
equation. Later Allen et al. (1969) proposed a single layer
“plate” model. By extending the plate model to several layers with air spaces between plates Allen et al. (1970) was
able to simulate multiple scattering which occurs as a result of the air space/cell wall discontinuities within the
mesophyll structure of a leaf (Gausmann, 1974). The
PROSPECT model (Jacquemoud and Baret, 1990) develops Allen’s multiple layer plate model and adopts a
solid angle of incident radiation instead of an isotropic
direction. This modification accommodates shadowing
caused by the undulating shape of the leaf surface at microscopic scales (Grant, 1987). Designed to illustrate the
effects of chlorophyll and water content of leaves on the
spectra of those leaves, PROSPECT has now been upgraded (Jacquemoud et al., 1996) to incorporate the biochemicals of cellulose, lignin, and protein. The K–M and
plate theories assume the absorption and scattering of
the radiation is distributed homogeneously throughout
the leaf when in fact it is characterized by the absorbing
biochemicals being localized into hydrated cells which
are separated by intercellular air spaces causing multiple
refractive index discontinuities.
Other leaf models have utilized ray tracing (Allen et
al., 1973) and stochastic methods (Tucker and Garratt,
1977), but these models are difficult to invert and require computer-intensive processing. In addition, existing
leaf models have usually been based upon broadleaf vegetation where the leaf structure is considered to be an
infinitely extending plane having distinct layers. Pine
needles present their own particular problem. They do
not contain a well-defined pallisade layer, and so a transverse section of a pine needle will display roughly spherical cells. There are also problems of how to characterize
and model the pine foliage elements. Because of the
complex spatial distribution of pine canopies, it may be
more appropriate to treat shoots (clumped needles) as
the independently located foliage element instead of individual needles (Stenberg et al., 1994). Finally, their
shape and size make it difficult to accurately measure the
spectral properties of individual needles even in the laboratory (Daughtry et al., 1989). LIBERTY (Leaf Incorporating Biochemistry Exhibiting Reflectance and Transmittance Yields) was developed specifically to address
these problems.
The objective was to generically characterize and
model conifer (particularly pine) needles at the cellular
level by adapting Melamed’s theory of light interaction
with suspended powders (Melamed, 1963) and infer leaf
optical parameters from stacked needles in the laboratory. An enhancement of LIBERTY to accommodate a
thickness parameter, thereby providing a transmittance
51
output, facilitates the modeling of individual conifer needle elements. Therefore, based upon known parameters
derived in the laboratory, LIBERTY can be coupled with
a suitable canopy model for investigations of forest canopy ref lectance. Inversion of LIBERTY, providing in
vivo absorption coefficients, indicate significant improvements in model accuracy and hint at the potential to estimate biochemical concentrations and biophysical variables directly from high spectral resolution remote
sensing (Dawson et al., 1997).
MODEL THEORY
Infinite Ref lectance Function
The total reflectance R of a medium, such as a leaf or
stacked leaves, will be the sum of the scattered radiation
f luxes emerging in an “upwards” direction out of the
leaf, assuming a horizontal leaf surface. R is derived by
first obtaining an approximate expression for the total ref lectance of an individual leaf cell as a function of the
optical absorption coefficient k of the cell medium and
taking into account both internal and external scattering.
The parameters and variables of R can then be related
to the bulk optical characteristics for the diffusion of radiation over the whole leaf.
The Interaction of Radiation with a Leaf Cell
Let us assume that the internal cells of a leaf are spherical particles whose surface will scatter radiation according
to Lambert’s cosine law and whose average reflectance coefficients for internally and externally incident radiation
are defined as mi and me, respectively. Leaves actually
consist of cells having different shapes and orientation
with respect to the surface, but we can approximate the
optical properties of the internal structure of a leaf by
assuming that the average surface-scattering effects and
transmission s of an aggregation of leaf cells with the
same mean diameter can be characterized by a spherical
model. In a perfect sphere, the angle at which a refracted ray is incident on the inside of the sphere is
equal to that at which it enters the sphere. However, as
emphasized by Melamed (1963), for an ensemble of irregularly shaped cells the two angles are uncorrelated
with the refracted ray having virtually an equal probability of encountering interior surfaces at all orientations.
The ref lectance coefficient of a surface is defined as
the ratio of the ref lectance of the surface to that of a
perfectly diffuse surface under the same conditions of illumination and measurement. Therefore, the reflection
coefficient m(h) for a direction h is determined by the
Fresnel equations for the specular ref lection of unpolarized radiation. The evaluation of the average ref lection
coefficients me and mi assume the cell surfaces are ideally
diffuse and obey Lambert’s cosine law whereby the reflected radiance in a direction h with respect to the nor-
52
Dawson et al.
mal will be proportional to cos h. The average value of
the external ref lectance coefficient me, for light moving
from a medium having a low refractive index to one having a high one will be Eq. (1):
p/2
me5# m(h) sin h cos h dh
0
(1)
and for radiation incident mi for when light passes from
a high to low medium Eq. (2):
hc
mi5(12sin2 hc)12# m(h) sin h cos h dh,
0
(2)
where hc is the critical angle.
The LIBERTY model assumes that the cell spheres
are separated by an air gap; therefore, me will be the reflectance coefficient for light passing from the air to the
cell. For unit flux radiating into the sphere from the surface, the intensity, defined as flux per unit solid angle,
in a direction h (with h taken along the diameter d of
the sphere) will be (1/p)cos h.
Let the medium of individual leaf cells absorb light
with absorption coefficient k. Then radiation reaching
the cell wall with an angle dh, in the direction h will be
Eq. (3):
(1/p)e2kd cos h cos h 2p sin h dh.
(3)
After one pass, therefore, the total radiation reaching the
surface M will be Eqs. (4,5):
p/2
M52# e2kd cos h cos h 2p sin h dh
0
52[12(kd11)e2kd]/(kd)2.
(4)
x5xu1(xas)xu1(xas)2xu1···,
(5)
which is a converging series where the solution at the
asymptotic limit will be
The proportion of the initial radiation emerging from the
cell will be miM since mi is the average reflectance coefficient of the cell surface for internally incident radiation.
Assuming that the cell has identical scattering properties
at every point on its surface, the total radiation after infinite interreflections is the sum of the geometric series in
miM. Therefore, the total transmitted component s will be
Eq. (6):
s5(12mi)M/(12miM),
(6)
and the component radiation that is absorbed will be
Eq. (7):
12s5(12M)/(12miM).
rounded by leaf material having a ref lectance R. However, the cells on the surface of the leaf are exposed on
the side of the material boundary and radiation must enter or leave by way of this boundary.
If we assume that the leaf surface is horizontal, then
we can define a set of parameters xu, xa, and xd, which
represent the fraction of the radiation emerging from the
interior of a cell in upward, adjacent, and downward directions, respectively, and which is then intercepted by
the overlying, adjacent, and underlying cells. Because the
radiance emerging from any point of an inner surface of
the cell is assumed to be isotropic, these parameters approximate the solid angle of the radiation, expressed as
fractions of 4p steradians.
For the special case at the medium boundary, the
fraction of the emitted radiation xu for cells in the surface
layer is scattered through an angle of approximately 2p
steradians, which is the angle of free space seen by the
emitted radiation. For simplification, the lateral radiance
xa can be resolved into its upward and downward components, thereby facilitating a one-dimensional solution to
the diffusion of radiation in a leaf. We define a probability coefficient x as the total fraction of the radiation
which emerges from the interior of a cell and which is
scattered upwards towards a cell layer one cell distance
closer to the leaf surface. Then we can define x as
(7)
Now consider an assembly of spherical cells of uniform
size each having a transmission s. By striking an individual cell, therefore, an incident light ray will be partially
reflected from the surface with a value me and the remainder (12me) will enter the cell. This component of the
radiation will reemerge from the cell with a value
(12me)s.
The Interaction of Radiation with a Layer of Cells
By assembling many cells in close proximity, a quasiinfinite thickness is achieved. Assuming that the cells are in
layers, all of the cells, save the surface cells, will be sur-
x5xu/(12xas).
(8)
At low absorption coefficients where kd,1, xd>xu, and
xu1xd1xa>1, we have Eq. (9):
x5xu/(12(122xu)s).
(9)
The parameter x is important as it can be treated as a
function of the intercellular air gap or scattering efficiency. By increasing x, we will have a higher ref lectance
due to increased radiation scattering from lower to upper layers.
Initially, however, the ref lected component me of an
external incident ray is scattered over an angle 2p steradians; therefore, xd is 0 and xu is twice the value of radiation which emerges from within a cell. The initial reflected component of radiation contributing to R for unit
incident radiation is 2xme with Eq. (8) expressing the effect of shadowing by the adjacent cells at the surface.
The remainder (122xme) enters the cell. Of this fraction,
the amount of radiation which is reemitted from the leaf
thereby contributing to the total ref lectance R is x(12
2xme)s. An amount (12x)(122xme)s is therefore transferred to the lower leaf layers, of ref lectance R. In a similar fashion, (12x)(122xme)sR is ref lected back by the
lower layers, returns to the surface cell, and the amount,
x(12x)(122xme)2s2R is transmitted upwards. The next in-
LIBERTY—Conifer Leaf Model
53
is the fraction of radiation that emerges after an infinite
number of interreflections for unit intensity striking the
lower layers, one cell depth below the surface.
In addition to the radiation which has emerged after
all interref lections of the initial radiation component, we
add the radiation which, after the second, third, and subsequent ref lections, entered the surface cells and was
scattered back into the interior. The sum of these components will be the residue of the right-hand component
of Eq. (10):
(12x)2(122xme)s[(12me)sR/(12meR)].
(12)
This term represents the initial intensity so by applying
Eq. (11), the fraction of Eq. (12) which emerges after
an infinite number of interref lections will be Eq. (13):
x(12x)2(122xme)s[(12me)sR/(12meR)]2,
(13)
and the fraction which returns to the interior of the leaf
will be Eq. (14):
(12x)3(122xme)s[(12me)sR/(12meR)]2.
(14)
By continuing this process, the equation for the sum of
all the radiative components which contribute to the total radiation emerging from the leaf surface Eq. (15):
R52xme1x(122xme)s
1x(12x)(122xme)s[(12me)sR/(12meR)]
Figure 1. A schematic representation of
LIBERTY showing the scattered radiation
paths in a leaf. Each sphere can represent the
same or a different cell. In an aggregate of
cells, each surface cell is surrounded on all
but one side by the bulk of the leaf having
reflectance R. The coefficient x represents the
fraction of the radiation that has emerged from
the interior of the cell and is scattered
upwards, me is the reflectance coefficient
for radiation passing from the intercellular air
space to the cell, s is the transmitted
component of radiation of an individual cell,
and R is the total ref lection of the leaf bulk.
1x(12x)2(122xme)s[(12me)sR/(12meR)]2
1x(12x)3(122xme)s[(12me)sR/(12meR)]31···,
(15)
which can be rewritten:
R5
2xme1x(122xme)s1x(12x)(122xme)2s2R
1x(12x)(122xme)2s2meR21x(12x)(122xme)2s2me2R3
1x(12x)(122xme)2s2me3R41···
52xme1x(122xme)s
(10)
A schematic representation of the mechanism is shown
in Figure 1. From an examination of Figure 1, the term
x[(12me)sR/(12meR)]
(16)
The form of Eq. (16) is quadratic in nature; therefore,
an approximation of the root for R can be resolved easily
using the Newton–Raphson iterative methodology (Jeffrey, 1986).
terreflection of the initial ray will contribute the component x(12x)(122xme)2s2meR2 to the total ref lectance R.
After an infinite number of interactions, the radiation being emitted by the leaf and contributing to the total radiation of the leaf R will be
1x(12x)(122xme)s[(12me)sR/(12meR)].
2xme1x(122xme)s(12meR)
.
(12meR)2(12x)(12me)sR
(11)
The Transmission of a Needle Having Finite Layers
An adaptation of LIBERTY is required to provide the
transmission of a single needle element. Laboratory measurements of the spectral properties of conifer needles
(Daughtry et al., 1989) have shown that, in the nearinfrared wavelengths (800–1300 nm), about 40% of the total incident radiation is transmitted while a slightly higher
percentage is reflected. The Melamed (1963) model was
therefore modified to determine the radiation components
as a function of leaf thickness. This was achieved by resolving the average reflectance and transmittance values
of a single layer of leaf cells and, through adaptation of a
procedure demonstrated by Benford (1946), providing a
measure of total reflectance and transmittance as a continuous function of thickness.
In considering a single layer of leaf cells, examina-
54
Dawson et al.
tion of Eq. (16) shows that, where there is no underlying
leaf material whose backscatter will contribute to the total
reflective radiation, the total reflection R will be equal to
R52xme1x(122xme)s.
(17)
In a series of techniques used by Benford (1946), the
number of individual layers of leaf cells, each having
identical ref lectance and transmittance functions, can be
increased providing a total ref lection and transmission
value as a function of thickness. When R reaches a maximum (i.e., infinite ref lectance, R∞), it can be shown that
R∞5R1
T 2R
,
(12R∞R)
(18)
where R and T are the values of ref lectance and transmittance for the single layer of leaf cells. Because Eq.
(18) relates the general terms T, R, and R∞ and the values of R∞ and R are known from Eqs. (16) and (17), respectively, we can determine T by solving Eq. (19):
R)
3(R 2R)(12R
4
R
T5
∞
∞
∞
1/2
.
(19)
The equations for Tn and Rn, where n is the number of
layers, have been derived and incorporated into LIBERTY
based upon a continuous function of thickness, where n
is not limited to an integral thickness. This enables us to
quantify total leaf transmittance and ref lection as a function of the average leaf thickness.
LEAF OPTICAL PROPERTIES USED
TO PARAMETERIZE LIBERTY
To parameterize LIBERTY, we used data from the laboratory analysis of jack pine (Pinus banksiana) needles. The
laboratory reflectance measurements made on stacked
freeze-dried and ground needles and pure and in vitro
leaf component biochemicals were made using a Perkin
Elmer Lambda 19 double-beam spectrophotometer
equipped with an integrating sphere. The instrument was
continually purged with gaseous nitrogen to remove atmospheric moisture. The calibration of the instrument
was performed using a barium sulfate (BaSO4) reference
plate and internal wavelength calibrations. The absorption was measured between wavelengths of 400 nm and
2500 nm at 1 nm intervals. To measure and to remove
leaf moisture, the samples were freeze-dried in an Edwards Modulyo freeze drier. Deep frozen (2308C) needles were placed in a vacuum oven and atmospheric
pressure was reduced to less than 1.431024 Torr. The
temperature was then increased slowly to 1308C for
48–60 h. The freeze-drying process is well suited to the
spectrophotometric studies of leaves as the low drying
temperatures do not denaturize the component biochemicals. All measured and adopted absorption coefficients
were standardized to zero absorption at the minima (occurring in the 800–900 nm wavelength region) and a
Figure 2. Pure combined chlorophyll-a and chlorophyll-b,
in vitro extracted pigments and pure lignin absorption in
visible wavelengths.
wavelength-independent linear absorption coefficient was
incorporated into the model. Jacquemoud and Baret
(1990) fixed the value of this elementary absorption using the estimated absorption of dry albino maize leaves
having the most compact structure. However, we allowed
this absorption to vary in order to i) analyze empirical
variation in spectra maxima as a function of biochemical
concentration and/or leaf internal structure and ii) quantify, through inversion studies, the causal effects of the
structure on the spectra as a result of water stress and/
or senescence (Peñuelas et al., 1996; Aldakheel and Danson, 1996).
Absorption in the Visible Wavelengths
Initial investigations of the absorption coefficient of
freeze-dried leaves in visible wavelengths showed that a
negative natural logarithmic absorption continuum in the
visible wavelengths was convolved with absorption attributed to pigments. This was verified by bleaching chopped
pine needles in 100% acetone. The albino leaves were
then air-dried and measured with the spectrophotometer. The observed 2ln absorption coefficent was incorporated into the model as it represented absorption due to
leaf structure and biochemicals, in particular lignin. This
absorption has been validated by others (Elvidge, 1990;
Schubert, 1965) and is near-identical to the absorption
coefficient of “pure” lignin (Fig. 2). Lignin has a strong
absorption in ultraviolet wavelengths peaking at a wavelength of 280 nm and extending through the visible and
near-infrared wavelengths.
The absorption spectra of pure biochemicals were
examined and combined linearly to determine the fit of
the total absorption effects of the leaf. Chlorophyll a and
b pigments were dissolved in 80% acetone and their respective absorption coefficients were measured and then
combined to a chlorophyll a/b ratio of 2.5;1. This ratio
has been shown to be reasonably constant for slash pine
needles grown in diverse environmental conditions (Kupiec, 1995). The resultant formulation was then compared
to absorption coefficients of total in vitro leaf pigments
LIBERTY—Conifer Leaf Model
55
extracted using the techniques of Mackinney (1941) (Fig.
2). A difference spectrum exhibits a close approximation
to published carotenoid absorption coefficients (Lichtenthaler, 1987) in the 440–500 nm wavelength region (Fig.
3). The large absorption maximum at a wavelength of
410 nm in the difference spectra is probably attributable
to extracted chlorophyll a and b components that have a
broader and higher blue region absorbency as a result of
the increased water content of solvent extracted pigments.
Acetone causes a shift of the pigment absorption peaks
to shorter wavelengths. The chlorophyll a maximum absorption peak in the red region had an in vivo maxima
at a wavelength of 672 nm and an in vitro (90% aqueous
acetone) maxima at a wavelength of 664 nm, a shift of 8
nm. Because of the increased water content and greater
interaction of the combined pigments, there was a further shift of about 2 nm between the absorption maxima
of the extracted whole pigments and the pure chlorophyll a and b mixture in the same aqueous acetone solution. Initially, the wavelength corrected in vitro absorption data were incorporated into the LIBERTY model.
cellulose concentrations in the slash pine needles used
here (Kupiec, 1995) showed that their mean concentrations were 23% and 35% of dry weight, respectively.
Their pure absorption coefficients were measured from
purchased laboratory powders (The Aldrich Chemical
Company Inc.) and, because of their reasonably positive
cocorrelation, combined linearly and adjusted to attain
the lowest root mean square error (RMSE) between the
empirical freeze-dried data set and LIBERTY-predicted
output. This resulted in a lignin to cellulose ratio of
1.13;1 which suggests that, although there is a larger
proportion of cellulose in conifer needles, lignin has a
stronger absorption weighting. This effect was probably
due to the encrusting nature of lignin (Schubert, 1965)
causing a masking of the cellulose and a reduction of its
interaction with radiation.
To incorporate the effects of nitrogen concentration,
an absorption spectrum of protein (which is dominated
spectrally by nitrogen) was adapted from the revised
PROSPECT (Jacquemoud et al., 1996) model. Using the
same method as that for lignin and cellulose absorption,
nitrogen concentration were set in the model to produce
the lowest RMSE between the measured spectra and
model spectra. Although the accuracy of the model spectra was increased, our studies did not produce a strong
correlation between nitrogen concentrations and spectral
variation as a result of variability in protein absorption.
Because leaf ref lectance and transmittance properties are more appropriately related to biochemical content (mass per unit leaf area) than concentrations (mass
per unit leaf dry mass), the absorption coefficients were
scaled using the specific leaf area (SLA) for jack pine
which has been estimated to be 80 g m22. Using biochemical content as the input variable enables the model
to be used to estimate the spectra of other conifer species with different SLAs.
Absorption in the Near-Infrared
The water absorption coefficient for LIBERTY was
based upon the published absorption coefficients of pure
distilled water over the spectral range 750–2500 nm
(Curcio and Petty, 1951), which has been shown to be
in agreement with published absorption coefficients of in
vivo leaf water (Jacquemoud and Baret, 1990) estimated
from PROSPECT inversion methods.
Cellulose and lignin are the most abundant of the
compounds found in the cell walls of conifer leaves. The
cellulose molecules are organized into highly hydrated
microfibrils which form the basic structural unit of the
cell wall. Extensive lignin deposition within the interfibrillar spaces confers considerable strength to the leaf
tissues. The absorption coefficients of these biochemicals
have similar features and their combined in vivo absorption peaks have proven difficult to separate due to their
intimate mixture. A biochemical analysis of lignin and
Characterization of LIBERTY Structural Parameters
To determine the refractive index of the air-cell interfaces,
leaves can be infiltrated with oil mixtures having variable
refractive indexes (Woolley, 1971; Gausman, 1974). The
ref lectance of leaves is minimal when the refractive index of the liquid matches the refractive index of the cell
wall. The effective refractive index of a typical leaf in the
visible wavelengths is not inconsistent with the published
refractive index, n51.47, of epicuticular wax, but Allen
et al. (1969) demonstrated that it decreases almost linearly with wavelength to a value of about 1.2 at a wavelength of 2500 nm. Refractive indexes incorporated into
LIBERTY were adopted from a regression equation of
calculated refractive indexes (Jacquemoud and Baret,
1990) against wavelength as a best approximation to the
average refractive indices of wet mesophyll cells for the
400–2500 nm wavelength region, respectively.
Examination of a transverse section through red spruce
Figure 3. A comparison of estimated and measured carotenoid absorption, determined by spectrophotometer
measurements of b-carotene extracted from carrot roots.
56
Dawson et al.
needles showed the diameter of internal leaf cells were in
the region of 30–60 lm (Rock et al., 1986). The scattering
efficiency of the Melamed (1963) model as a function of
the absorption coefficient in visible and near-infrared
wavelengths has been tested (Hapke and Wells, 1981) for
different sphere sizes against those of crushed glass powders. The measured values of the internal scattering curve
were indistinguishable from the Melamed (1963) model
for an average sphere diameter d535–50 lm.
VALIDATION DATA
To compare LIBERTY output with the ref lectance spectra of dried needles, spectrometer measurements were
made on 160 needle samples collected from sample sites
in Nipawin National Reserve, Saskatchewan, Canada as
part of the Boreal Ecosystem Atmosphere Study (BOREAS) in 1994. This site, comprising jack pine (Pinus
banksiana), provided 10 sample plots with 16 samples
collected from each plot; eight of these samples were
first year needles and eight were second year needles.
The reflectance of dried and finely-chopped samples
were measured to produce a mean ref lectance spectrum
for each plot and all ages of needle. The concentration
of chlorophyll, carotenoids, water content, nitrogen, cellulose, and lignin were measured using wet chemical
assay and stepwise linear regression techniques at the
Universities of Southampton and New Hampshire.
Comparison of LIBERTY output with the reflectance
spectra of fresh, stacked whole needles were made using
slash pine (Pinus elliottii) foliage samples collected from
Gainesville, Florida in 1992 (Curran and Kupiec, 1995).
Laboratory ref lectance measurements were made for 80
samples using an IRIS Mk IV spectroradiometer.
Both dried and fresh samples had been stacked to
ensure a sufficient optical thickness for infinite ref lectance, and the spectra were averaged and compared to
the LIBERTY-predicted outputs.
Figure 4. A comparison between measured and LIBERTY-predicted ref lectance and transmittance values for
several quasiinfinite and single needle experiments.
Validation of the single needle reflectance and transmittance model outputs were made using microspectrometer measurements of jack pine samples. The equipment
used was a Zeiss UMSP 50 (universal microspectrophotometer) microscope. Reflectance and transmittance measurements were taken at 1 nm steps over a wavelength
range of 400–800 nm, individual values being based on
a mean of 10 measurements taken along the length of
each needle.
RESULTS AND DISCUSSION
Based upon the model variables and biochemical data
outlined in Table 1, the laboratory spectrometer data and
the LIBERTY predictions were highly correlated (r50.99)
across all wavelengths (Fig. 4). For both the dried and
fresh needle samples, the RMSE between estimated and
measured spectra for the quasiinfinite setup were 2.87%
Table 1. Leaf Biochemical Variation and LIBERTY Variables Used for Stimulating the Spectra of Jack Pine (Pinus
banksiana) Needles
Biochemical
Mean
Maximum
Minimum
g21)
2.48
103.3
1.15
25.1
38.3
4.00
165
1.51
28.2
45.4
1.28
55.6
0.8
22.0
31.3
Structural Variable
Dried Needles
Fresh Needles
Chlorophyll (mg
Water (% dry mass)
Nitrogen (% dry mass)
Lignin (% dry mass)
Cellulose (% dry mass)
Average internal cell diameter (lm)
Intercellular air space determinant, xu
Leaf thickness
Baseline absorption
Specific Leaf Area (SLA) g m22
40
0.03
0.000446
80
45
0.028
1.62
0.00058
80
LIBERTY—Conifer Leaf Model
Figure 5a. LIBERTY-predicted and dried needle ref lectance spectra.
for the predicted freeze-dried needles (Fig. 5a) and
1.73% for fresh needles (Fig. 6a).
A sensitivity analysis of LIBERTY indicated that it
was necessary to reduce the average cell diameter for dry
needles, which is to be expected as water loss would
likely cause a contraction of the cells. In addition, the
scattering parameter x was increased for dry needles
where the model exhibits a higher reflectance due to
many more air/cell interfaces as a result of cell distortion.
All of the above observations agree with our underlying
physical understanding of leaves. However, an increase
in the linear absorption coefficient was also required to
reduce the ref lectance of fresh whole needles. This suggested that there were changes to the sample density
that had been unaccounted for in the model. The dried
needles had been finely chopped and stacked dry samples
were more compact than their fresh counterparts. This
difference in sample density affected both the depth of
radiation penetration and the degree of multiple scattering from adjacent needles.
The pigment absorption features in visible wavelengths were narrower in the predicted spectra as a result
of adapting the absorption coefficient of in vitro pigments
in acetone. Examination of different extracted pigment
Figure 5b. Revised LIBERTY-predicted and dried needle
ref lectance spectra using in vivo absorption coefficients
derived from an inversion of LIBERTY.
57
Figure 6a. LIBERTY-predicted and fresh slash pine needle
ref lectance spectra.
samples in aqueous acetone also highlighted large differences in the carotenoid absorption region between samples where chlorophyll concentrations are similar. This
suggested that separate carotenoid and chlorophyll absorption coefficients are necessary in the model. The
model output in particular shows an excessive absorption
region between wavelengths of 400–470 nm when compared to empirical spectra in both fresh and dried leaves.
Although LIBERTY exhibits the distinct side “lobes” observed on each side of the green reflectance peak of
measured conifer needles, centered around a wavelength
of 520 nm, the depth of these effects do not mirror those
in the empirical data very well.
Numerical inversion studies of LIBERTY, based
upon the Newton–Raphson iterative methodology, show
that the intermixing of the biochemicals affecting absorption in the visible wavelengths produces a distinct in vivo
absorption coefficient (Fig. 7) that is different from the
absorption due to in vitro pigments. The increased absorption can be accounted for by the addition of in vivo
lignin absorption effects and the fact that, in the chloroplast membrane of leaf cells, chlorophyll does not exist
in free solution, but as pigment-protein complexes. Therefore, the absorption spectrum of chlorophyll a, for exam-
Figure 6b. Revised LIBERTY-predicted and fresh jack pine
needle ref lectance spectra.
58
Dawson et al.
Figure 6c. Revised LIBERTY-predicted and fresh slash pine
needle ref lectance spectra.
ple, which has interacted with protein, gives rise to several chlorophyll a classes (French et al., 1972), each of
which contribute linearly to the total absorption of visible
light. The only other significant deviation between LIBERTY-predicted and measured reflectance for both fresh
and dry leaves is in the 1000–1600 nm wavelength region
where LIBERTY predicts alternatively higher and lower
reflectances in regions of low and high absorption peaks,
respectively. This may be the consequence of the logarithmic nature of the absorption of radiation. LIBERTY
is very sensitive to very subtle absorption effects in the
highest reflected regions of the wavelength; hence measurement errors of the absorption coefficients will be magnified where the total absorption coefficient is low. This
explanation also accounts for the high spectrometer instrument noise in absorption coefficient measurements when
reflection was high. Incorporating the predicted in vivo
absorption coefficient for combined chlorophyll and carotenoids improves model performance significantly in the
visible region, as is demonstrated by the revised quasiinfinite predictions for dry and fresh jack pine needles (Figs.
5b and 6b, respectively) and slash pine needles (Fig. 6c).
A comparison of the LIBERTY-predicted single needle ref lectance and transmittance spectra with measured
jack pine needles using the in-vivo-estimated pigment
Figure 7. Comparison of in vitro and LIBERTY-predicted
in vivo absorption in visible wavelengths.
Figure 8. Comparison of the measured and LIBERTY-predicted single needle ref lectance and transmittance for jack pine (leaf thickness parameter51.26).
absorption demonstrated a high accuracy for the model
prediction (RMSE for ref lectance and transmittance values were 1.84% and 1.12%, respectively) (Fig. 8). The
leaf thickness parameter was set to 1.62 which corresponded to a ref lectance and transmittance maxima of
53% and 32%, respectively, at a wavelength of 800 nm.
Wavelength mismatches between fresh needle and
predicted spectra in the near-infrared (Fig. 6a) and red
edge (Fig. 8) may be associated with calibration errors
between the different spectrometers.
Sensitivity studies on the effects of varying lignin/cellulose content with LIBERTY-predicted spectra on both
dried (Fig. 9) and fresh leaves (Fig. 10) have been conducted in which the average value of the cellulose/lignin
content was varied between 615% of mean (42.6–58.9 g
m22). This deviation was chosen as it ref lected normal
variations in measured leaf content (Kupiec, 1995; Martin and Aber, 1990). The model output demonstrates
that, in fresh leaves, the resultant variation in predicted
Figure 9. Sensitivity of the LIBERTY-predicted ref lectance
for dry needles to variation in combined cellulose and
lignin concentrations.
LIBERTY—Conifer Leaf Model
Figure 10. Sensitivity of the LIBERTY-predicted ref lectance for fresh needles to variation in combined cellulose
and lignin concentrations.
59
The research was funded by the Natural Environment Research
Council (Research grant GR3/7647 to P. J. C. and studentship
GT4/94/407/L to T. P. D.) and the University of New Hampshire (Accelerated Canopy Chemistry Program grant to P. J. C.).
The authors are indebted to many individuals who made this
work possible, notably John Kupiec (Scottish Natural Heritage),
Geoff Smith (Institute of Terrestrial Ecology, Monks Wood),
John Marshall (University of Southampton), and John Aber and
Mary Martin (University of New Hampshire). We are particularly grateful to Stephane Jacquemoud (University of Paris), who
allowed us to investigate and anatomize his PROSPECT model
and utilize some of the model absorption data sets.
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