Tree Physiology 21, 789–795
© 2001 Heron Publishing—Victoria, Canada
A theoretical analysis of the influence of heterogeneity in chlorophyll
distribution on leaf reflectance
CRAIG V. M. BARTON
Centre for Ecology and Hydrology Edinburgh, Bush Estate, Penicuik, Midlothian, EH26 0QB, U.K.
Received August 18, 2000
Summary Attempts to determine the vitality of vegetation
and to detect vegetation stress from remotely sensed data have
focused on chlorophyll concentration, because it influences the
reflectance of vegetation and tends to correlate with vegetation
health and stress. Pollution, pathogens and pests can cause localized regions of chlorosis and necrosis across a leaf surface,
but the extent to which these patches influence the overall
reflectance and spectral signature of the leaf and canopy has
not been tested.
A conifer leaf model (LIBERTY), which simulates the influence of leaf biochemical concentrations of chlorophyll, water, lignin, cellulose and protein on the reflectance of leaves
from 400 to 2500 nm, was used to determine the effect of
patches of chlorosis on leaf reflectance. A fraction of the leaf f
is assumed to be chlorotic with a chlorophyll concentration C1.
The remainder of the leaf has chlorophyll concentration C2
such that mean leaf chlorophyll concentration, Cmean = fC1 +
(1 – f )C2, is constant for a range of f and C1 values. LIBERTY
can be used to estimate the reflectance of a leaf with a particular chlorophyll concentration at a particular wavelength Rλ,C
(assuming other leaf properties remain constant), thus we can
estimate the reflectance of the chlorotic leaf as f Rλ , C 1 + (1 – f )
Rλ , C 2.
The model indicated that small areas of chlorosis have a disproportionately large influence on overall leaf reflectance. For
example, a leaf with 25% of its area chlorotic can have the
same reflectance (400–700 nm) as a homogeneous leaf with
60% less chlorophyll. Thus, determination of chlorophyll concentration from remotely sensed data is prone to underestimation when chlorophyll is nonuniformly distributed. Hence,
attempts to model leaf and canopy reflectance using radiative
transfer models will need to consider how to incorporate nonuniform chlorophyll distribution.
Keywords: chlorosis, LIBERTY, modeling, patchiness.
Introduction
The chlorophyll concentration of a leaf relates to its photosynthetic capacity and can give an indication of general plant
health and plant stress. Many environmental factors, both biotic and abiotic, can induce stress in a plant and result in a loss
of chlorophyll; e.g., nutrient deficiency, toxicity, drought, air
and soil pollution or extreme temperatures. Carter (1993,
1994) investigated the response of leaf spectral reflectance to
various causes of plant stress and concluded that some differences and sensitivity maxima in reflectance spectra could be
explained by stress-induced decreases in chlorophyll a concentration. Jago et al. (1999) estimated canopy chlorophyll
concentration from remotely sensed data for a grassland and
winter wheat crop and related chlorophyll concentration to
land contamination and crop yield. Thus, if we could deduce
chlorophyll concentration from remotely sensed information,
we might be able to estimate whether vegetation is healthy or
subject to stress.
Chlorophyll within a vegetation canopy tends to be positively related to the point of maximum slope at wavelengths
between 690 and 740 nm in the reflectance spectrum (Miller et
al. 1990). This point is known as the red edge position (REP)
and characterizes the effective boundary between the strong
absorption of red radiation by chlorophyll and the increased
multiple scattering of radiation in the near-infrared wavelengths. The REP can be determined as the position of the peak
in the first derivative of the reflectance spectrum and movement of this parameter toward shorter wavelengths (blue shift)
has been correlated with reductions in chlorophyll concentration (Curran et al. 1990, Jago et al. 1999) and plant stress
(Essery and Morse 1992, Carter 1994, Kraft et al. 1996,
Meinander et al. 1996, Jago et al. 1999).
One approach to aid the interpretation of remotely sensed
information, especially with regard to detection of pollution
stress, is the coupling of mechanistic physiological and radiative transfer models (Barton and Plummer 1999). The physiology model is driven by known vegetation type, site characteristics and weather, and yields vegetation parameters vital for
complex radiative transfer models, such as chlorophyll concentration, water thickness, leaf area index and leaf angle distribution. These variables are used either to constrain the inversion of the radiative transfer model or to predict canopy
reflectance using the model, the results of which are compared
with the target site in an attempt to detect vegetation stress.
Pollution, pathogens and pests can cause localized regions
of chlorosis and necrosis across a leaf surface. The question
arises as to how these patches influence the reflectance of the
leaf and canopy as a whole. Is chlorophyll concentration alone
adequate to model the reflectance of the leaf and canopy or is
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BARTON
some measure of distribution within the leaf or canopy also required?
This analysis investigates the extent to which nonuniform
distribution of chlorophyll influences overall leaf reflectance
and how this might impact our ability to deduce chlorophyll
concentrations based on remotely sensed information and to
model canopy reflectance accurately.
Materials and methods
The conifer leaf reflectance model LIBERTY (Dawson et al.
1998), which estimates the influence of leaf biochemical concentrations of chlorophyll, water, lignin, cellulose, and protein
on the reflectance of leaves from 400 to 2500 nm, was used to
determine the effect of patches of chlorosis on leaf reflectance.
LIBERTY is designed to model conifer needles at the cellular
level by adapting Melamed’s theory of light interaction with
suspended powders (Melamed 1963). The total reflectance of
a medium (R), such as a leaf or a stack of leaves, will be the
sum of the scattered radiation fluxes emerging in an “upward”
direction from the leaf, assuming a horizontal leaf surface. The
value of R is derived by first obtaining an approximate expression for the total reflectance 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 reflectance model, LIBERTY, requires input parameters for cell size, leaf thickness, and concentrations
of chlorophyll, water, lignin + cellulose and nitrogen (see Table 1). For the purpose of this investigation, “chlorophyll” refers to the combined light-absorbing pigments within the leaf
(chlorophylls a and b, carotenes, xanthophylls, etc.). Figure 1
shows the absorption coefficients for “chlorophyll” used by
LIBERTY.
If all leaf biochemical properties are held constant, apart
from chlorophyll concentration, then the output from LIBERTY can be treated as a function, Rλ,C, which is an estimate
of leaf reflectance of a leaf for a particular chlorophyll concentration at a particular wavelength. LIBERTY was run using
the parameter set for slash pine needles (Table 1, see Dawson
et al. 1998), but varying chlorophyll concentration, Cmean, over
the range 0–500 mg m –2. The runs covered the wavebands
from 400 to 800 nm in 5-nm steps. It was unnecessary to run
the model above 800 nm because chlorophyll does not absorb
above this wavelength.
A simple model of a leaf with patchy chlorosis was used, in
which the leaf area was split into two regions with distinct
chlorophyll concentrations. A fraction of the leaf f is assumed
chlorotic with a chlorophyll concentration C1, whereas the remainder of the leaf has chlorophyll concentration C2 such that
the mean leaf chlorophyll concentration, Cmean, is:
C mean = f C 1 + (1 − f ) C 2 .
(1)
The chlorophyll concentration of the chlorotic region can be
treated as a fraction, η, of the mean chlorophyll concentration,
so:
C 1 = ηC mean.
(2)
Thus, by rearranging Equations 1 and 2:
C 2 = (C mean − f ηC mean) (1 − f ).
(3)
If we assume linear mixing, i.e., radiation interacting with
one leaf region is scattered or absorbed without interacting
with the other leaf region (a reasonable assumption provided
the patches of chlorosis are large relative to leaf thickness), we
can examine the effects of the chlorotic area fraction, f, and the
degree of chlorosis, η, on the reflectance spectra of a patchy
chlorotic leaf R ′λ , C mean over a range of Cmean values:
R ′ λ , C mean = f Rλ , C 1 + (1 − f ) Rλ , C 2 .
(4)
Results
Reducing the chlorophyll concentration, Cmean, of a homogeneous leaf ( f = 0 or η = 1) leads to an increase in reflectance,
because the probability of light being scattered back from the
leaf increases with decreasing chlorophyll concentration (Figure 2). In optical wavebands, reflectance is inversely related to
chlorophyll concentration; however, the response varies with
wavelength because of differential absorption by leaf pig-
Table 1. LIBERTY parameter values used for the analysis (adapted from Dawson et al. 1998). Values are based on projected leaf area.
Parameter
Definition and units
Value
Cell diameter
Intercellular air space
Leaf thickness
Baseline
Albino absorption
Chlorophyll concentration
Water content
Lignin and cellulose
Nitrogen concentration
Mean leaf cell diameter (µm)
Determinant for the amount of radiative flux passing between cells
Arbitrary value to determine single leaf reflectance and transmittance from infinite reflectance criteria
Wavelength independent absorption to compensate for changes in absolute reflectance
Absorption in the visible region due to lignin
Chlorophyll (pigment) concentration (mg m –2 )
Water content (g m –2 )
Combined lignin and cellulose concentration (g m –2 )
Nitrogen concentration (g m –2 )
45
0.03
1.6
0.0005
0
250
100
30
1
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HETEROGENEITY IN CHLOROPHYLL DISTRIBUTION AND LEAF REFLECTANCE
Figure 1. Pigment or chlorophyll absorption spectrum used by LIBERTY.
ments (Figure 3). Blue (450 nm) and red (670 nm) wavelengths are absorbed more strongly than green (580 nm)
wavelengths, and so saturation of reflectance occurs more rapidly at these wavelengths. Chlorophyll does not absorb above
730 nm, hence the lack of sensitivity of reflectance to chlorophyll concentration at 760 nm (Figure 3).
Holding Cmean constant at 250 mg m –2 and η constant at
0.1, while increasing the fraction of the leaf that is chlorotic, f,
shows how the increase in chlorotic area fraction increases
overall reflectance (Figure 4). The shape of the response differs slightly from the reflectance spectrum of a homogeneous
leaf, as shown by comparing the spectrum of a leaf with a chlorophyll concentration of 150 mg m –2.
If Cmean is held at 250 mg m –2 and f is held at 0.1 but η is
varied, the overall reflectance increases as η decreases. As η
tends toward 1, the leaf becomes increasingly homogeneous
and the reflectance tends toward that of a homogeneous leaf
(Figure 5). Overlaying the spectrum for a homogeneous leaf
shows that heterogeneity of chlorophyll distribution alters the
shape of the spectral response.
The difference in the shape of the spectral response as f and
η are varied (compared with simply reducing Cmean) can be attributed to the nonlinearity of the relationship between reflect-
Figure 2. Modeled reflectance spectra (Rλ,C) for different chlorophyll
concentrations (Cmean; mg m –2).
791
Figure 3. Relationship between reflectance and chlorophyll concentration (Cmean) for four wavelengths 760, 580, 670 and 450 nm, showing that reflectance saturates more quickly at some wavelengths than
others.
ance and chlorophyll concentration and variation in response
with wavelength (Figure 3). The weighted average of the reflectances at the two chlorophyll concentrations will always
be larger than the reflectance at the weighted average of the
two chlorophyll concentrations.
The implications of this in terms of relating reflectance information to chlorophyll concentration can be highlighted
with a hypothetical set of leaves. If we have a healthy leaf with
a uniform chlorophyll concentration of 541 mg m –2 and vary
the chlorophyll concentration and distribution in response to
some hypothetical stress we can produce a variety of chlorotic
situations:
(i) healthy homogeneous leaf with 541 mg m –2;
(ii) uniform loss of chlorophyll to 200 mg m –2; e.g., a nutrient-deficient leaf;
(iii) spotty chlorosis such that 50% of the leaf maintains a
chlorophyll concentration of 541 mg m –2 and 50% is chlorotic
with a chlorophyll concentration of 118 mg m –2, giving a
Figure 4. Modeled reflectance as a fraction of chlorotic leaf area, f,
varies from 0 to 0.5 for a heterogeneous leaf with Cmean = 250 mg m –2
and the degree of chlorosis, η = 0.1. The boldface line shows the
reflectance spectrum for a homogeneous leaf with a chlorophyll concentration of 150 mg m –2.
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792
BARTON
Figure 5. Modeled reflectance as η varies from 0.1 to 1 (homogeneous) for a heterogeneous leaf with Cmean = 250 mg m –2 and f = 0.1.
The boldface line shows the reflectance spectrum for a homogeneous
leaf with a chlorophyll concentration of 150 mg m –2.
mean chlorophyll concentration of 330 mg m –2 (Cmean = 330, f
= 0.5, η = 0.36); e.g., leaves with localized damage caused by
air pollution;
(iv) interveinal chlorosis where 75% of the leaf has a chlorophyll concentration of 417 mg m –2 and 25% has a chlorophyll
concenration of 69 mg m –2, giving a mean chlorophyll concentration of 330 mg m –2(Cmean = 330, f = 0.25, η = 0.21); e.g.,
iron deficient leaves; and
(v) uniform loss of chlorophyll to 330 mg m –2.
Figure 6 shows the modeled reflectance spectra for the five
hypothetical leaves. The healthy leaf (i) has the lowest
reflectance followed by the homogeneous leaf with a chlorophyll concentration of 330 mg m –2 (v). The remaining three
leaves have similar reflectance spectra despite either a large
difference in mean chlorophyll concentration or the same
mean chlorophyll concentration but different distribution. The
reflectance spectra for these leaves are almost indistinguishable despite the 60% difference in mean chlorophyll concen-
Figure 6. Effect of heterogeneity of chlorophyll distribution on the
reflectance spectra. Modeled results for five leaves. Three homogeneous leaves with 200 (ii), 330 (v) and 541 (i) mg m –2 chlorophyll and
two heterogeneous leaves with 330 mg m –2 chlorophyll but differing
in heterogeneity, f = 0.5, η = 0.36 (iii) and f = 0.25, η = 0.21 (iv).
tration between leaf (ii) and leaves (iii) and (iv).
The spectra in the red–NIR wavebands for the five leaves
(i–v) are shown in Figure 7a and the first derivative of the
spectra in Figure 7b. The position of the peak in the first derivative of the spectra gives the REP. A better estimate of REP
can be obtained with the algorithm of Dawson and Curran
(1998), whereby Lagrangian interpolation is applied to the
first derivative of the reflectance spectrum. A second derivative is then performed on the Lagrangian equation to determine the maximum slope position. The REP moves to shorter
wavelengths as chlorophyll concentration declines in the homogeneous leaves from (i) 730 nm to (v) 716 nm to (ii) 713 nm
(see Figure 8). However, the two heterogeneous leaves (iii, iv)
with mean chlorophyll concentration of 330 mg m –2 have
much lower REPs (714 and 715 nm, respectively) than the homogeneous leaf with a chlorophyll concentration of 330 mg
m –2 (v). A logarithmic function was fitted between REP and
chlorophyll concentration for the homogeneous leaves. Inverting this function for the two heterogeneous leaves results
in estimates of chlorophyll concentration of 217 and 266 mg
m –2 for (iii) and (iv), respectively (see Figure 8), indicating
that the relationship between REP and chlorophyll concentration may break down in the presence of heterogeneous chlorophyll distribution. Although the position of the red edge for the
two heterogeneous leaves (iii and iv) moved to shorter wavelengths, closer to that of leaf (ii), inspection of the derivative
Figure 7. (a) Reflectance between 650 and 800 nm for five hypothetical leaves: three homogeneous leaves with 200 (ii), 330 (v) and 541 (i)
mg m –2 chlorophyll and two heterogeneous leaves with 330 mg m –2
chlorophyll but differing in heterogeneity, f = 0.5, η = 0.36 (iii) and f =
0.25, η = 0.21 (iv). (b) The first derivative of the reflectance where the
position of the peak indicates the red edge position.
TREE PHYSIOLOGY VOLUME 21, 2001
HETEROGENEITY IN CHLOROPHYLL DISTRIBUTION AND LEAF REFLECTANCE
Figure 8. Red edge position versus leaf chlorophyll concentration.
The solid circles denote the homogeneous leaves and the triangles denote the two heterogeneous leaves. The line is an empirical logarithmic function fitted to the homogenous leaf data. The broken lines
indicate the chlorophyll concentrations that would be estimated for
the heterogeneous leaves by inverting the logarithmic function based
on their red edge positions.
shows that leaf (ii) has a much narrower peak than leaves (iii)
and (iv), which have broader peaks more similar in shape to
that of leaf (v) with a chlorophyll concentration of 330 mg
m –2.
Discussion
The heterogeneity of chlorophyll distribution across a leaf can
strongly influence the overall reflectance spectrum of that
leaf, with chlorotic patches increasing reflectance. Figures 6
and 7 show that a leaf with a uniform chlorophyll distribution
may have an almost indistinguishable reflectance spectrum
from a heterogeneous leaf with 60% more chlorophyll. This
highlights a need for caution when attempting to determine
chlorophyll concentration from reflectance spectra (see Chappelle et al. 1992, Demarez et al. 1999, Jago et al. 1999).
In this analysis, edge effects were ignored; i.e., the transition between the chlorotic and non-chlorotic regions within a
leaf. The influence of the transition between the two regions
on reflectance is probably small, but it could be investigated
with a more complex model such as the 3-D ray-tracing model
of Govaerts et al. (1998). The influence of the edge effect will
increase as the chlorotic region is broken up into smaller
patches. Therefore, if the edge effect does affect reflectance it
will be more important in leaves with many small chlorotic
spots than in leaves with a few large chlorotic patches.
Another assumption implicit in this analysis is that chlorosis
partitions the leaf into two areas of uniform chlorophyll concentration, which is rarely the case in reality. It is more likely
that each chlorotic region has a gradient of chlorophyll concentration or that each chlorotic patch has a slightly different
chlorophyll concentration from other patches. This will cause
the spectral signature to lie somewhere between the modeled
heterogeneous and homogeneous signatures.
793
In this study, all physical and biochemical properties were
held constant while chlorophyll concentration was varied.
However, the sensitivity and response of reflectance to chlorophyll heterogeneity may vary with the values of the other leaf
properties. Furthermore, depending on the cause of chlorosis,
there may be concurrent changes to the leaf structure, such as
water-soaked spots, that will alter reflectance both within and
outside the visible wavebands.
The absorption spectrum was constant for this study,
whereas in reality the mix of light-absorbing pigments may
change in various ways in response to declining overall chlorophyll concentration or localized chlorosis. The ratio between chlorophylls a and b and the relative amount of carotenoids may change, especially in response to certain forms of
stress. The most important function of carotenes in higher
plants is not as an accessory pigment, but in dissipation of the
excess energy of chlorophyll and in detoxifying reactive forms
of O2 (Lawlor 1987). Therefore, one might expect an increase
in carotene concentration, with consequent decreased reflectance at 530 nm, where there is an increased requirement for
energy dissipation; e.g., damage to electron transport or increased requirement for detoxification such as exposure to
ozone. If other changes in the pigment mixture correlate with
chlorosis, there may be additional useful information in the
reflectance spectra that could be used to determine the degree
of chlorosis.
Even if it is not possible to determine chlorophyll concentration from reflectance spectra, changes in chlorophyll concentration and distribution may transmit useful information
via reflectance. Attempts have been made to use the commonly observed reduction in chlorophyll concentration in
stressed plants to infer stress from remotely sensed data
(Carter 1994, Jago et al. 1999). Carter (1994) found that certain ratios of reflectances increased in plants exposed to different stresses. He selected pairs of reflectance bands, one of
which was sensitive to stress and the other not. The two wavelengths least sensitive to stress were 420 and 760 nm, whereas
the most sensitive wavelengths were 605 and 695 nm. At
605 nm and 695 nm, absorption by chlorophylls a and b is relatively weak, thus as leaf chlorophyll concentration begins to
decrease with the occurrence of stress, leaf reflectance will increase first and most at or near these wavelengths. Additional
chlorophyll must be lost before reflectance will increase significantly at wavelengths where chlorophyll absorbs strongly,
such as 420 nm. The R760 is insensitive to chlorophyll but sensitive to leaf structure. Therefore, one might expect the two
reflectance ratios R605 /R760 and R695 /R420 to be sensitive to both
mean chlorophyll concentration and heterogeneity of chlorophyll distribution. Carter (1994) does not present chlorophyll
concentrations or mention chlorotic spots so it is not possible
to tell which factors were responsible for the close correlations
found between the reflectance ratios and stress. Changes in
pigment composition may also influence R695 /R420 and such
changes are likely to occur in a plant under stress (see below).
Thus, these ratios may correlate to stress through their sensitivity to chlorophyll concentration, to heterogeneity of chloro-
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BARTON
phyll, a combination of both or to something else.
Jago et al. (1999) used reflectance information to determine
the REP and then related the REP to chlorophyll concentration
and finally chlorophyll concentration to stress. Based on our
findings, we conclude that the approach used by Jago et al.
(1999) may yield misleading results because attempts to relate
REP to chlorophyll concentration can lead to errors where heterogeneity of chlorophyll is present, which is likely to be the
case in stressed vegetation. In the study of Jago et al. (1999),
the movement of REP in response to stress may have been a
result of reduced chlorophyll or a response to patchy chlorosis,
both of which are potential indicators of stress. It may be that
the intermediate step of determining chlorophyll concentration is unnecessary and even undesirable.
Differences in chlorophyll distribution may influence leaf
physiology, which raises the question of whether we wish to
measure total leaf chlorophyll content or the concentration and
distribution of chlorophyll and hence the efficiency of light
capture. A uniform distribution of chlorophyll maximizes the
amount of light absorbed per unit chlorophyll, but not necessarily light utilization because other constraints come into
play. In a heterogeneous leaf, more chlorophyll is needed to
absorb the same amount of light, therefore resource allocation
is not optimal and this may reflect a response to stress. Because both loss of chlorophyll and heterogeneity of distribution lead to a blue shift in the REP, measurement of this shift
may provide a more direct method of detecting stress than that
of attempting to determine chlorophyll concentration and relating it to stress.
The first derivative of the spectra may contain more information than just the REP (see Boochs et al. 1990). It was noted
that the shape of the peak of a heterogeneous leaf was more
similar to that of the homogeneous leaf with the same bulk
chlorophyll concentration than to the leaf with less chlorophyll but the same REP. Thus the derivative may contain information about heterogeneity of leaf properties. This requires
further investigation with spectra from real leaves rather than
just model output, because concurrent changes in other leaf
properties in response to stress may influence the REP and
shape of the reflectance spectrum. Although leaf reflectance
models are useful tools to investigate certain well-defined
questions under controlled conditions, one should be aware of
their limitations and attempt to validate results with measurements on real leaves.
Although this analysis focused on the leaf scale, the principle is scale invariant as long as linear mixing is appropriate,
and therefore could be equally valid for a crop or forest canopy
pixel where a diseased or stressed plant or patch of plants
within the pixel could strongly influence the reflectance and
lead to an incorrect determination of chlorophyll concentration. Furthermore, I have focused on chlorophyll, but other
leaf and crown properties may have similar nonlinear
reflectance relationships and give rise to the same difficulty
when trying to infer canopy biophysical properties from remote sensing or trying to model reflectance properties with
process-based canopy models.
Further experimental research is required with real leaves in
conjunction with modeling exercises to improve the understanding of any interactions between leaf structure, chlorophyll distribution and pigment composition so that we can
improve models of leaf and canopy reflectance. The next step
is to use a radiative transfer model to determine the extent to
which leaf-scale heterogeneity influences whole-canopy reflectance and thus determine how important accurate modeling of leaf-scale processes is when scaling stress effects to the
canopy.
Conclusion
This analysis shows that small areas of chlorosis can strongly
influence the reflectance of a leaf and that sensitivity of
reflectance to chlorosis varies with wavelength. Nevertheless,
a leaf with patchy chlorosis can have an almost indistinguishable reflectance spectrum to a homogeneous leaf with a significantly lower chlorophyll concentration. This finding implies
that it is not possible to relate broadband or single narrowband
reflectances to leaf chlorophyll concentration when the heterogeneity of chlorophyll distribution is unknown. Furthermore,
the similar reflectance spectra of certain homogeneous and
heterogeneous leaves make it almost impossible to distinguish
between them. Heterogeneity of chlorophyll distribution will
increase leaf reflectance and so the tendency would be to underestimate chlorophyll concentration. Conversely, if attempting to model leaf reflectance, knowledge of mean leaf
chlorophyll concentration is insufficient to describe leaf reflectance because some measure of heterogeneity is also required.
Acknowledgments
I thank Stephen Plummer for comments on the manuscript and Terry
Dawson for assistance with parameterization of LIBERTY. This
work was funded by a NSERC Fellowship GT5/98/25/DAEC under
the Environmental Diagnostics program.
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