int. j. remote sensing, 2002, vol. 23, no. 18, 3619–3648
Estimating leaf nitrogen concentration in ryegrass (Lolium spp.)
pasture using the chlorophyll red-edge: theoretical modelling and
experimental observations
D. W. LAMB*†, M. STEYN-ROSS‡, P. SCHAARE§,
M. M. HANNA¶, W. SILVESTER** and A. STEYN-ROSS‡
†Farrer Centre, School of Science & Technology, Charles Sturt University,
Wagga Wagga, NSW 2678, Australia; e-mail: [email protected]
‡Department of Physics & Electronic Engineering, University of Waikato,
Private Bag 3105, Hamilton, New Zealand
§HortResearch Technology Development Group, Private Bag 3123, Hamilton,
New Zealand
¶PO Box 4395, Hamilton, New Zealand
**Department of Biological Sciences, University of Waikato, Private Bag 3105,
Hamilton, New Zealand
(Received 13 November 2000; in Ž nal form 26 July 2001)
Abstract. Chlorophyll red-edge descriptors have been used to estimate leaf nitrogen concentration in ryegrass (L olium spp.) pasture. Two-layer model calculations
have been used to predict the in uence of chlorophyll content and Leaf Area Index
(LAI) on the shape and location of the peaks observed in the derivative spectra of
a ryegrass canopy. The complex structure of the resulting derivative spectra precluded extracting red-edge wavelengths by Ž tting inverted Gaussian curves to
re ectance proŽ les. Fitting a combination of three sigmoid curves to the calculated
re ectance spectra provided a better representation of subsequent derivative spectra.
The derivative spectra in the vicinity of the chlorophyll red-edge is predicted to
contain two peaks (~705 and ~725 nm), which on increasing the canopy LAI is
generally found to shift to longer wavelengths. However, for a canopy containing
leaves of low chlorophyll content and LAI>5, the wavelength of the Ž rst peak
becomes insensitive to changes in LAI. The same phenomenon is predicted for
high-chlorophyll leaves of LAI>10. The role of multiple scattering, primarily due
to increased leaf transmittance at higher wavelengths, has also been veriŽ ed. In
subsequent experiments, the predicted shape of the derivative spectra was observed
and the use of three sigmoid curves to better represent this shape veriŽ ed. Changes
in the descriptors used to describe the chlorophyll red-edge were observed to
explain 60% and 65% of the variance of leaf nitrogen concentration and total leaf
nitrogen content, respectively. The resulting regression equation was found to
predict leaf nitrogen concentration, in the range of 2–5.5%, with a standard error
of prediction (SEP) of 0.4%. The confounding in uence of canopy biomass on the
red-edge determination of leaf nitrogen concentration was found to be signiŽ cantly
less at higher canopy biomass, conŽ rming both theoretical predictions and the
potential of using the chlorophyll red-edge as a biomass-independent means of
estimating leaf chlorophyll, and hence nitrogen, concentration in high-LAI ryegrass
pastures.
*On sabbatical leave from Farrer Centre, Charles Sturt University, Wagga Wagga, NSW
2678 Australia.
International Journal of Remote Sensing
ISSN 0143-1161 print/ISSN 1366-5901 online © 2002 Taylor & Francis Ltd
http://www.tandf.co.uk/journals
DOI: 10.1080/01431160110114529
3620
1.
D. W. L amb et al.
Introduction
Nitrogen is one of six macronutrients that are essential for pasture growth; its
importance is well established (Simpson 1987). Nitrogen is necessary for the production of protein and chlorophyll and these are essential for plant development, yield,
post-grazing regrowth and reproduction (Vickery 1981). On the other hand, too
much nitrogen uptake in some pasture grasses promotes accumulation of nitrogenous
compounds, which are toxic to grazing animals, in the grass leaves. Under such
‘unfavourable’ conditions, pastures dominated by single species such as perennial
ryegrasses (L olium perrenne) may be hazardous to livestock (McDonald 1981).
Nitrogen is also important from the point of view of animal nutrition. Protein
or non-protein nitrogen are required by ruminant animals to sustain microbial
activity in the rumen and ensure an adequate supply of microbial protein for
subsequent digestion (McDonald et al. 1975). As such, one empirical measure
of the chemical composition of feed generally used is: Crude protein =nitrogen
concentration (%)×6.25 (Pearson and Ison 1987).
In-Ž eld fertilizer-response trials have long been used for determining the
‘adequacy’ of nitrogen levels in pasture production; however, they are increasingly
expensive and extrapolation to nearby soils is unreliable. Nowadays, direct measurement of leaf nitrogen concentration in pasture grasses, either as a means of assessing
pasture condition or nutritional value, is completed on pasture samples in the
laboratory either by a chemical process known widely as the Kjeldahl technique or
using near-infrared (NIR) re ectance spectroscopy. In the former, samples are ovendried, typically overnight, and then subjected to a destructive chemical extraction
process involving Kjeldahl digestion and subsequent determination of ammonia by
distillation (Jones and Moseley 1993). NIR spectroscopy involves measuring the
re ectance spectra of samples in the wavelength range of 800 nm to 2.5 mm. Prior to
measurement, samples are either oven-dried, powdered and packed, or chopped fresh
and packed into appropriate cuvettes. Nanometre-resolution spectrometers are necessary for NIR spectroscopy as it is often derivative spectra that are utilized in the
calibration and prediction analyses. The determination of nitrogen or crude protein
content is more precise using samples of fresh grass (Murray 1986). However, this
introduces diYculties in locations where there are no readily-available laboratory
facilities. Nevertheless, it is possible to calibrate for, and predict, crude protein
content in forage/grasses with an R2 >0.95 and a standard error of prediction
(SEP)<10.7 g kgÕ 1 (1.1%) respectively (summarized by Murray 1993). Because both
Kjeldahl and NIR processes involve Ž eld sampling and preparation of pasture
samples prior to laboratory measurements, the determination of nitrogen in pastures
can be time consuming and expensive, especially when large numbers of samples are
involved. Furthermore, the chemicals associated with the Kjeldahl technique makes
it potentially hazardous to the user.
Optical remote sensing of pasture nitrogen, based on canopy re ectance in the
visible–NIR wavelengths (400–900 nm), is a low-cost and feasible alternative to
laboratory-based analysis. Field re ectance spectroscopy is both non-destructive and
is completed in situ, precluding the need for time-consuming and costly Ž eld sampling,
sample preparation and subsequent laboratory analysis.
Nitrogen is a key component of chlorophyll and, as such, diVerent levels of
nitrogen in any given plant will generally be re ected in the concentration of
chlorophyll in plant leaves (Donahue et al. 1983). Nitrogen deŽ ciency results in
chlorosis (yellowing) of leaves due to a drop in chlorophyll content. A visible paling
Estimating leaf nitrogen concentration
3621
Ž rst occurs in older leaves while the young and developing leaves remain green. This
is characteristic of most plants as the nitrogen deŽ ciency initiates senescence on the
lower, older leaves while the metabolites from the breakdown of their proteins and
chlorophyll are transported to the upper, younger leaves (Devlin 1969, Atwell et al.
1999). Adequate nitrogen also produces thinner cell walls in plant leaves, resulting
in tender, more succulent plants (Donahue et al. 1983).
Since plant canopy re ectance in visible–NIR wavelengths is predominantly
in uenced by chlorophyll-related plant pigments (400–700 nm) and leaf cell structure
(600–900 nm) (Bonham-Carter 1987, Campbell 1996), plant nitrogen levels would
be expected to in uence canopy re ectance in these wavelengths.
To date, re ectance spectroscopy involving visible–NIR wavelengths has concentrated on the delineation of canopy chlorophyll content using features of the chlorophyll red-edge. The chlorophyll red-edge describes the region of steep positive
gradient in the re ectance spectra of chlorophyll-containing plants in the range
690–740 nm (Ž gure 1(a)). The region of low red re ectance (~690 nm) results
from chlorophyll absorption, and high NIR re ectance (~740 nm) results from
inter-cellular scattering within the leaves (Bonham-Carter 1987, Campbell 1996).
The ‘red-edge wavelength’ is deŽ ned as that wavelength within the range
690–740 nm corresponding to the maximum slope in the re ectance proŽ le. The
point of maximum slope is displaced towards longer wavelengths with increasing
chlorophyll concentration (Horler et al. 1983, Buschmann and Nagel 1993, Pinar
and Curran 1996). Because of the link between chlorophyll concentration and plant
growth and development (for example, Danks et al. 1983), the location of the rededge wavelength has been used to estimate nutritional status and developmental
stage (Horler et al. 1983, Boochs et al. 1990, Filella and Peñuelas 1994) and yield
(Munden et al. 1994) of agricultural crops and grasses.
The structure of the chlorophyll red-edge is best observed by plotting dR/dl, the
Ž rst derivative with respect to wavelength (Ž gure 1(b)). A common approach for
locating the red-edge wavelength has been to manually or computationally locate
the highest peak in the derivative spectra (Horler et al. 1983, Booschs et al. 1990,
Buschmann and Nagel 1993, Filella and Peñuelas 1994, Munden et al. 1994).
Alternatively, researchers Ž t a portion of a single Gaussian curve to the red-edge
and extract the maximum-slope wavelength from the resulting analytical expression
(Bonham-Carter 1987, Miller et al. 1990, Pinar and Curran 1996). The limitation of
both techniques is the implicit assumption that there is only a single maximum in
the gradient of the red-edge. In fact the chlorophyll red-edge has been observed to
contain two (or more) gradient maxima and consequently two (or more) peaks in
the derivative spectrum (Horler et al. 1983, Booschs et al. 1990, Miller et al. 1990,
Filella and Peñuelas 1994). Experimental results suggest the Ž rst peak in the derivative spectrum, at around 705 nm, is in uenced by chlorophyll concentration while a
second peak, at approximately 725 nm, is in uenced by the combination of chlorophyll concentration and multiple scattering within the plant canopy (Horler et al.
1983, Boochs et al. 1990); the latter related to leaf biomass.
The relative magnitudes of both peaks in the derivative spectrum depends on the
combination of chlorophyll concentration and the amount of multiple scattering
within the canopy. In a procedure where the wavelength of the largest peak in the
derivative spectra is recorded as a function of chlorophyll concentration for a plant
canopy, ‘gaps’ or ‘sudden transitions’ are observed in scatterplots of red-edge wavelength versus chlorophyll content. This occurs when the relative magnitude of the
3622
Figure 1.
D. W. L amb et al.
Idealized (a) re ectance and (b) derivative spectrum for typical chlorophyllcontaining vegetation.
peaks changes from that where the Ž rst peak is larger (‘phase 1’) to that where the
second peak is larger (‘phase 2’). Results suggest this transition occurs as the chlorophyll concentration in single leaves increases or as a result of multiple scattering
between leaves. The higher gradient of red-edge wavelength versus chlorophyll concentration for phase 2 compared to phase 1 is likely the result of the second peak
responding to total chlorophyll content (leaf chlorophyll concentration ×biomass).
When a single Gaussian curve is Ž tted to the chlorophyll red-edge, the retrieved
Estimating leaf nitrogen concentration
3623
single red-edge wavelength will lie between the two derivative peaks as evidenced in
Ž gure 1(a) of Miller et al. (1990). The retrieved ‘average’ red-edge wavelength will
yield stronger correlations with chlorophyll content than chlorophyll concentration
(Miller et al. 1990, Pinar and Curran 1996) because the average wavelength is
in uenced by the entire red-edge, a combination of chlorophyll concentration (Ž rst
peak in the derivative spectrum) and chlorophyll concentration/leaf biomass (second
peak in the derivative spectrum). Conversely, the same phenomenon reduces the
strength of the correlation between the average red-edge wavelength and total
biomass alone (for example, Pinar and Curran 1996).
Our understanding of the in uence of chlorophyll concentration and multiple
leaf scattering on the two peaks observed in the derivative spectra of plant canopies
is based on a very small number of experimental observations (Horler et al. 1983,
Boochs et al. 1990). For example, Horler et al. (1983) demonstrated that progressively
stacking single maize (Zea mays L.) leaves resulted in a signiŽ cant increase in the
magnitude of the second peak in the derivative spectra with little change to the
magnitude and wavelength of the Ž rst peak. This suggests the wavelength of the Ž rst
peak may be insensitive to Leaf Area Index (LAI), the parameter that speciŽ es the
average number of leaves encountered in a vertical traverse through a canopy.
Furthermore, derivative spectra acquired at spatial intervals along a single leaf,
where changes in chlorophyll concentration would be expected, showed signiŽ cant
diVerences in the magnitude of the Ž rst peak in the derivative spectra and no change
in the second, multiple scattering component. Miller et al. (1990) demonstrated
similar, although less dramatic, results for leaf stacking using leaves of Bur oak
(Quercus macrocarpa). However, to date, such experimental evidence is yet to be
supported by plant canopy model calculations.
Our own interest in the eVects of chlorophyll concentration and multiple scattering on the shape of the derivative spectra is motivated by our programme of
research investigating spectroscopic methods of estimating nitrogen content of dairy
pastures in the Waikato region of New Zealand (Lat. 38° S). We seek a simple
methodology for estimating leaf nitrogen concentration which avoids the need for
physical measurements of plant biophysical parameters such as biomass. The chlorophyll red-edge is a suitable candidate since plant nitrogen status is often related to
chlorophyll content (Everitt et al. 1985, Boochs et al. 1990) and experimental results
in unrelated plant types have suggested that the Ž rst peak in the derivative spectra
may be insensitive to changes in biomass (or LAI) (Horler et al. 1983, Boochs
et al. 1990).
Ryegrass (L olium spp.) is a key component of irrigated and rain-fed dairy pastures
in the moist temperate Waikato region of New Zealand. Typical Waikato dairy
pastures include the ryegrass and clover (T rifolium subterranean L.) in various mixes
ranging from pure ryegrass to an approximate mix of 80% ryegrass:15% clover.
Pasture biomass ranges from 200 to 4000 kg (dry weight) per hectare, LAI from 1
up to as high as 12, and moisture content from # 70% in summer to # 85% in early
winter (Hanna et al. 1999). Typical leaf nitrogen concentrations in the ryegrass
component of the pasture is observed to range from 2% to 5% by mass.
As a Ž rst step in our investigation of the chlorophyll red-edge, we wish to verify
the in uence of chlorophyll concentration and canopy biomass on the shape and
location of the peaks in the derivative spectra of pure ryegrass. In this paper, a
theoretical two-layer pasture canopy model, previously reported in Hanna et al.
(1999), has been constructed to calculate detailed spectral re ectance curves, and
D. W. L amb et al.
3624
consequently derivative spectra, of a realistic ryegrass pasture canopy for varying
levels of leaf chlorophyll concentration and biomass. In these calculations, canopy
biomass is expressed through LAI. Increasing the LAI of the top canopy for a given
single leaf type is equivalent to Ž xing the chlorophyll concentration but increasing
total chlorophyll traversed by the incident radiation within the canopy. In order to
conŽ gure the model to represent a ryegrass pasture canopy, detailed spectral
re ection/transmission characteristics for ryegrass and soil have also been measured.
Furthermore, we investigate an alternative method for extracting descriptors of the
chlorophyll red-edge, speciŽ cally the peak wavelengths, from the complex derivative
spectra of ryegrass canopies and compare this approach with the standard approach
of Ž tting a single inverted Gaussian to the re ectance proŽ les. The results of
the model calculations are discussed in terms of practical requirements of using
chlorophyll red-edge to estimate leaf nitrogen concentration in ryegrass pastures.
Following veriŽ cation of the nature of the derivative spectra of ryegrass canopies,
the alternative method of extracting red-edge descriptors is then applied to measured
spectral re ectance proŽ les of 100 sample sites of diVerent canopy biomass and leaf
nitrogen levels to estimate leaf nitrogen concentration and total nitrogen content.
2.
Two-layer canopy re ectance model
The two-layer canopy re ectance model, previously described in Hanna et al.
(1999), is based on the analytical solution of a two-stream plant canopy model
(Sellers 1985); which has the governing equations
m
­
mÅ
dI l
=I ­
l
dt
vl (1­
dI 3
l =I 3­ v (1­
l
l
dt
bl )I l ­
vl bl Il3­ vl b0 mkeÕ kt
bl )I 3
l ­ vl bl I l ­
vl (1­
b0 )mkeÕ kt
(1)
(2)
Here, m is the average inverse diVuse optical depth per unit leaf area in the canopy;
I l and I3
l are the wavelength-dependent upward and downward diVuse  uxes divided
by the incident solar  ux; t is the canopy LAI; vl is the sum of the wavelengthdependent single leaf re ectance rl , and transmittance, tl ; bl is the wavelengthdependent backscatter distribution function for the diVuse beam; b0 is the backscatter
parameter for the incident beam; and k is the optical depth of the direct beam per
unit leaf area.
The two-layer canopy model is generated by solving equations (1) and (2) for I
and I 3using appropriate boundary conditions for each speciŽ ed layer (see Appendix
for details). The wavelength-dependent canopy re ectance is computed using
Rl ¬I l (t=0)
(3)
where t=0 corresponds to the top of the canopy.
A simpliŽ ed diagram of the two-layer ryegrass pasture represented in the model
is given in Ž gure 2 and a detailed schematic is given in Ž gure A1. In this model we
specify the spectral characteristics and LAI of the top pasture canopy ( layer a), a
layer of dead material which usually exists within the pasture proŽ le (layer b), and
the re ectance characteristics of the underlying soil. The LAI of the layer of dead
material was set to unity and the LAI of the top ryegrass was canopy varied over
Estimating leaf nitrogen concentration
Figure 2.
3625
SimpliŽ ed diagram of the two-layer ryegrass canopy represented in the model.
the range of 1–10 to mimic the pasture conditions we observed during a number of
Ž eld visitations.
3. Single-leaf and soil spectral characteristics
In order to apply equations (1) and (2) to the model, the two-layer theory
requires detailed single leaf re ectance and transmittance data for each canopy layer,
and re ectance data for the underlying soil. In the previous work of Hanna et al.
(1999) involving only three re ectance wavebands (NIR, red and green), the model
was run using a combination of actual and synthetic maize data since appropriate
ryegrass data were unavailable. In this current work, however, the necessary re ection
and transmission characteristics of fresh ryegrass leaves were acquired from laboratory measurements, and soil re ectance measurements acquired from outdoor
measurements.
3.1. Single-leaf re ectance and transmittance data
Re ectance and transmittance measurements were completed on single high- and
low-chlorophyll content, chlorotic (very low chlorophyll content) and dead ryegrass
leaves. Single leaves were sampled from pure ryegrass plots used in a long-term
fertilizer treatment program by the Dairy Research Institute, Hamilton, New Zealand.
Leaf samples of high and low chlorophyll concentration were hand-picked from
400 kg ha and 0 kg ha nitrogen treatment plots, respectively. Chlorotic leaves, those
with a>50% surface coverage of rust, and dead leaf samples were also hand-picked
from the 0 kg ha nitrogen plot. The ryegrass samples were immediately placed in a
cooled black plastic bag and transported to the laboratory for subsequent analysis.
Re ectance and transmittance measurements were completed using a Zeiss
MMS-1 Monolithic Miniature Spectrometer (Carl Zeiss OEM Sensorik/Prozeßanalytik, Oberkochen GmbH ). The Zeiss spectrometer comprised a  at-Ž eld grating
of 366 lines mm, blazed for 330 nm. Coupled with a 70 mm×2500 mm entrance slit
and a 256-pixel linear diode array, the spectrometer had a useable wavelength range
of 305 nm to 1150 nm, with 3.3 nm resolution.
For re ectance measurements (Ž gure 3(a)), light from a 40 W quartz tungsten
halogen source (Ocean Optics LS-1, Ocean Optics Inc. Dunedin, FL, USA) was
directed onto the surface of a clamped leaf specimen via a dual-optical Ž bre coupler
comprising a hollow-hexagonal array of multimode Ž bres surrounding a central
multimode Ž bre (numerical aperture=0.2, core diameter=400 mm). The central Ž bre
directed the re ected light from the leaf surface into the input slit of the Zeiss
spectrometer. For each measurement, the leaf was clamped  at on the surface of
a>99% re ectance Spectralon re ectance target (SRT-99-100, Labsphere Inc.,
3626
D. W. L amb et al.
Sutton, NH, USA) and the Ž bre illumination/detection bundle was placed 9.5 mm
from, and normal to, the leaf surface using a precision spacer. Spectra were averaged
and recorded using ‘tec5’ software (Sensorik und Systemtechnik, GmbH ) on an IBMcompatible computer. The apparent re ectance was determined from the ratio of the
light measured from the leaf surface to that measured from the exposed Spectralon
panel ( leaf removed).
Since the measured intensity of the re ected light included multiple re ections/
transmissions of light from the Spectralon panel through the leaf body, it was
assumed that the abaxial and adaxial surface re ectances were equal. The leaf surface
re ectance was then calculated from the apparent re ectance following Methy et al.
(1998), using
(r¾ +1)­ ã (r¾l +1)2 ­ 4(r¾l ­ t2l )
rl = l
(4)
2
where rl is the re ectance of the leaf surface, r¾l is the apparent re ectance as
measured by the spectrometer and tl is the measured leaf transmittance.
Leaf transmittance was measured by directly illuminating the clamped leaf
samples from behind using a collimated 100 W quartz tungsten halogen light source
directed through a 3 mm thick frosted glass diVusing plate (Ž gure 3(b)). Transmitted
light was collected by the central Ž bre of the dual-optical Ž bre bundle (described
above), placed on the downstream side of the leaf and spaced 9.5 mm from, and
normal to, the leaf surface. Transmittance was calculated by measuring the intensity
of light with and without the leaf sample in place.
3.2. Soil re ectance
In-Ž eld soil re ectance measurements were acquired using the Zeiss MMS-1
spectrometer mounted in a Ž eld-portable conŽ guration complete with artiŽ cial target
illumination source and shroud to block ambient sunlight (Ž gure 4). The rigid shroud,
constructed from 3.5 mm thick black polyethylene plastic, housed the optical Ž bre
bundle and foreoptic for the Zeiss spectrometer (mounted on top of the shroud ) and
the artiŽ cial light source. The latter comprised two 20 W quartz tungsten halogen
light bulbs, spaced 40 mm on either side of the Ž bre foreoptic. The foreoptic and
light sources were held 0.52 m above the ground, at nadir, by the rigid shroud. The
foreoptic/Ž bre bundle provided the spectrometer with a 100 mm diameter circular
footprint on the ground, equivalent to a Ž eld of view of approximately 5.5°.
Soil re ectance spectra were acquired and averaged from a number of Ž eld
locations within the Dairy Research Institute, Hamilton, New Zealand.
4. Results of model calculations
4.1. Single leaf and soil spectral characteristics
Measured re ectance and transmittance spectra of single high-and lowchlorophyll, chlorotic and dead ryegrass leaves are given in Ž gure 5. The re ectance
spectra of bare soil is also included in Ž gure 5(a).
The derivative spectra of the single leaves corresponding to Ž gure 5(a) are given
in Ž gure 6. These were calculated using
A B
dR
R ­ R(lÕ 1)
= l
(5)
Dl
dl l
where Rl ­ R(lÕ 1) is the diVerence in re ectance measured across a single wavelength
increment centred at l and Dl is the wavelength increment of the spectrometer.
Estimating leaf nitrogen concentration
3627
(a)
(b)
Figure 3. Schematic diagram showing apparatus used for single leaf (a) re ectance and
(b) transmittance measurements.
From the curves of Ž gure 6 it is evident that the derivative spectra of the highand low- chlorophyll and chlorotic leaves contain peaks at both ~705 and ~725 nm.
For the low-chlorophyll and chlorotic leaves the Ž rst feature (~705 nm) is dominant.
In the high-chlorophyll leaves the second feature (~725 nm) is dominant.
4.2. Model predictions
Canopy re ectance proŽ les generated by the model using high-chlorophyll, lowchlorophyll and chlorotic leaves of LAI from 1 to 5 in the top canopy are given
in Ž gure 7.
3628
Figure 4.
D. W. L amb et al.
Schematic diagram of the Ž eld-portable spectrometer used for acquiring soil
re ectance spectra.
4.2.1. T he eVect of increasing L AI on the magnitude of peaks in the derivative
spectra
Derivative spectra corresponding to Ž gure 7 are given in Ž gure 8. It is evident
here that increasing the LAI of the top canopy produces a signiŽ cant increase in the
magnitude of the second peak in the derivative spectra, a phenomena supported by
the experimental observations of Horler et al. (1983) using maize leaves.
In the case of low-chlorophyll (Ž gure 8(b)) and chlorotic (Ž gure 8(c)) leaves, the
magnitude of the Ž rst peak is initially comparable to, or larger than, that of the
second peak at low LAI. The substantial increase in magnitude of the second peak
with increasing LAI is linked to an increase in the magnitude of the NIR plateau in
the individual re ectance proŽ les (Ž gure 7). This is attributed to signiŽ cantly greater
multiple scattering of radiation within the canopy in NIR red wavelengths due to
higher leaf re ectance and transmittance.
The eVect of multiple scattering can be veriŽ ed by modifying the transmittance
characteristics of one of the candidate leaf types. For example, if the transmittance
of a low-chlorophyll leaf is artiŽ cially reduced at higher wavelengths, as depicted in
Ž gure 9, then signiŽ cantly smaller increases in the magnitude of the second peak
with increasing LAI are observed (Ž gure 10).
4.2.2. Extracting red-edge parameters from the derivative spectra
Examples of modelled re ectance spectra for high and low chlorophyll-containing
ryegrass canopies (LAI=1) are reproduced in Ž gure 11. Superimposed on the
re ectance, and corresponding derivative spectra (Ž gure 12), are Ž tted curves corresponding to Ž tting a single inverted Gaussian (equation (6)—table 1) and a combination of three sigmoid functions (equation (7)—table 1) to the re ectance proŽ les.
The extracted red-edge wavelengths (lP ) and the sum of squared residuals (SSR) of
the respective Ž tted curves are also listed in table 2.
Estimating leaf nitrogen concentration
3629
(a)
(b)
Figure 5. (a) Measured re ectance spectra for single ryegrass leaves ( high- and lowchlorophyll, chlorotic and dead), and bare soil. (b) Single-leaf transmittance spectra
for high and low chlorophyll content, chlorotic and dead ryegrass leaves.
It is evident from Ž gures 11 and 12 that, like the single-leaf spectra of Ž gure 6,
the shape of the chlorophyll red-edge for ryegrass canopies is complex, containing
two local maxima in the gradient at approximately 705 and 725 nm, respectively.
Single, and combinations of two, three and four sigmoid functions were used to
construct curves to reproduce the observed re ectance proŽ les. In all cases, the use
of three sigmoids was found to yield the lowest SSR values, and always considerably
lower SSR values than the Ž tted Gaussian curve (table 2). In most test cases, the
three sigmoids resulting from the Ž tting procedure comprised two sigmoids of positive
gain and amplitude ( gn and An —table 1) corresponding to the two peaks observed
in the derivative spectra, hitherto referred to as l1 and l2 , respectively, as well as a
third sigmoid with a relatively small negative gain. In the particular, though representative examples of table 2, the wavelength of the third sigmoid (in brackets)
corresponds to the location of the peak chlorophyll absorption of red light where a
re ectance minimum is observed in the re ectance proŽ les (Ž gure 11).
3630
Figure 6.
D. W. L amb et al.
Single-leaf derivative re ectance spectra, (dR/dl), for high- and low-chlorophyll,
and chlorotic ryegrass.
As observed in the results of Miller et al. (1990), the single red-edge wavelength
predicted by the Gaussian Ž tting routine lies between the two peaks observed in the
complex derivative spectra. As expected (Miller et al. 1990, Pinar and Curran 1996),
both the single red-edge peak resulting from the Gaussian analysis and the two
peaks resulting from the sigmoid-Ž tting procedure have shifted to higher wavelengths
in response to higher leaf nitrogen content ( higher chlorophyll ).
4.2.3. T he eVect of increasing L AI on the wavelengths of peaks in the derivative spectra
The wavelengths corresponding to both peaks in the derivative spectra of the
calculated re ectance proŽ les were extracted following the procedure outlined above.
The eVects of increasing LAI on the wavelengths of the two peaks are summarized
in Ž gure 13.
It is evident from these model results that increasing LAI progressively shifts
both derivative peaks towards longer wavelengths. Progressively stacking leaves will
eVectively increase total chlorophyll absorption experienced by the incident radiation
through multiple scattering, thereby shifting the derivative peaks to higher wavelengths. The magnitude of the wavelength shift resulting from increasing LAI from
1 to 10 is greater for the second peak (Ž gure 13(b)). This is not surprising, given the
higher leaf transmittance and re ectance in the associated wavelength range
(724–740 nm) (Ž gure 5, table 3). This eVect is also observed to occur for the Ž rst
peak (Ž gure 13(a)), although to a lesser extent due to lower leaf re ectance and
transmittance in the corresponding wavelength range (702–709 nm) (Ž gure 5, table 3).
There is a partial overlap of the curve shoulders in Ž gure 13 for a small range of
red-edge wavelengths. The overlap of the Ž rst peak occurs for wavelengths
703–704.2 nm and for the second peak is 726–730 nm. This overlap demonstrates
the confounding in uence of leaf chlorophyll concentration and canopy LAI on
Estimating leaf nitrogen concentration
3631
(a)
(b)
(c)
Figure 7. Model-derived re ectance spectra for a ryegrass canopy containing a lower dead
layer (LAI =1) and a top canopy of (a) high-chlorophyll, (b) low-chlorophyll and
(c) chlorotic ryegrass leaves of LAI from 1 to 5.
D. W. L amb et al.
3632
(a)
(b)
(c)
Figure 8. Model-derived derivative spectra for a ryegrass canopy containing a lower dead
layer (LAI=1) and a top canopy of (a) high-chlorophyll, (b) low-chlorophyll and
(c) chlorotic ryegrass leaves of LAI from 1 to 5.
Estimating leaf nitrogen concentration
3633
Figure 9. Low-chlorophyll leaf transmittance proŽ les used in model calculations; the
actual proŽ le measured in the laboratory (from Ž gure 5(b)) and a synthesized proŽ le
calculated using
CG
t¾ =t ,
l l
lå
H
1
t¾ = t 715 nm + t ,
l
l=
10 l
715 nm
l>715 nm
D
where t¾l =synthesized transmittance, tl =actual transmittance.
red-edge wavelength, particularly at lower values of LAI. Here it would be possible
to determine total chlorophyll content but not chlorophyll concentration unless an
additional measurement of canopy LAI (or biomass) was completed.
The wavelength/LAI plots of both red-edge peaks tends to saturate at higher
LAI. This is in keeping with the fact that due to scattering and absorption, progressively less incident radiation interacts with additional leaves deeper within the canopy
as the radiation traverses vertically through the canopy. This is also supported by
the trends observed in the re ectance spectra with increasing LAI (Ž gure 7). For
LAI>10 for the high-chlorophyll leaves and LAI>5 for the low-chlorophyll and
chlorotic leaves, the wavelengths of both derivative peaks are no longer sensitive to
changes in LAI. The wavelength of the Ž rst peak of the chlorotic leaves appears
always insensitive to changes in LAI.
5. Experimental observations
The ryegrass plots studied in this work were located at the Dairy Research
Institute, Hamilton, New Zealand (Lat. 37° 47ê S, Long. 175° 17ê E). Detailed canopy
re ectance measurements were completed at 100 locations comprising a range of
canopy biomass and leaf nitrogen levels. Field samples were taken for laboratory
dissection and analysis of nitrogen content.
3634
D. W. L amb et al.
Figure 10. Calculated derivative spectra using actual and synthetic leaf transmittance data.
5.1. Measurement of canopy re ectance
In-Ž eld measurements of canopy re ectance were acquired using the spectrometer
described in §3.2.
Canopy re ectance was calculated by taking the ratio of the measured radiance
re ected oV the canopy to that re ected oV a>99% re ectance Spectralon re ectance
target (SRT-99-100, Labsphere Inc. Sutton, NH, USA). In order to minimize the
eVect of illumination/sensor azimuth on the measured radiance, canopy measurements were averaged for two readings, each taken at a relative azimuth of w=0°
and 90°.
5.2. Collection and dissection of Ž eld samples
Immediately following each re ectance measurement, the precise area corresponding to the footprint of the Ž eld spectrometer was harvested to soil level and packed
in bags for laboratory dissection into live leaf, live stem, chlorotic leaf, dead leaf
and ‘other species’ sub-groups. All samples were subsequently oven dried at 75°C
overnight and each sub-group weighed for total biomass.
5.3. Nitrogen analysis
Approximately 1 mg portions of each dried live-leaf sub-group was ground and
re-weighed. Leaf nitrogen concentration, expressed as a percentage of leaf dry weight,
and total nitrogen content, expressed in grams, were determined by Kjeldahl digestion
and subsequent determination of ammonia by distillation (Ministry of Agriculture,
Fisheries and Food 1986).
5.4. Extracting chlorophyll red-edge parameters f rom spectral proŽ les
The appropriateness of the three-sigmoid curve-Ž tting methodology described in
§4.2.2 was checked using representative measured re ectance spectra. Again, the
Estimating leaf nitrogen concentration
3635
(a)
(b)
Figure 11. Modelled and Ž tted re ectance proŽ le for a (a) high-chlorophyll and (b) chlorotic
ryegrass canopy of LAI=1.
measured re ectance spectra were also characterized using the standard procedure
of Ž tting portions of a Gaussian curve (table 1) to the spectra. In addition to rededge wavelengths described in table 1, the height of the red-edge step was calculated
from the area under each derivative spectrum using the analytical expression Ž tted
to each of the re ectance proŽ les according to
P
step height=
l= 780 nm dR
l dl=R ­
780
dl
l= 670 nm
R670
(6)
3636
D. W. L amb et al.
(a)
(b)
Figure 12. Derivative re ectance spectra of modelled and Ž tted curves for the (a) highchlorophyll and (b) chlorotic ryegrass canopy of Ž gure 11.
Here R670 and R780 are the calculated re ectances at 670 and 780 nm, respectively.
Multiple linear regression analyses, based on least squares, were completed using
combinations of the extracted red-edge descriptors and measured leaf nitrogen concentration and total leaf nitrogen content (nitrogen concentration ×leaf dry weight).
6. Results of experimental observations and discussion
6.1. Extracting red-edge parameters f rom the measured derivative spectra
Examples of measured re ectance spectra for known high and low nitrogencontaining ryegrass canopies are given in Ž gure 14. Corresponding derivative spectra,
given in Ž gure 15, were calculated using equation (5). Superimposed on the
re ectance and derivative spectra are Ž tted curves corresponding to equations (1)
Estimating leaf nitrogen concentration
Table 1.
Two curve-Ž tting procedures evaluated for extracting red-edge wavelengths (lP )
from measured re ectance proŽ les.
Equation type and
procedure
Formula
1. Fit single
Gaussian to
re ectance proŽ le
2. Fit n sigmoids to
re ectance proŽ le
Table 2.
Rl =Rmax ­ (Rmax ­ Rmin )eÕ {(l0 Õ l)2/2s} (6)
Rmax =average re ectance of NIR plateau
Rmin =re ectance at peak red absorption
l0 =wavelength (nm) of peak absorption (corresponding to
wavelength of Rmin )
s=width (nm) of Gaussian proŽ le
lP =l0 +s=wavelength (nm) of the point of in ection in Rl
(corresponding to the peak in derivative spectrum)
Rl =Sn {On + An /1+eÕ gn(lÕ lp) } (7)
On =re ectance oVset of sigmoid n
An =amplitude of sigmoid n
gn =gain of sigmoid n
lP =wavelength (nm) of the point of in ection in sigmoid n
(corresponding to a peak in the derivative spectrum)
Red-edge wavelengths and SSR values for Ž tted curves of Ž gure 11.
High chlorophyll
lP
SSR
3637
Chlorotic
Gaussian Ž t
Three-sigmoid Ž t
Gaussian Ž t
Three-sigmoid Ž t
719.7 nm
(675.1 nm)
703.6 nm
729.3 nm
1.08×10Õ 5
713.2 nm
(675.1 nm)
703.6 nm
724.0 nm
1.99×10Õ 5
1.92×10Õ 3
1.20×10Õ 4
and (2) (table 1 ). The extracted red-edge wavelengths (lP ) and SSR of the respective
Ž tted curves are also listed in table 4.
It is evident from Ž gures 14 and 15 that the shape of the chlorophyll red-edge
for ryegrass canopies is complex, containing two local maxima in the gradient at
approximately 700 and 720 nm, respectively. The shapes of the derivative spectra in
Ž gure 15, particularly the relative magnitudes of the two peaks corresponding to
high and low nitrogen content leaves, are similar to that predicted by the earlier
model calculations involving a canopy of rye grass containing leaves of high and
low chlorophyll concentration, respectively (Ž gure 8). As in evaluating the earlier
synthesized derivative spectra, the use of three sigmoids was again found to yield
the lowest SSR values of either a single or combinations of two, three or four sigmoid
functions. Again, considerably lower SSR values result from using the three-sigmoid
combination compared to the Ž tted Gaussian curve (table 4). Again, the single rededge wavelength predicted by the Gaussian Ž tting routine lies between the two peaks
observed in the complex derivative spectra. Furthermore, both the single red-edge
peak resulting from the Gaussian analysis and the two peaks resulting from the
sigmoid-Ž tting procedure have shifted to higher wavelengths in response to higher
leaf nitrogen content (higher chlorophyll ).
3638
D. W. L amb et al.
(a)
(b)
Figure 13. Extracted wavelengths, corresponding to the (a) Ž rst and (b) second peaks in the
derivative spectra, for varying LAI.
Estimating leaf nitrogen concentration
Table 3.
3639
Single wavelength transmittance and re ectance values extracted from Ž gure 5, and
calculated absorption coeYcient (a) assuming a=1­ r­ t.
a=1­
r­
Transmittance, t
Re ectance, r
l=706 nm
High chlorophyll
Low chlorophyll
Chlorotic
0.028
0.044
0.068
0.256
0.320
0.379
0.716
0.636
0.553
l=729 nm
High chlorophyll
Low chlorophyll
Chlorotic
0.063
0.074
0.096
0.589
0.605
0.657
0.348
0.321
0.247
t
6.2. Red-edge wavelength and canopy nitrogen content
The results of multiple linear regression analyses involving both red-edge wavelengths and step height, and leaf nitrogen concentration (%) and total leaf nitrogen
content (g), respectively, are summarized in table 5.
The two red-edge wavelengths used to describe the chlorophyll red-edge explain
52% and 65% of the variance in leaf nitrogen concentration and total leaf nitrogen
content, respectively. A higher level of explanation is achieved with total leaf nitrogen
because changes in canopy biomass, in response to diVerent nitrogen levels, are also
aVecting the measured spectral signature. This conclusion is further supported when
the step height at the red edge (equation (6)) is also included in the regression
analyses. The step height is related to the Vegetation Index which has been shown
to correlate strongly with biomass (Hanna et al. 1999). On its own, R780 ­ R670
explains 33% of the variance observed in changes in total leaf nitrogen content and
only 11% of changes in leaf nitrogen concentration. However, incorporating
R780 ­ R670 into the regression analyses involving leaf nitrogen concentration
increases R2 by acting to include changes in leaf biomass. On the other hand,
including R780 ­ R670 in the total leaf nitrogen content analyses does not change R2
values because the biomass in uence has already been accounted for in the measure
of total leaf nitrogen content (total leaf nitrogen=leaf nitrogen concentration ×leaf
dry weight).
Regression equations involving all three descriptors and both measured nitrogen
concentration (%) and total nitrogen content (g) are listed in table 6. According to the
criteria discussed by Whitlock et al. (1982), F/Fcrit " 4 and R2 ! 1 should form
benchmark requirements for using remotely sensed radiance in a linear regression
analysis. Both regression equations in table 6 are signiŽ cant and accordingly show a
reasonable predictive utility. In order to estimate the error in using the regression
equations to estimate nitrogen concentration (%N) and content (Ntot ), the data was
randomly assigned into calibration and test sets. The calibration test set was used to
generate regression equations for nitrogen concentration and content, respectively.
These equations were then used to estimate nitrogen concentration and content for the
test data based on the spectral measurements. Comparison between the estimated and
actual test data produced an average diVerence of ±0.4% in estimating nitrogen
concentration in the range 0–5%, and ±0.006 g in estimating nitrogen content in the
range 0.02–0.05 g. Scatterplots comparing the nitrogen concentration and content estimated by the respective regression equations and the actual values are given in Ž gure 16.
Generally, a signiŽ cant proportion of the total canopy nitrogen exists in the
3640
D. W. L amb et al.
(a)
(b)
Figure 14. Measured and Ž tted re ectance proŽ le for a (a) high-nitrogen and (b) low-nitrogen
ryegrass canopy.
upper-canopy leaves due to increased competition for available sunlight, especially
when the plant is nitrogen-stressed (Wolfe et al. 1988). Leaves of higher nitrogen
content have a lower transmittance and higher re ectance at NIR wavelengths
(Ž gure 5). Consequently, the detected scattered radiation could be predominantly
in uenced by the upper canopy, higher nitrogen content leaves. The scatterplots of
Estimating leaf nitrogen concentration
3641
(a)
(b)
Figure 15. Derivative re ectance spectra of measured and Ž tted proŽ les for a (a) high-nitrogen
and (b) low-nitrogen ryegrass canopy.
Ž gure 16 do show that nitrogen concentration is overestimated, although only at
lower nitrogen levels. This phenomenon is the subject of further investigation.
6.3. ConŽ rming the in uence of canopy biomass on red-edge determination of leaf
nitrogen concentration
Earlier model calculations (§4.2.3) predicted that the in uence of canopy LAI, or
in this case biomass, on the location of the red-edge wavelengths would progressively
D. W. L amb et al.
3642
Table 4. Red-edge wavelengths and SSR values for Ž tted curves of Ž gure 14.
High nitrogen
Gaussian Ž t
Three-sigmoid Ž t
Gaussian Ž t
Three-sigmoid Ž t
711.2 nm
(673.3 nm)
699.6 nm
722.5 nm
1.49×10Õ 5
707.1 nm
(675.1 nm)
697.8 nm
719.6 nm
7.36×10Õ 5
lP
SSR
Low nitrogen
2.62×10Õ 3
3.24×10Õ 4
Table 5. Results of multiple linear regression analyses between combinations of red-edge
parameters, leaf nitrogen concentration and total leaf nitrogen content.
Red-edge feature
Leaf nitrogen concentration
(% leaf dry weight)
R2
Total leaf nitrogen
content (g)
R2
0.60
0.65
0.52
0.40
0.52
0.11
0.64
0.62
0.62
0.33
Principal red-edge wavelengths
(l1 , l2 ) and R780 ­ R670
l1 and l2
l1
l2
R780 ­ R670
Table 6. Linear multiple regression equations generated using red-edge parameters and
measured leaf nitrogen concentration (%) and total leaf nitrogen content (g).
Regression equation
F /F crit
%N=­ 1.74­ 0.0005l1 +0.0029l2 ­ 0.0006 (R780 ­ R670 )
Ntot =­ 6.48­ 0.0070l1 +0.0022l2 ­ 0.00006 (R780 ­ R670 )
12.16
15.57
R2
P<1×10Õ 15
P< 1×10Õ 17
0.60
0.65
Table 7. Pearson correlation coeYcients (R) for red-edge wavelength and nitrogen concentration (%) for three canopy biomass levels ( high: 1.5–2.7 g, medium: 1.0–1.5 g,
low: 0.5–1.0 g). Correlation coeYcients relating total green matter and leaf nitrogen
concentration are also included (italics).
Total green
biomass level
High
1.5–2.8 g
Medium
1.0–1.5 g
Low
0.5–1.0 g
Principal
red-edge
wavelength
Nitrogen
concentration %
R
l1
l2
0.61
0.55
l1
l2
0.71
0.82
l1
l2
0.45
0.72
Total green
biomass (g)
R
(­ 0.20)
0.008
0.002
(0.32)
0.35
0.40
(0.30)
0.28
0.35
Estimating leaf nitrogen concentration
3643
(a)
(b)
Figure 16. (a) Leaf nitrogen concentration (%) estimated by the regression equation compared
to actual leaf nitrogen concentration (test dataset). (b) Leaf nitrogen content (g)
estimated by the regression equation compared to actual leaf nitrogen content (test
dataset). Solid lines represent a zero error of prediction (SEP=0).
diminish with increasing biomass. When the Ž eld-plot data is subsequently stratiŽ ed
according to low (0.5–1.0 g), medium (1.0–1.5 g) and high (1.5–2.8 g) values of total
green biomass (total green biomass=live leaf+live stem fractions) (table 7), correlations between the two principal red-edge wavelengths (l1 # 700 nm, l2 # 720 nm) and
total green biomass are almost zero for the high biomass grouping.
3644
D. W. L amb et al.
7.
Conclusion
A two-layer canopy re ectance model has been constructed to generate detailed
re ectance spectra, and corresponding derivative spectra, of a realistic ryegrass
pasture canopy comprising an upper layer of varying LAI, a middle layer of dead
material and underlying soil. Detailed spectral re ectance and transmittance values
for high-chlorophyll, low-chlorophyll, chlorotic and dead single ryegrass leaves, and
re ectance data for underlying soil, were acquired to initialize the model. A more
accurate method of extracting red-edge wavelengths from complex derivative spectra,
involving a combination of three sigmoid functions was proposed. Model calculations
demonstrated the confounding eVects of chlorophyll content and LAI on the location
and shape of peaks in the derivative spectra at low LAI. Increasing LAI in the
canopy is found to signiŽ cantly increase the magnitude of the second peak due to
higher leaf transmittance at these wavelengths. The wavelength of both peaks shift
to longer wavelengths with increasing LAI as a result of the increase in total
chlorophyll absorption by multiple scattering of incident radiation between individual leaves. This is found to occur to a greater extent with the longer-wavelength
second peak as increased leaf re ectance and transmittance makes it more sensitive
to multiple scattering eVects.
The complex shape of the derivative spectra of ryegrass was also observed in
Ž eld measurements and the appropriateness of Ž tting three sigmoid curves to
re ectance proŽ les in order to extract chlorophyll red-edge descriptors was veriŽ ed.
In subsequent measurements the descriptors of the chlorophyll red-edge explained
60% and 65% of the variance, respectively, in leaf nitrogen concentration and total
leaf nitrogen content. The resulting regression equation was found to predict leaf
nitrogen concentration in the range 2–5% with a SEP of 0.4%. The confounding
in uence of varying canopy biomass on the red-edge determination of leaf nitrogen
concentration was found to be signiŽ cantly less at higher canopy biomass, thereby
verifying model predictions. The tendency of the red-edge wavelengths to become
insensitive to changes in LAI at high values of LAI suggests that under appropriate
Ž eld conditions the red-edge wavelength could be a LAI (biomass)-independent
indicator of leaf chlorophyll concentration in ryegrass pasture canopies. For lowchlorophyll leaves calculations predicted this may occur for LAI as low as 5, although
the chlorotic leaf data suggests that this Ž gure may be even lower.
Leaf area index values of up to 12 are encountered in some Waikato pastures
(Hanna et al. 1999), albeit in irrigated Ž elds. Therefore, provided a quantitative link
between LAI and canopy biomass is established, and suYcient correlation exists
between leaf chlorophyll concentration and nitrogen content, the use of the chlorophyll red-edge as a biomass-independent measure of pasture nitrogen status is quite
possible in the Waikato region of New Zealand.
Acknowledgments
The authors gratefully acknowledge the assistance of Alec McGowen and Linda
Trolove (Agricultural Research Institute, Hamilton, New Zealand) in the acquisition
and dissection of pasture samples and Duncan Miers (Department of Biological
Sciences, University of Waikato, Hamilton, New Zealand) for completion of leaf
nitrogen analyses. The support of staV of the HortResearch Technology Development
Group in the acquisition of plant and soil spectral characteristics and the receipt of
a Special Studies Program Grant from Charles Sturt University (DL) are also
acknowledged.
Estimating leaf nitrogen concentration
3645
Appendix: Solution of the two-stream model for a two-layer canopy
Following the schematic of Ž gure A1:
I la =wavelength-dependent
incident solar  ux.
I3
la =wavelength-dependent
incident solar  ux.
I lb =wavelength-dependent
incident solar  ux.
=
I3
lb wavelength-dependent
incident solar  ux.
upward-directed  ux at the top of layer a divided by
downward-directed  ux at top of layer a divided by
upward directed  ux at the top of layer b divided by
downward-directed  ux at top of layer b divided by
Solution of equations (1) and (2) for the two canopy layers yields:
L ayer a
Ila (t)=Ca na exat +Da ua eÕ xat +Ea eÕ kt
xt
Õ xt
Õ kt
I3
la (t)=Ca ua e a +Da na e a +Fa e
L ayer b
Ilb (t)=Cb nb exbt +Db ub eÕ xbt +Eb eÕ kt
x t+
Õ x t+
Õ kt
=
I3
lb (t) Cb ub e b Db nb e b Fb e
Re ectance at the top canopy (top of layer a) for each wavelength l is given by:
Rla ¬I la (t=0)
Boundary conditions to determine the unknown coeYcients C, D, E and F:
I3
la (t =0)=0;
no downward  ux at top of layer a (t=0)
I la (t=ta )=I lb (t=ta );
continuity of upward  ux at interface between layers
3
I3
la (t=ta )=I lb (t=ta );
continuity of downward  ux at interface between layers
+
I lb (t=ta +tb )=rl {eÕ k(ta+ tb ) +I3
lb (ta tb )};
re ected  ux at soil surface=upward  ux at t=ta +tb
Figure A1. Detailed schematic diagram of the two-layer ryegrass canopy represented in the
model.
D. W. L amb et al.
3646
Equation coeYcients relevant to the solution of Ila :
Ca =
­
D a va
­
ua
Fa
Cb =Db a1 +a2
ua
a (a ­ a4 )
+ a6
Da = 5 6
a3 ­ a5
a +b1a
Ea = a
2
a ­ a4
Db = 6
a3 ­ a5
a +b1b
Eb = b
2
a ­ b1a
Fa = a
2
a ­
Fb = b
na =
A S
1
1+
2
1­ va
1­ va ga
B
nb =
A S
1
1+
2
ga =1­
1­ vb
1­ vb gb
B
2
A S
B
A S
B
1­ va
1­ va ga
[r +t +(ra ­ ta )cos2 h]
2 ba = a a
r a +t a
1
1­
2
ua =
va =ra +ta
b1b
1­ vb
1­ vb gb
[r +t +(rb ­ tb )cos2 h ]
2 bb = b b
rb +tb
1
1­
2
ub =
vb =rb +tb
gb =1­
Z
aa = 2 2a 2
k ­ xa
xa =
S
(1­
va ga ) (1­
m2
va )
Z
b1a = 2 1a 2
k ­ xa
Z2a =
k(S1 ­ S2 )
­
m
(S1 +S2 ) (1­
m2
va ga )
S1 =va mkb0
Z1a =
k(S1 +S2 )
­
m
(S1 ­
va )
S2 =va mk (1­
S2 ) (1­
m2
S
Z
ab = 2 2b 2
k ­ xb
xb =
(1­
b0 )
vb gb ) (1­
m2
Z
b1b = 2 1b 2
k ­ xb
Z2b =
k(S3 ­ S4 )
­
m
(S3 +S4 ) (1­
m2
vb gb )
S3 =vb mkb0
Z1b =
k(S3 +S4 )
­
m
(S3 ­
vb )
S4 =vb mk (1­
S4 ) (1­
m2
b0 )
vb )
Estimating leaf nitrogen concentration
A
A
B
a1 =
rs n b ­ u b
eÕ 2xb (ta+ tb )
nb ­ rs ub
a2 =
rs (1+Fb )­ Eb
eÕ (k+ xb )(ta+ tb )
nb ­ rs ub
C
B
a1 nb exb ta +ub eÕ xb ta
n2a
ua exb ta ­
exa ta
ua
a3 =
C
AB
A B
F a na
exa ta +(Eb ­ Ea )eÕ kta
ua
n2a
ua eÕ xa ta ­
exa ta
ua
a2 nb exb ta +
a4 =
C
C
a5 =
a6 =
D
AB
D
a1 ub exb ta +nb eÕ xb ta
na (eÕ xa ta ­ exa ta)
3647
D
D
a2 ub exb ta +Fa exa ta +(Fb ­ Fa )eÕ kta
na (eÕ xa ta ­ exa ta )
For each canopy: (a) k=0.5 for leaves having random orientations; (b) m=cosh=
±1, where h is the zenith angle for diVuse  ux, h=0° for upward directed  ux and
180° for downward directed  ux; (c) G(m)=km=±0.5; (d) m=á m/G dm=1 for leaves
having random orientations; (e) h=45° is the average leaf angle relative to the
horizontal; and (f ) b0 =0.5 is the backscatter parameter for the incident beam.
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