Full Terms & Conditions of access and use can be found at
https://www.tandfonline.com/action/journalInformation?journalCode=tfst20
Forest Science and Technology
ISSN: 2158-0103 (Print) 2158-0715 (Online) Journal homepage: https://www.tandfonline.com/loi/tfst20
Examination of the extinction coefficient in the
Beer–Lambert law for an accurate estimation of
the forest canopy leaf area index
Taku M. Saitoh , Shin Nagai , Hibiki M. Noda , Hiroyuki Muraoka & Kenlo
Nishida Nasahara
To cite this article: Taku M. Saitoh , Shin Nagai , Hibiki M. Noda , Hiroyuki Muraoka & Kenlo
Nishida Nasahara (2012) Examination of the extinction coefficient in the Beer–Lambert law for
an accurate estimation of the forest canopy leaf area index, Forest Science and Technology, 8:2,
67-76, DOI: 10.1080/21580103.2012.673744
To link to this article: https://doi.org/10.1080/21580103.2012.673744
Copyright Taylor and Francis Group, LLC
Published online: 26 Apr 2012.
Submit your article to this journal
Article views: 1993
View related articles
Citing articles: 9 View citing articles
Examination of the extinction coefficient in the Beer–Lambert law for an accurate estimation of the
forest canopy leaf area index
Taku M. Saitoha
*, Shin Nagaib
, Hibiki M. Nodac
, Hiroyuki Muraokaa
and Kenlo Nishida Nasaharac
a
River Basin Research Center, Gifu University, 1-1 Yanagido, Gifu 501-1193, Japan; b
Research Institute for Global Change, Japan
Agency for Marine–Earth Science and Technology (JAMSTEC), 3173-25 Showa-machi Kanazawa-ku, Yokohama 236-0001,
Japan; c
Faculty of Life and Environment Sciences, University of Tsukuba, 1-1-1 Tennohdai, Tsukuba 305-8572, Japan
(Received 1 December 2011; Accepted 29 February 2012)
Leaf area index (LAI) is a crucial ecological parameter that represents canopy structure and controls many
ecosystem functions and processes, but direct measurement and long-term monitoring of LAI are difficult, especially
in forests. An indirect method to estimate the seasonal pattern of LAI in a given forest is to measure the attenuation
of photosynthetically active radiation (PAR) by the canopy and then calculate LAI by the Beer–Lambert law. Use of
this method requires an estimate of the PAR extinction coefficient (k), a parameter needed to calculate PAR
attenuation. However, the determination of k itself requires direct measurement of LAI over seasons. Our goals were
to determine (1) the best way to model k values that may vary seasonally in a forest, and (2) the sensitivity of
estimates of canopy ecosystem functions to the errors in estimated LAI. We first analyzed the seasonal pattern of the
‘‘true’’ k (kp) under cloudy and sunny conditions in a Japanese deciduous broadleaved forest by using the inverted
form of the Beer–Lambert law with the true LAI and PAR. We next calculated the errors of PAR-based LAIs
estimated with an assumed constant k (LAIpred) and determined under what conditions we should expect k to be
approximately constant during the growing period. Finally, we examined the effect of errors in LAIpred on estimates
of gross primary production (GPP), net ecosystem production (NEP), and latent heat flux (LE) calculated with a
land-surface model using LAIpred as an input parameter. During the growing period, cloudy kp varied from 0.47 to
1.12 and sunny kp from 0.45 to 1.59. Results suggest that the value of LAIpred was adequately estimated with the kp
obtained under cloudy conditions during the fully-leaved period (0.53–0.57). However, LAIpred was overestimated by
up to 0.6 m2
m–2
in May and November. The errors in LAIpred propagated to errors in modeled carbon and latent heat
fluxes of –0.21 to 0.32 g C m–2
day–1
in GPP, –0.09 to 0.19 g C m–2
day–1
in NEP, and –3.2 to 3.9 W m–2
in LE, which is
close to the measurement errors recognized in the tower flux measurement. LAIpred estimated with an assumed constant
k can be useful for some ecosystem studies as a second-best alternative if k is equated to the value of kp measured under
cloudy conditions especially during the fully-leaved period.
Keywords: Beer–Lambert law; deciduous broadleaved forest; extinction coefficient; leaf area index; plant area index
Nomenclature
GPP: gross primary production
GPPpred: predicted gross primary
production
GPPtrue: reference gross primary
production
k: extinction coefficient
kp: true extinction coefficient for
plant area index
LAI: leaf area index
LAIpred: predicted leaf area index
LAItrue: true leaf area index
LE: latent heat flux
LEpred: predicted latent heat flux
LEtrue: reference latent heat flux
LMA: leaf mass per unit area
MBE: mean bias error
NEP: net ecosystem production
NEPpred: predicted net ecosystem
production
NEPtrue: reference net ecosystem
production
PAI: plant area index
PAItrue: true plant area index
PAR: photosynthetically active
radiation (400–700 nm)
PARb: downward PAR measured below
the canopy
PARi: incident PAR above the canopy
RMSE: root mean square error
WAI: woody area index
t: measure of PAR attenuation
Introduction
Leaf area index (LAI) is a crucial ecological parameter
that represents canopy structure and controls many
ecosystem functions and processes such as carbon
*Corresponding author. Email: taku@green.gifu-u.ac.jp
Forest Science and Technology
Vol. 8, No. 2, June 2012, 67–76
ISSN 2158-0103 print/ISSN 2158-0715 online
Ó 2012 Korean Forest Society
http://dx.doi.org/10.1080/21580103.2012.673744
http://www.tandfonline.com
fixation, canopy water interception, and the attenuation
of radiation (Bre´ da 2003). In many ecosystems,
especially in deciduous forest, there is significant
seasonality in LAI. It is therefore necessary to
accurately gauge the seasonal pattern of LAI in order
to evaluate related ecosystem functions and processes
(Weiss et al. 2004). Various direct and indirect methods
have been proposed to estimate LAI (e.g. Norman and
Campbell 1989; Chen and Cihlar 1995; Leblanc and
Chen 2001; Jonckheere et al. 2004; Muraoka and
Koizumi 2005; Behera et al. 2010). Direct measurements
and long-term monitoring of LAI are difficult,
especially in forests, but indirect methods are suitable
for long-term continuous monitoring. An indirect
optical method suitable for gauging the seasonal
pattern of LAI at plot scale is to measure the
transmittance of daily photosynthetically active radiation
(PAR) by the vegetation canopy and then
calculate LAI with an equation obtained from Monsi
and Saeki (1953) that expanded the Beer–Lambert law
to plant canopies:
LAI ¼ À
t
k
À WAI ð1Þ
in which
t ¼ À ln
PARb
PARi
 
ð2Þ
where k is the extinction coefficient for the PAR
waveband, t is the measure of PAR attenuation, WAI
is woody area index (including branches and stems),
PARb is downward PAR measured below the canopy,
and PARi is incident PAR above the canopy. If WAI is
assumed to be zero, k is the extinction coefficient for
LAI (e.g. Monsi and Saeki 1953). In contrast, if WAI is
not zero, as is the case in forests, k is the extinction
coefficient for the plant area index (PAI) (e.g. Holst
et al. 2004), which is defined as:
PAI ¼ LAI þ WAI ð3Þ
Continuous measurements of PAR can be made
with relatively few resources. However, the value of k is
itself a subject of canopy research, because changes in
solar altitude, canopy structures, and weather conditions
may cause it to vary during the growing period
(e.g. Campbell and Norman 1998; Duursma et al. 2003;
Holst et al. 2004; Wang et al. 2004). In practice, the
methods used to estimate k fall into two main
categories: estimation from the inversion of Equation
(1) by using direct LAI measurements (e.g. Hirata et al.
2007), and estimation from a simple model of k (e.g.
Campbell and Norman 1998; Saigusa et al. 2002). To
simplify calculations, many studies have estimated LAI
or PAI with a constant k over the growing period (e.g.
Maass et al. 1995; Granier et al. 2000; Wilson et al.
2001; Saigusa et al. 2005; Hirata et al. 2007). Use of
this simplification reflects the fact that it is costly in
terms of money and labor to quantify some model
parameters, such as leaf angle distribution and tree
shapes that influence seasonal variations of k. The
simplified method that uses Equation (1) with a
constant k over the growing period (i.e. ‘‘constant k
assumption’’) can utilize estimates of LAI that require
little in the way of electricity, money, and labor.
However, the constant k assumption and insufficient
examination of the value of k may lead to incorrect
estimates of LAI for part or all of the growing period.
In addition, the studies reporting the differences of the
seasonal pattern of actual k under two weather
conditions are quite limited irrespective of the importance
of those examinations in the field. Thus the
key questions we addressed in this study were therefore:
(1) how we can deal with k values under different
weather conditions that might be variable throughout
the seasons for a given type of vegetation, and (2) to
what extent errors in the estimation of LAI influence
the evaluation of canopy ecosystem functions.
Our goal was to evaluate the accuracy of estimates
of the seasonal pattern of LAI in a Japanese deciduous
broadleaved forest with the use of Equation (1) and
PAR measurements when we assumed that k was
constant during the growing period. First, we analyzed
the seasonal pattern of the ‘‘true’’ k during cloudy and
sunny weather by inverting Equation (1) to solve for k
with the true LAI and PAI. Second, we assessed the
accuracy of the estimate of PAR-based LAI with the
constant k assumption. Third, we investigated under
what conditions k was approximately constant during
the growing period. Finally, we examined the effect of
errors in the estimate of LAI on gross primary
production (GPP), net ecosystem production (NEP),
and latent heat flux (LE) calculated with a land-surface
model, when we used a PAR-based LAI estimated with
the constant k assumption as an input parameter. Our
results provide an accurate assessment of the PARbased
LAI estimated with the constant k assumption.
Materials and methods
Study site
The study was carried out in the Takayama cooltemperate
deciduous broadleaved forest site (‘‘TKY’’;
368080
N, 1378250
E, 1420 m a.s.l.), which belongs to
AsiaFlux (http://asiaflux.net) and is part of the Japan
Long-Term Ecological Research network (JaLTER:
http://www.jalter.org). The temperature and precipitation
from 1980 to 2002 showed clear seasonal patterns
(Mo et al. 2005), with an annual average of 7.28C and a
cumulative average of 2275 mm, respectively. The
dominant tree species in the forest canopy are Quercus
crispula, Betula ermanii, and Betula platyphylla var.
japonica. The height of the dominant forest canopy
ranges from 13 to 20 m. The forest floor is covered by
an evergreen dwarf bamboo (Sasa senanensis) with a
68 T.M. Saitoh et al.
height of 1.0–1.5 m. All the deciduous tree species flush
their leaves in late May after snowmelt (Nasahara et al.
2008). Leaves fall from late August to November. Mo
et al. (2005) and Ohtsuka et al. (2005) provide more
detailed descriptions of the study site.
True LAI and PAI
To calculate the true LAI (LAItrue), we coupled
periodic in situ monitoring of leaf area growth of
several sample shoots throughout the growing period
with measurements of litter fall in the autumn in
2005 (Nasahara et al. 2008). We selected 20 shoots of
18 individuals of a total of eight tree species (Q.
crispula, B. ermanii, B. platyphylla, Acer rufinerve,
Fagus crenata, Acer distylum, Viburnum furcatum,
and Hydrangea paniculata), which are dominant,
subdominant, or understory species. On 17 occasions
between day-of-year (DOY) 124 and DOY 316, we
recorded the number of all leaves and the size of
about 20 randomly selected leaves. We observed
canopy species from a canopy access tower (ecotower)
with a height of 18 m. We also collected litter
in 14 litter traps in a 1-ha plot around the eco-tower.
We retrieved the litter and sorted it by species on six
occasions between DOY 265 and DOY 316. The
results gave us the total LAI of the entire canopy
excluding evergreen dwarf bamboo (i.e. LAItrue) on
19 days throughout the growing period in 2005. We
linearly interpolated the values of LAItrue between
DOY 122 and 316 (Nasahara et al. 2008). Nasahara
et al. (2008) presents a complete description of
observation design and LAItrue evaluation procedure
at our study site.
We estimated the true PAI (PAItrue) as the sum of
LAItrue and WAI. We assumed a constant value of
0.8 m2
m–2
for WAI throughout the growing period
(Nasahara et al. 2008). On the basis of seasonal
changes in LAItrue, we defined three periods: DOY
122–170 as the leaf-expansion period, DOY 171–256
(LAItrue 4 4.0 m2
m–2
) as the fully-leaved period, and
DOY 257–316 as the leaf-fall period.
Daily PAR attenuation
PARi and PARb in Equation (2) are the downward
PAR measured over the course of the day at the top
of the eco-tower and above the forest understory
vegetation, respectively. We measured PAR as the
photosynthetically active photon flux density (mmol
m–2
s–1
) with quantum sensors (PAR-02, PREDE
Co. Ltd., Tokyo, Japan; IKS-27, Koito, Tokyo,
Japan). We calibrated all sensors against a standard
quantum sensor (Li-Cor, LI-190, Li-Cor, Lincoln,
NE, USA). All data were collected at 5-s intervals
and averaged over 5 min by a CR10X data-logger
(Campbell Scientific, Logan, UT, USA) during DOY
122–316 in 2005 (total of 195 days). To eliminate the
effect of spatial variation in PARb, we obtained the
mean value of PARb at five locations. Note that
standard deviation of PARb is small especially under
cloudy conditions (Figure 1a and b). We then
calculated daily values of t based on the daily
cumulative PARb and PARi to eliminate the effect of
random errors of PAR measurement. To evaluate the
effect of weather conditions on LAI estimates, we
categorized days as ‘‘sunny’’ or ‘‘cloudy’’ depending
on whether the ratio of diffuse radiation to solar
radiation was 0.7 or 40.7, respectively (Saitoh
et al. 2010). We estimated diffuse radiation according
to Spitters et al. (1986). If daily cumulative
precipitation was 410 mm, we categorized the day
as ‘‘disturbed’’. We filled gaps in cloudy t and in
sunny t between DOY 122 and 316 by cubic spline
interpolation (Figure 1c).
Figure 1. (a) Daily incident PAR above the canopy (PARi)
and downward PAR measured below the canopy (PARb) in
cloudy conditions, (b) daily PARi and PARb in sunny
conditions, and (c) observed PAR attenuation (t) on cloudy
and sunny days, and gap-filling lines calculated using a cubic
spline interpolation. Vertical bars in PARb indicate standard
deviation at five locations (i.e. the measure of spatial
variation).
Forest Science and Technology 69
True extinction coefficient
We estimated the true extinction coefficient (kp) with
the modified version of Equation (1) as follows:
kp ¼
t
PAItrue
ð4Þ
We estimated cloudy kp and sunny kp with values of t
calculated on cloudy and sunny days, respectively.
PAR-based LAI
We estimated LAIpred with a modification of Equation
(1) by assuming a constant k and constant WAI of
0.8 m2
m–2
throughout the growing period (Nasahara
et al. 2008) as follows:
LAIpred ¼ À
t
k
À 0:8 ð5Þ
We estimated LAIpred by using gap-filled cloudy t
values. Sunny t values were not useful for determining
LAIpred (see the Discussion section for details). To
estimate day-to-day variability in LAIpred, we substituted
each gap-filled cloudy kp value from the 195 days of the
growing period (i.e. cloudy kp in DOY122, DOY123 . . .
DOY316) for k in Equation (5) and then calculated 195
patterns of the seasonal variation of LAIpred.
Land Surface Model description
We examined the effects of different procedure for
calculating LAI on forest ecosystem functions GPP,
NEP, and LE, by introducing the LAI values into the
Land Surface Model (LSM) (Bonan 1996; http://daac.
ornl.gov/MODELS/guides/LSM_guide.html). We have
modified some ecophysiological parameters in this model
to adjust to our study site (Muraoka et al. 2010). A
detailed description of this meteorological/physiological/
hydrological combined model can be found in the user’s
manual (Bonan 1996). To calculate GPP, NEP, and LE
throughout the growing period, parameters such as LAI
can be input monthly, i.e. one value for each month at
the midpoint of the month. For convenience, we
determined the model output of GPP, NEP, and LE as
follows:
. We calculated GPPtrue, NEPtrue, and LEtrue with
LAItrue as an input parameter.
. We calculated GPPpred, NEPpred, and LEpred with
LAIpred as an input parameter.
The model was driven at an hourly time step by the
values for shortwave and longwave radiations, air
temperature, wind speed, precipitation, and air humidity
measured in 2005 at TKY. Then we obtained daily
cumulative values of GPP and NEP, and daily average
values of LE.
Evaluation of accuracy of LAIpred estimates
To evaluate the accuracy of the estimates of daily
LAIpred, GPPpred, NEPpred, and LEpred, we calculated
the RMSE (root mean square error) and MBE (mean
bias error) for each month:
RMSE ¼
1
n
X
Vpred À Vtrue
À Á2
( )1
2
ð6Þ
MBE ¼
1
n
X
Vpred À Vtrue
À Á
ð7Þ
where n is the number of sample days in the month (30
or 31, and 12 days in November). Vpred is either
LAIpred, GPPpred, NEPpred, or LEpred, and Vtrue is the
true value of the reference variable corresponding to
each Vpred.
Results
Seasonal patterns of LAI, PAI, and extinction
coefficient
Both LAItrue and PAItrue increased during the leaf
expansion period (DOY 122–170) and decreased
during the leaf-fall period (DOY 257–316) (Figure 2a,
b). During the fully-leaved period (DOY 171–256),
LAItrue and PAItrue were almost constant at about 4.5
and 5 m2
m–2
, respectively. Peak values of LAItrue and
PAItrue were 4.6 m2
m–2
and 5.4 m2
m–2
, respectively,
on DOY 192.
During the whole growing period, cloudy kp and
sunny kp varied from 0.47 to 1.12 and from 0.45 to
1.59, respectively (Figure 2d). In the fully-leaved
period, cloudy kp and sunny kp were relatively
constant, with ranges of 0.53–0.57 and 0.51–0.61,
respectively. However, kp values decreased rapidly
during the early leaf-expansion period (i.e. before
DOY 150) and increased rapidly during the late leaffall
period (i.e. after DOY 270). Cloudy kp and sunny
kp differed greatly during the leaf-fall period (Figure
2d).
Under cloudy conditions the relationship between
kp and LAItrue was similar during the leaf-expansion
and leaf-fall periods (Figure 3a), whereas under
sunny conditions it was different in each period (Figure
3b).
Accuracy of LAIpred estimate
LAIpred underestimated LAItrue, especially from July to
October (Figure 4), if LAIpred was calculated using
values of kp obtained during the leaf-expansion and
leaf-fall periods (Figure 5a, c). In contrast, the errors in
LAIpred were relatively small in May and November.
LAIpred agreed well with LAItrue from July to
October (RMSE and MBE + 0.42 m2
m–2
) if LAIpred
70 T.M. Saitoh et al.
was calculated using values of kp obtained during the
fully-leaved period (Figure 5b). In this case, there was
an overestimation of 0.5–0.6 m2
m–2
in May and
November (Figures 4, 5).
Examination of model analysis
GPP ranged from 0 to 14 g C m–2
day–1
and displayed
a clear seasonal pattern (Figure 6a). If k was estimated
with values of kp obtained during the leaf-expansion
and leaf-fall periods, large errors in GPP appeared
from June to October compared with May and
November (Figure 7a, g). If k was estimated with
values of kp obtained during the fully-leaved period,
the errors ranged from –0.21 to 0.32 g C m–2
day–1
in
May and November and were almost zero from June to
October (Figure 7d).
NEP ranged from –2 to 7 g C m–2
day–1
(Figure 7
b). If k was estimated with values of kp obtained during
the leaf-expansion period, RMSE and MBE varied
within the range of –1.32 to 1.47 g C m–2
day–1
from
June to October (Figure 7b). If k was estimated with
values of kp obtained during the fully-leaved period,
RMSE and MBE varied within the range of –0.09 to
0.19 g C m–2
day–1
during the whole growing period
(Figure 7e). If k was estimated with values of kp
obtained during the leaf-fall period, the maximum
values of errors reached +1.5–2.0 g C m–2
day–1
,
though the medians and minima of the errors were
almost zero (Figure 7h).
LE ranged from 30 to 130 W m–2
(Figure 6c). If k
was estimated with values of kp obtained during the
leaf-expansion period, the RMSE and MBE were
scattered during spring and summer (Figure 7c). If k
was estimated with values of kp obtained during the
fully-leaved period, the RMSE and MBE were almost
zero, except in May (Figure 7f). If k was estimated with
values of kp obtained during the leaf-fall period, the
RMSE and MBE varied within the range –3.5 to 4.6 W
m–2
(Figure 7i).
Figure 2. Seasonal patterns of (a) true leaf area index (LAItrue m2
m–2
), (b) true plant area index (PAItrue; m2
m–2
), (c) daily
maximum solar altitude, and (d) extinction coefficient for true plant area index (kp) estimated by inverting Equation (1) on
‘‘cloudy’’ and ‘‘sunny’’ days. Vertical bars in (a) and (b) show standard errors. Typical images of the canopy surface on (A)
DOY124, (B) DOY146, (C) DOY155, (D) DOY174, (E) DOY236, (F) DOY276, (G) DOY291, and (H) DOY316 are shown.
Forest Science and Technology 71
Discussion
Seasonal patterns of kp
Previous studies suggest that kp is relatively large
during the early leaf-expansion period and the late leaffall
period and small during the fully-leaved period
(e.g. Baldocchi et al. 1984; Wang et al. 2004). Holst
et al. (2004) suggest that the value of kp varies with
weather conditions. Our results suggest that accurate
estimation of LAI with Equation (1) requires consideration
of light conditions and the seasonal patterns
of kp.
Previous studies reported that daily average k for
PAR and PAI in the fully-leaved period ranged from
0.66–0.81 in deciduous broadleaved forest (Baldocchi
et al. 1984; Holst et al. 2004). Those k values were
larger than our kp value of 0.47–0.57 in the late leafexpansion,
fully-leaved, and early leaf-fall periods.
Nasahara et al. (2008) reported that clumping index
estimated using the Tracing Radiation and Architecture
of Canopies (TRAC) data ranged between 0.91
and 0.95 in our study site. Therefore, our small k
values, compared with previous studies, could not be
explained by clumping. However, we think our true
extinction coefficient (kp) is reasonable for the following
reasons. First, the previous two reports estimated
daily average k based on hourly k for PAR and PAI.
Our kp values estimated by using daily cumulative
PAR might be close to midday k values of hourly
estimation, because midday value of PAR mainly
dominate daily-based PAR value. As a result, our kp
values tend to be small, compared with the previous
two reports. Second, the difference in absolute values
of k between Holst et al. (2004) and ours were
influenced by the different methods to estimate LAI.
(Note that Baldocchi et al. (1984) did not describe the
estimation method of LAI.) Holst et al. (2004) used an
LAI-2000 plant canopy analyzer in the estimation of
LAI, while we used direct measurements (refer to the
Method section). Many previous studies reported that
an indirect method such as LAI-2000 underestimates
LAI compared with direct measurements. The reported
underestimation varies from 25% to 50% in several
forests including our forest (e.g. Bre´ da 2003; Nasahara
et al. 2008). If we calculate kp based on LAI using LAI-
2000 in our forest (see Nasahara et al. 2008), we
provided comparable k values.
LAI estimation under different weather conditions
Under sunny conditions, kp was different even for the
same LAItrue values (Figure 3). This must reflect the
different radiative properties between diffuse and direct
lights. The diffuse radiation can be explained by an
assemblage of parallel beams from all directions. On the
other hand, direct radiation can be explained by a beam
from one direction (Anderson 1966). The attenuation
beam of direct radiation and its path length in canopy
strongly depend on the geometrical relationship between
the solar altitude and canopy structure. Therefore,
under sunny condition when direct PAR
dominates, the values of t and k is remarkably
influenced by solar altitude (Figure 1 and Figure 2).
Thus LAI should be calculated with the data obtained
under cloudy conditions (Monsi and Saeki 1953). At
TKY the solar altitude was low during the leaf-fall
period (Figure 2c). As a result, under sunny conditions,
during which direct PAR dominates, the values of t and
k were larger during the leaf-fall period than during the
leaf-expansion period. In contrast, under cloudy conditions,
the calculated values of LAI at the same kp
values were almost the same for both periods.
LAI drastically increased and decreased during the
leaf-expansion and leaf-fall periods, respectively.
Therefore, detection of seasonal patterns in LAI
requires frequent measurements especially during those
periods. However, there is a trade-off between accurate
estimation of LAI with the assumption of a constant k
and the temporal gap of measured PAR attenuation.
The presence of direct radiation would easily increase
the threshold value of the diffuse-to-total solar radiation
ratio associated with ‘‘cloudy’’ conditions. The
Figure 3. Relationship between LAItrue and kp on (a)
cloudy and (b) sunny days.
Figure 4. Ranges of LAIpred estimated with the assumption
of a constant k during the whole growing period (DOY 122–
316). Light gray, k ¼ cloudy kp values during the whole
growing period (cloudy kp ¼ 0.47–1.12); dark gray,
k ¼ cloudy kp values during the fully-leaved period (cloudy
kp ¼ 0.53–0.57). Symbols indicate LAItrue as in Figure 2a.
72 T.M. Saitoh et al.
optimal threshold for defining ‘‘cloudy’’ might be
different for each measurement site. It is therefore
important to find the optimal threshold for defining
‘‘cloudy’’ before estimating LAI at each site.
Accuracy of LAI estimates with the constant k
assumption and application to ecosystem studies
Our results suggest that the use of average cloudy kp
values obtained during the fully-leaved period to
estimate the constant k in Equation (5) provided the
best estimates of LAI. Note that we can also
estimate LAI with the same magnitude of errors
by using cloudy kp values obtained during the
late leaf-expansion and early leaf-fall period when
LAItrue 42.0 m2
m72
approximately (Figures 2a, d
and 5).
The fact that the best result was a good estimate of
LAI from June to October (i.e. more than LAItrue of
2.0 m2
m–2
) suggests that estimation of the seasonal
pattern of LAI with the constant k assumption during
the growing period may be more suitable for evergreen
forests than for deciduous forests, as evergreen forests
have leaves even in winter, and hence there is little
seasonality of LAI compared with deciduous forests
(e.g. Saitoh et al. 2010).
In the case of the most reasonable result (i.e. use of
a constant k calculated from cloudy kp values
obtained during the fully-leaved period), the overestimation
of LAI appeared to be as much as 0.6 m2
m–2
in May and November. If those errors are
unacceptable for a study, researchers should measure
kp in the early leaf-expansion or late leaf-fall periods
in addition and then estimate the seasonal pattern of
LAI by using the values of kp appropriate for each
period.
Estimates of LAIpred with average kp values
obtained during the fully-leaved period led to errors
in LAIpred that, when propagated, caused errors in
calculated carbon and water fluxes in an ecosystem
model as follows:
Figure 6. Ranges of (a) GPPpred, (b) NEPpred, and (c)
LEpred estimated with a constant k during the whole growing
period (DOY 122–316). Light gray, k ¼ cloudy kp values
during the whole growing period (0.47–1.12); dark gray,
k ¼ cloudy kp values during the fully-leaved period (0.53–
0.57). Black line indicates each ‘‘true’’ value.
Figure 5. Possible values of RMSE and MBE of LAIpred in each month. The constant k in Equation (5) was the average of kp
values measured during (a) the leaf-expansion period, (b) the fully-leaved period, and (c) the leaf-fall period. Vertical bars indicate
range.
À 0:21 to 0:32 g C mÀ2
dayÀ1
in GPP
À 0:09 to 0:19 g C mÀ2
dayÀ1
in NEP
À 3:2 to 3:9 W mÀ2
in LE:
Forest Science and Technology 73
These errors are nevertheless close to those based on
current tower flux measurements: sampling errors have
ranged from +0.08 to +0.11 g C m–2
day–1
on a flat
landscape and have exceeded 0.27 g C m–2
day–1
on a
varied landscape (Baldocchi 2003). In addition, Foken
(2008) found typical measurement errors of LE to
be +20–50 W m–2
. Furthermore, the sum of the
sensible and latent heat fluxes in most experiments
has been smaller than the available energy. These
results suggest that critical estimation problems in
ecosystem studies are not always caused by errors in
LAIpred. Estimates of LAI with the constant k
assumption can therefore be useful for some ecosystem
studies as a second-best alternative.
Implications for highly accurate estimates of LAI
The relationships between kp and LAI during the leafexpansion
and leaf-fall periods did not completely
overlap even under cloudy conditions (Figure 2d). This
small difference could be important in ecosystem
studies. It seems to have been caused by several
combined factors.
The first reason is the effect of direct radiation,
which, unlike diffuse radiation, led to errors in the
estimates of LAI. We defined conditions to be
‘‘cloudy’’ when the ratio of diffuse radiation to solar
radiation was 4 0.7; so the presence of direct radiation
led to small errors in the estimates of LAI even under
cloudy conditions.
The second reason is the effect not only of
meteorological phenomena, but also of leaf properties
such as leaf mass per unit area (LMA), leaf transmittance,
leaf angle, and leaf water content. For instance,
the LMA of B. ermanii and Q. crispula gradually
increased during the growing period, and the LMA
during the late leaf-fall period was 1.5–2.0 times the
LMA during the early leaf-expansion period (Muraoka
and Koizumi 2005). In addition, the spectral reflectance
from a leaf surface changed with leaf color
during the growing period (Nagai et al. 2011). Wang
et al. (2004) suggest that a 10% difference in leaf
transmittance would lead to a 2.8% variation in LAI.
To estimate LAI with extreme accuracy, we must
therefore quantify the effect of individual parameters
such as solar radiation and leaf properties. A more
comprehensive understanding of the behavior of k will
provide useful input into simplified methods such as
LAI estimation with the constant k assumption.
Conclusion
Seasonal patterns associated with the ‘‘true’’ k differ
between sunny and cloudy conditions. This result
Figure 7. Possible values of RMSE and MBE of GPPpred, NEPpred, and LEpred in each month. The constant k in Equation (5)
was the mean of cloudy kp values that ranged as indicated during each period. Vertical bars indicate range.
74 T.M. Saitoh et al.
suggests that the use of the Beer–Lambert law to
accurately estimate LAI will require consideration of
light conditions and the seasonal pattern of k. In
some cases, periodic field measurements of k are
difficult owing to limitations in cost, labor, or access
to observation sites. It is therefore important to
estimate the seasonal pattern of LAI with sufficient
accuracy for use in individual ecosystem studies. The
estimation of LAI with the assumption of a constant
k can be useful for some ecosystem studies as a
second-best alternative if k is estimated under
cloudy conditions especially during the fully-leaved
period.
Acknowledgements
We thank Mr K. Kurumado and Mr Y. Miyamoto (River
Basin Research Center, Gifu University) and Mr H. Mikami
(University of Tsukuba) for their assistance in the field.
Thanks are also due to Dr I. Tamagawa of Gifu University
and anonymous reviewers for thoughtful suggestions. This
study was partly supported by the Japan Society for the
Promotion of Science (JSPS) 21st Century COE Program
(Satellite Ecology, Gifu University), the JSPS-NRF-NSFC
A3 Foresight Program, and a Global Change Observation
Mission (GCOM; PI#102) of the Japan Aerospace Exploration
Agency (JAXA); K.N. Nasahara by KAKENHI
(19688012; Grant-in-Aid for Young Scientists A by JSPS)
and H. Muraoka by JSPS Funding Program for Next
Generation World-Leading Researchers (NEXT Program).
References
Anderson MC. 1966. Stand structure and light penetration.
II. A theoretical analysis. J Appl Ecol. 3:41–54.
Baldocchi DD. 2003. Assessing the eddy covariance technique
for evaluating carbon dioxide exchange rates of
ecosystems: past, present and future. Global Change
Biol. 9:479–492.
Baldocchi DD, Matt DR, Hutchison BA, McMillen RT.
1984. Solar radiation within an oak-hickory forest: an
evaluation of extinction coefficients for several radiation
components during fully leafed and leafless periods.
Agric For Meteorol. 32:307–322.
Behera SK, Srivastava P, Pathre UV, Tuli R. 2010. An
indirect method of estimating leaf area index in Jatropha
curcas L. using LAI-2000 Plant Canopy Analyzer. Agric
For Meteorol. 150:307–311.
Bonan GB. 1996. A land surface model (LSM version 1.0) for
ecological, hydrological, and atmospheric studies: technical
description and user’s guide. NCAR Technical Note
NCAR/TN-417þSTR. Boulder (CO): National Center
for Atmospheric Research.
Bre´ da NJJ. 2003. Ground-based measurements of leaf area
index: a review of methods, instruments and current
controversies. J Exp Bot. 54:2403–2417.
Campbell GS, Norman JM. 1998. An introduction to
environmental biophysics. 2nd ed. New York: Springer
Verlag.
Chen JM, Cihlar J. 1995. Quantifying the effect of canopy
architecture on optical measurements of leaf area index
using two gap size analysis methods. IEEE Trans Geosci
Remote Sens. 33:777–787.
Duursma RA, Marshall JD, Robinson AP. 2003. Leaf area
index inferred from solar beam transmission in mixed
conifer forests on complex terrain. Agric For Meteorol.
118:221–236.
Foken T. 2008. The energy balance closure problem: an
overview. Ecol Appl. 18:1351–1367.
Granier A, Biron P, Lemoine D. 2000. Water balance,
transpiration and canopy conductance in two beech
stands. Agric For Meteorol. 100:291–308.
Hirata R, Hirano T, Saigusa N, Fujinuma Y, Inukai K,
Kitamori Y, Yamamoto S. 2007. Seasonal and interannual
variations in carbon dioxide exchange of a
temperate larch forest. Agric For Meteorol. 147:110–124.
Holst T, Hauser S, Kirchga¨ ßner A, Matzarakis A, Mayer H,
Schindler D. 2004. Measuring and modelling plant area
index in beech stands. Int J Biometeorol. 48:192–201.
Jonckheere I, Fleck S, Nackaerts K, Muys B, Coppin P, Weiss
M, Baret F. 2004. Review of methods for in situ leaf area
index determination Part I. Theories, sensors and hemispherical
photography. Agric For Meteorol. 121:19–35.
Leblanc SG, Chen JM. 2001. A practical scheme for
correcting multiple scattering effects on optical LAI
measurements. Agric For Meteorol. 110:125–139.
Maass JM, Vose JM, Swank WT, Martinez-Yrizar A. 1995.
Seasonal changes of leaf area index (LAI) in a tropical
deciduous forest in west Mexico. For Ecol Manage.
74:171–180.
Mo W, Lee M-S, Uchida M, Inatomi M, Saigusa N, Mariko
S, Koizumi H. 2005. Seasonal and annual variations in
soil respiration in a cool-temperate deciduous broadleaved
forest in Japan. Agric For Meteorol. 134:81–94.
Monsi M, Saeki T. 1953. U¨ ber den Lichtfaktor in den
Pflanzengesellschaften und seine Bedeutung fu¨ r die
Stoffproduktion. Jpn J Bot. 14:22–52. [Republished in
English: Monsi M, Saeki T. 2005. On the factor light in
plant communities and its importance for matter
production. Ann Bot. 95:549–567.]
Muraoka H, Koizumi H. 2005. Photosynthetic and structural
characteristics of canopy and shrub trees in a cool-temperate
deciduous broadleaved forest: implication to the ecosystem
carbon gain. Agric For Meteorol. 134:39–59.
Muraoka H, Saigusa N, Nasahara KN, Noda H, Yoshino J,
SaitohTM,NagaiS,Murayama S, KoizumiH.2010.Effects
of seasonal and interannual variations in leaf photosynthesis
and canopy leaf area index on gross primary production of a
cool-temperate deciduous broadleaf forest in Takayama,
Japan. J Plant Res. 123:563–576.
Nagai S, Maeda T, Gamo M, Muraoka H, Suzuki R,
Nasahara KN. 2011. Using digital camera images to
detect canopy condition of deciduous broad-leaved trees.
Plant Ecol Diversity 4:78–88.
Nasahara KN, Muraoka H, Nagai S, Mikami H. 2008.
Vertical integration of leaf area index in a Japanese
deciduous broad leaved forest. Agric For Meteorol.
148:1136–1146.
Norman JM, Campbell GS. 1989. Canopy structure. In:
Pearcy RW, Ehleringer JR, Mooney HA, Rundel PW.,
editors. Plant physiological ecology: field methods and
instrumentation. London: Chapman & Hall. p. 301–325.
Ohtsuka T, Akiyama T, Hashimoto Y, Inatomi M, Sakai T,
Jia S, Mo W, Tsuda S, Koizumi H. 2005. Biometric based
estimates of net primary production (NPP) in a cooltemperate
deciduous forest stand beneath a flux tower.
Agric For Meteorol. 134:27–38.
Saigusa N, Yamamoto S, Murayama S, Kondo H. 2005.
Inter-annual variability of carbon budget components in
an AsiaFlux forest site estimated by long-term flux
measurements. Agric For Meteorol. 134:4–16.
Saigusa N, Yamamoto S, Murayama S, Kondo H, Nishimura
S. 2002. Gross primary production and net
ecosystem exchange of a cool-temperate deciduous forest
estimated by the eddy covariance method. Agric For
Meteorol. 112:203–215.
Forest Science and Technology 75
Saitoh TM, Tamagawa I, Muraoka H, Lee N-YM, Yashiro
Y, Koizumi H. 2010. Carbon dioxide exchange in a cooltemperate
evergreen coniferous forest over complex
topography in Japan during two years with contrasting
climates. J Plant Res. 123:473–483.
Spitters CJT, Toussaint HAJM, Goudriaan J. 1986. Separating
the diffuse and direct component of global radiation
and its implications for modeling canopy photosynthesis
part I. Components of incoming radiation. Agric For
Meteorol. 38:217–229.
Wang Q, Tenhunen J, Granier A, Reichstein M, Bouriaud O,
Nguyen D, Breda N. 2004. Long-term variations in leaf
area index and light extinction in a Fagus sylvatica stand
as estimated from global radiation profiles. Theor Appl
Climatol. 79:225–238.
Weiss M, Baret F, Smith GJ, Jonckheere I, Coppin P. 2004.
Review of methods for in situ leaf area index (LAI)
determination: Part II. Estimation of LAI, errors and
sampling. Agric For Meteorol. 121:37–53.
Wilson KB, Hanson PJ, Mulholland PJ, Baldocchi DD,
Wullschleger SD. 2001. A comparison of methods for
determining forest evapotranspiration and its components:
sap-flow, soil water budget, eddy covariance and
catchment water balance. Agric For Meteorol. 106:153–
168.
76 T.M. Saitoh et al.