Impact of leaf physiology on gas exchange in a

Japanese evergreen broad-leaved forest

Yoshiko Kosugi a,*, Satoru Takanashi a, Naoko Matsuo a,Katsunori Tanaka b, Hiroki Tanaka c

a Graduate School of Agriculture, Kyoto University, Kyoto 606-8502, Japanb Frontier Research Center for Global Change, Japan Agency for Marine-Earth Science and Technology,

3173-25 Showamachi, Kanazawa-ku, Yokohama, Kanagawa 236-0001, Japanc Graduate School of Environmental Studies, Nagoya University, Nagoya 464-8601, Japan

Received 1 October 2005; received in revised form 26 June 2006; accepted 27 June 2006

Abstract

We used a multi-layer model to analyse the impact of leaf physiology on the diurnal, seasonal, and inter-annual fluctuations in

gas exchange in a warm-temperate evergreen broad-leaved forest in Japan. The influences of physiological parameters at the single

leaf scale on the canopy scale gas exchange were investigated, including normalised dark respiration rate, Rnleaf25, normalised

maximum carboxylation rate, Vcmax25, and the stomatal coefficient, m, of an improved ball-type stomatal conductance model.

Simulated sensible and latent heat fluxes and CO2 flux at the canopy roughly reproduced the amplitude and diurnal and seasonal

fluctuations in the observed fluxes, with the constant m and one set of reference Vcmax and Rnleaf with their temperature dependences.

Overestimations of latent heat flux and thus underestimation of sensible heat flux with a constant m demonstrated that additional

stomatal closure should be expected during a drought period. Overestimation of CO2 flux during the leaf expansion period and the

severe drought period with changing m values related to soil moisture conditions demonstrated that the decline in canopy scale CO2

uptake during these periods was related to some physiological restraints, other than simple uniform stomatal closure, at the single

leaf scale.

# 2006 Elsevier B.V. All rights reserved.

Keywords: Multi-layer model; Temperate evergreen broad-leaved forest; CO2 flux; Latent heat flux; Sensible heat flux; Leaf gas exchange

www.elsevier.com/locate/agrformet

Agricultural and Forest Meteorology 139 (2006) 182–199

1. Introduction

Eddy covariance fluxes have been measured at many

forest sites (e.g., Baldocchi et al., 2001), and the number

of long-term data sets that include diurnal, seasonal, and

inter-annual variations in heat, water vapor, and carbon

dioxide fluxes has increased. For most of the flux

* Corresponding author at: Laboratory of Forest Hydrology,

Division of Environmental Science and Technology, Graduate School

of Agriculture, Kyoto University, Kyoto 606-8502, Japan.

Tel.: +81 75 753 6089; fax: +81 75 753 6088.

E-mail address: ykosugi@kais.kyoto-u.ac.jp (Y. Kosugi).

0168-1923/$ – see front matter # 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.agrformet.2006.06.009

observation results, the seasonal trends in the fluxes,

especially the CO2 fluxes over the canopy, have been

described or explained simply as functions of environ-

mental factors, such as the photosynthetically active

radiation (PAR), temperature, or vapor pressure. To

understand the gas-exchange process, however, it is

critical to understand how the photosynthesis and

transpiration of leaves interact and how these processes

influence canopy-scale fluxes. Recently, analyses of

canopy fluxes using a multi-layer model have been

conducted to understand the physiological regulation of

the canopy fluxes (e.g., Leuning et al., 1995; Baldocchi

and Meyers, 1998; Lai et al., 2000a,b; Tanaka et al.,

Y. Kosugi et al. / Agricultural and Forest Meteorology 139 (2006) 182–199 183

2002). However, multi-layer analysis requires many

parameters determined by process studies, so long-term

comparisons with measured scalar eddy covariance

fluxes are rare.

Some of the most important parameters for the

evaluation of forest carbon uptake with a multi-layer

analysis are the physiological characteristics of gas

exchange via leaves (Leuning et al., 1995; Baldocchi

and Meyers, 1998; Lai et al., 2000a,b; Tanaka et al.,

2002). We analysed the impact of leaf physiology on the

diurnal, seasonal, and inter-annual fluctuation in gas

exchange of a warm-temperate evergreen broad-leaved

forest in Japan using a multi-layer model. A previous

multi-layer analysis by Tanaka et al. (2002) at the same

site dealt with the occasional flux data for five

individual days. Although it was too short in duration

to permit detailed assessment of how seasonal variation

in leaf stomatal and physiological attributes modify

ecosystem-scale fluxes. This study improves on the

previous analysis, using a long-term dataset including

3.5 years of scalar eddy covariance fluxes over the

canopy and intensive measurements of each process,

such as leaf gas exchange and soil respiration, to

evaluate the impact of leaf physiology on long-term

canopy gas exchange.

2. Methods

2.1. Model description

We used a modified version of a multi-layer model for

CO2 and H2O exchange in a C3 plant community

(Tanaka, 2002; Tanaka et al., 2002). The model contained

sub-models that calculated the following processes: (1)

Reynolds stress, sensible heat exchange, and CO2 and

H2O exchanges of leaves and the ground surface, (2)

stomatal conductance and net photosynthesis in indivi-

dual leaves, (3) radiative transfer within and above the

canopy, (4) the energy balance of leaves and the ground

surface, (5) atmospheric diffusion within and above the

canopy, (6) the interception of rainfall and the water

budget of leaves, and (7) soil respiration. This multi-layer

model computes the above-canopy fluxes based on

detailed processes characterized by the canopy structure

and biochemical processes. We modified sub-models 2

and 7 from the original version by Tanaka (2002) as

described in Appendix A to reflect the observation results

of gas exchange with the chamber method. Sub-model 3

was also modified by introducing the leaf-clumping

factor (V) to the radiative transfer. This model requires

the diurnal courses of 11 environmental variables (30-

min interval datasets were used in this study) as the input

data: incident shortwave, longwave, and photosynthes-

tically active radiations, air temperature, humidity, wind

velocity, precipitation and CO2 concentration at the

reference height above the canopy, the water content of

the soil, soil temperature at the reference depths, and

ground heat flux. In this model, parameters relating to

leaf area density (LAD), leaf gas exchange character-

istics, soil respiration characteristics and their seasonal

fluctuations, and characteristics related to radiative

transfer, are used to represent the characteristics for

each site listed in Table 1. Some of them will be discussed

in the results session.

2.2. Site

Field observations were carried out in a plantation

forest established in 1987 at 348440N, 1348220E in Akou,

Hyogo prefecture, Japan. This plantation includes 12

temperate evergreen (77.5% of total basal area) and four

deciduous (22.5% of total basal area) broad-leaved tree

species (Kosugi et al., 2005). Three-year-old seedlings

were planted in 1987 with a density of 1–2 stems m�2. In

January 2002, trees were 5.3 m average height (including

small shaded trees), 34 m�2 ha�1 basal areas, and tree

density was 11,150 stems ha�1. Tanaka et al. (2002)

conducted a study from 1993 to 1996 using a multi-layer

model and occasional canopy flux data. After 1996, Pinus

thunbergii that had been planted at this site were cut and

removed because of pine-wilt disease. In 2000, a new flux

tower (10 m in height) was established within the

plantation, and continuous canopy flux and meteorolo-

gical measurements began. The canopy height in 2002

was approximately 8.5 m near the tower. In both

evergreen and deciduous species, new leaves usually

flush in late April and expand until the end of May

(Matsuo and Kosugi, 2002). Four deciduous species

lose their leaves in November, and small seasonal

fluctuations of LAI at upper canopy can be seen (Fig. 1(a)

and (b)).

2.3. Measurements

Fluxes of momentum, sensible heat, water vapor, and

CO2 were measured by eddy covariance methods at a

tower height of 10.1 m. A three-dimensional sonic

anemo-thermometer (model DA-600T, KAIJO, Japan)

measured sound virtual temperatures and three-dimen-

sional wind speeds. A fast-response, closed-path

infrared gas analyser (IRGA; model LI-6262 or LI-

7000 (since 30 October, 2000), LI-COR Inc., Lincoln,

NE, USA) was used to measure water vapor and CO2

concentrations. Beginning 12 December 2002, gas

Y. Kosugi et al. / Agricultural and Forest Meteorology 139 (2006) 182–199184

Table 1

The parameters used in the model

Parameter Symbol Value Units Reference

Canopy structure

Canopy height 8.6 M This study

Total LAI 4.80 m�2 m�2 This study

Clumping factor V 1.0 This study

Leaf inclination 60 � 18 8 Tanaka et al. (2002)

Leaf physical and optical characteristics

Drag coefficient on both surfaces Cd 0.2 – Wilson and Shaw (1977)

Bulk coefficient for sensible heat on

both surfaces

Ch 0.06 Tanaka et al. (2002)

Water storage capacity on the upper

leaf surface

WUMAX 0.2 mm LAI�1 Watanabe and Mizutani (1996)

Water storage capacity on the lower

leaf surface

WLMAX 0.2 mm LAI�1 Tanaka et al. (2002)

Transmissivity of solar radiation and PAR t 0.2 and 0.06 – Ross (1975)

Reflectivity of solar radiation and PAR r 0.18 and 0.09 – This study

Soil physical, optical, and biotic characteristics

Bulk coefficient for sensible heat on

soil surface

Chs 0.015 This study

Moisture availability bsoil 0.2 – This study

Reflectivity of solar radiation and PAR asoil 0.26 and 0.064 – This study

Referential soil respiration rate at 25C FResoil 4.182 mmol m�2 s�1 Kosugi et al. (2005)

Q10 value of soil respiration rate Q10soil 2.247 Kosugi et al. (2005)

Coefficient and intercept for the dependency

of soil respiration on soil moisture

asres, bsres 15.18, 1.21 – Kosugi et al. (2005)

Thresholds to apply the dependency

of soil respiration on soil moisture

usmin, usmax 8.4, 9.2 Kosugi et al. (2005)

Leaf gas exchange characteristics

Stomatal coefficient in Eq. (A.22) m 7.7 – This study

Empirical value at which f(D)

halves in Eq. (A.23)

D0 2.0 kPa This study

Minimum stomatal conductance gsmin 0.01 mol m�2 s�1

Vcmax at 25C at the layer of z = 1 Vcmax25 (1) 32.4 mmol m�2 s�1 This study

Activation energy for Vcmax DHa(Vcmax) 48,000 J mol�1 Kosugi and Matsuo (2006)

Deactivation energy for Vcmax DHd(Vcmax) 220,000 J mol�1 Kosugi and Matsuo (2006)

Entropy term DS(Vcmax) 650 J K�1 mol�1 Kosugi and Matsuo (2006)

Extinction coefficient for Vcmax25 kVc 0.7 – This study

Proportion of Rnleaf25 to Vcmax25 kr 0.034 This study

Activation energy for Rdleaf DHa(Rdleaf) 58,800 J mol�1 Kosugi and Matsuo (2006)

Proportion of Jmax to Vcmax kj 2.1

Convexity factor u 0.9 This study

Leaf absorbance of Q e 0.85 This study (1.0 � tPAR � rpar)

Fraction of light loss not used

photosynthetically at the

chloroplast lamellae

1 � f 0.7 This study

Kc at 25C Kc25 27.5 Pa CO2 Harley and Baldocchi (1995)

Activation energy for Kc DHa(Kc) 80,470 J mol�1 Harley et al. (1992)

Ko at 25C Ko25 42,000 Pa O2 Harley and Baldocchi (1995)

Activation energy for Ko DHa(Ko) 14,510 J mol�1 Harley et al. (1992)

t at 25 8C t25 2,321 Harley and Baldocchi (1995)

Activation energy for t DHa(t) �29,000 J mol�1 Harley and Baldocchi (1995)

concentrations were measured with an open-path IRGA

(model LI-7500, LI-COR, Inc., Lincoln, NE, USA).

Analog signals from the sonic anemo-thermometer and

IRGAs were sampled by a data logger (CR10X,

Campbell Scientific, USA) at 8 Hz and sent to a

personal computer. Raw data were transferred to the

laboratory monthly. Fluxes of momentum, sensible

heat, water vapor, and CO2 were calculated at an

Y. Kosugi et al. / Agricultural and Forest Meteorology 139 (2006) 182–199 185

Fig. 1. (a) Seasonal fluctuation in the total leaf area index (LAI) and

(b) vertical distribution of camulative LAI measured with a LAI-2000

(Licor) with a simulated line.

average interval of 30 min. A Webb, Pearman, and

Leuning (WPL) correction for the effect of air density

fluctuations (Webb et al., 1980) was applied to the open-

path system data. The attenuation of density fluctuations

caused when air passes through a tube was corrected in

the closed-path system. We analysed the CO2 (Fc),

sensible (H) and water vapor (lE) fluxes observed from

August 2000 to December 2003. This forest had a

narrow fetch along the neighboring sea and grassland.

Consequently, data that did not meet the standards for

fetch analysis were rejected for the preparation of

reliable flux data. Details of the flux data processing

were reported by Kosugi et al. (2005). We estimated the

instantaneous net ecosystem production as �Fc

assuming that the CO2 storage term and dissolved

organic carbon loss were small enough to be neglected

in this forest (Kosugi et al., 2005).

Environmental conditions were measured at a

meteorological observation tower. Data were recorded

using a data logger (model CR10X, Campbell Scientific

Inc., USA). Air temperature and relative humidity

above the canopy were measured with a Vaisala-type

hygrothermometer (HMP-35C, Campbell Scientific,

USA). The Vaisala sensor was calibrated periodically

using an Assman psychrometer. The downward and

upward components of short-wave and long-wave

radiation were measured with a four-component

radiometer (model MR-40, EKO, Japan). The down-

ward and upward photosynthetically active radiation

(PAR) was measured with PAR sensors (PAR-01, Prede,

Japan) at the top of canopy and the forest floor. The soil

heat flux, G, was measured with heat flux plates (model

MF81, EKO, Japan) installed at 0.01-m depth on the

forest floor. Rainfall data were provided from a fire

station within 1 km of the plantation. Soil capillary

pressure was measured using tensiometers buried at

depths of 10, 20, 30, and 40 cm, and the volumetric soil

water content was measured using a water content

reflectometer (CS615, Campbell Scientific, USA)

buried in the soil at depths ranging from 0 to 30 cm.

Soil and leaf respiration rates were measured with

the chamber method to estimate ecosystem respiration.

The soil respiration rate was measured periodically at

four points with a closed chamber air circulation

method using hand-made chambers and an IRGA (Li-

6262, LI-COR Inc., Lincoln, NE, USA) as reported by

Kosugi et al. (2005). Leaf gas exchange measurements,

including the dark respiration rate of trees growing near

a gas exchange observation tower in the center of the

forest, were made with a portable steady-state photo-

synthetic system (Li-6400, LI-COR, Lincoln, NE,

USA), as reported by Kosugi and Matsuo (2006) and

Matsuo and Kosugi (2002). Seasonal fluctuations and

vertical profiles of LAI were estimated by the optical

method (LAI-2000, LI-COR Inc., Lincoln, NE, USA).

3. Results

3.1. Parameterization

The canopy was divided vertically into 86 equal

layers, with the top of the canopy set at 8.6 m. The

distribution of leaf inclination angle [g(a)] was assumed

to be normal with an average of 60.08 and standard

deviation of 18.08, as determined by the data collected

from 1000 leaves (Tanaka et al., 2002). Seasonal

fluctuations and vertical profiles of LAI measured with

an LAI-2000 are shown in Fig. 1(a) and (b). Small

seasonal fluctuations of LAI could be seen in the canopy

layer at this site because some deciduous species lose

their leaves in November. Vertical profiles of LAD and

the total LAI in the normal period were fitted with a

fourth-order polynomial equation. Seasonal fluctuations

Y. Kosugi et al. / Agricultural and Forest Meteorology 139 (2006) 182–199186

Fig. 2. Temperature dependence of maximum carboxylation rate

(Vcmax) and dark respiration rate (Rnleaf) for three evergreen broad-

leaved species and one deciduous broad-leaved species at the obser-

vation site and an average temperature dependence curve for each

parameter.

were obtained, with a linear relationship with the day of

year during the periods of leaf expansion and leaf fall.

Lines in Fig. 1(b) show the simulated results of these

procedures. Reflectivity of solar radiation on the soil

surface was determined from the observed relationships

between upward and downward solar radiation on the

soil surface (Tanaka et al., 2002). Reflectivity of solar

radiation on the leaf surface was determined by

comparison of observed and simulated upward solar

radiation above the canopy. Reflectivity of PAR on the

soil and leaf surfaces was determined in a similar way.

The bulk coefficient for sensible heat transfer of both

surfaces was determined by comparing observed and

simulated upward long-wave radiation above the

canopy. The bulk coefficients for sensible heat transfer

of the soil surface and for moisture availability were

determined using observations from other closed

forests. The dependence of the soil respiration rate

on temperature and its relationship with soil water

content were determined using chamber measurements

as described by Kosugi et al. (2005).

The parameters representing leaf gas exchange

characteristics are perhaps the most important measure-

ments. However, although the vertical and seasonal

fluctuations of leaf gas exchange characteristics are

among the most important factors regulating gas

exchange for the canopy as a whole, the mechanisms

inducing their non-stationarity remains a subject of active

research. Kosugi and Matsuo (2006) reported the

amplitude and seasonal fluctuations in three major leaf

gas exchange parameters (Vcmax, Rnleaf, and m) and

discussed their temperature dependences in three ever-

green and one deciduous species grown near the

observation tower at this site. Kosugi and Matsuo

(2006) concluded that one set of Vcmax25, Rnleaf25

parameters, and temperature dependence curves could

produce a satisfactory estimation of the leaf scale gas

exchange throughout the year in the case of the three

evergreens, except during the period of simultaneous leaf

falling and expanding in April and May in the wet year

(2001). In a deciduous oak, declines in Vcmax25 were

observed after summer, along with differences in Vcmax25

and Rnleaf25 during the leaf expansion period. For all four

species, the difference of the stomatal coefficient m

should be considered during periods of leaf expansion and

drought. In this study, we determined the reference values

and temperature dependences for Vcmax and Rnleaf by

averaging the curves for a normal period in four species

(Fig. 2) and testing the results as representative

parameters for the canopy leaves at this site. We sought

to evaluate the impact of leaf physiology on seasonal

fluctuation in gas exchange, i.e., the extent to which a

constant parameter set reproduces the amplitude and

seasonal fluctuations in canopy fluxes. Vertical distribu-

tion of Vcmax25 was scaled with a parameter kVc as

described in Eq. (A.24) in Appendix A. In this study,

Vcmax25(0) in Eq. (A.24) was determined so that Vcmax25 at

the layer with z = 1 was to be 32.4. Vcmax25 at the upper

layer was cut down after this calculation assuming a

uniform Vcmax at the top of canopy between 0 < j < 1.

We tested the change in R2, the coefficient of determina-

tion, in comparison with daytime observed and simulated

Fc with various kVc in Fig. 3, excluding expansion and

severe drought periods (April 2001–2003; August 2000;

August–December 2002). These comparisons suggest

Y. Kosugi et al. / Agricultural and Forest Meteorology 139 (2006) 182–199 187

Fig. 3. Simulation results (R2 in the comparison of daytime observed

and simulated CO2 flux (Fc)) with different the ectinction coefficient

for Vcmax25 ðkVc Þ.

that the optimal value for kVc is approximately 0.7. The

vertical distributions in Vcmax25 and Rnleaf25 were

determined as shown in Fig. 4, with kVc ¼ 0:7.

The parameters used in the simulation are listed in

Table 1.

3.2. Simulations

A simulation was run using data from August 2000 to

December 2003. Seasonal and inter-annual fluctuations

Fig. 4. Vertical profiles of three major physiological parameters,

normalised maximum carboxylation rate (Vcmax25), normalised leaf

dark respiration rate (Rnleaf25), and the total leaf area index (LAI), used

in the simulation (in the case of the ectinction coefficient for Vcmax25

ðkVc Þ = 0.7).

of meteorological and soil moisture conditions are

shown in Fig. 5. As shown by Kosugi et al. (2005), the

year 2003 was a wet and cloudy year, with low values of

daily solar radiation, air temperature, and vapor

pressure deficit (VPD) in summer. The total annual

precipitation was 788 mm in 2000, 1078 mm in 2001,

578 mm in 2002, and 1230 mm in 2003. This forest

experienced severe drought in August 2000 (only 3 mm

of total precipitation) and also from August to

December 2002 (138 mm of precipitation during 4

months). The drought in 2002 was especially severe and

caused the death of some trees.

Figs. 6–8 show the simulation results. These figures

compare the average diurnal courses of observed and

simulated sensible heat flux, latent heat flux, and CO2

flux for each month. Observed flux data were prepared

after the rejection by fetch analysis and were corrected

using the energy budget described by Kosugi et al.

(2005). Only in the case of Fc, night time CO2 efflux was

interpolated using the relationship between air and soil

temperatures. Daytime CO2 flux was interpolated using

the light response curve for each month. This is to assess

the impact of leaf physiology on net ecosystem

production (NEP), excluding the influence of under-

estimation of night time CO2 efflux and considerable

amount of daytime missing data after rejection by fetch.

Details of these procedures with the analysis of raw flux

data were described in Kosugi et al. (2005). The average

diurnal courses were calculated by averaging all

available 30-min eddy flux data in each month. Simulated

diurnal courses were also produced to correspond with

the observed courses and were averaged only when

observed or interpolated data were available. The gray

line in Fig. 6 shows the simulation results for the sensible

and latent heat fluxes with a constant m (=7.7) for a whole

period. The black line in Fig. 6 represents the simulated

values of the fluxes using a linear relationship between m

and soil water content to adjust the stomatal conductance.

The slope and the intercept were set as follows to produce

the optimal results:

m ¼ f ðuÞ ¼ ðb1 � b2Þðu � urÞðus � urÞ

þ b2

where u, ur, us are the actual (0–30 cm), residual, and

saturated volumetric soil water content, respectively. ur

and us were set at 0.05 and 0.30 for this site, based on the

results of PF-tests using 100-cm3 core samplers. The

coefficients b1, b2 are fitting parameters and were

optimized to be 32.0 and 1.0, respectively.

The gray line in Fig. 6 and the white dots in Fig. 8(a)

and (b) demonstrate that simulated sensible and latent

Y. Kosugi et al. / Agricultural and Forest Meteorology 139 (2006) 182–199188

Fig. 5. Daily aggregate solar radiation, daily maximum and average air temperatures, daytime maximum and daytime average vapor pressure

deficits (VPD) at a height of 9 m, daily total precipitation, and the volumetric water content at depths of 0–30 cm.

heat fluxes at the canopy with a constant m roughly

reproduced the amplitude, as well as the diurnal and

seasonal fluctuations in observed fluxes, with some

exceptions. Overestimations of latent heat flux, and thus

underestimation of sensible heat flux, were seen in

August and September 2000, August 2001, and from

August to November 2002. These periods correspond to

the drought periods (see Fig. 5). However, under-

estimations of latent heat flux were seen during summer

in 2003, which also correspond to the wetter soil

conditions. The black line in Fig. 6 and the black dots in

Fig. 8(a) and (b) show significant improvements in the

results and mostly explains the diurnal, seasonal, and

inter-annual fluctuations in the sensible and latent heat

fluxes. In September 2000, the black line still over-

estimated the latent heat flux. Underestimation of the

latent heat flux with a constant m in the summer of 2003

was also improved by changing m with soil moisture

conditions.

In the case of CO2 flux (Fig. 7 and Fig. 8(c)), we were

surprised that the average reference values of Vcmax and

Rnleaf – with their temperature dependences and m

values produced from the leaf level gas exchange

observations of the four investigated species – could

roughly reproduce the amplitude, as well as diurnal and

seasonal fluctuations in observed CO2 flux of the

canopy as a whole. Notable overestimations of CO2 flux

occurred in April of each year, as well as August 2000

and from August 2002 to May 2003. These periods

correspond to the leaf expansion period in April, a

severe short-term drought period in August 2000, and a

long-term severe drought from August to mid-Decem-

ber 2002, as well as the period preceding the long-term

severe drought in 2002. The decline in simulated CO2

absorption after summer 2002, which corresponded to

the severe and long-term drought, continued from after

the recovery of soil moisture in January until the new

leaves fully expanded in the following May. These

Y. Kosugi et al. / Agricultural and Forest Meteorology 139 (2006) 182–199 189

Fig. 6. Comparison of the monthly average diurnal changes in observed and simulated sensible and latent heat fluxes.

Y. Kosugi et al. / Agricultural and Forest Meteorology 139 (2006) 182–199190

Fig. 7. Comparison of the monthly average diurnal changes in observed and simulated CO2 flux (Fc). In the case of the ‘observed’ values, nighttime

CO2 efflux was replaced with the estimated ecosystem respiration, and gaps of daytime CO2 flux were interpolated using the light response curve for

each month (Kosugi et al., 2005).

underestimations did not improve by changing m with

the soil moisture conditions (gray and black lines in Fig.

7 and Fig. 8(c)).

4. Discussion

Fig. 6 strongly suggests that evapo-transpiration was

overestimated with a constant m under conditions of

Fig. 8. Comparisons of the monthly average observed and simulated: (a) se

plotted against the observed values. In the case of the ‘observed’ values of

ecosystem respiration, and gaps of daytime CO2 flux were interpolated usi

drought and that the parameter m changed with soil

moisture conditions at the site. Lai et al. (2000b) also

reported lower m values during the drought in their

analysis using the multi-layer model. It was also

detected from Fig. 6 that plants opened their stomata

wider during a wetter summer (2003) compared to

average years with more periods of drought during the

summer (2000, 2001, 2002). Thus the stomatal

nsible heat, (b) latent heat, and (c) CO2 fluxes. Simulated values are

CO2 flux (Fc), nighttime CO2 efflux was replaced with the estimated

ng the light response curve for each month (Kosugi et al., 2005).

Y. Kosugi et al. / Agricultural and Forest Meteorology 139 (2006) 182–199 191

conductance and evapotranspiration rate were larger

than expected with the constant behavior of m. The area

received a large amount of rain in mid-September

following severe drought conditions in August 2000,

and the simulation with changing m (black line in Fig. 6)

still overestimated the latent heat flux in September

2000. This is notable because this means that plants did

not open their stomata immediately after the drought

ended.

In the case of CO2 flux, simple stomatal closure

could not fully explain the decline during severe

drought conditions, and decline of ‘apparent’ Vcmax of a

single leaf should be counted in the evaluation of the

canopy CO2 fluxes (Fig. 7). Drought conditions might

also cause the decline in leaf respiration. In this case,

decline of ‘apparent’ Vcmax is considered to be more

severe.

Basically, single leaf Vcmax is determined by Rubisco

activity, which directly relates to the amount of Rubisco

and leaf nitrogen content. This involves complex

mechanisms of nitrogen allocation (e.g., Field, 1983;

Evans, 1987, 1993; Hikosaka and Terashima, 1995;

Niinemets and Tenhunen, 1997; Takashima et al.,

2004). In addition, there are many other potentially

influential factors. Internal conductance is one of the

most important factors to consider, since many isotope

studies that have determined the value of Cc using 13C

discrimination (e.g., von Caemmerer and Evans, 1991;

Loreto et al., 1992) support values of 0.7–0.8 or lower

for trees (e.g., Epron et al., 1995; Hanba et al., 1999,

2001). As demonstrated by Loreto et al. (1992), this

might be the major factor that determines the range of

‘apparent’ Vcmax for each species. However, there has

been no reported evidence that drought can cause

changes in internal conductance. The influence of

‘apparent’ Vcmax on the patchiness of stomatal opening

and closure or on photoinhibition also should be

considered in some situations (Takanashi et al., 2006).

The decline of simulated CO2 absorption between

August 2002 and May 2003 suggests that the severe and

long-term drought caused damage to the carboxylation

sites of individual leaves and thus contributed to the

drop in Vcmax. The amount of Rubisco and leaf nitrogen

content may change after leaves experience severe

damage due to long-term drought. Although a relation-

ship between leaf nitrogen and Vcmax for pines

examined by Lai et al. (2002) suggests that the decline

of Vcmax by a factor of 2, as is in this study, should be

accompanied with the decline of leaf nitrogen by a

factor of 3, which is unrealistic. Another possibility is

that the degradation of chlorophyll caused by excess

energy leads to a reduction of Vcmax. We have no

obvious evidence to explain this long-term drop in

Vcmax for the present. Damaged leaves did not fully

recover, and new leaves eventually expanded to replace

them in next spring (see January–May 2003 in Fig. 7).

In contrast, there has been no reported evidence to

suggest that short-term drought affects Rubisco activity.

We saw no difference in the characteristics of Vcmax

with mild drought in summer of 2001, although

stomatal behavior (m) was affected by a drought of

this extent (Kosugi and Matsuo, 2006). The summer

drought in 2000 was more severe than that of 2001. The

declines of electron transport rates at about half of the

expected values, as well as the temperature dependence

curve of normal periods, were detected from the diurnal

course observations of several canopy trees on August

23, 2000, using a portable chlorophyll fluorometer

(MINI-PAM, Heinz Walz GmbH, Effeltrich, Germany)

coupling with gas exchange measurements. However,

this decrease in the electron transport rate was not

enough to explain the decline of photosynthesis by itself

(unpublished data). The modulate patchiness of

stomatal openings and closures were observed in

Cinnamomum camphora at this site on September 26,

2000 (Takanashi et al., 2006). Although the degree of

patchiness observed on September 26, 2000 was not

enough to explain the decline of ‘apparent’ Vcmax in

August 2000, more severe drought conditions may

cause bimodal stomatal patchiness that have signifi-

cantly affected the ‘apparent’ Vcmax and also caused the

decline in photosynthesis (Takanashi et al., 2006).

All broad-leaved tree species, including evergreen

and deciduous, expand their new leaves at this site

beginning in mid-April, and evergreen species also drop

most part of old leaves (the previous-year leaves) from

April to May. Leaf scale measurements also reveal that

newly expanding leaves have quite different character-

istics in terms of gas exchange, i.e., large Rnleaf and m,

and small Vcmax (Kosugi and Matsuo, 2006). Under-

estimations of CO2 flux every April demonstrate that the

phenological differences of the gas exchange char-

acteristics of expanding leaves also could influence gas

exchange in the canopy as a whole. In a leaf-level

analysis, newly expanding leaves still showed the

different characteristics in May, but this phenomenon

was mitigated at the canopy scale. This may be due in

part to the fact that some deciduous trees, even though

they constitute about 25% of the LAI at most (see

Fig. 1(a) and (b)), show the gas exchange characteristics

of mature leaves in mid-May. The previous-year leaves

of evergreen species also contribute, and newly

expanding leaves gradually mature as well (Kosugi

and Matsuo, 2006).

Y. Kosugi et al. / Agricultural and Forest Meteorology 139 (2006) 182–199192

Fig. 9. Comparison of observed and simulated monthly NEP. The simulated values with constant m and changing m were shown with normal and

bold lines, respectively. The ‘observed’ values were shown with gray line, with which nighttime CO2 efflux was replaced with the estimated

ecosystem respiration, and gaps of daytime CO2 flux were interpolated using the light response curve for each month (Kosugi et al., 2005).

These results corresponded very well to the results

from the extended big-leaf analysis at the same site

reported by Kosugi et al. (2005), which indicates the

impact of single leaf physiology at the canopy directly

influenced the bulk characteristics of canopy scale

fluxes. Seasonal variability of Vcmax was also reported in

a pine plantation (Juang et al., 2006). They showed the

seasonal osillations of an effective Vcmax for the canopy

as much as 50%, which was coupled with a porometry

data at the leaf scale (Ellsworth, 2000).

Comparison of the observed and simulated monthly

NEP (Fig. 9) showed that the differences of the

observed and simulated NEP with changing m in leaf

expansion period (April) were 39, 67, and

32 g C m�2 month�1 in 2001, 2002, and 2003. The

difference of the observed and simulated NEP in severe

drought period in summer (August and September

2002) was 272 g C m�2 month�1 even after considering

the changing m with soil moisture condition. The

depression of canopy CO2 uptake attributable to the

change of the ‘apparent Vcmax’ during leaf expansion

and severe drought period was estimated to be

427 g C m�2 year�1 in 2002.

5. Conclusions

The impact of leaf physiology on the diurnal,

seasonal, and inter-annual fluctuation in gas exchange

of a warm-temperate evergreen broad-leaved forest in

Japan over 3.5 years was evaluated using a multi-layer

model. Simulated sensible and latent heat fluxes and CO2

flux at the canopy were used to roughly reproduce the

amplitude, as well as diurnal and seasonal fluctuations in

observed fluxes, with one set of parameters. This method

validated the descriptions of the multi-layer model.

Overestimation of latent heat flux and subsequent

underestimation of sensible heat flux—without con-

sidering the additional stomatal closure-under conditions

of drought demonstrated that different stomatal beha-

viour should be considered during a period of drought.

Overestimation of CO2 flux during leaf expansion

periods and severe drought periods, even including

additional stomatal closure, demonstrated that the

declines in canopy scale CO2 uptake during these

periods were related to some physiological restraints

besides simple uniform stomatal closure at the single leaf

scale. These results indicate that the impact of leaf

physiology on long-term gas exchange is an important

factor that should be considered in detail, even in an

evergreen broad-leaved forest.

Acknowledgments

We thank the Kansai Electric Power Co., Inc., and

Kansai Environmental Engineering Co., Ltd. (KANSO)

for their help with our field observations at the Akou

Power Station. We also thank Dr. Tsunahide Shidei, Dr.

Shozo Shibata, and Dr. Makoto Tani for their support of

the project at this site, and Dr. Nobuhito Ohte, Ms.

Motoko Higuchi, Ms. Noriko Hama, Mr. Masato Yano,

Mr. Tatsuya Katayama, Dr. Masatoshi Kawasaki, Mr.

Tomonori Mitani, and Mr. Shinjiro Ohkubo for

collecting the field data. We also thank the reviewers

who provided several valuable comments to improve

the discussion.

Appendix A

A.1. Sub-model (1): Reynolds stress, sensible heat

exchange, leaf CO2 and H2O exchange, and ground

surface

Applying time and horizontal averages, the differ-

ences between two levels of homogeneous canopy

Y. Kosugi et al. / Agricultural and Forest Meteorology 139 (2006) 182–199 193

planes (z, z + dz) in the Reynolds stress ðu0w0Þ and in

fluxes of sensible heat, water vapor, and CO2

ðw0T 0; w0q0; w0c0Þ, are written as

du0w0 ¼ u0w0ðzþ dzÞ � u0w0ðzÞ ¼ �Cdu2 d f (A.1)

dw0T 0 ¼ w0T 0ðzþ dzÞ � w0T 0ðzÞ ¼ ChuðTc � TÞd f

(A.2)

dw0q0 ¼ w0q0ðzþ dzÞ � w0q0ðzÞ

¼ ðCesl d f sl þ Cesh d f shÞu½qSATðTcÞ � q� (A.3)

dw0c0 ¼ w0c0ðzþ dzÞ � w0c0ðzÞ

¼ �ðAsl d f sl þ Ash d f shÞ (A.4)

where Cd, Ch, and Ce are the leaf transfer coefficients for

momentum (both leaf surfaces), sensible heat (both leaf

surfaces), and transpiration (lower leaf surface), respec-

tively; u, w, T, q, and c are the horizontal wind velocity,

vertical wind velocity, air temperature, specific humid-

ity, and ambient CO2 concentration, respectively. In

addition, Tc and qSAT(Tc) are the leaf temperature and

saturated specific humidity at Tc, respectively; A the net

assimilation rate per unit leaf area, df the leaf area index

within a layer, and the subscripts sl and sh denote sunlit

and shaded areas, respectively. Ce is dependent on the

whole-leaf average stomatal conductance (gsleaf) and

the boundary layer conductance (gb) as follows:

Ce ¼�

1

gb

þ 1

gsleaf

��11

u(A.5)

At the ground surface

u0w0ð0Þ ¼ �Cdsu2 (A.6)

w0T 0ð0Þ ¼ ChsuðTs � TÞ (A.7)

w0q0ð0Þ ¼ bsoilChsu½qSATðT sÞ � q� (A.8)

where Cds and Chs are the bulk transfer coefficients at

the soil surface for momentum and sensible heat,

respectively; Ts and qSAT(Ts) are the soil surface tem-

perature and saturated specific humidity at Ts respec-

tively, and bsoil is the moisture available at the ground

surface. To calculate the fluxes at the ground surface we

used the wind velocity at dz (0.1 m in this study) from

the soil surface. Supposing that Chs and Cds are similar,

they are fixed as follows:

Chs � Cds ¼ 0:015 (A.9)

Soil respiration rate is substituted for CO2 flux at the

ground surface.

A.2. Sub-model (2): stomatal conductance and net

photosynthesis for individual leaves

Assimilation rate of an individual leaf at each layer

was determined with a biochemical photosynthesis

model (Farquhar et al., 1980), using values for the

stomatal conductance of each patch given by the

distribution:

A ¼ Vc

�1� pðG �Þ

pðCcÞ

�� Rdleaf (A.10)

pðG �Þ ¼pðOÞ2t

(A.11)

where A is the net assimilation rate (mmol m�2 s�1), Vc

the rate of carboxylation in the photosynthetic carbon

reduction (PCR) cycle (mmol m�2 s�1), Rdleaf the non-

photorespiratory respiration rate (mmol m�2 s�1), p(G*)

the CO2 compensation point without non-photorespira-

tory respiration (Pa), t the specificity factor of Rubisco,

and p(Cc) (Pa), and p(O) (21,000 Pa) are the partial

pressures of CO2 and O2 at the sites of carboxylation

and oxygenation, respectively. The lowest value among

the electron transport-limited rate of carboxylation (Wj)

and the RuBP saturated rate of carboxylation (Wc) was

used as the velocity of carboxylation (Vc), as follows:

Wc ¼ Vcmax

pðCcÞpðCcÞ þ Kcð1þ ð pðOÞ=KoÞÞ

(A.12)

W j ¼J

4þ 8 pðG �Þ= pðCcÞ(A.13)

where Vcmax is the maximum rate of carboxylation

(mmol m�2 s�1), Kc and Ko are the Michaelis–Menten

constants of Rubisco for CO2 and O2, respectively, and J

is the electron transport rate. J is expressed as the

smaller root of the following nonrectangular hyperbola

representing the relationship to absorbed photosynthe-

tically active radiation (Farquhar and Wong, 1984).

uJ2 ��

Jmax þeð1� f Þ

2Q

�J þ Jmax

eð1� f Þ2

Q ¼ 0

(A.14)

In this equation, Q is the incident PAR (mmol m�2 s�1),

e the leaf absorbance of Q, f the fraction of light loss not

used photosynthetically at the chloroplast lamellae,

Jmax the maximum potential rate of electron transport,

and u is a convexity factor. The values of u (0.9) and

1 � f (0.7) were approximated using the results of light

curve measurements of the electron transport rate. The

value of e (0.85) was approximated using measurements

of the light penetration of the canopy leaves. Based on

Y. Kosugi et al. / Agricultural and Forest Meteorology 139 (2006) 182–199194

Wullschleger (1993), Jmax is related to Vcmax as follows:

Jmax ¼ k jVcmax (A.15)

The Arrhenius function is used for the temperature

dependences of parameters Kc, Ko, t, and Rnleaf as

follows:

f ðTl:kÞ ¼ f ðT refÞ exp

��1� T ref

Tl:k

�DHa

RT ref

�(A.16)

and a simplified equation from Sharpe and DeMichele

(1977) is used for the temperature dependences of Vcmax

as follows:

f ðTl:kÞ ¼f ðT refÞexp½1� ðT ref=Tl:kÞðDHa=RT refÞ�

1þ exp½ðDSTl:k � DHdÞ=RTl:k�(A.17)

where f(Tl.k) is the value of a given parameter at leaf

temperature Tl.k(K), f(298) is the reference value of that

parameter at 25 8C (Kc25, Ko25, Rdleaf25, t25, and

Vcmax25), DHa is the activation energy (J mol�1), DHd

is the deactivation energy (J mol�1), and DS is an

entropy term (J K�1 mol�1). The choice of the Rubisco

kinetic parameters and their temperature dependences is

a matter of considerable uncertainty (Dreyer et al.,

2001). The values of the Rubisco kinetic parameters

and their temperature dependences used in this study

(Table 1) followed Harley et al. (1992), mainly based on

the experiment of Jordan and Ogren (1984) using

spinach. Rdleaf is scaled using the relationship with

the dark respiration rate (Rnleaf) based on the results

of Brooks and Farquhar (1985) as follows:

Rdleaf25 ¼Rnleaf25 for Q< 5;

Rnleaf25½0:5� 0:05 lnðQÞ� for Q� 5

�

(A.18)

Rnleaf25 is related to Vcmax as follows:

Rnleaf25 ¼ krVcmax25 (A.19)

The CO2 concentration in the chloroplasts (Cc) was

calculated under the assumption that this parameter

equalled the intercellular concentration of CO2 as fol-

lows:

Cc ¼ Ci ¼ðgtc � E=2ÞCa � A

gtc þ E=2(A.20)

1

gtc

¼ 1

gbc

þ 1

gsc

(A.21)

where Ca is the ambient CO2 concentration

(mmol mol�1), Ci the intercellular CO2 concentration

(mmol mol�1), E the transpiration rate (mol m�2 s�1),

and gtc is the total conductance of CO2

(mol CO2 m�2 s�1). gbc is the boundary layer conduc-

tance of CO2 (mol CO2 m�2 s�1) such that gbc = gbw/

1.62/3, and gsc is the stomatal conductance of CO2

(mol CO2 m�2 s�1) such that gsc = gsw/1.6, where gbw

is the boundary layer conductance of H2O

(mol H2O m�2 s�1), and gsw is the stomatal conductance

of H2O (mol H2O m�2 s�1). Eq. (A.20) uses the correc-

tion described by Jarman (1974) and von Caemmerer and

Farquhar (1981) to account for the convective effects of

transpiration at stomatal pores. The corresponding values

of A and Cc are determined as the point of intersection of

the ‘demand function’ described by Eq. (A.10) and the

‘supply function’ described by Eq. (A.20).

An improved version of the model by Ball et al.

(1987) and Leuning (1995) was used for estimations of

stomatal conductance, which is described as follows:

gsw ¼ mA f ðDÞCs � G

þ gswmin (A.22)

f ðDÞ ¼ 1

1þ ðD=D0Þ(A.23)

where f(D) is the non-linear function of the vapor

pressure deficit, m the slope of the relationship between

the stomatal index (Af(D)/(Cs � G)) and the stomatal

conductance, Cs the CO2 concentration at the leaf sur-

face (mmol mol�1), G the CO2 compensation point

(mmol mol�1), and gswmin is the minimum stomatal

conductance. A hyperbolic form function similar to

that of Lohammer et al. (1980)-type was used for

f(D), where D is the vapor pressure deficit (kPa) of

the air, and D0 is the empirical value at which f(D)

halves. The CO2 concentration at the leaf surface (Cs)

was calculated using the CO2 concentration of the air in

the chamber, a constant boundary layer conductance,

and the net assimilation rate.

Photosynthetic capacity was expected to decline

exponentially with the cumulative LAI as follows:

Vcmax25ðjÞ ¼ Vcmax25ð0Þ expð�kVcjÞ (A.24)

where j is the cumulative LAI measured downwards

from the top of the canopy, and kVc is the extinction

coefficient for Vcmax25.

A.3. Sub-model (3): radiative transfer within and

above the canopy

The transfer of direct solar radiation (Sb # ) within a

canopy is written as

Sb # ðz;HÞ ¼ IbSb # ðzþ dz;HÞ (A.25)

Y. Kosugi et al. / Agricultural and Forest Meteorology 139 (2006) 182–199 195

where Ib is the probability of no contact with direct

radiation within a layer between z and z + dz, and H is

solar elevation. The transfer of direct PAR (SPARb # )

within a canopy is written analogously to (A.25). Ib is

written as

IbðHÞ ¼ 1�VGlayerðHÞd f

sin H(A.26)

The second term on the right is the shaded area that

the foliage within a layer projects on the unit horizontal

plane. V is a clumping factor and ranges from 0 to 1.

Glayer decotes the ratio of the area of leaves ‘in situ’,

projected into a plane normal to the solar elevation (H),

to the leaf area index within that layer. Glayer is the sum

of the G functions for each individual leaf within a layer

(Gleaf). Gleaf is a function of solar elevation (H), leaf

inclination angle (a), leaf orientation angle (b), and the

direction of the sun (fs). Glayer can be represented by

Gleaf and the distributions of leaf inclination angle

[g(a)] and leaf orientation angle [g(b)] within a layer.

Assuming that leaf orientation angle is constantly

distributed [g(b)] = p/2], the direction of the sun can be

ignored, and Glayer can be written as follows:

GlayerðHÞ ¼Z 2p

0

1

2p

Z p=2

0

gðaÞGleafða;b;HÞda db

(A.27)

Gleaf is written as

Gleafða;b;HÞ ¼ jcos a sin H þ sin a cos b cos Hj(A.28)

Id, the probability of no contact with diffuse radiation

within a layer between z and z + dz, is computed by

integrating Ib over the sky hemisphere, assuming that

diffuse solar radiation and PAR arrive uniformly from

every angle of the sky hemisphere as follows:

Id ¼ 2

Z p=2

0

IbðHÞ sin H cos H dH (A.29)

Downward diffuse solar radiation (Sd#) is written using

Id, leaf transmissivity (ts), and leaf reflectivity (rs) as

follows:

Sd # ðz;HÞ ¼ Sd # ðzþ dz;HÞ½tsð1� IdÞ þ Id�

þ Sd " ðz;HÞrsð1� IdÞ

þ Sb # ðzþ dzÞtsð1� IbÞ (A.30)

Upward diffuse solar radiation (Sd") is shown as

Sd " ðzþ dz;HÞ

¼ Sd " ðz;HÞ½tsð1� IdÞ þ Id�

þ Sd # ðzþ dz;HÞrsð1� IdÞ

þ Sb # ðzþ dzÞrsð1� IbÞ (A.31)

The values of Sd# or Sd" in the adjacent layers are

required to solve Eqs. (A.30) and (A.31), respectively.

These values are initially unknown, but they can be

solved using the methods of Baldocchi and Hutchison

(1986). Downward and upward diffuse PAR (SPARd#,SPARd") are calculated by substituting PAR (tPAR, rPAR)

for leaf transmissivity (ts) and reflectivity (rs) in

Eqs. (A.30) and (A.31). Solar radiation on the ground

is written as follows:

Sd " ð0Þ ¼ aSsoil½Sb # ð0Þ þ Sb " ð0Þ� (A.32)

where aSsoil is the reflectivity of solar radiation on the

ground. PAR on the ground is written by substituting the

reflectivity of PAR on the ground (aPARsoil) for aSsoil in

Eq. (A.32).

Downward long-wave radiation (L#) is calculated as

L # ðzÞ ¼ L # ðzþ dzÞId þ e0sT4c ð1� IdÞ (A.33)

and upward long-wave radiation (L") is calculated as

L " ðzþ dzÞ ¼ L " ðzÞId þ e0sT4c ð1� IdÞ (A.34)

where e0 is the surface emissivity (1.0) and s is the

Stefan–Boltzmann constant (5.67 � 10�8 kg s�3 K�4).

Upward long-wave radiation on the ground is written as

L " ð0Þ ¼ e0sT4s (A.35)

A radiative transfer model is also required to evaluate

the area of sunlit and shaded leaves. The sunlit LAI

(dfsu) is written as

d f su ¼Sb # ðzþ dz;HÞ � Sb # ðz;HÞ

Sb # ðh;HÞsin H

VGlayerðHÞ(A.36)

where h is canopy height and Sb#(h, H) is the direct solar

radiation above the canopy. When Sb#(h, H) = 0,

dfsu = 0. The shaded LAI (dfsh) is shown as

d f sh ¼ d f � d f su (A.37)

The amount of PAR reaching the shaded part of a layer

between z and z + dz (SPARsh) is written as follows

(Baldocchi and Hutchison, 1986):

SPARsh ¼ SPARd # ðzþ dzÞ þ SPARd " ðzÞ (A.38)

Y. Kosugi et al. / Agricultural and Forest Meteorology 139 (2006) 182–199196

Considering SPARsh and direct PAR above the canopy

(SPARb(h, H)#), the amount of PAR reaching the sunlit

part of a layer (SPARsu) is shown (Baldocchi and Hutch-

ison, 1986):

SPARsu ¼ SPARsh þ SPARb # ðh;HÞVGlayerðHÞ

sin H(A.39)

According to the Bouguer and Berlage equations,

direct solar radiation and sky solar radiation on the top

of canopy on a clear day are written as follows:

Sb # ¼ S0A1=sin HT sin H (A.40)

and

Sd # ¼ 1:2S0 sin Hð1� ATÞð1� A

1=sin HT Þ

ð1� 1:4 ln ATÞ(A.41)

respectively, where S0 is the solar constant, AT the

atmospheric transmissivity, and H the solar elevation.

The amount of global solar radiation is the sum of sky

and direct solar radiation.

A.4. Sub-model (4): leaf and ground surface energy

balance

Ignoring both the heat storage in leaves and the

energy stored by photosynthesis, the energy balance of

leaves within a layer is written as

ð1� ts � rsÞfð1� IbÞSb # ðzþ dzÞþ ð1� IdÞ½Sd # ðzþ dzÞ þ Sd " ðzÞ�gþ ð1� IdÞ½L # ðzþ dzÞ þ L " ðzÞ�¼ lra dw0q0 þ c pra dw0T 0

þ 2e0sðTc þ 273Þ4ð1� IdÞ (A.42)

where l is the latent heat of vaporization of water, cp the

specific heat of air at a constant pressure, and ra is the

density of air.

The energy balance at the soil surface can be written

as

ð1� asSoilÞ½Sb # ð0Þ þ Sd # ð0Þ� þ L # ð0Þ¼ lraw0q0ð0Þ þ cpraw0T 0ð0Þ þ e0sT4

s þ G (A.43)

where G is the grand heat flux.

A.5. Sub-model (5): atmospheric diffusion within

and above the canopy

A second-order closure model (Watanabe, 1993)

was used to describe atmospheric diffusion within

and above the canopy. Reynolds stress, turbulent

kinetic energy, variance of the vertical wind component,

and heat, water vapor, and CO2 fluxes are written as

follows:

R

eynolds stress ðu0w0Þ:

� w02du

dzþ 2

d

dz

�el1

du0w0

dz

�

� e

3l2

u0w0 þ xe2 du

dz¼ 0 (A.44)

T

urblent energy (e2):

� 2u0w0du

dzþ d

dz

�el1

�de2

dzþ 2

dw02

dz

��

þ 2Cdau3 � 2e3

l3

¼ 0 (A.45)

v

ariance of the vertical wind component ðw02Þ:

3d

dz

�el1

dw02

dz

�� e

3l2

�w02 � e2

3

�� 2e3

3l3

¼ 0

(A.46)

s

ensible heat flux ðw0T 0Þ:

�w02dT

dzþ 2

d

dz

�el1

dw0T 0

dz

�� e

3l4

w0T 0 ¼ 0

(A.47)

w

ater vapor flux ðw0q0Þ:

�w02dq

dzþ 2

d

dz

�el1

dw0q0

dz

�� e

3l4

w0q0 ¼ 0

(A.48)

C

O2 flux ðw0c0Þ:

�w02dc

dzþ 2

d

dz

�el1

dw0c0

dz

�� e

3l4

w0c0 ¼ 0 (A.49)

where a is leaf area density, u0 and w0 are the

fluctuations in the horizontal and vertical wind

velocities, respectively, li(i = 1–4) the length scale,

e2 twice the turbulent kinetic energy, and x is a constant

related to the energy redistribution. The length scales

are written as follows:

li ¼ dil (A.50)

where di is a constant and l is the mixing length.

Watanabe and Kondo (1990) described the maximum

mixing length within and above a canopy (0 < z < h,

h < z) and the mixing length at canopy height (z = h)

with the following equation, taking into account the

limitation of mixing length by both canopy elements

Y. Kosugi et al. / Agricultural and Forest Meteorology 139 (2006) 182–199 197

and the ground surface.

lðzÞ k

Z z

0

�r exp

��Z r

0

mðz� tÞdt

�mðz� rÞ

�dr

þ kz exp

��Z z

0

mðz� tÞdt

�; ð0< z< h; h< zÞ

(A.51)���� dl

dz

���� k ðz ¼ hÞ (A.52)

z = h

lðhÞ ¼ k

Z h

0

�r exp

��Z r

0

mðh� tÞdt

�mðh� rÞ

�dr

þ kh exp

��Z h

0

mðh� tÞdt

�(A.53)

mðzÞ� CdaðzÞ2k2

(A.54)

where r is the distance from the point at z to a lower

point 0 r z. The value of d1 is 0.23 based on the

work of Mellor and Yamada (1974), and the values of

x (=0.077), d2 (=0.85), d3 (=16.6), and d4 (=0.567) are

determined by the following boundary conditions above

a canopy (h z; Watanabe, 1993):

w0x0 ¼ �u�x� (A.55)

dx

dz¼ x�

l(A.56)

de

dz¼ dw02

dz¼ dw0x0

dz¼ 0 (A.57)

where x corresponds to u, T, q, and c, and u*, T*, q*, and

c* are the friction velocity, temperature, specific humid-

ity, and CO2 concentration, respectively.

Following Wilson and Shaw (1977), the boundary

conditions at 2h (twice the canopy height) are written

as

e2

u2�¼ 6:5 (A.58)

w02

u2�¼ 1:5 (A.59)

A.6. Sub-model (6): interception of rainfall and the

leaf water budget

When the difference between the saturated specific

humidity of the leaf temperature [qSAT(Tc)] and the

specific humidity of the air (q) within a layer is positive,

transpiration occurs from dry areas of the lower leaf

surfaces, and evaporation occurs from wet areas of both

leaf surfaces. In contrast, when the difference is

negative, condensation occurs on both leaf surfaces.

The difference in water vapor flux between two heights

in the canopy can be written as

[

q qSAT (Tc)]

dw0q0 ¼ ½ðCesl d f sl þ Cesh d f shÞd f Ldry

d f

þ 0:5Chðd f Lwet þ d f UwetÞ�u½qSATðTcÞ � q�(A.60)

[

q > qSAT (Tc)]

dw0q0 ¼ Chu½qSATðTcÞ � q�d f (A.61)

where the subscripts L, U, dry, and wet denote lower

leaf surface, upper leaf surface, dry, and wet,

respectively. Photosynthesis occurs from dry areas of

the lower leaf surfaces as follows:

�dw0c0 ¼ �ðAsl d f sl þ Ash d f shÞ

d f Ldry

d f

�: (A.62)

Both rainfall and condensation supply water to dry areas

of the upper leaf surfaces, while only condensation

supplies water to dry areas of the lower leaf surfaces.

Water added to the wet area by rainfall or condensation

is regarded as drainage. The vertical profile of leaf water

storage (W) is written as

W ¼ WL þWU (A.63)

where WL and WU are the water storage on the lower and

upper surfaces of leaves per leaf area, respectively.

Precipitation (P) within a canopy is written analogously

to direct beam radiation transfer, assuming the

vertical incident angle of rainfall ðVGlayerp=2Þ=ðsin p=2ÞÞ ¼ Flayer. The amounts of WL and WU are

governed by the following equations:

(

q qSAT (Tc))

@WL

@t¼ �Ep

WL

WLMAX

(A.64)

@WU

@t¼ Flayer

�1� WU

WUMAX

�P� Ep

WU

WUMAX

(A.65)

PðzÞ ¼ ½1� Flayer d f Udry�Pðzþ dzÞ (A.66)

Y. Kosugi et al. / Agricultural and Forest Meteorology 139 (2006) 182–199198

(q > qSAT (Tc))

@WL ¼ �Ep

�1� WL

�(A.67)

@t WLMAX

@WU

@t¼�

FlayerP� Ep

��1� WU

WUMAX

�(A.68)

PðzÞ ¼ ½1� Flayer d f Udry�Pðzþ dzÞ

þ �Epðd f Lwet þ d f UwetÞ (A.69)

where Ep is the evaporation or condensation rate per unit

area on one side.

The wet leaf area indices on the lower and upper

sides are written as

d f Lwet ¼WL

WLMAX d f(A.70)

d f Uwet ¼WU

WUMAX d f(A.71)

where WLMAX and WUMAX are the water storage capa-

cities on the lower and upper leaf surfaces, respectively.

The dry leaf area index is written as

d f dry ¼ d f � d f wet ¼�

1� W

WMAX

�d f (A.72)

A.7. Sub-model (7): soil respiration

A Q10 function was applied to evaluate the soil

respiration rate, as follows:

w0c0ð0Þ ¼ FREsoil ¼ FREsoil25Q10soilððTs�25Þ=10Þ (A.73)

where FREsoil is the flux from the soil (mg m�2 s�1),

Ts soil temperature at a reference depth (2 cm), FREsoil25

(mg m�2 s�1) is the FREsoil at a soil temperature of

25 8C at the reference depth, and Q10soil is the Q10 value

for the temperature dependence in soil respiration rate.

The influence of drought on soil respiration was also

considered as follows based on the results of Kosugi

et al. (2005):

½usmin <VWC< qsmax�; FREsoil25 ¼ asresVWC� bsres

(A.74)

where VWC is volumetric water content of the soil,

asres, bsres are the slope and intercept, respectively. In

addition, usmin and usmax are the thresholds to apply this

equation.

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