Plant canopy effects on soil thermal and hydrological properties and soil respiration

e c o l o g i c a l m o d e l l i n g 1 9 6 ( 2 0 0 6 ) 32–44

available at www.sciencedirect.com

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Plant canopy effects on soil thermal and hydrological properties and soil respiration Katsunori Tanaka a,∗ , Shoji Hashimoto b a

Frontier Research Center for Global Change, Japan Agency for Marine-Earth Science and Technology, 3173-25 Showamachi, Kanazawa-ku, Yokohama, Kanagawa 236-0001, Japan b Department of Forest Site Environment, Forestry and Forest Products Research Institute Incorporated Administrative Agency, 1 Matsunosato, Tsukuba, Ibaraki 305-8687, Japan

a r t i c l e

i n f o

a b s t r a c t

Article history:

A soil–plant–air continuum multilayer model was developed to simulate soil respiration.

Received 15 August 2005

The model can be used to investigate the effects of three canopy characteristics on soil

Received in revised form 12 January

thermal and hydrological properties and soil respiration: leaf area index, the maximum

2006

rate of carboxylation, and the vertical profile of leaf area density. The model did not con-

Accepted 30 January 2006

sider physiological effects of canopy characteristics, such as the effect of photosynthesis

Published on line 20 March 2006

on root respiration. Rather, it examined how changes in temperature and moisture in the soil layers, caused by changes in the plant canopy, affect soil respiration. Model validation

Keywords:

and numerical experiments were performed using above-canopy hydrometeorological vari-

Hydrological effects

ables, including seasonal changes related to a dry season with strong evaporative demand

Plant canopy characteristics

(high solar radiation and high temperature) and a rainy season with weaker evaporative

Soil respiration

demand. The results suggest that the model can successfully reproduce seasonal changes

Thermal effects

in soil profiles of moisture, temperature, CO2 gas concentration, and respiration, and that canopy characteristics can limit soil respiration because of thermal and hydrological effects. An increase in leaf area decreased soil respiration in two ways: by decreasing soil temperature through a reduction in net radiation to the soil surface and by decreasing soil moisture through an increase in canopy transpiration. An increase in the maximum rate of carboxylation decreased soil respiration because it decreased soil moisture by increasing canopy transpiration; there was little thermal effect on soil respiration. A canopy with a denser leaf area in the upper layers created a faster wind velocity in the lower portion and on the ground than did a canopy with the same leaf area index, but with a denser leaf area in the lower layers. The faster wind velocity significantly decreased soil moisture at the soil surface and decreased soil temperature through an increase in soil evaporation; these effects decreased soil respiration. The hydrological effects of the three parameters were most evident in the dry season, while the thermal effects were evident year-round. © 2006 Elsevier B.V. All rights reserved.

1.

Introduction

Recently, human activity has caused changes in land use, and a large increase in deforested areas (e.g., Myers, 1991;

∗

Corresponding author. Tel.: +81 45 778 5547; fax: +81 45 778 5706. E-mail address: [email protected] (K. Tanaka). 0304-3800/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2006.01.004

Houghton, 1994). The changes that occur following deforestation are mainly the loss of canopy or decline in leaf area from the standpoint of land surface parameters (Sellers et al., 1996). Thus, the ground surface is exposed to stronger solar radi-

e c o l o g i c a l m o d e l l i n g 1 9 6 ( 2 0 0 6 ) 32–44

ation and wind, without the interception of precipitation by a canopy (Chen et al., 1993). Chen et al. (1993) found that the diurnal mean soil temperature of the soil surface layer (0.1 m depth) was lower in a forest than in a clear-cut area over several growing seasons. Hashimoto and Suzuki (2004) found that the annual mean soil temperatures in deeper soil layers (0.5–3 m depths) increased by 1.4–2.2 ◦ C after clear-cutting, compared to temperatures in uncut forest. Soil respiration is likely to be affected by this rise in temperature, in addition to the effects of photosynthetic loss, due to the absence of a plant canopy. Soil moisture will be greatly altered by changes in hydrological processes, such as soil evaporation, transpiration, and canopy interception, and these changes will also affect soil respiration. Thermal and hydrological changes may also occur because of small changes in leaf area. Soil respiration and canopy photosynthesis should be modeled to determine the effects of altered plant canopy characteristics. Most models of soil respiration are based on empirical relationships between soil respiration and environmental variables such as soil temperature and moisture (e.g., Howard and Howard, 1993; Lloyd and Taylor, 1994). These models estimate soil respiration based on variables measured at a particular point (not always in the soil). In contrast, several detailed multilayer soil respiration models have been proposed, and these consider the exchange of CO2 , heat, and water, and ˇ unek ˚ and the production of CO2 in the soil layers (e.g., Sim Suarez, 1993; Jassal et al., 2004). Detailed multilayer models can reflect changes in both soil CO2 gas production and diffusion based on the physical soil temperature and moisture content of each layer during soil respiration. They can also be used to investigate the contribution of each soil layer to CO2 gas production. However, these models have not been used to examine how soil respiration is affected by changes in heat balance and water cycles due to changes in leaf area, because they have not been coupled with plant canopy models of heat and water exchange. Since the simulations with these models have been performed using hydrometeorological variables measured at the top of the soil layer, the hydrometeorological variables included the effects of radiation transfer and atmospheric diffusion within the plant canopy. Thus, to examine the effect of a plant canopy on soil respiration, a multilayer soil respiration model should be coupled with a plant canopy model for heat, water, and CO2 exchange, and the coupled models then used to simulate soil respiration using abovecanopy hydrometeorological variables. Previous models, such as those for determining the relationships among soil respiration, temperature, and moisture, which have been coupled with both plant canopy and soil models for heat and water exchange, have examined these effects. Baldocchi and Meyers (1998) used this method to show a decline in the ratio of soil respiration to photosynthesis with increases in both LAI and the photosynthetic capacity of individual leaves (i.e., the maximum carboxylation rate; Farquhar et al., 1980). Soil respiration was then calculated based on the soil temperature measured at a particular point. This method of using hydrometeorological variables measured at a particular point, however, may lead to errors in the estimation of soil respiration when the contribution of each soil layer to CO2 gas production differs greatly, with drastic variations in the vertical profile of soil temperature and soil moisture under different weather conditions.

33

The goal of this study was to show the effects of the plant canopy on soil thermal and hydrological properties and soil respiration. A soil–plant–air continuum (SPAC) numerical model (Tanaka et al., 2004) was developed to simulate soil respiration. A sub-model of the physical CO2 , heat, and water exchange, and soil CO2 gas production in the soil layers is simiˇ unek ˚ lar to the above-mentioned models (i.e., Sim and Suarez, 1993; Jassal et al., 2004). The physiological effects of photosynthesis on root respiration have been observed in trees (e.g., ¨ Hogberg et al., 2001; Ekblad et al., 2005; Tang et al., 2005). Therefore, changes in canopy characteristics are likely to affect soil respiration through subsequent changes in the intensity of root respiration, as well as changes in hydrometeorological variables, such as soil temperature and soil moisture. Here, we focused on the effects of changes in both temperature and moisture in the soil layers, although the effects of canopy characteristics on soil respiration also include physiological and physical aspects. The LAI and the maximum carboxylation rate (VcMAX ) of individual leaves, which strongly affect canopy transpiration and photosynthesis (Tanaka et al., 2003), were used as the plant canopy characteristics. The effect of the vertical proportion of leaf area density (LAD), which affects the atmospheric diffusion within a canopy, was also investigated. Model validation and simulations were conducted using hydrometeorological variables that included seasonal changes, i.e., a dry season with strong evaporative demand (high solar radiation and high temperature) and a rainy season with weaker evaporative demand, to examine the thermal and hydrological effects of the plant canopy on soil respiration.

2.

Methods

2.1. Multilayer model for heat, water, and CO2 exchange within canopy and soil layers A one-dimensional SPAC model (Tanaka et al., 2004) was used in this study. The model consists of a soil multilayer model (Kondo and Xu, 1997) and a canopy multilayer model (Tanaka et al., 2003). The soil multilayer model considers changes in albedo and evaporation efficiency with changes in soil moisture at the top of the soil column (Kondo and Xu, 1997). The canopy multilayer model (Tanaka et al., 2003) for sensible and latent heat and CO2 gas exchange consists of a second-order closure model for atmospheric diffusion, coupled with a radiation transfer model (Tanaka, 2002), a rainfall interception model (Tanaka, 2002), a Farquhar-type photosynthesis model (Farquhar et al., 1980), and a stomatal conductance model (Ball, 1988). Combined, the two multilayer models by Kondo and Xu (1997) and Tanaka et al. (2003) consider the loss of soil moisture by water uptake (or transpiration) and the effect of soil water content on stomatal closure (Gollan et al., 1985). In the model, the canopy was divided into 50 layers, and each soil layer was 0.1 m thick. To simulate soil respiration and CO2 concentration, the processes of CO2 gas transfer and production in the soil were added to the model. Thus, the model simulates heat, water, and CO2 exchange within both the canopy and soil layers, and can estimate the effect of the canopy on soil respiration. The added soil processes will be explained in

34

e c o l o g i c a l m o d e l l i n g 1 9 6 ( 2 0 0 6 ) 32–44

Section 2.2; the others are described in detail in Kondo and Xu (1997), Tanaka (2002), Tanaka et al. (2002, 2003, 2004).

2.2.

CO2 gas transfer and gas production in the soil

This study assumes that the CO2 fluxes caused by diffusion in the liquid phase and convection in the gas phase, i.e., FdL and FcG , respectively, are negligible, and considers the loss of dissolved CO2 via water uptake by roots. In this case, the onedimensional CO2 transport in unsaturated soil is d[
cL + (
s −
)cG ] ∂ Eu = − [FdG + FcL ] − cL + S, dt ∂z w

(1)

where c is the CO2 concentration in the soil; subscripts L and G the liquid and gas phases, respectively;
s and
the saturated volumetric water content and the volumetric water content, respectively, and the difference (
s −
) corresponds to the volumetric air content; t time; z depth (positive downward); F the CO2 flux in the soil; subscripts d and c the diffusion and convection, respectively; Eu the water uptake; w the liquid water density; S the production rate of CO2 gas by root and microbial respiration, and cL is represented as the sum of the different C-species concentrations [CO2 (L), H2 CO3 , HCO3 − , and CO3 2− ] in soil solution (Jassal et al., 2004), and is calculated after Jassal et al. (2004) as cL = rLG cG .

(2)

Here, rLG =

1 K2 K2 K 3 K2 K3 K4 + + + , 2 K1 K1 K1 [H+ ] K1 [H+ ]

(3)

where rLG is the ratio of cL to cG ; K1 –K4 the equilibrium constants, which depend on temperature (Harned and Davies, 1943); and [H+ ] is the hydrogen ion concentration. Jassal et al. (2004) described the temperature functions and the values of K1 –K4 at 25 ◦ C. FdG is calculated as FdG = −DCG

∂cG . ∂z

(4)

Here,

S = rf (Ts )f (
).

P0 P


T 1.75 s

T0

,

(5)

where DCG is the CO2 diffusivity in soil air; fG the gas phase diffusion impedance factor or tortuosity, which is assumed to be constant (1/1.5) after Jackson et al. (1974); and Dc is the CO2 diffusivity (1.39 × 10−5 m2 s−1 ) in air at a reference air temperature T0 (293.16 K) and its corresponding pressure P0 (101.3 kPa). The soil temperature Ts (K) and air pressure P (kPa) functions in the equation follow Campbell and Norman (1998). FcL is calculated as


d ∂
d
∂z



− 1 cL ,

(7)

Here, f (Ts ) = exp(aTemp (Ts − 40)),

(8)

and f (
) =

DCG = (
s −
)fG Dc

FcL = −K

The water uptake at depth z was assumed to be proportional to the ratio of the extractable to the entire extractable soilwater content (We ; Tanaka et al., 2004). The sum of the water uptakes corresponds to the temporal canopy transpiration. When canopy transpiration can be supplied by the entire extractable soilwater content at 0–1 m depths, where the major plant nutrients C, N, P, and K appear to be concentrated (Jackson et al., 2000), We is calculated between the depths of 0–1 m from which the water uptake is supplied. In the other case, We is calculated as the extractable soilwater content between 1 m and the maximum rooting depth (ZRoot ), and the water uptake is supplied from soil layers at 1 m to the maximum rooting depth. This assumption of water uptake is simple compared to the often-used weighting scheme, which is based on the assumption that the root length density distribution throughout the soil profile is proportional to water extraction throughout the profile (e.g., Dickinson et al., 1993; Desborough, 1997). However, Radersma and Ong (2004) did not find a clear relationship between root length density and water extraction, and several other researchers have questioned the various proposed relationships between root length density and water uptake (e.g., Dardanelli et al., 2004). This suggests that the process of water uptake by roots is not entirely clear. Therefore, we used the simpler assumption and did not consider the root length density distribution. The rate of CO2 gas production by root respiration and microbial respiration (S) depends on both soil temperature (Ts ) and water content (
). When root and microbial respiration differ in relation to Ts and
, S should consist of both components. Here, the two processes are assumed to be the same, and S was not divided into root respiration and microbial respiration. S at z was calculated as



−


(
MAX −
OPT )/(
OPT −
MIN ) MIN MAX −

OPT −
MIN


MAX −
OPT

,

(9)

where r is the CO2 gas-production rate at a soil temperature of 40 ◦ C and an optimum volumetric water content (
OPT ); f(Ts ) and f(
) the functions of Ts and
, respectively, where the values of f(40 ◦ C) and f(
OPT ) are 1; aTemp the temperature coefficient;
MAX the maximum volumetric water content, which is assumed to correspond to the volumetric saturated water content
s , and
MIN is the minimum volumetric water content, which is assumed to correspond to the residual water content
r . The vertical distribution of r is calculated as r = rall gr (z).

(10)

(6)

where K is the hydraulic conductivity, and is the soil water potential. The calculation of K is detailed in Tanaka et al. (2004).

Here, gr (z) =

aDis exp[aDis (zMAX − z)] , [exp(aDis zMAX ) − 1]

(11)

35

e c o l o g i c a l m o d e l l i n g 1 9 6 ( 2 0 0 6 ) 32–44

where rall is the CO  z2 gas-production rate in the entire soil column (i.e., rall = 0 MAX r(z)dz); gr (z) the function of the distriz bution ( 0 MAX gr (z)dz = 1; the unit is m−1 ); aDis the coefficient, and zMAX is the deepest depth at which roots and microbes exist. The r appears to be related to the amount of roots and microbes (i.e., organic matter), and is likely to decrease during decomposition, and increase with root growth and the supply of plant litter; r can also depend on tree photosyn¨ thesis and LAI, because Hogberg et al. (2001) found that the intensity of root respiration was strongly dependent on tree photosynthesis, and Curiel Yuste et al. (2004) found that soil respiration was positively correlated with seasonal changes in LAI. Nonetheless, r was assumed to be constant in this study, regardless of time, tree photosynthesis, and LAI. Thus, we did not consider the root length density distribution, as in the assumption of water uptake. However, the model should consider the root length density distribution when the sensitivity of root respiration to both temperature (Ts ) and water content (
) is noticeably different from that of microbial respiration and when the effect of seasonal changes in tree photosynthesis on root respiration is large compared to the sensitivity to both Ts and
.

2.3. Model parameters and hydrometeorological variables as input data and boundary conditions, and validation data The parameter values were chosen based on an evergreen forest in northern Thailand (18◦ 48 N, 98◦ 54 E; Tanaka et al., 2004) with a canopy height of ∼30 m. LAI ranged from 3.5 to 5.5 (Takizawa et al., 2001). The soil texture was classified as silty sand, verified by Kondo and Xu (1997). A rooting depth of 4–5 m was required to effectively simulate dry season transpiration and annual discharge (Tanaka et al., 2004). The hydrogen ion concentration [H+ ] was set at 3.98 × 10−3 mol m−3 for a pH of 5.4, as reported by Tangtham (1974). All parameter values are detailed in Kondo and Xu (1997), Tanaka et al. (2003), and Tanaka et al. (2004), except those related to CO2 gas transfer and gas production in the soil. Fig. 1 shows the functions of Ts and
[f(Ts ) and f(
), respectively], and the CO2 gas-production rate (r) profile at a soil temperature of 40 ◦ C and optimum volumetric water content. These functions describe CO2 gas production in the soil, and were used in this study. The parameter values for the functions are shown in Table 1. The value of aTemp in f(Ts ) is 0.079, and corresponds to the Q10 value of 2.2 (Hashimoto, 2005) obtained at the site of the experimental system (Hashimoto and Suzuki, 2002). The values of
MAX and
MIN were assumed to correspond to the saturated and residual volumetric water contents,
s = 0.4 and
r = 0.024, respectively (Kondo and Xu, 1997). The value of
OPT was set at 0.38 because soil respiration increased as
increased to an almost saturated level (Hashimoto et al., 2004), and CO2 gas production should cease because of a deficiency of oxygen at
= 0.4 (or
s ); zMAX in the distribution function g(z) was assumed to correspond to a maximum rooting depth of 5 m (Tanaka et al., 2004). The value of aDis was set at 5 m−1 , and r was mostly from soil depths of 0–0.8 m, despite the zMAX at 5 m. The proportionate vertical profile of r was similar to that for organic matter

Fig. 1 – (a) The function of soil temperature Ts [f(Ts )], showing the effect of Ts on the CO2 gas-production rate; (b) the function of soil moisture
[f(
)], showing the effect of
on the CO2 gas-production rate; and (c) the CO2 gas-production rate profile at a soil temperature of 40 ◦ C and an optimum volumetric water content
OPT (r). These three functions were used in the numerical simulations in Figs. 4–8.

measured at the site (Tangtham, 1974). The value of rall was set at 30 ␮mol m−2 s−1 . The maximum rate of carboxylation (VcMAX ), which indicates leaf photosynthetic capacity, decreases with the exponential increase in irradiance (e.g., Hirose and Werger, 1987). In this study, the vertical distribution of VcMAX was given as VcMAX (h) = V¯ cMAX LAI

ce exp(ce iLAI (h)) , exp(ce LAI) − 1

(12)

where V¯ cMAX is the averaged VcMAX ; h the height above the ground surface, ce an extinction coefficient (here, −0.5), and iLAI is the leaf area index integrated from the canopy height hcanopy to h. The integration of VcMAX (h) from the canopy to the forest floor corresponds to V¯ cMAX LAI.

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e c o l o g i c a l m o d e l l i n g 1 9 6 ( 2 0 0 6 ) 32–44

Table 1 – Parameters for CO2 gas production model and characteristics of the canopy used in the simulation Parameter Parameter for CO2 gas-production model CO2 gas-production rate profile at a soil temperature of 40 ◦ C and
OPT CO2 gas-production rate in the entire soil column in the function r Function of the vertical distribution in the function r Relationship between soil temperature (Ts ) and CO2 gas-production rate (S) Relationship between volumetric soil moisture (
) and S Deepest depth in the distribution function gr (z) Coefficient in the distribution function gr (z)

Symbol

Value

r rall

The distribution is similar to that for organic matter measured at the site (Tangtham, 1974; see Fig. 1c) 30 ␮mol m−2 s−1

gr (z) f(Ts )

The value at 40 ◦ C [i.e., f(40 ◦ C)] is 1 (see Fig. 1a)

f(
)

The value of f(
OPT ) is 1; the values of f(
MIN ) and f(
MAX ) are 0 (see Fig. 1b) Assumed to correspond to a maximum rooting depth of 5 m (Tanaka et al., 2004) The value was set so that the distribution of r was similar to that of organic matter measured at the site (Tangtham, 1974; see Fig. 1c) The value was measured at the experimental system site (Hashimoto and Suzuki, 2002; Hashimoto, 2004) and corresponds to a Q10 of 2.2 (Hashimoto, 2005) Assumed to correspond to the volumetric residual water content
r . The value of
r is from Tanaka et al. (2004) Soil respiration increased as
increased to an almost saturated level (Hashimoto et al., 2004) Assumed to correspond to the volumetric saturated water content
s . The value of
s is from Tanaka et al. (2004)

zMAX

5m

aDis

5 m−1

Temperature coefficient in the partial function f(Ts )

aTemp

0.079

Minimum volumetric soil moisture in the partial function f(
)


MIN

0.024

Optimum volumetric soil moisture in the partial function f(
) Maximum volumetric soil moisture in the partial function f(
)


OPT

0.38


MAX

0.4

LAI

0–9

Canopy characteristics Leaf area index

Reference or remarks

Vertical profile of leaf area density (LAD)

a(z)

Average maximum rate of carboxylation at 25 ◦ C Canopy height

V¯ cMAX 25

10–40 ␮mol m−2 s−1

The value for the evergreen forest is 3.5–5.5 (Takizawa et al., 2001) LAD is regarded as a beta distribution. Two distributions of LAD LAI−1 were used (see Fig. 3) Tanaka et al. (2003)

hcanopy

∼30 m

Tanaka et al. (2003)

Hydrometeorological variables, such as downward shortand long-wave radiation, air temperature, water vapor, wind velocity, and precipitation measured over the forest in 2001 and 2002, were used as model input. Seasonal changes in rainfall and air temperature in 2002 indicate three seasons: a rainy season, an early dry season, and a late dry season (Fig. 2; Hashimoto et al., 2004; Tanaka et al., 2003, 2004). High solar radiation and vapor pressure deficit in the late dry season cause the strongest evaporative demand in a year (Fig. 2). Although the early dry season includes both November and December, in 2002, a large amount of rain fell during these months, similar to that of the rainy season. Hashimoto et al. (2004) found that the increase in soil water content increased soil respiration at the site, and the hydrometeorological variables are likely to reproduce the hydrological effect of a plant canopy on soil respiration, as well as the thermal effect (Baldocchi and Meyers, 1998). Volumetric soil moisture at 0.1, 0.2, 0.3, 0.4, and 0.5 m, soil temperature at 0.1 and 0.3 m, soil respiration, and soil CO2 gas concentration at 0.1, 0.2, 0.4, and 0.6 m were used for model validation (Hashimoto, 2004). Details of these measurements were provided by Hashimoto et al. (2004). The time interval was set at 3 min within the soil multilayer model because of the thin soil layer (0.1 m), while it was

set at 15 min within the canopy multilayer model. The soil depth was 1 m deeper than the rooting depth (i.e., 6 m in total). The soil water potential ( ) at 6 m depth was set at −100 m; this condition never produced a groundwater table or surface flow in the numerical experiments, i.e., the condition led to unsaturated soil conditions (Tanaka et al., 2004). Here, the differences in both thermal flux (Ft ) and CO2 flux between the 5.9- and 6-m soil layers, which have neither water uptake Eu nor soil CO2 gas production S (i.e., these values are 0 in Eq. (1)), were assumed to be negligible [i.e., Ft (6 m) − Ft (5.9 m) = 0 and [FdG (6 m) + FcL (6 m)] − [FdG (5.9 m) + FcL (5.9 m)] = 0 (see Eq. (1)), respectively]. Hydrometeorological variables from 2001 were used to describe the vertical profiles of soil moisture, soil temperature, and the soil CO2 concentration at the start of the time series in 2002. Therefore, simulation results for 2002 will be shown. To investigate the effect of LAI and the average VcMAX at 25 ◦ C (V¯ cMAX 25 ), LAI and V¯ cMAX 25 were set at 0–9 and 10–40 ␮mol m−2 s−1 , respectively (Table 1). LAI of 0 corresponds to bare soil. The range of V¯ cMAX 25 was determined based on measurements of the net photosynthetic rate of individual leaves (Tanaka et al., 2003). The two vertical distributions of the proportion of LAD to LAI were assumed as a beta distribution (Fig. 3). The F-type leaf distribution had a maximum

e c o l o g i c a l m o d e l l i n g 1 9 6 ( 2 0 0 6 ) 32–44

Fig. 2 – Seasonal changes in rainfall, air temperature, saturated vapor pressure (eSAT ), water vapor pressure (e), the difference between eSAT and e (vapor pressure deficit), and downward solar radiation (S↓) above the canopy. These hydrometeorological variables were used in the numerical simulations in Figs. 4–8.

leaf area density at a height of 25 m, which is similar to that of a forest (Wilson and Shaw, 1977); the G-type leaf distribution had a maximum leaf area density at a height of 10 m, which is similar to that of other vegetation types, such as grassland, although the maximum canopy height is high in this study. In the model validation, LAI and V¯ cMAX 25 were set at 3.5 and 5.5 (Takizawa et al., 2001), and 10 and 40 ␮mol m−2 s−1 (Tanaka et al., 2003), respectively. F- and G-type leaf distributions were also used, because these distributions have never been investigated. In all, eight simulation combinations were performed for the two values of LAI and V¯ cMAX 25 and two leaf distributions. This range of simulations may indicate both spatial and temporal changes.

Fig. 3 – The vertical profiles of the proportion of leaf area density (LAD) to leaf area index (LAI). The two profiles were used in the numerical simulations (F-type leaf area distribution (forest), Figs. 4–8; G-type leaf area distribution (grassland), Figs. 4–6 and 8).

3.

Results

3.1.

Model validation

37

Fig. 4 shows seasonal changes in measured and simulated volumetric soil moisture at depths of 0.1, 0.2, 0.3, 0.4, and 0.5 m, soil temperature at 0.1 and 0.3 m, soil respiration, and soil CO2 gas concentration at 0.1, 0.2, 0.4, and 0.6 m for the two values of LAI and V¯ cMAX 25 and two leaf distributions. The top and bottom of the shaded area in Fig. 4 indicate the maximum and minimum values, respectively, from the eight simulations. The simulated and measured seasonal changes in the soil moisture profile corresponded well. The differences between the simulated maximum and minimum were largest in the late dry season, whereas they were smallest in the rainy season. Most of the measured soil temperatures occurred between the simulated maximum and minimum, except in the late dry season, when the measured minimum values were approximately 2 ◦ C lower than the simulated minimum values. This may have occurred because in dry conditions, the measured thermal conductivity of dry litter on the soil surface and the porous soil surface layer, which includes sufficient organic matter, was lower than that modeled. The difference between the simulated maximum and minimum values is almost constant year-round, although it is somewhat greater in the late dry season. Simulated and measured (using more than six chambers; Hashimoto et al., 2004) soil respiration were similar; both showed that soil respiration was much lower in dry than in wet conditions. The difference between these simulated maximum and minimum values is largest in the late dry season. The simulated and measured seasonal changes in soil CO2 gas concentration profiles were in apparent agreement; however, the simulated values at 0.2 m were higher than those measured, and the measured values at 0.1 m were similar to simulated values at 0.2 m. This was probably because of the higher measured than simulated CO2 gas diffusivity caused by a shallower porous soil layer between the two depths. Generally, the simulations indicate that the model can simulate the seasonal changes in these variables well.

3.2.

Numerical simulation

Fig. 5 shows how changes in soil temperature and moisture caused by LAI, V¯ cMAX 25 , and the vertical profile of LAD affect annual soil respiration. Simulated annual soil respiration ranged from 1250 to 2100 g C m−2 y−1 for upper and lower values. Annual soil respiration was highest at LAI = 0 (i.e., bare soil). Annual soil respiration decreased with increased LAI, but the rate slowed, and the annual respiration seemed to approach two values (i.e., ∼1250 and 1300 g C m−2 y−1 , respectively), which were distinguished by the two LAD profiles. At a given LAI, the annual soil respiration simulated at a V¯ cMAX 25 of 10 ␮mol m−2 s−1 was larger than at a V¯ cMAX 25 of 40 ␮mol m−2 s−1 , while the annual soil respiration simulated for the G-type LAD distribution was larger than that for the Ftype LAD distribution. There was a large difference in annual soil respiration between the two V¯ cMAX 25 values at a small LAI, but the difference decreased as LAI increased, and the difference was very small at LAIs of 8–9. In contrast, the differences

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e c o l o g i c a l m o d e l l i n g 1 9 6 ( 2 0 0 6 ) 32–44

Fig. 4 – Time series of measured and simulated volumetric soil moisture at depths of 0.1–0.5 m, soil temperature at 0.1 and 0.3 m, soil respiration, and soil CO2 gas concentration at 0.1, 0.2, 0.4, and 0.6 m. All values are daily averages, except for measured soil respiration and measured soil CO2 gas concentration, which are instantaneous values. The top and bottom of the shaded area indicate the maximum and minimum values, respectively, from eight simulations (i.e., combinations of ¯ cMAX 25 = 10 and 40 ␮mol m−2 s−1 , and F- and G-type LAD). LAI = 3.5 and 4.5, V

between the two LAD profiles with V¯ cMAX 25 were almost constant at any LAI. Compared to annual soil respiration, the annual liquid phase CO2 flux, caused by convection at the top and bottom soil layers, and the loss of liquid phase CO2 by water uptake by the roots were very small (all ≤0.01 g C m−2 y−1 in unsaturated conditions and a pH of 5.4). Fig. 6a–c shows seasonal changes in soil respiration simulated at an LAI of 1 and 4, a V¯ cMAX 25 of 10 and 40 ␮mol m−2 s−1 , and with G- and F-type LAD profiles, respectively. In Fig. 6a, V¯ cMAX 25 and the LAD profile were set at 25 ␮mol m−2 s−1 and

Fig. 5 – The relationship between leaf area index (LAI) and annual soil respiration.

F-type, respectively; in Fig. 6b, the LAI and LAD profiles were set at 4 and F-type, respectively; and in Fig. 6c, the LAI and LAD profiles were set at 4 and 25 ␮mol m−2 s−1 , respectively. These simulations were performed to investigate seasonal changes in the effects of soil thermal and hydrological properties caused by each parameter on soil respiration. The combinations of parameter values were chosen to clearly demonstrate the effects of each parameter in comparison to the simulation results in Fig. 5 (e.g., the effects of V¯ cMAX 25 are small when LAI = 8 or 9). These figures show that the simulated soil respiration is generally larger in the rainy season than in the dry season because of well-watered soil conditions, as the measurements of soil respiration also show (Fig. 4). They also show that the smaller values of LAI and V¯ cMAX 25 , and the G-type LAD profile always resulted in greater soil respiration. The difference in soil respiration between the two LAIs in the rainy season was almost identical to that in the late dry season (Figs. 2 and 6a). In contrast, the difference in soil respiration between the two values of V¯ cMAX 25 and between the two LAD profiles was smaller in the rainy season than in the dry season (Fig. 6b and c). In particular, there was little difference between the two values of V¯ cMAX 25 in the rainy season, indicating that changes in soil temperature and/or moisture caused by V¯ cMAX 25 affect soil respiration only in the late dry season, whereas those caused by LAI affect soil respiration year-round. Fig. 6d–f shows the seasonal changes in the ratio of the difference to the sum of the two simulated soil respiration values (Y1 and Y2 , and Y1 > Y2 ), demonstrating the effects of LAI, V¯ cMAX 25 , and the LAD profile on soil respiration (from Fig. 6a–c, respectively). Here, we can more clearly see the effect of LAI, V¯ cMAX 25 , and the LAD profile than in Fig. 6a–c. The higher value of (Y1 − Y2 )/(Y1 + Y2 ) shows a greater effect of LAI, V¯ cMAX 25 , and

e c o l o g i c a l m o d e l l i n g 1 9 6 ( 2 0 0 6 ) 32–44

39

Fig. 6 – Seasonal changes in soil respiration (Y1 and Y2 ) simulated for (a) two values of LAI (1 and 4, respectively) under a ¯ cMAX 25 of 25 ␮mol m−2 s−1 and F-type LAD (see Fig. 3); (b) for two values of V ¯ cMAX 25 (10 and 40 ␮mol m−2 s−1 , respectively) V ¯ cMAX 25 under an LAI of 4 and F-type LAD; and (c) for two types of LAD (G- and F-type, respectively) under an LAI of 4 and a V of 25 ␮mol m−2 s−1 . (d–f) Show the ratio of the difference to the sum of the two simulated soil respiration values (Y1 and Y2 , and Y1 > Y2 ) from (a–c), respectively.

the LAD profile. The peak in the effect of LAI on soil respiration appeared in April during the late dry season (Fig. 6d), when solar radiation was highest (Fig. 2). In contrast, the peaks in the effects of both V¯ cMAX 25 and the LAD profile appeared in March during the late dry season (Fig. 6e and f), when there was little rainfall (Fig. 2). The effect of LAI in the rainy season was about one-third of the peak in the late dry season, whereas the effects of both V¯ cMAX 25 and the LAD profile in the rainy season were much smaller than their respective peaks in the late dry season. Thus, among the three canopy characteristics, LAI had the largest effect on annual soil respiration through changes in soil thermal and hydrological properties (Fig. 5). To interpret how LAI, V¯ cMAX 25 , and the LAD profile affected soil respiration, the following variables are shown in Figs. 7 and 8: the profiles of wind velocity, net radiation, latent and sensible heat fluxes within a canopy, soil temperature, soil moisture, the functions f(Ts ) and f(
), CO2 gas production [S, or rf(Ts ) f(
)], and soil CO2 gas concentration. The values are the monthly averages for March, when effects on soil respiration were large (Fig. 6). Although LAI had the greatest effect in April, the profiles from March, during which there was little rainfall, showed hydrological, as well as thermal, effects on soil respiration more clearly than in April. Fig. 7 shows how LAI affected soil respiration using hydrometeorological variable profiles within the canopy and soil layers. Increased LAI decreased the wind velocity and net radiation within a canopy (Fig. 7a–c). The faster wind velocity and higher net radiation on the forest floor caused by decreased LAI resulted in an increase in latent heat flux on the forest floor (i.e., soil evaporation; Fig. 7d). However, the latent heat flux increased with increases in height, and the latent heat flux over the canopy at a larger LAI was greater than that at a smaller LAI because of greater transpiration (note that little rainfall in March resulted in little canopy inter-

ception; Figs. 2 and 7d). In contrast, sensible heat flux on the forest floor decreased with increasing LAI (Fig. 7e). Sensible heat flux over the canopy was larger at LAI = 2 than at LAI = 1, and the highest transpiration, which occurred at LAI = 4, produced the lowest sensible heat flux over the canopy (Fig. 7e). Increased LAI decreased net radiation and subsequently lowered the soil temperature (Fig. 7f). Soil moisture decreased in the lower portion of the soil (i.e., below 0.1 m) with increased LAI (Fig. 7g) because of the increase in water uptake caused by increased transpiration. Soil moisture at the surface layer decreased with decreased LAI (Fig. 7g) because of increased evaporation from the soil. Lower soil temperatures resulting from increased LAI resulted in a decrease in f(Ts ) (Fig. 7h). The profiles of f(
) resembled those of soil moisture (Fig. 7i). CO2 gas production in the soil surface layer was somewhat lower at an LAI of 2 compared to an LAI of 4 (Fig. 7j) because of the larger effect attributable to the lower value of f(
) compared to the effect of the higher value of f(Ts ). However, CO2 gas production increased in the lower layers of the soil (i.e., below 0.1 m depth) with decreased LAI (Fig. 7j) because of the increased values of both f(Ts ) and f(
) (Fig. 7h and i). In this case, CO2 gas production in the lower soil layers greatly affected total soil respiration. Therefore, soil respiration increased with decreased LAI (Fig. 5). The profile of soil CO2 gas concentration became dense with decreased LAI (Fig. 7k) as the profile of soil CO2 gas production increased with decreased LAI (Fig. 7j). Fig. 8 shows how V¯ cMAX 25 and the profiles of LAD affected soil respiration, as in Fig. 7. First, we discuss how differences in V¯ cMAX 25 affected the soil respiration for the G-type canopy (Fig. 8a). Differences in V¯ cMAX 25 had little effect on the net radiation at the forest floor (Fig. 8c) because of the similar interception of radiation by the same LAI. The higher value of V¯ cMAX 25 (40 ␮mol m−2 s−1 ) resulted in larger latent fluxes over the canopy than did the lower value (10 ␮mol m−2 s−1 ) because of greater transpiration by the leaf layers; there was no dif-

40

e c o l o g i c a l m o d e l l i n g 1 9 6 ( 2 0 0 6 ) 32–44

Fig. 7 – The effect of LAI on the vertical profiles of the simulated variables. Profiles of (a) leaf area density (LAD); (b) wind velocity (u); (c) net radiation (NR); (d) latent heat flux (LHF); (e) sensible heat flux (SHF); (f) soil temperature (Ts ); (g) soil moisture (
); (h) the function of Ts [f(Ts )]; (i) the function of
[f(
)]; (j) CO2 gas production [rf(Ts )f(
)]; (k) soil CO2 gas concentration (cG ). The values are the monthly averages for March, which is the late dry season (see Figs. 2 and 6), for an LAI ¯ cMAX 25 of 25 ␮mol m−2 s−1 and F-type LAD (see Fig. 3). of 1 (gray line), 2 (dotted line), and 4 (solid line) with a V

¯ cMAX 25 on the vertical profiles of the simulated variables. The format is the same as in Fig. 7. Fig. 8 – The effect of LAD and V ¯ cMAX 25 of 10 ␮mol m−2 s−1 and a G-type The values are the monthly averages for March, which is the late dry season, for a V −2 −1 ¯ cMAX 25 of 40 ␮mol m−2 s−1 and an ¯ LAD (gray line); a VcMAX 25 of 40 ␮mol m s and a G-type LAD (dotted line); and a V F-type LAD (line), respectively, with LAI = 4.

e c o l o g i c a l m o d e l l i n g 1 9 6 ( 2 0 0 6 ) 32–44

ference in soil evaporation (Fig. 8d). Therefore, the sensible heat flux was smaller within and above the canopy at a larger opposed to a lower V¯ cMAX 25 (Fig. 8e). The absorption of sensible heat into leaves within the canopy above ∼20 m was also shown in the G-type canopy with the higher V¯ cMAX 25 because of the large cooling effect caused by the latent heat exchange. Differences in V¯ cMAX 25 had only a small effect on soil temperature (Fig. 8f) because of a similar energy budget on the forest floor (Fig. 8c–e). Soil moisture was greater throughout the soil layers at the smaller than at the higher V¯ cMAX 25 (Fig. 8g) because of a decline in water uptake from the soil layers caused by lower transpiration. The profiles of soil temperature and moisture affected the profiles of f(Ts ) and f(
), respectively (Fig. 8h and i). The profile of f(Ts ) at the lower V¯ cMAX 25 was almost the same as that at the higher V¯ cMAX 25 because of the small difference in the soil temperatures (Fig. 8h), whereas the higher soil moisture at the lower V¯ cMAX 25 increased the values of f(
) (Fig. 8i). The larger f(
) at the lower V¯ cMAX 25 increased CO2 gas production throughout the soil layers. Thus, the lower V¯ cMAX 25 caused higher soil respiration. The profiles of soil CO2 gas concentration were similar to those of CO2 gas production, and were greater at the smaller than at the higher V¯ cMAX 25 . Next, we discuss how the LAD profile (i.e., F- and G-type; Fig. 8a) affected soil respiration. The difference in the LAD profile resulted in a difference in the wind velocity profile (Fig. 8b). The F-type canopy had a slight increase in wind velocity in the lower portions with few leaves (Wilson and Shaw, 1977), while wind velocity decreased with decreased height in the G-type canopy. Thus, the F-type canopy created a faster wind velocity on the forest floor. The net radiation on the forest floor of the F-type canopy was a little larger than that of the G-type canopy (Fig. 8c). The faster wind velocity on the floor of the F-type canopy increased soil evaporation compared to that in the G-type canopy (Fig. 8d). However, changes in the LAD profile at a constant V¯ cMAX 25 (40 ␮mol m−2 s−1 ) had little effect on canopy transpiration; thus, the difference in the latent heat flux over the canopy for the F- and G-type canopies was caused by differences in soil evaporation. At a constant V¯ cMAX 25 (40 ␮mol m−2 s−1 ), greater absorption of sensible heat into leaves higher than ∼27 m was shown in the F-type than in the G-type canopy (Fig. 8e). The soil temperature was lower by 1 ◦ C in the F-type than the G-type canopy (Fig. 8f). This is because the larger soil evaporation in the F-type canopy lowered both the surface soil temperature and the downward soil heat flux more than in the G-type canopy (Fig. 8e). The decreased soil surface temperature slightly increased the net radiation on the forest floor through a decrease in upward long-wave radiation (Fig. 8c). The soil moisture was lower in the F-type than in the G-type canopy (at V¯ cMAX 25 = 40 ␮mol m−2 s−1 ), particularly at the top soil layer, because of greater soil evaporation caused by faster wind velocity. In the F-type canopy, the lower soil temperature and moisture decreased the f(Ts ) and f(
), respectively (Fig. 8h and i), and in particular, f(
) at the soil surface. This resulted in decreased CO2 gas production throughout the soil layers in the F-type canopy, and particularly at the top layer (Fig. 8j). Thus, even with the same LAI, different LAD profiles affected soil respiration by causing differences in wind velocity on the forest floor (Fig. 5). The soil CO2 gas concentration profiles also

41

reflected the CO2 gas production, and were smaller in an Ftype than in a G-type canopy with the same V¯ cMAX 25 .

4.

Discussion

In this study, a multilayer model for soil respiration (Jassal et al., 2004) was coupled with both a plant canopy multilayer model for heat, water, and CO2 gas exchange (Tanaka et al., 2003), and a soil multilayer model for heat and water exchange (Kondo and Xu, 1997). Soil respiration was simulated using hydrometeorological variables measured above the canopy to examine how changes in temperature and moisture in the soil layers, caused by changes in the plant canopy, affect soil respiration. We did not consider physiological effects of canopy characteristics, such as the effects of photosynthesis (or LAI) ¨ on root respiration (Hogberg et al., 2001), and the temporal dependence of the parameter r. The numerical simulations suggest that the model can capture the seasonal changes in profiles of soil moisture, soil temperature, and soil CO2 gas concentration, and soil respiration well (Fig. 4), and that plant canopy characteristics, such as LAI, V¯ cMAX , and the LAD distribution, can affect soil respiration through changes in soil thermal and hydrological properties (Fig. 5). The mechanisms could be interpreted by examining the profiles of the hydrometeorological variables within the canopy and soil layers (Figs. 7 and 8). A decrease in LAI increased net radiation on the forest floor and decreased canopy transpiration. The larger net radiation and lower transpiration increased soil temperature and soil moisture, respectively; increases in both soil temperature and moisture resulted in an increase in soil respiration, although the drastic decline in soil surface moisture caused by greater soil evaporation because of a smaller LAI decreased soil CO2 gas production. An increased V¯ cMAX resulted in increased canopy transpiration, and the subsequent decline in soil moisture caused decreased soil respiration (Fig. 8). Both hydrological and thermal effects were found in this study, although Baldocchi and Meyers (1998) previously showed a thermal effect on soil respiration. The canopy with denser leaf area in the upper layers, similar to the structure of a forest (Wilson and Shaw, 1977), caused a faster wind velocity on the forest floor; this faster wind velocity subsequently decreased both soil moisture, particularly in the surface soil layer, and soil temperature through greater soil evaporation, and these declines reduced soil respiration (Fig. 8). These phenomena reflect features of vegetation that had a forest-type vertical LAD profile. Tanaka et al. (2003) showed that the effect of canopy characteristics such as LAI, V¯ cMAX , and the LAD profile on simulated transpiration appeared to be greatest in the late dry season because of the high evaporative demand caused by high solar radiation and vapor pressure deficit (Fig. 2). In contrast, the effects were small during the rainy season because of the lower evaporative demand. The difference in the simulated soil respiration was also most apparent in the late dry season during March or April (Figs. 4 and 6). The soil moisture profiles showed little change during the rainy season among the different levels of LAI, V¯ cMAX , and LAD profiles (Fig. 4). This is because high levels of rainfall strongly affected the profiles, more so than the small effect of canopy characteristics

42

e c o l o g i c a l m o d e l l i n g 1 9 6 ( 2 0 0 6 ) 32–44

on transpiration during the rainy season, in particular during June–September. Thus, the changes in soil moisture profiles caused by changes in canopy characteristics were negligible during the rainy season, with some sensitivity to transpiration. The simulation test for V¯ cMAX indicated a hydrological effect on soil respiration in the late dry season; thus, there was little effect of V¯ cMAX in the rainy season (Fig. 6b and e) because of the small thermal effect. The thermal effect of LAI on respiration appeared year-round, even in the rainy season, because of soil temperature changes caused by changes in net radiation on the forest floor (Fig. 6a and d). Fig. 7j shows that CO2 gas production in the late dry season was similar at depths of 0–0.1 m for LAIs of 1 and 2. This was because of the drastic decrease in soil moisture at the surface layer owing to higher soil evaporation, regardless of higher soil temperatures. Moreover, few differences in CO2 gas production were apparent at the surface layer for an LAI of 2–4. In contrast, there was little difference in the average monthly soil moisture profile among the different LAIs during the rainy season, as mentioned previously. The CO2 gas production in the soil was much larger at the soil surface layer than in any other layers during the rainy season, regardless of increased soil evaporation with decreased LAI. These results indicate that the proportional contribution of each soil layer to CO2 gas production likely changes drastically, in particular at the soil surface, between the rainy and the late dry seasons. Based on the shallower soil surface conditions, a small LAI of 1–2 is likely to lead to the underestimation of soil respiration because of the drastic reduction in soil moisture caused by the high level of soil evaporation. The model used in this study did not include effects of tree ¨ photosynthesis on root respiration (Hogberg et al., 2001). An increase in photosynthesis caused by higher LAI and VcMAX can supply more production for root growth and maintenance. In contrast, we found that a simultaneous decline in soil moisture and temperature may decrease root respiration. A decline in LAI and VcMAX can decrease soil respiration through the subsequent decline in root respiration, whereas a simultaneous increase in soil moisture and temperature may also increase root respiration. Thus, the effects on root respiration of changes in soil thermal and hydrological conditions and photosynthesis caused by changes in plant canopy characteristics may cancel each other. Annual soil respiration from bare soil may be lower than that simulated (Fig. 5) because of a lack of root respiration. Because the evergreen forest that was simulated appears to show small seasonal changes in tree photosynthesis compared to deciduous forests, the effects of seasonal changes in tree photosynthesis on root respiration may have been less clear in terms of soil respiration than in deciduous forests. Thus, the model should incorporate the effects of tree photosynthesis on root respiration, as stated by ¨ Hogberg et al. (2001). Nonetheless, the detailed estimation of the effects of changes in soil thermal and hydrological properties caused by changes in a plant canopy using the current model should be useful in detecting physiological effects, such as effects of tree photosynthesis, from combinations of different effects. Although we did not consider temporal changes in parameter r, i.e., loss during decomposition and gain of plant litter, changes in soil thermal and hydrological properties caused

by changes in both plant canopy characteristics and hydrometeorological variables above the canopy are likely to affect soil organic matter decomposition in an SPAC system. In contrast, changes in soil organic matter decomposition may also affect the canopy. Both LAI and V¯ cMAX (Farquhar et al., 1980) are related to nitrogen content. Soil organic matter decomposition produces dissolved nitrogen that can be absorbed by trees, and nitrogen plays an important role in the formation of leaves (LAI) and in V¯ cMAX , affecting canopy transpiration, interception, and photosynthesis. Therefore, neglecting nitrogen input from outside the system, both increased LAI and V¯ cMAX will decrease soil organic matter decomposition, and the small amount of regenerated dissolved nitrogen may subsequently reduce LAI and V¯ cMAX . Oren et al. (2001) showed that the increment in CO2 -induced biomass carbon without added nutrients was undetectable at a nutritionally poor site, and that at a nutritionally moderate site was transient, stabilizing at a marginal gain after 3 years. This implies that the supply of dissolved nitrogen from decomposition may control the biomass carbon increment, although elevated atmospheric CO2 is likely to increase canopy net photosynthesis. Even if the biomass carbon increment, such as an increase in LAI, temporally appeared in elevated atmospheric CO2 , the increment is likely to decrease net radiation to the forest floor, and increase canopy transpiration. Lower net radiation could decrease soil temperatures, and an increase in canopy transpiration could decrease soil moisture, as this study showed. The decline in both soil temperature and moisture could lead to a decrease in soil respiration, and the decrease in the supply of dissolved nitrogen during decomposition may result in a decrease in both LAI and V¯ cMAX , resulting in a decline in net canopy photosynthesis. To interpret the phenomena shown by Oren et al. (2001) and predict CO2 sequestration by vegetation under climate changes such as global warming, processes such as nitrification (the production of dissolved nitrogen during decomposition of organic matter in the soil), the uptake of dissolved nitrogen by the roots, and the consequent changes in LAI and V¯ cMAX (or growth), as well as the carbon balance (e.g., changes in above- and belowground biomass, and the distribution of r by the supply of litterfall, root growth, and decomposition) should be added to the physical-based model for the hydrological cycle and energy balance used here. Although biochemical reactions related to different C species concentrations in soil solution had little effect on soil respiration in this study, biochemical reactions related to different N species concentrations (NH4 + , NO3 − , and N2 O− ) in the soil solution (Zhang et al., 2002) may play an important role in estimating plant growth, such as the increase in LAI and V¯ cMAX . In addition to the hydrogen ion concentration, soil conditions such as soil moisture and temperature profiles, soil CO2 gas production by decomposition, and soil CO2 concentrations, will affect the biochemical reactions.

Acknowledgments We thank Prof. Masakazu Suzuki of the University of Tokyo, Dr. Hideki Takizawa of Nihon University, Dr. Tomonori Kume of the University of Tokyo, and Mr. Chatchai Tantasirin of Kaset-

ecological modelling

sart University for helpful suggestions. We are also grateful to Prof. Hiroshi Takeda of Kyoto University, who provided K. Tanaka the impetus for conducting this study.

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