A one-dimensional, multilayer model that infers the fluxes of heat, water vapor, and CO2 in a biosphere-atmosphere system, as well as their sources and sinks, was described and evaluated in a secondary broad-leaved forest. Coupling of a third-order closure model allows the model to infer profiles of scalar fluxes, sinks, and sources with the computed velocity statistics. Furthermore, the model combines a leaf water process model and makes it possible to capture the impacts of rainfall events on the fluxes, sinks, and sources. The model test was conducted for the two periods (rain and nonrain events) to investigate whether the proposed model can reproduce the profiles of scalar fluxes, sinks, and sources in different weather conditions in the experimental forest. Modeled scalar and heat fluxes for the nonrainfall period showed generally good agreement with measurements. Model calculation showed that CO2 sink of the canopy during rainfall decreased, since the deep canopy layers work as a source due to least radiation transferred to the deep layers. After rainfall, evaporation from wetted leaves caused low vapor pressure deficit (VPD) between the leaf and air, creating favorable conditions for stomatal conductance and intercellular CO2 concentration, which consequently increases carboxylation rates in the photorespiratory carbon oxidation cycle. These results suggest that photosynthesis rates during and after rainfall events are primarily influenced by radiation as well as a variety of environmental factors, particularly VPD. The model results also indicated that the maximum source/sink strengths of heat and H2O were distributed within the top 30% of the canopy and that the CO2 distribution had the feature of the vegetation shape. These differences imply that the roughness heights of individual components are different, causing different effective exchange heights.
 Concern about increasing atmospheric CO2 concentration and the probable resulting changes in global climate makes the investigation of the responses of terrestrial ecosystems to the environmental changes essential. A number of studies have been conducted at various terrestrial ecosystems across the globe [Baldocchi et al., 2001]. The observations highlighted the extrapolation of how vegetated surfaces interact with their local microclimate, which in turn influences the exchange of CO2, water vapor, and heat with the atmosphere. They provided a large body of data sets on the response of vegetation to the environment and produced many multilevel scalar transport models to represent the complex interactions between the canopy microclimate and the atmosphere [Meyers and Paw U, 1987; Baldocchi and Harley, 1995; Su et al., 1996; Williams et al., 1996; Lai et al., 2000; Pyles et al., 2000; Tanaka, 2002].
 One of the major characteristics of the multilayer model is that it explicitly considers the nonuniform vertical structure of the canopy, thereby resolving the subsequent feedbacks of such nonuniformity on the microclimate via formulation of the complex turbulent transfer processes. These feedbacks had been represented successfully by combining physiological and biochemical functions derived from leaf-level measurements, radiation transfer, and canopy microclimate to estimate scalar fluxes above the canopy [Baldocchi, 1992; Baldocchi et al., 1997; Baldocchi and Meyers, 1998]. Scalar turbulent fluxes related closely to mean scalar concentration gradient within the canopy are influenced by foliage distribution [Meyers and Paw U, 1987]. Great research efforts have been spent on using canopy flow model to determine the relationship between foliage distribution and turbulent fluxes within the canopy. The K theory is the most widely used formulation for turbulent flow. Although limitations of K theory are now well recognized inside plant canopies [Raupach, 1988] and have been documented by many experiments [Denmead and Bradley, 1985] and laboratory studies [Coppin et al., 1986], they are still widely used to determine turbulent fluxes within and above the canopy.
 To circumvent the limitations of K theory, the higher-order closure model has been proposed and successfully tested for short vegetations and forest stands [Wilson and Shaw, 1977; Meyers and Paw U, 1986; Wilson, 1988; Meyers and Baldocchi, 1991; Katul and Albertson, 1988]. Recently, some multilayer models have used higher-order closure model, to compute the effects of foliage distribution on scalar and heat fluxes in the canopy [Lai et al., 2000; Pyles et al., 2000; Tanaka, 2002]. They have also led to widespread agreement that the specification of turbulent processes within the canopy will better the representation of the atmosphere-vegetation exchanges of CO2, water vapor and heat. In this study, we propose a multilayer model to estimate scalar and heat transports in forest canopies by coupling a third-order closure approach to formulation for the physiological and biochemical processes in plant canopies.
 Over the past decade, many multilayer models that were developed to estimate scalar source-sink distributions and vertical fluxes within and above forest canopies showed qualitatively good reproduction [Katul and Albertson, 1999; Lai et al., 2000; Siqueira et al., 2000; Siqueira and Katul, 2002]. However, some of the multilayer models are restricted in their application to estimate scalar and heat source-sink related to specific weather conditions such as rainfall events, because they do not consider the impact of rainfall events on scalar behaviors. Tanaka  proposed a multilayer model to examine the impact of a rainfall event on CO2 flux over a plant canopy and found that wet leaves caused more net CO2 absorption by the canopy during and after a rainfall event. However, we do not have enough knowledge for scalar and heat source-sink distributions during and after rainfall events. One of the major reasons could be related to the difficulty of measuring scalar concentration profile during rainfall. Therefore numerical simulations for rainfall events should be a good method to fill the identified knowledge gap.
 The key objectives of this paper are twofold: (1) to describe a multilayer, biosphere-atmosphere exchange model that combines physiological, biochemical and micrometeorological models; and (2) to simulate scalar and heat source-sink profiles and fluxes within and above a deciduous forest canopy during sunshine and rainfall conditions.
2. Model Characteristics
 A one-dimensional, multilayer biosphere-atmosphere exchange model has been developed to compute water vapor, heat, and CO2 fluxes. The model consists of both micrometeorological and eco-physiological modules. The micrometeorological modules compute leaf and soil energy exchange, turbulent diffusion and radiative transfer throughout the canopy, rainfall interception and water budget of leaves, and soil thermal and hydrological processes. These modules incorporate a third-order closure treatment of turbulent transfer within and above the canopy. The environmental variables computed by micrometeorological modules drive the eco-physiological modules that compute leaf photosynthesis, stomatal conductance, transpiration, and leaf, soil, stem, and bole respiration. The structural system of the model is discussed below.
2.1. Micrometeorology and Turbulent Closure
 A canopy turbulence model that uses higher-order closure principles [Meyers and Paw U, 1986, 1987] calculates velocity statistics and scalar fluxes within and above the canopy. The model consists of equations for the mean quantities of velocity and scalar variables and their turbulent fluxes, as well as equations for the third-order transport terms that appear in the second-order equations. To compute the mean scalar profiles, the velocity statistics have to be estimated a priori. The estimated velocity statistics are then used to estimate mean scalar profiles. Applying time and horizontal averaging, the steady state, planar homogeneous scalar flow equation is
where x represents scalar variables (i.e., air temperature, specific humidity, and CO2 concentration), is the scalar vertical flux, t is time, z is vertical coordinate, Sx is sources/sinks of scalar variables, the overbar and bracket denote time and horizontal averaging, respectively, and prime denotes fluctuation from time average.
 The time and horizontally averaged budget equation for the scalar vertical flux can be written as
where the first term (PT) on the right-hand side of (2) represents the production of turbulent flux in terms of interactions between turbulence and mean profile, TF is the turbulent flux transport term whose budget equation is simplified by neglecting shear production, adopting the quasi-Gaussian hypothesis for the quadruple velocity (moment) correlation and replacing the terms involving pressure with a simple return-towards-isotropy term, DC is the fluctuating pressure-velocity interaction term that acts to destroy the correlation as rapidly as it is produced by PT, and the last term BC is buoyant contribution that acts as source/sink for unstable/stable condition. In equation (2), pressure, scalar drag, and waving source production are neglected. For example, CO2 turbulent flux can be rewritten as
where is the vertical velocity variance, p is the static pressure, β is the thermal expansion coefficient, g is the gravitational constant, θv indicates the virtual potential temperature used in the buoyancy term to include the effect of humidity on the air density, and is the vertical turbulent transport of CO2.
 The turbulent closure equations include several terms requiring parameterization. Such parameterizations are necessary for canopy drag, pressure correlations, and viscous dissipation, which are impossible to estimate directly from first principles within the canopy microenvironment. For such parameterizations, many algorithms were developed and used. Further details of the higher-order closure model can be found in Meyers and Paw U [1986, 1987].
2.2. Radiative Transfer
 Forest canopies are very complicated in their structure. The canopy structure causes a distinct light environment on leaves, which nonlinearly contributes to biophysical processes. Thus light transfer through the canopy must be simulated to evaluate photosynthesis, stomatal conductance, and leaf and soil surface energy balance. We used a multilayer radiative transfer model derived by Norman . Leaves usually have different spectral properties for individual spectral bands. Therefore the extraterrestrial radiation was decomposed into solar radiation and thermal radiation (IR). Subsequently, the solar radiation was divided into direct beam and diffuse radiation because their penetration processes through canopy are quite different. The proportions of beam components transmitted through the canopy are computed separately for sunlit and shaded leaves to estimate photosynthetically active radiation (PAR) and near-infrared radiation (NIR) absorbed by the leaves. In this study, we modeled a sparse forest canopy. Therefore a spherical leaf inclination distribution adopted ten classes of leaf angle with equal intervals between 0 and π/2.
 The radiative transfer model assumes that foliage is randomly distributed and the Sun is a point source. The transfer of direct radiation through a canopy (Qb↓) is written as
where IB is the probability of direct beam penetration within a layer which is calculated using a Poisson distribution. However, since the forest canopies are often clumped, the Poisson probability density function is inadequate for computing probabilities of beam transmission through the canopy. Instead, the Markov model is used as an alternative solution for the problem [Myneni et al., 1989; Baldocchi and Meyers, 1998], where IB is
where Ω is a clumping factor ranging between zero and unity, L is leaf area index, H is the solar elevation angle, and F represents the ratio of the area of leaves “in situ,” projected into a plane normal to H and to L within that layer. F is the sum of the G functions for each individual leaf within a layer.
 The probability of sunflecks is equal to the derivative of IB with respect to L times the average cosine of the leaf-Sun angle [Gutschick, 1991]:
The integration of equation (6) with respect to leaf area yields the sunlit leaf area.
 Assuming diffuse and direct beam radiation are uniformly distributed over every angle of the sky hemisphere, the probability of diffuse radiation penetration is computed by integrating equation (5) over the solid angels of the sky hemisphere. The fluxes of diffuse and thermal radiation are computed by the slab approach of Norman .
2.3. Energy and Water Balance on Leaves and Soil Surface
 The energy budget of the leaf surface of each layer within the canopy is used to compute the absorbed radiation and the mean leaf surface temperature needed for estimating stomatal conductance:
where Ra is the absorbed radiation, ρa is air density, Cp is specific heat of air at constant pressure, Ta is air temperature, λ is latent heat of vaporization, rb is leaf boundary layer resistance, rs is leaf stomatal resistance to water vapor, qa is the specific humidity in the air, and qs(Tl) is the saturated specific humidity at leaf temperature. A quadratic equation of the difference between leaf and air temperature is derived from the leaf energy balance to obtain an analytical solution for Tl [Paw U, 1987]. The estimated Tl is used to determine enzymatic rates associated with carboxylation, electron transport, and respiration, and to evaluate latent and sensible heat fluxes and infrared emission.
 This model took into account the evaporation from leaves wetted by rainfall and condensation. Evaporation from the wetted surface was computed by the model proposed by Tanaka , which included the water budget (W) of the two sides of leaves:
where WU and WL are the water storage on the upper and lower of leaves per leaf area, respectively. Both rainfall and condensation supply water to dry areas of the upper leaf surfaces, while condensation alone supplies water to dry areas of the lower leaf surfaces. In contrast, the wetted leaf area is dried by evaporation (Ep). When water added to the wetted area exceeds the maximum water storage capacity (WMAX), it flows down to the lower layer as drainage, and may become a source of soil water. When Ep > 0, the basic equations for predicting the vertical profiles of water storage on leaf surfaces and rainfall including drainage from leaves (P) are
where Fl denotes the ratio of the area of leaves “in situ,” projected into a plane normal to the rainfall incident. For the case of Ep < 0, the corresponding equations are given as
 The dried leaf area index (Ldry) is given by
where Lwet is the wet leaf area index. The evaporation or condensation rate per unit area on one side can be determined from
 Energy balance at the soil surface is expressed by
where Qs is the absorbed energy (incoming shortwave radiation minus reflected shortwave radiation), ɛs is thermal emissivity of the surface, G is ground heat flux, Ts is surface temperature, and Ch is a bulk transfer coefficient between the ground surface and the second grid point. The soil energy budget is fueled by the effective radiation apportioned to soil surface, which depends on leaf and soil optical properties and leaf area index. Surface temperature is computed by the quartic energy balance formulation [Paw U, 1987], using estimated near-ground values of mean wind, temperature, humidity, and radiation. The estimated surface temperature and soil evaporation is used as boundary conditions for calculations of soil processes.
2.4. Physiological Response
 The exchange rates of scalar sources between leaves and the ambient atmosphere are correlated with plant physiological controls. The source terms can be expressed using a Fickian formulation of diffusion through the stomatal cavity and the leaf boundary layer:
where Cd is drag coefficient, aL is the leaf area density, and An is the net CO2 uptake rate at the leaf surface. Subscripts m, θ, q, and c on the left-hand side of equations (18) to (21) refer to momentum, temperature, specific humidity, and CO2 concentration, respectively.
 During rainfall events when the difference between qs(Ts) and qa is positive, evaporation from wet leaves and transpiration from the dry area of lower leaf surface occur simultaneously. The exchange rate of H2O source in such case is given by
On the other hand, when condensation occurs on both sides of leaves, the H2O exchange rate is expressed by
 When rainfall and condensation occur, the exchange rate of CO2 is given by
 The estimation of the canopy boundary layer conductance (gb = 1/rb) is based on the mean wind speed profile within the canopy, which is modeled by higher-order closure principles [Baldocchi and Meyers, 1998], and is given by
where Nu is the Nusselt number, νθ is the thermal molecular diffusivity of air, and ld is the characteristic leaf length scale. The value of gb is assumed to be the same for heat, moisture and CO2, because transfer processes within a plant canopy is dominated by turbulent airflow.
 The stomatal conductance (gs = 1/rs) is closely correlated to An, relative humidity (rh), and CO2 concentration at the leaf surface (Cs). Collatz et al.  developed a physiological model to relate gs to leaf photosynthesis, given by
where the coefficient m is a dimensionless slope and g0 is the zero intercept. It should be noted that many studies have addressed criticisms of equation (26), including breakdown at very low light, humidity, and CO2 levels. Furthermore, some studies proved that gs was more dependent on water vapor saturation deficit [Aphalo and Jarvis, 1991] and transpiration [Mott and Parkhurst, 1991; Monteith, 1995] than relative humidity. However, this scheme uses few tuning parameters and simultaneously provides us with an algorithm that allows us to evaluate how stomatal conductance correlates with ecophysiological and biogeochemical factors, such as leaf photosynthesis, nutrition, and ambient CO2 concentration. Stomatal conductance is estimated for each canopy layer, using leaf temperature, radiation, humidity, wind speed, and CO2 concentration within each canopy layer. In order to account for stomatal response to environmental conditions, the stomatal conductance model is combined with the Farquhar and von Caemmerer  photosynthesis equations.
 Net photosynthesis rate, which is a function of the carboxylation (Vc), oxygenation (Vo), and dark respiration (Rd), is given by
where Γ is the CO2 compensation point in the absence of dark respiration and Ci is the intercellular CO2 concentration. The term min[JR, JE] is assessed by the minimum between JR, the rate of carboxylation when ribulose bisphosphate (RuBP) is saturated, and JE, the carboxylation rate when RuBP regeneration is limited by electron transport.
 If JR is minimal, then
where Vcmax is the maximum carboxylation rate when RuBP is saturated, Oi is the intercellular O2 concentration, and KC and KO are the Michaelis constants for CO2 and O2, respectively. JE, which describes the dependence of leaf photosynthesis on PAR, is given by
 Soil constitutes the lowest boundary of a canopy-scale, water vapor, heat, and CO2 exchange model. Heat and water transport through the soil profile is estimated by solving the second-order, time-dependent differential equations, adapted to a soil structure with layered hydraulic and thermal properties. Profile of soil temperature, T, with depth z and the conduction flux of heat through the soil profile can be obtained by
where cs is the volumetric soil heat capacity, λs is the soil thermal conductivity, and QH is the heat source term at the soil surface.
 The time rate of change in soil water content, Θ, with depth is given by Richard's equation:
where K is the soil hydraulic conductivity, ψ is the soil water potential, Kg is the drainage due to gravitational forces, and U is the volumetric water sink. At the soil surface, U accounts for the difference between soil evaporation and infiltration rates. Below the surface, it represents the water extracted from a given soil layer by plant roots [Campbell, 1985]. Drying of soil by root uptake was assumed to take place until 1.0 m below the soil surface. The lower boundary conditions for heat and water were set to constant values.
3. Numerical Simulation
 Numerical simulations were carried out to determine the source-sink distributions of water vapor, heat, and CO2 during and after rainfall events, using meteorological data measured at the experimental forest. During rainfall, the evaporation from intercepted water is driven by radiation or extra energy (i.e., downward sensible heat). Immediately after the rainfall, high radiation leads to rapid evaporation of intercepted water and increases stomatal conductance and photosynthetic capacity. Even during rainfall, transpiration and photosynthesis can occur, dependent on dry area of lower leaf surface. Therefore it can be surmised that the behavior of CO2 and heat during and after rainfall events are related to meteorological conditions. Of course, canopy structure should also influence these behaviors. To investigate scalar and heat source/sink distributions during rainfall, model simulation was carried out for 6 days that it was rain over 1 mm every day (period 2). Because the eddy correlation system is difficult to operate and obtain accurate flux data during rainfall events, comparison of model performance for scalar and heat source/sink distributions during rainfall events is impossible against measurements. Thus model simulation was additionally conducted for 6 sunshine days (period 1), and then the soundness of the simulation was checked based on the comparison with measurements for period 1. The two periods range within June 2003.
4. Model Parameterization and Computation
 In order to simulate heat, water vapor and CO2 exchange rates in the biosphere-atmosphere system, the multilayer model requires site-specific parameters for a range of meteorological, physiological, and hydrological conditions. The model inputs are half hour mean solar radiation, PAR, air temperature, humidity, wind speed, rainfall, and CO2 concentration above the canopy. CO2 concentration was set to 400 ppm. Vertical L profile, canopy height, Vcmax, and minimum stomatal conductance are the key input parameters for the plant canopy; and leaf reflectance and transmittance values were also required to compute radiative transfer within the canopy. Initial profile of soil temperature was interpolated using grid exponential weighting function between air temperature and the lowest soil temperature, and initial soil water profile was set to be constant to all layers. Table 1 lists parameter values used for the model calculation.
 The reference value of Vcmax at an optimal temperature (311K) is equal to 35 μmol m−2 s−1, which is similar to values reviewed by Wullschleger . Vcmax was assumed to be vertically different throughout the canopy depth because of its dependency on vertical variations in specific leaf weight and nitrogen concentration. For the purpose of these computations, it was assumed that Vcmax is linearly decreased with canopy depth. Other biochemical rate constants, such as Jmax and Rd, were scaled to Vcmax [Wullschleger, 1993; Leuning, 1997]. For leaf temperatures of 25°C, for example, Jmax equals 2.14 times Vcmax [Leuning, 1997]. Kinetic coefficients (Kc, Ko, and Γ) for biochemical reactions were also adjusted using the algorithm of Harley and Tenhunen .
 The coefficients within stomatal conductance equation (26) vary with plant species and sites. The model assumes a linear relationship between gs and An adjusted for rh and Cs. The slope coefficient (m) was determined as 12.5, and the zero intercept was 0.01 mol m−2 s−1. The values were distributed within the range derived from a wide range of C3 species [Leuning, 1990; Collatz et al., 1991].
 For aerodynamic calculations, the zero plane displacement, d, was assumed to be 75% of canopy height. The roughness parameter was set at 7% of the canopy height. Canopy drag coefficient was taken from Wilson and Shaw .
 Turbulent closure models require iterative procedure for steady state solutions of the governing set of equations. Each iteration cycle repeats until convergence is reached, i.e., when change in energy flux estimates at the top of the canopy was less than 0.5 W m−2. To enhance numerical stability as the model iterates toward a solution, closure models employs some assumptions. Wind speed and temperature variances were prevented from becoming negative. The case in which wind shear above the top of canopy becomes negative is physically unreasonable and does not appear in observations. Therefore wind speed less than 0.3 m s−1 was set to 0.3 m s−1.
 The forest canopy of 12 m height is divided into 20 layers, and the atmospheric boundary layer spans twice the canopy height. The vertical profile of leaf area was fitted with a Beta distribution to provide a smooth and continuous profile of the leaf area density.
 Measurements of scalar and heat fluxes and meteorology were made at a suburban forest near Toyota City, Japan (35°2′N, 137°11′E), located over 41 to 105 m above sea level with an area of 1.5 ha on steep slope. The site is a secondary broad-leaved forest mixed by evergreen trees where the canopy is divided into an upper and a lower layer. The upper layer is overlapped by Quercus serrata and Quercus variabilis with a mean height of 12 m, and the lower layer consists of numerous sapling and shrubs of various species, such as Ilex pedunculosa, Eurya japonica, Cleyera japonica and etc. The planting density is 3651 trees ha−1, and the basal area is 30.2 m2 ha−1. Leaf area index was 4.5 in the foliated period and 1.0 in the defoliated period. New leaves from deciduous trees generally begin to open in the middle of April and are completed by the end of May. Defoliation period was during the middle of November to the middle of December. According to meteorological measurement over 2000 to 2002, the mean annual rainfall was 1270 mm, and mean annual air temperature was 14.8°C.
 The eddy covariance method was used to measure turbulent flux densities of water vapor, sensible heat, and CO2, using an H2O and CO2 infrared gas analyzer (LI-7500, LI-Cor) and a triaxial sonic anemometer (DAT-600, Kaijo). The gas analyzer and anemometer were installed at 19 m above the ground surface. Analog signals from the system were sampled at 20 Hz and transferred to a portable computer via a RS232 interface. The eddy flux measurement system captured most flux eddies by averaging velocity-scalar fluctuation products for 15 min. Vertical flux densities were evaluated each 15-min by computing the mean covariance of water and sensible heat fluctuations with the fluctuating vertical velocity. Fluctuations of velocity and scalars from the mean were determined from the difference between the instantaneous values and the mean scalar quantities. The fluxes were corrected for the effect of density fluctuations [Webb et al., 1980].
 A number of instruments were installed to measure micrometeorological conditions within and above the canopy. Measured environmental and meteorological variables were averaged over half-hour intervals and logged on a personal computer. Soil temperature was measured at six levels using a multilevel thermocouple probe, and soil water content was measured hourly at four soil depths from time-domain reflectometers (TDR). Instruments and their measurement details are listed in Table 2.
Table 2. Variables Measured in the Experimental Forest
Measurement Height, m
Downward global solar radiation
Eiko Seiki Co., MS-42
17.5 10.1 7.3 4.5 1.5
Upward global solar radiation
Eiko Seiki Co., MS-42
Eiko Seiki Co., MF-11
19.5 8.6 1.2
Downward and upward longwave radiation
Eiko Seiki Co., MS-200
Downward and upward PAR
Koito Co., IKS-27
Ground heat flux
soil heat flux plate
Eiko Seiki Co., MF-81
Eiko Seiki Co., MH-020T
18.2 14.5 11.7 9.5 6.5 0.7
Eiko Seiki Co., MH-020T
18.2 14.5 11.7 9.5 6.5 0.7
Wind speed and direction
Eiko Seiki Co., MA-130
15.5 10.5 7.5
open-path gas analyzer
LI-COR Inc., LI-750
Three-dimensional wind velocity
three-dimensional sonic anemometer
Leaf area index
LI-COR Inc., LI-2000
Leaf area density
LI-COR Inc., LI-2000
Net assimilation rate
portable photosynthesis system
LI-COR Inc., LI-6400
Soil CO2 flux
infrared CO2 gas analyzer
LI-COR Inc., LI-800
0.7 0.5 0.2 0.1 0.0
Soil water content
Campbell Inc., CS615
0.6 0.4 0.2 0.1
 The canopy leaf area index was measured with a leaf area analyzer (LAI-2000, Li-cor). The vertical variation of the plant canopy was measured by gap fraction technique suggested by Norman and Welles . A pair of optical sensors with hemispherical sensors (LAI-2000) was used for measurements of canopy light transmittance from which gap fraction and plant area densities were calculated. The measurements were made at 1 m interval downward from the canopy top.
 Parameters on leaf photosynthetic properties were derived from measurements by an environmentally controlled cuvette system (LI-6400, Li-cor). Measurements were performed on about 100 sunlit leaves of six temperate broad-leaved deciduous trees (Quercus serrata, Quercus glauca) per measurement day. Value of Vcmax was scaled according to leaf temperature.
6. Results and Discussion
 The ability of a one-dimensional model to reproduce the measured scalar fluxes, sources and sinks and vertical profiles of the canopy microclimate was investigated in the study. Since the velocity statistics are required to model scalar sources, sinks, and fluxes, we present the velocity statistics estimated by the third-order closure model. We also present the characteristics of radiation transfer and energy fluxes used to derive physiological sources and sinks; we compare the modeled scalar fluxes to field measurements; and evaluate the model sensitivity to input parameters.
6.1. Velocity Field
 Using the drag property and leaf area density, the higher-order closure model computes velocity statistics within the canopy. Figure 1 shows profiles of the computed and along with the measured normalized leaf area density as a function of the normalized height.
 All the leaves of the canopy are concentrated in the upper 9 m of the canopy. The canopy structure makes turbulence distribution within the canopy unique; as demonstrated by many turbulent-flow measurements, strong momentum extraction by foliage occurs in the upper half zone of the canopy. The closure model also reproduced a small secondary wind speed maximum that is often observed in the trunk space of tall canopies [Wilson and Shaw, 1977; Meyers and Paw U, 1986]. The vertical profiles of the second moment in turbulent kinetic energy budget show unique structure; the peaks of the moments occur near the top of the canopy and then decrease dramatically.
 Modeled profiles of air temperature and specific humidity on DOY 167 show good correspondence with the measurements (Figure 2). On DOY 167, rain of 0.5 mm occurred at 10:30, and 15 mm fell intensively between 13:30 to 16:00. Before the rainfall (see the curve for 9:00), stable stratification of temperature was formed within the canopy layer (Figure 2a). After the onset of rainfall, however, the temperature gradient became greatly unstable with rainfall intensity (curves of 10:00, 14:00, and 15:00); evaporative cooling induced an inversion above the canopy and a downward sensible heat flux from the atmosphere, creating thermal instability in the air beneath the canopy. At night longwave radiation emission from the canopy did give rise to a temperature decrease below the canopy and induced canopy cooling so that the humidity profile was inverted (see 23:00). Leaf wetness due to rainfall lowers the canopy resistance and enhances evaporation, increasing air humidity (see 14:00 h and 15:00) (Figure 2b).
 The form of the CO2 profile reflects the fact that the canopy is a carbon dioxide sink and the soil is a source (Figure 2c). However, the profile was different following climatic conditions. The canopy was a net carbon dioxide sink during nonrainfall (9:00), and CO2 concentration was depressed in the upper canopy. During rainfall, however, CO2 sink of the canopy decreased so that CO2 concentration within the canopy increased, especially under intense rainfall (14:00). Although intense rainfall and small radiation were poor condition for photosynthesis, the upper 20% of the canopy was slightly absorbing CO2. The reason why the canopy absorbs CO2 during rainfall will be described in the section 6.4. At night both the soil and the canopy were sources (23:00).
6.2. Comparison of Radiation and Energy Fluxes
Figure 3 shows a comparison between Rn and LE + H + G, in which all of the components are half hourly measurements during the experimental period. The comparison shows a significant agreement, indicating that measurement errors associated with the eddy flux measurement were relatively small.
 Leaf biophysical and biochemical processes are driven by radiation absorbed at different levels within the canopy. The radiation flux density absorbed by leaves at each discrete layer was calculated separately for the sunlit and shaded fractions, and then it was integrated along the canopy height. Figures 4a and 4e present the comparison between the modeled Rn and the measurement for the two periods. In period 1 the modeled Rn closely followed the diurnal pattern of the measurement, while the model tended to overestimate Rn of the period 2. The overestimation can be attributed to the overestimation of Rn over the soil surface by the model. The model tended to overestimate the soil surface temperature at midday (data not shown). Incorrect measurement of net radiometer during rainfall might also be a source of error.
 The model calculations were tested against half hourly flux measurements in the two periods with different conditions. In period 1, comparisons between measurements and calculations for H and LE show good agreement (Figures 4b and 4c), as well as high correlation (Table 3). The modeled H shows similar diurnal pattern with the measurement, but it tends to be underestimated at midday. The calculation of LE was largely satisfactory, but the model overestimated LE at midday with a strong Rn, where H was underestimated. For instance, at midday on DOY 159, LE was estimated to be about 10% higher than the actual measurement. LE is primarily driven by available radiation and by additional sources such as Tl, VPD and gs [Verma et al., 1986]. If the overestimation of Tl is a determinant for the overestimation of LE, H would have also been simultaneously overestimated because H is dependent on the driving potential (Tl − Ta). Therefore the influence of VPD on the overestimation should not be considerable because VPD is dependent on Tl. This model used the algorithm of Collatz et al.  to estimate gs. The algorithm is advantageous in its requirement of fewer tuning factors, but the influence of model parameters determined from the leaf experiment on the model test was not negligible. Impacts of parameter m within equation (26) on LE had been already found in a coniferous forest [Law et al., 2000] and in an evergreen forest [Tanaka et al., 2002]. The gs algorithm (26) has a weakness more dependent on relative humidity deficit than on the vapor pressure deficit at the leaf's surface. Thus, on the short term, humidity deficits and hydraulic response to the relatively low soil moisture content can restrict stomatal opening [Baldocchi and Meyers, 1998]. There was enough antecedent rainfall to wet soil on DOY 154. So, the restriction of soil water to gs was not expected. On the other hand, Tanaka et al.  found that the impact of Vcmax on energy fluxes was larger than that of the error values of leaf area index in spring and autumn with well-watered soil.
Table 3. Sensitivity Analysis of the Model for Maximum Water Storage (WMAX) and CO2 Concentrationa
The model was rerun for periods 1 and 2, with modified parameter values. We determined r2 and slope from linear regression of measured versus modeled fluxes, fitted through the origin (n = 415).
 In period 2, the modeled LE shows good agreement with the measurements (Figure 4f), although the model slightly underestimated LE at midday. Since the eddy correlation system during rainfall does not work well, it is possible to doubt the data. Thus only data lapsed 3 hours from rainfall cessation were selected for comparison. The model simulated that LE during the rainfall was dominated by evaporation from wetted leaves (Figure 5). The evaporation from wet leaves began to increase with radiative energy. With the lapse of time, water vapor flux was gradually dominated by transpiration. The model described well the hydrologic processes for evaporation and transpiration in leaf surfaces, including the nighttime evaporation maintained by the downward sensible heat. Moreover, the model reproduced the evaporation from dew formed by condensation or guttation.
6.3. CO2 Fluxes
 Model calculation of CO2 flux (FC) shows good agreement with the measurement (Figures 4d and 4h). The comparison indicates that FC was saturated at about −25 μmol m−2 s−1. Light is essential factor for photosynthesis. As demonstrated by previous studies [Reich et al., 1990; Weber and Gates, 1990; Baldocchi and Harley, 1995; Valentini et al., 1996], FC has a curvilinear relationship with PPFD (Figure 6). At low radiation, photosynthesis and respiration are minimal, producing negligible net CO2 uptake. As radiation increases, photosynthetic uptake and respiration loss increase as a result of temperature activation of enzymes. However, uptake exceeds loss for a net CO2 gain. As radiation increases further, photosynthesis attains a maximum rate and then decreases. This indicates that the initial slope is limited by radiation absorption, which controls the rate of electron transport in the light reactions. At light saturation, the photosynthetic rate is limited either by the amount of CO2 or by rubisco. In closed forest, the majority of leaves are shaded. Leaves growing in shaded environment achieve no photosynthetic gain under high radiation. This is a result of the investment of energetically expensive rubisco. On the other hand, sunlit leaves have high Vcmax so as to maximize the photosynthetic rates [Baldocchi and Harley, 1995; Bonan, 1995]. As hydraulic limitations increase in high soil water deficit, the Rubisco effect becomes more dominant, with stomatal closure reducing maximum photosynthetic rates [Williams et al., 1998]. As the evaporative demand is strong (i.e., high radiation and temperature and low humidity), FC is also significantly dependent on Rubisco [Tanaka et al., 2002].
 The calculated FC accounted for over 50% of the variance in the measurements (Table 3). The remaining error occurs mainly during daylight period and could be attributed to the time lag of the peak between calculation and measurement. In the morning, low VPD and increasing radiation makes a good environment for CO2 uptake. At midday, strong radiation causes higher VPD that leads to stomatal closure to maintain turgor. The eddy correlation system was able to sense such leaf photosynthetic mechanisms well. However, the model reproduced the FC's peak around midday when strong light irradiates, maximizing leaf temperature. In the biochemical model for leaf photosynthesis (27), photosynthesis is given by the minimum between JR and JE. Equation (27) includes parameters (i.e., Γ, KC, KO, Rd, Vcmax, and Jmax) that depend on leaf temperature. The reason that the model reproduced the maximum of FC around midday is readily apparent from these parameters. The high leaf temperature directly affects the parameters related to photosynthesis [Harley et al., 1992]. From leaf experiments, Dang et al.  found that impacts of temperature were significant on Rd and Γ.
 For period 2, the model simulated that though FC during rainfall was depressed; it again increased after rainfall cessation. For instance, on DOY 169 when there was a rainfall of 14.5 mm during daytime, leaves were absorbing CO2. The depression rate of FC by rainfall was unexpectedly not so large. The reason that CO2 uptake during rainfall occurs will be discussed in a later section.
6.4. Scalar Sources and Sinks Within the Canopy
 For period 1 and 2 the modeled source/sink strengths for heat, H2O and CO2 are shown as an ensemble contour map as the function of time and canopy depth (Figures 7 and 8). The source/sink strengths of the three components show different time-depth distribution. CO2 source/sink strength is broadly distributed within the upper half layers of the canopy. Heat source/sink strength was similar to the assessment made for a coniferous forest by Lai et al. , who found that its maximum was located within the top 25% of the canopy. On the other hand, maximum source/sink strength of H2O was distributed within the top 30% of the canopy. The difference in the maximum heights implies that the roughness heights of heat, H2O and CO2 are individually different. The differences in the heights change the effective height in which the individual components are exchanged with the atmosphere. Similarly, Lai et al.  argued that the differences were caused by different zero-plane displacement heights. Biophysical phenomena, such as strong momentum and radiation absorptions, mainly occur in the upper canopy layers. In the upper canopy zone, higher radiation absorption increases leaf surface temperature, thereby causing high VPD and high temperature potential. These conditions increase the exchange of H2O and heat.
 The CO2 source/sink strength has features of the vegetation shape profiles (Figure 1); that is, strong CO2 sink occurs in the main portion (9 m) of the canopy, although the magnitude of the source/sink strength is dependent on climatic condition. The profile indicates that the CO2 source/sink strength is closely related to leaf area. The upper canopy layers have low CO2 sink strength despite availability of high radiation. In the upper canopy zone, turbulent mixing is good. The efficient mixing reduces the accumulation of CO2 respired from leaves or soil. Furthermore, large radiation absorption in the upper canopy layers causes higher leaf temperature, which increases vapor pressure gradients across leaf surfaces. The higher VPD often closes stomata, hence decreasing CO2 assimilation. Dang et al.  also found, from leaf experiments of aspen and jack pine, that the stomatal sensitivity to VPD was greater in the foliage of the upper canopy than in the ones of the lower canopy. On the other hand, the lower canopy layers work as CO2 sources. The lower part of the canopy is shaded and has a low leaf area index. The lower leaf area index has a small CO2-fixing ability, and the lower availability of radiation also limits CO2 assimilation. Moreover, the poor mixing in the lower canopy parts may also decrease CO2 exchange.
 Our simulation suggests that leaves actually take up CO2 during the rainfall event. Notice that VPD during daytime was positive (Figure 9a). The positive value indicates that the atmospheric condition enables stomata to keep open (Figure 9b). This model assumed that upper leaf surfaces are wetted by either rainfall or condensation, and that only condensation provides water to the lower leaf surfaces. In nature, the condensation seldom occurs during the daytime. It sometime occurs under conditions of heavy rainfall, wet soil, and light winds [Norman and Campbell, 1983]. Considering these facts, the simulation result that the leaves absorb CO2 during the daytime of the rainfall events may not be so strange. However, FC on DOY 167 and 169 shows a dramatic reduction in the afternoon (Figure 4), despite the positive VPD. The decrease was due to decrease in radiation caused by intense rainfall: For example, at 15:30 on DOY 169 the measured PPFD was 29 μmol m−2 s−1. The small amount of radiation was absorbed almost within the top 30% of canopy layers. The least radiation is transferred to the deep canopy layers so that the deep canopy layers work as source area for CO2 (Figure 8c). When the radiation is below a certain level, about 10–40 μmol photon m−2 s−1 of CO2 uptake during photosynthesis is balanced by CO2 loss during respiration so that net assimilation is zero [Bonan, 2002].
 A variety of environmental factors influence CO2 source/sink strength. As stated earlier, CO2 source/sink strength during and after rainfall is primarily dependent on the radiation force [Williams et al., 1998]. In the following, we examine factors that influence the CO2 source/sink strength during and after rainfall. Rainfall decreases leaf temperature. The temperature affects photosynthetic rates because sufficient heat is a prerequisite for biochemical reactions. However, photosynthetic rates are not proportional to leaf temperature. Photosynthetic rates are only restricted when leaf temperature is beyond an optimal range to inhibit biological activity. The optimum temperature range for most C3 plants is generally from 15°C to 30°C [Bonan, 2002]. This suggests that photosynthetic rates increase within the optimum temperature range, even though it is raining. On the other hand, the decreased temperature derives less respiratory loss. The decline in respiratory CO2 release counterbalances net CO2 absorption. After rainfall, increasing radiation increases evaporation from wetted leaves. The evaporation increases the humidity of air, decreasing VPD between the leaf and air. Such conditions create high potentials for stomatal conductance and intercellular CO2 concentration, which consequently increase carboxylation rates in the photorespiratory carbon oxidation cycle [Tanaka, 2002]. From leaf measurements, Dang et al.  found that increases in VPD at the leaf surface decreased leaf stomatal conductance. A relationship between FC and VPD for the two periods is presented in Figure 10, though the points are greatly scattered. In period 2, the leaves were absorbing CO2 at <3 hPa. The CO2 flux in period 1 distributed within wide range of VPD and did tend to decrease with VPD. This shows that CO2 uptake during and after rainfall events should be closely related to VPD. On the other hand, Williams et al.  found that in the dry season, peak carbon assimilation declines at VPD > 1.5 kPa and the degree of the reduction depends on the magnitude of the belowground hydraulic resistance.
6.5. Sensitivity Analysis
 The flux calculations had already been tested against the measurements. It is thus necessary to examine the sensitivity of the flux calculations to input parameters. For the sensitivity analysis, WMAX and atmospheric CO2 concentration were selected, both of which were not measured in this forest. This model was rerun for the two periods with parameters which varied individually ±50%. Table 3 presents regression analysis between measurements and calculations for the two factors. In period 1, all the flux calculations were sensitive to variation in CO2 concentration. As can be expected, changes in WMAX clearly affected to LE in period 2.
Figure 11a illustrates how CO2 concentration variation modifies LE and FC. With respect to the change of CO2 concentration, LE did respond more sensitively than FC. There was an inversely proportional relationship between LE and CO2 concentration. The effect of CO2 concentration on LE was more significant in period 1 than in period 2 (Table 3). Enhanced CO2 concentration decreases stomatal conductance, resulting in less LE. Transpiration increases with stomatal conductance. The decrease of transpiration causes leaf temperature to increase, which derives a high H. On the other hand, CO2 flux responded proportionately to changes in CO2 concentration. Photosynthetic rates are enhanced by higher concentration of CO2 in the air. The enhanced CO2 concentration reduces photorespiration by increasing the ratio of CO2-to-O2 reacting with rubisco. A strong interaction between CO2 concentration and photosynthesis has been already demonstrated by numerous experimental studies [Eamus and Jarvis, 1989; Harley et al., 1992; Baldocchi and Harley, 1995; Williams et al., 1998].
 When a rain event occurs, evaporation from wetted surfaces is dependent on water amount stored on canopy layers and on climatic conditions. Under the same weather conditions, large canopy storage would cause more evaporation over long time. In contrast, small canopy storage would quickly be lost. The same phenomenon was well demonstrated in the model simulation for DOY 166 when there were rainfall events of 0.5 mm evenly at 2:30 and 7:00. As can be expected, the model reproduced higher LE in larger WMAX (Figure 11b). However, our simulation shows an interesting result for FC; an inverse phenomenon between FCs occurred at 9:00. After rainfall ends, most of the radiation is ideally used for evaporation of water stored on canopy. A canopy with large water storage uses a great amount of radiation compared to a canopy of small storage. Instead, transpiration occurs faster in the canopy with small water storage than in the one with large water storage. This inverse phenomenon suggests that evaporation is so fast in the canopy of small water storage such that transpiration and photosynthesis are also preceded. The biochemistry of photosynthesis is linked to stomata action and the biophysics of transpiration (see equation (26)). Transpiration increases proportionally with increasing stomatal conductance. Net photosynthetic rates also increases with increasing stomatal conductance.
 A one-dimensional multilayer model that computes heat, H2O and CO2 fluxes and infers their source/sink profiles was described and field-tested in a broad-leaved deciduous forest. The modeled fluxes showed generally good agreement with measurements. However, errors were observed between measurements and calculations for LE and FC; the overestimation in the peak of LE and the time lag in FC occurred simultaneously. These could be attributed, in part, to poor parameterizations related to radiation, energy and photosynthesis. On the other hand, the inclusion of leaf water process model allows the model to capture the impacts of rainfall events on the fluxes. The model simulation showed that CO2 uptake of the canopy during rainfall decreased and it rapidly increased after rainfall ends. This indirectly demonstrates successful model calculation for leaf hydrological processes; a significant amount of radiation is used to evaporate water on leaves, and LE is dominated by transpiration with time.
 In this study, we used model simulations to investigate heat and scalar source/sink strengths during and after rainfall. Model calculations indicated that the maximum source/sink strengths of heat and H2O were distributed within the top 30% of the canopy and that the CO2 distribution had the feature of the vegetation shape. These differences imply that the roughness heights of individual components are different, causing different effective exchange heights. The model simulated that photosynthesis rates during and after rainfall were primarily influenced by radiation as well as a variety of environmental factors. For instance, evaporation from wetted leaves after rainfall results in low VPD, which increases stomatal conductance. From sensitivity analysis, under equivalent climatic conditions, CO2 uptake is higher in small water storage than in large storage.
 The authors would like to thank Takafumi Tanaka, Aiko Deguchi, and Naoko Iwata for their help in the data collection during the experiment. This project was funded by Aichi Prefecture Collaboration of Regional Entities for the Advancement of Technological Excellence, Japan Science and Technology Corporation and a grant from the Ministry of Education, Science and Culture of Japan (#14206018).