A Multi-Layer Model for Transpiration of Urban Trees Considering Vertical Structure

: As the intensity of the urban heat island e ﬀ ect increases, the cooling e ﬀ ect of urban trees has become important. Urban trees cool surfaces during the day via shading, increasing albedo and transpiration. Many studies are being conducted to calculate the transpiration rate; however, most approaches are not suitable for urban trees and oversimplify plant physiological processes. We propose a multi-layer model for the transpiration of urban trees, accounting for plant physiological processes and considering the vertical structure of trees and buildings. It has been expanded from an urban canopy model to accurately simulate the photosynthetically active radiation and leaf surface temperature. To evaluate how tree and surrounding building conditions a ﬀ ect transpiration, we simulated the transpiration of trees in di ﬀ erent scenarios such as building height (i.e., 1H, 2H and 3H, H = 12 m), tree location (i.e., south tree and north tree in a E-W street), and vertical leaf area density (LAD) (i.e., constant density, high density with few layers, high density in middle layers, and high density in lower layers). The transpiration rate was estimated to be more sensitive to the building height and tree location than the LAD distribution. Transpiration-e ﬃ cient trees di ﬀ ered depending on the surrounding condition and plant location. This model is a useful tool that provides guidelines on the planting of thermo-e ﬃ cient trees depending on the structure or environment of the city.


Introduction
The urban heat island effect refers to the phenomenon in which urban areas are significantly warmer than surrounding areas due to human activities; this results in higher temperatures, and increases the violence of urban residents, which directly and indirectly affects human health and well-being [1]. The urban heat island effect is becoming more serious due to urbanization and climate change [2][3][4].
One of the representative ways to solve the problem of the heat island in cities is the cooling effect of trees [5][6][7][8][9][10][11]. The cooling effect of trees can be distinguished by radiative heat reduction and transpiration [12,13]. Radiative heat reduction is when the trees reduce the radiant heat reaching the surface of an urban area by blocking or reflecting the radiant heat [10,14]. It is an effective way to cool the space under the trees by generating shadows [15]. Additionally, the surface temperature of First, photosynthetically active radiation (PAR) is calculated using the MMRT model with meteorological and geometric data, and tree properties. Subsequently, the parameter of transpiration is calculated using the input data obtained earlier. To calculate the transpiration and reflect the interaction between transpiration and leaf surface temperature, two strategies are used: (1) simultaneous calculation: calculate the transpiration and leaf surface temperature simultaneously using the resistance values calculated by the parameters; (2) feedback: calculate the surface temperature by temporarily using the atmospheric temperature as the leaf surface temperature, and the resistances and transpiration rate are then calculated.

Model Description
In this study, the multi-layer model reflecting the vertical structure of a tree consists of n layers of crown area at intervals of 1 m, except for the ground level of a single tree ( Figure 2). Among the variables needed to calculate the transpiration, the structural properties (height, trunk height, crown area, and LAD of each layer) are given. PAR are given at each layer through the MMRT model. The multi-layer model calculates leaf surface temperature, three resistances, and transpiration rate at each layer, and finally calculates the total transpiration rate of tree.

Input Data
The main input data for calculating transpiration are meteorological data and tree properties ( Table 1). Meteorological data can be obtained from the surrounding automatic weather station (AWS). Table 1. Meteorological data and tree properties for input data.

Parameter
Units Air temperature ℃ Wind speed

Model Description
In this study, the multi-layer model reflecting the vertical structure of a tree consists of n layers of crown area at intervals of 1 m, except for the ground level of a single tree ( Figure 2). Among the variables needed to calculate the transpiration, the structural properties (height, trunk height, crown area, and LAD of each layer) are given. PAR are given at each layer through the MMRT model. The multi-layer model calculates leaf surface temperature, three resistances, and transpiration rate at each layer, and finally calculates the total transpiration rate of tree. First, photosynthetically active radiation (PAR) is calculated using the MMRT model with meteorological and geometric data, and tree properties. Subsequently, the parameter of transpiration is calculated using the input data obtained earlier. To calculate the transpiration and reflect the interaction between transpiration and leaf surface temperature, two strategies are used: (1) simultaneous calculation: calculate the transpiration and leaf surface temperature simultaneously using the resistance values calculated by the parameters; (2) feedback: calculate the surface temperature by temporarily using the atmospheric temperature as the leaf surface temperature, and the resistances and transpiration rate are then calculated.

Model Description
In this study, the multi-layer model reflecting the vertical structure of a tree consists of n layers of crown area at intervals of 1 m, except for the ground level of a single tree ( Figure 2). Among the variables needed to calculate the transpiration, the structural properties (height, trunk height, crown area, and LAD of each layer) are given. PAR are given at each layer through the MMRT model. The multi-layer model calculates leaf surface temperature, three resistances, and transpiration rate at each layer, and finally calculates the total transpiration rate of tree.

Input Data
The main input data for calculating transpiration are meteorological data and tree properties (Table 1). Meteorological data can be obtained from the surrounding automatic weather station (AWS).

Input Data
The main input data for calculating transpiration are meteorological data and tree properties (Table 1). Meteorological data can be obtained from the surrounding automatic weather station (AWS). The proposed model for calculating transpiration is based on the analogy with Ohm's law, which is used in many leaf energy flux studies [31,36].
where q a (−) is the specific humidity of the air at the reference height z atm (m), q sat (T s ) (−) is the specific humidity at saturation at the leaf surface temperature T s (°C), P a kgm −3 is the air density, which can be calculated using the ideal gas law, expressed as a function of air temperature T a (°C) and atmospheric pressure P atm (Pa), and, r a , r b , and r s (sm −1 ) are the aerodynamic resistance, leaf boundary resistance, and stomatal resistance, respectively. The specific humidity at saturation and specific humidity of air were calculated from [37]. The air vapor pressure e a was calculated using the saturation vapor pressure e sat and relative humidity RH (%). The saturation vapor pressure is calculated from the Arden-Buck equation [38,39].

Photosynthetically Active Radiation (PAR)
One of the key parts of the model is the calculation of transpiration using PAR in each layer, which is calculated by the MMRT model [30]. The MMRT model simulates shortwave and longwave radiation exchanges for the view factor between each urban element, including air temperature, dew point, wind speed, cloud cover, and relative humidity. We calculated the shortwave radiation of each layer using the MMRT model to reflect the variation in transpiration caused by different PAR depending on the location within the tree. The detailed algorithm was described in [30]. Because the result of the MMRT model is shortwave radiation SW Wm −2 , we multiply it by 4.57 to convert the unit (µmol m −2 s −1 , [40]) and by 0.45 again because the proportion of PAR (often defined as 400 to 700 nm) in total solar radiation is approximately 45% [41]; previous studies have used this approach [42][43][44] Leaf Boundary Layer Resistance The leaf boundary layer resistance is calculated from the mean plant leaf boundary conductance g b ms −1 , which is a function of wind speed and therefore of height within the canopy, using Equation (3). We follow Equation (4) from [45] and used by [37,46,47].
where a = 0.01 ms −1/2 is an empirical coefficient [46], d lea f (m) is the characteristic leaf dimension, often referred to as the leaf width, and u(H k ) ms −1 is the wind speed at each layer height H k . The wind speed profile is assumed to be logarithmic above the urban canopy and exponential within the urban canyon using Equations (5) and (6) [35,48,49] u H c = u a ln where u a ms −1 is the wind speed at reference height, and β (−) is the light extinction parameter, which is calculated from [50]; d 0 (m) and z o (m) are the zero displacement height and aerodynamic roughness length, respectively, which are calculated according to the approach developed by [51] and modified by [52] as follows, using Equations (7) and (8): where k = 0.4 (−) is the von Karman constant, and α A = 0.43 (−), β A = 1 (−), and C Db = 1.2 (−) are parameter values for staggered arrays [51]. H c (m) is the canopy height, λ p (−) is the plan area index of the urban roughness elements, A f ,b (m) is the actual frontal area of buildings, A f ,v (m) is the actual frontal area of vegetation, A tot (m) is the total urban plan area, and P v (−) is the ratio between vegetation drag C Dv and building drag C Db . These parameters were calculated from [35,[52][53][54] using the height of trees and buildings. For volumetric/aerodynamic porosity, the light extinction parameter is calculated as given by [17], assuming a spherical leaf angle distribution.

Aerodynamic Resistance
The aerodynamic resistance is calculated by a simpler method [37], which assumes a neutral condition as follows using Equations (9) and (10): Here, z oh (m) is the roughness length for heat.

Stomatal Resistance
As the reciprocal of stomatal conductance is stomatal resistance, stomatal conductance g s mol m −2 s −1 is calculated first. Many studies have reported that stomatal conductance is closely coupled with leaf photosynthesis [55,56]. In the proposed model, the stomatal conductance is calculated as a function of leaf photosynthesis A n µmol m −2 s −1 using Equation (11) from [57] used by [55,58].
where m (−) is the slope, g 0 mol m −2 s −1 is the zero intercept, and hs and C s (ppm) are the relative humidity and CO 2 concentration at the leaf surface, respectively. In this model, a modified equation is used from [59], by using the CO 2 concentration C a (ppm) and relative humidity rh (−) in the air as follows, using Equation (12): Leaf photosynthesis was simulated according to [60]. The version of the model proposed by [59] was used, which calculates photosynthesis without including the potential limitation arising from the triose phosphate utilization, and is used by [36]. where W c µmol m −2 s −1 is the carboxylation rate when the ribulose bisphosphate (RuBP) is saturated, W j µmol m −2 s −1 is the carboxylation rate when the RuBP regeneration is limited by the electron transport, τ is the specificity factor for RuBisCO [61], R d µmol m −2 s −1 is the rate of CO 2 evolution in light that results from processes other than photorespiration, and O and C i (Pa) are the partial pressures of O 2 and CO 2 in the interior leaf, respectively. In the proposed model, where C a (Pa) is the partial pressure of CO 2 in air typically observed with C3 plants under favorable conditions [56,62,63]. W c obeys competitive Michaelis-Menten kinetics with respect to CO 2 and O 2 as follows, using Equation (14): where V cmax µmol m −2 s −1 is the maximum rate of carboxylation, and K c and K o (Pa) are the Michaelis constants of RuBisCO for carboxylation and oxygenation, respectively. W j is controlled by the rate of electron transport, J µmol m −2 s −1 , which depends on PAR. They are calculated as follows, using Equations (15) and (16): where J max µmol m −2 s −1 is the light-saturated rate of electron transport and α is the quantum yield, indicating the efficiency of light energy conversion on an incident light basis. The coefficients for V cmax , J max , K c , K o , R d , and τ are strong, non-linear functions of temperature [64,65]. One temperature function used for K c , K o , R d , and τ is given by Equation (17) from [59]: where c (−) is a dimensionless, scaling constant, ∆H a J mol −1 is the activation energy, R 8.3143JK −1 mol −1 is the gas constant, and T s (K) is the leaf surface temperature. The temperature dependence of V cmax and J max is expressed by Equation (18) from [59,66]: Here, ∆H d J mol −1 is the energy of deactivation and ∆S JK −1 mol −1 is an entropy term. Linear relationships were commonly observed between the leaf photosynthetic capacities and amount of leaf nitrogen on an area basis N a g m −2 [59,[67][68][69]. To account for linear relationships, the scaling factors c for V cmax , J max , and R d and are calculated by Equation (19) from [70].
In the proposed model, the amount of leaf nitrogen is estimated from the mean daily PAR intercepted by the leaves, PAR i mol m −2 d −1 , by an empirical linear relationship; Equation (20) from [71]: The stomatal resistance through the stomatal conductance of Equation (11) is expressed in biochemical units of m 2 s mol −1 . The conversion to common units (s m −1 ) for Equation (1) is obtained as follows, using Equation (21) from [72].
Here, T f = 273.15 (K) is the freezing temperature and P atm, 0 = 101325 (Pa) is a reference atmospheric pressure.
A complete list of the parameters for calculating resistances is presented in Table 2. Table 2. Values, units, and sources of the parameters for resistances.

Parameter Value
Unit Source Leaf Surface Temperature Energy budget for a leaf is Equation (22): where γ Pa K −1 is a psychrometric constant, and Equation (23) is generally used [74].
where C p = 1005 J kg −1 K −1 is the specific heat of air at constant pressure, ε = 0.622 (−) is the ratio of molecular weight of water vapor/dry air, and λ = 1000(2501.3 − 2.351 * T a ) J kg −1 is the latent heat of water vaporization. To calculate transpiration and leaf surface temperature simultaneously, the slope of the saturation vapor pressure function ∆ (Pa) was used from [75].
The latent heat term can be linearized using the saturation vapor pressure function as follows: Using Equations (22) and (26), Equation (27) can be written as Subsequently, Equation (28) can be readily solved for the leaf surface temperature to obtain

Scenario Simulation
We simulated PAR, leaf surface temperature, and transpiration to evaluate and compare various scenarios including the height of surrounding buildings, location of tree, and LAD distribution of each layer. The parameters of the MMRT model are listed in the Table A1.
The domain for the simulation is presented in Figure 3. In the domain, two buildings, two sidewalks, one road, two trees, and the width and height of each are denoted. The tree height is 12 m, tree crown width is 6 m, and tree vertical layer thickness is 1 m.
Forests 2020, 11, x FOR PEER REVIEW 8 of 19 Using Equations (22) and (26), Equation (27) can be written as Subsequently, Equation (28) can be readily solved for the leaf surface temperature to obtain

Scenario Simulation
We simulated PAR, leaf surface temperature, and transpiration to evaluate and compare various scenarios including the height of surrounding buildings, location of tree, and LAD distribution of each layer. The parameters of the MMRT model are listed in the Table A1.
The domain for the simulation is presented in Figure 3. In the domain, two buildings, two sidewalks, one road, two trees, and the width and height of each are denoted. The tree height is 12 m, tree crown width is 6 m, and tree vertical layer thickness is 1 m.

Tree Location
Transpiration can vary by tree position in relation to buildings because of the solar radiance absorption. To evaluate the differences depending on the location of the tree, an E-W street is set so that two trees are located north and south (Figure 3a).

Building Height
The building environment surrounding trees affects the transpiration [76]; for example, by reflecting radiation, intercepting shortwave radiation, emitting longwave radiation, and changing the urban canopy height. The intensity of the urban heat island changes with the height/width ratio [77]. To evaluate the effect of various building environments, we controlled the building height in three cases (1H, 2H, and 3H). Case 1H is an urban canyon with 12 m buildings; case 2H is an urban canyon with 24 m buildings; and case 3H is an urban canyon with 36 m buildings. H denotes the tree

Tree Location
Transpiration can vary by tree position in relation to buildings because of the solar radiance absorption. To evaluate the differences depending on the location of the tree, an E-W street is set so that two trees are located north and south (Figure 3a).

Building Height
The building environment surrounding trees affects the transpiration [76]; for example, by reflecting radiation, intercepting shortwave radiation, emitting longwave radiation, and changing the urban canopy height. The intensity of the urban heat island changes with the height/width ratio [77]. To evaluate the effect of various building environments, we controlled the building height in three cases (1H, 2H, and 3H). Case 1H is an urban canyon with 12 m buildings; case 2H is an urban canyon with 24 m buildings; and case 3H is an urban canyon with 36 m buildings. H denotes the tree canopy height.

LAD Distribution
A higher leaf area index (LAI) of trees must lead to higher transpiration. However, the LAD distribution can vary in the same LAI. We evaluated the transpiration for four vertical structure cases:  (Figure 3b).
The settings of scenarios are summarized in Figure 4.  (ppm) were set as 21,000 and 401.91 [78], respectively. Vertical variations in RH and were ignored because they were relatively small and vary with stable air [79,80]. To calculate the amount of leaf nitrogen, the mean daily PAR was simulated for 1 month (182-212th day of the year, July) using the MMRT model. The values of the main parameters and references used in the simulation are presented in Table  2. To compare transpiration in all cases, the parameters for calculating the resistance were fixed and mainly derived by [59,70]. The leaf width was set as 7.5 cm of Ginkgo biloba, which is planted with the largest proportion of street trees in Seoul [73].

Other Input Data/Parameters
For the simulation, we selected seven days (213th-219th day of the year, August 1) in 2018 in Seoul (126.9658, 37.57142). August is the hottest and most humid month of the year. Figure 5 presents the 7 day average of climate data for the simulations. For the simulation, O (Pa) and C a (ppm) were set as 21,000 and 401.91 [78], respectively. Vertical variations in RH and C a were ignored because they were relatively small and vary with stable air [79,80]. To calculate the amount of leaf nitrogen, the mean daily PAR was simulated for 1 month (182-212th day of the year, July) using the MMRT model.

Other Input Data/Parameters
For the simulation, we selected seven days (213th-219th day of the year, August 1) in 2018 in Seoul (126.9658, 37.57142). August is the hottest and most humid month of the year. Figure 5 presents the 7 day average of climate data for the simulations. For the simulation, O (Pa) and (ppm) were set as 21,000 and 401.91 [78], respectively. Vertical variations in RH and were ignored because they were relatively small and vary with stable air [79,80]. To calculate the amount of leaf nitrogen, the mean daily PAR was simulated for 1 month (182-212th day of the year, July) using the MMRT model. The values of the main parameters and references used in the simulation are presented in Table  2. To compare transpiration in all cases, the parameters for calculating the resistance were fixed and mainly derived by [59,70]. The leaf width was set as 7.5 cm of Ginkgo biloba, which is planted with the largest proportion of street trees in Seoul [73]. The values of the main parameters and references used in the simulation are presented in Table 2.

Results
To compare transpiration in all cases, the parameters for calculating the resistance were fixed and mainly derived by [59,70]. The leaf width d lea f was set as 7.5 cm of Ginkgo biloba, which is planted with the largest proportion of street trees in Seoul [73].

PAR and Leaf Surface Temperature
The results of PAR and leaf surface temperature at 15:00 on the 213th day simulated by the MMRT and transpiration models are shown in Figure 6. Not surprisingly, higher PAR and surface temperature occur when the building is low. PAR showed a decreasing shape depending on the height, but the vertical profile of the surface temperature does not. The highest surface temperature is in the upper layer, but that of the lower layer close to the ground is sometimes greater than that of the middle layer because of the high longwave radiation from the ground. This is similar to higher results, as with the surface temperature of the tree trunk near the surface [81]. The pattern is obvious in the 3H, north tree scenario, where the solar radiation is largely intercepted by the building, resulting in a small difference between the high and low layers. results, as with the surface temperature of the tree trunk near the surface [81]. The pattern is obvious in the 3H, north tree scenario, where the solar radiation is largely intercepted by the building, resulting in a small difference between the high and low layers.

Temporal Variation of Transpiration
Leaf surface temperature and photosynthetically active radiation are the main factors affecting the transpiration rate. Figure 7 shows the hourly transpiration rate of the tree along with the PAR and leaf surface temperature of the top layer. Despite the temperature dependence of plant transpiration, PAR is regarded as a dominant factor for the change in transpiration rate. Leaf surface temperature rather decreases because of the latent heat loss by transpiration. On the 219th day, the transpiration rate is relatively small, despite the high leaf surface temperature. Low PAR of the 219th day induces a low carboxylation rate ( ), which is limited by the electron transport. Therefore, the transpiration rate is high when the surface temperature and PAR are simultaneously high.

Temporal Variation of Transpiration
Leaf surface temperature and photosynthetically active radiation are the main factors affecting the transpiration rate. Figure 7 shows the hourly transpiration rate of the tree along with the PAR and leaf surface temperature of the top layer. Despite the temperature dependence of plant transpiration, PAR is regarded as a dominant factor for the change in transpiration rate. Leaf surface temperature rather decreases because of the latent heat loss by transpiration. On the 219th day, the transpiration rate is relatively small, despite the high leaf surface temperature. Low PAR of the 219th day induces a low carboxylation rate (W j ), which is limited by the electron transport. Therefore, the transpiration rate is high when the surface temperature and PAR are simultaneously high.
transpiration, PAR is regarded as a dominant factor for the change in transpiration rate. Leaf surface temperature rather decreases because of the latent heat loss by transpiration. On the 219th day, the transpiration rate is relatively small, despite the high leaf surface temperature. Low PAR of the 219th day induces a low carboxylation rate ( ), which is limited by the electron transport. Therefore, the transpiration rate is high when the surface temperature and PAR are simultaneously high.

Scenario Simulations
In all the tree location scenarios, the lower the height of the surrounding buildings, the higher the transpiration rate ( Figure 8). The difference in transpiration rate mainly occurs during the day. However, the variation of the south tree is higher than that of the north tree according to the building height. In the C.D case, the difference in tree transpiration is up to 12.9% (south) and 7.3% (north) depending on the building height. The south tree is more sensitive to the height of the building, because it is close to the building forming the shadow. A similar tendency is shown for every LAD distribution scenario (11.3% of south and 6.4% of north in all scenarios). This can be amplified when the distance between the tree and building is lower.

Scenario Simulations
In all the tree location scenarios, the lower the height of the surrounding buildings, the higher the transpiration rate ( Figure 8). The difference in transpiration rate mainly occurs during the day. However, the variation of the south tree is higher than that of the north tree according to the building height. In the C.D case, the difference in tree transpiration is up to 12.9% (south) and 7.3% (north) depending on the building height. The south tree is more sensitive to the height of the building, because it is close to the building forming the shadow. A similar tendency is shown for every LAD distribution scenario (11.3% of south and 6.4% of north in all scenarios). This can be amplified when the distance between the tree and building is lower. The results show that the change in transpiration rate by tree location is larger in the high building case than the others, as shown in Figure 9 (blue and brown lines). The rate averages of each building height case are 5.3% (1H), 9.3% (2H), and 10.1% (3H) because of the sensitivity of the south tree to building height, as mentioned earlier. In comparison to the location condition, the LAD distribution condition shows less of an effect.  The results show that the change in transpiration rate by tree location is larger in the high building case than the others, as shown in Figure 9 (blue and brown lines). The rate averages of each building height case are 5.3% (1H), 9.3% (2H), and 10.1% (3H) because of the sensitivity of the south tree to building height, as mentioned earlier. In comparison to the location condition, the LAD distribution condition shows less of an effect.    Meanwhile, the case of L.H.D showed the lowest transpiration rate in all scenarios. The differences of transpiration between cases are small, in which the maximum rate difference is 4.6% in the south tree, 3H condition, while the minimum is 2.2% in the north tree, 2H condition.

Variation of Transpiration Across Different Scenarios
This study proposes a multi-layer model that considers the vertical structure of trees and buildings to calculate the transpiration rate of urban trees. It is not surprising that the lower the building heights and the further north the trees are located, which also indicates that they are relatively further away from buildings, the higher the transpiration rate. However, in the case of trees located near high buildings (3H) or at the south side, the transpiration was more sensitive to other factors, due to insufficient light conditions caused by building interception of shortwave radiation (Figures 8 and 9).
In this study, the LAD distribution of trees is a relatively less important factor for the transpiration rate than other factors, such as the tree location and building height. The maximum rate differences were 12.9% by the building height, 10.1% by the tree location, and 4.6% by the LAD distribution. Nevertheless, this result is meaningful because LAD distribution may be the only one that can be improved or changed for urban cooling among the three factors.

Strategies for Urban Heat Island
Urban planners and designers have paid less attention to the tree's role in cooling effects, particularly evapotranspiration. However, since most of the deep urban canyons are shaded, the importance of cooling effects from evapotranspiration will increase, and the need to consider LAD distribution increases ( Figure 10). As shown in the results, the most efficient/inefficient trees vary depending on surrounding building condition and the arrangement of trees ( Figure 10). In particular, it is noteworthy that L.H.D cases, with the high density in lower layers, show the worst efficiency in most cases because of relatively lower PAR and wind speed in lower layers around the leaves. The H.D. case, which has a high LAD density and few layers, is the most efficient at 3H scenarios, while the C.D. case is the most efficient at 1H scenarios.
The results of the scenario simulation suggest that the location and shape of trees that are efficient for cooling vary depending on the urban environment. This model can better evaluate the cooling effect of trees by considering the radiant heat intercepting effect of trees. For example, the shallow canyon can be hotter due to the high exposure of canyon surfaces to intense solar radiation [77,82]. The air temperature with taller buildings is lower due to their shading effect [83]. Therefore,

Variation of Transpiration Across Different Scenarios
This study proposes a multi-layer model that considers the vertical structure of trees and buildings to calculate the transpiration rate of urban trees. It is not surprising that the lower the building heights and the further north the trees are located, which also indicates that they are relatively further away from buildings, the higher the transpiration rate. However, in the case of trees located near high buildings (3H) or at the south side, the transpiration was more sensitive to other factors, due to insufficient light conditions caused by building interception of shortwave radiation (Figures 8 and 9).
In this study, the LAD distribution of trees is a relatively less important factor for the transpiration rate than other factors, such as the tree location and building height. The maximum rate differences were 12.9% by the building height, 10.1% by the tree location, and 4.6% by the LAD distribution. Nevertheless, this result is meaningful because LAD distribution may be the only one that can be improved or changed for urban cooling among the three factors.

Strategies for Urban Heat Island
Urban planners and designers have paid less attention to the tree's role in cooling effects, particularly evapotranspiration. However, since most of the deep urban canyons are shaded, the importance of cooling effects from evapotranspiration will increase, and the need to consider LAD distribution increases ( Figure 10). As shown in the results, the most efficient/inefficient trees vary depending on surrounding building condition and the arrangement of trees ( Figure 10). In particular, it is noteworthy that L.H.D cases, with the high density in lower layers, show the worst efficiency in most cases because of relatively lower PAR and wind speed in lower layers around the leaves. The H.D. case, which has a high LAD density and few layers, is the most efficient at 3H scenarios, while the C.D. case is the most efficient at 1H scenarios.
The results of the scenario simulation suggest that the location and shape of trees that are efficient for cooling vary depending on the urban environment. This model can better evaluate the cooling effect of trees by considering the radiant heat intercepting effect of trees. For example, the shallow canyon can be hotter due to the high exposure of canyon surfaces to intense solar radiation [77,82]. The air temperature with taller buildings is lower due to their shading effect [83]. Therefore, considering the fact that the shallow street canyon needs a higher cooling effect, trees with large crowns could be effective in terms of both transpiration and shading [84,85]. We expect that applying this model will be warranted in future studies to help simulation-informed street tree planning and design.

Model Limitations and Future Development
During the calculation of transpiration rate, the model generates a difference between the vapor pressure deficit, wind speed, and resistance values, which results in a difference in the result of transpiration depending on the scenarios. Although many parameters that can lead to restrictive results were fixed to simulate transpiration, it is meaningful to compare the relative transpiration rate of each scenario. Future studies need to estimate and verify the parameters of the model to improve accuracy.
In this study, transpiration was calculated assuming a constant C i /C a . This implies that the stomatal conductance does not affect the internal CO 2 concentration. To increase accuracy, this limit could be developed through a feedback that calculates This study only dealt with the transpiration among the tree's cooling effects. Considering the radiative heat reduction of trees in the future will be a more accurate assessment of the cooling effect of trees. Under various conditions, there will be different cooling requirements, along with other thermal environments, and the shadow effects will vary significantly.
The results show LAD distribution of trees is a relatively less important factor for the transpiration rate than other factors. In actual urban space, however, variation in the leaf area distribution will increase dramatically, both vertically and horizontally, resulting in a larger effect on the transpiration rate. The variations include tree height, crown width, crown shape, leaf shape, etc. Future study should consider these variations and suggest the most efficient tree variations for effective tree planting.

Conclusions
We propose a multi-layer model for calculating the transpiration of urban trees. The advantage of the model is that it simulates transpiration by considering the vertical structure of trees and buildings. To effectively reflect the vertical structure, PAR was simulated using the MMRT model, which is an urban canopy model. For evaluating the model accuracy, two strategies (simultaneous calculation and feedback) are used in this study. The proposed model includes a detailed representation of the plant biophysical and echophysiological characteristics and urban conditions.
Simulations were conducted on four LAD distributions of trees with three types of buildings (12,24, and 36 m) and two types of tree locations (south and north). In this study, the transpiration rate is more sensitive to building height and tree location than to LAD distribution. The results of the scenario simulation suggest that the location and shape of trees that are efficient for cooling effects vary depending on the urban environment. Our results suggest that tree shape and location need to be considered with the surrounding built environment when an urban planner designs planting for the mitigation of the urban heat island. This model will be a useful tool that provides guidelines on the plantation of thermo-efficient trees depending on the structure or environment of the city.

Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.