Estimation of Sensible and Latent Heat Fluxes of an Isolated Tree in Japanese Summer

Abstract

Considering that the characteristics of the heat balance between an isolated tree and the urban atmosphere have not yet been sufficiently clarified, we quantify both the sensible heat flux ($H_{T}$) and latent heat flux ($lE_{T}$) to and from an isolated Z. Serrata in the Japanese summer. To estimate the whole-tree transpiration rate (E_T) and $lE_{T}$ values, we apply a previously developed method using a weighing lysimeter. To estimate the boundary-layer heat conductance ($g_{hT}$) of the total leaf area of the tree crown and the sensible heat flux ($H_{T}$), we apply a scaling-up approach using the heat-balance two-state (HB-TS) method, which previously only targeted single leaves, to the tree crown. Two sample trees with similar crown shape and total leaf area are selected for the HB-TS method but under different irrigation conditions, and $g_{hT}$ is estimated. The E_T values of the tree change three times during the dry-down experiment (during which time irrigation was halted). We also compare H_T and lE_T values between two different days under different irrigation and soil–water conditions. The most important result from this comparison is that the tendencies of H_T and lE_T were reversed on these days, and the Bowen ratio ($\beta = H_{T} /lE_{T}$) dramatically varies between 0.29 and 2.2. These results indicate that the Bowen ratio of isolated trees at urban sites can vary between the previously reported values for forest sites and those for artificial urban sites within a short period, owing to urban-unique conditions (e.g., limited water supply and rooting space, and artificial sealing).

1 Introduction

Transpiration is a physiological function of trees that has a cooling effect on the urban thermal environment. Transpiration from a leaf surface is described as the movement of water vapour through stomata driven by the water potential difference between the leaf and atmosphere. Transpiration releases latent heat from the leaf surface, cooling both the leaf and the atmosphere. The transpiration rate ($E$) and latent heat flux ($lE$), where $l$ is the latent heat of vaporization, of trees have typically been estimated using the porometer method (Leverenz et al. 1982; DeRocher et al. 1995), the sap-flow method (Swanson and Whitfield 1981; Granier 1987), and the lysimeter method (Edwards 1986; Lorite et al. 2012). Whole-tree transpiration can be accurately measured using weighing lysimeters if other factors involved in the water balance can be controlled or measured, and wind noise can be eliminated in the outdoor environment. Asawa et al. (2012, 2014a) developed a novel method to quantitatively measure the whole-tree transpiration rate ($E_{T}$) of a container-grown tree with a height of several metres using a weighing lysimeter. Asawa et al. (2017) quantified $E_{T}$ for a Z. serrata tree, which had reached a height of 6.4 m over 3 years, by applying a data-quality control protocol for the long-term measurement of weight change to remove wind noise and other error factors. Urban trees tend to readily close stomata to decrease transpiration because of drought stress caused by significant vapour-pressure deficit, limited water supply and root space, and significant soil compaction (e.g., Kjelgren and Clark 1993; Cregg 1995; McCarthy and Pataki 2010; Osone et al. 2014; Kagotani et al. 2015). The container-grown conditions of Asawa et al. (2017) were set under the assumption that the root space for urban trees is limited by both shallow soil and pavements. Therefore, the effects of these urban-unique conditions on $E_{T}$ values were effectively analyzed using the weighing-lysimeter method.

To reveal the thermal effect that the tree crown has on the surrounding atmosphere on a quantitative basis, it is necessary to quantify the sensible heat flux ($H_{T}$) for the total leaf area as well as the latent heat flux ($lE_{T}$). In the present study, $H_{T}$ and $lE_{T}$ are defined over the total leaf area (W m⁻²) of an isolated tree. Net radiation (R_n, per leaf area) is converted into sensible and latent heat on the foliage of the crown; thus, to understand the effects on the urban thermal environment, it is insufficient to only estimate $lE_{T}$. Sensible heat transfer warms the surrounding atmosphere; consequently, the thermal effects on an urban environment largely depend on whether the heat flux from trees is mainly composed of sensible heat or latent heat. There is abundant research estimating $H$ and $lE$ over forests and vegetative land surfaces (see Sect. 2.1). To determine $H$ and $lE$ for such land cover, consideration of the horizontal distribution of heat fluxes is unnecessary except at the edges of such an environment, and one-dimensional heat and water exchange can be assumed between soil, plant, and atmosphere. However, difficulties arise when estimating $H_{T}$ for the total leaf area of an individual tree, as described in the following: (a) A tree crown has a complex three-dimensional geometry, and its leaf area is distributed over the entire three-dimensional space within the crown. The three-dimensional distribution of the leaves affects the total amount of solar radiation received by the crown, and the radiative exchange within the crown and with its surroundings (Law et al. 2001; Yang and Friedl 2003; Parker et al. 2004); (b) Isolated trees, such as those in a street or garden, are often exposed to a greater advection of air than those in a forest. These effects produce an increase in evapotranspiration in urban areas, which is termed the oasis or leading-edge effect (Oke 1987; Kanda 2007; Hagishima et al. 2007); (c) Tree canopies are not the only source of heat and moisture. The forest floor is a source too (Roberts 1983; Schaap and Bouten 1997; Baldocchi et al. 2000), implying that separating the different components of the heat flux (e.g., transpiration or evaporation from wet ground) from the observations is difficult. Owing to such difficulties, the characteristics of $H_{T}$ for isolated trees have not yet been sufficiently clarified.

Because $H_{T}$ cannot be measured directly, it needs to be estimated. Focusing on the heat and water balance of individual leaves, scalar transfer (e.g., heat and mass) between the leaf and the surrounding atmosphere is driven by scalar density differences (e.g., temperature and mass density difference) and is dominated by the leaf boundary-layer conductance (g_a). For transpiration, the stomatal conductance (g_s) is also a dominant factor. So far, theoretical examination and experiments to discern g_a have been made to understand both the absorption efficiency of carbon dioxide and the water-use efficiency for production by plants undergoing photosynthesis (Chen 2003; Shibuya et al. 2006). The boundary-layer heat conductance (g_h) is responsible for sensible heat transfer, and is dominated by the flow around the leaf surface as well as the leaf geometry and size (Hasebe 1984). In general, formulating g_h using a dimensionless number (e.g., the Nusselt number) for an outdoor environment in heat transfer theory is difficult (Hasebe 1984), because the leaves and branches sway freely in natural flow and are affected by complex turbulence (Schuepp 1972; Schuepp 1980). In addition, tree crowns are composed of foliage, the aggregate of individual leaves, and do not have a flat and large surface as with the wall of a building or the ground. Therefore, the g_h value of foliage covers the conductance between the collection of leaves and the surrounding atmosphere. A novel study by Asawa et al. (2016) estimated g_h for the total leaf area (g_hT) of Z. Serrata in an outdoor environment by using the heat-balance two-state (HB-TS) method, based on the aforementioned weighing-lysimeter method. The parameter g_hT is defined as the convective heat transfer coefficient (W m⁻² K⁻¹) between a tree crown and the ambient air at a reference position, which is determined based on the total leaf area of the tree. The reference position is set at the outside of the tree crown where the aerodynamic effect of the tree can be neglected. The difference between g_h and g_hT arises from the difference in the method to measure heat transport, i.e., the former is based on a measurement of a single leaf, whereas the latter is based on the estimation of the total amount of heat transport between an isolated tree and the ambient air, divided by the total leaf area. It is clear that the latter is more difficult to determine than the former, as mentioned above.

In the present study, we identify the $H_{T}$ values of Z. Serrata in an outdoor environment in summer by using the HB-TS method and quantitatively compare this with the $lE_{T}$ values. The ratio of $H_{T}$ and $lE_{T}$,the Bowen ratio, should change with the soil–water content; thus, the soil–water content is considered in the estimation and comparison process. The questions addressed are as follows: (a) How can the HB-TS method be applied to the estimation of the $H_{T}$ value of an isolated tree? (b) What is the balance between the $H_{T}$ and $lE_{T}$ values under adequate irrigation in urban conditions? (c) How does the balance change under drought conditions? The data acquired to resolve these questions will inform our understanding of the cooling effect from urban trees and facilitate the investigation of appropriate irrigation control for isolated trees in an urban environment. These data will also be applied to the validation and parametrization of energy balance models for urban trees in microclimate simulations (Bruse and Fleer 1998; Asawa et al. 2008; Chen et al. 2011).

2 Literature Review

2.1 Methods Based on Remote Sensing

The eddy-covariance method is one of the most widely applied methods for measuring $H$ and $lE$ over forests, tree canopies, and vegetative surfaces (Anderson et al. 1984; Verma et al. 1986). Methods based on remote sensing have also been applied for the estimation of $H$ and $lE$ over these surfaces (Kalma et al. 2008), because the radiometric surface temperature is closely related to $H$ (Lhomme et al. 1992; Lhomme et al. 1994; Zhan et al. 1996); it is also regarded as the primary parameter in estimating $lE$ (Blad and Rosenberg 1976; Choudhury et al. 1986; Miglietta et al. 2009). Radiometric surface temperatures have been obtained from satellite remote sensing for regional-scale areas (Sucksdorff and Ottle 1990; Mecikalski et al. 1999), airborne remote sensing for medium-scale areas (Kustas et al. 1989; Norman et al. 1995), and ground-based measurements for microscale areas (Vining and Blad 1992; Jones et al. 2018). In addition, energy balance models have been applied to remotely-sensed radiometric temperature data to estimate energy fluxes (sensible and latent heat fluxes) (Timmermans et al. 2007; Kalma et al. 2008). The two-source energy balance (TSEB) model (Cammalleri et al. 2012; Kustas et al. 2012; Colaizzi et al. 2012) and the surface energy balance algorithm for land (SEBAL) model (Bastiaanssen 2000; Paul et al. 2013; Tang et al. 2013) also have been frequently used in recent years. The primary target of all these methods is the calculation of one-dimensional fluxes and energy balances for target sites, including both homogeneous and heterogeneous land cover; however, this is not suitable for flux estimations of three-dimensional total leaf area for a tree crown of an isolated tree. This is because three-dimensional factors, including radiation and airflow, affect the energy balance of the tree crown. However, it has been suggested that remotely-sensed radiometric surface temperature has a high potential for representing $H_{T}$ from the tree crown. In addition, the difficulties and limitations for flux estimations of the tree crown are not derived from the observation of the radiometric surface temperatures of the foliage (see Sect. 3.5) but from one-dimensional assumptions used in the estimation process.

2.2 Heat-Balance Method

There have been many studies showing the fundamental effects of leaf size and surrounding airflow on g_a based on dimensionless-number heat transfer theory (e.g., the Nusselt number, Balding and Cunningham 1976) that examine the detailed effects of turbulence (Schuepp 1972) and leaf flutter on g_a (Schuepp 1980). In particular, several studies suggest that g_a is increased by turbulence and leaf flutter in a natural environment because the leaf boundary layer becomes thinner owing to these effects (Schuepp 1980). This indicates the importance of the estimation of g_a in the natural environment, specifically outdoor spaces.

To measure g_a experimentally, several methods have been proposed for both real and artificial leaves (e.g., Defraeye et al. 2013). The representative methods are the water-loss technique for mass transfer and the heat-balance method for heat transfer. For the water-loss technique, an artificial leaf is wetted and weighed before and after the experiment, and the convective mass transfer coefficient is estimated from the water loss and vapour-pressure deficit on the leaf surface. The water-loss technique has also been applied to both artificial and small potted plants by measuring the total weight after wetting the leaves (Landsberg and Powell 1973).

For the heat-balance method, the g_h value of a leaf is estimated from the residual leaf heat balance by measuring R_n, $E$, and the temperature difference between the leaf surface and surrounding atmosphere (Kumar and Barthakur 1971; Parlange and Waggoner 1972; Martin et al. 1999). This method can be applied to both real and artificial leaves. For use on artificial leaves, the leaf is often heated artificially using a heater, thereby introducing an additional term (the heating term) to the leaf heat balance (Parkhurst et al. 1968; Murphy and Knoerr 1977). The HB-TS method, another type of heat-balance method, estimates g_h by setting two states for a pair of leaves, usually with and without transpiration. This method can eliminate heat-flow factors that are difficult to measure in the field, such as absorbed radiation, by applying simultaneous heat-balance equations for two states. For example, the transpiration of one leaf is suppressed by coating the leaf surface with Vaseline (Thrope and Butler 1977) or by using anti-transpirants on the plants (Kitano et al. 1995), which close the stomata physiologically. These methods are considered to be valid under the condition that radiation absorbed is equivalent for the two leaves. The heat balances of leaves (both sides) with and without transpiration are given by

$$ aS_{i} + \varepsilon L_{i} = lE + 2g_{h} \left( {T_{l1} - T_{a} } \right) + 2\sigma \varepsilon T_{l1}^{4} , $$

(1)

$$ aS_{i} + \varepsilon L_{i} = 2g_{h} \left( {T_{l2} - T_{a} } \right) + 2\sigma \varepsilon T_{l2}^{4} . $$

(2)

By combining these equations simultaneously, g_h is given by

$$ g_{h} = \frac{{0.5lE - \sigma \varepsilon \left( {T_{l2}^{4} - T_{l1}^{4} } \right)}}{{\left( {T_{l2} - T_{l1} } \right)}}. $$

(3)

By using the g_h value, the sensible heat fluxes from the leaves are then given by

$$ H_{1} = 2g_{h} \left( {T_{l1} - T_{a} } \right) , $$

(4)

$$ H_{2} = 2g_{h} \left( {T_{l2} - T_{a} } \right) , $$

(5)

where $a$ is the absorptance for shortwave radiation of a leaf, $S_{i}$ is incoming shortwave radiation, $\varepsilon$ is emissivity, $L_{i}$ is incoming longwave radiation, $g_{h}$ is boundary-layer heat conductance (W m⁻² K⁻¹), $T_{l}$ is leaf temperature, $T_{a}$ is the air temperature, $\sigma$ is the Stefan–Boltzmann constant (= 5.67 × 10⁻⁸ W m⁻² K⁻⁴), and subscripts 1 and 2 refer to leaf 1 with transpiration and leaf 2 without transpiration, respectively.

As shown by Eq. 3, it is necessary for there to be a large temperature difference between the two leaves used in the HB-TS method. Because there is much research concerning the detection of the degree of water stress in plants by observing leaf temperature ($T_{l}$) (Tanner 1963; Jackson et al. 1981; Hatfield 1983), differences in $E$ and $T_{l}$ can be considered to be appropriate indices for the HB-TS method (Jones 2004; Blonquist Jr. et al. 2009). The HB-TS method has also been applied to artificial leaves; in this case one leaf was heated by a heater, and therefore, the differences in $T_{l}$ were artificially set instead of occurring naturally via transpiration (Brenner and Jarvis 1995). Both the heat-balance method and the HB-TS method are applied to the estimation of g_h on walls under outdoor solar radiation and natural wind (the heat-balance method: Hagishima and Tanimoto 2003; Clear et al. 2003; the HB-TS method: Ito et al. 1972; Sharples 1984; Loveday and Taki 1996); thus, the application range for these methods is very wide. In general, an increase in the number of the variables to be measured leads to the accumulation of errors of measurement and estimation in the final results. However, the HB-TS method only requires the temperature differences for the two states of the leaves and $E$ (or heating flux from a heater) as variables to be measured, if the absorbed radiation is assumed to be equivalent.

For both methods, most research targets an individual leaf, except when using small plants. Kitano et al. (1995) estimated the averaged g_a value for an entire individual plant (e.g., cucumber or lettuce) using an anti-transpirant (abscisic acid) and by weighing the plant under the two states (before and after applying the abscisic acid). Another novel trial by Asawa et al. (2016) estimated g_hT for the total leaf area of an isolated tree by applying the HB-TS method. In the study, $E_{T}$ was measured using the weighing-lysimeter method (Asawa et al. 2017). The present study is implemented based on the methods of these two studies, targeting a real-sized tree.

3 Materials and Methods

3.1 Theoretical Examination

Considering the above-mentioned literature review and discussion, the important factors for estimating g_hT and $H_{T}$ are as follows: (1) estimations of g_hT and $H_{T}$ should include the movement of branches and leaf-flutter under natural wind conditions. (2) The HB-TS method is effective in reducing errors in the accumulation and propagation of measurements and estimations. (3) The difference in $E_{T}$ and $T_{l}$ between the two states is an effective parameter for estimation. (4) Changes to $E_{T}$ cause clear changes in $T_{l} .$ (5) The $E_{T}$ and $lE_{T}$ values of an isolated tree are measurable by using weighing lysimeters. (6) The radiometric surface temperature of a tree crown ($T_{r}$) has a high potential in representing $T_{l}$ and $H_{T} .$ (7) To minimize instrumental error (systematic error), the amount of equipment used for measurements and the number of variables measured should be minimized. As suggested, we apply the HB-TS method and the weighing-lysimeter method to the isolated tree and estimate $H_{T}$ and $lE_{T}$ for the two states with different $T_{l}$ and $E_{T}$ values. The estimation of total leaf area is also important in the method; thus, we apply a terrestrial-laser scanning system for the accurate estimation of the total leaf area of an isolated tree (Asawa et al. 2014b).

3.2 Plant Materials and Study Site

The sample tree was a 13-year-old Z. serrata, this being the third most popular street tree species in Japan (NILIM 2014), with a short trunk and long, upward-spreading stems covered with plentiful leaves. The shape of the tree implies that leaves and branches generally sway in natural wind; thus, the g_hT values are considered to be greater than for most urban trees. To apply the HB-TS method to the tree crowns, we selected two Z. serrata with similar features as sample plants (Fig. 1). The selection process was as follows: we prepared seven Z. serrata in the experimental field. All were produced by grafting in the same field on the same day in 1997. All were of almost the same height and were transplanted into large containers at the same time (February 2010). From these seven trees, we carefully selected two sample trees for measurement, which had similar crown shapes and leaf areas. The heights and trunk diameters in 2010 were 6.4 m and 0.11 m for tree A, and 6.3 m and 0.10 m for tree A′, respectively.

Fig. 1

Layout and information for tree A and tree A′

We measured the leaf areas of the two trees using a terrestrial-laser scanning system (VZ-400, RIEGL, Horn, Austria) in the summer of 2010. We then applied the voxel-based canopy profiling method to the laser-scanned data for the estimation of the total leaf areas (Hosoi and Omasa 2006; Oshio et al. 2015). In a previous study (Asawa et al. 2014b), we validated the method by comparison with the stratified clipping method and confirmed that this method estimates the total leaf area with an accuracy of 6% for Z. serrata. On 3 September, 2010, one-sided total leaf areas were found to be 13.2 m² for tree A and 11.9 m² for tree A′, respectively. The difference in the leaf area was 10%, which presumably results in a 10% error in the estimation of $H_{T}$ using Eq. 10 (see Sect. 3.3). The Z. serrata trees were planted in large containers with an area of 1 m² and a depth of 0.6 m. The box volume was determined based on the rooting space of a general street tree (MLIT Japan 2005). The root-zone depth was 0.5 m, and the soil was composed of Kanto loam (70%), perlite (20%), and leaf mould (10%). Tree A had adequate transpiration under full irrigation (except for several days because of dry-down experiments). In contrast, we regarded tree A′ as a reference tree for the HB-TS method; this tree had the least transpiration because of the cessation of irrigation for several successive days. Therefore, tree A′ suffered from drought stress and closed stomata on these days.

The study site chosen was an experimental field with an open area of 8800 m² in the city of Miyoshi, Aichi Prefecture, Japan (35° 8′ N, 137° 6′ E). There were no obstacles within 40 m of the sample trees, except several container-grown trees of 5-m height. Distances between these trees were > 4 m; thus, they were exposed to solar radiation and airflow. This may be regarded as an isolated condition for these sample trees.

3.3 Estimation of Boundary-Layer Heat Conductance (g_hT) and Sensible Heat Flux ($H_{T}$) of the Total Leaf Area

Asawa et al. (2016) estimated the averaged g_hT value of the total leaf area of the isolated tree. The present study deals with g_hT in the same way, using an estimation of $H_{T}$. To express $H$ and lE for tree canopies, g_a and g_h are scaled up from single leaves to tree canopies (Campbell and Norman 1998; Blonquist Jr et al. 2009). If the transpiration rate of the tree canopies ($E_{c}$) can be estimated, then the latent heat flux from tree canopies is expressed as $lE_{c}$. The sensible heat flux from tree canopies ($H_{c}$) is expressed as

$$ H_{c} = g_{hc} \left( {T_{c} - T_{a} } \right) , $$

(6)

where $T_{c}$ is canopy temperature and $g_{hc}$ is the boundary-layer heat conductance of the tree canopy (W m⁻² K⁻¹). Equation 6 treats the canopy as a “big-leaf” for estimating $g_{hc}$ (Baldocchi et al. 1991), while $T_{c}$ is the effective temperature of the canopy for $H_{c}$ that satisfies Eq. 6 (Kustas and Norman 2000). Previously, $T_{c}$ was mostly estimated from the measurement of surface radiometric temperature ($T_{r}$), and the difference between $T_{c}$ and $T_{r}$ was used (Norman et al. 1995; Blonquist Jr. et al. 2009). The difference between $T_{c}$ and $T_{r}$ increases when the infrared radiometer used to measure $T_{c}$ also measures the underlying soil through the foliage gaps. In addition, an appropriate correction for surface emissivity is required for accurate surface temperature measurements for the tree canopy, if $T_{r}$ is significantly different from the behind temperature (i.e., radiant temperature from the direction of the reflection, e.g., the sky temperature behind the thermal infrared camera). In addition, Eq. 6 assumes that the measured values of $T_{c}$ are representative of the entire canopy, applying the same weighting from all the individual leaves. The radiometric temperature is a composite value weighted from all the elements within the radiometer field of view. The calculated value of $g_{hc}$ is valid for the canopy within the field of view and is representative of the entire canopy or field only when the canopy is homogeneous (Blonquist Jr. et al. 2009). These points are also discussed in Sect. 3.5 for the measurement of $T_{r}$ for a tree crown. The present study applies the same scaling-up approach for the estimation of the $g_{hT}$ and $H_{T}$ values of the total leaf area of an isolated tree, using $T_{r}$ as the representative of the foliage temperature ($T_{T}$). However, both the estimation method and the procedure are new and relatively untested.

To estimate the $g_{hT}$ and $H_{T}$ values of the total leaf area, the HB-TS method is applied to the heat balance of two individual tree crowns (tree A and tree A′) with different $E_{T}$ values in the same outdoor environment (Fig. 2). The difference in $E_{T}$ between two trees is made by controlling irrigation conditions. Here, the net heat balance is estimated for the tree crown, and the fluxes (radiation flux, $H_{T}$ and $lE_{T}$) are estimated per leaf area of the foliage. The primary requirement of applying the HB-TS method to the total leaf areas of isolated trees is that tree A and tree A′ are the same species of tree, same age, same size, and have the same leaf area. If two trees are in the same environment and the crown shape and leaf areas are very similar, the incoming radiation fluxes and the $g_{hT}$ values can be assumed to be equivalent.

Fig. 2

Image of the HB-TS method for the total leaf areas of isolated trees

Therefore, the heat balances of tree A and tree A′, based on that of single leaves (Eqs. 1 and 2), are given by

$$ a_{T} S_{iT} + \varepsilon_{T} L_{iT} = lE_{T} + 2g_{hT} \left( {T_{T} - T_{a} } \right) + 2\sigma \varepsilon_{T} T_{T}^{4} , $$

(7)

$$ a_{T} S_{iT} + \varepsilon_{T} L_{iT} = lE_{T}^{'} + 2g_{hT} \left( {T_{T}^{'} - T_{a} } \right) + 2\sigma \varepsilon_{T} T_{T}^{'4} , $$

(8)

where subscript $T$ indicates the average value over the total leaf area, and $T_{a}$ is air temperature at a reference position with negligible aerodynamic effect of the tree.

When there is large difference in $E_{T}$ values between tree A and tree A′, foliage temperature ($T_{T}$) should also differ between them. Therefore, if values for $E_{T}$ and $T_{T}$ are identified for these trees, the relation for g_hT can be obtained from the simultaneous calculation of Eqs. 7 and 8,

$$ g_{hT} = \frac{{0.5\left( {lE_{T}^{'} - lE_{T} } \right) - \sigma \varepsilon \left( {T_{T}^{'4} - T_{T}^{4} } \right)}}{{\left( {T_{T}^{'} - T_{T} } \right)}}. $$

(9)

This equation is also equivalent to that for single leaves as shown by Eq. 3. Although it is quite difficult to ensure perfect equality in the crown shape and total leaf area of the two trees, the difference in $T_{T}$ is the primary factor for the estimation of g_hT. Therefore, small differences in geometric factors (shape and leaf area) do not produce a significant error in the result for g_hT.

The $H_{T}$ value can be estimated from the g_hT and $T_{T}$ values via

$$ H_{T} = 2g_{hT} \left( {T_{T} - T_{a} } \right), $$

(10)

where $H_{T}$ is the sensible heat flux per leaf area (considering both sides). Here, $T_{T}$ is obtained from the remotely-sensed $T_{r}$ value as explained in Sect. 3.5. If needed, the $H_{T}$ value can be converted into that based on the ground area by multiplying by the leaf area index ($LAI$ = total leaf area of one side divided by the vertical projected area of the crown). Here, the $LAI$ value of the target tree (tree A) is 2.4.

3.4 Estimation of Latent Heat Flux of the Total Leaf Area ($lE_{T}$)

We applied the weighing-lysimeter method developed by Asawa et al. (2012, 2017) for the estimation of $lE_{T}$. For this method, a container-grown tree was placed on a platform weighing machine, and the total weight of the tree, container, and soil was measured. All water balances were controlled by an automated irrigation system, and $E_{T}$ (whole-tree transpiration rate) could be identified from the measured changes in weight and the total leaf area obtained from the laser-scanning data. The weighing machine and container were both enclosed within a structure to protect them from wind, rainfall, and solar radiation. It was confirmed that this method measures the weight change of the target Z. serrata, which had a height of 6.4 m, with an accuracy of $\pm$ 0.1 kg h⁻¹. This is considered to be of sufficient accuracy to quantify a value of $E_{T}$ for the analysis of urban tree transpiration, because the weight change by the whole-tree transpiration rate of the target tree was found to be greater than 3 kg h⁻¹ during hot, summer days. We applied this weighing-lysimeter method to tree A, which was necessary to estimate $lE_{T}$ values.

We could not apply the weighing-lysimeter method to tree A′ because of the limitations of cost and experimental effort. Therefore we applied the sap-flow method (Granier’s thermal dissipation sensor) (Granier 1987) to tree A′ to check whether the sap flow (transpiration rate) approached zero with the interruption in irrigation during the day, for accurate estimation of g_hT. The sap-flow methods are frequently used for studying whole-tree and stand-scale water use (Swanson and Whitfield 1981). However, the sap-flow velocity measured at chest height can be shifted from the actual E_T value by a few hours (e.g., Saugier et al. 1997). In addition, the widely-used Granier’s thermal dissipation sensor (Granier 1987) is known to be sensitive to environmental radiation and temperature (Oren et al. 1999; Lu et al. 2004), and this can be problematic in the measurement of isolated (i.e., urban) trees under hot summer conditions. However, tree A′ is a reference tree in our experiment, and the transpiration was minimized by the cessation of irrigation. In the experimental design, we considered that the sap-flow method does not produce a significant error in the estimation of g_hT under such drought conditions. On the day of measurement (30 August, 2010), irrigation had been stopped for tree A′ for 7 days, and the pF of the soil was near 4.2, which is the permanent wilting point for plants. The pF is defined as the logarithm of soil matric potential and it was estimated from the measured soil–water content (amplitude-domain reflectometry sensor; Thetaprobe ML2x, Delta-T Devices, Cambridge, UK) and the water retention curve (pF curve) of the sample soil. The result of the soil pF indicated that transpiration was physiologically limited. In addition, the sap flow of tree A′, measured by the Granier’s thermal dissipation sensor, was below one-tenth of that of tree A. To verify the assumption that the $E_{T}^{'}$ value was close to zero, we checked the change in the soil–water content of tree A′ (see Appendix). The measurement for soil–water content strongly indicated that there was no water uptake from the soil to the root, and the transpiration was completely limited. From these points, we comprehensively concluded that the $E_{T}^{'}$ value of tree A′ was negligible for the g_hT estimation.

3.5 Measurement of Foliage Temperature (T_T)

We applied a thermal infrared camera for the measurement of $T_{T}$. To ensure the validity of the use of $T_{r}$ to estimate $T_{T}$, as measured by the thermal infrared camera, the following points were considered based on the examination described in Sect. 3.3.

(i) To extract $T_{r}$ from the foliage in a thermal image, the temperature difference with the background (i.e., the gaps between the leaves and surroundings of the foliage) is needed. Therefore, we set the thermal infrared camera to face the crowns of the trees (the middle height was 5.3 m above ground) from the south and then changed the elevation angle slightly upwards. In more detail, we put the camera with a tripod on the roof of the one-box car used for observation and set the height of the camera at 3.7 m from the ground. The elevation angle was 4°, and the distance between the camera and trees was 10 m. The spatial resolution of the camera is also important in the detection of $T_{r}$, noting that the instantaneous field of view of the camera was 2.5 mrad, implying that the spatial resolution of the target from a distance of 10 m was 25 mm. This resolution can distinguish leaves and foliage from the background sky (i.e., pure pixel); however, the boundaries between the foliage and sky are identified as mixed-pixels. Therefore, we extracted the mixed-pixels using a temperature-difference index, D₀, as shown in Fig. 3 and the relation

Fig. 3

Extraction of $T_{r}$ of the foliage from a thermal image

$$ D_{0} = \mathop \sum \limits_{i = 1}^{N} \left| {T_{0} - T_{i} } \right| , $$

(11)

where $T_{0}$ is the temperature of the centre pixel, $T_{i}$ is the temperature of the surrounding pixels, and $N$ (= 8) is the number of surrounding pixels.

D₀ indicated the sum of the temperature differences of the surrounding eight pixels for the centre pixel. The threshold of D₀ for the extraction was determined for the sample tree, and the mixed-pixels were all deleted from the $T_{r}$ estimation. The threshold of D₀ was approximately 2.5, and the value was slightly changed with meteorological conditions (e.g., cloud conditions of the background sky) and solar position.

(ii) An emissivity correction for the foliage is needed when $T_{r}$ is largely different from the behind temperature ($T_{\text{Behind}}$) (i.e., the radiant temperature from the direction of the reflection). In this case, the area behind the infrared camera measurement was populated with tree canopies. The distance between the target trees and tree canopies was 11 m, which is relatively close. This indicates that $T_{r}$ and $T_{\text{Behind}}$ are almost equal, and no emissivity ($\varepsilon$) correction is necessary because the reflected radiation equals the fraction of radiation not emitted (1–$\varepsilon$) by the target (Blonquist Jr. et al. 2009). Therefore, we used the measured $T_{r}$ value for the $T_{T}$ value in Eqs. 9 and 10. These two points were considered to ensure an accurate estimation of $g_{hT}$ using the HB-TS method.

(iii) The number of instruments used for measurement should be minimized to reduce instrumental error (systematic error), as discussed in Sect. 3.1. This implies that if different thermal infrared cameras are used for each individual tree, differences in the instrumental feature, condition, or calibration may cause systematic errors in the measured $T_{r}$ values. Therefore, one thermal infrared camera was used to detect the $T_{r}$ values of both trees (tree A and tree A′) simultaneously.

(iv) Obtaining an average temperature for all the leaves in the crown is desirable. However, $T_{r}$ as obtained from the thermal infrared camera is an approximation of the average temperature, because the camera cannot detect all leaf surfaces. We considered that the $T_{r}$ value gained from the thermal infrared camera could be used as the averaged foliate temperature ($T_{T}$) for the following reasons. The sample tree was a young tree and had a relatively low leaf area density (LAI = 2.4), implying that there were small leaves hidden from the view of the camera. In addition, the preliminary measurement results for $T_{r}$ from all four directions using the thermal infrared camera showed that differences in the temperature from the different directions were small (within 0.7 K at maximum). For these reasons, we used the results from one direction (south) for successive measurements.

We also checked whether the $T_{r}$ values of both trees were identical under dual-irrigated conditions. We obtained the $T_{r}$ values of both trees on 3 September, under sunny conditions when these trees were fully irrigated. The difference in $T_{r}$ (tree A′–tree A) was $0.09 \pm 0.18$ K. This was sufficiently small and supports the assumption that these trees had the same radiometric condition, transpiration, and leaf temperature.

3.6 Meteorological and Measurement Conditions

Meteorological data were obtained in the northern part of the experimental field using a solar radiometer (MS-402, Eko Instruments, Tokyo, Japan), an air temperature sensor (4 wires Pt100Ω, Taiyo Keki, Tokyo, Japan) with an aspirated radiation shield (Model 43502, R. M. Young Co., Traverse, Michigan, USA), a relative humidity sensor (CS215, Campbell Scientific, Logan, Utah, USA), a tipping bucket gauge for precipitation (TE525MM, Campbell Scientific), a three-dimensional ultrasonic anemometer (Model 81000, R. M. Young Co.), and a photosynthetically active radiation (PAR) sensor (LI-190, Li-Cor Inc., Lincoln, Nebraska, USA). This position was set as the reference position. To analyze the effects of airflow on $T_{r}$ and g_hT, the anemometer was located 4.3 m from the Z. serrata (Fig. 1). This location was determined to be as close as possible to the tree while minimizing the drag-force effect that the tree would have on the wind measurements. The height of the anemometer was 4 m, similar to the height of the centre of the tree crown.

Measurements were carried out in the summer of 2010, which was hot and dry across Japan, and the longest stretch of sun at the study site was 18 days, from 21 August through 7 September. We irrigated approximately 30–50 kg m⁻² of soil daily, determined by using the $E_{T}$ values from the preceding days, which was sufficient to compensate for the water loss from daily transpiration. We confirmed that ample irrigation was not problematic for the $E_{T}$ estimation, because any excess of water over the field capacity was soon discharged. We irrigated at night-time (from 0300 LST to 0500 LST) almost every day during the season, except the period of the dry-down experiments on tree A. Times are expressed in local standard time (LST = UTC + 9 h). For the dry-down experiments, irrigation was stopped for two to four successive days to ascertain the effects of drought stress while minimizing the damage to the growth of the tree. For tree A′, irrigation was stopped for several successive days to minimize $E_{T}^{'}$ and $lE_{T}^{'}$ for the HB-TS method, as explained in Sects. 3.3 and 3.4. The condition of these trees was carefully checked during the test period to avoid damaging the tree (e.g., via withering or defoliation).

We paid close attention to selecting a date for the estimation of g_hT and heat fluxes as we needed to use comparable dates for the two different conditions. To estimate g_hT using the HB-TS method, we selected the date of 30 August for tree A and tree A′. 30 August experienced a clear sky during the day and the $E_{T}^{'}$ value of tree A′ was confirmed to be minimized, as checked by the sap flow and soil–water content by the method explained in Sect. 3.4. In contrast, tree A showed almost maximum transpiration owing to the ample irrigation over the four successive days. This means we waited for both conditions, minimizing the transpiration of tree A′ and recovering that of tree A after the dry-down experiment by carefully checking the weather and tree conditions. Consequently, we could make a large difference in $E_{T}$ and $T_{T}$ between these trees as expected.

4 Results

4.1 Foliage Temperature (T_T)

Figure 4 shows an example of the thermal images for tree A and tree A′, and Fig. 5 shows the results of averaged foliage temperatures (T_T, T_T′) for tree A and tree A′ on 30 August obtained from the thermal image (e.g., Fig. 4). It is confirmed that the T_T value was a maximum of 1 K higher than T_a, and the T_T′ value was 3 K higher than T_a. This means that the transpiration from tree A caused a decrease in the foliage temperature of up to 2 K. The results for (T_T–T_a) and (T_T′–T_a) show that these trends corresponded significantly with the solar radiation. Increases in solar radiation caused simultaneous increases in the foliage temperature. In particular, the effect of an instantaneous reduction in solar radiation between 0900 LST and 1000 LST was reflected as a reduction in the foliage temperatures. The result of (T_T′–T_T) shows that there was little difference between T_T′ and T_T during the night-time. This means that the radiation transfer characteristics and the g_hT value were equivalent for the two sample trees, and only $E_{T}$ caused a difference in the foliage temperatures. During the daytime, the changing trend of (T_T′–T_T) corresponded well with the E_T value. These results support the theoretical and literature-derived idea in Sect. 3.3 that g_hT can be estimated from Eq. 9 with (T_T′–T_T) and E_T. Thus, $H_{T}$ can also be estimated using these results with Eq. 10.

Fig. 4

Thermal images for the two trees under different irrigation conditions

Fig. 5

Averaged foliage temperatures for tree A and tree A′ on 30 August obtained from infrared thermography: a averaged foliage temperatures (T_T, T_T′); b difference between averaged foliage temperatures and air temperature (T_T–T_a, T_T′–T_a); c difference in averaged foliage temperature between tree A′ and tree A (T_T′–T_T); d solar radiation per ground area (R_S) and wind speed (V); and e whole-tree transpiration rate of tree A (E_T) per hour per leaf area are shown

4.2 Boundary-Layer Heat Conductance of the Total Leaf Area (g_hT)

Figure 6 shows the results for the g_hT value estimated in Asawa et al. (2016) and the relationship with the wind speed outside the tree crown. The wind speed was estimated via the composition of the three-dimensional vectors of the instantaneous velocity components, averaged over 1 h. If the $lE_{T}$ value of tree A and the foliage temperature difference between two trees (T_T′–T_T) is small, the estimation error for g_hT should become large. Therefore, we used the data when $lE_{T}$ > 50 W m⁻² and the temperature difference (T_T′–T_T) > 1 K, respectively, for the g_hT estimation. In the figure, the g_h value of an individual leaf from tree A was also plotted for the comparison. The wind speed for the individual leaf was measured at a distance 0.3 m from the leaf. The wind speed ranged from 1.1 to 2.5 m s⁻¹ for the tree crown, and from 0.4 to 2.0 m s⁻¹ for the individual leaf, respectively. The main findings with this figure obtained from Asawa et al. (2016) are as follows.

Fig. 6

Estimation result of the boundary-layer heat conductance (g_hT) per leaf area of the tree crown with the relationship to the wind speed outside the tree crown. The g_h value of an individual leaf of tree A was also plotted. Both results were estimated in Asawa et al. (2016)

The g_hT value of the tree crown and the g_h value of the individual leaf both increased with the wind speed, and the plots almost overlapped. By applying linear regression, the slopes were found to be almost equivalent, and the intercepts differed by only 1 W m⁻² K⁻¹. This difference is considered to be derived from the difference in the measurement positions of wind speed (i.e., the wind speed outside the tree crown was higher than that near the leaf owing to the drag-force effect of the tree crown). The coefficients of determination, R,² were 0.56 for the tree crown and 0.77 for the individual leaf. Although the R² value of the tree crown is smaller than that of the individual leaf, there is a clear relationship between the wind speed and g_hT for the tree crown. These results show that the g_hT value was effectively estimated with the HB-TS method by using the $E_{T}$ value and the foliage temperature difference (T_T′–T_T).

4.3 Whole-Tree Transpiration Rate (E_T)

Figure 7 shows the E_T value of tree A from 21 to 30 August, 2010. Here, E_T was estimated per hour per leaf area to check hourly and daily changes. In this figure, soil–water content, photosynthetic photon flux density, vapour-pressure deficit, air temperature, and wind speed are also shown. Clear skies and high temperatures (> 32 °C) occurred over the entire period. For the dry-down experiment within the period, irrigation was stopped from 24 to 26 August, and was continued on the other days. From 21 to 23 August, when sufficient irrigation had been supplied, the E_T value increased with the photosynthetic photon flux density and vapour-pressure deficit. A peak in E_T occurred at around midday, from 1300 LST to 1500 LST. The timing was close to that of the vapour-pressure deficit and was delayed compared with the photosynthetic photon flux density. The E_T value reached a peak of over 250 g h⁻¹ m⁻² during the day. The same tendencies were obtained on 29 and 30 August, when sufficient irrigation was also supplied after the dry-down experiment. At night-time, the E_T value was close to 5 g h⁻¹ m⁻² for the entire period. During the dry-down experiment, the E_T value decreased with the reduction in the soil–water content. The reduction of soil–water content corresponded with the reduction in E_T. This result clearly shows that tree A closed stomata because of the drought stress during the dry-down experiment. The E_T value on 26 August was approximately one-third that on 23 August, with the pF value of the soil of tree A estimated at 4.5 on 26 August. We judged that the soil–water condition reached the permanent wilting point of plants on that day (26 August), and so resumed irrigation the next day (27 August). After 27 August, the E_T value recovered gradually within 3 days with sufficient soil water. By 29 August, the E_T value was well recovered. These results show that the change in E_T was adequately measured along with the soil–water content by the weighing lysimeter, and the E_T value differed three times under different soil–water content during successive sunny days.

Fig. 7

Whole-tree transpiration rate (E_T) of tree A per hour per leaf area from 21 August to 30 August. Soil–water content (W), photosynthetic photon flux density (PPFD), vapour-pressure deficit (VPD), air temperature (T_a), and wind speed (V) are also shown

4.4 Sensible and Latent Heat Fluxes of the Total Leaf Area (H_T, lE_T)

From the results of the T_T, g_hT, and E_T values of tree A, we estimated H_T and lE_T over the total leaf area to the atmosphere. We applied these results to Eq. 10 to estimate H_T. We compared two different days: 30 August, on which E_T was large with sufficient irrigation and higher soil–water content, and 26 August, on which E_T was small without irrigation and soil–water content was at its lowest because of the dry-down experiment. Figure 8e, f shows the H_T and lE_T values of tree A for both days. In this figure, global solar radiation per leaf area and wind speed near the tree (Fig. 8a, b), the difference between averaged foliage temperatures and air temperature (T_T–T_a), and the boundary-layer heat conductance (g_hT) over the total leaf area (Fig. 8c, d), are also depicted. On 26 August, the wind speed was higher than on 30 August; thus, the g_hT value was also larger. The value of (T_T–T_a) was greater on 26 August than on 30 August during the daytime owing to drought stress caused by the cease in irrigation. On 30 August, the peak of lE_T was over 80 W m⁻² at 1300 LST, and this value was approximately 2.5 times larger than that of H_T. The appearance of two peaks for H_T was equivalent to that of the solar radiation. The second peak of H_T appeared at 1300 LST, and the tendencies of H_T and lE_T were similar. These results imply that the solar energy received by the total leaf area was mainly converted to lE_T, and the rest was converted to H_T. During the daytime (from 0900 LST to 1600 LST), the Bowen ratio ($\beta = H_{T} /lE_{T}$) was 0.29 on average. During the night-time, the H_T and lE_T values were both very small, and H_T was negative. In contrast, for 26 August, the peak of H_T was approximately 80 W m⁻², 2.5 times larger than that of lE_T. The appearance of two peaks and the tendency of H_T were similar to those of the solar radiation. The $\beta$ value was 2.2 during the daytime. The tendencies of H_T and lE_T reversed between the 2 days under different irrigation conditions, and the $\beta$ value largely changed along with irrigation and soil–water conditions.

Fig. 8

Estimation results of the sensible heat flux (H_T) and latent heat flux (lE_T) per leaf area under different irrigation conditions (30 August with sufficient irrigation and 26 August without irrigation): a, b show solar radiation per leaf area (R_S) and wind speed (V); c, d show the difference between averaged foliage temperatures and air temperature (T_T–T_a), and boundary-layer heat conductance (g_hT) over the total leaf area; and e, f show sensible heat flux (H_T) and latent heat flux (lE_T)

5 Discussion

5.1 Energy Closure

For energy flux observations over forest sites, energy closure is verified by comparing the surface energy flux of H_T + lE_T with the available energy (R_n – G, where R_n is the net radiation and G is the storage heat flux) (Wilson et al. 2002b). The error shown in the H_T + lE_T estimation is known as the “imbalance problem” or “energy closure problem” (e.g., Mahrt 1998; Moriwaki and Kanda 2004). Wilson et al. (2002b) reported that the lack of energy closure at FLUXNET sites was about 20% on average. In contrast to energy flux observations over forest sites, the present observation cannot apply the same energy closure method because one-dimensional energy fluxes cannot be assumed over the total leaf area of an isolated tree. Therefore, we directly compared H_T + lE_T between different days with similar solar radiation and different water content conditions (30 August and 26 August).

Table 1 shows the daily solar radiation (R_S), daily H_T, daily lE_T, and daily H_T + lE_T for both days. For the total leaf area of an isolated tree, R_n–G is not quantifiable. Therefore, R_S was used to check the similarity of the radiation environment (R_n) between the 2 days. G is considered to be very small and negligible for the foliage of the tree crown, because changes in T_T closely followed corresponding changes in R_S, without any significant delays, as shown in Fig. 5. From Table 1, although the daily H_T and daily lE_T values changed significantly because of different soil–water content (W) on the 2 days, the difference in daily H_T + lE_T was approximately 1%. The 2 days had similar daily R_S values. There is a limitation in that this is only the comparison between 2 days that had full sets of measurements; however, the energy closure is more precise than that of flux observations over forest sites (Wilson et al. 2002b). This result shows the energy was appropriately close on the 2 days, and this result is sufficiently accurate for discussing the characteristics of H_T and lE_T.

Table 1 Daily solar radiation (R_S), daily H_T, daily lE_T, and daily H_T + lE_T on 30 August and 26 August. All results were estimated per leaf area

5.2 Comparison with Flux Data over Forests

Wilson et al. (2002a) reported the results of energy partitioning between lE and H during the warm season at FLUXNET (a global network of micrometeorological flux measurement based on the eddy-covariance method) sites with different climatic regions and forest types. Of the different forest and agricultural sites, deciduous forest had the lowest value of $\beta$ (0.25–0.50), equivalent to that of agricultural sites. The value of $\beta$ obtained in the present study is 0.29 under irrigated conditions, which is almost the same as that of the deciduous forest sites. For the interannual variation in $\beta$ at individual sites, drought was one expected source (Wilson et al. 2002a). Baldocchi (1997) observed the effects of soil moisture deficits and high temperature stress on lE values over a temperate broad-leaved forest. There was no great change in lE values from the growing season (well-watered season) to the drought season, despite large changes in the canopy drought-stress index. Even during a period in which the lowest pre-down water potentials were experienced, the lE values were 25% lower than that during the well-watered period, as the forest had experienced a prolonged period of soil-moisture deficit. The same finding was also reported by Greco and Baldocchi (1996) and Oliphant et al. (2004), and the effectiveness of deep roots in sourcing water stored in the soil column was also suggested (Baldocchi 1997; Oliphant et al. 2004). Wilson and Baldocchi (2000) reported that the daytime $\beta$ value during the drought stress period (in 1995) for broad-leaved temperate deciduous forest was about twice that during the wetter periods (in 1996 and 1997). In contrast, the present study shows that the lE_T value was reduced by 60% owing to drought stress for an isolated tree. In addition, the daytime $\beta$ value on the drought day (26 August) was 7.6 times larger than that on the wetter day (30 August). The great reduction in lE_T can be explained by the characteristics of the urban-unique conditions of tree planting (i.e., drought stress from a large vapour-pressure deficit and limits to water supply, soil volume, and root space) (see Sect. 5.3). For a deciduous forest, such a dramatic change in H_T and lE_T was only observed before and after leaf emergence within about a 6–8 week period (Wilson and Baldocchi 2000). However, the present results suggest that dramatic changes to H_T and lE_T for isolated trees can occur within several days in urban environments.

5.3 Comparison with Flux Data for Urban Sites

Next, our results are compared with flux measurements for urban sites. The value for $\beta$ in previous studies mainly ranged between 1 and 5 for daytime conditions at different urban sites (Grimmond et al. 2009); meanwhile, in the present study, the $\beta$ value was 2.2 under drought conditions, which is within the range obtained previously at urban sites. Moriwaki and Kanda (2004) reported that $\beta$ at a residential area of Tokyo, Japan was 1.8 during daytime summer, which was smaller than the $\beta$ value for the drought condition in the present study. This means that the trees do not cool the urban atmosphere because of low transpiration rates under drought conditions; thus, urban trees reach drought conditions within a short period. Urban trees can be exposed to drought stress because of both high air temperatures and reduced water availability (Gillner et al. 2013; Savi et al. 2015), because impervious pavements prevent the infiltration of rainwater resulting in significantly lower soil–water content beneath these pavements (Morgenroth et al. 2013). In addition, compacted urban soils reduce infiltration by water and increase surface runoff (Yang and Zhang 2011). These phenomena are collectively known as the anthropogenic sealing of soils (Scalenghe and Marsan 2009). The present results, together with these findings, indicate the importance of regular irrigation or the sufficient utilization of rainwater to obtain a cooling effect from urban trees as well as maintain the health of the trees.

5.4 Oasis Effect

Moriwaki and Kanda (2004) reported that the lE value over a suburban area in Tokyo, Japan, was 183 W m⁻² at noon in summer, and was considered to be the area-averaged flux, including fluxes from both natural and artificial surfaces. The authors suggested that the lE value per unit of natural coverage (e.g., trees, shrubs, and bare soil) should be at 631 W m⁻², considering that 29% of the total land area was natural coverage, and the relatively high amount of evaporation is consistent with the oasis effect. For the present result, the lE_T value per unit ground area on the horizontal plane was a maximum of 400 W m⁻² under irrigated conditions and 160 W m⁻² under drought conditions. These results do not include evaporation from the ground; however, these results have much lower values than those observed by Moriwaki and Kanda (2004) at an urban site. The present results are inconsistent with this result. The verification of consistency between the transpiration of trees and area-averaged lE over urban sites is a possible subject for future research. We consider this inconsistency to be a very important topic for urban flux studies. Here, the next research question has been derived: what is the main source of transpiration in urban sites, indicated by Moriwaki and Kanda (2004)?

6 Conclusions

We have quantified both the sensible heat flux (H_T) and latent heat flux (lE_T) of the total leaf area of Z. Serrata in an outdoor environment during the Japanese summer. We applied the weighing-lysimeter method to quantify the whole-tree transpiration rate (E_T) and latent heat flux lE_T over successive days with different soil–water conditions. To estimate the boundary-layer heat conductance ($g_{hT}$) and $H_{T}$, we carefully applied the scaling-up approach of the heat-balance two-state (HB-TS) method from single leaves to a tree crown based on comprehensive literature reviews and theoretical considerations. Two sample trees were selected for the estimation, with similar crown shapes and leaf areas; the difference in leaf area was 10% between the two trees, expected to result in a 10% error in $H_{T}$ estimation. We varied soil–water conditions for the trees by controlling irrigation conditions to achieve the different foliage temperatures ($T_{T}$) and whole-tree transpiration (E_T) required for the HB-TS method.

The measurement of E_T during the dry-down experiment showed that its change corresponded well with the soil–water content, and E_T was successfully quantified using the weighing-lysimeter method. The E_T values differed three times during the dry-drown experiment within several days. We compared H_T and lE_T between two different days with different irrigation and soil–water conditions during the dry-down experiment. The most important result was that the tendencies of H_T and lE_T were reversed between these 2 days, and the Bowen ratio ($\beta = H_{T} /lE_{T}$) dramatically changed. The $\beta$ value was 0.29 for daytime with adequate irrigation, for the largest E_T value, and almost the same as that for deciduous forest sites (Wilson et al. 2002a). In contrast, the $\beta$ value was 2.2 during the daytime under drought conditions, with the smallest E_T value, and similar to results obtained from urban sites (Grimmond et al. 2009). From these informative findings, we indicated that the $\beta$ values of isolated trees in urban sites can change between forest-like values and urban-like values within a short time period owing to urban-unique conditions (e.g., large vapour-pressure deficit, limited water supply and root space, impervious pavements, and strong soil compaction). We suggested the importance of regular irrigation or the effective utilization of rain water not only for healthy growth of urban trees but also for allowing the cooling effect of the trees from transpiration. These data are expected to be applied for the optimization of irrigation control in urban landscapes, maintaining a cooling effect while minimizing the use of water resources. For urban meteorology, these data are expected to be used for the parameterization of g_hT, the modelling of the soil–plant–atmosphere continuum for urban trees, and the validation of simulated H_T and lE_T under different irrigation conditions.

Appendix

As shown in Fig. 7, the soil–water content corresponded well with the transpiration rate, as there was no intake nor drainage of water without transpiration when the irrigation was stopped. Figure 9 shows the measurement results of soil–water content and soil–water content change per hour for tree A′. For the irrigated period until 23 August, the soil–water content change was over 1.5% per hour during the daytime owing to the transpiration. The value decreased after the cease in irrigation on 24 August. On 27 August, the value became one-tenth of that on the irrigated days. To make sure the transpiration was completely (bio-physiologically) limited and negligible for g_hT and H_T estimation, we waited three more days. On 30 August, the value became one-twentieth of that on the irrigated days, as we expected. Therefore, we judged this day to be applicable to the estimation.

Fig. 9

Measurement results of soil water content (W) and soil water content change per hour (∆W) for tree A′. Gray bands show the period of irrigation