Journal of Heat Island Institute International Vol.7-2 (2012)
Academic Article
Field Measurement of the Energy Budget for an Isolated Plant Unit
Atsumasa Yoshida
Yumi Kataoka
Kosuke Nii
Shin’ichi Kinoshita
Osaka Prefecture University, Sakai, Osaka, JAPAN
Corresponding author email: ayoshida@me.osakafu-u.ac.jp
ABSTRACT
It is necessary to evaluate a green effect quantitatively to promote urban greening. The energy balance
of a plant is important information for thermal environment design. In urban spaces, a lot of isolated plants
(e.g., vegetation at individual residences and street trees) are seen. However, there are few studies of the
energy balance of such isolated plants, and useful data are hard to obtain. In this study, the energy balance of
an isolated plant unit was measured or expected, and a quantitative evaluation was performed for urban space
planning.
Introduction
The thermal environment in urban areas keeps
deteriorating due to the heat island phenomenon, which has
become aggravated in recent years. To solve this problem, the
role of plants was reviewed. For a quantitative forecast of the
climate-easing effect of plants, it is important to understand the
energy budget of the plant body. Much research has been
conducted thus far, and the basic data are from technical studies
of the energy budget of large-scale forest belts, meadows, and
plants for rooftop gardening (Kanda et al. 1997; Misaka et al.
2007). Few studies have been done on the energy budget of
isolated plants, such as those used in planting, gardening, and
street trees in urban spaces. In the present study, the energy
balance of an isolated plant unit was measured in the field, and a
quantitative evaluation was performed for urban space planning.
The plant units are shown in Figure 1. The camphor tree is
one of the wood species often used in Japan as a street tree. The
hibiscus is popular in Japan as a garden plant. The energy
budgets of the isolated single tree and the potted plant were
evaluated in the present study. The heat-transfer coefficient for
the leaf side and the evaporation efficiency of the water surface
are discussed.
(a) camphor tree
(b) hibiscus
Figure 1. Isolated tree and potted plant
- 142 -
Energy Budget for an Isolated Single Tree
temperature Tl, and vapor-pressure deficit D is shown in Figure
2 for the data from 2008. The vapor-pressure deficit D was
defined by the difference between the saturated water-vapor
pressure on the leaf side and the water-vapor pressure of the
atmosphere. Some correlation was found between the
transpiration rate and these weather conditions, respectively.
However, there was a comparatively large dispersion, and the
transpiration action was understood to be affected by the
combined influence of the various factors. Moreover, the
measured transpiration rate was only obtained for a single leaf.
Therefore, it is necessary to estimate the amount of transpiration
for the whole tree to evaluate the energy budget of a single tree,
as described later.
It is difficult to directly measure the amount of
transpiration and the radiation balance of a tree planted in an
urban area. A forecast model of the surrounding metrological
elements was examined, based on the fragmentary measured
results. A camphor tree was selected as the major target.
Prediction of Transpiration Rate for a Single Leaf
The physiological factors of the plant are related to the
factors that control evaporation and to the transpiration rate. For
instance, the transpiration rate approaches a constant incident
number of photons for solar irradiation, as shown in Figure 3 for
the data from 2005 to 2008.
The transpiration rate of a single leaf is generally
20
18
18
16
16
16
14
12
10
8
Jp [µ g/cm2 /s]
20
18
Jp [µ g/cm 2 /s]
20
14
12
10
8
14
12
10
8
6
6
6
4
4
4
2
2
2
0
0
20
200
400
600
800
1000
Q [ µ mol/s/cm2]
25
30
35
40
0
5
10
T l [℃]
(a) Photon number
15
20
25
camphor tree
20
15
10
5
200
400
600
800
1000
Solar radiation [W/m2]
Figure 3. Relationship between transpiration rate and solar irradiation
- 143 -
30
(c) Vapor-pressure deficit
Figure 2. Relationship between the transpiration rate of a single leaf of a camphor tree,
photon number, leaf temperature, and vapor-pressure deficit
0
25
D [hPa]
(b) Leaf temperature
Jp[ µ g/cm2/s]
Jp [µ g/cm2/s]
Measurement of Transpiration Rate of Single Leaf
The transpiration rate for each unit area of each leaf Jpobs
[μg/cm2/s] was obtained by using a diffusion-type polometer on
the site. Air temperature Ta, leaf temperature Tl, relative
humidity Rh, and photon number Q in a specific wavelength
region (400–700 nm) of solar irradiation effective for
photosynthesis were measured at the same time as the
surrounding metrological elements. The target tree was a
camphor tree, with height of about 10 m, on the campus of
Osaka Prefecture University. This kind of tree is widely planted
in urban parks and along streets.
The relationship between the transpiration rate Jp of a
single leaf of the camphor tree, photon number Q, leaf
35
40
expressed by the following equation.
Jp =
gb g s ( ρl − ρc )
gb + g s
(1)
where gb is the conductance of the boundary layer on the leaf
side, gs is the stomatal conductance, ρl is the water-vapor
concentration on the leaf side, and ρc is the water-vapor
concentration of the surrounding atmosphere, respectively.
The physics model that Jarvis (1976) proposed for
stomatal conductance was employed in the present study. For
Jarvis’s model, the stomatal conductance is shown by Eq. (2) as
a product of the independent function of photon number Q,
vapor-pressure deficit D, and leaf temperature Tl. Those values
were regularized so each function may also take the value of 0 to
1.
(2)
g s = g s max f1 (Q) f 2 ( D) f 3 (Tl )
The values of gsmax and the parameters in each function were
decided to suit the data according to the nonlinear least square
method. The transpiration rate Jppre was predicted by obtaining gs
by using these values and substituting the obtained value for Eq.
(1). Figure 4 shows the correlation between the actual data Jpobs
and the predicted values. As for the transpiration rate from a
single leaf, the prediction was found to be almost possible
according to the surrounding weather conditions.
Model of Radiation Transfer and Transpiration of a Single
Tree
In general, because the camphor tree grows thick and
spheroidal, its tree canopy was assumed to be a globe. The
influence of the branch and the trunk was disregarded. All leaves
were assumed to be attached parallel to the ground, and not to
interfere with each other. A double layer of the spherical shell
was adopted as a group of leaves. The leaf area index was set at
8.0. This index was defined as the ratio of the gross area of all
the leaves that exist in the upper side with the area of the ground
surface. In the globe shown in Figure 5, the axis of polar
coordinates (θ = 0o) was assumed to be in a perpendicular
direction, and the surface area was divided in the direction of the
zenithal angle θ and azimuthal angle φ at intervals of 5o,
Figure 4. Correlation between data and predicted values for the transpiration rate of a single leaf from a camphor tree
solar radiation
Z
θ dθ
θ= 0°
leaf
r dθ
camphor
canopy
y
inner layer
layer2
r
layer1
outer layer
r sinθdψ
x
reflection
ground
dψ
Figure 5. Outline of a tree model for a camphor tree
- 144 -
respectively. The radiation balance was estimated for each
element.
The solar-radiation transfer was handled separately for
two wavelength bands PAR (photosynthetically active radiation)
and NIR (near-infrared radiation). PAR is about 0.4 to 0.7 µm
effective for photosynthesis. NIR is a longer wavelength band
than PAR. The reflectivity (0.1 and 0.4) and the transmissivity
(0.1 and 0.5) of the plant leaf were greatly different in PAR and
NIR. Direct solar radiation accounted for 90% of global solar
radiation on a fine day, and the ratio was different for the two
wavelength bands. It was assumed that direct solar radiation is
equally received in the hemisphere in the incident direction. The
diffuse solar radiation from the sky and the ground was assumed
to be received in the upper and lower hemisphere, respectively.
The characteristics of the ground were assumed to be the same
as the reflection property of the leaves in the meadow where the
camphor tree was planted.
As for the infrared radiation, the sky radiation and the
emitted radiation from the leaves were considered in the upper
hemisphere, and the emitted radiation from the ground and
leaves was considered in the lower hemisphere; 0.98 was given
to the emissivity of the leaf and ground. Emissivity has been
reported to be more than 0.8, excluding metals (Yoshida et al.
2004). The surface temperature of the ground was equal to the
leaf temperature. The leaf temperature Tl [oC] was requested by
using the following empirical equation (Ikezawa et al. 1995),
expressed by air temperature Ta [oC] and horizontal total solar
radiation Sr [W/m2].
Tl = 0.882Ta + 0.0036 S r + 1.86
(3)
The transpiration rates Jppre for the unit area and the unit
time were requested by entering the metrological elements (e.g.,
air temperature, relative humidity, and solar radiation) into
Jarvis’s model (1976). Next, the amounts of transpiration for the
unit time of each leaf element were requested by multiplying the
element area by Jppre. The total amount of transpiration from the
tree was calculated as the sum of the elements. The validity of
the tree model was verified by comparing the amounts of
transpiration obtained in relation to the sap-flow speed, as
described later.
Estimated Energy Budget of an Isolated Single Tree
The energy budget was estimated using the meteorological
data measured on July 15, 2008 from 9:00 AM to 3:00 PM, at
intervals of 10 minutes. The amount of transpiration from a
camphor tree was calculated by the method described in the
previous paragraph. Latent heat flux lE was obtained by
multiplying the evaporative latent heat by the estimated value,
and dividing the projected area of the tree as seen from the sky.
Net radiation flux Rn was also obtained by this method. Because
the temperature difference on both sides of the leaf was small,
the conductive-heat flux and thermal storage were disregarded.
Sensible-heat flux H was assumed to be the remainder. Figure 6a
shows the time variation of the energy budget for a single
camphor tree. lE(model) in this figure means the estimated latent
heat flux. lE (measurement) means the latent heat flux obtained
from the measured result of the sap-flow speed, as explained in
the following section. Figure 6b shows each element of the
radiation balance. The absorbed amount of each wavelength
band of PAR and NIR was clarified for solar radiation. The
absorbed amount in the inner layer of the double spherical shell
layers (see Figure 5) is separately displayed. Infrared radiation
from the atmosphere and the leaves is displayed.
As shown in Figure 6a, the estimated latent-heat transfer
1400
1000
Heat flux [W/m 2]
2008/7/15
800
Rn
lE(model)
lE(mesurement)
H
600
400
1000
(leaves)
800
600
400
200
200
0
Radiation [W/m 2 ]
1200
Solar irradiation (total)
solar radiation
Absorbed absorption
solar radiation (total, double)
short wave radiation
(PAR, double)
PAR absorption(all)
(PAR, inner)
PAR absorption (surround)
NIR absorption (all)
(NIR, double)
NIR absorption (surround)
(NIR, inner)
atmosphericEmitted
radiation
infrared radiation (sky)
IR from leaf
10:00
10
12:00
12
14:00
14
0
8:00
8
Time
10:00
10
12:00
12
14:00
14
Time
(a) Energy balance components
(b) Radiation components
Figure 6. Estimated energy budget of an isolated camphor tree in daytime in the summer
- 145 -
16:00
16
accounted for 35% to 50% of the net radiation. It was clarified
that the sensible-heat transfer also played a key role in the
thermal transfer of the isolated single tree. A difference was
found between the energy budget of the isolated tree and that of
a colony tree (i.e., in a forest). It was understood that the ratio
for the net radiation of the latent-heat transfer was similar to that
for herb plant, described later. As shown in Figure 6b, it was
understood that the majority of the absorbed solar radiation to
the leaves was in the wavelength band of PAR, which influences
transpiration activity. It was shown that the absorbed radiation in
the outer layer of the double spherical shells (see Figure 5) was
predominant. The time variation of the infrared radiation was not
large, and the radiation cooling continued. The difference
between the leaf temperature and the air temperature was small
(i.e., about 1o C).
Measurement of Sap-Flow Speed in a Tree Trunk
The sap-flow speed in the trunk of a camphor tree was
measured using Granier’s (1987) method to verify the accuracy
of the amount of transpiration estimated by the tree model.
TDP-80 of Dynamax Co. was used for the measurement. Two
pairs of sensors of the T type thermocouple were arranged in the
device and were inserted into the tree trunk. The heater was built
into the upper sensor, and heat was given regularly. The
temperature difference between these two sensors was measured.
When the sap-flow speed stopped, the temperature difference
between the sensors was at its maximum. If the relationship
between the temperature difference and the sap-flow speed is
known, the calculation of the sap-flow speed can be easily
obtained. The amount of transpiration of a single tree can be
calculated by taking the cross-sectional distribution of the
sap-flow speed and integrating it with the cross section. The
measurements were taken at two points of the southern and
northern parts, at 70 mm and 15 mm from the surface, every
minute. The core sample was extracted to find the sectional area
in the sap wood through which the sap passed, and the area was
determined visually. The latent-heat transfer was obtained by
multiplying the sap-flow speed by the area. A ginkgo tree was
measured as well as a camphor tree.
Figure 7 shows the relationship between the latent-heat
transfer and the global solar irradiation obtained from the
sap-flow speed of a camphor tree and a ginkgo tree, respectively.
It was understood that the tree also consumed 20% to 30% of the
global solar irradiation as latent-heat transfer. Figure 6 shows the
latent-heat transfer lE (measurement) on July 15, obtained
according to the sap-flow speed. It roughly agreed with the
latent-heat transfer obtained according to the model, and the
validity of the tree model was confirmed.
Energy Budget of a Potted Plant
The energy budget of a potted plant was examined
outdoors. The radiation balance measured directly, without a
model. A hibiscus, which is a plant for general gardening, was
used as the examination target. The measurements were
performed in an open space on the campus of Osaka Prefecture
University. The diameter of the potted hibiscus was about 55 cm,
the height on the soil side of the pot was about 45 cm, and the
(a) Camphor tree
(b) Ginkgo tree
Figure 7. Relation between global solar irradiation and latent-heat transfer
Table 1 Measurement items and instruments
Items
Air temperature/Relative humidity
Leaf and ground temperature
Radiation flux
Wind velocity
Transpiration
- 146 -
Instruments
Thermohygrometer
Thermocouple
Net radiometer
Super sonic anemometer
Top-loading balance
leaf area index was 1.71. Enough water was given to the plant on
the morning of the measurement day, and the soil face in the pot
was covered with vinyl film. The electronic balance was
assessed every 30 minutes, and the amount of transpiration was
obtained. The measurement items and equipment are shown in
Table 1. All data, except for the transpiration rate, were recorded
with a data logger (EKO, SOLAC V) every minute. The
measurement height for air temperature, humidity, and wind
velocity was 1.0 m.
The net radiation in the potted plant was obtained as
follows.
(4)
Rn = S ↓ + L ↓ − Sp ↑ − Lp ↑
Rn = H + lE + G
(5)
where Rn is net radiation, S↓ is incident solar radiation, L↓ is
incident infrared radiation, Sp↑is reflected solar radiation from
the plant, Lp↑is emitted infrared radiation from the plant, H is
sensible-heat flux, lE is latent-heat flux and G is conductive-heat
flux [W/㎡]. The upward radiation on the plant canopy was
obtained by considering the influence of the sensors, excluding
the potted plant. The radiation balance on the bottom of the
canopy consisted of the transmitted solar radiation through the
plant canopy, the reflected solar radiation from the ground, and
the emitted infrared radiation from the bottom of the plant
canopy and the ground. The conduction-heat transfer in the plant
canopy was thought to be 0 because no difference was found
between the surface temperatures inside and outside the leaf.
Results for the energy budget of a pot-grown plant were
summarized. The evaluated time was 30 minutes. Figure 8
shows the ratio of the latent-heat transfer flux obtained by using
the projected area of the plant to the net radiation flux. The net
radiation flux has increased so that the absorbed radiation flux
received under the plant canopy could increase in the pot-grown
plant compared with the colony plant. However, the
transpiration rate had the tendency to reach the ceiling for the
solar radiation irradiated on account of the physiological traits of
the plant, as shown in Figure 3. Therefore, the ratio of the
latent-heat transfer flux to the net radiation flux was only about
50%, at most, even in summer, when transpiration is active, and
it decreased in autumn. The date when the daytime temperature
was greater than 25o C was expediently expressed as summer. It
has been reported that the latent-heat transfer accounted for
about 70% of the radiation transfer in a forest (Kanda et al.
1997). The ratio of the latent-heat transfer in the pot-grown plant
was obviously smaller than that in the forest. It agreed with the
aforementioned results for an isolated single camphor tree. The
results for the pot-grown plant also indicated that transpiration
control can be influenced through decreasing the soil moisture
content of the pot. It is estimated that the plant keeps its energy
balance by increasing the difference between leaf temperature
and air temperature as much as possible, and increasing the
sensible-heat transfer when stress caused by soil moisture or air
temperature is added. A maximum difference between leaf
temperature and air temperature of 7o C was observed,
depending on the weather conditions. This issue will be
examined in the future. From the aforementioned results, it is
necessary to pay attention not only to the transpiration action of
plant, but also to the sensible-heat transfer from the plant.
Heat Transfer Coefficient on Leaf Side
The heat-transfer coefficient on the leaf side was
examined in consideration of the active sensible-heat transfer
from the plant. First of all, the heat-transfer coefficient on the
leaf side of pot-grown plant was presumed on the basis of the
sensible-heat transfer of the crowd of leaves estimated from the
energy balance data. The measurements were executed using the
Figure 8. Relation between net solar radiation and latent-heat transfer of potted plant
- 147 -
potted hibiscus and a mock body of color and shape modeled on
a hibiscus and made of dry material (i.e., an artificial plant), on
November 21, 2007 and June 17, 2008. The artificial plant did
not have any transpiring action. Therefore, it was thought that
sensible-heat transfer would be more exactly appreciable for the
living plant. The exchange of sensible heat of the artificial plant
and the potted hibiscus was assumed to be performed on the leaf
front and the back. Thus, the heat-transfer coefficient of the leaf
side of the artificial plant and the potted hibiscus was calculated
from the difference between the sensible-heat transfer flux, the
leaf area index, and the temperature difference between the leaf
surface and the surrounding air, as shown by the following
equation.
a=
H
(Tl − Ta )× 2 × LAI
(6)
where α is heat-transfer coefficient [W/m2/K], H is sensible-heat
flux [W/m2], Tl is leaf temperature [oC] , Ta is air temperature
[oC] and LAI is leaf area index.
The heat-transfer coefficient of paper was measured
outdoors for a comparison with the potted plant. The
measurement was executed from summer to autumn in 2008
using black paper. The measurement place was the
aforementioned open space, and the measuring instruments and
the measurement items were the same as in Table 1. Paper of
various sizes was used to examine the effect of the size on the
heat-transfer coefficient. Figure 9 shows the averaged
heat-transfer coefficient for 30 minutes of the leaves of the
potted hibiscus and artificial plant, and the different sizes of
paper. The temperature difference between air and leaf of the
hibiscus was about 1° C to 5° C. The average leaf sizes of the
potted hibiscus and the artificial plant were about 5 cm and 7 cm,
respectively. The observed range of the wind speed narrowed
comparatively because the wind was weak on the measured
dates of the heat-transfer coefficients for the paper. It was
understood that the heat-transfer coefficients of the potted
hibiscus and artificial plant tended to be greater than those
obtained from Jurges’ formula expressed by Eq. (7), generally
used in the field of architectural engineering, or those obtained
from the empirical equation used in the heat-transfer field of
mechanical engineering.
α = 6.2 + 4.3U (wind speed U<4.9[m/s]、rough surface) (7)
It was confirmed that the heat-transfer coefficients
increased as the paper sizes decreased. The size of the leaf was
estimated to be one of the main reasons the heat-transfer
coefficient on the leaf side was larger than that on infinite flat
surface. The sensible-heat transfer flux of an isolated camphor
tree H was obtained from the rest term of the net radiation flux
and the latent heat flux was estimated by the physical model, as
explained in the preceding section, and then the heat-transfer
coefficient α was calculated using Eq. (6). Figure 10 shows the
results for a camphor tree. The heat-transfer coefficients of the
leaf side of the camphor tree were about 20 to 30 W/m2/K
against the surrounding wind speed of 0.5 to 1.5m/s, and were at
the same level as those of the potted plant. The heat-transfer
coefficients of the plant leaf and small piece of paper were larger
than the values obtained from the empirical equations. For a
physical explanation, it was determined that the thermal
boundary layer on the object side did not develop enough and
turbulent mixing with the main current was active. As a result,
the difference between the air temperature and the leaf
temperature tended to decrease. It will be necessary to assess the
correlation between the heat-transfer coefficient of the leaf and
the canopy structure in the future.
Figure 9. Heat-transfer coefficient for paper, a potted plant leaf, and an artificial plant leaf
- 148 -
Wind speed [m/s]
Figure 10. Heat-transfer coefficient of leaf of camphor tree
Evaporation Efficiency of an Isolated Tree and Potted
Plant
β=
The mass-transfer coefficient κ was obtained from Eq. (8)
by assuming an analogy with the heat-transfer coefficient α. The
evaporation efficiency β was calculated by using Eq. (9) from
the ratio of the evaporation rate of the camphor tree, estimated
according to the model or the measured value of the potted
hibiscus E and the product of mass-transfer coefficient κ and the
vapor-pressure deficit (Xs-Xa). The evaporation efficiency was
defined as a ratio of an actual transpiration rate to the
evaporation rate on the water surface.
κ=
α
C p × Le
(8)
E
κ × (X s − X a )
(9)
where κ is mass transfer coefficient [kg/m2/s], Cp is specific heat
of air [J/kg/K], Le is Lewes number (= 0.83), β is evaporation
efficiency, E is actual evaporation rate [kg/m2/s], Xs is saturated
absolute humidity at surface temperature [kg/kgDA] and Xa is
absolute humidity of air [kg/kgDA], respectively.
Figure 11 shows the evaporation efficiency of an isolated
camphor tree and potted hibiscus. The evaporation efficiency
was about 0.05 to 0.2 in daytime, regardless of solar irradiation.
The evaporation efficiency of a natural lawn with sufficient
watering and a water retentive pavement in daytime after water
Figure 11. Evaporation efficiency of an isolated tree and potted plant
- 149 -
sprinkling was reported to be 0.7 and 0.2-0.3, respectively
(Umeda et al. 2006; Misaka et al. 2007). The evaporation from
soil in addition to the transpiration from leaves was assumed to
be active in a natural lawn. These were used on the roof or the
road as mitigation countermeasures to decrease air temperature
in an urban area. However, evaporation from the soil under each
plant was not included in the present study. The isolated tree was
thought to contribute significantly to mitigation of the thermal
environment in an urban space, depending only on rainwater and
creating shade in summer, although the evaporation efficiency of
the tree was not large.
Japan, 669-670.
Yoshida Atsumasa, Sejima Takeshi and Washio Seiichi, 2004,
Development System on Radiative Properties of Solid Materials
in Infrared Region at Near Room Temperature, Proceedings of
the 7th Asian Thermophysical Properties Conference E028 1-13.
Umeda Kazuhiko, Fukao Hitoshi and Tamura Akihiro, 2006,
Basic Investigation on Transpiration of a Tree in Summer for
Evaluation of Thermal Environments, Journal of Environmental
Engineering (Transactions of AIJ) No.601 15-20.
Summary
(Received Feb 9, 2012, Accepted Oct 10, 2012)
1. The latent heat-transfer of an isolated tree and potted plant
occupied 50% at most of the radiation transfer, and the
sensible-heat transfer played an important role with respect
to the energy balance of the plants.
2. It was found that the heat-transfer coefficient on the leaf side
was greater than that on the semi-infinite flat plate. One of
the main causes is thought to be the small size of the leaf,
based on the theory of boundary layers.
3. The evaporation efficiency of the tree was less than that of a
natural lawn, including evaporation from the soil, but it did
not change greatly as a result to solar irradiation.
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