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URBAN HEAT BUDGET AND GEOMETRICAL STRUCTURE OF BUILDING CANOPY Hirofumi Sugawara*, Nobuhisa Yasuda**, Genichi Naito * Earth and Ocean Sciences, National Defense Academy of Japan, ** Geophysics, Tohoku University, Japan
*
Abstract We used theory and obs ervations to examine the heat exchange between the urban canopy layer and the overlaying atmosphere over 1-km horizontal scales . The heat budget parameters in an urban area depend on the geometry of the urban canopy. Here, we propose an estimation method for the heat budget parameters using city planning GIS data. The estimated parameters allow us to determine the surface heat flux within an estimated error of 45 Wm -2 and the surface temperature to within 1 °C. Analys es of the major cities in eastern Japan reveal that their canopy structures should influence their heat budget and thus could cause the heat island phenomena. Keywords: Heat budget, urban canopy, urban morphology 1. INTRODUCTION The heat island phenomenon is a result of complex processes in which many factors play a role. The building canopy structure is thought to be one of these factors; however, little is known about the effect of geometrical structure on the canopy heat budget during the day and at night. The purpose of this study is to determine how geometrical structures affect the heat budget of urban canopies. 2. HORIZONTAL SCALE IN ANALYSIS Auto correlation coefficient
A target scale must assess the whole urban canopy. This scale should be roughly one kilometer in size, according to 0.8 the following analysis . We analyzed the building height distribution using city planning data made by the Tokyo 0.4 City Planning Bureau. The auto-correlation and spatial power spectrum were then calculated for building heights 0 along the 7-km-long N-S and E-W baselines. Figure 1 shows the auto correlation coefficient along the E-W -0.4 baseline. We do not show the N-S baseline data, but it is 0 100 200 300 400 500 similar to the E-W data. The figure indicates a scale size in Horizontal distance [m] the city that is less than 40 m. This size equals that of a typical city block. Therefore, at least for the horizontal Fig.1 Auto correlation coefficient of building height along the 7-km long E-W baseline in highly built-up area, Tokyo. scale, one kilometer should be large enough to treat the complex urban area as a simple rough surface. Thus, the shape of each building is insignificant. 3. CALCULATION METHOD AND HEAT BUDGET PARAMETERS Here we calculate the heat budget of the representative surface of the urban canopy, which is the whole surface including the buildings and roads (Voogt and Oke, 1997). The temperature on that surface was determined to be the equivalent temperature for the upward longwave radiation flux. The surface heat budget is evaluated using a modified method of Matsushima and Kondo (1995). The surface heat budget is written as
(1 − α ) S + εL rad = H + lE + G + εσTs4
. (1)
The sensible heat flux H and latent heat flux lE can be parameterized as
H = C P ρa *
U Ts − T a rM rH
and (2)
Corresponding author address: Hirofumi SUGAWARA, Earth and Ocean Sciences, National Defense Academy of Japan, Yokosuka, Kanagawa 239-8686 Japan, e-mail:
[email protected]
lE = lρa
U (q sat (Ts ) − q a ) rM rE
. (3)
Here, rM, rH, and rE are the transfer resistances for momentum, sensible heat flux, and water vapor, respectively. Following Kondo (1992), we approximate the underground temperature using a cyclic function for the ground heat flux G: G= jωcρλ Tsj cos( jωt − φ + π 4 ) . (4)
∑ j
Here, Tsj is the amplitude of surface temperature at frequency ω, cρ is the heat capacity, and λ is the thermal conductance. Up to 20 diurnal components were included in the sum. These parameterizations transform (1) into an equation for surface temperature. For input, the calculation requires the diurnal variation in solar radiation, air temperature, wind speed, water vapor, and also the heat budget parameters: α, ε, cρλ, z 0, z T, and z q. These heat budget parameters were experimentally determined and their regression equation is made as a function of the geometry indexes. The results of the calculation are the diurnal variation in the heat flux and the surface temperature. 4. HEAT BUDGET PARAMETERS 4.1. Albedo (α ) The spectral upward radiation was measured during helicopter flights over Sapporo and Tokyo. From this data, the surface spectral reflectance was obtained by solving the radiation transfer equations for the radiation between the flight level and the ground surface. Then the albedo was determined by integrating the reflectance with the solar spectrum as a weighting function. The obtained albedo showed a good correlation to the sky view factor and thus we fitted a polynomial to their interdependence. 4.2. Stanton number 30 kB -1
field observation
20 10 0 1
kB-1/kB0-1
We used the eddy correlation method to make continuous measurements of the sensible heat flux over an urban canopy. At the same time, we measured the radiometric temperature of the canopy surface. For a total time of one month of data, we calculated the roughness length for the air temperature z T at 30-min intervals. The resulted kB-1 (ln(z 0/z T)) averaged 7.1 for the daytime and the diurnal amplitude was about 15. We estimated how kB-1 depends on the canopy geometrical structure using the wind-tunnel data from Narita et al. (2000). The latter study determined the sensible heat transfer coefficient at each surface component of model buildings (roofs, walls and canopy floor). We calculated the heat transfer coefficient over the canopy by averaging over the surface components, each weighted by its surface area. The resulting kB-1 is shown in Fig.2. The result of the filed observation was also shown. In the heat budget calculation, the roughness length for the temperature zT was evaluated using the data in Fig.2.
wind tunnel experiment in Narita et al. (2000)
0.8 0.6 0.4 0
0.2 0.4 0.6 0.8 sky view factor
1
Fig. 2 kB -1 over urban canopy. The wind tunnel experiments are from Narita et al. (2000).
4.3. Thermal property parameter (cρ λ ) The ground heat flux G was parameterized with the canopy thermal property parameter cρλ. In general, the cρλ of an urban canopy is larger than that of the building’s material because of the larger surface area in the canopy and the trapping of longwave radiation inside the canopy. The canopy value for cρλ was calculated using the canopy model applied to nocturnal radiative cooling (Sugawara et al., 2001). As input, this method needs the cρλ of the building materials; however, once those values are known, the method can handle any canyon shape. The calculated value for the canopy cρλ was consistent with the measured surface temperature during nocturnal cooling. 4.4. Other parameters The surface emissivity is unity here because the previously shown cρλ includes the effect of longwave radiation trapping. We determined the roughness length z 0 and zero-plane displacement z d using the method of Macdonald et al. (1998). 5. VALIDATION OF CALCULATION
This heat budget calculation was validated by the observed sensible heat flux. The areas analyzed for the validation included a roughly 80-km 2 area in central Tokyo and a 50-km 2 area near Sapporo. Aircraft observations of the atmospheric boundary layer heat budget were made, and the surface sensible heat fluxes were acquired as a residual. This method allows us to average over a wider area than that from using the eddy correlation method based on tower measurements. Cleugh and Grimmond (2001) also determined the surface sensible heat flux from the observed heat budget of an atmospheric boundary layer over a large area that included a city. Our method for evaluating the atmospheric boundary layer heat budget is as follows. The heat budget can be expressed as
QH − advection + H top + H '+Qcondensation + Qradiation = 0
, (5)
where QH-advection is the net horizontal advective flux, Htop is the vertical flux at the top of the boundary layer, and H’ is the surface sensible heat flux. Qcondensation is the latent heat of condensation and Qradiation is the net radiation flux. Here, H' is determined as a residual. Because there were no clouds during the observation period, Qcondensation was assumed to be zero. We assume a simple mixed layer model and determine the vertical flux Htop using the entrainment factor Ae:
H top = − Ae H '
. (6)
Ae was set to 0.1, in agreement with values noted in Stull (1988). The net horizontal advection flux QH-advection was calculated using
QH − advection = C P ρa ∫
Z top
0
δT Udz δx
,
(7)
heat flux [Wm- 2]
where δT is the temperature difference along the wind path. 400 T was measured using the helicopter’s on-board sensor. The M ar. 13, 1996 T oky o H mixed layer depth z top was determined from the profiles of 300 G potential temperature and wind speed. The radiative heating R net Qradiation was calculated from the air temperature and 200 H( B L budge t) humidity data. Uncertainties in the estimates of z top and 100 Qradiation and observational errors in U and δT result in a heat budget observation error of 45 W m -2. 0 Figure 3 shows the calculated and observed heat fluxes. In the calculation, we set the rE infinity because the -100 vegetation is only 7% of the target area. The radiometric temperature variability and parameter estimation error 0:00 6:00 12:00 18:00 0:00 resulted in a flux calculation error of 25 W m -2. This LST calculation is in good agreement with the observations. Fig. 3 Evaluated urban canopy heat budget. The solid circle is the sensible heat flux observed from the Therefore, the surface heat budget computation using boundary layer heat budget. The lines are calculation. surface parameters was confirmed to be accurate. The anthropogenic heat was ignored here, but it would be 20 to 50 W m -2 according to Ichinose et al. (1999). 6. CALCULATION SETTINGS
sky view factor
This study focuses on the effect of geometrical structure on the heat 1 B A balance. We did an off-line simulation as follows. We set up the t l o n p s 0.8 external conditions of the surface heat budget, specifically, the air D k e qj rg I temperature and wind speed, at the reference height of 30-m AGL. 0.6 bf a cd Thus, we can study different city structures in one local climate. uh 1x Typical summer conditions in Tokyo were used. Anthropogenic heat 14 m 0.4 8 vy6 C and evaporation are not considered here because the focus is on the 92 13 4 w geometrical structure. 0.2 7 11 3z15 10 Structure indices were determined in previous studies for 20 12 5 cities in the Kanto plain (Nakagawa and Nakayama, 1995), 13 areas 0 in Tokyo (Nakamura et al., 2000), 6 areas in Sendai (Kawamura et al., 0 0.2 0.4 0.6 0.8 1 2001), and one area in Sapporo. By grouping the data in Fig. 4, we roof area ratio classify city canopies into the following four groups: A normal urban Fig. 4 Morphological grouping for the cities in the eastern Japan. canopy (broken line A), An open canopy (B), A crowded canopy (C), and A rural canopy (D). Here, the roof area ratio is the ratio of the roof area, which is the building base area, to the total lot area including the building base area. 7. CALCULATION RESULTS We now examine the four groups of urban canopy structures. Figure 5 shows the daytime maximum value of the heat flux and surface temperature versus the roof area ratio for four groups in Fig. 4. The flux in Fig. 5 shows that the influence of the sky view factor on the flux, in order of high flux to low, is crowded, normal, open, and rural areas. Thus, the more crowded the canopy, the greater the ground heat flux. The daytime sensible heat flux
-4
c ρλ[J s k m ]
5.0E-03
3.0E-03 2.0E-03 1.0E-03
2 -1 -2
CH
4.0E-03 normal open crowded flat
0.0E+00 0.0
0.2
0.4 roof area ratio
0.6
0.8
Fig. 6 Sensible heat transfer coefficient used in the calculation.
4.7E+07 4.2E+07 3.7E+07 3.2E+07 2.7E+07 2.2E+07 1.7E+07 1.2E+07 7.0E+06 2.0E+06 0.0
normal open crowded flat
da y
0.8 0.6 0.4 0.2 0.8
0.4 0.2 0
0
0.2
0.4 0.6 roof area ratio
0.8
Fig. 7 Thermal property parameter of urban canopy used in the calculation.
0.4 ro of a rea ra tio
0.6
0.8
Fig.5 Heat flux dependency on the canopy structure.
28 27 26 25 24 23 22 21 20 19 18 40
0.2
crowded normal open flat rural
d ay
0.6
c anyon air tem p. [ o C]
6.0E-03
1
c any on air tem p. [o C]
H / R net
G/ R net
appears as an upward convex distribution for the roof area ratio. The daytime ground heat flux is also downward convex. Figure 6 shows the sensible heat transfer coefficient CH in neutral stability and Fig. 7 shows the thermal property parameter cρλ, both plotted to show their dependence on the roof area ratio. The maximum CH occurred for a roof area ratio of 0.35. Such a canopy structure causes the maximum sensible heat flux and facilitates the discharge of heat into the atmosphere. The value of cρλ also affects the peak position in daytime because a large cρλ increases the ground heat flux. Using these results, the air temperature inside a canopy was calculated from the heat budget of the canopy airmass. Figure 8 shows the daily maximum and minimum air temperatures. This figure shows the following. 1) The canyon air temperature is negatively correlated with the roof area ratio in daytime. 2) The air temperature can vary up to 12 ºC in the daytime and up to 7 ºC at night according to the canopy structure. 3) The temperatures in deeper canyons are higher due to the weak heat exchange with the overlaying air. 4) The air temperature difference from that of a flat rural canopy corresponds to the heat island intensity. Thus, the canopy structure produces a heat island at night.
no rmal ca nyo n crow de d can yon op en ca nyo n fl at rura l
night
day
36 32 28 24 0.1
0.2
0.3 0.4 roof area ratio
0.5
0.6
Fig. 8 Calculated air temperature inside canopy.
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