Prediction of urban air temperature variations using the analytical CTTC model

Energy and Buildings, 14 (1990) 313 - 324

313

Prediction of Urban Air Temperature Variations using the Analytical CTTCModel HANNA SWAID and MILO E. HOFFMAN National Building Research Institute, Faculty o f Civil Engineering, Technion -- Israel Institute o f Technology, Haifa 32 000 (Israel) (Received May 17, 1989; accepted October 23, 1989; revised paper received February 20, 1990)

ABSTRACT

The impact of buildings on the thermal climate in built.up environments is considered. Urban geometry, construction details and thermal characteristics o f typical urban fabrics are investigated in connection with their role in the evolution and intensity o f urban-rural and intra-urban thermal differences. In consequence, the cluster thermal time constant (CTTC) analytical model for predicting air temperature variations in the urban canopy layer (UCL) is developed. The CTTC parameter, which expresses the thermal inertia o f urban landscapes, is virtually proportional to the urban surface area within the UCL relative to the plot area of the neighbourhood. This model simulates, with good agreement, air temperature measurements conducted over a fair-weather summer period in selected clusters at the city centre of Jerusalem (c. 750 m above sea-level, 32 °N, 34 °E). Consistent intercluster differences of up to 4 K were observed, and consequently calculated by CTTC model simulation. Neighbourhoods characterized by extensive shaded area and high CTTC parameter exhibited negative heat-island (cool-island) intensities over most o f the day and positive intensities at night.

factors evolved by intuition or from case studies, and thus lack general predictive potential. Nevertheless, the nocturnal heatisland development and intensity in large mid-latitude cities under calm, clear summer conditions were attributed to reduced longwave radiation loss and increased sub-surface heat storage in the UCL compared with rural environments [2, 3]. Urban geometry and differences in surface thermal characteristics are responsible for these mechanisms, respectively. The features of daytime urbanrural temperature anomalies were less studied and are still unclear. In this work, the climatic effects of urban geometry, construction details and contrasts in thermal ~properties of surfaces and substrate materials are investigated. On the strength of our STTC (surface thermal time constant) model [4], the analytical cluster thermal time constant (CTTC) model for predicting diurnal air temperature variations in the UCL is developed. In its final form, the established CTTC analytical model is capable of producing forecasts and estimates of future climatic patterns in planned builtup environments. Air-temperature measurements conducted under typical fair-weather summer conditions in Jerusalem were used in validating the proposed model.

1. INTRODUCTION

2. THEORY

The existence of urban-rural and intraurban air temperature differences has been extensively reported and documented for many cities [1]. Oke [2] listed seven causative factors of the heat-island phenomenon in the urban canopy layer (UCL) suggested by urban meteorologists. Most of these

2.1. The CTTC parameter Figure 1 shows a homogeneous ground-air system in two thermal-equilibrium cases. Initially, as shown in Fig. l(a), no solar radiation impinges on the ground surface and a uniform temperature profile is assumed throughout the diurnal participating ground

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314 AI

.To, 2

°rc, I

I

/

Os,1 I

x-O

Os,z.

[ (penetration depth) t

8i, 1 =0

I

8i,z=O

(a)

ao(x,t)

(b)

Fig. 1. Schematic representation of participating ground layer-air system in two thermal equilibrium situations: (a) initial; (b) final.

layer. At time t = 0, a step change of magnitude A/ in solar radiation occurs and part of it, mA/, is absorbed on the ground surface. As a consequence, the groundsurface and air temperatures rise, and eventually a new thermal equilibrium is achieved, as shown in Fig. l(b). In extended areas with horizontal homogeneity where advection may be considered negligible, temperature variations are affected only by local conditions. Assuming an impervious ground surface with insignificant evaporation, the heat balance there at t > 0 can be written in the form:

oo
=

mAI+

h [ T a ( t ) --

-- INLWR(t)

=

Ta. 1 + ATa"(t)

o,(t) = 0,.~

A0, (t)

[ (

a20(x,t)

- ~

(1)

(2)

(3)

(4)

(5)

ax 2

by the method explained in the Appendix of ref. 4, yields an expression for the time pattern of the surface temperature rise beginning with t = 0 as follows: A0,"(t) = (mAllh) X L/k 1 -- exp

•

1/h + L/k L/h

+

STT

STTC(1/h + L/k) X

f

ATa"(k)exp" STTC

dk

k=0

(6) where STTC, the surface thermal time constant, is given by: 1

The left-hand side of eqn. (1) represents conduction from the surface to the ground (storage), and the right-hand side represents the solar-radiation absorption, heat-convection flux and net long-wave radiation flux exchange between the surface and the atmosphere. Sharlin and Hoffman [5] found that the time pattern of air temperature rise in response to a step change of magnitude m A / in the absorbed solar radiation at the ground surface at t = 0, can be expressed by an exponential response function, namely, ATa"(t) = m A / 1 -- exp •

at

STTC= gL0c x

O,(t)]

where

Ta(t)

and proposed an experimental procedure to determine the CTTC parameter of existing clusters* in the Tel-Aviv coastal urban complex. Assuming invariant temperature at the b o t t o m of the participating layer (penetration depth, x = L) and constant INLWR flux at the surface, the solution of Fourier's one
L I 1/h U/h+-L/k )

On the basis of eqns. (6), (4) and (2), the variation of the heat conduction flux into the ground over its initial steady-state magnitude, for sufficiently long periods of time (t > STTC) can be expressed in the form:

[(

AQG ( t ) - 1/h + L/k + ~Lpc(L/k)

1-- exp -- STT exp -t

÷

1

LpetL/k)"

(

1 + c

X exp -- STTC + CTTC

rc

)1

(7)

*"cluster" refers to a grouping or mmemblage o f buildings on a site having specific geometrical, thermal, and airflow characteristics.

315

A n interesting feature of the heat storage rate is that it leads the m a x i m u m surface temperature by 1/8 of a period (3 hours) for periodic diurnal cycles [6, 7]. At the final thermal equilibrium situation (Fig. l(b)) the long-term rise of surface temperature, as can be inferred from eqn. (6), is: A0s"(t -~ oo) = 2(mAI/h) × L/k

(8)

1/h + L/k With a linear temperature profile developed through the participating layer, the steadystate conduction flux (increase) is given by: AQG"(t ~ oo) = (k/L)(Os.2 -- 0i) -

2(reAl~h) 1/h + L/k

(9) Knowing that CTTC ~ STTC (experimentally determined CTTCs [5] compared with analytically calculated STTCs [4]), the time interval t = CTTC + STTC is considered sufficiently long for development o f the steadystate conduction flux as per eqn. (9). Substituting t = CTTC + STTC in eqn. (7) and equating with eqn. (9), we obtain the CTTC parameter of homogeneous soil (see Appendix): 1 CTTC = ~ L p c ( L / k ) (10) The CTTC is stored in the per unit change In the case of is given by:

defined as the heat energy participating ground layer in the heat flux through it. two-layered soft, the CTTC

L2 + (1/2Llplcl + 1/2L2p2c2) -~2

(11)*

The penetration depth o f the temperature cycle into homogeneous soil is given by [8, 9]: L =

(12)

\pc~

*In the general c u e o f n-layered soil the CTTC is given by:

" t=1

[1 L~ \~

K!

L_.j~ jffil+!

kj!

where n is counted from the surface inwards.

where C is a constant proportional to the size of the cycle (diurnal, annual) and to the assumed temperature profile through the participating layer (linear, parabolic, etc.). Substituting the above in eqn. (10) we find: 1 CTTC = --C 2 = constant (13) 2 which means that the CTTC p a r a m e t e r representing the inertia of the active thermal mass in a locality to air temperature variations -- is constant irrespective of the thermal properties of the substrate material, provided the ground surface is impervious. Multilayered soil has the same CTTC as per eqn. (13), because it is always possible to find a homogeneous equivalent soil subject to the same depth of penetration as the layered soil. This finding was verified experimentally by reconsideration of temperature measurements of three contrasting surfaces reported in a previous publication [4]. CTTCs of bare dry soil, 5 cm asphalt pavement and 10 cm concrete slab-on-grade were calculated. Results are presented in Table 1. The minor discrepancies between the calculated CTTCs are due to experimental inaccuracy in determining the penetration depths and thermal properties of the substrate materials. A value of 8 h is adopted later on for the CTTC of impervious grounds and massive building walls. Buildings covering part of the ground in a built-up environment render that particular part thermally inert (by preventing immediate contact with radiation and the outside air) while their external walls contribute extra active mass to the locality. This concept is presented schematically, for an ideal urban vertical cross-section (consiting of repeated symmetrical urban street canyons), in Fig. 2. The CTTCs of typical external building walls in Israeli cities were also calculated and included in the above Table. CTTC o f massive external walls (e.g., stone masonry) is the same as for semi-infinite soil (8 h) while less massive ones (e.g., concrete or hollow concrete bricks) have a value of about six hours. The CTTC of a built-up environment can now be evaluated on the basis of its geometry (building density and relative external wall area) and construction details (type of representative external wall) as follows [10]:

316

TABLE 1 Surface and cluster thermal time constants (STTC and CTTC) of bare dry soil, asphalt pavement, concrete slabon-grade, and of typical stone and concrete external walls Element and description

STTC* (h)

CTTC (h)

Bare soil: homogeneous bare dry soil** Asphalt pavements: 5 cm thick asphalt pavement on ground** Concrete pavement: 10 cm thick concrete slab-on-grade** Typical stone wall: external 5 cm thick stones, 14 cm c(mcrete and internal 10 cm thick hollow concrete bricks*** Concrete wall: 20 cm thick concrete wall***

1.3 1.8 2.2

8.6 8.1 7.9

2.5 2.1

8.0 6.3

*Calculated with h = 16 W/m2 K. **For further details see Swaid and Hoffman [4]. ***Theoretical values.

~',

// Thermal aclwe surface --

Thermol inert surfoca

Building

Street

L F

o

,± --r

w

_L T

Fig. 2. Vertical crou-seetion in typical urban street canyon. 0 = tan-1 (/-//0.5 W).

introduced by using eqn. (15) is not serious since the diffuse fraction is such a small component of the global solar irradiance. This simplification will be overlooked in our future work when dealing with more familiar, non-ideal weather conditions. Air temperature rise in a built-up environment in response to a general change in solar radiation intensity beginning with t = 0 can now be expressed, making use of eqn. (4) and the superposition integral [11], in the form:

(CTTC)BE = (1 - - FA/S)(CTTC)ground + (WA/S)(CTTC)wam

(14)

where (1 -- FA/S) is the partial open-space area (streets and courtyards) and (WA/S) the external wall area relative to the plot area (the thermal mass of the roofs is disregarded). In densely built-up clusters with uniform building heights and deep street canyons, only weak coupling is assumed between the thermal processes at mean roof level and ground level in daytime. The shading effect of the buildings reduces solar radiation absorption on the ground surface. The mean direct solar radiation intensity incident on the open-space surfaces of a built-up environment is determined according to the partial shaded area, namely,

Ip~,.(t) = I(t)[1 -- PSA(t)]

(15)

This relation does not describe the availability of the diffuse component of the solar irradiance. As our datasets used in the experimental verification of the proposed model are still restricted to fair-weather conditions (clear skies and weak airflow), the error

A Ta,soh~( t )

? t m alper~(t) J h aX k=O X [1--exp(

CTTC]j-t---X/ld]~ (16)

or in summation form: ATuo~(t ) =

t

m~Jp~(k)

~,--0

h (17)

where CTTC is as per eqn. (14) and as per eqn. (15).

Ip~(t)

2.2. N L WR contribution to air temperature variations The net long-wave radiation exchange flux, INLWa, was considered constant in eqn. (1). This enabled us to evaluate the contribution of changes in solar-radiation absorption to air temperature variation separately. Assuming the emissivity of all urban canopy layer

317 TABLE 2 Comparison between NLWR exchange fluxes for bare dry soil, asphalt pavement and concrete slab-on-grade as calculated by eqns. (18) and (19) Time (h)

Air temp. (oC)

05:00 06:00 08:00 13:00 14:00

17.5 17.0 16.0 21.5 22.0

Surface temp. (°C) Soft

Asphalt

14

14

36

34.5

(eo0s 4 - - aBrTa4) * (W/m 2) Concrete

Soil

Asphalt

Concrete

12.2

32

oTa4 -- oSrTa 4

(W/m 2)

75 86

86

188

179

174 150

*Calculations done with e = 0.9 and B r = 0.65.

(UCL) surfaces is uniform and equals that of a blackbody (e = 1), the mean canopy layer net outgoing long-wave radiation flux can be written as [10, 12, 13] : INLWR(t) = ( a T a 4 - -

oBrTa4)SVF

(18)

where SVF is the sky-view factor as developed by Oke [13, 14] and Ta is expressed in K. Generally, the (dimensionless) SVF expresses the extent to which any point on a surface is open to the sky. Here it is used as a measure of the mean openness of UCL surfaces to the sky long-wave radiation sink. Assuming that the street c a n y o n is the basic geometric unit of the urban physical structure and that the urban crosssection consists of such repeated units, the SVF is proportional to the ratio (H/W) where H is the average height of the c a n y o n walls and W the mean street width (see Fig. 2; (H/W) is often referred to as the " m e a n aspect ratio" of a canyon). The INLWR term in eqn. (18) was calculated for three adjoining surfaces described in ref. 4. Furthermore, it was compared in Table 2 with NLWR fluxes of the same surfaces as calculated by the formulation proposed by Sharlin and Hoffman [ 5 ], namely, INLWR(t) = (eO0s4 --

oBrTa4)SVF

(oTa4 oBrTa4)SVF -

ATNLvm(t) =

-

h

(20)

h being the mean overall heat transfer coefficient at the surfaces (h = he + hr). At night (usually between 20:00 and 06:00), cooling of the unobstructed (relative to the outer space sink) r o o f surfaces of densely built-up clusters with deep street canyons (high H/W) is stronger than that of the obstructed canopy surfaces due to greater NLWR flux loss from the former. Consequently, canyon air is warmer than the air layer at roof level. Buoyancy forces generated by this unstable thermal stratification cause cold air to descend from r o o f level to ground level, thereby accelerating air cooling near the ground. Such a process was described qualitatively by Givoni [15]. With this "nocturnal coM-air drainage" established, the contribution of NLWR loss to c a n y o n temperature at night is governed by the partial area of the roof surfaces (FA/S) and the sky-view factors of both the canyon and r o o f surfaces, namely,

/tTNLwR(t)= (aTa4--aBrTa4)SVF(I_ ? )

(19)

where 0s and Ta are likewise expressed in K. According to our formulation the NLWR flux is almost invariant over a day, while varying w i t h i n 100% of its minimum value according to the latter. The contribution of the NLWR exchange flux between the canopy layer surfaces and the atmosphere to the ground-level air temperature is given by:

(21) where SVF' is the sky-viewfactor of the roof surfaces (obstruction due to topography) and hR~~ the overall heat transfer coefficient at roof surfaces. The cooling effect obtained by eqn. (21) would be used in predicting nocturnal air temperature variation as long as its value exceeds that obtained by eqn.

318

(20), i.e., all over the period during which the combined cooling contribution of r o o f t o p and street-surface emissions is more efficient than the radiation emitted by street surfaces alone. 2.3. C T T C m o d e l

The contribution of solar and long-wave radiation to air temperature variation in the UCL during fair-weather periods can be integrated in the analytical CTTC model. Urban air temperature at time t can be expressed by [ 5 ] : Ta(t) = To + ATa.sohr(t) - - ATNLwR(t)

(22)

where To is the base (background) temperature for regional air temperature variation (to be explained later). The solar radiation contribution AT~,johr(t) is calculated by means of eqn. (17), and the NLWR contribution by eqn. (20). In densely built-up clusters with deep street canyons, the nocturnal contribution of the NLWR flux is given b y eqn. (21).

3. EXPERIMENTAL PROCEDURE

Fig. 3. Study area of Jerusalem.

In the summer ( A u g u s t - S e p t e m b e r ) of 1986, series of climatological observations were conducted in the city of Jerusalem. Three clusters in the city centre (JQ - - t h e Jewish Quarter of the old city, MR the Ben Yehuda mall, AA -- Abu-al-Afia) and a traverse route connecting them were chosen, as representatives of different urban forms and geometries subject to the constraints of undulating relief, insignificant anthropogenic heat release (including that of m o t o r traffic) and transpiring surfaces. Selected measurements taken under clear and calm conditions (12 14 September, less than t w o octas mean cloud cover and mean wind speed less than 2 m/s, as monitored in the studied clusters) were use in the validation study of the proposed CTTC model. Concurrently, official climatological observations (run by the Israel Meteorological Service) at Atarot Airport were also used. The study area is shown in Fig. 3. Three permanent stations, equipped with thermo-hygrographs and m a x i m u m - m i n i m u m thermometers, were used for recording standard screen height air temperatures in -

-

-

the studied clusters. A fourth station was m o u n t e d on the r o o f of a five-storey building in the city centre. The measurement programme involved also air-temperature measuring trips (walks) every t w o and three hours during the day and at night, respectively. Unobstructed solar-radiation intensity was measured continuously with a pyranometer at the r o o f station. Wind speeds at two metres above the ground were measured continuously in each cluster next to the local station. Representative mean groundsurface absorptivity was experimentally obtained from measurements of solar radiation (incident global radiation and reflected by the ground surface) in each cluster. In parallel, a comprehensive urban survey, including assessment of the time pattern of the partial shaded area, was undertaken. The relevant urban variables are given in Table 3. The mean overall heat transfer coefficient at the UCL surfaces was calculated according to the 1970 I.H.V.E. Guide [16], namely, h = 9.8 + 4.1u(t)

(23)

319 TABLE

3

Urban variables of JQ, M R and A A clusters,extracted from the urban survey

Cluster

FAIS

WA/S

H! W

CTTC (h)

SVF**

SVF'

m

JQ MR AA

0.7 0.55 0.65

0.7 0.39 0.25

1.1 0.75 0.58

8 6.7 4.8

0.41 0.55 0.65

0.9 1 0.85

0.6 0.6 0.65

*Mean aspect ratio. **Calculated according to Oke [ 14 ].

while at roof level (hRoof) it was taken as 22.7 W/(m 2 K) corresponding to 3.35 m/s mean wind speed [17]. The Brunt number (Br), which represents the ratio of radiant energy emitted by the air to the energy emitted by a blackbody at the same temperature, was found to be 0.65 during the analysis period.

4. RESULTS AND DISCUSSION

Mean hourly solar irradiance on the ground surface (Ip~r~(t)), partial unshaded area (PUSA(t) = 1 -- PSA(t)) and wind speed at 2 m height (u) for the studied clusters are shown in Figs. 4- 6. Daily mean wind speeds of 1.25, 1.75, and 1.5 m/s were recorded in the JQ, M R and A A clusters, respectively, corresponding to daily mean overall heat transfer coefficients of 15, 17 and 16 W / ( m 2 K). The highest mean partial shaded area (P-gX) between 10:00 - 14:00 was in the JQ (43%, due to the high building density and aspect ratio of the street canyons) followed by the MR (PSA) = 38%) and AA (iS~-A) = 32%). • ~lati~

600-

intt~Sity

Figures 7 - 9 show the calculated contribution of solar-radiation absorption to hourly air temperature variation A T = , , o ~ ( t - - t m ~ , as compared with measured mean variations, A T a ( t - - t ' m ~ ) , beginning with the hour of daily minimum (t "m=) in each cluster. Generally, there is reasonable agreement between A Ta,so~r( t -- t m ~ , and A Ta( t -- t "mm}, especially during the day (05:00- 18:00) where air temperature variations are basically governed by solar-radiation absorption. As the expression for AT~,,ohr(t) does not in600-

I

• Radiation intensity

i

• Hind speed 500-

v

400-

,e

3oo-

3~

~- ~oo

,~

2 -~

0

.....

0

~

4

~

6

e

~

t~].metZ{hr ]~4

16

-

Is

~

ZO

•0

0

22

24

Fig. 5. Daily variation of hourly mean solar irradiance on ground surface, partial unshaded area and wind speed at 2 m above ground over the study period: MR cluster. ~00-

I ~idiition intensity

.8 400 -

4OO

i

8

6

300

300

3i

zoofi

/..f

~.

~

~-+-2 -

!

,4 <

~

.3~,

f/

.6

-

g too -

0

0

2

4

6

9

0 2 4 Tlme [m"

6

9

20

22

0

24

Fig. 4. Daily variation of hourly mean solar irradiance on ground surface, partial unshaded area and wind speed at 2 m above ground over the study period: JQ cluster.

o

-

2

4

6

9

i

0 2 4 Time [hr]

-o

15 .

9

?0

~2

Fig. 6. Daily variation of hourly mean solar irradiance on ground surface, partial unshaded area and wind speed at 2 m above ground over the study period: AA cluster.

320 9'" • Measured

AA

D MR

o JO

B7-

54-

g

oa

32li

i

'2 '4 ~- ~ I~imelZ ~,[hriB

o"

1~

~o h u

Fig. 7. A T u o l ~ ( t - - t ~ n ) vs. measured air temperature variation relative to local daily m i n i m u m : JQ cluster. 10 •

~asureO

99"-}

7-

g

5-

•

3-

'~

o

', ~

i

i

'8 i~imei2 ,,[hri6 ]B

~o

~2

2,

Fig. 8. ATa, s o l ~ ( t - - t r ~ n ) vs. measured air temperature variation relative to local dally m i n i m u m : MR cluster. tS

t4"

•

Moasured

t3t2" i

i09a7654324 i-4 0

i

z

i

4

-~

6

i

B

i

~o

i

~2

Time

i

14

i

~6 [hr]

i

~B

!_

2o

i

2~

~i

Fig. 9. AT~solar(t--train) vs. measured air temperature variation relative to local daily m i n i m u m : A A cluster.

corporate the cooling effect of NLWR exchange, the calculated temperature changes shown in Figs. 7 - 9 are consistently higher than their measured counterparts (by c. 1 - 2 K).

~ime~2 [hri4 ~s Is

~0 ~2 24

Fig. 10. Cooling effect of net long-wave radiation exchange flux in studied clusters.

The calculated cooling effect of NLWR exchange is shown in Fig. 10. These almost unvarying contributions include the cooling effect of nocturnal cold air drainage described earlier. The daily mean cooling cont r i b u t i o n s w e r e 6.1, 5.4 and 4.4 K in the AA, MR and JQ, respectively. The highest daily mean effect of 6.1 K is a result of the minor obstruction (SVF = 0.65) of the street canyon surfaces in the AA cluster. At the other extreme, the high aspect ratio of the canyons in the JQ (mean (H/W) = 1.1 and SVF = 0.41) resulted in the lowest mean cooling contribution, of 4.4 K. The calculated daily variation of air temperature was obtained b y considering both the solar radiation absorption and NLWR exchange contributions as integrated in eqn. (22). In Figs. 1 1 - 1 3 the calculated and measured variations for each cluster are presented side b y side with the daily temperature variation observed at the Atarot station. Simulated temperatures by means of the CTTC model are in good agreement with measured values. The root mean square error (RMSE) [18] of the differences between measured and calculated values was found to be 0.22, 0.34, and 0.43 K for the JQ, MR and AA clusters, respectively. The relatively large differences observed between measured and calculated temperatures at midday in AA cluster are attributed to extra warming of the local air caused b y heat release from the limited m o t o r traffic in the neighbourhood, which is excluded from the energy input flux to the CTTC model (the other clusters are closed to m o t o r traffic altogether). The delayed daily minimum and

321 30

TABLE 4

• IIiSti'ed

2B-

o

Temporal variation of heat island intensity ( A T u _ r ) and temperature differences between JQ and A A clusters (ATjQ_AA)

Calculated

22c-

ATu_r* (K)

ATjQ_AA**

(h)

jQ

MR

AA

(K)

02:00 05:00 08:00 11:00 14:00 17:00 20:00 23:00

1.7 1.7 1.1 --1.3 --0.7 0.2 2.8 2.8

1.3 1.2 0.9 0 1 0.4 1.0 1.8 2.2

0.1 0.0 --0.6 1.7 1.8 1.3 1.1 1.1

1.6 1.7 1.7 --3.0 --2.5 --1.1 1.7 1.7

I 28-

tB-

I

|6---

12

'B4

~B

Iiimel20_[hr~]4

]6

IB

~8 ~22!

Fig. 11. Calculated vs. measured air temperature variation over study period: JQ cluster. 3 0 /|

• ~uuned

|

28~ |

~

Time

[] ~lc.l,t,d

AtrOt

-

-~

~

I

22

c_

16

0

i

?

i

4

i

6

i

8

i

i

i

0 2 i4 Time {hr]

i

16

I

B

i

20

i

22 E4

Fig. 12. Calculated vs. measured air temperature variation over study period: MR cluster.

• Measured 30"

o Calculated

2422-

20" t8" t6

'2

',

'6

'R

Io 12 [h~4r] IB Time

18 ~

~ 24

Fig. 13. Calculated vs. measured air temperature variation over study period: A A cluster.

maximum temperatures in the JQ ( 0 7 : 0 0 and 14:00) are due to total ground shading during early morning hours and to the high CTTC of the locality, respectively. In the MR and AA clusters the minimum and maximum temperatures occur at 06:00 and 13:00, respectively.

*The maximum intensity measured during the analysis period was 2.8 °C. **The lowest difference measured during the analysis period was --3.7 °(3.

Urban-rural and intra-urban thermal differences over the study period are shown in Table 4. The heat island intensities ( ~ T u - r ) observed in the studied clusters (relative to the rural Atarot station), as well as the temperature differences between the two most contrasted clusters, the JQ and AA, are presented by time of day. Over a 24-hour period, the MR and AA clusters exhibited positive heat intensity, while the JQ exhibited negative intensity (cool island) during most of the daytime hours (10:0017:00), but also the highest intensity at night and in the early morning hours. The extreme temperature anomaly observed in the urban stations was --3.7 K between the maximum temperatures in the JQ and AA clusters. The air in the former was warmer by 1.7 K in the mean at night and in the early morning. The densely built-up JQ with high CTTC and PSA, exhibited a damped diurnal temperature cycle as compared with the rural station and the other urban stations. The lowest daily temperature range of 7.3 K was measured in the JQ compared with range of 8.9 K and 12.9 K in the MR and AA, respectively. According to the general formulation of the CTTC model, the base temperature of the climatic region, To, is given by: To = Ta(t) - - A T a . s o l a r ( t ) +

ATNLwR(t )

(24)

Knowing the terms of the right-hand side [measured Ta(t ) and calculated ATa,,o~r(t)

322 TABLE 5 Calculated base temperature (To) for studied clusters

Cluster

Mesa. daily minimum (°(2)

ATe, sol=( t = train) (K)

A T N L w R (t ffitrain) (K)

TO (°C)

JQ MR AA

20.0 19.6 18.1

0.3 1.0 0.6

4.0 4.7 5.7

23.7 23.3 23.2

and ATNLwa(t)], To can be evaluated. The calculation was performed at t = t~n where ATa.,~a~(t) decays and reaches its lowest value during a diurnal cycle. Results axe given in Table 5, which shows that To is relatively uniform for the different clusters (within +0.5 K) and almost identical to the mean daily temperature at the representative rural meteorological station during the study period which was 23.2 °C.

5. CONCLUSIONS

Urban forms (geometry and morphology) were found to be the most significant factor influencing urban-rural and intra-urban air temperature differences. The following parameters and physical processes are mainly affected b y the features of the built-up environment: - - s o l a r radiation input to the UCL represented in the model b y the partial unshaded area of the open space (PUSA); - - a c t i v e thermal mass per unit horizontal ground area, represented by the CTTC parameter; -- obstruction of UCL surfaces from the sky temperature sink for long-wave radiation exchange, represented by the sky-view factor (SVF). Substrate thermal properties of impervious ground surfaces were found to be irrelevant to the thermal inertia of a neighbourhood and not to affect air temperature variations and thermal urban-rural differentials. Basically, the partial shading effect of buildings during the day causes low local temperature (cool island) in a built-up environment, relative to neighbouring unshaded rural environments. Shaded surfaces in clusters do not warm directly by absorbing solar radiation. Concurrently, adjoining unshaded surfaces warm rapidly and, hence, heat the

air in contact with them. As the heated air is not stagnant, it loses part of the gained sensible heat to the nearby " c o l d " shaded surfaces which act as thermal sinks in built-up environments. The resultant warming of the air after this process is moderate compared with that encountered in unshaded environments. However, the air in clusters with low thermal inertia (low CTTC) and intensive anthropogenic heat sources may warm even more than the unshaded rural environs during the day. In sudh clusters the heat island phenomenon would exist over a 24-hour period. At night the effect of NLWR exchange on thermal differentials is more pronounced while solar radiation absorption effects are damped. The model proposed here offers an adequate tool for assessment of climatic impacts of urban design alternatives and strategies. Its transferability potential to other climatic zones and applicability to urban climatic design will be illustrated in a subsequent paper.

LIST OF SYMBOLS Br c

C CTTC

Brunt number specific heat of matter (J/kg K) ~onstant cluster thermal time constant

(h) FA H h hc h~

plan area of building roofs in cluster (m 2) average height of buildings in cluster (m) overall heat transfer coefficient at surface (W/m 2 K) convective heat transfer coefficient (W/m 2 K) radiative heat transfer coefficient (W/m 2 K)

323 h Roof

I(t)

INLwa(t)

k L tn

PSA

PSA PUSA S STTC

overall heat transfer coefficient at r o o f surfaces (W/m z K) unobstructed solar radiation intensity (W/m 2) net long-wave radiation exchange flux (W/m 2) mean solar radiation intensity incident on g r o u n d surface in built-up environment (W/m 2) thermal conductivity of substrate matter (W/m K) penetration depth of diurnal temperature cycle (m) solar radiation absorptivity of surfaces partial shaded area of open space in cluster mean partial shaded area at midday partial unshaded area (PUSA = 1 -- PSA) plot area (m 2) surface thermal time constant

(h) SVF SVF' t T.(t)

To u

W

WA x

sky-view factor of street canyon surfaces sky-view factor of roof surfaces time (h) air temperature (°C) base (background) temperature (°C) wind speed (m/sec) average width of streets in cluster (m) external wall area of buildings in cluster (m 2) depth below ground surface (m)

Greek symbols AI step change in solar radiation intensity (W/m 2) ATa(t) air temperature change at time t (K) ATa"(t ) air temperature rise at time t in response to step change mAI in solar radiation intensity at t = 0 (K) contribution of solar radiation AT~,so~,(t) absorption to air temperature

(K) ~TNLwa(t)

contribution of net long-wave radiation exchange to air temperature (K)

h0s"(t)

ground surface temperature rise at time t in response to step change m A / in solar radiation intensity at t = 0

e

surface emissivity ground temperature (°C) time (h) density of matter (kg/m 3) Stefan-Boltzmann constant (5.67 × 10 -s W/m 2 K 4)

(K) O(x,t) k P 0

Subscripts 1,2 a

BE i s

initial and final, or first and second layer air built-up environment internal surface

REFERENCES 1 H. Landsberg, The Urban Climate, International Geophysics Series 28, 1981. 2 T. Oke, The energetic basis of the urban heat island, Q. J. Roy. Meteorol. Soc., 108 (1982) 1 - 24. 3 T. Oke, Canyon geometry and nocturnal urban heat island: comparison of scale model with field observations, J. Climatol., 1 (1981) 2 3 7 254. 4 H. Swaid and M. E. Hoffman, The prediction of impervious ground surface temperature b y the surface thermal time constant (STTC) model, Energy Build., 13 (1989) 149 - 157. 5 N. Sharlin and M. E. Hoffman, The urbam complex as a factor in the air-temperature pattern in Mediterranean coastal region, Energy Build., 7 (1984) 149 - 158. 6 H. Carslaw and J. Jaeger, Conduction o f Heat in Solids, Oxford University Press, 1965. 7 M. Hoffert and J. Storch, A scheme for computing surface fluxes from mean flow observations, Boundary-Layer Meteorol., 17 (1979) 429 - 442. 8 V. Gupta and J. Srinavasan, Heat and Mass Transfer, Tata McGraw-Hill, 1978. 9 L. Burmeister, Convective Heat Transfer, WileyInterscience, 1982. 10 H. Swaid, The physical basis of the analyticalexperimental model for predicting the urban climate, D.Sc. Thesis, Faculty of Civil Engineering, Technion, Haifa, 1988. 11 H. Hsu, Fourier Analysis, Simon and Schuster, N e w York, 1978. 12 K. Kimura, Scientific Basis o f Air Conditioning, Architectural Science Series, 1977. 13 R. Fleagle, Radiation theory of local temperature differences, J. Meteorol., 7 (1949) 1 1 3 120.

324 14 T. Oke, Street design and urban canopy layer climate, Energy Build., 11 (1988) 103 - 113. 15 B. Givoni, Urban design guidelines for hot-dry regions, Proc. 2nd International Symposium on New Developments in Building Climatology, Moscow, 1987, CIB, W-71, 1987. 16 /.H.V.E., Guide Book A: Design Data, I.H.V.E., London, 1970. 17 ASHRAE Handbook of Fundamentals, ASHRAE Inc., New York, 1972. 18 T. Won, Model validation methods, Handbook of Methods of Estimating Solar Radiation, Swedish Council for Building Research, Stockholm, 1984.

[4]. On the other hand, experimentally determined CTTCs reported in ref. 5 were comparatively m u c h higher, namely 1 0 . 5 41 h. Bearing in mind the rapid decrease of exponential functions with growing negative powers, the following assumptions were done in order to simplify eqn. (A1)

(_ STCC + CTTC 1 exp

§TTC

] -~ 0

I/(STTC + CTTC) ~ I/CTTC

(A2)

(A3)

With the above assumptions incorporated in eqn. (AI), itsimplifiesto the form

APPENDIX

1 L( 1 exp(--CTTC/STTC)I ~ L p c X ~- CTTC + ~ / =1

Substituting t = STTC + CTTC in eqn. (7) and equating with eqn. (9), we have:

(A4) mAI/h l~+~k

[(1 -- e x p ( -

STTC_ + C T T C I I STTC ]]

+ ~ L p c X --~ X STTC exp

(_ STT_+_crc/ STTC

]

%

1 L + (1 -- exp(--1)) + -~Lpc × z 1 exp(--1) X STTC + CTTC

-

2m~kI/h 1/h + L / k (A1)

Typical STTC values of common urban ground surfaces were found to be 1.3 - 2.2 h

Again, assuming (ST~C X exp (

CTTC I I ~ 0

s-Y H

we have: 1 L CTTC = -~Lpc X - (A5) k The m a x i m u m possible error resulting from the above assumptions would be less than 10% of the CTTC value adopted in this work (8 h -- see under Discussion), and would have a rather marginal effect on urban temperature prediction by the proposed model (c. 0.3 K in the daily maximum).