Jul 11, 1996 - Summary. This paper outlines a computer simulation model designed to assess the thermal characteristics of the urban canopy layer (UCL).
Theor. Appl. Climatol. 57, 229-244 (1997)
Theoretical c Applied and limatolbgy © Springer-Verlag 1997 Printed in Austria
Department of Geography, UCLA, Los Angeles, CA, U.S.A.
An Urban Canopy-Layer Climate Model G. Mills With 6 Figures Received July 11, 1996
Summary This paper outlines a computer simulation model designed to assess the thermal characteristics of the urban canopy layer (UCL). In contrast to other UCL models, the layer simulated
here includes both closed volumes (buildings) and open volumes (canyons).The purpose of the model is to allow the comparison of the climate impacts of differentbuilding group configurations. Traditional boundary-layer theory is applied to the surface urban boundary layer (UBL) which lies above the UCL and the derived relations are used to parameterize exchanges of momentum and heat across the UBL/UCL interface. The exterior energy budgets of the roof, walls and floor of the canopy are solved using an equilibrium surface temperature method. The open canopy and interior building air temperatures are found which are in agreement with the surface exchanges. Using measured data for Los Angeles in June, the output of the model is examined. The results show some agreement with measurement studies and suggest that the density of structures can have a substantial impact on UCL/UBL interaction.
1. Introduction M u c h climatology work is undertaken with the objective that the results can be used to guide urban design decisions. However, urban climate research as conducted by urban designers differs considerably from that by climatologists. In general, climatological work is not focussed on urban design issues and the results of these studies are not readily accessible to urban designers (Oke, 1984). The motivation for this work has been upon understanding the processes that are responsible for the urban climate and attention has
been paid to measuring and simulating the fluxes of energy at 'active' surfaces (e.g., Nunez and Oke, 1977; Terjung and Louie, 1974). By contrast, designers have an explicitly bioclimatic view of the climate/building relationship; an efficient structure is one which creates a comfortable climate with minimal need for energy use (Gupta, 1984; Knowles, 1974). M u c h climate work in this field examines traditional building designs in harsh climates in an attempt to explain the form and composition of the structure in terms of climate principles (Olgyay, 1963; Givoni, 1981). In this paper I will present a model for building groups which attempts to link urban climatology knowledge and concepts to urban design concerns. The model simulates the thermal response of simple building groups to environmental stresses and it is intended to use this model to evaluate the role of building group configuration and composition in moderating these stresses. A simulation run is completed to illustrate the capabilities of the model and some comparisons with published empirical work are presented.
2. Model Description The urban climate exists at two distinctive scales. The urban b o u n d a r y layer (UBL) forms above the roughness elements and derives its characteristics through exchanges at its lower 'surface', a loosely defined interface located at roof level. In studies of the UBL, the interface can be treated as a rough,
230
G. Mills
flat, surface with generalized roughness, thermal and radiative characteristics. The urban canopy layer (UCL) lies between this interface and the ground and its climate is the result of complex exchanges between surfaces and between the UBL and UCL. These interactions are infinitely varied and may be characterized in limited circumstances only (such as for urban canyons). The open canopy has generally been the concern of the urban climatologist whereas the closed canopy has been the chief preserve of the architect/urban designer. The present model is distinguished from others in its attempt to simulate the exchanges of energy within the UCL and between the UCL and the UBL. In this model a building group is composed of identical structures placed at regular intervals on a flat surface. Individual buildings are formed by five surfaces with dimesions of depth, length and height. The disposition of the structures relative to each other is specified completely with two orthogonal separating widths. The group so defined is considered to be sufficiently extensive that a representative portion of the UCL can be chosen (Fig. 1), which consists of a single structure and the open space between it and the neighboring structures. Inputs to the model are of three types:
PLAN VIEW
~
~ ,
.
.
.
.
~"FALSE WALL" .
.
.
~ , i
REPRESENTATIVE UCL
SECTION LINE --~
', ',
--
,
-- ~-'cLosED" --~VOLUME (BUILDING) "OPEN" VOLUME CANYON)
CROSS SECTION VIEW
"CL
VIE
UOL t
REPRESENTATIVE UCL
Fig. t. Model layout as viewed from above (plan view) and along a cross-section drawn through the UCL
1. Location and time of year: latitude, longitude, month and day, 2. Meteorology: temperatures and wind velocities at regular intervals for a reference level located above the UCL and 3. UCL characteristics: a. building orientation, dimensions and separation distances and, b. substrate thermal and surface radiative properties. The substrate material may differ for the walls, roof and canyon floor but is homogeneous with depth. For the walls and roof this depth corresponds to facet thickness but for the floor it refers to the depth at which the diurnal temperature range is minimal. In the terminology employed here the UCL consists of closed and open volumes. The former consists of a building volume and its enclosing surfaces. The open volume (referred to hereafter as the canyon) shares the wall surfaces of the structure and is enclosed by the solid canopy floor and an open 'surface' at roof height. The UCL interacts with the overlying UBL through the canyon top and the structure roof. The model simulates the energy balances of the surfaces and volumes of the UCL and evaluates thermal stresses associated with different building configurations under different climates. In the case of the canyon, exchanges at the building walls, the canyon floor and the UBL/UCL interface are simulated. Numerical methods are employed to obtain canyon surface and air temperatures which are in equilibrium with each other. The UBL is connected to the open canopy through exchanges occurring at the canyon top; as the building group is considered to be extensive, no horizontal exchanges are considered. Fluxes of heat and momentum at this level have been acknowledged in field work as significant component of the canopy energy balance (Nunez and Oke, 1977; Arnfield and Mills, 1994). However, short of comprehensive threedimensional flow models, there are no easily adapted guidelines in published work which specify exchanges rates between the canyon and overlying UBL. Exchanges of heat and momentum at this level are estimated using bulk transfer relations for a neutral atmosphere. The momentum flux is used to simulate the canyon windfield
An Urban Canopy-Layer Climate Model
which is used in calculating the sensible heat flux at the canyon walls and floor. The canyon top sensible heat flux is used to calculate the canyon air temperature. The building volume is linked to the external climate through exchanges that occur across the solid structure envelope, the walls and roof. The temperature at points located at regular intervals within the substrate are updated at each timestep and provide the 'memory' for the simulated system. Unlike surface temperatures, which are considered to be instantly responsive to current conditions, the substrate temperature profile represents the accumulated history of surface/ substrate exchanges. This profile is updated at each time step and is integrated forward to the next simulation time. The interior building energy budget is solved based upon the updated temperature profile. The building and canyon volumes are linked through exchanges across the wall facets and the building volume is linked to the UBL through exchanges across the roof facet. 2.1 U B L / U C L Exchange As the simulated urban surface is composed of regularly spaced identical structures over extensive areas, I have chosen to use the boundarylayer empirical relations for a neutral atmosphere to simulate the constant flux layer of the UBL, located just above the UCL top. A bulk drag coefficient is used to estimate the momentum flux into the canopy layer (Garratt, 1992), ~= p CD V2 = p ~t2,
(1)
where z is the momentum flux, V~ is the wind velocity at a reference height (z~), p is air density and It, is the friction velocity. The bulk drag coefficient (Cv) is obtained from, k2
(
231
from
HA* 2A'
z°-
(3)
A* is the area presented by an individual element to the ambient wind and 1/A is the density of elements. This relationship was derived for roughness elements placed at regularly spaced intervals and would seem appropriate for the simulated building groups under discussion (Lettau, 1969). The zero plane displacement level (do) accounts for the elevation of the aerodynamic surface and is parameterized here as equal to two-thirds the height of the roughness elements, i.e. the buildings (Oke, 1987). The exchange of sensible heat at the canyon top (Qm) is treated analogously to the momentum flUX,
Q~t = Vr CI~[pCp(Tc -- Tr)],
(4)
where Cp is the specific heat of air and (Tc - Tr) is the difference between 'surface' (Tc) and the reference air (Tr) temperatures. The bulk coefficient for heat transfer (C/~) is obtained from (Garratt, 1992), k2 =
.
(5)
log (z~ Z do) log Zo
The model assumes that the canyon air volume is isothermal and therefore the 'surface' temperature is placed at a height equal to that of the canyon top (H). Field work has found that much of the canyon is isothermal except close to surfaces where temperatures can differ by ~ 2 °C from the rest of the volume (Arnfield and Mills, 1994; Nakamura and Oke, 1991). The implications of this pattern for the energy balance of the surfaces are not considered in the model. 2.1.1 Within-Canyon Velocities
,
where k is von Karman's constant (0.4), z o is roughness length and d o is the zero plane displacement. I have assumed that the aerodynamic effects of the canopy extend a distance equal to 1.5 times the height of the roughness elements and ambient air temperature (T~) and wind (V~) refer to this height (z~). The roughness length is calculated
Simulation of the within-canyon wind velocity is based upon an approach used by Yamartino and Wiegand (1986) who found that measmed canyon velocities showed close agreement to a model which partitioned ambient airflow into down and transverse-canyon components. The former causes an along-canyon flow which is superimposed upon a vortex motion driven by the latter. The horizontal (u) and vertical (w) components of
232
G. Mills
the vortex are given by the model of Hotchkiss and Harlow (1973), ux,z = u.(1
-
fl)- [7(1 +
- fl(1 - ky)/7 ] sin (kx), wx, z = - u , ky( l - t~)- 1 [7 -/?/7] cos (kx),
(6) (7)
where k = re/W,/~ = exp ( - 2 kH), y = (z - H) and 7 = exp (ky). The coordinates x and z represent the horizontal and vertical coordinates of the canyon cross-section, u~r is cross-canyon windspeed at the canyon midpoint and roof level (H). The alongcanyon windspeed at mid-canyon is simulated with a log profile, vz = vH log(z)/log (H),
(8)
where vu is down-canyon windspeed at roof level. The ambient velocity at roof level (VH) from which the cross- and along-canyon components (u~ and vu) are derived is estimated from a logarithmic wind profile applied to the UBL, g~ = ~- log
.
(9)
In this approach VH is treated as an average velocity found between the roughness elements and the dependence of roughness on wind azimuth is ignored. Some validation of this approach is possible, based upon comparison with measurements made by Nakamura and Oke (1989) in a canyon of H/W equal to 1. They found that within-canyon windspeeds (measured at 1 m elevation at the center of the street) were approximately 0.67 of those measured 3 m above the rooftop. In similar circumstances the model employed here yielded ratios of between 0.40 and 0.60 depending on the respective azimuths of the ambient velocity and the canyon. In addition, wind tunnel work by Dabberdt and Hoydysh (1988) has found that the rotor velocity averages about 0.25 of the ambient velocity where flow is perpendicular to the axis of a symmetrical canyon of H / W = 1. The model employed here calculates rotor velocities of 0.2 V~ in similar circumstances. However, this model is probably applicable to a limited range of building configurations. Although field work in long canyons has found close correspondence between ambient and canyon airflow in the manner described by the equations outlined above (e.g., DePaul and Shieh, 1989),
wind tunnel work using regularly spaced arrays of buildings (similar to the urban settings modeled here) has shown that for shorter and wider canyons, horizontally oriented vortices formed at the canyon ends can dominate the flow regime (Dabberdt and Hoydysh, 1991; Wedding et al., 1977). Moreover, even for long canyons (for which endeffects can be ignored) the vortex motion as described by these equations only forms at close spacing (Hussein and Lee, 1980). At a wider spacing the wake that formed in the lee of one structure begins to interact with the downwash of the downwind structure. At still wider spacing, individual recirculating vortices form in the lee and windward side of each structure and each building behaves in an isolated fashion. A representative canyon velocity is obtained for each axis of the orthogonal street grid for use in evaluating the sensible heat exchange at wall facets and the canyon floor. Apart from experimental studies, there are few guidelines regarding the relationship between the 'adjacent' velocity and the surface under consideration. In the model the rotor and down-canyon velocities are estimated at different heights at the center of the street: at 0.1 H in the case of the rotor components and at 0.5 H in the case of along-canyon velocity. As the model for along-canyon flow (Eq. (8)) does not assess flow adjacent to wall facets, 0.5 H was considered an adequate location to assess this velocity. A representative canyon velocity (Vc) is obtained as the resultant of these two vectors. 2.2 Surface Energy Balances
The energy balance of each exterior solid surface (i)-this includes the roof, four walls and canyon floor-is expressed as K~,i-K'~i+L~.i-L~i-=QH(i)+Qc~(i),
(10)
where K symbolizes shortwave and L longwave radiation and the arrows indicate the direction of the transfer. The non-radiative terms included are the sensible heat fluxes into the atmosphere (QH) and the substrate (QG). Each term represents an average for the entire surface. The building group is considered to be horizontally extensive and this is approximated by including a solid wall surrounding the eight nearest neighbors in all view factor and shading calculations (Fig. 1). This wall has a height equal to that of the buildings. In the
An Urban Canopy-Layer Climate Model following sections, the equations for only the building facets are shown. The terms for the floor surface are identical to those for the facet and are only mentioned when required. 2.2.1 Radiation Terms Each of the radiative terms can be decomposed into exchanges with the atmosphere and the surrounding terrain. For an individual surface (i),
K'~i =
233
ation from the sky is treated as isotropic so that,
Dsky(i ) = (I 0 cos Z) R kIAi.~sky ,
where 2 is a transmission factor for diffuse radiation in the atmosphere, Z is the sun's zenith angle and kt/i_~sky is the sky view factor. The longwave radiation components are treated in a similar manner. Longwave radiation from the sky is given by, g,~sky(i) = (aaO- Tr4) ~i--,sky,
S i '[- Dsky(i ) -[-
Deny(i),
(11)
(14)
(15)
where S is direct solar radiation and D is diffuse radiation from the sky (Dsky) and environment (Deny). The direct radiation on a building facet is obtained from
where Tr is ambient air temperature, a is the Stefan-Bolzman constant and ea is atmospheric emissivity calculated from Brutsaert's (1975) empirical relationship derived with regard to vapor pressure (e,),
Si = \[ I°
ea = 0.575 e~/7.
-
cos
(12)
Longwave radiation receipt is calculated from, where I 0 is the solar constant, ~ is a transmission factor which represents the proportion of incoming radiation which is not depleted, A~ is the area of the facet, A~(~)is the area of the facet in shadow and 0i is the angle between the sun and the facet. The shadow area is calculated by considering the unique (non-overlapping) shadows of the neighboring structures cast toward the central structure. For the floor, its radiation receipt is estimated as the radiation entering the building group at roof level minus that intercepted by the wall and roof surfaces. Diffuse radiation from the environment (Deny) occurs as a result of reflection from surfaces within the UCL. For an individual facet it is approximated as a single, diffuse, reflection event from all facets (j) of all other buildings and the floor (f), De~v(i) = I j ~ 1K'~
u~i~jl+K'fUgi.f,
(13)
where K l" is reflected shortwave radiation and W~_~j is the view factor of facet j with regard to surface i. Incident radiation upon each of these reflecting surfaces is assumed to be representative of the whole surface (no account is taken of sunlit and shaded parts). As all buildings are identical, each surface interacts with just four different surfaces, three walls (as a surface cannot see itself) and the floor. The boundary walls are included in these view factors as parallel and perpendicular surfaces and given wall properties. Diffuse radi-
L~env = Ij=~
L'rWi_~jI+LTWi.f,
(16)
where all subscripts are identical to those employed for Denv. Longwave emission is given by, 4 LTi = aia T(i,1),
(17)
in which T(i,ll is surface temperature. 2.2.2 View Factors The view factors of each building wall and the floor with regard to surfaces within the UCL and the sky are required to solve the diffuse radiation components of the energy budget. The view factor of the roof is entirely taken up with the sky and it does not interact with other UCL surfaces. All wall surfaces (including the boundary wall) are either perpendicular or parallel to the viewing facet and view factors for these situations are easily obtainable (e.g., Edwards, 1983)o For those surfaces obscured by other facets, the view factor is obtained iteratively by dividing the obscured and viewing surfaces into parts and summing over the parts. The symmetrical nature of the building disposition greatly diminishes the difficulty of this task. Once the view factor (W) of a wall with regard to other building surfaces is obtained, those of the floor and sky remain,
kIJi-->f ~- kt/i-->sky =
j=l 2
(18)
234
G. Mills
The view factor of the floor with regard to the wall facets is estimated by considering the relative areas of the floor and the facet in question; and that with respect to the sky is obtained as the residual after that with regard to the building surfaces is considered. 2.2.3 Sensible Heat Fluxes The sensible heat flux is calculated from,
QH(O= hc(T(~,l)- T,),
(19)
where hc is the heat transfer coefficient, T~i,1) is the exterior surface temperature and Ta is the air temperature. The parameterization employed in this research is (Cole and Sturrock, 1977), he= 1.7V+ 5.1. For the roof, ambient air temperature (7;) and velocity (V~) are used in these equations. For the canyon facets and the floor, a canyon velocity (Vc) and temperature (T~) are employed. A representative canyon velocity is obtained from the wind model and T~ is found by iteratively seeking the air temperature which simultaneously solves the surface and canyon energy balances. The substrate heat flux (QG) is obtained from,
Q(?(i) =
k A z (T(i'I) - T(i'2))'
(20)
where k is the conductivity of the material and Az is the distance separating the surface (T(i,1)) and subsurface (T(i,2)) temperatures.
surfaces, 4-
A, QHt = 2 ~ AjQH; + AtQHf , j=l
(21)
where A refers to area and the subscripts refer to each of the wall surfaces (j), the floor (f) and the top of the open canopy (t). In addition, Qm may be expressed as a function of difference between the reference and canyon air temperatures, the reference wind velocity and drag coefficient (Eq. 4). Together these equations are employed to yield a new value for To, which may be different from that used in the calculation of sensible heat flux. If the difference is significant (>~ 0.005 °C), the surface energy balance is recalculated using the new value, and this process is repeated until Tc is stable. At this point the canyon surface fluxes are considered to be in equilibrium with each other.
2.4 Substrate All surfaces in the model are composed of a homogeneous material of a given thickness (d). The model simulates temperatures at five equally spaced positions within the material, beginning with exterior surface temperature (T(i ' 1))" The fifth position corresponds to the location of the interior facet temperature in the case of buildings and the unchanging substrate temperature for the floor. Under the assumption that these boundary conditions are constant over a given time interval (At), substrate temperatures at the other three positions are adjusted,
Atk 2.3 Canyon Energy Balance The unknown surface temperature (T(i,1)) in these equations is obtained by numerical methods. For the roof the solution is easily obtained as the roof surface does not interact with other UCL surfaces. However, for the canyon surfaces (walls and floor) the energy balance of each is partially dependent upon the other surfaces and each cannot be solved independently of each other. Solving Eq. (10) requires that surface temperatures are known, which depend upon canyon air temperature (To). This equation is solved numerically by an iterative process which considers T c to be in equilibrium with surface exchanges so that sensible heat exchange through the canyon top must equal that added to the canyon volume at the other
A T ( i j ) - Cs(Az) 2 (T(i,j_l)- 2T(i,j)+ T(i,j+l)), (22) where T refers to temperature at positionj within the substrate, At is the timestep, C s is heat capacity and Az refers to the distance separating these positions. For the floor, At corresponds to the time intervals at which the surface temperature is calculated. However, in the case of the walls and roof, the interior surface temperature is altered as it adjusts to building air temperature. A large timestep (such as 1 hour) causes physically impossible changes in building air temperature which, in turn, affects the substrate temperature profile. The solution employed here is to maintain a constant exterior surface temperature over the period until the next surface temperature is calculated and
An Urban Canopy-Layer Climate Model then adjust substrate and building air temperatures using smaller time increments during this period. 2.5 Interior Building Energy Budget
The exterior conditions are conducted to the building interior through the walls and roof. The energy budget of any surface (i) within the structure can be expressed as follows,
235
Table 1. Properties of UCL Structural Parts Indicating the Material of which it is Composed and its Depth (d, in m), Albedo (~), Emissivity (~), Conductivity (k, JK-1 m-1) and Heat Capacity ( Cs, M J K - l m - 3). Values obtained fi'om Oke (1987), Tables 7.4 and 8.2
Walls Roof Floor
Material
d
~
brick clay tile asphalt
0.2 0.1 1.0
0.30 0.91 0.83 1.37 0.20 0.90 0.84 1.77 0.15 0.95 0.75 1.94
e
k
Cs
6
(23)
L ,[.j Wj_ 1 - L "ri = Qmi) + QG(i), j=l
where the j refers to all the other surfaces that enclose the volume. Unlike the exterior surface, only the longwave radiation components need to be considered. As all surfaces are either parallel or perpendicular to each other, solving for the view factors is easily accomplished. The energy budget can be rewritten as 6
4
4
C,j(7 T(j,5)u[zJi~j -- ,~i(y T(i,5 ) j=l
k = A~ (T(i,5) - T(i,4)) + hc(T(i,5 ) -
Tb)
,
(24)
where the subscripts i and j refer to the interior building surfaces. All terms have the same meaning as for exterior surfaces, T b refers to the air temperature of the building volume and he, the heat transfer coefficient, is assumed to have a constant velocity of 0.25 m s - 1. The building floor is omitted as an active surface in this model as the purpose is to examine the impact of external stresses on the building structure. This is accomplished by assigning the floor surface the same temperature as the building volume (Tb). The energy balances of the five remaining surfaces (the walls and roof) are solved as previously. The interior building temperature (Tb) is computed based upon the sensible heat exchange occurring at the interior surfaces. In contrast to the canyon energy budget, the building volume is considered to be closed and all exchanges with the environment occur v~a the solid walls and roof,
l
j~- i Q u j A j
1
where A is facet area and V is the building air volume. The air temperature (Tb) is adjusted by the increment ATb and this is employed in the
substrate and interior building energy budget calculations at time (t + At). 3.
Simulations
The results from a set of simulations are presented both to demonstrate the capabilities of the model and to examine the consequences of altering building density. In these examples the urban settings consist of cube-shaped structures (H = L = D = 10 m) separated by streets oriented east-west and north-south. The building group is located in the subtropics close to the summer solstice. The properties of the U C L are held constant: building walls are brick, the roof is clay tile and the canyon floor is asphalt. The thermal and radiative properties of each surface are listed in Table 1. Four building densities are examined associated with building height to street width ratios ( H / W ) of 4, 2, 1 and 0.5. Ambient hourly conditions are provided by measurements of velocity, temperature and relative humidity from a South Coast Air Quality Management station located at Claremont in Los Angeles county (34.1°N, 117.6°W). These measurements were made on 18th June 1989 and illustrate a diurnal regime typical of a Mediterranean climate (Fig. 4). The average daily air temperature is 20°C and the range is 13.5 °C. The maximum temperature (26.5 °C) occurs at 1400 and the minimum (12.1 °C) at 0500. A sea-breeze develops in the late afternoon when velocities reach 3.8 ms-1; however, from 2100 until 0800 h, winds are weak ( < 1 m s - 1). An initial building air temperature of 17 °C was chosen and for the canyon floor an unchanging temperature of 13 °C at a depth of 1 m. The initial substrate temperatures were established by applying a linear function to the temperature differ-
236
G. Mills H/W=1
600" SOUTH
600- EAST
400-
400.
ff20o ~ 2 o o 01~ . ...........
-20C
•o
o
.. ............
3:0 61o 9:0 1~.o 1~.o 16.o 21'.o 24.o2°°do a:o 610 910 1~.0 1~.0 1~,0 21'.0 24.0 Time
.
_ _ a * ............... QG
Time
600- N O R T H
600- W E S T
,oo-
,oo
~E 200"
200-
O" ~
0-
... ....... /
............ •
:••.,., ......
,...............
ooLoo
"200O.03:061091012.015.018.021'.024.0"2000.013106109~01'~.0 lg.018.0 21'.0 24.0 Time Time
%
400-
400-
200-
200-
O-
0•
,.
.... o•--•-'
2°°0!
•",
y••'•'
3:0 6:0 9:0 ,~01~01;~"~;~-a02°0o!0 ]3me
I
3:0 6:0 9:0 1~0,40 ,~0 2,'.0 240 Time
ence between the surface and the substrate. To allow the model to adjust to initial conditions, this daily run was completed ten times with unchanging ambient conditions, and only the final run is shown here. Canyon and rooftop surface simulations were completed at each hour. Exterior facet temperatures were treated as constant over the following hour and substrate conditions allowed to adjust. The building facets and volume used a time step (At) of 50 s for calculating substrate and air temperatures. This shorter timestep was selected by trial and error•
3.1 Results I will discuss the results associated with the configuration formed with H/W= 1 in some detail before examining the effects of altering building spacing. The energy budgets of the five building
Fig. 2. T h e e n e r g y b u d g e t s of t h e b u i l d i n g walls (identified b y the d i r e c t i o n they face) a n d roof, a n d the c a n y o n floor
surfaces and the canyon floor are given in Fig. 2, which clearly show the effects both of facet orientation and multiple reflection. The south wall displays a symmetrical pattern in Q* and QG, the latter being the dominant component in the energy budget (Q, changes little over the course of the day). The north wall receives direct radiation in the early morning and late afternoon and experiences a slight peak at noon as a result of reflected radiation from the south wall of the adjacent structure; however, the exchanges at this surface are weak. The passage of the sun across the sky at this time of year means that the east and west wails and the roof are the most active facets for the building. Both walls show major and minor peaks (at opposite times of the day) associated with direct radiation in the former case and reflected radiation in the latter. For the roof, Q* peaks at about 650 W m - 2 and has a minimum of
An Urban Canopy-LayerClimate Model H/W=
b
1
70- S O U T H
70. E A S T
60-
60 .
50-
50-
40-
4o-
30-
30-
20-
20"
19 a:o 6:0 9:0 1~.o14.o18.02i%2~.o l°0 7o- NORTH
b
Time
70.
6o-
60"
5o-
50-
40-
40"
30-
30-
20-
20"
1(
_,= ' 3,0 6.0
70] ROOF
237
.
............ Interior .
.
.
Exterior
3.0 6.0 9.0 12.0 15,0 18,0 21',0 2J,.O Time WEST
9:0 1~.0 1-/.0 18,0 21'.0 24.0 % 0 3:o 6:0 9:0 1~.0 t8.0 180 21'i0 2,i.0 Time
A
70-
Time
6050=
b
40"
40
30-
30
20"
202
lO~ 310 60'
90' 1 2 0 1 54'0 108 0 2'1 0 Time
_
21 Time
- 7 6 W i n -2 overnight. At this facet, the dominance of Q~ is clear in the morning hours when the substrate gradient is strong. In the afternoon, the warming of the substrate and increased wind velocity combine to increase Q~. Overnight a weak positive flux of Q~ is supported by heat drawn out of storage. By contrast, the diurnal ranges in the fluxes for the floor are much smaller; (2* peaks at 472 W m - 2 and is nearly constant at - 2 5 Wm -2 overnight. In addition, (2~/and (2G have nearly identical diurnal patterns, the former accounting for 80% of Q* at noon. Exchanges between the UCL and UBL (Fig. 5) were calculated as flux densities at this level. For example, net radiation is obtained from,
Q ~CL =
A I + A~
.
(26)
240
Fig. 3. The interior and exterior surfacetemperatures of buildingfacets and floor
Note that this scheme divides the total flux at the exterior surfaces (including the contribution of vertical surfaces) by the horizontal area of the UBL/UCL interface. At H/W = 1 (Fig. 5) the energy budget displays the symmetrical patterns of the floor and roof; the individual wall patterns are not apparent in the aggregate exchange. The effects of the walls are noticeable in QG, which is closer in magnitude to Q~ during the day than is the case for the floor alone. Figure 3 shows the exterior and interior surface temperatures for the building facets and the surface temperature for the floor. The exterior temperatures show the same patterns suggested by Q* while the interior temperatures display diurnal patterns that are out of phase (by approximately 6 hours) and have shorter amplitudes. The absence of shadowing on the roof surface and its lower albedo and smaller depth (compared to the
238
G. Mills H/W= 1
40- ~ ' h
~* ~ : ] ~ 4 i ~ 1 ~
~ Ir
.,~J~j~.
\vr 30-
Tb'~
*°°''°'"
C'~ 20- ~
10-
0.0
a!o
6~0
9!0
1~.0
lS'.o
18'.0
2~'.0
24'.0
Time
Fig. 4. The simulated building (Tb) and canyon (T~) air temperatures and the measured reference air temperature (T,) and wind velocity (V,). The arrows indicate the azimuth of the wind and their length indicates relative strength
wall surfaces) results in the large interior surface temperature range experienced by this surface. The extreme noontime temperature on the floor is the result of its comparatively low conductivity and albedo (Table 1). Figure 4 shows the reference wind velocity and air temperature measurements and the simulated canyon (Tc) and building (Tb) air temperatures. The latter varies in a regular manner over the day with a minimum (26.4 °C) occurring at 1000 h and a maximum (30.1°C) at 2000h. This pattern is approximately 6 hours out of phase compared to both Tc and Tr. The average T b value is 10°C higher than the initial temperature of 17 °C. The paths of Tr and Tc are similar throughout the day; however Tc is always higher than Tr. The magnitude of this difference is largest from morning until mid-afternoon (~1.5°C) and is smallest ( < 0.1 °C) in the late evening (Fig. 6a). Overnight the difference is small ( 1) are dominated by wall surfaces so that their contribution to canyon top exchange increases. The sensitivity of canyon air temperature to Qu at the walls and canyon floor depends largely on the canyon surface-area-to-volume ratio (Table 2). Although, for a given ambient velocity, the canyon top exchange rate is greatest for more dense configuration (Table 2), the area-to-volume effect is greater and, for a given Qu at the walls and floor, the magnitude ofATc_ r is greatest for higher H/W. In the simulations, nighttime canyon top exchanges are weak (ambient wind velocities are small) and ATe_ r is greatest at H/W= 4. Canyon surfaces, particularly the floor, cool at a rate controlled largely by the sky view factor which is greatest at H/W= 0.5. The weak sensible heat exchanges in this case result in values of AT~_r close to zero. By contrast, the smaller volume and warmer surfaces at H/W= 4 result in ATc_r near 1 °C at night. At sunrise, canyon top exchanges are still weak but solar receipt results in rapid warming of canyon surfaces. Solar access is greatest for the least dense configuration and ATc_r is largest for this group. During the daylight period, ambient wind velocity increases and the canyon becomes less isolated from the UBL (increased canyon top exchange); as a result AT~_~ decreases toward sunset. Unlike the canyon airspace, building volume is independent of H/W and the differences in building air temperatures (Tb) in the simulation run are governed by exchanges at wall surfaces. The average temperature is highest (~29 °C) for widely spaced structures (H/W= 0.5) due to their access to the direct solar beam. The timing of maximum and minimum Tb is identical at all H/W. However, the daily temperature range differs by ~ 1 °C. Structures at the densest spacing experience the
An Urban Canopy-LayerClimate Model smaller temperature range owing to their restricted solar access during the day (limiting heating) and sky access overnight (limiting cooling).
3.3 Empirical Evidence Some of these model results are supported in part by the empirical findings by others. However, most of this work has examined exchanges associated with a single configuration, usually with a H/W,~ 1. The patterns of fluxes on the east and west walls of the buildings are similar to those measured by Nunez and Oke (1977) for a northsouth oriented canyon. While the magnitudes of the fluxes differ considerably this may be explained by the comparatively high latitude (Vancouver, Canada) and wall albedos (0.52 and 0.62) of their experimental canyon coupled with dates of measurements (9-11 September) and the presence of a latent heat flux. The magnitudes of the simulated differences between canyon and reference air temperatures is comparable to those measured in a canyon of H / W ~ 1 during August at 36 °N (Nakamura and Oke, 1988). Their work found ATc_r to be positive and largest just after noon ( ~ 0.5-1 °C), to decline in magnitude but remain positive until midnight and to be small and negative ( ~ - 0 . 3 °C) for the remainder of the night and the early morning hours. The differences in diurnal pattern between these observations and the simulations presented may be explained by the east-west orientation of the measurement canyon. In both circumstances the maximum positive ATc_r occurred when canyon walls warm rapidly: in the measurement canyon, this occurs near noon when the angle between the sun and the south-facing wall is least; in the simulations it occurs when the east-facing wall is warmed in the morning hours. Aida (1982) measured solar absorptivity for a physical model consisting of a concrete surface composed of blocks at various spacings. Different block configurations were found to increase the absorptivity of the surface by 20% compared to a flat surface. One experiment was conducted with cube spaced at H/Wof 1 at 33.5 °N on June 15 and is similar to the situation simulated here. A UCL albedo, comparable to that measured by Aida, was calculated here as the area-weighted average of the ratio of (S + Dsky) to KT (Table 3). I have presented the albedo obtained in this manner for
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two times of the day to illustrate that the measured albedo of the UCL 'surface' will change depending on the solar position with respect to the walls, roof and canyon floor. For all configurations, the simulated albedo of the UCL is less than that expected of a flat surface with UCL properties. For the case of the H/W= 1 configuration, the albedo is 76% of that for a flat surface at noon, which compares well with that found by Aida (Model 3, Fig. 4 in Aida, 1982). 4. Conclusions
This paper describes a model designed to evaluate the effects of simple building configurations on the external and internal thermal climate of the UCL. The advantage of this approach over others is its comprehensive treatment of the UCL. In this model the UCL is treated as a single layer composed of enclosed building and open canyon volumes. The fluxes of heat and momentum connecting the UBL and canyon volume are simulated so that the energy budgets of the canyon surfaces and volume may be solved. The behavior of the building volume in response to the exterior is examined by considering exchanges across the wall and roof facets. The structure of the model allows one to examine the consequences (in terms in indoor and outdoor thermal stresses) associated with different building configurations in different climates. The results shown here refer to simple cubical structures arranged on a north-south oriented grid. The response of the UCL to hourly meteorological conditions provided by a measuring station in Los Angeles was examined. Various configurations were examined by changing the height-to-width ratio equally for the rows and columns. The results for configurations of H/W= 1 are supported in essence by the empirical findings of others. Changing H/W has the effect of altering the diurnal UCL/UBL energy fluxes and canyon air temperature. These responses are due to the changing geometry of the canyon and the different behaviors of the walls compared to the canyon floor. By comparison, wall facets experience less diurnal variation in Q/~, and consequentially dense configurations exhibit the same behavior. It is intended to employ this model to examine the response of UCL climate to changes in ambi-
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G. Mills: An Urban Canopy-Layer Climate Model
ent c o n d i t i o n s a n d b u i l d i n g g r o u p c o n f i g u r a t i o n s . I n p a r t i c u l a r this m o d e l will be e m p l o y e d to e x a m i n e the t h e r m a l b e h a v i o r of b u i l d i n g s a n d a i r s p a c e s w i t h i n the U C L a n d to e v a l u a t e the role o f g r o u p design in g o v e r n i n g this b e h a v i o r .
Acknowledgements The author wishes to thank John Arnfield for comments on an early draft of this paper and Chase Langford who completed the diagrams.
References Aida, M., 1982: Urban albedo as a function of the urban structure A model experiment (Part I). Bound. Layer Meteorol., 23, 405-413. Arnfield, A. J., Mills, G. M., 1994: An analysis of the circulation characteristics and energy budget of a dry, asymmetric, east-west urban canyon II. Energy budget. Int. J. Climatol., 14, 239-261. Brutsaert, W., 1975: On a derivable formula for long-wave radiation from clear skies. Water Resources Res., 11, 742744. Cole, R. J., Sturrock, N. S., 1977: The convective heat exchange at the external surface of buildings. Building and Envir., 12, 207-214. Dabberdt, W. F., Hoydysh, W. G., 1991: Street canyon dispersion: Sensitivity to block shape and entrainment. Atmos. Environ., 25A, 1143-1153. Edwards, D. K., 1983: Radiation transfer between perfectly diffuse surfaces, chapter 2.9.3. In: Heat Exchange Design Handbook, Vol. 2. Fluid Mechanics and Heat Transfer. New York: Hemisphere Publishing Corporation. Garratt, J. R., 1992: The Atmospheric Boundary Layer. New York: Cambridge University Press, 316pp. Givoni, B., 1981: Man, Climate and Architecture, 2nd edn. New York: Von Nostrand Reinhold 483pp.
Gupta, V. K., 1984: Solar radiation and urban design in hot climates. Environ. and Planning, Bll, 435 454. Hotchkiss, R. S., Harlow, F. H., 1973: Air pollution transport in street canyons, EPA-R4-73-029. Hussein, M., Lee, B. E., 1980: A wind tunnel study of the mean pressure forces acting on large groups of low-rise buildings. J. Wind Eng. and Ind. Aerodyn., 6, 207-225. Knowles, R. L., 1974: Energy and Form: An Ecological Approach to Urban Growth. Cambridge, Mass: The MIT Press, 198pp. Lettau, H., 1969: Note on aerodynamic roughness-parameter estimation on the basis of roughness-element description. J. Appl. Meteorol., 8, 828-832. Nakamura, Y., Oke, T. R., 1988: Wind, temperature and stability conditions in an east-west oriented urban canyon. Atmos. Environ., 22, 2691-2700. Nunez, M., Oke, T. R., 1977: The energy balance of an urban canyon. J. Appl. Meteor., 16, 11-19. Olgyay, V., 1963: Design with Climate. Princeton, NJ: Princeton University Press. Oke, T. R., 1984: Towards a prescription for the greater use of climatic principles in settlement planning. Energy and Buildings, 7, 1-10. Oke, T. R., 1987: Boundary Layer Climates, 2nd edn. London, New York: Routledge, 435pp. Terjung, W. H., Louie, S. S-F., 1974: A climatic model of urban energy budgets. Geographical Analysis, 6, 341367. Wedding, J. B., Lombardi, D., Cermak, J., 1977: A wind tunnel study of gaseous pollutants in street canyons. J. Air Pollution Control Association, 27, 557-566. Yamartino, R. J., Wiegand, G., 1986: Development and evaluation of simple models for the flow, turbulence and pollutant concentration fields within an urban street canyon. Atmos. Environ., 20, 2137-2156. Author's address: Dr. Gerald Mills, Department of Geography, UCLA, 1255, Bunche Hall, 405 Hilgard Avenue, Los Angeles, CA, 90095-1524, U.S.A.
