Energy and Buildings, 14 (1990) 117 - 131 117

Street Design and Urban Canyon Solar Access

A. J. ARNFIELD

Department of Geography, The Ohio State University, Columbus, 0H43210 (U.S.A.)

(Received July 16, 1988; accepted November 1, 1988; revised paper received September 11, 1989)

ABSTRACT

In his recent papers, Oke has challenged urban climatologists to establish quantitative and readily understood guidelines which might assist planners in the design o f climat- ically rational cities, and has shown by ex- ample how such an approach might be taken for street canyon geometry. This s tudy pursues Oke's arguments relating canyon structure to solar access within the canyon space using a numerical simulation method- ology to explore the dependence o f irradiance on the canyon facets, on a pedestrian within the canyon and the net irradiance at the canyon top on aspect ratio, street orientation, city latitude, season and sky condition. In addition, wall, f loor and pedestrian 'access indices' are defined as the relevant irradiances divided by the equivalent horizontal surface, open-site solar irradiance, and it is suggested that such quantities, i f presented in a form convenient to the planning practitioner, might constitute one type o f parameter o f use in an urban planning context.

INTRODUCTION

An encouraging trend in recent years has been the recognition on the part of urban planners and architects of the role played by climatic interactions with land use and urban form on human health, environmental quality and energy use in cities [ 1 - 5 ] . Concomitantly, there are signs that urban climatologists are beginning to appreciate the needs of such ~ractition~s for data and models [6, 7]. Oke [8] has challenged cli- matologists working in the built environment to establish quantitative and easily under- stood relationships which might help in the formulation of urban design guidelines. This

convergence of interest at the climatology- planning interface is a welcome one given the increasing urbanization of world popula- tion, especially in those regions outside the temperate mid-latitudes within which most urban development has hitherto been con- centrated, in the tropics [9] and, to a lesser extent, in the high latitudes. While climatic criteria must take their place alongside architectural, aesthetic, social, economic and other guidelines in the planning process, the compromise and weighing of alternatives which is the essence of planning practice is only possible if urban climatic research is able to provide the types of quantitative predictions of the effects of urban design prescribed by Oke [8]. It is to this end and, more specifically, as a response to the question "Does urban climate research have quantitative guidelines to offer regarding street geometry?" [8], that this work is offered.

The urban street canyon has been adopted as the basic structural unit of analysis in much urban climate research, both measure- ment- and modelling-based [10- 16]. At its simplest, the urban canyon may be conceived as a rectangular trough (height H, width W), with specified surface materials, oriented at some angle 0 (in this study measured clock- wise from north). In many applications, the absolute dimensions of the canyon are not relevant and its geometry may be charac- terized by its 'aspect ratio', H/W. Oke [8] sought to find a 'zone of compatibility' among aspect ratios for a hypothetical mid- latitude city in terms of shelter and warmth of street-level air (favoured by large H/W) and pollution diffusion and solar access (requiriv~ small H/W). His review of the urban climate literature suggests that the range 0.4 ~ H/W ~ 0.6 represents an accep- table compromise in meeting these criteria.

0378-7788/90/$3.50 © Elsevier Sequoia/Printed in The Netherlands

118

This study focuses on one of the goals discussed by Oke -- that of maintaining solar access to the intra-canyon environment. Solar radiation availability on surfaces within street canyons is of major significance to the efficiency of solar collectors in city environments [17], to the heat budgets of the buildings bordering the canyons (and, hence, to the energetic costs of heating and/or cooling them), to the daylighting of building interiors [18], to illumination levels on the street and to the radiation budgets o f organisms, including plant life and humans, occupying the canyon floor.

Oke suggests that a maximum H/W ratio near 0.6 would be satisfactory for a canyon with 0 = ~r/2 at 45 ° latitude to ensure winter noont ime direct beam irradiation of the equator-facing wall over two-thirds of its area and to provide adequate diffuse irradi- ance on walls under cloudy skies [8]. How- ever, his conclusions were not based on irradiances for the canyon facets. This s tudy seeks to re~valuate this aspect ratio criterion using such data and to extend the analysis for a wider range of canyon types, site lati- tudes and dates.

METHODS

The approach taken here is to simulate numerically some irradiances of significance to the planning process (see below) for a variety of canyon geometries, sky condi- tions, dates and latitudes. The computational scheme employed is that of Arnfield [19, 20]. However, a number of modifications have been introduced into the algorithm which improve its generality-and computational speed. Initialization of the canyon multiple reflection model for the diffuse solar irradi- ances follows Arnfield [21] with skyline zenith angles computed from receptor and canyon geometry. The radiance distribution employed may be isotropic or may be de- scribed by empirical formulae for clear skies [22] or for an overcast sky [23]. In addition, integration of multiply reflected contribu- tions along the x-axis (i.e., up- and down- canyon) is performed analytically rather than numerically, as was done in ref. 19.

The numerical experiments reported are for the following model inputs. Canyon H/W ~ ratios are 0.25, 0.5, 1.0, 2.0, 3.0 and 4.0

to represent a variety of surface geometries found in urban areas. Uniform albedos of 0.3 and 0.15 are employed for the walls and floor, respectively. These magnitudes represent approximate means for typical construction materials on these facets (see, for example, ref. 24, Table 8.2) and are also those adopted by Terjung and Louie [25] for their 'ci ty structure systems'. Data are presented for nor th-south and eas t -west canyons, and for the average of these two orientations to represent approximately a city with a 'gridiron' street pattern.

Initialization of the canyon radiation model requires irradiances of direct and diffuse solar radiation on an unobstructed, horizontal plane; these are provided for clear skies by the MAC model [26]. Gaseous at tenuation by Rayleigh scatter and absorp- tion due to water vapour and ozone are pammeterized using 'bulk' radiative properties [26 - 28]. Aerosol at tenuation makes use of a zenithal sun transmission of 0.91, a single scattering albedo of 0.98 and a forward-to- total-scatter ratio of 0.85 [26]. The 'back- scatterance' contr ibution to the diffuse irra- diance uses a surface albedo of 0.15 to represent an urban area [24]. Under clear conditions the diffuse radiation is treated as isotropic. Estimates of wi th in~anyon irra- diances are made also for overcast conditions. Cloud at tenuation of the clear sky global radiation follows [29] using the transmission for stratocumulus cloud from ref. 30 and the radiance distribution of ref. 23. The global solar irradiance is treated as totally diffuse under overcast skies. Calculations are per- formed at half-hourly intervals for the fif- teenth day- of each month for latitudes from 0 ° to 70 ° N, at 10 ° increments. (Results are applicable to southern hemisphere locations for dates approximately half a year away from the months used here.) Precipitable water inputs to the MAC model are zonal means.

Instantaneous irradiances at points within the canyon are used to compute the follow- ing:

(a) wall irmdiance (K~w), the mean irrad- lance over all elements on both walls;

(b) f loor irradiance (K~F), the mean it- radiance over all elements across the canyon floor;

(c) the irmdiance on a model human (K~p), situated in that part of the canyon

119

floor which is typically used by pedestrian traffic, and

(d) the absorbed irradiance at the canyon top (K'T), averaged over all elements across the canyon at roof height.

Quantity (c) is represented by the mean irradiance on the vertical surfaces and top ends of vertical right-cylinders with height/ radius ratios of 14.1 [31] located at distances from each wall equal to 15% of the canyon width. Direct irradiance is determined from solar position [32] and the shadow pattern on the canyon floor. Diffuse irradiances are contributed from the sky, by multiple reflec- tions between the facets of the canyon and by reflection of the global irradiance from the canyon floor.

The half-hourly irradiances for the fif- teenth day of each month are averaged to yield the month ly mean. Monthly means are averaged to approximate the annual mean.

In addition, all of the quantities defined above are expressed in dimensionless form, as proportions of the unobstructed global solar irradiance on a horizontal surface (K~). For K~w, K~F and K~p this number represents the proportion of the potentially available solar energy intercepted by the facet or solid; these ratios are referred to below as 'solar access indices' and are symbolized by Ow, aF and ap. For K ' T , the ratio with K~ is the canyon system absorptivity, aT.

RESULTS

The experiments described in the previous Section yielded 6912 monthly means and 576 annual means (and many more half-hourly values) for cloudless conditions alone. Only a Small ~mple of these data is reported here*.

Clear-sky canyon-floor irradiance The irradiance K ~ F is a major component

in the energy budget of the canyon floor and, as such, will play an important role in the thermal and moisture status of low vegetation at street level (e.g. lawns, ground covers),

*A comprehensive tabulat ion of all mean irrad- iances generated in the numerical experiments de- scribed is available on request.

in determining the thermal stress p lacedon paving materials and, possibly, in modifying ice incidence on urban streets and sidewalks. It may also be taken as a useful surrogate for the general illumination level for pedes- trians and road traffic within the canyon.

Figure 1 shows m e a n g ~ F data for De- cember, June and the year, by latitude, for all canyon configurations investigated. In all cases, floor irradiance decreases with in- creasing H/W, with the dependence being strongest for shallower canyon types. In winter, irradiances are qualitatively similar for N-S, E-W and grid configurations; with increasing latitude, solar elevation decreases, leading to complete shading in canyons of decreasiv~ aspect ratio. The floors of shallow canyons still receive higher K ~ F , however, because of their larger view factors for the sky and, hence, larger diffuse radiation receipts.

In summer, mean irradiances for N-S canyons vary relatively little with latitude (~100 W/m 2 in the most extreme case). However, E-W canyons show large changes with latitude at higher H/W ratios. Peak irradiances are at latitudes close to the solar declination where high solar elevations permit maximal penetration into the canyon cavity. At such latitudes, the e~fect of canyon depth is least apparent; for example, at 30 ° N, the floor of an E-W canyon with I-I/W = 4 receives about half of the solar irradiance incident on an unobstructed horizontal surface. Irradiances generally fall off away from the subtropics, more rapidly towards the equator than towards the pole. For example, all E-W canyons except that with a square cross section have higher g ~ F values at 70 ° N than at the equator. Because of the relative independence of latitude in K ~ F with N-S canyons, the iatitudinal pattern of gr id K ~ F resembles that for E-W can- yons, with reduced magnitudes. About one third of the unobstructed June K~ reaches street level at 30 ° latitude for the deep- est canyons arranged in a grid pattern, and high latitude canyon floors can still show an excess of radiation over those in equatorial regions.

Annual means of K ~ F for shallow E-W canyons decrease towards the pole while deeper ones show peak irradiance in the sub- tropics with decreases towards both higher

120

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Fig. 1. C a n y o n f loor i r radiances (W/m 2) by l a t i tude (° N), c a n y o n o r i en t a t i on , season and aspec t rat io. Line sym- bols d e n o t e aspect rat ios, as fol lows: + - - + H/W = 0 .25; x - - × H/W = 0.5; . - - * H/W = 1.0; B--[] H/W= 2 . 0 ; / ~ - / x H/W = 3.0; o - - o H/W = 4.0. Broken l ine shows i r radiance o n an u n o b s t r u c t e d , h o r i z o n t a l surface. ' G R I D ' d e n o t e s m e a n of i r radiances for n o r t h - s o u t h ( ' N - S ' ) and e a s t - w e s t ( ' E - W ' ) c a n y o n or ien ta t ions .

and lower latitudes. Intermediate canyon aspect ratios result in relatively constant K ~ F

in low latitudes with decreases polewards in mid-latitudes. Canyons oriented N-S show decreased K~F as latitude increases bu t gradients are much smaller than in the December case. Grid annual mean K~F decreases little between the equator and 20 ° N (for deeper canyons, it increases slightly); beyond that latitude it declines poleward.

The irmdiance on an urban canyon floor obviously depends both upon the character- istics of the surface geometry and on the irradisnce at the canyon top. Since the latter factor varies with latitude through its effect on solar elevation and day length, Fig. I does

not isolate the dependence of solar access on canyon form. This object ive is best satisfied by computing the canyon floor solar access index, aF. This ratio, for the grid street pattern only, is depicted in Fig. 2, for the year, for December and June, and for the average of data for March and September (to represent spring/autumn). The K~F and K~ data vary slightly between the two transition season months due to varying solar declination on the fif teenth day of the month and differences in precipitable water data at higher latitudes. However, differences in aF are small enough that averaged data are quite representative of the individual sea- s o n s .

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Fig. 2. C~yon floor access indices for a ~ d street pattern by ~pect ratio, latitude (o N) and se~on. Isoline inter- val is 0.1.

In both the June and March/September graphs, zones of higher solar access to the street are found at latitudes close to the solar declination, where high solar elevations permit direct irradiation of the floors of E-W canyons for large port ions of the day, even for deep canyons. These latitudes are those in which roof-level irradiances are also high due to solar position; hence the high canyon-floor irradiances depicted in Fig. 1 are due to the combined effect of solar path on K~ and OF. For bo th summer and spring/ autumn, deep canyons vary markedly in the amount of solar access which they permit at different latitudes while, for shallower structures, OF is only weakly dependent on location. The largest gradients of solar access lie on the periphery of high OF values and at small I-I/W ratios, with only modes t changes at la t i tude-aspect ratio combinations

in which much of the street is shaded for large portions of the daylight period. In the December case, maximum OF will be in the southern hemisphere, around the Tropic of Capricorn. Solar radiation penetrat ion to street level is only weakly dependent on latitude but changes rapidly as H/W increases to 1.5, with less-marked changes beyond that.

Annual data show some aspects of all three patterns. Latitudinal gradients of canyon-floor solar access are small in low latitudes (even reversed for deeper canyons) but OF decreases rapidly poleward of the subtropics, especially for deep canyons. For a street canyon with a square cross section, for example, about 60% of the annual roof- level irradiance will be available at street level at 0 ° latitude but this percentage will decline to 50% at 30 ° and to about 30% at 70 ° latitude.

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Fig. 3. Canyon wall i rradiances (W/m 2) by la t i tude (° N), canyon or ien ta t ion , season and aspect ratio. Line symbols deno t e aspect rat ios as fol lows: +- -+ H/W = 0.25; × - - x H/W = 0.5; * - - * H/W = 1.0; D--B H/W = 2.0; ix--ix H/W = 3.0; O--O H/W = 4.0. Broken line shows irradiance on an unobs t ruc t ed , hor izonta l surface. ' G R I D ' deno te s mean o f irradiances for n o r t h - s o u t h ( ' N - S ' ) and e a s t - w e s t ( ' E - W ' ) canyon or ienta t ions .

Clear-sky canyon-wall irradiance The irmdiance K~w is a significant com-

ponent in the energy budget of buildings bordering the stzeet and, as such, will play an important role in the energetic costs of heating and cooling them to maintain a comfortable environment for human activities within. In addition, K~w may be taken as an appropriate surrogate for the daylighting of interior building spaces through fenestra- tion.

Figure 3 shows mean K~w data for the solstice months and for the whole year, for all canyon configurations, by latitude. Overall, irmdiances are smaller than those on the canyon floor, with the difference

being most marked at low latitudes. In addition, KCw shows a much smaller depen- dence on latitude than does K'F, a reflection of the tendency for lower horizontal surface irradiances at high latitudes to be offset by smaller angles of incidence on vertical sur- faces, such as canyon walls. In common with Fig. 1, however, canyon-wall mean irradiances decline with increasing H/W in all cases.

In June, K~w for N-S canyons is virtually independent of latitude for high aspect ratios while shallower structures actually exhibit increased, wall irmdiances at high latitudes. Canyons with an E-W orientation show smaller differences between the canyon forms, with minimum irradlance at latitudes

123

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Fig. 4. Canyon wall access indices for a grid street pattern by aspect ratio, latitude (° N) and season. Isoline inter- val is 0.1.

close to the solar declination where solar paths will result in large angles of incidence for vertical receptors. The highest K~w values are at 70 ° N with small H/W ratios. For a grid canyon pattern, K~w is virtually independent of latitude for deep canyons while shallow ones exhibit an increase in K~w with increasing latitude.

In December, wall irradiances decrease monotonically with latitude for N-S canyons, gradients being greater for the shallow forms. For E-W streets, results are more com- plicated. Aspect ratios of 2, 3 and 4 give an inverse relationship between K~ w and lati- tude. Smaller H/W ratios, however, show peak K~w in the subtropics, with the latitude of the maximum moving poleward, especially for the shallowest canyons, a result of the inter- action between decreasing K~ and more favourable angles of incidence with increasing

latitude, and the increasing importance of shading effects on south-facing walls with a high solar zenith angle. It is noteworthy that at 50 ° and 60 ° N, the walls of an E-W canyon with H/W = 0.25 receive a higher global solar irradiance in December than does an unobstructed horizontal surface. Grid results for December show small gradients in the equatorial and tropical regions with relatively weak decreases towards the poles in the mid-latitudes.

Annual K~w data show remarkably little dependence on latitude for N-S, E-W or grid canyon forms, especially for larger aspect ratios. For a gridiron street pattern, for ex- ample, the largest difference between K~w at the equator and 70 ° N is about 50 W/m 2 (for a square cros~section canyon).

Figure 4 shows data for grid street pattern Ow for the same time periods as were used for

124

O" F in Fig. 2. Largely, these figures isolate the effect of solar elevation on an~le of incidence and on mutual shading by canyon walls. In both June and in the equinox months, lowest solar access is found at latitudes near the solar declination for the date, where high solar elevations minimize the irradiance on canyon walls. The data for December reflect this in the decreasing values of ~w apparent at latitudes below 20 ° N. Higher solar access is found at high latitudes with small H/W; this tendency is most marked in December (when Ow for the grid street pattern is near 1) and least apparent in June, again a manifestation of the advantage of a low sun for vertical surface irradiance. At larger H/W, mutual shading of canyon walls under low sun conditions partially offsets this advantage, leading to smaller access indices and a weaker dependence on latitude. While gradients of aw are smaller in the annual data, the ad- vantage of high latitude to the walls of open canyons is still apparent. Naturally, this tendency, when combined with the latitudinal dependence of K~, is the explanation for the weak dependence of K~w on latitude in Fig. 3.

Clear-sky irradiance on model pedestrian The calculations for the model pedestrian

are intended to provide preliminary data on an important component of the energy budget (and hence comfort) of a human being, exposed within canyons of varying geometries at different latitudes. Any applica- tion of these results should recognize that the method of computation implies, outdoor human activity within the urban environment to be random with respect to time of the day and with respect to the sunlit and shaded portions of the canyon floor.

Figure 5 shows mean irmdiances on the model pedestrian for June and December and for annual conditions, for N-S, E-W and grid configurations. As in the previous results, irradiance decreases as H/W increases, with the largest changes occurring at small aspect ratios. Latitudinal patterns depicted in Fig. 5 are very similar to those for canyon walls (cf. Fig. 3). This is perhaps unsurprising given the location of the pedestrian modelled, at the margin of the canyon floor, and the fact that 97% of the surface area of the solid used to simulate a person is vertical. Mag-

nitudes of irradiances are generally lower than those for walls, however, since direct solar radiation can be received on only half of the vertical surface of the model. In June, K~p varies little with latitude for deep N-S canyons and increases slightly with latitude for shallow ones. For E-W streets, however, deep canyons show a maximum at latitudes close to the solar declination, brought about primarily by reflection of K~F onto the vertical surfaces of the model pedestrian (cf. Fig. 1). In winter, K~p is very small for deep canyons and decreases poleward for shallow ones. On an annual basis, mean irradiances on the model pedestrian show remarkably little spatial variation; location within the city, manifested in varying canyon geometry, is likely to play a far more potent role in de- termining this component of the human energy budget than is the city's location by latitude.

Figure 6 shows values of the solar access index o~ for a grid street pattern. Despite the similar latitudinal dependence of K$~ and K~w their differing magnitudes result in lower values of av than aw and a rather different distribution by latitude and H/W. In June, the previously mentioned effect of enhanced floor reflection in deep canyons beneath a high sun is apparent for canyons with H/W > 1.5. For small aspect ratios, o~ shows little latitudinal dependence. A similar distribution occurs in the transitional seasons, with highest solar access now occur- ring at near-equatorial latitudes for deep canyons and with only small chau~es in op with location for small H/W. In December, all canyon forms give op magnitudes which vary little with latitude, except for those with H/W greater than ~1 at high latitudes. However, the significance of these high latitude differences is less than might be implied by the solar access indices because of the small horizontal surface global solar irradiances at this time of the year. On an annual basis, solar access to pedestrians shows independence of latitude at H/W ~ 1.0, increases slightly with latitude for shallower canyons and is extremely small with a tendency to decrease with latitude for H/W > 1.0.

Table 1 shows K~p data for the grid canyon configuration at selected dates and latitudes, expressed as a ratio of the same irradlance

125

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Fig. 5. Irradiances on model pedestrian (W/m 2) by latitude (° N), canyon orientation, season and aspect ratio. Line symbols denote aspect ratios as follows: +--+ H/W = 0.25; ×--X H/W = 0.5; *--* H/W = 1.0;D--[] H/W= 2.0; A--A H/W ffi 3.0; o--o H/W = 4.0. Broken line shows irradiance on an unobstructed, horizontal surface. 'GRID' denotes mean of irradiances for north-south ('N-S') and east-west ('E-W') canyon orientations.

fo r an o p e n site, u n o b s t r u c t e d b y buildings, f o r a m o d e l h u m a n s tanding on a surface wi th the same a lbedo as t he c a n y o n f loor . These da ta isolate t he e f fec t s o f c a n y o n g e o m e t r y (as d is t inc t f~om r e c e p t o r geom- e t ry ) o n t he solar access to a pedestr ian. In win ter , w h e n o p e n site KSp decreases po leward , c a n y o n shading e f fec t s r educe the i r radiance o n a pe r son wi th in the c a n y o n f u r t h e r w i th increasing la t i tude , as c a n y o n b o t t o m s and walls are t h r o w n increasingly in to shade (cf. Fig. 5), e x c e p t f o r the deepes t c anyons wh ich are signif icantly shaded at any la t i tude . In summer , K~p ac tua l ly in- creases slightly wi th l a t i tude at an o p e n site and , a l though c a n y o n wall shading reduces

the m ean i r radiance significantly, even fo r cases wi th H/W = 0.25 o r H/W = 0.5, i t does n o t o f f se t t h e general la t i tudinal t r end ; indeed, f o r la t i tudes less t h a n 40 ° N in Tab le 1, t he posi t ive associat ion b e t w e e n KSp and la t i tude is enhanced .

Clear.sI~y net so~ar irradiance at canyon top Figure 7 shows mean net solar irradiance

at the canyon top for June, December and the whole year, for all canyon forms and latitudes investigated. In all cases, maximum absorbed radiation decreases as H/W de- creases. However, irradiance differences for different canyon depths are extremely s~nall (about 35 W/m 2 maximum), far smaller than

126

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Fig. 6. Access indices for model pedestrian for a grid street pattern by aspect ratio, latitude (° N) and season. I~oline interval is 0.1.

TABLE 1

Mean irradiance on model pedestrian within street canyons in grid configuration expressed as a proportion of that on the same solid figure located in an open site with the same surface albedo as the canyon floor

Latitude Month H/W (degree)

0.25 0.50 1.0 2.0 3.0 4.0

0 ° N June 0.77 0.58 0.43 0.19 0.12 0.08 December 0.78 0.58 0.43 0.19 0.12 0.08

20 ° N June 0.77 0.64 0.49 0.32 0.23 0.17 December 0.65 0.52 0.27 0.16 0.10 0.08

40 ° N June 0.77 0.67 0.48 0.32 0.24 0.17 December 0.60 0.35 0.22 0.12 0.10 0.06

60 ° N June 0.72 0.55 0.42 0.20 0.14 0.11 December 0.34 0.24 0.15 0.10 0.10 0.10

t h e d i f f e r e n c e s g e n e r a l l y f o u n d b y a s p e c t r a t i o f o r t h e i r r ad i ances o n t h e c a n y o n f l o o r a n d wa l l s a n d o n t h e m o d e l p e d e s t r i a n .

D i f f e r e n c e s d u e t o c a n y o n o r i e n t a t i o n are e v e n smal ler . F o r all c a n y o n s in J u n e , K* T inc reases b e t w e e n t h e e q u a t o r a n d t h e T r o p i c

127

N - - S

I E - - W

G R I D

4 B B

3 S B

3 B M

2 5 ~

2 B B

1 S B

I B B

5 ~

4 B B

3 S B

313¢a

2 5 B

21313

1 5 B

1 ~

513

4 ~ I B

3 S ( 3

313B

2S13

2 B I ~

1 5 @

11313

S B

D E C E M B E R J U N E A N N U A L

113 213 313 413 513 613 713 113 213 3B 4B. 513 [~13 ~ B 113 213 313 413 513 6 B 71~

L A T I T U D E

Fig. 7. Net ix~adiemcas at cemyon t op (W/m 2) by la t i tude (° N), cemyon or ien ta t ion , season and empeet rat io. L ine symbols denote aspect rat ios as fo l lows: + - -+ H/W = 0.9-5; X--X H/W = 0.5; * - - * ~/W = 1.0; n--[~ H/W = ~-.0; /~--/~ ~/W = 3.0; O--O H/W = 4.0. ] ~oken l ine shows i~radiemce on an unobstructed, ho~i~.ontaJ surface. 'GRTD' denotes mean o f ixcadiances ~or no r t h - sou th ( ' N - S ' ) a~d east-west ( 'E -W ' ) cemyon o~ientations.

of Cancer, after which it varies little to 70 ° N. In December, K * T decreases poleward for all canyons.

In all months, aT is only weakly dependent on latitude, varying in the range 0.85 - 0.94, implying a canyon ' top albedo' of 0.06 - 0.15 (Table 2). The lowest albedos are associated with the deepest canyons bu t Table 2 suggests that, at least in the transitional seasons and winter, albedo tends to increase poleward.

Since no divergence of solar radiation occurs in the canyon air volume in the model employed, it follows that

K* T = ( H / W ) K ~ w ( I - - O~w) + K ~ F ( I - - O~F)

where, aw and o/F are the wall and floor albedos, respectively. The rather smooth

dependence of K * T o n latitude and the small differences among canyon types contrasts markedly with the latitudinal behavior of K~w and K~F in many of the graphs in Figs. 1 and 3, suggesting a low degree of association between the individual irradiances on the right-hand side of the above equation and that on the left. This is revealed in Table 3, which shows the linear correlation coefficient between K~w, K ~ F and K~p and K ' T , by month. For much of the year, the net canyon top irradiance is a poor predictor of the irradiances on the canyon facets or on a model pedestrian for canyons of different orientation, aspect ratio and location. In general, the highest correlations are found in that part o f the year when the solar de-

128

TABLE 2

Top albedo of street canyons in grid configuration by aspect ratio, season and latitude

Latitude H/W (December) H/W (March/September) I-I/W (June) (degree)

0.25 1.0 4.0 0.25 1.0 4.0 0.25 1.0 4.0

0 ° N 0.13 0.10 0.08 0.13 0.09 0.06 0.13 0.10 0.08 20 ° N 0.13 0.10 0.09 0.13 0.09 0.07 0.13 0.09 0.06 40 ° N 0.13 0.11 0.10 0.13 0.10 0.09 0.13 0.09 0.07 60°N 0.15 0.15 0.15 0.13 0.12 0.10 0.11 0.10 0.08

TABLE 3

Linear correlation coefficient between net solar irradiance at canyon top and irradiances on canyon facets and model pedestrian

Month Correlation between canyon top K* and irradiance on:

Wall Floor Pedestrian

January 0.74 0.63 0.58 February 0.64 0.60 0.52 March 0.30 0.59 0.43 April -0 .15 0.43 0.19 May --0.42 0.08 --0.13 June --0.16 --0.15 --0.06 July --0.31 --0.14 --0.13 August --0.30 0.28 0.01 September 0.07 0.54 0.35 October 0.53 0.60 0.47 November 0.72 0.56 0.56 December 0.75 0.64 0.59

TABLE 4

Canyon absorptivity and solar access indices for overcast skies, by aspect ratio

Aspect Canyon ratio absorptivity H/W

Solar access index

Wall Floor Pedestrian

0.25 0.87 0.45 0.84 0.42 0.50 0.89 0.41 0.70 0.34 1.00 0.90 0.34 0.51 0.25 2.00 0.92 0.24 0.30 0.15 3.00 0.92 0.18 0.21 0 .11 4.00 0.92 0.14 0.16 0.08

c l ina t ion is in the s ou t he rn h e m i s p h e r e and s imple gradients o f all i rmdiances t e n d to exis t b e t w e e n the e q u a t o r and 70 ° N.

T h e p o o r cor re la t ions shown in Tab le 3 suggest t h a t an empir ica l a p p r o a c h to s t ree t c a n y o n design, using r e m o t e l y sensed u rban te r ra in a lbedos [ 3 3 - 35] as sur roga tes fo r

i r radiances on c a n y o n face t s o r pedes t r ians at s t ree t level, can be e x p e c t e d to have on ly l imi ted appl icabi l i ty .

Overcast-sky irradiance The simulation procedure employed in this

study for overcast conditions gives K~w, K~F, K~p and K*T data which are independent of canyon orientation. Expressed relative to the unobstructed local global irradiance, as Ow, OF, Op and aT, the data become addi- tionally independent of latitude and month. Table 4 shows these results as functions of canyon aspect ratio. As with the clear sky results , solar access indices decrease and c a n y o n abso rp t iv i ty increases as H/W in- creases. In general , however , t he d i f fe rences are smal ler t h a n in Figs. 2, 4 and 6 because deep c a n y o n s are n o t so m a r k e d l y depr ived o f i r radia t ion o n the i r f loors and lower walls since shading e f fec t s are n o t s ignif icant and a heavy overcas t gives high rad iance in t he zeni tha l reg ion o f t he sky [18, 23 ] , max imiz - ing p e n e t r a t i o n to s t ree t level.

THE ZONE OF COMPATIBILITY: SOME OBSERVATIONS

Mid-latitude cities under clear skies O k e ' s [8] suggested maximx~m aspec t ra t io

o f 0.6 fo r an E - W c a n y o n a t 45 ° l a t i tude is a f o r m suf f ic ien t t o ma in t a in d i r ec t -beam i r rad ia t ion over two- th i rds o f the equa tor - facing wall a t n o o n o n the win te r solstice. T h e resul ts p re sen ted a b o v e show t h a t an u r b a n surface w i th a gr id i ron s t ree t p a t t e r n o f N - S and E - W c a n y o n s having this a spec t ra t io will expe r i ence wall i r radiances equa l t o 64%, 36% and 51% o f K~ u n d e r c loudf ree skies in win te r , s u m m e r and sp r i ng / au tumn , respect ive ly . O n an annua l basis, t he walls will receive s o m e w h a t less t h a n one-ha l f

(46%) of the horizontal surface irradiance. The access index Ow is smaller in the high sun season, so that K~w will not increase as much from winter to summer as will K~, a desirable at tr ibute in the temperate lati- tudes where buildings may require heating in winter and cooling in summer.

This maximum desirable aspect ratio will result in f loor irradiances of 42%, 70%, 56% and 60% of the available horizontal surface flux density in winter, summer, the transitional seasons and the year as a whole, respectively. Pedestrians will intercept about 30% of the potential solar radiation on an annual basis.

Canyons at the lower end of Oke's zone of compatibil i ty (with H/W = 0.4) in all cases exhibit access indices greater than those for the maximum recommended aspect ratio; K~w is increased by 15% in winter bu t remains nearly unchanged in the summer. Street, level solar irradiances are increased (by 11% on an annual basis and up to 17% in winter), as are radiation loads on pedes- trians (7% annual, 11% in winter).

More generally, for the mid-latitude belt be tween 35 ° and 55 ° latitude, aspect ratios in the range 0.4 - 0.6 will result in irradiances on the floor, walls and model pedestrians which are 58 - 75%, 42 - 55% and 27 - 36% of the yearly total of K~, respectively.

Tropical cities under clear skies Under low latitude conditions, minimiza-

t ion of solar irradiances within the urban environment may of ten be a desirable criter- ion in urban design. For gridiron canyons with H/W ratios in the zone of compatibil i ty, annual access indices decrease equatorward of 35 ° latitude to magnitudes around one- third at the equator. The dominance of the direct component of the global solar irrad- iance under clear high-sun conditions ensures the favourable circumstance that Ow will be small when K~ is hrge. Solar access to walls can always be decreased by increasing H/W to larger values than those appropriate for the temperate latitudes. However, signif- icant reductions in Ow require extreme changes; for example, at 0 ° latitude, a fivefold increase in H/W from 0.6 would be necessary to reduce annual totals of wall irradiance by one-half. Floor irradiances are more readily manipulated by changing ratios of

129

wall height to street width, the practical benefit of which is reflected in the vernacular architecture of parts of the dry tropical world (e.g., Arab housing in North Africa [18]). For example, at 25 ° latitude, OF varies from 0.78 at H/W = 0.4, to 0.68 at the high end of the mid-latitude zone of compatibility, and has been reduced to 0.34 for buildiugs which are twice as high as the street is wide. Controlling canyon floor solar radiation may be more critical than doing so for building walls given that solar geometry requires that the floor access index at low latitudes will increase as K~ increases.

Under sunny tropical conditions, human irradiances may be excessive and their reduc- tion may be a realistic objective of urban planning. At 25 ° latitude, for example, an aspect ratio of 0.6 will give ~p = 0.26. This can be halved by increasing H/W to about 2.0. In tropical latitudes, ~p varies little with season so that K~p will be approximately proportional to K~ throughout the year (although this irradiance varies relatively little under clear conditions in such regions).

High latitude cities under clear shies Poleward of 55 ° latitude, city buildings

will require heating and street-level environ- ments will exhibit adverse characteristics, by virtue of low temperatures, for a signif- icant port ion of the year. While solar access indices are in some cases markedly dependent on street geometry at high latitudes, the small magnitudes of K~ may militate against manipulation of canyon geometry for solar access at the expense of the competing requirements of shelter and nocturnal heat- island intensity. Indeed, poleward of the Arctic (and Antarctic) Circles, solar access arguments will be irrelevant for much of the year during polar night. Nevertheless, the energetic costs of 'high rise' construction are profound in a relative sense. For example, at 70 ° latitude, the annual total of K~ w is halved as H/W increases beyond the mid- latitude zone of compatibil i ty to 1.7 and is reduced to one-third by H/W = 2.8. Street- level irradiance is halved with a square canyon cross section and is reduced to one<luarter by H/W = 2.75.

Cities under overcast sidles In climates characterized by a high fre-

quency of heavy cloud cover, control of

130

solar access by the manipulation of street geometry is less readily achieved. For all latitudes under such conditions, a canyon with H/W = 0.6 will receive 39% of annual K~ on its walls, 66% on its floor and 32% on a human located within its pedestrian zone. Widening the canyon to an aspect ratio of 0.4 will increase floor irradiance to 75% of annual K~ but the other irradiances will show only minor increases.

CONCLUDING REMARKS

The major purpose of this study has been to present and explore the potential utility of a methodology intended to .assist in the formulation of urban design guidelines from the point of view of solar access to street canyon facets and to the human occupants of those canyons. Numerical simulations of 'solar access indices' are proposed as a simple means of exploring the interactions of a far larger number o f combinations of potentially plannable characteristics of street canyons than would be convenient with even a large measurement program. In this study, only the simplest combinations of these variables have been treated. In a particular planning application, the effects of a greater diversity of canyon geometries, construction materials and seasonally dependent source geometries (especially seasonally varying diffuse pro- portions brought about by cloud cover) could be investigated. Moreover, in some cases, access indices applicable for different time periods from those used here might be more appropriate; for example, access indices for pedestrians might be more usefully based on the human activity period in the outdoor city environment. Access index data could be conveniently tabulated, pre- sented in nomogram form or approximated by interpolating formulae for use by the planning practitioners. Such instruments would constitute the types of quantitative and easily understood rehtionships sought by Oke, at least within the limited context of manipulating the solar radiation environ- ment within the urban canopy layer.

ACKNOWLEDGEMENTS

This work was made possible with com- puter time provided by the Instruction and

Research Computer Center of the Ohio State University and by the Ohio Super- computer Center. Some of the Figures were produced by Gerald Mills.

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