the influence of urban canopy configuration on urban albedo

THE INFLUENCE OF URBAN CANOPY CONFIGURATION ON URBANALBEDO

AKIRA KONDO, MEGUMI UENO and AKIKAZU KAGADepartment of Environmental Engineering, Graduate School of Engineering, Osaka University,

Osaka, Japan

KATSUHITO YAMAGUCHIDepartment of Global Architecture, Graduate School of Engineering, Osaka University, Osaka,

Japan

(Received in final form 18 January 2001)

Abstract. We propose a calculation method for shortwave radiation flux and longwave radiation fluxwithin the urban canopy and investigate the influence of urban canopy configuration on net radiationflux. In the assumed urban configuration, buildings of equal size are arranged in a regular latticewithin the urban canopy. The net shortwave radiation flux and longwave radiation flux within theurban canopy were calculated by the photon tracking method based on the Monte Carlo method. Thealbedo value obtained by this method shows close agreement with experimental data, and the averagesky view factor shows almost perfect agreement with the theoretical value. Moreover, we calculatedthe urban albedo for the urban canopy configuration including roads and building height distribution.We found that the sky view factor of the ground surface is high when building coverage is low,building height is low, open space by roads exists, and building height is non-uniform. Moreover, wefound that the albedo value is high when building height is small, open space by roads is wide, andbuilding height is uniform. The albedo value was found to vary in a complicated manner with changein building coverage.

Keywords: Albedo, Longwave radiation, Monte Carlo method, Shortwave radiation, Sky viewfactor, Urban canopy.

1. Introduction

The primary causes of the heat island phenomenon accompanying urbanizationare considered to be increased anthropogenic heat, reduced water evaporation, in-creased flux in shortwave absorption by the urban canopy (reduction of albedo),and reduced flux in longwave radiation emitted to the sky from the urban canopy(Oke, 1982). The heat island phenomenon was first observed in large urban areasin the 1960s. During the past forty years, many researchers have studied the heatisland phenomenon through observation, experimentation, and mathematical mod-els. Nakamura and Oke (1988) measured the temperature distribution in the urbancanopy and elucidated the relation between building wall orientation and temper-ature. Aida (1982) reported the relation between urban albedo and solar altitudeangle obtained for an idealized urban model, and Arnfield (1988) evaluated his

Boundary-Layer Meteorology 100: 225242, 2001. 2001 Kluwer Academic Publishers. Printed in the Netherlands.

226 AKIRA KONDO ET AL.

urban canyon radiation model to the albedo measurement data of Aida (1982), andSwaid (1993a) reported the relation between the sunlit faces of a building and solaraltitude angle. Kimura and Takahashi (1991) and Saitoh et al. (1996) elucidated theheat island phenomenon by use of a meso-scale numerical model. Uno et al. (1989)applied the numerical model developed for the vegetation canopy layer (Wilsonand Shaw, 1977; Yamada, 1982) to the urban canopy layer, and elucidated theatmospheric and thermal environment in the urban canopy. As mentioned above,calculating net radiation flux in the urban canopy is difficult, because the buildingconfiguration and orientation have complicated influences.

In this study, shortwave and longwave radiation fluxes in the urban canopy arecalculated by the photon tracking method based on the Monte Carlo method, underthe assumption that buildings of uniform size are arranged regularly within theurban canopy; the accuracy of this calculation method was verified. Next, we pro-pose a calculation method for shortwave and longwave radiation fluxes within theurban canopy that takes into consideration roads and building height distribution.Finally, we discuss the influence of urban canopy configuration on albedo and skyview factor.

2. Calculation Method for Radiation Flux within the Urban Canopy

2.1. UNIFORM URBAN CANOPY CONFIGURATION

2.1.1. Modelling of Urban Canopy ConfigurationBuildings of equal size are assumed to be arranged in a regular lattice within theurban canopy (Figure 1a). We call the small region including only one buildingBLOCK 1 (Figure 1b). The size of BLOCK 1 is WSX WSY and the volume ofone building in BLOCK 1 is WBX WBY hC (urban canopy height). The longaxis of the building is oriented east-west. Building coverage () is given by

= WBXWBYWSXWSY

. (1)

2.1.2. Calculation Method for Shortwave and Longwave Radiation FluxesBecause of the existence of buildings, the temporal change in the flux of radiationinto the urban canopy is complicated. Radiation energy is transported by photons.If the behaviour of all photons could be tracked, the radiation flux into the urbancanopy could be calculated perfectly, but tracking all photons is time consuming.Therefore we extended the two-dimensional photon tracking method based on theMonte Carlo method, used by Aida and Gotoh (1982), to three dimensions, andcalculated net radiation flux within the urban canopy. Kobayashi and Takamura(1994) used the same method in order to calculate longwave radiation. The short-wave radiation flux into the urban canopy top is composed of direct solar radiation

THE INFLUENCE OF URBAN CANOPY CONFIGURATION ON URBAN ALBEDO 227

Figure 1. (a) Idealized configuration of uniform urban canopy. (b) Schematic diagram of BLOCK1.

ID and diffuse solar radiation IS , which are given by Bougures Equation (2) andNagatas Equation (3), respectively (see Utagawa, 1984),

ID = I0T 1/ sin() sin(), (2)IS = (I0 ID) sin()(0.66 0.32 sin()) {0.5 + (0.4 0.3T ) sin()} , (3)

where I0 is the solar constant, T is the coefficient of atmospheric transmission, and is the solar altitude angle. Figure 2 is a schematic diagram of the photon trackingprocesses for diffuse and direct solar radiation within BLOCK 1. The trackingprocesses for shortwave radiation are as follows.1. A photon is cast into the urban canopy from the top face of BLOCK 1. In the

case of direct solar radiation, the incident direction of a photon is determinedfrom the solar altitude angle and the hour angle. In the case of diffuse solarradiation, the incident direction of a photon is determined from azimuth a andincidence angle a given by

a = 2r1, a = cos1(1 2r1), (4)

where r1 is a value selected from the uniform random number series (0 1).2. When a photon collides with a facet (including the ground surface), a fraction

of its energy is absorbed by the facet, and the remainder is reflected in eithermirror reflection or diffuse reflection. Although the combination of reflectionscan be determined by reference to a predetermined ratio, we assume that onlydiffuse reflection occurs in all facets. The direction of the diffuse reflection isdetermined by azimuth a and incidence angle a . Incidence angle is based onLambelts cosine law, and given by

a = 2r2, a = cos1

1 r2, (5)


Figure 2. Schematic diagram of photon tracking method.

where r2 is another value selected from the uniform random number series (01).

3. Operations 1, 2 are repeated until a photon exits BLOCK 1 through its topface. (The maximum number of repetitions is limited to 20.) When a photonexits BLOCK 1 through a lateral face, a photon with the same incident direc-tion is recast from the opposite lateral face. As shown in Figure 2, the photonthat exits BLOCK 1 from point A is recast from point A.

The above procedures 13 are repeated for numerous photons.The albedo of the urban canopy is expressed by,

Albedo = (ND FD)ID + (NS FS)ISNDID +NSIS , (6)

where N is the number of the photons cast into BLOCK 1, F is the total numberof photons absorbed by the faces, and the subscripts D and S represent direct solarradiation and the diffuse solar radiation, respectively.

The tracking processes for longwave radiation are composed of the followingtwo steps.1. A photon is cast into BLOCK 1 from a specified facet. The direction of the

radiation is determined by Equation (5). When a photon exits BLOCK 1through a lateral face, the same operations employed for the tracking methodof shortwave radiation flux are executed.

2. When the released photon collides with another facet, including the top face ofBLOCK 1, tracking is terminated. The emissivity of all facets is assumed tobe 1.


The above procedures are applied to all facets. The view factor Fij is calculated bythe following,

Fij = NijNi

, (7)

where Ni is the number of photons released from facet i, and Nij is the number ofphotons among Ni that are absorbed by facet j . In the case where facet j is the topface of BLOCK 1, the view factor is called the sky view factor (SVF).

2.2. URBAN CANOPY CONFIGURATION INCLUDING ROADS

2.2.1. Modelling of Urban Canopy ConfigurationThe urban canopy configuration including roads is divided into three patterns, ac-cording to the orientation of the roads. The urban canopy configuration with roadsrunning east-west is shown in Figure 3a. In this pattern, n buildings of equal sizeexist between two roads. Similarly, the urban canopy configuration with roads run-ning north-south and that with both roads running north-south and roads runningeast-west are shown in Figures 3b and 3c, respectively. In each of Figures 3a3c,the region surrounded by the thick line is designated the basic unit. As shown inFigure 4, which is an enlarged view of a portion of Figure 3a, the width of a roadrunning east-west is WRY , the area of one lot is WSXWSY , and the volume of onebuilding is WBX WBY hC .

2.2.2. Calculation Method for Shortwave and Longwave Radiation FluxesWe now explain the calculation method for radiation flux within the urban canopyshown in Figure 3a. If the photon tracking method based on the Monte Carlomethod described in Section 2.1 is applied directly to the basic unit, calculationis very time consuming when the number of lots is large. Therefore, we propose amethod that can calculate radiation flux within the basic unit by considering onlyone road and one lot, as shown in Figure 4 (called BLOCK 2 hereafter.). Thephoton tracking method is almost identical with the method described in Section2.1, with a few differences.

The points of difference from the shortwave radiation tracking method de-scribed in Section 2.1 are as follows.1. The ratio of the number of the photons cast into BLOCK 2 from the top face

over the road to the number of photons cast into BLOCK 2 from the top faceover the lot is set equal to the ratio of WRY : n WSY , where n is the numberof lots in the basic unit.

2. When a photon exits BLOCK 2 through a lateral face, it is re-cast intoBLOCK 2 from the opposite lateral face with the same incident direction.However, in the case where a photon reaches section C-C or section B-Bshown in Figure 4, parameter n determines whether a photon is recast to theroad region or to the next lot region. That is, every nth photon reaching section


Figure 3. (a) Urban canopy configuration with roads running east-west. (b) Urban canopy config-uration with roads running north-south. (c) Urban canopy configuration with both roads runningnorth-south and roads running east-west.

C-C is recast into the road region of BLOCK 2 from section A-A, and theremaining photons are recast into the lot region of BLOCK 2 from sectionB-B. Similarly, every nth photon reaching section B-B enters the road regionas is, and the remaining photons collide with the facet of the next building orare recast into the lot region of BLOCK 2 from section C-C.

The points of difference from the longwave radiation tracking method describedin Section 2.1 are as follows.


Figure 4. Schematic diagram of BLOCK 2.

1. The ratio of the number of the photons cast into BLOCK 2 from a facetwithin the road region to the number of photons cast into BLOCK 2 from afacet within the lot region is set equal to the ratio of WRY :nWSY .

2. When a photon exits BLOCK 2 through a lateral face and a photon reachessection C-C or section B-B, the same procedures described above areexecuted.

The shortwave and longwave radiation fluxes of the configurations in Figures 3band 3c can be calculated by the same procedures.

2.3. URBAN CANOPY CONFIGURATION INCLUDING BUILDING HEIGHTDISTRIBUTION

2.3.1. Modelling of Urban Canopy ConfigurationBuildings of different heights are assumed to be arranged in a regular lattice withinthe urban canopy, as shown in Figure 5. The region including only one building isnamed BLOCK 3, as shown in Figure 6. The area of BLOCK 3 is WSX WSY ,and the volume of one building is WBX WBY h (building height). The canopyheight hC is defined as the height of the highest building.

2.3.2. Calculation Method for Shortwave and Longwave Radiation FluxesThe shortwave radiation tracking method is almost identical with the methoddescribed in Section 2.1. The points of difference are as follows.1. The height of one building in BLOCK 3 and the height of two buildings adja-

cent to BLOCK 3 are determined by a random number, following a specifiedbuilding height distribution.

2. When a photon exits BLOCK 3 through a lateral face, it is recast intoBLOCK 3 from the opposite lateral face with the same incident direction,and the heights of buildings are determined again by a random number. Whena photon exits BLOCK 3 through point A as shown in Figure 6, it is recast


Figure 5. Urban canopy configuration including building height distribution.

Figure 6. Schematic diagram of BLOCK 3.

into BLOCK 3 from point A located on the opposite lateral face. At thattime, the new height of the southern building must be equal to the last buildingheight in BLOCK 3, and the new building height in BLOCK 3 and that ofthe eastern building are determined again by random numbers.

The longwave radiation tracking method is identical with the method described inSection 2.1, except that building height is changed.

2.4. NET RADIATION FLUX WITHIN URBAN CANOPY

The shortwave radiation flux Ie absorbed by a facet i is given by

Ie = AsAi

(F iD

NDID + F

iS

NSIS

), (8)

where As is the area of BLOCK, Ai is the area of a facet i, and F i is the numberof the photons absorbed by a facet i. Moreover, the ratio of the shortwave radiation


flux absorbed by a facet i and the shortwave radiation flux above the urban canopyis given by

ab,i = IeID + IS

= AsAi

(F iD/ND)ID + (F iS/NS)ISID + IS . (9)

From the ratio ab,i (Equation (9)) and the view factor Fij (Equation (7)), the netradiation flux Rnet,i on a facet i is given by

Rnet,i = ab,iRS !iT 4i + !iFisRL +

j

Fij !jT4j

(10)

where RS and RL are the downward shortwave radiation flux and longwaveradiation flux respectively, Ti is the temperature on a facet i, ! is the emissivity,and is the StefanBolzmann constant. Given the net radiation flux, the temper-ature distribution within the urban canopy can be obtained by resolving the energybudget equation on all facets (Kondo et al., 1998).

3. Calculation Results

The influence of urban canopy configuration on shortwave and longwave radiationfluxes was investigated. The factors characterizing the urban canopy configura-tion are: (1) building coverage, (2) canopy height, (3) orientation of roads, and(4) building height distribution. Table I shows the values of each factor used in16 calculations. The building coverage and the canopy height of our calculationsare a little large compared with that of the real city (Arnfield, 1982; Voogt andOke, 1997). The solar altitude angle is calculated from latitude, longitude, and thedate shown in Table II. Reflectivity is assumed to be 0.45 for all building wallsand the ground surface, a value corresponding approximately to bricks with highreflectivity (Arnfield, 1982). The number of photons cast into the calculated unit is1.92 million in all cases exhibiting convergence of solutions (Figure 7).

3.1. ACCURACY OF CALCULATION METHOD

Aida (1982) manufactured an urban model with numerous concrete blocks of0.15 m 0.15 m 0.15 m arranged on a concrete foundation at 0.15-m in-tervals, and measured solar radiation flux and reflected shortwave radiation fluxfrom the urban model, and obtained the albedo value from the ratio of incidentsolar radiation flux to shortwave radiation flux reflected from concrete blocks. He


TABLE IUrban canopy configuration and the value of sky view factor of the ground surface.

hC WSX WSY WBX WBY WRX WRY n Fgs() (m) (m) (m) (m) (m) (m) (m) () ()

Case 1-1 0.09 25 50 50 15 15 0.736Case 1-2 0.16 25 50 50 20 20 0.649Case 1-3 0.25 25 50 50 25 25 0.557Case 1-4 0.36 25 50 50 30 30 0.457Case 1-5 0.49 25 50 50 35 35 0.348Case 1-6 0.64 25 50 50 40 40 0.229Case 2-1 0.25 5 50 50 25 25 0.876Case 2-2 0.25 15 50 50 25 25 0.688Case 2-3 0.25 25 50 50 25 25 0.557Case 2-4 0.25 30 50 50 25 25 0.505Case 2-5 0.25 40 50 50 25 25 0.424Case 2-6 0.25 50 50 50 25 25 0.363Case 3-1 0.36 25 50 50 30 30 0.457Case 3-2 0.36a 25 50 50 34.2 34.2 30 2 0.526Case 3-3 0.36a 25 50 50 34.2 34.2 30 2 0.526Case 3-4 0.36a 25 50 50 39 39 30 30 2 2 0.582Case 4-1 0.36 25 50 50 30 30 0.457Case 4-2 0.36 25b 50 50 30 30 0.471

Building height distribution 15 m (0.3), 25 m (0.4), 35 m (0.3)Case 4-3 0.36 25b 50 50 30 30 0.466

Building height distribution 20 m (0.6), 30 m (0.3), 40 m (0.1)WRX: Width of a road running north-south.a Building coverage of area including roads.b Average building height.Case 1-3 and Case 2-3 are the same calculations.Case 1-4, Case 3-1 and Case 4-1 are the same calculations.

TABLE IIConstants to calculate shortwave flux.

Latitude 34.8 [deg]Longitude 135 [deg]Date The summer solstice.


Figure 7. Convergence of solutions for Case 13.

Figure 8. Comparison of the experiment and the calculated albedo. Experiment value was quotedfrom Aida (1982).

reported that the albedo value of this concrete was 0.4. Shortwave radiation fluxwas calculated on the basis of the same conditions employed in the present exper-iment and the calculated albedo value was compared with the measured value. Asshown in Figure 8, the value measured at approximately 1500 local time is greaterthan the calculated value, but the two values show close agreement at other times.This figure demonstrates that the calculation method for shortwave radiation fluxdescribed in Section 2 is reasonable.


TABLE IIIComparison of the values of average sky view factor.

hC Average sky view factorBy Monte Carlo method By Equation (11)

() (m) () ()

Case 1-1 0.09 25 0.603 0.603Case 1-2 0.16 25 0.512 0.512Case 1-3 0.25 25 0.428 0.428Case 1-4 0.36 25 0.347 0.347Case 1-5 0.49 25 0.267 0.267Case 1-6 0.64 25 0.183 0.183

Case 2-1 0.25 5 0.789 0.789Case 2-2 0.25 15 0.556 0.556Case 2-3 0.25 25 0.428 0.428Case 2-4 0.25 30 0.384 0.384Case 2-5 0.25 40 0.319 0.319Case 2-6 0.25 50 0.272 0.272

Swaid (1993b) defined the average sky view factor in a uniform urban canopyby the following,

SV F = WSXWSY WBXWBYWSXWSY WBXWBY + 2hC(WBX +WBY ) . (11)

In contrast, the average sky view factor calculated by the Monte Carlo methodis given by

SV F =

AiFisAi

, (12)

where Ai is the area of facet i, and Fi,s is the sky view factor of facet i. Table IIIshows the average sky view factors obtained by Equations (11) and (12) for sev-eral urban canopy configurations. The two average sky view factors show almostperfect agreement. Therefore, the calculation method for longwave radiation fluxdescribed in Section 2 is also accurate.

3.2. CALCULATED RESULTS OF SHORTWAVE RADIATION FLUX FORDIFFERENT VALUES OF BUILDING COVERAGE

Six calculations were carried out, differing in building coverage in the uniformurban canopy configuration ( = 0.09 for Case 1-1, 0.16 for Case 1-2, 0.25 for


Figure 9. Diurnal variations of albedo by changing of building coverage.

Case 1-3, 0.36 for Case 1-4, 0.49 for Case 1-5, and 0.64 for Case 1-6). Diurnalvariation of the albedo is shown in Fig. 9. For high solar altitude angle, the albedovalues in Case 1-6, in which building coverage is high, and Case 1-1 and Case 1-2,in which building coverages are low, are greater than in Case 1-4 and Case 1-5, andthe amount of the direct solar radiation is about eight times the amount of diffusesolar radiation (Figure 10).

The albedo value of Case 1-1 becomes large, because a photon of direct solarradiation can easily exit the urban canopy. The albedo value of Case 1-6 alsobecomes large, because a large number of photons are reflected to sky by roof.As the solar altitude angle decreases, the proportion of diffuse solar radiationincreases. Therefore, because a photon cannot easily exit the urban canopy (aphoton repeatedly collides with buildings), the albedo value in the case of lowbuilding coverage becomes small. In addition, the albedo has the local maximumat about 1800 local time because solar azimuth becomes 90 degrees and directsolar radiation collides easily with a ground surface. These results are shown in thecalculations of Armfield (1982).

3.3. CALCULATED RESULTS OF SHORTWAVE RADIATION FLUX FORDIFFERENT CANOPY HEIGHTS

Six calculations were carried out, differing in canopy height in the uniform urbancanopy configuration (hC = 5 m for Case 2-1, 15 m for Case 2-2, 25 m for Case2-3, 30 m for Case 2-4, 40 m for Case 2-5, and 50 m for Case 2-6). Diurnal vari-


Figure 10. Diurnal variations ratio of the direct solar radiation and the diffuse solar radiation for theincoming solar radiation.

ations of the albedo value are shown in Figure 11. For all times, as hC decreases,the albedo value increases. These results are same as the calculations of Arnfield(1982). Moreover, as the solar altitude angle increases, the difference in albedovalue attributable to building height increases. This is because a photon cannoteasily exit the urban canopy in the case of higher buildings.

3.4. CALCULATED RESULTS OF SHORTWAVE RADIATION FLUX FORDIFFERENT ROAD ORIENTATIONS

Three calculations were carried out, differing in road orientation (east-west forCase 3-2, north-south for Case 3-3, and both east-west and north-south for Case3-4). In all three cases, building height and building coverage are equal to those inCase 3-1, and the number of lots within the basic unit is two. Diurnal variations ofthe albedo value are shown in Figure 12. At all times the albedo value of Case 3-1 isthe lowest among these four cases, because the open space by roads is wide in threecases (all except Case 3-1). Until about 1500 local time, when the solar altitudeangle is still high, Case 3-4 shows the highest albedo value, Case 3-1 shows thelowest albedo value, and Case 3-2 and Case 3-3 show intermediate albedo valuesthat are almost equal. After 1500 hours, the albedo value is lower in Case 3-3than in Case 3-2, because the greater portions of roads running north-south are inshadow, since the solar altitude angle is low. As a result, a photon tends to collidewith building walls and cannot easily exit the urban canopy.


Figure 11. Diurnal variations of albedo by changing of building height.

Figure 12. Diurnal variations of albedo for different road orientations.


Figure 13. Diurnal variations of albedo for different building height distributions.

3.5. CALCULATED RESULTS OF SHORTWAVE RADIATION FLUX FORDIFFERENT BUILDING HEIGHT DISTRIBUTIONS

Two calculations were carried out, differing in building height distribution. In bothcases, average building height is equal to that in Case 4- 1, and other parametervalues are also equal to those in Case 4-1. Figure 13 shows diurnal variations ofthe albedo value. In Case 4-1, a photon that collides with a building roof is alwaysreflected to the sky. In both Case 4-2 and Case 4-3, a photon that collides witha building roof may subsequently collide with the wall of another building. Con-sequently, the albedo values in Case 4-2 and Case 4-3 are smaller than in Case 4-1.The difference of the albedo is especially seen after 1700 hours. There is almost nodifference between Case 4-2 and Case 4-3.

3.6. CALCULATED RESULTS OF SKY VIEW FACTOR

Table I shows the value of sky view factor of the ground surface Fgs . Sky viewfactor decreases as building coverage becomes denser or as building height in-creases. For given values of building coverage and building height, sky view factorincreases with width of the open space by roads. The values in Case 3-2 and Case3-3 are in perfect agreement, because the urban canopy configurations in Case 3-2and Case 3-3 are mutually symmetrical. In the case where average building heightis equal to that in Case 4-1, the values of sky view factor in Case 4-2 and Case4-3 with building height distribution are greater than that in Case 4-1 with same


building height. Sky view factor was greater in Case 4-2 than in Case 4-3, becausethe building height distribution in Case 4-3 is approximately uniform.

4. Conclusions

Shortwave radiation flux and longwave radiation flux in the urban canopy werecalculated precisely by the photon tracking method based on the Monte Carlomethod. The influence of urban canopy configuration on net radiation flux wasinvestigated by varying four factors; (1) building coverage, (2) canopy height, (3)orientation of roads, and (4) building height distribution. The albedo value wasfound to decrease, with increasing building height and decreasing uniformity ofbuilding height distribution. When solar altitude angle is high, the albedo valueis large, regardless of the building coverage value. When solar altitude angle islow, the albedo value is small in the case of low building coverage. Albedo valuechanges in a complicated manner with road orientation, because of differences inbuilding shadows at low solar altitude angles, but generally increases with widthof open space due to roads. Sky view factor of the ground surface decreases withincreasing building coverage or increasing building height. Moreover, sky viewfactor increases with width of open space due to roads or lower uniformity ofbuilding height distribution.

In future investigations, we plan to calculate the albedo value in a real city byuse of the method described in this paper.

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the influence of urban canopy configuration on urban albedo

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