Journal of Heat Island Institute International Vol. 9-2 (2014)

Academic Article

Fundamental Urban Morphology Analysis for Use in Urban
Canopy Model
Yoichi Kawamoto*1*1

Faculty of Design, Kyushu University

Corresponding author: Yoichi Kawamoto, kawamoto@design.kyushu-u.ac.jp
ABSTRACTFor urban climate analysis, mesoscale meteorological models are widely utilized. The urban canopy models
are used as sub-models of land surface models in mesoscale meteorological models to represent the effect of urban
morphology in terms of kinetic effects and surface energy budgets. Normally, in an urban canopy model, buildings
in an analysis mesh are assumed to be uniform. However, in reality, the buildings in any given area are not uniform;
they can differ in terms of their heights, areas, and shapes. This raises the question whether the gaps between themorphologies of the presumably uniform modelled buildings and the real non-uniform buildings are significant or
not. In this study, the urban morphology in Japanese cities is analyzed by the means of Geographical Information
System (GIS). Some urban canopy models represent the variations in buildings’ heights based on normal
distribution. However, in this study, building distribution in terms of heights reflects power-law distribution on amacro scale in entire Japan, and on a micro scale with a resolution of about 1 square kilometer.
Key Words: Urban Morphology, Building Height, Geographical Information System, Urban Canopy Model

height distributions; the single layer urban canopy model in

1. Introduction

WRF(3) uses standard deviation to reflect building heights
In the field of urban climatology, numerical simulation tools,

distribution. However, building heights may not exhibit asuch as mesoscale meteorological models, are useful. To

normal distribution.

reflect the effects of buildings (e.g. decreasing wind velocity,

The author’s group developed an urban canopy model inproduction of turbulence, solar radiation shading and trapping,

previous studies(4), (5), (6). To utilize that urban canopy model

decreasing the sky view factor, etc.), urban canopy models areaccurately, building geometric datasets have to be prepared.

coupled with mesoscale models. For urban canopy models,

Furthermore, effects of non-uniformity that are neglected inbuilding geometries are essential input data to parameterize

uniform urban canopy models have to be investigated. In

the effects of the urban canopy layer consisting of building

addition, the urban canopy model must be modified to include

complexes. Grimmond et al. showed that building geometries

non-uniformity if necessary. The objective of this study is toaffect the calculated energy budget at the surface in the urban

clarify non-uniformity of urban morphology, especially for(1), (2). Accurate analysis by urban canopy

building height distributions, to revise the uniform urban

models requires accurate input data. Therefore, both

canopy model to a non-uniform urban canopy model withsophisticated analysis models and accurate building geometricactual urban morphology datasets as input.

canopy models

data are necessary as input for accurate surface energy budget
analysis in mesoscale models coupled with urban canopy

2. Materials and Methods

models.
On the other hand, most of the urban canopy models are based

The urban morphology data for Japan used in this study, wason uniform building complexes, meaning that building

published by ESRI Japan in 2012. A total of 46,974,800

geometries (building height, building width, and canyonbuilding shapes, heights, and locations are recorded in thewidth) in each analysis mesh are determined by averagedataset, and these data were analyzed using ArcGIS 10.2.

values. There is an urban canopy model that reflects building

Building height was determined by multiplying number of- 44 -

stories by a fixing height of 3.0 m. Thus, all double storied

100,000,000

buildings were considered to be 6.0 m tall. Moreover, building

10,000,000
1,000,000

Statistics were based on the “Basic Grid Square” (Third Areain latitude and longitude of 30 seconds 45 seconds,
respectively. “Basic Grid Square” is widely used for statistics

100,000
Frequency

Partition) with a resolution of about 1 km2 and a grid spacing

10,0001,000

on population, land-use, and urban planning, among others, bynational and local governments in Japan. About 1 km2

100

resolution is also suitable for input data to the urban canopy

10

model coupled with the mesoscale model. Buildings are1

allocated to the Basic Grid Square based on these centroids. If

6
9
12
15
18
21
24
27
30
33
36
39
42
45
48
51
54
57
60
63
66
69
72
75
78
81
84
87
90
93
96
99
102
105
108
111
114
117
120
123
126
129
132
135
138
141
144
147
150
153
156
159
162
165
168

heights were discrete values every 3.0 m.

44,611,224 (95.0%)
1,483,123 (3.2%)
444,419 (0.9%)
192,655 (0.4%)
66,596 (0.1%)
51,114 (0.1%)
35,780 (0.1%)
23,763 (0.1%)
22,748 (0.0%)
15,064 (0.0%)
6,683 (0.0%)
5,120 (0.0%)
9,201 (0.0%)
4,351 (0.0%)286 (0.0%)229 (0.0%)252 (0.0%)247 (0.0%)330 (0.0%)
166 (0.0%)
129 (0.0%)111 (0.0%)
126 (0.0%)
125 (0.0%)
75 (0.0%)65 (0.0%)77 (0.0%)61 (0.0%)112 (0.0%)
90 (0.0%)73 (0.0%)48 (0.0%)29 (0.0%)34 (0.0%)
27 (0.0%)29 (0.0%)29 (0.0%)
14 (0.0%)40 (0.0%)
17 (0.0%)
21 (0.0%)22 (0.0%)
11 (0.0%)
14 (0.0%)5 (0.0%)11 (0.0%)
10 (0.0%)
3 (0.0%)9 (0.0%)4 (0.0%)4 (0.0%)2 (0.0%)9 (0.0%)3 (0.0%)1 (0.0%)

Average: 6.289m

Building Height [m]any building overlaps more than one Basic Grid Square, it isFig.1 Histogram of building heights in Japan. The following 9

allocated to the mesh that includes the centroid. A total ofbuildings are neglected in this histogram: two buildings with

46,974,800 buildings in the dataset were allocated to 124,160

heights of 174 m, one building with a height of 177 m, twomeshes and analyzed.

buildings with heights of 180 m, one building with a height of
210 m (Landmark Tower, Kanagawa), one building with a

3. Urban morphology analysis of building heightheight of 234 m (Fukuoka Tower, Fukuoka), one building
with a height of 333 m (Tokyo Tower, Tokyo), and one

3.1 Buildings’ heights distribution in whole of Japanbuilding with a height of 810 m (Tokyo Sky Tree, Tokyo).

Fig.1 shows a histogram of building heights in Japan. Notethat the vertical axis is logarithmic. Moreover, 9 buildings

100,000,000

with heights over 171 m were not plotted because of

10,000,000

discontinuous distribution in Fig1.

1,000,000
100,000

double story buildings are dominant. As a result, average

10,000Frequency

About 95.0% of building heights are 6.0 m, indicating thatbuilding height of whole buildings in Japan is 6.289 m. The
distribution of building heights does not show normal

1,000
100

distribution. Moreover, a sudden drop between 45 m and 48 m

10

is apparent. In Japan, earthquake-resistance safety measures1

require buildings over 45 m to be analyzed with a

0.1

Time-History Response Analysis and certified by the Minister0.01

of the Ministry of Land, Infrastructure, Transport, and

0.001

1

10

100

1000

y = 19,955,858,359.486 x-4.325
R² = 0.938
Building Height [m]Tourism. Therefore, the quantity of buildings taller than 45 m

Fig.2 Double logarithmic scatter plot of building heightis small.

distribution in Japan. The approximation equation was

To clarify the distribution characteristics, the building height

estimated by the least square method, and the R2 value is thehistogram was redrawn on a double logarithmic plot (Fig.2).

determination coefficient for this approximation equation.

Nine buildings, which were neglected in Fig.1, are included inFig. 2. The scatter plot data can be fit with straight line on the

3.2 Buildings’ heights distribution in Basic Grid Squares

double logarithmic plot. Thus, the building height distribution

Approximation equations expressing the relationship between

in Japan follows a power-law distribution. The determinationbuilding heights and their frequency were estimated using thecoefficient for the approximation equation estimated by theleast square method for 124,160 meshes. However, if allleast square method is 0.938. This result describes Japanesebuildings in any mesh are the same height, the approximationbuilding height distributions from a macroscopic point of view,equation cannot be estimated. Therefore, 55,972 meshes with

but does not describe distribution characteristics from abuilding height variation are plotted in Fig.3. Fig.3 shows the

microscopic point of view. Mesh statistics with a resolution ofrelationship between the number of buildings in each mesh

2

1 km are detailed in the next section.

and the determination coefficient (R2) for the approximation
equation calculated using the power law function. Fig.4 showsa histogram of determination coefficients (R2) for 55,972
meshes.

- 45 -

1000

The results indicate that a power law approximation isappropriate to estimate building height distribution. In 63.14%
of meshes, determination coefficients were greater than 0.90,

100

and 82.75% of meshes had determination coefficients greater
Frequency

than 0.80. There is an apparent trend of larger determination
coefficients with a larger number of buildings. The urban
canopy model is intended to be applied in the urbanized area.

10
y = 30,205.653 x-2.256
R² = 0.806

Therefore, three samples were chosen to investigate mesheswith greater than 1,000 buildings (Fig.5): Marunouchi in

1
1Tokyo (highest average building height), Nishi-Shinjuku in

10

100

1000

Tokyo (largest standard deviation of buildings’ heights), and0.1

Kokura in Fukuoka (largest number of buildings). In these

Building Height [m]a) Marunouchi, Tokyo

three meshes, determination coefficients ranged from 0.806 to

1000

0.880. Fig. 6 shows the scatter plot of average building height
versus standard deviation for 14,347 meshes with a number ofbuildings greater than 1,000.

Frequency100

y = 11,099.655 x-1.882
R² = 0.857

10

1
1

10

100

1000

0.1
Building Height [m]b) Nish-Shinjuku, Tokyo
10000

1000

Frequency

Fig.3 Scatter plot of the number of buildings and the2determination coefficient R for the power law approximationof 55,472 meshes.

49.49%

25,000

0.05
0.10
0.15
0.20

0

90.00%
80.00%

1
1

70.00%
60.00%
50.00%
40.00%
30.00%

10

100

Building Height [m]c) Kokura, Fukuoka
Fig.5 Double logarithmic scatter plot of building height
distribution in a) Marunouchi, b) Nishi-Shinjuku, and c)
Kokura. The approximation equation was estimated by the

20.00%

least square method, and the R2 value is the determination

10.00%

coefficient for this approximation equation.

0.00%

0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00

5,000

0.40
0.45

10,000

0.25
0.30
0.35

15,000

0.00%
0.01%
0.01%
0.02%
0.04%
0.07%
0.13%
0.24%
0.50%
0.88%
1.56%
2.77%
4.67%
7.87%
12.21%
17.25%
27.26%
36.86%

Frequency

20,00010

100.00%

Cumulative %Cumulative %Frequency

100.00%30,000y = 19,185,228.519 x-5.150
R² = 0.880

100

R2 Range

Fig.4 Histogram of the determination coefficient R2 for the
power law approximation of 55,972 meshes and theircumulative frequency.

- 46 -

Standard Deviation

20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0

Nishi-Shinjuku
Num.: 1183
Ave. Height: 15.98m
Std. Dev.: 18.42

Fn12 

Marunouchi
Num.: 1010
Ave. Height: 18.83m
Std. Dev.: 13.35

b
1  1 bhtan 1
tan

h
2 
a2  h2 
a2  h2(2)Here, a is the height of surface 2 [m], b is the width of surface
2 [m], and h is the distance between the centres of surface 1
and surface 2 [m]. Then, the sky view factor Fgsky can becalculated.

6

7

8

KokuraNum.: 5416
Ave. Height: 6.14m
Std. Dev.: 1.02
9
10 11 12 13 14 15
Average Building Height [m]Fgsky  1 Fgw
16

17

18

20

19

Fgw5

b

Fig.6 Average building height vs. standard deviation for

Fgw6

14,347 meshes with a number of buildings greater than 1,000.



canopy

b/2

Fgw4

B
A

by estimation of the sky view factor. For the uniform
geometric urban canopy model, a simplified estimation



Fagw  Fgw1  Fgw 2  Fgw3  8
w/2

method for sky view factor was proposed(4), (5), (6). The

N

Fgw3
Fgw2

Fgw1

In the urban canopy model, long wave radiation and diffuse
sky radiation intensity to urban canyons are strongly affected

Fbgw  Fgw4  Fgw5  Fgw6  4

w

4. Sky view factor estimation in non-uniform urban

(3)

b

w

b

simplified estimation method for sky view factor uses averageFig.7 Schematic graph of the calculation for view factors frombuilding height, average building width, and average canyon

ground to building sidewalls.

width, assuming that the building complex is uniform. Other
effects of urban canopy in the urban canopy model, including

4.2 Comparison of simplified method and GIS analysis fordrag forces and production of turbulence, are based on thesky view factor calculation

assumption of uniformity. Therefore, this simplified method

To estimate the average sky view factor in an area withfor sky view factor estimation matches the uniform urban

ArcGIS, observation points are set at random locations inside

canopy model. On the other hand, this method has not been

the area. The average sky view factor calculated for a large

tested for non-uniform geometric urban canopies. By targeting

number of samples converges to specific value. However, athe three meshes described above, the sky view factors

larger number of samples incur higher calculation costs.

estimated by the simplified method for uniform canopy and

Therefore, the average sky view factor calculated using 1,000

the three-dimensional GIS analysis were compared.

and 10,000 sampling points in Marunouchi were firstcompared. Calculation times were about 35 hours for 1,000

4.1 Outline of simplified sky view factor calculation

samples and about 350 hours for 10,000 samples. Table 1

method in uniform urban canopy

shows the average sky view factors calculated by the

A simplified model for the sky view factor was proposed as

simplified method and GIS analysis. In Marunouchi, thefollows.

results using 1,000 samples and 10,000 samples were almost

From the ground, only the view factors for building sidewalls

the same. Therefore, 1,000 random sampling points were

and the sky were considered. Firstly, the view factor for the

adopted hereafter. Comparing the simplified method and GIS

building sidewall was calculated. View factors from point A

analysis, the Kokura results show large error. Fig.8 shows theand point B were area-weight averaged to calculate theKokura area and the random sampling points used to calculate

normalized view factor, Fgw, from the ground for the sidewall

sky view factors. In the uniform geometric urban canopy(Fig.7).

model, buildings are arranged at equal spaces. However, in

Fgw   w 2 Fagw  2wbFbgw  /  w 2  2wb

(1)real space, buildings are arranged in blocks, and open spaces
are preserved between the blocks. This kind of contrast in

View factors from surface 1 (a small surface on the ground) tobuilding density is not reflected in the uniform geometricsurface 2 (building sidewall) can be calculated analyticallyurban canopy model, which could be the reason for error inusing Eq. (2)(7).

the average sky view factor estimation by the simplified- 47 -

method. Furthermore, as shown in the previous section,

5. Summary

buildings height distribution tends to show power-law
distribution. This characteristic has to be considered in the

In this study, urban morphology in Japanese cities wascalculation of sky view factors for non-uniform urban areas

analyzed to create an input data set for the urban canopy

usingfunction.

model and to investigate the non-uniformity of urban canopies

Representation of the non-uniformity of urban morphology inby means of GIS. The results show that the building heightthe calculation of sky view factors remains a pressing issue.

distribution in entire Japan follows a power-law distribution.

apower-lawprobability

distribution

At a local scale with a resolution of about 1 km2, building
Table 1 Average Sky View Factors Calculated by theheight distribution also showed a power-law distribution.

Simplified Method and GIS Analysis.

Furthermore, sky view factors calculated by GIS analysis andLocation

Marunouchi

Average Building
Height [m]Average Building
Width [m]Average Canyon
Width [m]Nishi-Shinjuku Kokura

18.82615.9796.140

20.48417.172

9.644

11.693

9.644

4.407

the simplified method for real urban areas were compared.
The results of the simplified method displayed non-negligible
errors because of the lack of consideration for contrasts inbuilding density within meshes. These analytical results will
be used to update the non-uniform urban canopy model infuture work.
Acknowledgement

Simplified Method

This work was supported by the “Japan Society for the

Average Sky View Factor

0.370

by Simplified Method

0.465

0.394

Promotion of Science” Grant-in-Aid for Young Scientists (A)(Grant Number: 25709053).

GIS Analysis
Number of Samples

1,000 10,000

1,000

1,000

0.403

0.410

0.418

0.615

Medium

0.419

0.427

0.411

0.617

Standard Deviation

0.158

0.154

0.165

0.182

Minimum

0.025

0.010

0.019

0.114

Maximum

0.727

0.730

0.733

0.930

Average Sky View Factor
by GIS Analysis

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Balance Models Comparison Project: First Results from
Phase 1, J. Appl. Meteor. Climatol., 49, 1268–1292 (2010)(2) C.S.B. Grimmond et al., Initial results from Phase 2 of
the international urban energy balance model comparison, Int.
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Model

For

Atmospheric

Models:Comparison

With

Multi-Layer And Slab Models, Bound.-Layer Meteor., 101,
329–358 (2001).
(4)

Y. Kawamoto et al., Improvement of the prediction

accuracy of radiation calculation in the urban canopy model
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0 100 200

400

600

800

1,000

1,200

1,400
m

Fig.8 Map of the Kokura area. Grey polygons are buildings
and black points are sampling points set in ArcGIS tocalculate sky view factors.

(6) Y. Kawamoto and R. Ooka, Analysis of the radiation
field at pedestrian level using a meso-scale meteorologicalmodel incorporating the urban canopy model, the 6thInternational Conference on Urban Climate, pp.221-225,(2006).
(7)

E.R.G. Eckert, et al., Heat and Mass Transfer,

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(Received Dec. 8, 2014, Accepted Dec. 27, 2014)- 48 -