INTERNATIONAL JOURNAL OF CLIMATOLOGY
Int. J. Climatol. 27: 1931–1942 (2007)
Published online 5 October 2007 in Wiley InterScience
(www.interscience.wiley.com) DOI: 10.1002/joc.1624
Validation of a numerical model for urban energy-exchange
using outdoor scale-model measurements
Toru Kawai,a* Manabu Kanda,a Kenichi Naritab and Aya Hagishimac
a Department of International Development Engineering, Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo 152-8552, Japan
b Department of Engineering, Nippon Institute of Technology, Japan
c Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Japan
Abstract:
The objectives of our study are (1) to evaluate the simple urban energy balance model for mesoscale simulation (SUMM)
using such data that are free from many real world uncertainties in respect to spatial variability in material, geometry,
and land use, and (2) to analyse the sensitivity of land surface parameters (LSP), which are used in the model. The
model was evaluated using the data obtained from comprehensive outdoor scale-model (COSMO) experiments during a
period, which covers roughly half of a year (winter and spring-early summer) including various wind conditions. SUMM
simulated surface layer energy fluxes, surface temperature, and interior temperature fairly well under windy conditions
while it underestimated sensible heat flux under calm conditions. On average, simulated sensible heat flux underestimated
observed value by 30% (0.73 MJ m−2 d−1) in daytime. Errors of net radiation (4%; 0.40 MJ m−2 d−1) and heat storage
(5%; 0.33 MJ m−2 d−1) were smaller than that of sensible heat flux in daytime. This underestimation of sensible heat flux
can be attributed to the inadequate parameterization of the surface layer bulk transfer coefficient used in SUMM under
calm conditions. On the basis of the sensitivity analyses, parameterization of the surface layer bulk transfer coefficient
using Monin-Obukhov similarity theory (MOST) shows that the model performance is very sensitive to this coefficient,
while it is less sensitive to the relative values of the bulk transfer coefficients of local faces. Copyright  2007 Royal
Meteorological Society
KEY WORDS model validation; outdoor scale-model experiment; urban energy balance model
Received 1 October 2006; Revised 23 July 2007; Accepted 12 August 2007
INTRODUCTION
The geometry of an urban surface has a large influence
on the energy exchange between that urban surface and
the atmosphere. Therefore, it is important to examine
the thermally effective surface area in urban energy bal-
ance models and ensure that the impact of urbanization
is reflected in mesoscale models. In recent years, phys-
ically based urban canopy models (UCMs) have rapidly
progressed (Masson, 2000; Kusaka et al., 2001; Martilli
et al., 2002; Kanda et al., 2005a; Kondo et al., 2005).
Although evaluation of these UCMs is important (Mas-
son, 2006), few validation studies using observed energy
balance data have been conducted (e.g. Arnfield and
Grimmond, 1998; Masson et al., 2002; Lemonsu et al.,
2004).
In April 2003, we began the comprehensive outdoor
scale-model (COSMO) experiments for urban climate
(Kanda et al., 2006, 2007). The dataset obtained from
COSMO is useful for basic model evaluations because
* Correspondence to: Toru Kawai, Department of International Devel-
opment Engineering, Tokyo Institute of Technology, 2-12-1
O-okayama, Meguro-ku, Tokyo 152-8552, Japan.
E-mail: kawai@ide.titech.ac.jp
COSMO has uniform surface geometry and no vegeta-
tion. Here we evaluated the simple urban energy balance
model for mesoscale simulation (SUMM; Kanda et al.,
2005a) using data obtained from COSMO.
SIMPLE URBAN ENERGY BALANCE MODEL FOR
MESOSCALE SIMULATION (SUMM)
The urban surface layer energy balance (SEB) is com-
monly expressed as the energy balance of a ‘volume’
that has its upper boundary at the inertial sublayer and
its lower boundary at the zero-flux conduction depth of
cities; this set-up simplifies the intractable physical pro-
cesses within the urban roughness sublayer (Oke, 1987).
If assuming extensive terrain with uniform buildings, no
human activities, and no hydrological energetic contribu-
tions to the volume (e.g. energy supply or removal by
rainfall, dewfall and/or runoff), then the energy balance
of the volume can be written simply as
Q∗ =
Qs + QH + QE (1)
where Q∗ is the net all-wave radiation,
Qs is the net
heat storage of the volume, and QH and QE are the
Copyright  2007 Royal Meteorological Society

1932 T. KAWAI ET AL.
sensible and latent heat flux at the upper boundary of the
volume, respectively.
The SUMM (Kanda et al., 2005a) assumes a simple
building array and simulates energy fluxes of constituent
faces (e.g. roof, floor, and four vertical walls). We briefly
describe the features of SUMM below. More detailed
descriptions are provided by Kanda et al. (2005a).
Model geometry
Figure 1 illustrates the surface geometry of SUMM.
The model explicitly considers three-dimensional urban
surfaces composed of six local faces (roof, floor, and
four vertical walls). Each building has a square horizontal
cross-section and is regularly arranged. Such a simple
three-dimensional surface geometry can be identified
using only two geometrical parameters such as the plane
area index (λp) defined by Equation (2) and frontal area
index (λf ) defined by Equation (3):
λp =
W 2
(W + L)2
(2)
λf =
WH
(W + L)2
(3)
where W is the horizontal dimension of the buildings, L
is the width of the streets, and H is the height of the
buildings. Street orientation relative to north–south and
sun position relative to the horizontal plane are expressed
by the street direction ω, the solar elevation angle α, and
the solar azimuth angle β (Figure 1).
Theoretical radiation scheme
SUMM theoretically solves the multi-reflection of short-
wave (direct and diffuse components) and long-wave
radiations among the six faces by using view factors
and sunlit/shadow distributions (Kanda et al., 2005b).
Reflected short-wave and long-wave radiations were
isotropic and then no mirror reflection component was
considered in the model, although the dependency of
the facet albedo of direct short-wave radiation on its
incident angle to the faces was considered at the time
of its first reflection. This unique theoretical radiation
scheme greatly reduces the computational costs.
Sun
Street axis
South
North
za
H
WL
R
L
W
R
a b w
Figure 1. Model geometry and sun position relative to the building
array and north–south axis. The area framed by the bold lines is the
unit area, composed of a roof, a floor, and four vertical walls. Where, L,
H , W , and R are street width, building height, horizontal dimension of
the buildings, and horizontal dimension of a unit area; α and β are the
solar elevation angle and the solar azimuth angle; ω is street direction
measured from north–south in counterclockwise rotation, respectively.
Top-down parameterization for bulk transfer coefficients
The sensible and latent heat fluxes of the six faces
were calculated using a network of resistance formulation
(Kanda et al., 2005a) similar to other UCMs (Masson,
2000; Kusaka et al., 2001). The sensible heat fluxes from
each constituent face to the sky (QH(i); Figure 2(b)) are
calculated by
QH (i) = cpρ CH (i) Ua{TS(i) − Ta}, (4)
where i is the face number from 1 to 6 corresponding
to the four vertical walls, the roof, and the floor, cp
is the specific heat, ρ is the air density, CH (i) is the
bulk transfer coefficient between face i and the reference
height za . Ua and Ta are the wind velocity and the
air temperature at the reference height, respectively, and
TS(i) is the surface temperature of face i. The sensible
heat flux from the whole surface (QH ; Figure 2(a)) is
(a) (b)
za
zT + zd
CH
CH(floor)
CH(wall)
CH(roof)
za
Figure 2. Network of resistance used in SUMM. Figures show the resistances of (a) the whole surface layer (CH ) and (b) the individual faces
(CH (i); i = roof, floor, and four vertical walls).
Copyright  2007 Royal Meteorological Society Int. J. Climatol. 27: 1931–1942 (2007)
DOI: 10.1002/joc