Urban Energy Balance Obtained from the Comprehensive

Urban Energy Balance Obtained from the Comprehensive Outdoor Scale ModelExperiment. Part I: Basic Features of the Surface Energy Balance

TORU KAWAI*

Center for Marine Environmental Studies, Ehime University, Matsuyama, Japan

MANABU KANDA

Department of International Development Engineering, Tokyo Institute of Technology, Tokyo, Japan

(Manuscript received 5 March 2008, in final form 20 March 2010)

ABSTRACT

The objective of this study is to examine the basic features of the surface energy balance (SEB) using the

data obtained from the Comprehensive Outdoor Scale Model (COSMO). COSMO is an idealized miniature

city that has no vegetation, no human activity, and no heterogeneity of the surface geometry. The basic

features of the SEB such as energy balance closure, the ensemble mean of the diurnal variation of the energy

balance, and the daytime and daily statistics of the energy balance were investigated. The following were the

main findings of the study: 1) A surface energy imbalance was observed. The sum of sensible and latent heat

fluxes estimated by the eddy correlation method underestimated the available energy by 1% during the

daytime and by 44% during the night. 2) Large heat storage in the daytime and small radiative cooling at night

sustained positive sensible heat fluxes throughout the night in all seasons and in all sunshine conditions. 3) The

daytime ratio of heat storage DQS to net radiation Q*, DQS/Q*, depended on the friction velocity u*

and

decreased with increasing u*

. 4) The values of DQS/Q* tended to be larger in winter than in summer. The

annual averaged value of this ratio was approximately 0.6. 5) The large volumetric heat capacity of the surface

materials and the resulting large energetic hysteresis produced nonzero total daily values of heat storage. The

total daily values of heat storage largely depended on the weather (i.e., sunshine condition and with or without

rainfall) and showed positive and negative values on clear-sky days and rainy days, respectively.

1. Introduction

The surface energy balance (SEB) is an essential el-

ement of the boundary layer meteorology and clima-

tology. The SEB is strongly related to, for example, the

stability formation, dispersion of scalars and momentum,

and mixing layer growth within the boundary layer. As is

well known, urbanization through erecting buildings and

other urban components alters the energy exchange be-

tween the surface and the atmosphere from that of the

preexisting landscape. This unique urban SEB is consid-

ered to be intricately tied with urban climatic phenomena

such as localized heavy rain and/or urban heat islands.

Thus, better understanding and appropriate numerical

predictions of the urban SEB are necessary.

In recent years, sophisticated urban parameterizations

have rapidly evolved (e.g., Masson 2000; Kusaka et al.

2001; Martilli et al. 2002; Kondo et al. 2005; Kanda et al.

2005a,b; Kawai et al. 2007, 2009; Dupont and Mestayer

2006; Dupont et al. 2006). On the other hand, observations

of urban SEB are few, especially in highly urbanized areas.

Moreover, most of these experimental studies were based

on short-term observations (e.g., Oke 1988; Oke et al.

1999; Grimmond and Oke 1999; Grimmond et al. 2004).

Only in recent years have some long-term observation

programs been conducted. These observation programs

include the Kugahara experiment in Japan (Moriwaki

and Kanda 2004) and the Basel Urban Boundary Layer

Experiment (BUBBLE; Christen and Vogt 2004; Rotach

et al. 2005). In addition to the limited datasets, field ob-

servations are accompanied by various uncertainties.

These uncertainties arise, for example, from the estimates

* Current affiliation: Research Center for Environmental Risk,

National Institute of Environmental Studies, Tsukuba, Japan.

Corresponding author address: Toru Kawai, Research Center for

Environmental Risk, National Institute of Environmental Studies,

16-2 Onogawa, Tsukuba, Ibaraki, 305-8506, Japan.

E-mail: [email protected]

VOLUME 49 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y JULY 2010

DOI: 10.1175/2010JAMC1992.1

� 2010 American Meteorological Society 1341

of heat storage based on the energy balance residual,

seasonal changes of vegetation and anthropogenic heat,

and/or heterogeneity of the surface geometry and material.

With such uncertainties, interpretations of the results

from field observations may be difficult.

A useful alternative to field measurements is an out-

door scale-model experiment (Pearlmutter et al. 2005;

Kanda et al. 2005a). In such an experiment, the surface

geometry and material can be controlled to produce ho-

mogeneous fetch conditions, which reduce the uncer-

tainties associated with the difference in the source areas

between the measured radiation and the turbulence fluxes.

An experiment also allows detailed measurements within

and above the canopy layer, including direct measure-

ments of heat storage, which are extremely difficult to

obtain in real cities. Furthermore, systematic datasets

from an outdoor scale-model experiment provide ample

opportunities for validation studies with numerical models

(Kanda et al. 2005a; Kawai et al. 2007). Therefore, this

method is useful as long as the model meets the require-

ments of physical scale similarities (i.e., radiation, flow,

and thermal inertia; Kanda 2006).

Since December of 2004, the Comprehensive Outdoor

Scale Model (COSMO) experiments have been con-

ducted (Kanda et al. 2007; Kawai et al. 2007; Inagaki and

Kanda 2008; Nakayoshi et al. 2009; Kanda and Moriizumi

2009) on an ongoing basis. The model has been created by

arranging large concrete cubes on a concrete base to en-

sure thermal inertia similarity with real cities (appendix A).

This study is presented in a series of two papers. These

papers address the findings on the urban SEB using a

one-year dataset obtained from COSMO. The objective

of Part I is to investigate the basic features of the SEB

of COSMO: the energy balance closure, the ensemble

mean of the diurnal variation of the energy balance, and

the daytime and daily statistics of the energy balance in

terms of the season and weather conditions (i.e., sun-

shine condition, with or without precipitation, and wind

velocity). In Kawai and Kanda (2010, hereinafter referred

to as Part II), the results from the COSMO experiments

will be compared with those from field observations using

a new energy partitioning method.

2. Method

The urban SEB is commonly expressed as

Q* 1 QF

5 DQS

1 QH

1 QE

1 DQA

, (1)

where Q* is net radiation, QF is anthropogenic heat,

DQS is heat storage, QH is sensible heat, QE is latent

heat, and DQA is net advective heat flux (Oke 1987).

Here, Q* is calculated from upward ([) and downward

(Y) shortwave radiation QK and longwave radiation QL as

Q* 5 QK

Y�QK

[ 1 QL

Y�QL

[. (2)

The units of all terms in Eqs. (1) and (2) are watts per

meter squared. In COSMO, QF and DQA in Eq. (1) can

be neglected because the geometry and material of the

model setup are homogeneous and there exist no human

activities.

In the next part of this section, a brief summary of

COSMO will be provided. More detailed information

on these experiments is given in Kanda et al. (2007) and

Kawai et al. (2007).

a. The Comprehensive Outdoor ScaleModel experiments

The COSMO experimental site was located in the

northern side of the Kanto Plain in Japan (398049N,

1398079E) and was characterized by temperate climate

with a rainy season in June–July and a dry season in winter

(Table 1). The data analyzed in this study were collected

for one year from April 2006 to March 2007. The domi-

nant wind directions of the site were northwesterly in

winter (October–April) and southeasterly in summer

(May–November). Rice paddies (northwest side) and

sparse residences extended at least a few tens of kilo-

meters around the site. Two outdoor scale models of a

city that were scaled at 1/5 and 1/50 relative to the area of

the Kugahara site were deployed (Fig. 1). These models

are referred to as the 1/5 model and the 1/50 model here-

inafter. As described in appendix A, the geometrical scale

of the 1/50 model is considered to be too small to ensure

thermal inertia similarity with a city. Therefore, data

obtained from the 1/5 model are mainly used in this study.

The 1/5 model consisted of cubic concrete blocks with 1.5-m

height H and 0.1-m wall thickness. The blocks were

empty inside. A total of 512 blocks were regularly ar-

ranged on a flat concrete base with a surface area of

50 m 3 100 m and thickness of 0.15 m. One of the two

street directions pointed 438 counterclockwise from north.

The plan area of roughness elements, defined as the ratio

of the roof area to the total horizontal area of the model

city, was 0.25. The same concrete material was used for

the blocks and the basement, and all surfaces were painted

with a water-pervious dark-gray paint. Therefore, thermal

and radiative properties of all surfaces were the same.

In the 1/5 model, a measurement tower with height of

11 m was deployed at the center point of the site. On the

tower, four components of radiation (QKY, QK[, QLY,

and QL[) were measured using a radiation balance

meter [MR40 from Eko Instruments Co, Ltd., with Inter-

national Organization for Standardization (ISO) second-

class accuracy] at 1 Hz. To estimate turbulence fluxes

(QH and QE) by the eddy-correlation method, a sonic

anemometer with a 5-cm sensor span (DA 600 from

1342 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 49

Kaijo, Inc.) and an open-path H2O/CO2 analyzer (LI7500

from Li-Cor, Inc.) were operated at 50 and 20 Hz, re-

spectively, on the same tower. Measurement heights of

radiation and turbulence fluxes were 3 and 2 times the

obstacle height above the ground, respectively. The height

at which the sonic anemometer and H2O/CO2 analyzer

were installed is located within the internal boundary

layer and above the roughness sublayer (1.5 times the

obstacle height; Inagaki and Kanda 2008).

Heat storage DQS was also directly measured near the

measurement tower using thin (300 mm 3 300 mm 3

0.4 mm in size) and highly accurate (instrumental accu-

racy within 65%) heat flux plates (HF-300 from Captec

Enterprise Co.). To close the energy balance precisely, a

total of 164 heat flux plates were attached to a sample

unit that consisted of a block and its surrounding streets.

The heat flux plates also measured the surface tempera-

ture. By measuring the heat storage directly, we were able

to close the surface energy balance, which allows us to

analyze and discuss the surface energy imbalance (sec-

tion 3). All of the heat flux plates were operated at 1 Hz.

b. Data handling

Days with complete datasets (i.e., radiation, turbulence

fluxes, heat storage, and surface temperature) were se-

lected for analyses in sections 3–5. The number of se-

lected days for each month (ND) is shown in Tables 1

and 2. In section 6b, all available data of heat storage and

TABLE 1. Summary of monthly averaged values of total daytime (Q* $ 0) energy fluxes (Q*, DQS, QH, and QE) and flux ratios (QH/QE,

DQS/Q*, QH/Q*, and QE/Q*) and daytime-averaged u*

obtained in three sunshine conditions (DRR 5 0–0.5, DRR 5 0.5–0.8, and

DRR 5 0.8–1.0). DRR is the ratio of daytime diffuse to daytime global shortwave radiations as defined in Eq. (3); ND indicates the

number of observation days within a month. The total rainfall reported by the Japan Meteorological Agency is also shown (8 km away

from the COSMO site).

Month

Rain (mm)

[days] DRR ND u*

(m s21)

Energy flux (MJ m22) Ratio

Q* DQS QH QE QH/QE DQS/Q* QH/Q* QE/Q*

Apr 2006 63 [12] 0–0.5 4 0.59 17.06 8.87 5.93 2.26 2.62 0.52 0.35 0.13

0.5–0.8 5 0.37 13.16 7.17 4.43 1.56 2.83 0.54 0.34 0.12

0.8–1 2 0.27 6.60 3.22 2.59 0.80 3.25 0.49 0.39 0.12

May 2006 134 [16] 0–0.5 5 0.26 18.83 9.94 6.35 2.54 2.50 0.53 0.34 0.14

0.5–0.8 4 0.25 14.94 8.18 5.00 1.76 2.84 0.55 0.33 0.12

0.8–1 3 0.25 6.97 3.66 2.38 0.93 2.57 0.52 0.34 0.13

Jun 2006 117 [11] 0–0.5 1 0.20 16.71 8.88 5.62 2.20 2.55 0.53 0.34 0.13

0.5–0.8 3 0.26 15.57 8.37 5.00 2.20 2.28 0.54 0.32 0.14

0.8–1 5 0.20 7.41 3.80 2.50 1.11 2.26 0.51 0.34 0.15

Jul 2006 210 [14] 0–0.5 2 0.22 17.79 9.41 5.49 2.89 1.90 0.53 0.31 0.16

0.5–0.8 2 0.29 14.30 6.57 5.59 2.14 2.61 0.46 0.39 0.15

0.8–1 7 0.17 7.96 4.37 2.26 1.33 1.70 0.55 0.28 0.17

Aug 2006 43 [6] 0–0.5 1 0.20 15.41 9.17 4.74 1.50 3.16 0.59 0.31 0.10

0.5–0.8 2 0.24 14.83 8.08 4.81 1.93 2.49 0.55 0.32 0.13

0.8–1 4 0.19 5.59 2.43 2.13 1.03 2.06 0.44 0.38 0.18

Sep 2006 187 [10] 0–0.5 6 0.23 14.54 8.47 4.26 1.81 2.35 0.58 0.29 0.12

0.5–0.8 6 0.24 10.34 6.01 3.15 1.18 2.67 0.58 0.30 0.11

0.8–1 6 0.20 6.58 3.90 1.71 0.97 1.77 0.59 0.26 0.15

Oct 2006 298 [10] 0–0.5 1 0.24 11.37 7.60 2.59 1.17 2.21 0.67 0.23 0.10

0.5–0.8 6 0.21 8.85 5.34 2.69 0.81 3.32 0.60 0.30 0.09

0.8–1 2 0.13 6.32 4.17 1.27 0.88 1.43 0.66 0.20 0.14

Nov 2006 96 [7] 0–0.5 6 0.27 8.55 5.69 2.10 0.75 2.80 0.67 0.25 0.09

0.5–0.8 0 — — — — — — — — —

0.8–1 0 — — — — — — — — —

Dec 2006 185 [5] 0–0.5 12 0.32 7.02 4.45 1.79 0.78 2.29 0.63 0.25 0.11

0.5–0.8 4 0.16 4.09 3.10 0.76 0.23 3.38 0.76 0.19 0.06

0.8–1 6 0.16 2.16 1.67 0.29 0.21 1.40 0.77 0.13 0.10

Jan 2007 38 [3] 0–0.5 14 0.40 8.35 5.32 2.10 0.94 2.24 0.64 0.25 0.11

0.5–0.8 7 0.17 5.90 3.97 1.53 0.40 3.78 0.67 0.26 0.07

0.8–1 1 0.09 3.31 2.53 0.57 0.21 2.65 0.76 0.17 0.06

Feb 2007 21 [5] 0–0.5 12 0.39 10.16 6.29 3.04 0.82 3.71 0.62 0.30 0.08

0.5–0.8 1 0.19 7.87 5.49 2.02 0.36 5.64 0.70 0.26 0.05

0.8–1 1 0.19 2.63 1.08 0.94 0.61 1.54 0.41 0.36 0.23

Mar 2007 23 [4] 0–0.5 4 0.42 14.26 7.77 5.07 1.11 4.57 0.54 0.36 0.08

0.5–0.8 7 0.27 10.53 6.25 3.46 0.58 6.00 0.59 0.33 0.05

0.8–1 3 0.28 4.10 2.51 0.85 0.56 1.51 0.61 0.21 0.14

JULY 2010 K A W A I A N D K A N D A 1343

surface temperature were analyzed. The selected days

in section 6b, which included rainy days, covered nearly

1 year (351 days).

1) CLASSIFICATION OF OBSERVATION DAYS

Observation days were classified according to rainfall,

sunshine condition, and season. If there was any pre-

cipitation on a day, the day is defined as ‘‘rainy.’’ Daily

data of rainfall were collected from the Japan Meteo-

rological Agency 8 km away from the COSMO site. The

rainy days included all sunshine conditions. Days with-

out precipitation were classified according to the diffuse

shortwave radiation ratio DRR, defined as

DRR 5

ðsunset

sunrise

QK

Y dt �ðsunset

sunrise

QKT

Y dt

ðsunset

sunrise

QK

Y dt

, (3)

where QKTY is the downward direct shortwave radiation

measured at a point a few meters away from the 1/5

model. Three kinds of sunshine conditions were defined:

DRR 5 0–0.5 for ‘‘clear sky,’’ DRR 5 0.5–0.8 for ‘‘oc-

casionally cloudy,’’ and DRR 5 0.8–1 for ‘‘cloudy.’’ All

observation days were also classified into four seasons:

winter, spring, summer, and autumn. These four seasons

were simply defined by dividing one year into four pe-

riods based on the solstice and equinox days.

2) DATA PROCESSING

All of the sampled data were averaged over 30 min.

Because of the difference in sampling frequencies be-

tween the sonic anemometer and the open-path H2O/

CO2 analyzer, data from these instruments were re-

sampled at 10 Hz. Coordinate rotation (McMillen 1988)

was applied to the observed three components of the

wind velocity (u, y, and w). In the estimation of latent

heat flux by the eddy-correlation method, the density

effect was corrected (Webb et al. 1980). Based on the

discussions to be presented in section 3, the sensible and

latent heat fluxes were found to be underestimated with

respect to the available energy. Therefore, for the ana-

lyses in sections 4–6, the sensible and latent heat fluxes were

corrected by the Bowen ratio method; that is, available

energy (Q* 2 DQS) was distributed into these two fluxes

using the Bowen ratio estimated by the eddy-correlation

method.

3. Energy balance closure

A large volume of data observed over various forests

has shown that the sum of sensible and latent heat fluxes

estimated by the eddy-correlation method, QECH 1 QECE,

often underestimates the available energy, Q* 1 QF 2

DQS 2 DQA (e.g., Lee 1998; Wilson et al. 2002). This

phenomenon is called surface energy imbalance (SEI).

Although organized large-scale turbulence structures are

a possible physical mechanism that accounts for the SEI

(Kanda et al. 2004), other various factors could contribute

to the SEI in field measurements (Mahrt 1998). Offerle

et al. (2005) investigated the energy balance closure for

qodz, Poland, by estimating the heat storage term DQS

with the use of the element surface temperature method.

Nonetheless, research on SEI in urban areas is still rare

because of the difficulties in measuring DQS. In COSMO,

the estimation of SEI is possible with the direct mea-

surements of conductive heat flux.

Figure 2a compares QECH 1 QECE with the available

energy Q* 2 DQS. A significant SEI was observed even

for the present urbanlike rough surface. In total, QECH 1

QECE underestimated Q* 2 DQS by 10% (the slope was

0.9). This underestimation is slightly smaller than the

commonly observed value for forests of 20% (Wilson et al.

FIG. 1. Photographs of the scale models: (a) 1/5 model and (b) 1/50 model.


2002). The differences between the daytime and nighttime

results were evident. At night with weak turbulence, a

significant SEI was observed: QECH 1 QECE under-

estimated Q* 2 DQS by 44% (the slope was 0.56), with

a relatively large scatter (r2 5 0.55). The disagreement

between QECH 1 QECE and Q* 2 DQS was small in the

daytime (slope 5 0.99; r2 5 0.81). A similar result was

found by Offerle et al. (2005).

Previous research (Wilson et al. 2002; Kanda et al.

2004; Offerle et al. 2005) reported increasing values of

SEI with decreasing u*

both in daytime and nighttime.

Figure 2b illustrates the dependency of SEI on the

friction velocity u*, where the SEI is defined as

SEI 5(Q

ECH1 Q

ECE)� (Q*� DQ

S)

Q*� DQS

. (4)

The values of SEI are larger in calm conditions (u*

#

0.2 m s21) than in windy conditions. In strong winds

(approximately u*

$ 0.6 m s21), the values of SEI are

slightly negative. These slightly negative values of SEI

might, in part, be attributable to advection below the

flux measurement level removing heat.

4. Ensemble mean of the diurnal variationof the energy balance

This section will discusses the ensemble mean of the

diurnal variation of SEB in four seasons (winter, spring,

summer, and autumn) and three sunshine conditions

(DRR 5 0–0.5, 0.5–0.8, and 0.8–1; Fig. 3). Figure 3 also

shows the ensemble mean of the wind velocity U and

radiative temperature TR, converted from the upward

TABLE 2. As in Table 1, but for the monthly average values of total daily energy fluxes, flux ratios, and daily averaged values of the

friction velocity.

Month DRR ND u*

(m s21)

Energy flux (MJ m22) Ratio

Q* DQS QH QE QH/QE DQS/Q* QH/Q* QE/Q*

Apr 2006 0–0.5 4 0.45 13.61 2.99 7.69 2.93 2.62 0.22 0.56 0.22

0.5–0.8 5 0.29 10.18 1.95 6.02 2.21 2.73 0.19 0.59 0.22

0.8–1 2 0.20 4.17 21.36 4.27 1.26 3.39 20.33 1.02 0.30

May 2006 0–0.5 5 0.21 15.39 3.53 8.80 3.06 2.87 0.23 0.57 0.20

0.5–0.8 4 0.22 12.25 2.59 7.30 2.36 3.10 0.21 0.60 0.19

0.8–1 3 0.21 5.54 0.18 3.89 1.47 2.65 0.03 0.70 0.27

Jun 2006 0–0.5 1 0.19 13.37 1.48 9.04 2.85 3.17 0.11 0.68 0.21

0.5–0.8 3 0.21 13.33 3.53 6.96 2.84 2.45 0.26 0.52 0.21

0.8–1 5 0.19 5.85 0.45 3.88 1.52 2.55 0.08 0.66 0.26

Jul 2006 0–0.5 2 0.19 15.42 4.01 7.76 3.65 2.13 0.26 0.50 0.24

0.5–0.8 2 0.25 12.63 1.67 8.16 2.80 2.91 0.13 0.65 0.22

0.8–1 7 0.15 6.62 1.43 3.45 1.75 1.98 0.22 0.52 0.26

Aug 2006 0–0.5 1 0.15 12.09 3.00 7.00 2.10 3.33 0.25 0.58 0.17

0.5–0.8 2 0.20 12.22 2.09 7.44 2.69 2.77 0.17 0.61 0.22

0.8–1 4 0.16 3.70 21.58 3.69 1.59 2.33 20.43 1.00 0.43

Sep 2006 0–0.5 6 0.19 11.47 2.15 6.71 2.60 2.58 0.19 0.59 0.23

0.5–0.8 6 0.19 7.47 0.79 5.01 1.67 3.00 0.11 0.67 0.22

0.8–1 6 0.16 4.85 0.40 2.93 1.52 1.93 0.08 0.60 0.31

Oct 2006 0–0.5 1 0.20 7.31 0.49 5.07 1.75 2.89 0.07 0.69 0.24

0.5–0.8 6 0.15 5.52 20.55 4.83 1.24 3.90 20.10 0.88 0.22

0.8–1 2 0.11 4.44 0.81 2.31 1.32 1.76 0.18 0.52 0.30

Nov 2006 0–0.5 6 0.20 4.67 20.44 3.67 1.45 2.54 20.10 0.79 0.31

0.5–0.8 0 — — — — — — — — —

0.8–1 0 — — — — — — — — —

Dec 2006 0–0.5 12 0.25 3.66 21.23 3.01 1.88 1.60 20.34 0.82 0.51

0.5–0.8 4 0.12 1.14 21.36 1.89 0.60 3.13 21.20 1.67 0.53

0.8–1 6 0.11 0.15 21.46 1.09 0.52 2.08 29.48 7.08 3.40

Jan 2007 0–0.5 14 0.29 5.15 20.24 3.40 1.99 1.71 20.05 0.66 0.39

0.5–0.8 7 0.14 3.17 20.81 3.04 0.93 3.25 20.26 0.96 0.30

0.8–1 1 0.09 1.61 20.59 1.35 0.84 1.61 20.37 0.84 0.52

Feb 2007 0–0.5 12 0.29 6.33 20.12 4.78 1.67 2.86 20.02 0.75 0.26

0.5–0.8 1 0.11 5.39 0.61 3.71 1.07 3.47 0.11 0.69 0.20

0.8–1 1 0.14 0.97 22.06 2.00 1.02 1.96 22.12 2.06 1.05

Mar 2007 0–0.5 4 0.33 10.45 0.63 7.96 1.87 4.26 0.06 0.76 0.18

0.5–0.8 7 0.22 7.68 0.55 6.06 1.06 5.71 0.07 0.79 0.14

0.8–1 3 0.23 1.76 21.59 2.05 1.30 1.58 20.91 1.17 0.74


longwave radiation assuming a canopy emissivity of 0.95

(Arnfield 1982). The SEB depends on the wind velocity

(section 5a), but variations in the ensemble mean of the

wind velocity among the four different seasons and sun-

shine conditions were small (within 1 m s21). This allows

us to examine the influence of the seasons and sunshine

conditions on the SEB with the current dataset.

a. Results for clear-sky days

In daytime, the urban SEB is often characterized by

large heat storage DQS (e.g., Oke 1988; Arnfield 2003),

and DQS becomes larger than turbulence fluxes in highly

urbanized areas with little vegetation (Oke et al. 1999;

Grimmond and Oke 1999). Such a trend is also clear in

FIG. 2. (a) A comparison of the sum of sensible and latent heat fluxes estimated by the eddy

correlation method, QECH 1 QECE, with available energy, Q* 2 DQS. Daytime and nighttime

are defined as Q* $ 0 and Q* , 0, respectively. A linear regression with a zero intercept was

performed individually for the daytime data, nighttime data, and all of the data combined.

(b) The relationship between the values of the SEI and the friction velocity u*

for the daytime

and nighttime. The values of the SEI were calculated from Eq. (4). The figure displays the data

only from jQ* 2 DQSj $ 50 W m22.


FIG. 3. Ensemble mean of diurnal variations of energy balance Q* 5 DQS 1 QH 1 QE, wind velocity U, and

radiative temperature TR for three sunshine conditions (clear sky, occasionally cloudy, and cloudy) in four

seasons. The total number of days used for the calculation is shown in each panel.


COSMO: the net radiation Q* was predominantly par-

titioned into DQS in all seasons. The maximum value of

DQS was roughly 2 times that of the sensible heat flux.

The magnitude of the latent heat flux QE was the smallest

of all the components considered, but is nonnegligible.

The nonzero value of QE observed in COSMO sug-

gests that urban evaporation was released not only from

vegetation and/or permeable soil but also from the con-

crete material. Therefore, nonzero evaporation from the

urban surface should not automatically be assumed in

urban surface parameterizations. In a rainy season (i.e.,

summer), the values of QE were larger than those in the

other seasons. In the driest season (i.e., winter), the values

of QE were generally nonzero and reached a maximum

of 30–40 W m22. To examine such nonzero evapora-

tion, an additional experiment was conducted to evalu-

ate the weight change of a sample unit of a block and its

surrounding streets in the 1/50 model (appendix B). This

experiment determined that the sample unit absorbed

some of the rainwater and continuously released it over

a period of several days. In winter, the sample unit also

absorbed dew during nighttime and released the ab-

sorbed water during daytime. This diurnal cycle, in part,

sustained the daytime evaporation; the dew, if it exists,

can become a source of urban evaporation. On the other

hand, the ensemble means of nighttime QE showed

slightly positive values in this season, suggesting that

dewfall did not always occur.

Distinct phase differences were observed among the

energy fluxes. Heat storage DQS shows hysteresis in re-

lation to the net radiation throughout the year in COSMO

as found in the previous literature (e.g., Grimmond et al.

1991; Grimmond and Oke 1999). The daily maximum

value of DQS occurred approximately 1 h prior to that

of Q*. This phase lag produced a phase lag of QH with

respect to Q* (approximately 2 h). The large thermal

inertia of the 1/5 model also produced a phase lag of the

radiative temperature TR from Q*. The pattern of the

diurnal variation of TR roughly followed that of QH with

only a slight lag. The maximum value of QE was ob-

served around noon.

Throughout the year, the nocturnal values of QH and

QE were positive while those of DQS were negative. The

positive values of QH at night are one of the unique fea-

tures of urban areas and are not common for less evap-

orative surfaces, such as desert or flat concrete. There are

two possible reasons for this observation. First, the en-

ergy storage in daytime in urban areas is large (Oke et al.

1999). This is also supported by the 1/50 model experi-

ments. In the 1/50 model with a small volumetric heat

capacity, the values of QH at nighttime were nearly zero

rather than positive (appendix A). Second, radiative

cooling is small in an urban area because of its reduced

sky-view factor in the urban canyon (Oke 1981; Oke et al.

1999). It is likely that both of these urban effects con-

tribute to sustain the positive QH throughout the night.

b. Results for various sunshine conditions

In daytime, as the diffuse shortwave radiation ratio

DRR increased; all fluxes decreased as a result of the

reduced radiative energy supply. However, the relative

magnitudes of the energy fluxes remained approximately

the same in all sunshine conditions. Regardless of the

sunshine condition and season, DQS was the most domi-

nant energy flux and the value of QE was nonzero. The

values of QH and QE on occasionally cloudy and cloudy

days were always positive throughout the daytime and

nighttime; the dominant partition of Q* into DQS in

daytime together with the restrained nocturnal radiative

cooling sustained the positive value of QH throughout

the night. These conditions led to unstable stratification

above the canopy layer both on occasionally cloudy and

cloudy days. On cloudy days, the diurnal variations of QH

were reduced, with the value of QH being small positive in

daytime. The diurnal hysteresis of DQS in relation to Q*

became less evident with increasing DRR.

5. Daytime statistics

Energy fluxes are frequently normalized by net radi-

ation Q* to study the surface energy partition. However,

Q* is not physically appropriate for the normalization

of the energy fluxes because Q* implicitly includes the

surface temperature through QL[. The surface temper-

ature is determined as a result of the energy partitioning

process. Therefore, Q* also depends on the energy par-

titioning process itself and is not appropriate for the

normalization of the energy fluxes. Therefore, instead of

Q*, an effective incoming energy should be introduced

for the normalization. This issue will be discussed in

detail in Part II, in which the surface energy partitioning

for COSMO and field data will be compared using a new

normalization method. In the remainder of this section

and section 6a, with the awareness of the limited nature

of net radiation Q* for the normalization procedure, the

surface energy partition of COSMO will be studied us-

ing the conventional method of normalizing by Q*.

a. Effects of day-to-day variability of wind velocityon surface energy balance

The effects of wind velocity on the urban SEB have not

been thoroughly investigated with field data (Grimmond

and Oke 1999). Section 5a will investigate the influence of

wind conditions on the urban SEB.


The dependency of the total daytime values of DQS/Q*

on the daytime-averaged values of u*

(m s21) was in-

vestigated for various weather conditions in all four

seasons (Fig. 4), and the relationship between these two

variables was quantified as the slope of the linear regres-

sion line for the variables (Table 3). Here, u*

is used in-

stead of the wind velocity because of the height-dependent

nature of the wind velocity. On clear-sky days, DQS/Q*

clearly decreased with increasing u*

. For winter and

spring, the linear regression analysis was performed by

using data that were collected over a sufficiently large

number of days (35 and 36 days, respectively), and these

data were characterized by a wide range of u*. In these

cases, the slopes of the linear regression lines were dis-

tinctly negative (20.35 and 20.31) with relatively high

correlation coefficients squared r2 (0.64 and 0.59; Table 3).

This dependency of the daytime values of DQS/Q* on

u*

can be explained by the enhancement of turbulence

fluxes and the resulting reduction of heat storage with

increasing wind speed. On occasionally cloudy and cloudy

days, the values of DQS/Q* were observed within a rela-

tively narrow range of u*, and few data were available for

analysis within each season. These factors probably con-

tributed to the small values of r2 in Table 3. However, in

all of the seasons analyzed here, the slopes on occasion-

ally cloudy and cloudy days consistently showed negative

values, and these negative values tended to be large in

magnitude as compared with those on clear-sky days.

b. Seasonal change of the surface energy balance

Table 1 shows the monthly averages of the total day-

time energy fluxes (Q*, DQS, QH, and QE) and flux ra-

tios (DQS/Q*, QH/Q*, QE/Q*, and QH/QE). The same

flux ratios and the daytime-averaged values of u*

are

shown in Fig. 5.

On clear-sky days, as discussed in section 4, heat stor-

age was dominant and latent heat flux was the smallest.

The annual averaged values of DQS/Q*, QH/Q*, and

QE/Q* on clear-sky days were 0.61, 0.29, and 0.10, respec-

tively. The value here of DQS/Q* of 0.61 is larger than

most of the values of DQS/Q* previously reported for

urban and suburban areas (Grimmond and Oke 1999).

Values of DQS/Q* for cities with little vegetation and/or

little water availability tend to be larger than those for

suburban areas because of the reduced values of QE/Q*

(Oke et al. 1999; Roth 2007). In the same way, lack of

vegetation in COSMO likely accounted for the large

TABLE 3. Results of linear regressions of the daytime values of

DQS/Q* onto the daytime u*

. The linear regressions were performed

separately for three sunshine conditions and four seasons unless the

number of observation days (no. day) was less than 10. The maxi-

mum (max) and minimum (min) values of u*

, slopes, and corre-

lation coefficients (r2) from the individual linear regressions are

shown.

Season No. day

u*

(m s21)

Slope (r2)Max Min

DRR 5 0–0.5

Winter 35 0.81 0.10 20.35 (0.64)

Spring 36 0.90 0.16 20.31 (0.59)

DRR 5 0.5–0.8

Winter 11 0.32 0.11 20.24 (0.05)

Spring 15 0.66 0.16 20.27 (0.23)

Autumn 14 0.41 0.14 20.95 (0.76)

DRR 5 0.8–1

Summer 15 0.38 0.11 21.22 (0.20)

Autumn 12 0.26 0.11 22.20 (0.13)

FIG. 4. The relationship between the daytime (Q* $ 0) ratio of heat storage to net radiation

(DQS/Q*) and the daytime-averaged values of u*

. The data were obtained in three sunshine

conditions (clear sky, occasionally cloudy, and cloudy) in four seasons.


value of DQS/Q*. In addition, relatively small values of u*

in COSMO contributed to the large value of DQS/Q*

(section 5a).

Monthly averaged values of u*

on clear-sky days were

slightly larger in winter than in summer and autumn and

reached their peak in April. If the seasonal trend of u*

accounted for the seasonal trend of DQS/Q*, DQS/Q*

would be larger in the months of May–July than in

October–February. Because this result was not observed,

the seasonal trend of DQS/Q* cannot be explained by the

seasonal trend of u*. Thus, the seasonal trend of DQS/Q*

would appear even if the values of u*

remained the same

throughout the year. The seasonal trend of DQS/Q* orig-

inates from that of Q* itself as will be discussed in Part II.

The monthly averaged value of the Bowen ratio

QH/QE on clear-sky days reached its peak in early spring

(4.57 in March) and was approximately 2 in other months.

The peak of the Bowen ratio in early spring has been also

observed in vegetated cities (Moriwaki and Kanda 2004;

Christen and Vogt 2004; Kanda 2007). The frequency of

rainfall influenced the seasonal variation of the Bowen

ratio. The value of QE/Q* was smaller in the dry season

(i.e., in winter) than in other seasons.

On occasionally cloudy and cloudy days, the values of

u*

were slightly larger in summer than in winter, and the

seasonal variations of u*

were less obvious than those on

clear-sky days. The seasonal trend of the SEB from

occasionally cloudy and cloudy days did not differ sig-

nificantly from that from clear-sky days, although the

month-to-month variation of the monthly value of each

flux ratio increased with increasing DRR. The values of

DQS/Q* were generally larger in winter than in summer

both for the occasionally cloudy and cloudy days. The

annual averaged values of DQS/Q* on occasionally cloudy

and cloudy days, 0.60 and 0.58, respectively, were similar

to that on clear-sky days of 0.61.

6. Daily total statistics

a. Seasonal change of the surface energy balance

Table 2 summarizes the monthly averaged values of

the total daily energy fluxes (Q*, DQS, QH, and QE) and

flux ratios (DQS/Q*, QH/Q*, QE/Q*, and QH/QE). The

flux ratios and daily averaged values of u*

are shown

in Fig. 6. Unlike for the daytime case, the daily values of

DQS/Q* were only slightly dependent on u*

(not shown).

Therefore, this dependency is not considered in the fol-

lowing discussions.

Regardless of sunshine conditions, similar to what has

been observed for most land surfaces, the total daily

values of Q* were always positive, although their mag-

nitudes were reduced from the daytime values as a result

of the radiative cooling at night. The total daily values of

QH and QE were larger than the daytime values because

FIG. 5. Monthly averaged values of the daytime (Q* $ 0) flux ratios (QH/Q*, QE/Q*, DQS/Q*, and QH/QE) and the daytime-averaged

values of u*

. The statistics are presented separately for the three sunshine conditions (clear sky, occasionally cloudy, and cloudy).


of the positive values of QH and QE at night (see sec-

tion 4). The values of the Bowen ratios for the daily case

were roughly the same as those for the daytime. The most

significant difference between the daytime and daily cases

was observed in the heat storage: nocturnal cooling of

the blocks contributed to a substantial reduction of

the total daily values of DQS from the daytime values.

However, the monthly averaged values of DQS never

became 0 but rather were always positive or negative.

On clear-sky days, the values of DQS/Q* were positive

in spring and autumn and negative in winter. Such sea-

sonal variations of DQS/Q* have often been reported for

urban areas such as DQS/Q* 5 0.16 for winter in Mexico

City, Mexico, and DQS/Q* 5 0.35 for Vancouver, British

Columbia, Canada, in summer (Grimmond and Oke

1999). On cloudy days, the seasonal variations of DQS/

Q* were somewhat different from those on clear-sky

days. The values of DQS/Q* became negative even in

spring (March and April) and summer (August) and sig-

nificantly negative in winter (e.g., December) on cloudy

days.

The significant differences between daytime DQS and

total daily DQS, and the positive or negative values of

the total daily DQS with nonnegligible magnitudes sug-

gest that heat storage is a key to understanding the

daily total of the surface energy partition. The char-

acteristics of the total daily DQS will be investigated in

section 6b.

b. The characteristics of the total daily heat storage

The total daily heat storage is the sum of the daytime

storage and the nighttime loss of energy. Therefore, the

total daily heat storage represents the day-to-day ener-

getic hysteresis of a city.

The total daily heat storage DQS can be directly re-

lated to the day-to-day temperature change of the urban

substrate DTS [5TSj2400 2 TSj0000 (K day21), where TS

(K) is the average temperature from surface to the hy-

pothetical depth leff]. The hypothetical depth leff (m) is

the depth at which energetic contributions to DTS be-

come negligible in a daily cycle. The relationship be-

tween DTS and DQS can be written as

DTS

51

cSr

Sleff

DQS

5 ahDQ

S, where a

h5

1

cSr

Sleff

,

(5)

with cSrS (MJ m23 K21) being the average volumetric

heat capacity from the surface to the depth leff and ah

being the coefficient of proportionality between DTS

and DQS. In the current study, the complete surface

temperature TC (Voogt and Oke 1997), which is a simple

area-averaged surface temperature, was used instead of

TS. Also, DQS was related to DTC in an approximately

linear fashion (Fig. 7). The slope of the linear relation-

ship ah was approximately constant at 1.2 for all weather

FIG. 6. As in Fig. 5, but for the monthly averaged values of the daily flux ratios and the daily averaged values of u*

.


conditions (see legend in Fig. 7). This result suggests that

the value of leff was relatively insensitive to the weather

condition.

For a given DTC, the data of DQS varied by more than

65 MJ m22 day21 around the determined linear rela-

tionship. Such variations of the total daily values of DQS

were much larger than the variations of the monthly av-

erage of the total daily values of DQS among various

seasons and sunshine conditions (Table 2). With these

large variations of the total daily values of DQS, the total

daily values of DQS clearly depended on the weather:

they tended to be positive on clear-sky days and occa-

sionally cloudy days and negative on rainy days. This trend

suggests that energy tended to be stored on clear-sky days

and occasionally cloudy days and that the stored energy

tended to be flushed out on rainy days.

The total annual values of DQS were nonzero for all of

the weather conditions (Table 4) although the total an-

nual value of DQS from all the weather conditions com-

bined was relatively small at 13.56 MJ m22 yr21. In some

literature, the value of DQS accumulated over several

days has been assumed to be zero (e.g., Christen and

Vogt 2004). However, if the data from rainy days are

excluded for this computation, DQS may be positive and

significantly different from zero.

Next, the seasonal variations of the total daily values

of DQS were investigated (Fig. 8). In addition to the total

daily values, Fig. 8 shows the monthly averaged values

(Total) and standard deviations (STD) of the total daily

DQS from all of the weather conditions combined. Similar

to the seasonal trend of the surface temperature, the total

daily values of DQS were positive for March–August and

negative for November–February (Fig. 8). The day-to-

day variation of the total daily heat storage was larger

than the seasonal variation of the monthly average of the

total daily heat storage. The day-to-day variation of the

total daily heat storage was smaller in winter than in

nonwinter seasons (see STD in Fig. 8). This observation

may be related to seasonal weather trends. The winter

during the COSMO experiments was characterized by

continuous clear-sky days whereas the spring and au-

tumn were characterized by frequent weather changes

and the frequent occurrence of rainy days.

To investigate the influence of the day-to-day weather

change on the total daily heat storage, the total daily heat

storage DQS was compared with the weather condition of

the day under consideration and that of the preceding day

(Fig. 9). Although the error bars on the ensemble mean

values were large because of the data collected under

various synoptic conditions, the ensemble mean values

showed well-organized trends. The total daily value of

heat storage DQS depended on the weather conditions

of both the day under consideration and the preceding

day. Pairs of days with similar weather condition yielded

DQS close to zero. This result implies that the day-to-day

weather change was an essential factor in producing a

significant day-to-day energetic hysteresis of a city. For

a given weather condition on the preceding day, the

FIG. 7. The relationship between the total daily heat storage DQS and the change in the

complete surface temperature DTC over a day. The plotted data were observed in four weather

conditions (clear sky, occasionally cloudy, cloudy, and rainy). Linear regressions with 0 in-

tercept were performed for the relationships separately for each weather condition, where the

values of ah are the coefficient of proportionality between DTC and DQS.


ensemble mean value of the total daily heat storage took

a larger positive value on clear-sky and occasionally

cloudy days than on cloudy days. Also, for a given weather

condition on the preceding day, the ensemble mean value

of the total daily heat storage on rainy days was nega-

tive and smaller than that on no-precipitation days. For

a given weather condition on the day under consider-

ation, the ensemble mean value of the total daily heat

storage took the largest positive values following a rainy

day and the smallest values following a clear-sky or oc-

casionally cloudy day. In general, the urban substrate

stored energy most effectively on days after a rainy day

and lost energy most effectively on rainy days following

a clear-sky day.

7. Concluding remarks

The Comprehensive Outdoor Scale Model experiments

were conducted. The direct measurement of heat storage

in COSMO yielded a dataset with closed energy balance

for analysis. A one-year dataset from a large outdoor scale

model, the 1/5 model, which is similar in thermal inertia to

a real city, was analyzed in this study.

The basic features of the surface energy balance of

COSMO were investigated, such as the energy balance

closure, the ensemble mean of the diurnal variation of

the SEB, and the statistics of the daytime and total daily

SEB. The following are the five main findings of this

study:

1) A surface energy imbalance was observed for the

urbanlike rough surface. The magnitudes of the SEI

were 1% and 44% for the daytime and nighttime,

respectively; thus they differed significantly between

the daytime and nighttime. The magnitude of the SEI

for both daytime and nighttime combined was 10%,

smaller than the typical magnitude for a forest of

20%.

2) A positive sensible heat flux was observed through-

out the nighttime in all seasons and for all sunshine

conditions. This observation can be explained by the

urban effects of large heat storage in the daytime and

reduced radiative cooling at nighttime.

TABLE 4. Summary of total annual heat storages obtained in clear-

sky, occasionally cloudy, cloudy, and rainy days; N is the number of

days for the respective weather conditions.

N

ðyear

DQS dt

(MJ m22 yr21)

ðyear

DQS dt/N

(MJ m22 day21)

Clear sky 110 63.44 0.58

Occasionally cloudy 74 69.51 0.94

Cloudy 69 20.75 20.01

Rainy 98 2118.64 21.21

All weather conditions 351 13.56 0.04

FIG. 8. Variations of the total daily heat storage with the day of the year. The data from the

four weather conditions (clear sky, occasionally cloudy, cloudy, and rainy) are plotted together.

The solid line and dotted line indicate the monthly averaged values (Total) and standard de-

viations (STD), respectively, of the total daily heat storage from all weather conditions.


3) The surface energy balance was dependent on the

wind velocity (as represented by the friction velocity).

The daytime ratio of heat storage to net radiation

(DQS/Q*) decreased with increasing friction velocity.

4) Seasonal changes of the daytime surface energy bal-

ance were confirmed even with no seasonal change of

vegetation and no human activities. In COSMO,

the values of DQS/Q* were larger in winter than in

summer.

5) A relationship was found between the day-to-day

energetic hysteresis (i.e., total daily values of heat

storage) and the weather conditions. In general, the

urban substrate stored energy on clear-sky and oc-

casionally cloudy days, and the stored energy was

flushed out on rainy days.

Acknowledgments. This work was supported by the

Core Research for Evolutional Science and Technology

(CREST) of the Japan Science and Technology Co-

operation, by the Ehime University Global COE Pro-

gramme under the Ministry of Education, Culture, Sports,

Science and Technology, the Government of Japan, and

by Japan Society for the Promotion of Science Grant-in-

Aid for Young Scientists (B) (21710033). We gratefully

acknowledge Prof. Kenichi Narita of the Nippon Institute

of Technology and Prof. Aya Hagishima of Kyushu

University.

APPENDIX A

Requirements for Physical Scale Similarities

Physical scale similarity requires similarities of radia-

tion, flow, and thermal inertia (Kanda 2006). As discussed

in this section, the thermal inertia similarity is not often

met in reduced model experiments with respect to a real

city. This section mainly examines the validity of the

thermal inertia similarity of the 1/5 model by comparing

the results obtained from the 1/5 and the 1/50 model ex-

periments (section b of appendix A) as well as those

from numerical simulations (section c of appendix A).

a. The 1/50 model experiments

A series of 1/50 model (Fig. 1b) experiments were con-

ducted simultaneously with the 1/5 model experiments.

These two models were separated by 13 m. The objective

of this experiment was to investigate the effects of the

geometrical scales of the model on the surface energy

balance. The experiments were conducted for the pe-

riods of November–December 2004 and March–May

2005. Data from 24 and 7 clear-sky days were analyzed

from the two periods, respectively.

The surface geometry (i.e., the plan area and frontal

area of roughness elements) and the material of the 1/50

model were the same as those of the 1/5 model. However,

the geometrical scale was considerably different: the height

of the cubic blocks was 0.15 m in the 1/50 model—1/10th

that in the 1/5 model. As in the 1/5 model experiments,

four components of radiation and turbulence fluxes were

measured by the same instruments at the same sample

frequencies. The radiation and flux measurement heights

were also the same in terms of the relative heights to the

block height between the 1/5 and 1/50 model experiments.

Heat storage and the surface temperature were also di-

rectly measured using the same heat flux sensors as for

the 1/5 model experiments except for the size (50 3 50 3

0.4 mm). A total of 72 sensors were attached to a sample

unit that consisted of a block and its surrounding streets.

All observed data were handled in the same way as in the1/5 model experiments (see section b of appendix A). The

same meteorological forcing, geometry, and constituent

material between the 1/5 and 1/50 models made it easy to

compare the results obtained from these two models.

b. Comparison between the 1/50 and 1/5 modelexperiments

The albedo a can be adequately used as an index to

examine the radiation similarity because shortwave ra-

diation is free from the influence of the surface temper-

ature unlike longwave radiation. The ensemble means

of a observed from the 1/5 and 1/50 models showed good

FIG. 9. The dependency of the ensemble mean value of the total

daily heat storage on weather condition of the day under consid-

eration and of the preceding day. The weather condition of the day

under consideration is classified by DRR (see label in upper-left

corner of each panel). Based on the weather condition of the pre-

ceding day, a set of four ensemble mean values of the total daily heat

storage is calculated for each weather condition on the day under

consideration. The symbols indicating the weather condition of the

preceding day are shown at the bottom of the figure. The error bars

indicate the range of the total daily values of heat storage that are

included in ensemble averaging.


agreement in the diurnal variations and the daily aver-

aged values, both in winter and in summer (not shown);

thus radiation similarity to a real city was met, regardless

of the scale, for both models. This is due to the fact that

radiation wavelengths were much shorter than the build-

ing dimensions.

A thorough investigation of the flow similarity was

difficult with the current setup because no adequate in-

struments were available to estimate the detailed turbu-

lence statistics within the canopy layer of the 1/50 model.

Kanda et al. (2007) evaluated the roughness lengths for

momentum both for the 1/5 and 1/50 models. The values of

FIG. A1. Ensemble mean of the diurnal variation of the surface energy balance (Q* 5 DQS 1 QH 1 QE) obtained from the 1/5 and 1/50

model experiments in two seasons (November–December 2004 and March–May 2005).

TABLE A1. Summary of daytime (Q* $ 0)-averaged values of albedo a, daily average (avg), maximum (max), and minimum (min)

values of complete surface temperature TC and daytime and total daily energy fluxes (Q*, DQS, QH, and QE) and flux ratios (QH/QE,

DQS/Q*, QH/Q*, and QE/Q*) obtained from the 1/5 and 1/50 model experiments. Results are from clear-sky days in two seasons

(November–December 2004 and March–May 2005).

Model Period ND a

TC (K) Energy flux (MJ m22 day21) Ratio

Avg Max Min Q* DQS QH QE DQS/Q* QH/Q* QE/Q* QE/QH

Daytime (Q* . 0)

1/5 model Nov–Dec 24 0.007 — — — 7.13 5.46 1.28 0.39 0.77 0.18 0.05 0.30

1/50 model Nov–Dec 24 0.007 — — — 7.12 3.53 3.09 0.49 0.50 0.43 0.07 0.16

1/5 model Mar–May 7 0.007 — — — 16.86 9.45 5.55 1.86 0.56 0.33 0.11 0.34

1/50 model Mar–May 7 0.007 — — — 16.01 6.08 8.92 1.01 0.38 0.56 0.06 0.11

Daily

1/5 model Nov–Dec 24 — 12.14 20.08 6.03 3.11 20.99 3.22 0.88 20.32 1.04 0.28 0.27

1/50 model Nov–Dec 24 — 10.91 22.90 3.53 3.24 20.54 3.26 0.52 20.17 1.01 0.16 0.16

1/5 model Mar–May 7 — 18.88 30.30 9.11 14.93 2.86 9.20 2.87 0.19 0.62 0.19 0.31

1/50 model Mar–May 7 — 18.28 32.08 7.49 13.80 2.11 10.41 1.28 0.15 0.75 0.09 0.12


the roughness lengths showed good agreement, which may

be considered as indirect evidence of the flow similarity.

To examine the thermal inertia similarity, the diurnal

variations of the surface energy balance (Fig. A1) and

the complete surface temperature TC were evaluated

for the 1/5 and 1/50 models for both winter and summer.

Table A1 summarizes Fig. A1 in terms of the daytime and

daily statistics of the energy fluxes and flux ratios, and

daily average, maximum, and minimum values of TC. In

both of the seasons, differences in the results between

the 1/5 and 1/50 model experiments are evident. The vol-

umetric heat capacity of the 1/50 model was smaller than

that of the 1/5 model. Therefore, the daytime values of

DQS were smaller in the 1/50 model than in the 1/5 model,

and, as a result, the daytime values of the sensible heat flux

QH were larger for the 1/50 model than for the 1/5 model.

At night, the values of QH became almost zero for the1/50 model while measurable positive values of QH were

observed for the 1/5 model. Furthermore, the diurnal

variations of TC in the 1/5 model were larger than those in

the 1/50 model (see the maximum and minimum values of

TC in Table A1). These results suggest that the 1/50 model,

because of its small roughness elements, did not meet the

requirements for thermal inertia similarity with a real

city. Therefore, the 1/50 model is considered not to be

useful for studying the energy balance for an urban area.

The results above also indicate an essential influence of

urbanization on the energy balance; that is, roughness

elements with large volumetric heat capacities increase

the daytime heat storage, and this, in part, sustains posi-

tive sensible heat fluxes at night.

An investigation of the thermal inertia similarity be-

tween the 1/5 model and real cities is not currently feasible

experimentally. Therefore, this similarity is investigated

with the aid of numerical simulation as described in sec-

tion c of appendix A.

c. Numerical experiments

Numerical experiments were conducted using the sim-

ple urban energy balance model for mesoscale simu-

lation (SUMM; Kanda et al. 2005a,b; Kawai et al. 2007,

2009). Kawai et al. (2007) confirmed that SUMM sim-

ulates the surface energy balance, surface temperature,

FIG. A2. The dependency of mc on the wall thickness, where mc is

the building mass per unit surface area. REAL refers to a real city

investigated by Moriwaki and Kanda (2004). The plane and frontal

area aspect ratios of the city are the same as those of COSMO. The

building height of the city was 7.3 m.

FIG. A3. (a) Comparisons of simulated heat storage from case 2 (wall thickness 5 0.25 m) and case 3 (wall thickness 5 0.50 m) with

simulated heat storage from case 1 (wall thickness 5 0.10 m). As a reference, observed storage is also compared with simulated heat

storage from case 1. The plotted data are hourly averaged values. Linear regressions with a 0 intercept were performed for the re-

lationships between each pair of the simulated results. (b) As in (a), but for the difference between the hourly complete surface tem-

perature and the daily average of the complete surface temperature. (c) As in (a), but for the difference between the hourly interior

temperature and the daily average of the interior temperature.


and interior temperature of the 1/5 model well for windy

conditions (u*

$ 0.3 m s21). For the following analyses,

a total of 37 windy days from all seasons were selected,

and, except for the wall thickness, the simulation set-

tings were the same as those in Kawai et al. (2007).

The building mass per unit surface area mc (kg m22)

and the thickness of the thermally active building walls

(wall thickness hereinafter) can be used as indices for

evaluating the thermal inertia similarity (Pearlmutter

et al. 2005). Based on a field survey, Tso et al. (1990)

reported 700 kg m22 for a typical value of mc.

To study the thermal inertia similarity between the 1/5

model and a real city, the dependencies of mc on the wall

thickness are compared between the 1/5 model and the

actual city (REAL) that was investigated by Moriwaki

and Kanda (2004; Fig. A2). In this figure, a building

height of 7.3 m is assumed for the city and the plan and

frontal areas of roughness elements of the city are as-

sumed to be the same as for COSMO. Lines are drawn

on Fig. A2 for the values of the wall thickness for REAL,

0.25 m, and for the 1/5 model, 0.35 m for mc 5 700 kg m22

(Tso et al. 1990). The value of mc of the 1/5 model is

267 kg m22, which is smaller than the typical value from

the field.

To examine the influence of such a small value of mc,

a series of numerical experiments were conducted for

three cases with different wall thicknesses because mc

and wall thickness are related as in Fig. A2. The three

cases are: case 1 with a wall thickness 5 0.10 m and mc 5

267 kg m22, case 2 with a wall thickness 5 0.25 m and

mc 5 557 kg m22, and case 3 with a wall thickness 5

0.50 m and mc 5 826 kg m22. The results of these ex-

periments are shown in Fig. A3. The heat storage DQS

and the surface temperature Tc of the three cases gen-

erally show good agreement as indicated by high cor-

relation coefficients (Fig. A3a). The heat storage and the

surface temperature are underestimated in cases 2 and 3

with respect to those in case 1, because of the increase of

volumetric heat capacity of the blocks. However, these

underestimations are negligible. Even in case 3 with

significantly larger wall thickness and thus with a signif-

icantly larger value of mc, the underestimations are 5%

for the heat storage and 2% for surface temperature, as

indicated by the slopes. On the contrary, the correla-

tions of the interior temperature among the three cases

are poor (Fig. A3b) because of the reduced diurnal var-

iation of the interior temperature with increasing wall

thickness.

The above results may suggest that the influence of

the thickness of the thermally active building wall is

relatively small on the diurnal variations of the surface

energy balance and of the surface temperature. Thus,

the wall thickness of 0.1 m in the 1/5 model may be

considered to be roughly similar in thermal inertia to

those of a real city.

APPENDIX B

Measurement of the Weight Change of aSample Unit

To observe the temporal variations of the latent heat

flux from the concrete surface, change in water content

within the concrete was monitored using a sample unit

of the 1/50 model. The sample unit consisted of a block

and its surrounding streets with a surface area of 0.3 3

0.3 m2 and walls that were 0.15 m in thickness. The

weight change was measured using an electrical balance

meter with 0.1 g instrumental accuracy (IS64EDE-H from

Sartorius AG; Fig. B1). The measurements were made

during the period between November 2004 and January

2005. All observed data were sampled at 1 Hz and av-

eraged over 30 min.

Figure B2 shows temporal weight change of the sample

unit during five successive days immediately after a rain-

fall (Fig. B2a; case 1) and that during four successive rain-

free days after a 10-day period with no rain (Fig. B2b;

case 2). The time series of latent heat fluxes in these fig-

ures were calculated from the weight change of the sample

unit.

Case 1 shows that the sample unit absorbed some of the

water supplied by rain and released it over the period of

a few days. Such continuous release of absorbed water

resulted in a daytime latent heat flux with maximum

values of 10–20 W m22. The influence of the continuous

release of absorbed water on the latent heat flux was

present even 2 weeks after rainfall (case 2). In case 2, dew

formation was also observed at night. The sample unit

absorbed water from dew and released it during the day-

time. This diurnal cycle of dew had a significant influence

on the value of the daytime latent heat flux in case 2

FIG. B1. Schematic vertical cross section of the electric balance

equipment for measuring weight change of a sample unit of the 1/50

model.


although its absolute magnitude was relatively small,

approximately 10 W m22 at maximum.

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Urban Energy Balance Obtained from the Comprehensive