United States
Environmental Protection
Agency
Environmental Sciences Research ~^
Laboratory ' \ ,
Research Triangle Park NC 27711
&EPA
Research and Development
EPA-600/S3-82-062 August 1982
Project Summary
An Experimental Study of
Turbulence in an Urban
Environment
John F. Clarke, J. K. S. Ching, and J. M. Godowitch
The structure of turbulence in the ur-
ban surface boundary layer is discussed.
Wind and temperature fluctuations were
measured with fast-response sensors at
a height of 31 m in four land-use areas in
the St. Louis environs (a rural and three
urban sites). The second moments of the
fluctuations were computed for one-
hour time series and analyzed within the
framework of the Monin-Obukhov simi-
larity theory (i.e., normalized by appro-
priate velocity and temperature scales).
The results are discussed relative to ob-
served land-use features and calculated
surface roughness lengths for each of
the sites.
Average surface roughness lengths
ranged from 0.7 to 1.7 m for the urban
sites, varying by several meters as a
function of wind direction at individual
sites. The normalized velocity and tem-
perature variances for the rural site were
consistent with the Monin-Obukhov simi-
larity theory. For the urban sites, plots of
the normalized velocity variances showed
an orderly departure from similarity
theory for both neutral and unstable
stratifications; they were smaller than
the corresponding normalized variance
for the rural site.
The urban anomalies to similarity
theory are discussed relative to the
terms in the turbulent kinetic energy
budget equation. For neutral stratifica-
tion, the anomaly is suggested to be due
to the wake region of the roughness ele-
ments extending to near the height of
the measurements. For unstable stratifi-
cation, it is suggested to be due to in-
creased importance of vertical transport
processes within the urban area.
Ancillary analyses suggest that the
spectral peak wavelength may be a more
appropriate scaling length for free con-
vection similarity than the height of the
mixed layer, z,. During the afternoon
transition period the two scales may dif-
fer significantly.
This Project Summary was developed
by EPA's Environmental Sciences Re-
search Laboratory, Research Triangle
Park, NC, to announce key findings of
the research project that is fully docu-
mented in a separate report of the same
title fsee Project Report ordering infor-
mation at back).
Introduction
The research reported here is con-
cerned with the structure of turbulence
in the surface boundary layer over a city.
It is based on extensive observations of
the turbulent wind and temperature
above four land-use areas in the St. Louis,
Missouri, environs. The purpose of the
study is to suggest a framework for pa-
rameterizing urban turbulence statistics.
The research was designed to seek
relations between turbulence parameters
based on the interpretation of empirical
data. The form of select nondimension-
alized urban turbulence statistics as a
function of atmospheric stratification is
tested against the form predicted by the
Monin-Obukhov similarity theory. In this
respect, the empirical specifications of
similarity relationships resulting from
the Kansas and Minnesota boundary
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layer experiments are used as standards
for comparing the urban results.
Within the constant stress layer, the
Monin-Obukhov similarity theory is a
useful tool for making predictions about
certain statistics of atmospheric turbu-
lence. According to similarity theory, the
mean velocity gradients and turbulence
characteristics are completely deter-
mined by the height z, the surface mo-
mentum flux TO/Q, the kinematic heat
flux H/pCp, and the buoyancy parameter
g/T. From these parameters velocity,
temperature, and length scales can be
defined as:
u* = -u'w'1/2 = T0/e
where the prime quantities are the fluc-
tuating components of the wind and
temperature. It follows that any other
parameter describing the structure of
ideal flow in the surface boundary layer,
nondimensionalized by the above scal-
ing parameters, should be a universal
function of the only other dimensionless
quantity that can be formed, i.e., the
Monin-Obukhov stability ratio z/L. Some
parameters which scale with z/L include
the velocity and temperature gradients,
the second moments of the fluctuations
of the velocity components and temper-
ature, spectra and cospectra, and other
higher-order quantities.
The Monin-Obukhov similarity rela-
tionships cannot be expected to hold a
priori tor urban areas due to the large and
nonhomogeneous surface features. Thus
the specific objectives of this study are:
(1 ) to determine how extensively the
similarity relationships, as verified
empirically for ideal rural sites, ap-
ply to urban data; and
(2) to discuss significant and orderly
differences between the urban re-
sults and the similarity predictions
in terms of site land-use, i.e., sur-
face scaling features.
Procedure
The analyses in this study are based
on high resolution fast response mea-
surements of the three components of
the wind and temperature at 3 1 m above
four land-use areas in the St. Louis envi-
rons during the summer and fall of 1 976.
Profile data were not obtained and thus
the study is limited to turbulent quanti-
ties. In other respects the data are exten-
sive, covering a total of nine weeks dur-
ing two seasonal periods; approximately
3800 hours of data were obtained. With
few exceptions, all the data were used in
the analyses; that is, the data were not
screened to eliminate nonstationary peri-
ods or nonhomogeneous flow situations.
The turbulence measurements were
obtained at RAPS Regional Air Monitor-
ing Systems (RAMS) sites 105, 107,
109, and 111 .Site 105 was located in a
high density urban commercial area 3
km south of the urban center and 1 km
west of the Mississippi River. Land in the
vicinity of the station was used for truck-
ing, warehousing, and commercial oper-
ations. Buildings, predominately two-
story and of large aerial extent, contri-
buted ~ 25 percent of the land-use
features. Approximately 60 percent of
the area was paved; the remainder was
primarily lawn with a few small trees
along the streets.
Site 107 was located in the northwest
section of St. Louis about 6 km from the
center of the city. Land use for several
kilometers surrounding the site con-
sisted mostly of older single family and
duplex two-story dwellings. Population
density is high and the area is considered
urban in nature. However, in contrast to
site 105, ~ 60 percent of the land area is
covered by trees or grass. Twenty-five
percent of the land is used for buildings;
streets and other paved surfaces make
up the remaining 15 percent.
Site 109 was located in a rural agricul-
tural area ~ 10 km east of the city. Farm
land generally surrounded the station;
however, a group of farm buildings was
located in the immediate northeast qua-
drant, and small trees and underbrush oc-
cupied the immediate southeast quadrant.
Small fields separated by hedgerows
and scattered homes characterized the
land use at greater distances in the east-
erly quadrants.
Site 111 was located in an older resi-
dential community approximately 9 km
southwest of the urban center. The area
immediately surrounding the site was
composed of high-density single family
residences. Buildings at an average
height of 7.5 m covered ~ 1 5 percent of
the area and trees averaging ~ 13.5 m
made up ~ 25 percent of the land use.
Turbulence instrumentation at all sites
consisted of a Gill UVW anemometer
and a fast response temperature system
of inhouse design. Net radiation was
measured with a Swissteco net radiom-
eter at sites 105 and 109. Humidity
fluctuations were obtained for a short
period of time (several days) at sites 105
and 109. All instruments were located
31m above the surface. The 3-compc
nent wind, temperature, and humidit
data were recorded at a frequency c
2/s. Land-use characteristics, displace
ment lengths, and roughness lengths fc
the four sites are presented in Table 1.
Results
Land use features varied significant!'
among the four sites. Thus, at the outse
each site was characterized numericalh
by an estimated displacement lengtf
and a site-averaged roughness length
calculated through the similarity wine
profile formulation. Estimated displace
ment lengths, d, ranged from 2 to 6 m a
the urban sites and site-averaged rough
ness lengths, Z0, ranged from 0.7 to 1.7
m (Table 1). Surface roughness length
varied significantly with wind direction
at both urban and rural sites as demon-
strated in Figure 1 for site 107, suggest-
ing the surface features were not homo-
geneous in space. The -surface wind
stress, u *, was proportional to Z0 (as ex-
pected from the method of calculation of
Z0). Relatively large values of u* occurred
at the urban sites throughout the diurnal
cycle. The value of u * for the convective
period of the day was 0.2 m/s or larger at
all sites.
The surface energy budget also varied
with the composition of land use fea-
tures. Afternoon values of heat flux at
the urban commercial site 105, which
has a high percentage of paved areas
and few trees, were about twice those at
the rural site 109. During the nocturnal
hours, the heat flux was generally nega-
tive at site 109, but was seldom nega-
tive at site 105. Latent heat flux was sig-
nificantly greater at site 109 than at site
105; afternoon Bowen ratios of 0.5 and
2.0 were characteristic of sites 109 and
105, respectively. The heat flux at ur-
ban site 107, which had numerous tall
trees, was similar to that at site 109 dur-
ing daylight hours. At night, site 107
had a zero or very small negative heat
flux characteristic of an urban site.
The boundary layer stratification re-
flected the land-use features responding
to the ambient air flow and solar radiation.
Based on computations of z'/L (z' = z-d),
which includes the effects of both heat
flux and surface stress, site 109 was
strongly stable at night and strongly un-
stable during the afternoon. Site 105
was neutral and strongly unstable for the
two periods, respectively. Site 107 was
essentially neutral at night but only
slightly to moderately unstable during
the convective period of the day (due to
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Table 1.
Site Land-Use Characteristics and Estimated Displacement (d) and
Roughness (ZJ Lengths Based on the Work ofKutzback (K) and Counihan
1C) and Average Calculated Values
Site
105
107
777
703
Land Use
Buildings
Trees
Paved
Grass
d(K)
d(C)
Z0(K)
Z0(C>
Calculated Values
d(1)
Z0(2)
Z0<3)
h
Ar/A (m)
.25 5.5
.01 5.5
.59 0
.15 0
4.0
1.65
1.2
1.65
2
0.67
0.67
h
Ar/A (m)
.25 7.5
.25 12
.16 0
.34 0
8.4
6.3
#
1.17
6
1.39
1.20
h
Ar/A (m)
.16 7.5
.25 13.5
.14 0
.45 0
9.2
5.8
*
1.89
6
1.71
1.37
h
Ar/A (m)
.05 4.5
.05 3.0
.Of 0.0
.89 0.0
.84
.19
.04
.06
0
0.33
0.46
* Method of calculation not valid for this category of Ar/A.
(1) Estimated for use in wind profile equation.
(2) Calculated from profile equation.
(3)Z0 = h/8.15.
s
O Neutral
a Unstable
A Stable
100
200 300
Wind Direction, degrees
400
Figure 1. Surface roughness length vs. wind direction for site 107.
the large surface stress and relatively
small heat flux).
Partly in response to the temporal and
spatial variation of stratification, the di-
urnal variation of most turbulence pa-
rameters differed significantly between
the urban and rural environs. The turbu-
lent wind standard deviations, turbulence
intensities, and the spectral peak wave-
lengths were higher at the urban sites
during nocturnal hours due to the urban
heat island and associated deeper mo-
mentum boundary layer. The turbulence
parameters tended to converge during
the morning transition period (i.e., the
normalized turbulence structure was
similar in both the urban and rural envi-
rons between 8 a.m. and 10 a.m.) and
diverged during the afternoon transition
of the boundary layer to stable stratifica-
tion.
The afternoon transition of the boun-
dary layer from unstable to stable strati-
fication in both urban and rural environs
occurred over a relatively long period of
time. Both horizontal and vertical turbu-
lence intensity components reached a
maximum about noon and declined stead-
ily to near their nocturnal equilibrium
value by 6 p.m. The velocity variances
and peak wavelengths, while peaking
about 12m. (noon), declined only slight-
ly to 2 p. m., and then decreased steadily
to 7 p.m. Figure 2 demonstrates this
feature for the peak wavelength of the
longitudinal component of the wind for
sites 105, 107 and 109. Note that the
decline after 2 p.m. is well in advance of
the decline in the mixing height. These
observations suggest that free convec-
tive turbulence may be scaled to the
peak wavelength of the horizontal velo-
city components rather than the height
of the mixed layer. During the late after-
npon period these two scale lengths may
differ significantly. Turbulent mixing to
the top of the "mixed layer," as speci-
fied by lidar or temperature-dewpoint
profiles, probably does not cease abrupt-
ly after the heat flux peaks. It is sug-
gested, however, tnat the probability of
any thermal reaching the top of the
"mixed layer" decreases significantly
after 1 p.m. to 2 p.m. and continues to
decrease to near zero prior to sunset,
such that the peaK in tne energy spec-
trum is continually shifting to higher fre-
quencies. The prooability of a thermal
reaching z, or any heignt within the mixed
layer after 2 p.m. likely oepends on the
heignt and strengtn of the mixed layer
capping inversion, meso and synoptic
scale advective processes, and on the
surface energy budget which may have
significant spatial variability in urban
environs.
Resuits of the validation tests of cur-
rent similarity parameterizations using
this data set were mixed. The nondimen-
sionaiized turbulence parameters (i.e.,
the velocity and temperature variances,
turbulence intensities, and spectra) for
site 109 generally behaved as expected
from similarity theory; the average mag-
nitude of tne data as a function of z'/L
was consistent with corresponding
vaiues at idea! sites. However, the iarge
scatter of data points (for example, see
plots for ow/u* in Figure 3) probably re-
suited from the nonhomogeneous distri-
bution of iand-use features and the
abrupt cnange in roughness features
near tne tower in tne eastern quadrants.
A fully deveiopea turbulent boundary
layer may not have existed with easterly
winds. The observational scatter for site
109 probably reflects the uncertainty in-
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herent in the application of the similarity
approach to practical diffusion problems.
The nondimensionalized turbulence
parameters for the urban sites were gen-
eratty an orderly function of z VL; the data
exhibited less scatter than the corres-
ponding ratio for site 109. The plots of
some urban parameterizations (e.g., ojl
T*) were in very good agreement with
the empirical expressions derived by
others for flat homogeneous sites (such
as Kansas). Other nondimensionalized
ratios for the urban sites (for example,
ow/u* for site 105 in Figure 3), depart
noticeably from the Monin-Obukhov
similarity theory as empirically verified
for homogeneous sites of small rough-
ness. For small z'/L the slope of ow/u* is
smaller than expected. For large -z'/L
(approaching free convection), the ratio
was lower than expected, however, the
slope is approximately proportional to
(-z'/L)tt as predicted by similarity theory.
Even under neutral stratification the data
suggest site specific differences; the
normalized vertical velocity variance de-
creases with increasing Z0. Similar ano-
malies occurred with ov/u* and ou/u*.
The lateral and vertical turbulence in-
tensities were essentially as expected
from the similarity wind profile equation
for neutral stratification, but much lower
in magnitude than expected for z'/L =
-0.5. The nondimensionalized dissipa-
tion rate of turbulent kinetic energy $t
behaved much like the ratio ow/u *. At ur-
ban site 107, 4£ was significantly less
than the expected value of unity for neu-
tral stratification, and at site 105 it was
lower than expected throughout the
range of unstable stratification. The re-
sults for <|>t for site 109 were in general
agreement with similarity theory; how-
ever, the scatter was large.
The differences between the derived
empirical similarity forms for the urban
sites and those for the rural sites are ~
10 percent to 1 5 percent for neutral and
stable stratifications and about a factor
of ~ two for unstable stratification. For
many applications (e.g., atmospheric
diffusion estimates) these differences
are within the reliability of the applica-
tion form such that the Monin-Obukhov
similarity theory, or a simple modifica-
tion, derived out of the analysis, can be
applied to urban areas.
Conclusions
The purpose of this study was to de-
scribe the structure of turbulence in the
surface boundary layer of an urban area.
From the extensive analyses of the tur-
bulence data obtained in the St. Louis
environs, it is concluded that parametric
formulations for many nondimensional-
ized turbulence parameterizations (e.g.,
ow/u*, ou/u*, ov/u*) for the urban sites
differ significantly from existing theory,
although the parameterizations for the
rural site were in general agreement with
similarity theory. The following more
1 I I I I I I I I I I I I I I 151 I I I I I I I
Site JOS ° °
Site 107 °
Site 109
Mixing Height O
1600
1400
1200
1000
S 500
"5
1 600
-j
400
200
Q\ i I I I i I i I I I i i I I I I I I I I I I I I
0 24 6 8 10 12 14 16 18 20 22
Time (CSTJ, hr
Figure 2. Estimated fit to plots of peak wavelength of longitudinal velocity
component.
specific findings amplify this gener
conclusion:
• The standard deviation of the vert
cal velocity at both urban and run
sites can be described as a f unctio
of u *, w T', g/T and z. The horizon
tal velocity standard deviations seal
with u*, wT', g/T and Zj (height c
the mixed layer). In this respect th
urban data can be described withi:
the framework of similarity theory.
• For neutral stratification, the nor
malized velocity standard deviation;
were inversely proportional to sur
face roughness. The nondimension
alized dissipation rate had a simila
tendency—it was considerably less
than unity at site 107. These ano
malies from similarity theory are be
lieved due to the roughness wake
region extending to the height of the
instrumentation at site 107.
4
3
2
3
2
* 3
4
3
2
1
-5 -4 -3 -2-1 01
z'/L
Figure 3. Plots of aw/u* vs. z'/L for
indicated sites. The solid
lines represent cr*/u* =
1.3f1-z'/LJ1/3.
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For unstable stratification, the ur-
ban velocity standard deviations,
turbulence intensities, and ^ were
smaller than expected from similarity
theory. Flux divergence of turbulent
energy due to organized and possi-
bly stationary vertical motions over
portions of the city is the likely
cause of the anomalies.
For stable stratification, the velocity
variances were a linear function of
u* (i.e., ow/u* = constant) at each
of the sites. The individual slopes
(for each site) appear to be a func-
tion of Z0.
Temperature spectra at all sites
compared well with the Kansas em-
pirical form of the Monin-Obukhov
similarity theory.
For neutral stratification, turbulence
length scales were largest for the ur-
ban sites suggesting that $m may be
correspondingly smaller above the
rougher urban surface.
The peak wavelength of the longitu-
dinal velocity spectrum appears
more appropriate than Z, for free
convection scaling. During the after-
noon transition of the boundary
layer to stable stratification, the
two length scales may differ signifi-
cantly.
The EPA authors John F. Clarke (also the EPA Project Officer, see below), J. K.
S. Ching. and J. M. Godowitch are on assignment to the Environmental
Sciences Research Laboratory, Research Triangle Park, NC 27711 from the
National Oceanic and Atmospheric Administration.
The complete report, entitled An Experimental Study of Turbulence in an Urban
Environment," (Order No. PB 82-226 085; Cost: $15.00, subject to change)
will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The £PA Project Officer can be contacted at:
Environmental Sciences Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
U. S. GOVERNMENT PRINTING OFFICE: I982/559-092/0492
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