United States
Environmental Protection
Agency
Environmental Sciences Research
Laboratory
Research Triangle Park NC 27711
Research and Development
EPA-600/S3-84-091 Sept. 1984
&EPA Project Summary
An Indirect Estimation of
Convective Boundary Layer
Structure for Use in Routine
Dispersion Models
James M. Wilczak and Mary Sue Phillips
Dispersion models of the convectively
driven atmospheric boundary layer often
require as input meteorological param-
eters that are based on measurements
not routinely taken. These parameters
include (but are not limited to) the
surf ace heat and momentum f luxes w'$'
and u'w', the height of the capping
inversion Z,, the jrjean wind-speed U(z),
wind-direction A2(z), and temperature
profiles djz) up to Z,, and the profiles of
the turbulent wind components cru(z),
0v(z), and crw(z). Through use of a simple
inversion rise model, surface-layer flux-
profile relationships and similarity scal-
ing laws for the convective atmospheric
boundary layer, we demonstrate how
the required meteorological parameters
can be deduced using much simpler and
more readily available measurements.
These measurements consist of an early
morning temperature profile obtained
from a radiosonde ascent; single-level,
surface-layer values of U, AZ, cru. a»;
two levels of mean temperature near
the surface; and an estimate of local
surface roughness.
Predicted values of each of the re-
quired parameters are compared to
directly measured values of 26 days of
data. Except for AZ(z), each of these
parameters can be estimated with an
average error of 10 to 30%. For light
wind speeds, the mean wind-direction
profile is strongly affected by slight
terrain inhomogeneities, and simple
AZ(z)parameterizationsfail. Finally, the
role of averaging time in estimating the
error of an individual realization is
discussed.
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 (see Project Report ordering in-
formation at back).
Introduction
Models of atmospheric dispersion,
which have been designed to predict the
transport and diffusion of atmospheric
pollutants, often require as input meteor-
ological information that is not routinely
available. It is possible, however, through
judicious use of simple measurements
that are routinely taken, to estimate the
more complex and detailed meteorologi-
cal parameters required by the models
The purpose of this analysis, therefore, is
to draw together various semi-empirical
theories of the convective atmospheric
boundary layer (ABL). Using these theo-
ries, along with readily available measure-
ments, we demonstrate the accuracy with
which one can deduce the mean and
turbulent structure of the convective ABL.
We assume that the meteorological
parameters required for dispersion Icu-
lat ions are the vertical profiles of D, AZ, ~§,
cru, CTV, and crw up to the height of the
capping inversionZ,, as well as the surface
heat flux w'ff and momentum flux u'w'
These parameters will need to be known
as a function of time, which beg ins shortly
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after sunrise and continues through the
day until late afternoon. The direct meas-
urements that will be used to predict
these parameters consist of
• An early morning temperature sound-
ing, obtained from a rawinsonde
ascent,
• The mean surface wind speed Us and
direction AZS measured at one height
(nominally 10 m) as well as the turbu-
lent velocities au and crv at the same
height,
• Two levels of_mean_temperature near
the surface, 01 and 02 (nominally 2 and
10 m), and
• An estimate of the local surface rough-
ness Z0.
Twenty-six days of data are used m this
analysis. These data were taken in the
late summer over two consecutive years
at the Boulder Atmospheric Observatory
(BAO). The surface wind speed and
direction and heat flux and stress were
measured with a three-axis sonic-
anemometer/platinum-wire-thermom-
eter system mounted on a short mast at a
height of 9.8 m, located either 20 or 100
m west of the BAO tower Also on the
short mast were two aspirated quartz-
crystal thermometers, mounted at eight 2
and 8 m or 1.7 and 9.2 m. The thermom-
eters measured the mean temperature
with an accuracy of 0.05°C. In addition,
the 300-m tower has eight levels of sonic
anemometers and quartz-crystal ther-
mometers, which provided direct meas-
urements of the mean profiles and
turbulent velocity moments for compari-
son to the indirect predictions. Finally,
direct measurements of Z, were obtained
from the BAO tower, sodar, lidar, and
rawmsondes.
Procedure
The approach taken is to estimate w'0'
and u'w' by applying the surface-layer,
flux-profile equations to Us, Si, 62, and z0
The surface heat flux, surface stress, and
morning temperature sounding are then
used to calculate the growth of Z, during
the day. Next, w'ff, u'w', 9, andZ, are used
to form the similarity scaling parameters
L, u», and w». This approach allows us to
compute each of the required profiles
from previously published mixed-layer
and surface-layer similarity profiles.
The use of the surface-layer, flux-profile
equations to estimate the fluxes of heat
and momentum from measurements of
mean wind speed and temperature is a
well-known technique. The flux-profile
equations can be written as
U(z,z0, u,, 0,) = _y±. jln(z/z0) - 0,(z/L)}
k (1)
0(Z,Z0, U*, 0.)- 0o =
KHL A. jln(z/z0) - 0z(z/L)}. (2)
Kh k
For unstable conditions
(3)
(4)
(5)
(6)
of the convectively driven mixed layer art
given by
2 2
-2tan~1(x)+7r/2
where x = (1 - y, z/l)1'4
y = (1 -y2z/L)1/
while k, Km/Kh, yi and y2 are empirically
determined constants.
After rewriting Eqs. (1} and (2) in terms
of u* and 0», we solve for u* and 0» using
the following iterative procedure:
(1) Assume L = -<»; 0), and y is the lapse rate
above the inversion. Equation (1 3) repre-
sents a closure assumption based on
laboratory and atmospheric measure-
ments with A = 0.2 and B = 5.
The above set of nonlinear equations
are solved numerically with a fourth-
order, Runge-Kutta integration scheme
with a variable time step The time step,
which varies for 1 to 20 min, is chosen
objectively on the basis of a stability
analysis of the input data. Up to 10 levels
of y are derived from the morning radio-
sonde ascent
Once the surface heat flux and stress
and the inversion height are known, it is
possible to estimate the wind speed,
temperature, and turbulent velocity pro-
files based on similarity scaling laws The
scaling laws used here are the surface-
layer, flux-profile relations, as well as
turbulent velocity profiles derived from
the 1973 Minnesota experiment, from
aircraft measurements, and from labora-
tory water-tank studies.
The ABL wind speed and temperature
profiles are assumed to follow their
surface-layer forms up to a height which,
for a given value of -Z/L, is a fixed
fraction of the ABL height, and to be
constant above that height. For large
valuesof-Z,/L(as is the case for nearly all
of the present data set, with -Z,/L = 200
typically) we found 0.2 Z, to give good
results.
Based on the assumption of a well-
mixed boundary layer, we simply assume
that the mean wind direction is constant
with height through the ABL. This value is
taken a the mean wind direction at 10 m.
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Tha ABL profiles of au, <7V, and crw are
based on the published results of both
laboratory and atmospheric measure-
ments. The parameterization
C[0.5{2 - (z/Z,)1'4) + 0.1 (z/Z,)2]1'2 (11)
is used to describe the horizontal velocity
fluctuations, while the parameterization
[1.8(z/Z,)2'3(1 -.91 (z/Z,))]1
(12)
is used for the vertical component fluc-
tuations.
Results —
Surface fluxes were computed for 20-
min periods which usually started approx-
imately 40 min after sunrise Ensemble
values were also calculated by averaging
together the same 20-min periods relative
to sunrise, using times when only both
measured and calculated values were
available.
For the surface heat flux, each calcu-
lated 20-min ensemble value was within
10% of the meaured ensemble value,
while the average bias for all the data was
on the order of 2 to 3%. Despite the high
accuracy of the average calculated heat
flux, a relatively large scatter was present
for individual 20-min realizations, with a
standard deviation of approximately 50%.
When 1 -h values of measured and calcu-
lated heat fluxes were used, the standard
deviation was reduced to less than 30%.
This reduction indicates that a large part
of the error of an individual realization, in
fact results from the measured value's
not being representative of the true
surface heat flux because of insufficient
averaging time
The surface stress errors were some-
what larger, with ensemble 20-min
values within 30% of the calculated
values, and a standard deviation for
individual realization of 100%, which
could be reduced to 70% by using 1-h
values
With the calculated surface fluxes used
as input, inversion heights (Z,) were com-
puted. Ensemble 20-min calculated Z,
values agreed with measured values to
within better than 10%. The standard
deviation for individual 20-min realiza-
tions was approximately 30% of Z,
throughout the day
Temperature and wind profiles were
calculated by extrapolating surface winds
and temperatures up to 0.2 Z, In the
lowest half of the ABL, the average bias
error in the temperature at any level was
less than 0.15°C, while in the upper part
of the boundary layer, the average meas-
ured temperature was as much as 0.5°C
warmer than the calculated value. This
difference probably derives from unpa-
rameterized entramment effects. The
temperature standard deviation varied
from approximately 0.1 5°Cforz/Z><0.5,
and increased to 0.4°C for z/Z, >0.5. The
ensemble wind-speed profile was also
quite accurate, with a maximum bias at
any level of less than 10%. Standard
deviations were generally less than 30%,
giving a wind-speed error range from 0.2
to 0.6 m s"1.
The poorest predictions were those for
the mean wind direction AZ(z). Ensemble
values gave a mean bias of 5° in the
lowest half of the ABL, which increased
to approximately 30° near Z,, while the
standard deviation increased from 10° at
the surface to 60° near Z,. We attribute
these large errors to terrain inhomogene-
ities. The terrain varied from a gently
sloping of the local terrain, to the Front
Range of the Rocky Mountains, 20 km to
the west.
The errors for the turbulent velocity
components 0\,,v,» all have similar values,
with a mean bias of approximately 15%
and a standard deviation of 25% These
ranges correspond roughly to 0.15 to
0.25 ms~1. Increasing the averaging time
from 20 min to 1 h decreased the stan-
dard deviation of au,v by 30% while for aw
the reduction was almost 50%.
Conclusion
It has been shown that most of the
detailed meteorological parameters need-
ed for routine dispersion calculations can
be estimated from simple, readily avail-
able meteorological measurements, with
an accuracy of 10 to 30% The most
difficult parameter to predict accurately is
the wind direction in situations of inho-
mogeneous terrain and light geostrophic
wind speeds.
James M. Wilczak and Mary Sue Phillips are with the National Oceanic and
Atmospheric Administration, Boulder. CO 80303.
Peter L. Finkelstein is the EPA Project Officer (see below).
The complete report, entitled "An Indirect Estimation of Connective Boundary
Layer Structure for Use in Routine Dispersion Models," {Order No. PB 84-238
260; Cost: $11.50, subject to change) will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Environmental Sciences Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
•ur U S GOVERNMENT PRINTING OFFICE. 1984 — 759-015/7826
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