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Importance of Using Observations of Mixing Depths in order to Avoid LargePrediction Errors by a Transport and Dispersion Model
J. M. WHITE AND J. F. BOWERS
Dugway Proving Ground, Dugway, Utah
S. R. HANNA
Hanna Consultants, Inc., Kennebunkport, Maine
J. K. LUNDQUIST
Lawrence Livermore National Laboratory, Livermore, California
(Manuscript received 10 March 2008, in final form 9 June 2008)
ABSTRACT
The mixing depth of the boundary layer is an input to most atmospheric transport and dispersion (ATD)
models, which obtain mixing depths in one of four ways: 1) observations by radiosondes, sodars, or other
devices; 2) simulations by regional or mesoscale meteorological models; 3) parameterizations based on
boundary layer similarity theory; or 4) climatological averages. This paper describes a situation during a
field experiment when exceptionally low mixing depths persisted in the morning and led to relatively high
observed tracer concentrations. The low mixing depths were caused by synoptic effects associated with a
nearby stationary front and the outflow from a mesoscale thunderstorm complex located 20–50 km away.
For the same time period, the ATD model-parameterized mixing depth was a factor of 5–10 higher, leading
to predicted concentrations that were less than the observations by a factor of 5–10. The synoptic situation
is described and local radiosonde and radar observations of mixing depth are presented, including com-
parisons with other more typical days. Time series of local observations of near-surface sensible heat fluxes
are also plotted to demonstrate the suppression of turbulence by negative sensible heat fluxes during the
period in question.
1. Background and objectives
Nearly all atmospheric transport and dispersion
(ATD) models make use of inputs of the mixing depth,
also known as the mixing height or the planetary
boundary layer height (Arya 1999). The mixing depth
defines the top of the layer near the surface where tur-
bulent mixing is occurring. During the daytime, the
mixed layer typically has an adiabatic or superadiabatic
temperature lapse rate and the mixing depth is often
marked by a capping inversion. During sunny convec-
tive conditions, the turbulence in the mixed layer is
mostly generated by the sensible heat flux. When the
wind is strong, the mixed layer near the surface is nearly
adiabatic at all times of the day and the turbulence is
mostly mechanically generated. There may be a cap-
ping inversion at the top of the windy boundary layer
during clear conditions. During the night, the mixed
layer may be stable near the ground if conditions are
mostly clear. There is usually a shallow mixed layer
very near the surface in stable conditions due to gen-
eration of turbulence by wind shear, although the
mixed layer may be only a few meters deep.
The mixing depth can be observed by a variety of
methods. The most widely used method employs radio-
sonde soundings, which provide vertical profiles of tem-
perature and relative humidity (RH). The mixing depth
can often be identified on these vertical profiles by the
capping inversion and also by a sharp drop in RH.
However, these criteria do not always work because the
temperature and RH profiles sometimes can be am-
biguous. Also, there can be elevated ‘‘residual’’ mixing
Corresponding author address: John M. White, TEDT-DPW-
ME MS#6, 4531 B Street, Dugway, UT 84022-5006.
E-mail: [email protected]
22 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 26
DOI: 10.1175/2008JTECHA1134.1
� 2009 American Meteorological SocietyUnauthenticated | Downloaded 04/01/22 01:06 PM UTC
depths that are holdovers from the previous day or may
have formed some distance upwind and were advected
over the region of interest. Other methods of observing
the mixing depth include remote sensing devices such
as radars (Angevine et al. 1994; Bianco and Wilczak
2002) and lidars (Cohn and Angevine 2000). In this case
the mixing height is indicated by a discontinuity in a
remotely observed variable.
Most of the methods for estimating mixing depth will
have difficulties during stable nights when the mixing
depth may be less than 10 or 20 m and the radiosonde
or remote sounder cannot measure that close to the
ground. In this case, an instrumented tower is useful,
with temperature sensors at multiple heights through
30–40 m.
An alternate source of mixing depth estimates is a
regional or mesoscale meteorological model. Mesoscale
meteorological models such as the fifth-generation
Pennsylvania State University–National Center for At-
mospheric Research Mesoscale Model (MM5) (Liu et
al. 2006) produce outputs of mixing depth that can be
based on the height where the model-simulated turbu-
lent kinetic energy (TKE) first drops below some frac-
tion of its value at the surface or below some arbitrary
lower limit based on experience. Alternatively, the mix-
ing depth can be based on the height where the bulk
Richardson number for the model outputs surpasses a
critical value (as discussed in Angevine and Mitchell
2001).
Many modern dispersion models contain methods to
parameterize the mixing depth in the absence of nearby
direct observations of the mixing height or without the
aid of mesoscale meteorological models. For example,
the American Meteorological Society (AMS)/Environ-
mental Protection Agency (EPA) Regulatory Model
(AERMOD) Meteorological Processor (AERMET)
model (EPA 2004) is a meteorological preprocessor that
parameterizes mixing depth. For convective conditions,
these methods rely on the morning (1200 UTC) radiosonde
profile and an estimate of the sensible heat flux. For neu-
tral and stable conditions, the methods rely on an em-
pirical function that includes the friction velocity u* and
the Monin–Obukhov length L (e.g., Sykes et al. 2007).
The current study focuses on a specific model—the
Hazard Prediction and Assessment Capability (HPAC)
(DTRA 2004), which is a comprehensive modeling sys-
tem that includes the Second-Order Closure Integrated
Puff (SCIPUFF) ATD model (Sykes et al. 2007). The
HPAC application in this paper uses observations from
the Joint Urban 2003 field experiment (JU2003) (Allwine
et al. 2004; Clawson et al. 2005), which was conducted in
the Oklahoma City (OKC) area in July 2003. JU2003
provides an extensive dataset for transport and disper-
sion model evaluation. JU2003 included 10 intensive
observation periods (IOPs) during which the tracer
sulfur hexafluoride (SF6) was released for 30-min pe-
riods. An IOP was conducted on a day that was deemed
favorable by the field managers of the study. This paper
addresses IOPs 3, 4, 5, and 6, which took place during
the daytime on 7, 9, 13, and 16 July 2003, respectively
(these are sometimes referred to in the JU2003 reports
as Julian days 188, 190, 194, and 197). Each of these
IOPs included three 30-min continuous tracer releases,
separated by 2 h. The SF6 from these releases was
sampled by bag samplers at outer arc distances of 1, 2,
and 4 km from the release location. Numerous other
samplers operated at distances less than 1 km. In addi-
tion to the numerous tracer samplers used in JU2003,
extensive meteorological measurements were taken
from diverse observational platforms that were set up
across a broad area, ranging from the downtown area to
rural areas located 10 to 20 km upwind and downwind of
the city.
It was originally thought that meteorological condi-
tions were ‘‘similar’’ during the four daytime IOPs.
However, independent evaluations of the HPAC/
SCIPUFF ATD model by Warner et al. (2008) and
Hanna et al. (2007a) report large underpredictions in
concentration by HPAC/SCIPUFF during IOP 5 (13
July 2003), when tracer releases took place at 0800,
1000, and 1200 LST (1400, 1600, and 1800 UTC). These
large underpredictions did not occur during the other
daytime IOPs (3, 4, and 6). The observed concentra-
tions during IOP 5, which were a factor of 10 or more
larger than the concentrations observed during the
other daytime IOPs, were more typical of concentra-
tions observed during the nighttime IOPs (7, 8, 9, and
10). The current paper describes the results of an in-
vestigation of the reasons for the large underpredic-
tions during IOP 5. It appears that the large observed
concentrations were caused by a relatively low mixing
depth, as observed by on-site remote sounders and as
explained by looking at synoptic and radar maps. The
HPAC/SCIPUFF model, on the other hand, was using
parameterized mixing depths that were much larger
and more typical of climatological values. Even when
using the MM5 outputs of mixing depth, there were still
large underpredictions by HPAC/SCIPUFF, although
not as large as when the parameterized values were
used.
2. Observations and ATD model predictions ofconcentrations during daytime IOPs
Figure 1 shows the observed arc maximum tracer
concentrations C, normalized by source emission rate
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Q, at downwind distances of 1, 2, and 4 km for the
tracer releases during daytime IOPs 3, 4, 5, and 6 (in-
dicated on the histogram by different shaded bars). The
concentration averaging time is 30 min. For each re-
lease time in the figure, there are three groupings of
vertical bars, indicating the normalized concentrations
at the three arc distances. The start times for the 30-min
SF6 releases during IOPs 3 and 4 were 1600, 1800, and
2000 UTC (1000, 1200, and 1400 LST), while the start
times for the SF6 releases during IOPs 5 and 6 were
1400, 1600, and 1800 UTC (0800, 1000, and 1200 LST).
Note that, because of the different IOP start times, Fig.
1 shows arc maximum concentrations for only two IOPs
for the 1400 and 2000 UTC release times.
It is seen in Fig. 1 that the maximum concentrations
measured during the first two SF6 releases of IOP 5
(1400 and 1600 UTC, or 0800 and 1000 LST) were al-
most an order of magnitude higher than those mea-
sured at the same times of day during the first two
releases of IOP 6 and the first release of IOPs 3 and 4.
The maximum concentration measured during the third
release of IOP 5 (1800 UTC or 1200 LST) was compa-
rable to the levels measured during the other IOPs for
the same time period. Later it will be shown that the
observed mixing depth during IOP 5 was much less
than the other IOPs for the releases at 0800 and 1000
LST, but had increased to close to the values for the
other IOPs by 1200 LST.
The HPAC/SCIPUFF ATD model (version 4.04),
with standard options, was used to calculate the 30-min
average arc maximum normalized concentrations, C/Q,
for comparison with the observed concentrations dur-
ing the daytime IOPs. The same HPAC urban disper-
sion model option and meteorological inputs, including
point wind measurements from a special field experi-
ment site about 1 km upwind of the tracer release, were
used in the HPAC predictions for all daytime IOPs. It
should be noted that the model’s parameterized mixing
depths were used in the ATD model runs reported
here.
Figure 2 compares the predicted and observed arc
maximum normalized concentrations for each of the
three tracer releases for IOPs 3, 4, 5, and 6. For the arc
maximum concentrations, the predicted and observed
values at each sampling arc do not necessarily occur at
the same sampling location on the arc. In Fig. 2, the
solid diagonal line represents perfect agreement and
the dashed lines represent factor of 2 differences be-
tween predicted and observed normalized concentra-
tions. The general tendency in the figure is for HPAC
to underpredict the observed normalized concentra-
tions, with most of the values for IOPs 3, 4, and 6 near
the line indicating a factor of 2 underprediction. How-
ever, the HPAC predictions for the first two releases of
IOP 5 are about an order of magnitude lower than the
observations. The correspondence between predicted
and observed concentrations for the third release of
IOP 5 is comparable to that obtained for the other
IOPs.
An investigation was mounted to determine the rea-
FIG. 1. Comparison of arc maximum 30-min average concentrations over the three outer
sampling arcs. Note that LST 5 UTC 2 6 h.
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sons for the high observed concentrations and severe
model underpredictions for IOP 5. Possible reasons
could be low wind speeds, low turbulence intensities, or
low mixing depths. Low wind speeds were unlikely to
be the cause, since a previous study by Hanna et al.
(2007b) found that the IOP average wind speed differ-
ence between daytime IOPs was relatively small. Our
primary hypothesis was that the higher observed nor-
malized concentrations were related to relatively low
mixing depths, which were less than mixing depths pa-
rameterized by HPAC/SCIPUFF when run in the de-
fault mode.
3. Observations of mixing depth
Vertical profiles of temperature and humidity from
the Argonne National Laboratory (ANL) and Pacific
Northwest National Laboratory (PNNL) radiosonde
soundings during JU2003 were studied to determine the
observed mixing depths during IOPs 3, 4, 5, and 6. Ad-
ditionally, the observed mixing depths estimated from
the boundary layer turbulence measurements by Dug-
way Proving Ground’s Frequency Modulated/Con-
tinuous Wave (FM/CW) radar (Gallagher et al. 2004)
were studied. The ANL radiosonde site was approxi-
mately 4.3 km north of the tracer release site, the
PNNL radiosonde site was approximately 2.2 km south-
west of the release site, and the FM/CW radar was
approximately 1.5 km north of the release site. The
tracer release sites were within the Central Business
District (CBD) or on its upwind edge. The radiosonde
releases and the radar were generally located in the
suburbs, as opposed to the CBD. The radiosonde
launch times occurred at or near the start of each of the
tracer releases.
The FM/CW radar provides continuous readings of
the boundary layer turbulence structure. Mixing depths
are estimated using the knowledge that the radar return
in a convective boundary layer is large in the superadia-
batic layer near the surface, small in the well-mixed
portion of the boundary layer above the surface layer,
and large again in the elevated inversion layer at the
top of the mixed layer (Gallagher et al. 2004). The ra-
dar can also provide details on the complexity of the
FIG. 2. Comparison of arc maximum observed and HPAC-predicted normalized 30-min
average concentrations for IOPs 3, 4, 5, and 6.
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near-instantaneous structure of the daytime boundary
layer.
As an illustration of the use of the radiosonde pro-
files to estimate mixing depth, Fig. 3 contains the ver-
tical profiles of temperature and RH observed by the
PNNL radiosonde during IOP 5. The height of the cap-
ping temperature inversion and the height where RH
sharply decreases clearly indicate the mixing height for
FIG. 3. Vertical profiles of temperature and humidity from the PNNL radiosonde datasets
for the continuous release trials of IOP 5.
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the 1400 and 1600 UTC profiles (about 100 and 210 m,
respectively). The profiles are less sharp at 1800 UTC,
but still suggest a mixing depth at about 400–450 m.
Tables 1 and 2 list the mixing depths observed by the
two on-site radiosondes and the FM/CW radar during
IOPs 5 and 6, respectively. The FM/CW mixing depths
were estimated at the start times of the tracer releases
using the procedures described by Gallagher et al.
(2004). As shown by the fourth column in each table,
the average observed mixing depth ranged from ap-
proximately 100 to 490 m for IOP 5 and from approxi-
mately 430 to 1200 m for IOP 6. Thus, the observed
mean mixing depths for IOP 5 were 3–4 times smaller
than the mean mixing depths for IOP 6.
Figure 4 contains continuous time series of the esti-
mated FM/CW radar mixing depths for the four day-
time IOPs. The estimation method, based on the paper
by Gallagher et al. (2004), is described three paragraphs
above. The black, green, red, and blue lines represent
IOPs 3, 4, 5, and 6, respectively. The red horizontal
lines at the top of the figure identify the tracer gas
release periods. It is obvious in the figure that the mix-
ing depths for IOP 5 are considerably lower than the
depths for the other daytime IOPs.
4. Turbulence observations during the daytimeIOPs
Data from a meteorological tower on the northern
edge of Oklahoma City were inspected to determine
whether anomalous mixing conditions occurred during
IOP 5. Mean and fluctuating velocity and virtual tem-
perature measurements were available from the
Lawrence Livermore National Laboratory (LLNL)
crane pseudotower, which was located approximately
750 m NNW of the downtown area (Lundquist et al.
2004). This pseudotower consisted of a cable ladder
under tension, anchored by a construction crane. Eight
R. M. Young Model 81000 ultrasonic anemometers
were mounted along this pseudotower, from approxi-
mately 8 to 84 m above the surface. The LLNL crane
pseudotower microscale dataset provides high-resolu-
tion wind speed observations necessary for the calcula-
tion of variances, TKE, and the local dissipation of
TKE. The crane data have been tilt corrected, using the
correction algorithm suggested by Wilczak et al. (2001),
lending credibility to the calculation of vertical fluxes in
particular. More details on the construction of this
pseudotower are presented in Gouveia et al. (2007).
The measurements of sensible heat flux from the
LLNL crane pseudotower shown in Fig. 5 reveal a clear
distinction between the delayed development of the
convective boundary layer during IOP 5 and the more
typical growth observed during IOPs 3, 4, and 6. Note
that days 188, 190, 194, and 197 in the x-axis labels in
Fig. 5 correspond to IOPs 3, 4, 5, and 6, respectively.
The heat flux time series in IOPs 3, 4, and 6 show
typical daytime behavior, following an approximate
sine wave, starting to increase at 0700 or 0800 LST and
reaching a maximum at about 1300 or 1400 LST. The
time series for IOP 5 (lower left) remain negative or
near zero, with plus and minus variations, until after
1100 LST. Note that tracer releases occurred at 0800,
1000, and 1200 LST. The negative heat fluxes observed
during IOP 5 are associated with the influences of a
distant thunderstorm complex, and suppress mixing ac-
tivity and boundary layer growth in the JU2003 do-
main.
5. Synoptic maps and radar maps during IOP 5
The synoptic situation was studied for IOP 5 (13 July
2003) to find an explanation for the anomalously low
mixing depths. NWS observations at the nearby Wiley
Post Airfield indicated mostly cloudy to cloudy condi-
tions over the area from 0700 to 1400 UTC (0100–0800
LST) 13 July 2003, but no precipitation. However, some
of the surface observations from the Norman, Oklaho-
ma, weather station, located to the south of OKC, re-
ported lightning to the distant NW direction during this
time period. The surface weather map analysis for 0000
UTC 13 July 2003 (or 1800 LST on the previous day)
TABLE 1. Mixing depths observed for IOP 5 by ANL and PNNL
radiosonde soundings and FM/CW radar turbulence profiles.
Note that LST 5 UTC 2 6 h.
Time
(UTC)
ANL
radiosonde
(m)
PNNL
radiosonde
(m)
FM/CW
radar
(m)
Average
(m)
1400 100 100 100 100
1600 180 210 170 190
1800 530 430 510 490
TABLE 2. Mixing depths observed for IOP 6 by ANL and PNNL
radiosonde soundings and FM/CW radar turbulence profiles. Note
that LST 5 UTC 2 6 h.
Time
(UTC)
ANL
radiosonde
(m)
PNNL
radiosonde
(m)
FM/CW
radar
(m)
Average
(m)
1400 No data 450 420 430
1600 870 740 650 750
1800 1210 1290 1100 1200
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showed a propagating wave moving along a stationary
front, with the frontal boundary over OKC and areas of
rain showers in central Oklahoma. The surface map for
1200 UTC (0600 LST) 13 July, which is given in Fig. 6,
shows that the wave moved into northwest Arkansas
and the area of rain over central Oklahoma increased.
The radar map analysis at 1045 UTC (0445 LST) 13
July 2003 showed a general area of rain generated by
convective activity from southwest to north of OKC.
This is consistent with the observation of lightning re-
ported by the Norman weather station. Figure 7 [the
radar map at 1345 UTC (0745 LST)] shows that there is
a moderate area of convection NW of Oklahoma City,
and a larger line of cells centered along the Oklahoma–
Arkansas border. This mesoscale convective complex is
active at the time (0800 LST) of the first tracer release
during IOP 5. The timing of this development corre-
sponds to the location of the propagating wave along
the frontal boundary at 1200 UTC 13 July (Fig. 6).
We suggest that the combination of the outflow from
the nearby convective activity and the propagating
wave along the frontal boundary caused the surface
heat flux to be nearly zero and sometimes negative on
the morning of IOP 5. These factors inhibited the
growth of the mixing depth. The low mixing depths
(100–200 m) during the first two tracer releases are
more representative of nighttime situations.
6. Mixing depths estimated by MM5
As part of JU2003, high-resolution (4-km horizontal
grid spacing) runs were made with MM5 (Liu et al.
2006). The HPAC/SCIPUFF ATD model is able to di-
rectly use mixing depth (and other) outputs from MM5.
The Hanna et al. (2007a) HPAC/SCIPUFF (version
4.04) model evaluation exercise using the JU2003 field
data considered the MM5 mixing depth input option as
well as the observed and the HPAC/SCIPUFF param-
eterized mixing depth inputs. The MM5 mixing depths,
which partially account for the stationary front and the
rain showers, are about halfway in between the param-
eterized and the observed mixing depths and thus
partly correct for the large HPAC/SCIPUFF underpre-
dictions. However, since it is difficult for MM5 to simu-
late the timing and the spatial patterns of the outflow
from the mesoscale convective complexes, the ex-
tremely low mixing depths during IOP 5 were not cap-
tured by MM5.
7. HPAC/SCIPUFF model-parameterized mixingdepths compared with observations, and revisedHPAC/SCIPUFF runs with observed mixingdepths
The mixing depths parameterized by the HPAC/
SCIPUFF (version 4.04) model, when run in its default
mode, have been compared with the observations by
the PNNL radiosonde. The comparisons are shown in
Fig. 8 for each release time of IOPs 3, 4, 5, and 6. The
HPAC/SCIPUFF parameterized mixing depths for IOP
5 are seen to be much larger than the observed mixing
depths. For example, for the first IOP 5 tracer release
(at 0800 LST), the HPAC/SCIPUFF parameterized
FIG. 4. FM/CW radar boundary layer height estimates for the daytime IOPs.
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FIG. 5. Observed time variation of heat flux (m K s21) from seven levels (lowest level not plotted) at
the LLNL crane pseudotower for IOPs 3, 4, 5, and 6 (days 188, 190, 194, and 197, respectively) where
fluctuating quantities are calculated from 30-min averages centered at the data point. The heaviest solid
line denotes data from the top level, 83 m. The light dotted line denotes data from the lowest level, 15
m. The remaining solid lines represent data from 22, 28, 43, 56, and 70 m. The horizontal line indicates
zero heat flux. LST 5 UTC 2 6 h. Tracer releases were at 1000, 1200, and 1400 LST during IOPs 3 and
4 and at 0800, 1000, and 1200 during IOPs 5 and 6.
FIG. 6. Surface weather map analysis for 1200 UTC 13 Jul 2003. The star shows the location of OKC.
JANUARY 2009 W H I T E E T A L . 29
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mixing depth is about 650 m while the observed mixing
depth is about 100 m. In contrast to the mixing depth
discrepancies found for IOP 5, all of the mixing depths
parameterized by HPAC/SCIPUFF for the other day-
time IOPs are within a factor of 2 of the observed val-
ues in Fig. 8.
The HPAC/SCIPUFF model calculations were re-
peated for IOPs 3 through 6 using the same meteoro-
logical data and urban modeling options as in the pre-
vious runs, but with the mixing depths based on the
radiosonde observations. The use of the observed mix-
ing depths increases the simulated IOP 5 concentra-
tions so that they are within the range of the simulated
concentrations for IOPs 3, 4, and 6.
8. Conclusions
This study shows that the high normalized tracer con-
centrations observed during the morning releases of
JU2003 IOP 5 can be attributed to unusually low mix-
ing depths, which are evident in the radiosonde and
FIG. 7. Radar map analysis at 1345 UTC 13 Jul 2003. The blue star shows the location of OKC.
FIG. 8. Comparison of observed boundary layer heights with
HPAC default boundary layer heights for IOPs 3, 4, 5, and 6.
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FM/CW radar soundings and, by inference, from the
measurements of sensible heat flux at a meteorological
tower. The low observed mixing depths were likely
caused by the presence of a stationary front combined
with the effects of outflows from nearby thunderstorm
complexes. The standard mixing depth parameteriza-
tion in the HPAC/SCIPUFF ATD model, which is simi-
lar to the parameterizations in other state-of-the-art
ATD models, led to large underpredictions of the ob-
served concentrations during IOP 5. Thus, standard op-
erational use of an ATD model may not account for
atypical weather situations and may lead to large er-
rors. Underpredictions are especially undesirable be-
cause the public may not be adequately protected from
serious air quality impacts. Clearly, it is better to make
use of local meteorological soundings or analyses that
capture those conditions in the place of the model de-
fault parameters.
This detailed investigation of mixing depths has been
possible only because of the intensive research-grade
observations taken during JU2003. The soundings were
made often and produced excellent vertical resolution.
Routine soundings are seldom available at this time and
space resolution. Thus, our recommendation that local
soundings be available to better observe mixing depths
would require large expenditures. Nevertheless, our
study has shown that without realistic mixing depths,
the ATD model may have large errors, including the
potentially harmful underpredictions described here.
Perhaps a compromise would be to install enhanced
vertical sounders in critical locations such as near large
cities or where pollution problems are severe.
Finally, atmospheric dispersion field studies almost
always are conducted under fair-weather conditions,
because of safety concerns and because of the desire for
well-behaved dispersion patterns. But, as illustrated by
the tracer concentration measurements made during
JU2003 IOP 5, critical meteorological regimes resulting
in the highest concentrations can be missed when field
studies are restricted to fair weather. We recommend
that more field experiments be planned and carried out
during non–fair-weather conditions.
Acknowledgments. The research by J. White, J. Bow-
ers, and S. Hanna was sponsored by the Defense Threat
Reduction Agency, with Rick Fry as project manager.
S. Hanna’s research was cosponsored by the National
Science Foundation and by the Department of Home-
land Security. J. Lundquist’s research was supported by
the LLNL Laboratory-Directed Research and Devel-
opment program, and was performed under the aus-
pices of the U.S. Department of Energy by Lawrence
Livermore National Laboratory under Contract DE-
AC52-07NA27344.
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