Atmospheric Environment 35 (2001) 3509–3519 Simulation of large particle transport near the surface under stable conditions: comparison with the Hanford tracer experiments Eugene Kim, Timothy Larson* Department of Civil and Environmental Engineering, Box 352700, University of Washington, Seattle, WA 98195, USA Received 7 July 2000; accepted 4 January 2001 Abstract A plume model is presented describing the downwind transport of large particles (1–100 mm) under stable conditions. The model includes both vertical variations in wind speed and turbulence intensity as well as an algorithm for particle deposition at the surface. Model predictions compare favorably with the Hanford single and dual tracer experiments of crosswind integrated concentration (for particles: relative bias ¼ 0:02 and 0.16, normalized mean square error=0.61 and 0.14, for the single and dual tracer experiments, respectively), whereas the US EPA’s fugitive dust model consistently overestimates the observed concentrations at downwind distances beyond several hundred meters (for particles: relative bias=0.31 and 2.26, mean square error=0.42 and 1.71, respectively). For either plume model, the measured ratio of particle to gas concentration is consistently overestimated when using the deposition velocity algorithm of Sehmel and Hodgson (1978. DOE Report PNL-SA-6721, Pacific Northwest Laboratories, Richland, WA). In contrast, these same ratios are predicted with relatively little bias when using the algorithm of Kim et al. (2000. Atmospheric Environment 34 (15), 2387–2397). # 2001 Elsevier Science Ltd. All rights reserved. Keywords: Monte Carlo Model; Fugitive Dust Model (FDM); Particle deposition; Plume model; Hanford tracer experiments 1. Introduction Human activities that disturb soil will produce airborne fugitive dust near the surface. Because both toxic chemicals and radionuclides can adhere to large, resuspended particles, these particles can act as an airborne vector for these compounds. In planning remediation activities and assessing fugitive dust source impacts, the transport of contaminated large particles near the surface must be carefully considered in order to make accurate estimates of environmental and occupa- tional exposures. To this end, simple steady state plume models have generally been employed. The most common of these in the US are the ISC model (US EPA, 1987) and the Fugitive Dust Model (FDM, Winges, 1990a). Both models make an important simplifying assumption, namely that there is no vertical variation in either the wind speed or turbulence intensity, even though particles have an imposed vertical velocity due to gravity and therefore experience differing air motions during set- tling. It is therefore important to examine the effect of these simplifying assumptions by considering less restrictive models and by comparing model predictions with observations. In this paper, we develop a Monte Carlo plume model for large particles (1–100 mm) that includes both particle settling and vertical variations in wind speed and turbulence intensity. It is patterned after earlier models (Hall, 1975; Hanna, 1979; Ley, 1982; Brusasca et al., 1989; Luhar and Rao, 1993; Hernandez et al., 1997), but includes a more detailed description of turbulence under *Corresponding author. Tel.: +1-206-543-6815; fax: +1- 206-685-3836. E-mail address: [email protected] (T. Larson). 1352-2310/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved. PII:S1352-2310(01)00113-3
Transcript
Atmospheric Environment 35 (2001) 3509–3519
Simulation of large particle transport near the surface understable conditions: comparison with the Hanford tracer
experiments
Eugene Kim, Timothy Larson*
Department of Civil and Environmental Engineering, Box 352700, University of Washington, Seattle, WA 98195, USA
Received 7 July 2000; accepted 4 January 2001
Abstract
A plume model is presented describing the downwind transport of large particles (1–100 mm) under stable conditions.
The model includes both vertical variations in wind speed and turbulence intensity as well as an algorithm for particledeposition at the surface. Model predictions compare favorably with the Hanford single and dual tracer experiments ofcrosswind integrated concentration (for particles: relative bias ¼ � 0:02 and 0.16, normalized mean square error=0.61and 0.14, for the single and dual tracer experiments, respectively), whereas the US EPA’s fugitive dust model
consistently overestimates the observed concentrations at downwind distances beyond several hundred meters (forparticles: relative bias=0.31 and 2.26, mean square error=0.42 and 1.71, respectively). For either plume model, themeasured ratio of particle to gas concentration is consistently overestimated when using the deposition velocity
algorithm of Sehmel and Hodgson (1978. DOE Report PNL-SA-6721, Pacific Northwest Laboratories, Richland, WA).In contrast, these same ratios are predicted with relatively little bias when using the algorithm of Kim et al. (2000.Atmospheric Environment 34 (15), 2387–2397). # 2001 Elsevier Science Ltd. All rights reserved.
Keywords: Monte Carlo Model; Fugitive Dust Model (FDM); Particle deposition; Plume model; Hanford tracer experiments
1. Introduction
Human activities that disturb soil will produce
airborne fugitive dust near the surface. Because bothtoxic chemicals and radionuclides can adhere to large,resuspended particles, these particles can act as an
airborne vector for these compounds. In planningremediation activities and assessing fugitive dust sourceimpacts, the transport of contaminated large particles
near the surface must be carefully considered in order tomake accurate estimates of environmental and occupa-tional exposures.
To this end, simple steady state plume models have
generally been employed. The most common of these in
the US are the ISC model (US EPA, 1987) and theFugitive Dust Model (FDM, Winges, 1990a). Bothmodels make an important simplifying assumption,
namely that there is no vertical variation in either thewind speed or turbulence intensity, even though particleshave an imposed vertical velocity due to gravity and
therefore experience differing air motions during set-tling. It is therefore important to examine the effect ofthese simplifying assumptions by considering less
restrictive models and by comparing model predictionswith observations.
In this paper, we develop a Monte Carlo plume modelfor large particles (1–100 mm) that includes both particle
settling and vertical variations in wind speed andturbulence intensity. It is patterned after earlier models(Hall, 1975; Hanna, 1979; Ley, 1982; Brusasca et al.,
1989; Luhar and Rao, 1993; Hernandez et al., 1997), butincludes a more detailed description of turbulence under
1352-2310/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved.
PII: S 1 3 5 2 - 2 3 1 0 ( 0 1 ) 0 0 1 1 3 - 3
stable conditions, an algorithm for deposition at the
surface, and an additional parameterization of deposi-tion velocity taken from our previous work (Kim et al.,2000).
We then compare the model predictions with experi-mental data and also with the predictions of US EPA’s
FDM (Winges, 1990a), the deposition and transportmodel primarily used in the US for fugitive dust.
2. The particle transport models
2.1. Monte Carlo plume model (MC model )
In general, this model consists of tracking the paths of
thousands of individual air parcels as they traveldownwind from a given location (Smith, 1968; Thomp-son, 1971; Reid, 1979). As applied to airborne particles,
we modify the individual particle trajectories to includean additional downward vertical component due togravitational settling. A given air parcel height varies
with time ( and therefore downwind distance) as follows:
zt ¼ zt�Dt þ w� Vg
� �Dt ð1Þ
In this model, w is taken as the sum of an auto-correlated component, wauto, and a random component,wrand, and is calculated according to Eq. (2) (Hanna
et al., 1982; Wilson et al., 1981; Davis, 1983; Walklate,1987; Hashem and Parkin, 1991; Sawford and Guest,1991).
w vertical wind velocity (m s�1)x downwind distance from source (m)z height above ground (m)
zi mixing height (m)z0 roughness length (m)
Greek lettersrp particle density (g cm�3)
mg geometric mean of particle diameter (mm)sg geometric standard deviation of particle
diameter
Dt time step (s)swm mechanical portion of vertical turbulenceswml mechanical portion of vertical turbulence
within the boundary layer
swmr mechanical portion of vertical turbulenceabove the boundary layer
sy standard deviation of concentration distri-
bution in the y directionn kinematic viscosity of air (m2 s�1)
E. Kim, T. Larson / Atmospheric Environment 35 (2001) 3509–35193510
et al. (2000). Specifically,
Vdð Þb¼ u*�10 �2:8=Stkeð Þ þ Vg: ð8Þ
Particle deposition flux is computed as an exponentialreduction in the particle mass associated with air parcels
that pass near the surface during a given time step:
mp
� �t¼ mp
� �t�Dt exp �
Vdð Þbtd
z0
� �: ð9Þ
As shown in Fig. 1, td is related to z0 as follows:
td ¼ Dtz0 � zt
zt�Dt � ztfor zt5z05zt�Dt: ð10Þ
Therefore, each particle loses some fraction of its initialmass each time it passes near the surface on its
downwind trajectory. However, all particles are trackedin the model out to the most distant sampling arc, eventhose whose mass has been significantly depleted by
interaction with the surface. For comparison purposes,the MC model was run with ðVdÞb from both Kim et al.(2000) and Sehmel and Hodgson (1978).
The uncertainties in model predictions are due to boththe uncertainties in meteorological variables as well asthe uncertainty associated with the finite sampling time
downwind. To assess the former uncertainties, 100different sets of input variables were created from
distributions of each of the meteorological parameters.These distributions, in turn, were based on uncertaintiesin these parameters as suggested by Hanna et al. (1998).
Specifically, we used a 95% confidence interval of30% of the mean values for all parameters excepttemperature, where we assumed 3 K.
The uncertainty in sampling time arises because we
assume in the MC model that the initial vertical velocityof any given trajectory is independent of prior trajec-tories. Inherent in this assumption is the fact that the
time between trajectory releases is greater than theLagrangian time scale. This implies a maximum numberof independent trajectories that are associated with any
given downwind sampling time. This maximum numberwas estimated for each Hanford dual tracer experimentand is shown in Table 1.
To assess the combined uncertainty in the modelprediction due to both these uncertainties, MC modelruns were conducted with 100 different sets of inputvariables. For each set, the maximum number of
independent particle trajectories associated with themean input parameters for that set was used. The 95%confidence intervals for the predictions are based on the
3rd and 98th ranked predicted values (Hanna et al.,1998). In a few instances, these intervals include a valueof zero as a lower limit. This is physically plausible given
that the model’s uncertainty at a fixed downwindlocation includes the effect of a limited number ofindependent trajectories.
2.2. Fugitive dust model (FDM)
The FDM is an Eulerian, steady state model based on
the analytical solution of Ermak (1977) and specificallydesigned for the transport of fugitive dusts near thesurface (Winges, 1990a). The FDM assumes a constantFig. 1. Hypothetical trajectory of an air parcel near the surface.
Table 1
Meteorological data and turbulence parameters of Hanford dual tracer experiments
Exp. no. Values from Doran et al. (1984) Estimated values (this study)
U2m (m s�1) WDa (deg) u� (m s�1) L (m) T2m (K) Stability class z0 (m) zi (m) No. of
trajectoriesb
DT1 3.63 308 0.40 166 287.7 5 0.017 582 751
DT2 1.42 293 0.26 44 292.5 6 0.191 305 555
DT3 2.02 288 0.27 77 290.5 5 0.045 323 570
DT4 1.50 292 0.20 34 287.9 6 0.053 206 461
DT5 1.41 269 0.26 59 287.1 6 0.425 305 555
DT6 1.54 310 0.30 71 293.5 6 0.170 378 613
a Wind direction.b =0.5 (averaging time)/Tz
L, where TzL is evaluated at z¼ 2 m.
E. Kim, T. Larson / Atmospheric Environment 35 (2001) 3509–3519 3511
wind speed and eddy diffusivity at all heights, andadopts Vd from Sehmel and Hodgson (1978) as follows:
Vd ¼Vg
1 � exp Vg=u*� �
Int1 and 2 þ Int3½ �� �; ð11Þ
where Int1 and 2 is an atmospheric integral resistanceapplicable from 1 cm up to 1 m above the surface; andInt3 is a surface integral resistance from the surface to1 cm above it.
The FDM was run in standard, default mode withdeposition velocities as a function of particle size thatare based on the particle deposition algorithm of Sehmel
and Hodgson (1978) as modified by the California AirResource Board (CARB) (Winges, 1990a). In the FDM,the particle deposition flux is calculated using the surface
concentration. However, as shown in Eq. (11), thedeposition model includes a transport resistance termthat is based on the concentration 1 m above the surface.
To avoid this inconsistency, FDM was also run with thefollowing modification of Eq. (11):
Vdð Þb¼Vg
1 � exp Vg=u*� �
Int3
� � ð12Þ
For completeness, we also ran the FDM with ðVdÞbcomputed directly from Eq. (8).
For the comparison with Hanford tracer experiments,the normalized cross-wind integrated concentration(Cy=Q) was directly computed at receptor height z using
Cy=Q ¼C x; 0; zð Þ
Q
ffiffiffiffiffiffi2p
psy: ð13Þ
In the FDM, sy is computed from a modified form of
the traditional Pasquill–Gifford–Turner formula asfollows:
sy ¼ 1:342xz0:20 tan�1 0:0175 a� b ln 10�3x
� �� � �; ð14Þ
where a ¼ 8:33, 6.25 and 4.17 and b ¼ 0:72, 0.54 and0.36 for stability classes 4, 5 and 6, respectively.
The uncertainties in the FDM predictions wereassumed to be exclusively associated with the uncertain-ties in the meteorological parameters. The stability classwas estimated from Golder’s relationship between L and
z0 (Golder, 1972) and did not vary within any givensimulation. Given these uncertainties, FDM runs wereconducted with 100 different sets of input variables.
3. Hanford tracer experiments
The model predictions were compared to data
collected at the US Department of Energy’s (DOE)Hanford site in eastern Washington, USA. These dataconsist of 2 types of experiments: dual tracer experi-
ments (Doran et al., 1984) and single tracer experiments(Nickola, 1977; Nickola et al., 1983).
The dual tracer experiments represent 6 atmosphericdispersion experiments that were conducted in 1983, and
used for the evaluation of the Gaussian plume-depletionmodel (Doran and Horst, 1985), the ISC model (Cole,1988), and the FDM (Winges, 1990b). In the dual tracer
experiments, concentrations of gaseous (SF6) andparticulate (ZnS) tracers were measured at five samplingarcs located downwind from a fixed release point. Fig. 2
Fig. 2. Tracer particle mass frequency distribution (a) ZnS used
for Hanford dual tracer experiments. rp¼ 4:0 g cm�3, mg¼ 6 mm
and sg ¼ 2 (Doran et al., 1984). (b) ZnS used for Hanford
single tracer experiments. rp¼ 4:1 g cm�3, mg¼ 4:1 mm and
sg=1.6. (c) fluorescein used for Hanford single tracer experi-
ments. rp¼ 1:53 g cm�3, mg¼ 18:6 mm and sg ¼ 2:5 (Nickola,
1977).
E. Kim, T. Larson / Atmospheric Environment 35 (2001) 3509–35193512
shows the size distribution of tracer particles used forthe experiments. Each sampling arc contained up to 42
equally spaced sampling points. The tracers werereleased at 2 m and measured at 1.5 m above ground.
The single tracer experiments include over 400 atmo-
spheric dispersion experiments beginning in 1960. Inthese experiments, either ZnS or fluorescein was used asa tracer particle. Only surface release (z ¼ 1:5 or 2 m)and surface sampling (z¼ 1:5 m) experiments were
compared with model predictions. In both the singleand dual tracer experiments, the measured downwindconcentrations along a given sampling arc were used to
compute the cross-wind integrated concentration (Cy)at a given downwind distance. Values of Cy=Q werereported for each sampling arc.
In the dual tracer experiments, meteorological datawere concurrently collected at two meteorologicaltowers. The values of u* and L were taken from sonic
anemometer data (Doran et al., 1984). They reported a
value of z0 ¼ 0:03 m based on their measurements andon a previous analysis (Horst and Elderkin, 1970). We
re-examined the reported values of z0 for each experi-ment. Given the reported average wind speed, as well asthe value of u* and L measured via sonic anemometry,
we were able to estimate z0 using the similarity functions(Paulson, 1970). As shown in Table 1, our estimates ofz0 differ from and are mostly larger than the previouslyreported value of 0.03 m. Experiment DT5 (see Table 1)
has the largest z0 and its average wind direction alsodiffered from the other experiments. Therefore anaverage value of z0 ¼ 0:095 m was used in this study
for experiments DT1 through DT4, and DT6. Inexperiment DT5, there was a significantly greater degreeof meander of the wind direction. Therefore, we treated
this experiment separately from the others and reportedthe overall results with and without this experiment. Forexperiment DT5, z0 was set to 0.425 m. zi was computed
from cloud cover and wind velocity at 2 m above ground
Table 2
Meteorological data and turbulence parameters of Hanford single tracer experiments
Exp. no. Values from Nickola (1977), Nickola et al. (1983) and Cole (1988) Estimated values (this study)
U2m (m s�1) T (K) Stability class dT=dz (K m�1) u� (m s�1) L (m) zi (m)
D1 1.2 288.1a 5 0.06c 0.09 13.8 55.2
D1A 1.2 288.1 5 0.06 0.09 13.8 55.2
D2 1.9 291.2 4 0.20 0.15 11.4 260.0
D2A 1.9 291.2 4 0.20 0.15 11.4 260.0
D3 2.6 294.8 5 0.06 0.14 21.0 80.0
D3A 2.6 294.8 5 0.06 0.14 21.0 80.0
U57 1.5 289.8 5 0.20 0.05 3.1 80.0
U58 3.2 289.4 4 0.20 0.28 61.9 330.6
U63 3.0 291.6 5 0.04 0.29 80.3 331.4
U64 1.6 290.7 5 0.18 0.11 8.8 114.1
U70 4.8 294.2 4 0.01 0.45 739.9 635.0
FT43 2.3 291.1b 5 0.06d 0.20 34.3 195.1
FT50 4.1 283.9 4 0.04 0.38 105.2 532.9
FT54 1.9 296.1 4 0.17 0.16 12.7 258.6
FT55 2.5 292.3 5 0.06 0.22 36.6 322.1
FT56 0.8 297.1 4 0.13 0.09 7.9 250.1
FT57 2.6 293.9 5 0.06 0.22 39.4 242.8
FT64 3.1 301.2 4 0.26 0.07 5.4 79.3
FT66 3.3 301.9 4 0.05 0.29 63.8 361.8
FT67 1.7 299.6 4 0.11 0.11 10.6 83.0
FT68 3.8 303.7 5 0.04 0.35 93.2 494.0
FT69 4.5 301.7 4 0.03 0.39 144.3 553.7
FT70 2.9 300.2 4 0.03 0.26 74.0 260.6
FT71 1.9 296.6 6 0.01 0.17 77.1 72.2
U48F 1.5 283.3 4 0.09 0.14 16.8 566.5
U54F 3.3 277.7 4 0.08 0.28 41.5 396.1
a Temperature at the height of 0.9 m.b Temperature at the height of 2.1 m.c Based on temperature at the height of 3 and 50 ft.d Based on temperature at the height of 7 and 50 ft.
E. Kim, T. Larson / Atmospheric Environment 35 (2001) 3509–3519 3513
using the algorithms in AERMET (US EPA, 1998b),the meteorological pre-processor for the AERMOD,
assuming Bowen ratio of 0.3 and Albedo of 0.14(values of cultivated land in spring}Paine, 1987). Theresulting meteorological variables are summarized in
Table 1.In the single tracer experiments, the vertical profiles
of wind speed, wind direction, standard deviation ofwind direction, and temperature were reported as
meteorological data. Because turbulence parameterswere not reported in these experiments, the u* , L andzi values were estimated using similarity functions
(Paulson, 1970) and the algorithms in AERMET (USEPA, 1998b). Only the 26 runs with either stable orweakly stable conditions are analyzed here. The
associated meteorological parameters are summarizedin Table 2.
4. Model evaluation
The model predictions and corresponding uncertain-ties (95% C.I.) are compared with the Hanford dualtracer experiments in Fig. 3. As shown, the FDM
consistently overestimates the measured values of bothtracer particle and tracer gas concentration. In contrast,the MC model predictions are consistent with themeasurements. Fig. 4 shows the measured versus pre-
dicted values for the Hanford single tracer experiments.In this case, the FDM systematically overestimates themeasured values only at the largest downwind distances.
Several statistical indices for evaluating air qualitymodels using paired comparisons with observationshave been suggested (Hanna, 1988; Brusasca et al.,
1989). To measure the performance of both the FDMand MC model, relative bias (RB) and normalized mean
Fig. 3. Measured Cy=Q versus predicted Cy=Q (prediction and 95% C.I.) for Hanford dual tracer experiments: (a) FDM for particles
with default Vd; (b) MC model for particles with ðVdÞb from Kim et al. (2000); (c) FDM for gas; (d) MC model for gas. Lower dotted
error bars include 0 s m�2.
E. Kim, T. Larson / Atmospheric Environment 35 (2001) 3509–35193514
Fig. 4. Measured Cy=Q versus predicted Cy=Q of tracer
particles (ZnS, fluorescein) for Hanford single tracer experi-
ments (stable and weakly stable atmospheric condition). (a)
FDM with default Vd (b) MC model with ðVdÞb from Kim et al.
(2000).
Table 3
Statistics for the comparison of Cy=Q between model predictions and Hanford tracer experiments
Tracer Model simulation Average RB Average NMSE Percentagea
FDM with Kim et al. ðVdÞb 1.57 (1.70) 1.17 (1.33) 12.7 (10.1)
FDM with Sehmel et al. ðVdÞb 1.98 (2.26) 1.49 (1.74) 8.0 (3.3)
MC model with Kim et al. ðVdÞb 0.16 (0.18) 0.14 (0.17) 79.1 (75.5)
MC model with Sehmel et al. ðVdÞb 0.25 (0.30) 0.15 (0.17) 66.2 (61.2)
Particlesc FDM with default Vd 0.31 0.42 44.9
MC model with Kim et al. ðVdÞb �0.02 0.61 40.2
Gasb FDM 1.36 (1.40) 0.92 (0.98) 20.0 (18.3)
MC model �0.08 (�0.05) 0.21 (0.24) 82.9 (80.0)
a Percentage of the R values between 1 and 2 (see text).b Hanford dual tracer experiments.c Hanford single tracer experiments.d ( ) indicates statistics without experiment DT5.
Fig. 5. The cumulative frequency distributions of R for
E. Kim, T. Larson / Atmospheric Environment 35 (2001) 3509–3519 3515
square error (NMSE) for Cy=Q values have beencalculated as follows:
RB ¼P�Mð ÞM
; ð15Þ
NMSE ¼P�Mð Þ2
PM; ð16Þ
where for any sampling arc, M is measured value of
Cy=Q and P is the predicted value.We can also define the ratio R ¼ M=P, where R ¼
ð1=RÞ if R51. For a perfect model, the value of RB and
NMSE are zero and the value of R is 1. The averagevalues for both the single and dual tracer experimentsare summarized in Table 3. We also show these statisticscomputed without considering experiment DT5. For the
dual tracer experiments, the cumulative frequencydistributions of R are shown in Fig. 5. We can alsoconsider the ratio of particle to gas concentrations at a
given downwind distance from the source. Specifically
we can define this ratio at the measurement height
f1:5 ¼Cy=Q� �
particle
Cy=Q� �
gas
�����z¼1:5m
: ð17Þ
We can further define the ratio of vertically integratedvalues at a given downwind distance
f z ¼
R zi0 Cy=Q� �
particledzR zi
0 Cy=Q� �
gasdz
ð18Þ
Using either the MC or FDM models, there exists a highdegree of correlation (R2 > 0:98) and a nearly one to one
correspondence (0.915slope50.94) between the pre-dicted values of f1:5 and f z over all sampling arcs in thedual tracer experiments. For this reason, we canconsider f1:5 a surrogate for the fraction of non-
deposited particles at a given downwind distance.Fig. 6 shows the predicted versus observed f1:5 values
as a function of both the plume model and the algorithm
used to estimate ðVdÞb. Test statistics for the f1:5 values
Fig. 6. Measured f1:5 versus predicted f1:5 for Hanford dual tracer experiments by (a) FDM with ðVdÞb from Kim et al. (2000), (b) MC
model with ðVdÞb from Kim et al. (2000), (c) FDM with ðVdÞb from Sehmel et al. (1978), and (d) MC model with ðVdÞb from Sehmel
et al. (1978).
E. Kim, T. Larson / Atmospheric Environment 35 (2001) 3509–35193516
are summarized in Table 4. The ðVdÞb algorithm of Kimet al. (2000) (Eq. (8)) shows less bias than that of Sehmel
and Hodgson (1978) (Eq. (12)) when used in eitherplume model; the NMSE is similar for all models.
5. Discussion
For the dual tracer experiments, the default FDM
performs poorly when compared with the other modelsexamined here (see Table 3). This is notable because theFDM is widely used as a tool in environmental
assessment and has been shown to outperform its mainalternative, US EPA’s Industrial Source Complex (ISC)model (Winges, 1990b). Our analysis shows that under
stable conditions the FDM consistently overestimatesthe airborne concentrations of large particles (1–100mm)at downwind distances beyond several hundred metersand therefore underestimates the deposition of these
particles. In contrast, the MC model has significantlybetter prediction power, especially when it incorporatesthe deposition velocity algorithm of Kim et al. (2000).
The MC model has little or no bias and reasonably lowgross error. Considering the uncertainty intervals pre-sented in Fig. 3, we can say that its predictions are
consistent with the dual tracer experiments.The FDM also differs from the MC model in its
prediction of tracer gas concentrations. Here again, the
FDM overestimates the observed downwind values,whereas the MC model shows little or no bias or grosserror. This inability of the FDM to correctly describetracer gas concentrations is one important reason for its
inability to accurately predict downwind particle con-centrations. A second reason is FDM’s underestimatesof the particle deposition velocity. In the default mode,
FDM uses the deposition velocity described by Sehmeland Hodgson (1978). For the meteorological conditionsof the dual tracer experiments, Sehmel et al. algorithm
predicts velocities that are several times less than thosepredicted by Kim et al. This is reflected in the results
shown in Fig. 6 and Table 4, where for either plumemodel the measured ratios of particle to gas concentra-
tion ( f1:5) are consistently overestimated when theSehmel et al. algorithm is used. In contrast, these sameratios are predicted without bias when the Kim et al.algorithm is used. Therefore, in the large-scale, dual
tracer field experiments Kim et al. ðVdÞb algorithmshows better agreement with measurements than Sehmelet al. ðVdÞb algorithm. Interestingly, we reached the same
conclusion in studies of deposition onto an isolated,surrogate surface (Kim et al., 2000).
For the single tracer experiments, the MC model has
less bias than the FDM, but both models havecomparable mean error. However it is difficult to makeconclusions about the relative performance of the twomodels for the single tracer experiments versus the dual
tracer experiments. One main reason for this is that thedual tracer experiments were done under more stronglystable atmospheric conditions than the earlier, single
tracer experiments. Another reason is that sonicanemometry data is not available for the earlier, singletracer experiments. Perhaps the MC model performs
better than the FDM under these more stronglystable conditions, or perhaps the sonic anemometerdoes a better job of describing the turbulence
under more strongly stable conditions than the profilemethod. Valid comparisons require comparableturbulence measurements under comparable stabilityconditions.
On average, 39% of the MC model’s uncertainty forparticles shown in Fig. 3 is associated with the smallaveraging time appropriate to the Hanford tracer experi-
ments, the remainder being associated with the uncer-tainty in the meteorological input variables. Therefore,in future particle transport experiments, larger sampling
times (>30 min) can further reduce this uncertaintyand therefore provide for a better comparison.
The computational overhead of the MC model islarger than that of the FDM. Using a 700 MHz Pentium
III microprocessor, it takes about 7 min to compute the
Table 4
Statistics for the comparison of f1:5 between model predictions and Hanford dual tracer experiments
Model simulation Average RB Average NMSE
FDM With default Vda 0.38 (0.42)d 0.13 (0.15)
With Kim et al. ðVdÞbb 0.02 (0.04) 0.06 (0.07)
With Sehmel et al. ðVdÞbc 0.30 (0.34) 0.10 (0.11)
MC model With Kim et al. ðVdÞbb 0.18 (0.13) 0.12 (0.12)
With Sehmel et al. ðVdÞbc 0.29 (0.28) 0.09 (0.09)
a Eq. (11) in text.b Eq. (8).c Eq. (12).d ( ) indicates statistics without experiment DT5.
E. Kim, T. Larson / Atmospheric Environment 35 (2001) 3509–3519 3517
concentration and deposition field out to 1 km down-wind for five different particle sizes. This computation
includes 10,000 individual particle trajectories for eachof these five different sizes. In contrast, this samecalculation would take less than one second using the
FDM. Therefore there is a tradeoff between accuracyand computation time when selecting between these twomodels.
6. Conclusions
Our analysis shows that under stable conditions theFDM consistently overestimates the airborne concen-trations of large particles (1–100mm) at downwind
distances beyond several hundred meters and thereforeunderestimates the deposition of these particles. Incontrast, the MC model predictions are consistent with
the measurements, especially when the model incorpo-rates the deposition velocity algorithm of Kim et al.(2000).
For either plume model, the measured ratio of particle
to gas concentrations at a given downwind distance isoverestimated when using the deposition velocity algo-rithm of Sehmel and Hodgson (1978). In contrast, these
same ratios are predicted with little bias when using thealgorithm of Kim et al. (2000).
Acknowledgements
The comments of an anonymous referee are gratefullyacknowledged. This study was funded by the Con-sortium for Risk Evaluation with Stakeholder Participa-tion (CRESP) by Department of Energy Cooperative
Agreement #DE-FCO1-95EW55084. This support doesnot constitute an endorsement by US DOE of the viewsexpressed.
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