Soil Physics
Evaluation of Wind Erosion Emissions Factors
for Air Quality Modeling
The exposure to airborne particulates and surface deposition are important pathways for many human health
assessments. Our primary focus is on air quality modeling issues associated with the emission of airborne particulates from contaminated surfaces via wind erosion and the subsequent deposition onto other areas. In this context,
the analysis is directed at long-term impacts associated with wind-erosion-induced movement from a contaminated area onto residential and other property. For this type of application, detailed inputs on soil moisture, armoring,
and other factors are typically not known as a function of time. The defined scope and data limitations generally
render more detailed and data-intensive approaches impractical compared with more simplified empirical models.
We compare and contrast selected empirical models to show the central tendency as a function of the type of applications (flat–regional and flat–local) as examples. This review demonstrates the importance of applying empirical
wind erosion equations in a manner that is consistent with their development and with due consideration of sitespecific features and the specific air quality analysis under evaluation. Of importance to this review are: the scale of
analysis, flat vs. pile (elevated) sources, and an appropriate representation of uncertainty. Without consideration of
such factors within dispersion modeling analyses of airborne particulate concentrations or surface deposition rates,
the exposure analysis can be substantially biased.
David A. Sullivan
Sullivan Environmental Consulting, Inc.
1900 Elkin St., Suite 200
Alexandria, VA 22308
Husein A. Ajwa*
Dep. of Plant Sciences
Univ. of California-Davis
1636 E. Alisal St.
Salinas, CA 93905
Abbreviations: TSP, total suspended particulates.
W
ind erosion produces an episodic source of suspendible particles from erodible surfaces. Wind erosion is a complex process. Until the wind speed
reaches a critical threshold to initiate particulate movement within the saltation
range, which is a function of the erodible material (Chepil, 1956), the erodible particles remain at rest. Particle movement requires a wind speed that is strong enough
to overcome the cohesive force of the adsorbed water films surrounding the soil particles at the surface as well as gravitation forces (Toy, 2002). The distribution of particles at the surface that are available for wind erosion processes is dynamic, which
includes a two-part process of abrasion: (i) disintegration of nonerodible units into
erodible particles, and (ii) the wearing away of erodible particles into suspendible
particles (Chepil, 1958). The suspendible fraction of an eroding surface cannot be
well represented by in situ particle size distributions (Lu and Shao, 1999).
As the critical wind speed approaches and then surpasses the wind erosion
threshold, some of the saltation-size particles, in the range of 60 to 2000 mm
(Greeley and Iversen, 1985) with a major contribution from 100 to 500 mm (Lyles,
1977; Shao, 2001; Canada Department of Agriculture, 1943), first begin to oscillate at frequencies consistent with the peak frequency of atmospheric turbulence,
approximately 2 Hz (Lyles, 1977), and ultimately the saltation particles, which are
large enough to protrude into the turbulent layer above the viscous surface layer,
begin to move to heights of tens of centimeters above the surface. The specific range
of particles involved in wind erosion is a function of wind speed and surface conditions; particles as large as 2 to 3 mm can be involved under exceedingly high wind
speed conditions (Beasley et al., 1984; Chepil, 1941). The size fraction >500 mm
Soil Sci. Soc. Am. J. 75:2011
Posted online 23 June 2011
doi:10.2136/sssaj2010:0132
Received 16 Mar. 2011.
*Corresponding author ([email protected]).
© Soil Science Society of America, 5585 Guilford Rd., Madison WI 53711 USA
All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by
any means, electronic or mechanical, including photocopying, recording, or any information storage
and retrieval system, without permission in writing from the publisher. Permission for printing and for
reprinting the material contained herein has been obtained by the publisher.
SSSAJ: Volume 75: Number 4 • July–August 2011
1271
is generally associated with surface creep. The ranges of particles
in suspension, saltation, and surface creep overlap considerably
as a function of wind speed (Canada Department of Agriculture,
1943). The lowest wind speed to produce wind erosion for a
smooth, dry, and highly erodible surface is approximately 4.4 m
s−1 at 0.30 m above the surface (Chepil, 1958), which is a wind
speed of approximately 7 m s−1 at a 10-m reference wind speed
and 1-cm roughness length. Because of the nonstationary nature
of atmospheric turbulence, wind erosion can occur with mean
wind speeds below the wind erosion threshold as measured in a
wind tunnel (Fan and Disrud, 1977).
Saltating particles are generally lifted only a short distance
above the surface along a generally parabolic trajectory and then
bounce from the surface at a higher angle than the incident angle
because of imparted spin (up to 200 to 1000 times per second)
when launched (Chepil, 1945). The saltating particles also move
surface particles that are too large to move in the air stream,
which is the surface creep process involving particles in the range
of 500 to 2000 mm or more (Chepil, 1941; Canada Department
of Agriculture, 1943).
Small particles have interparticle forces that produce cohesion. These forces include the effects of moisture, van der Waals
forces, electrostatic charges, and forces between adsorbed films
(Iversen and White, 1982). Without saltation, small particles do
not erode spontaneously because such particles do not protrude
above the viscous, nonturbulent layer of air next to the surface
(Chepil, 1958). The saltating particles release smaller particles
through sandblasting bombardment, which separates suspendible particles from larger clusters, and also through direct displacement of suspendible dust caused by saltating particles as
they plow craters into the eroding surface (Lu and Shao, 1999).
This process is highly complex, with different forces releasing and
sustaining the horizontal flux of large particles (by saltation and
surface creep) than those for vertical flux of suspendible particles.
Suspendible particles are <60 mm and include silt (39–62 mm)
and clay particles (<39 mm), with the fine dust fraction (2–10
mm) and smaller that, absent precipitation events, can remain in
suspension for long periods of time (Greeley and Iversen, 1985).
Suspendible dust can be transported great distances because
these relatively light particles move well above the saltation layer
as they are transported and dispersed with the ambient flow.
Starting with the upwind edge of an erodible surface, the mass
of saltating particles, which are contained within the first meter
above the surface, increases to an equilibrium point, with the effective surface roughness length increasing and, thereby, also the
surface stress. The distance to equilibrium is a function of the
erodibility of the surface as well as the wind speed and associated
turbulent intensity acting on the erodible surface. Particles >30
and <70 mm can be suspended for relatively short distances, with
particles <30 mm referred to as the total suspended particulate
fraction. In some cases, only the fraction of suspended particulates that are £2.5 or £10 mm, which are referred to as PM2.5 or
PM10, respectively, are evaluated in terms of ambient air quality
standards. The actual size limit and horizontal extent of move1272
ment of saltating particles is a function of particle diameter, particle shape, and density (Lyles, 1977).
The release of suspendible dust occurs, as a function of the
intensity of the saltation process, from the start of saltation all
along the fetch across the eroding field. In other words, the vertical flux of suspended particulate matter needs to be integrated
across the fetch across an erodible surface to estimate the total
mass loss of suspendible particulates from the field. In comparison, the horizontal flux results in a net loss of particles from the
eroding field only at the downwind edge. This results in the significance of the horizontal and vertical fluxes, relative to total
loss from the field, being very different.
Wind erosion can be an important source of airborne particulate loadings as well as of specific toxic constituents. Wind
erosion can also produce environmental degradation through
the deposition of contaminants onto surfaces (land and water),
leading to secondary exposures. There can be considerable uncertainty associated with the use of wind erosion emission factors
within air quality modeling analyses. The scale of analysis and
the degree of exposure are important factors for the evaluation
of airborne exposure from wind erosion. Such issues are particularly important when wind erosion emission rates are input to
dispersion modeling analysis of airborne and surface deposition
impacts of particulates and their toxic constituents. It is also necessary to consider the temporal variability and episodic nature of
wind erosion releases and the variability and uncertainty in the
application of such formulas. It is important to apply empirical
wind erosion equations in a manner that is consistent with their
development and with due consideration for the site-specific
features and the specific air quality analysis that is under evaluation. The applicability of this review is to long-term average air
pollution applications with the use of relatively simple empirical
formulas that rely on readily available data.
It is important to define the terms scale of analysis and degree of exposure within the context of the wind erosion process.
Suspendible dust can be transported great distances because
these relatively light particles move well above the saltation layer
and are transported and dispersed with the general wind flow.
The scale of analysis refers to the modeling domain to which the
emission rates will be applied. Scales range from near field (e.g.,
within 1 km) to a more regional scale (e.g., tens of kilometers or
more). Suspendible particles can travel relatively great distances,
but as travel time and distance increase, much of the mass is lost
through gravitational settling and filtration effects (Watson and
Chow, 2000). The scale of analysis to which the emissions are
applied, therefore, is an essential consideration.
The degree of exposure and wind speeds also determine the
magnitude of the surface stress on erodible particles. For example, the enhanced turbulent intensity in the vicinity of a dune or
pile increases the magnitude of emissions and lowers the threshold wind speed for wind erosion relative to flat terrain (Frank
and Kocurek, 1996; Xuan and Robins, 1994; Xuan, 2004). Flat
surfaces, therefore, have much lower exposure to wind erosion
forces than surfaces such as sand dunes and storage or waste piles.
SSSAJ: Volume 75: Number 4 • July–August 2011
Based on the above, there is a need to estimate the best fit
and 95th percentile range for scenarios where it is necessary to
reconstruct airborne concentrations and deposition from contaminated surfaces. This type of analysis generally is done several
to many years after the event. Unlike a planned experiment where
soil moisture, crusting conditions, etc., can be monitored and
input to an analysis, in this case it is necessary to make best approximation based on simple empirical formulas. The objective
of this review was to determine central tendency values for differences in scale and exposure, i.e., for flat terrain with regional and
localized exposures that can occur for flat source areas and waste
piles, for example, that may be heavily contaminated by heavy
metals. In our judgment, it is important to: (i) specify the best fit
but acknowledge the uncertainty in the estimates; and (ii) recognize the differences in scales of analysis and degrees of exposure
(flat vs. vertical exposure) because failure to consider such factors
leads to a biased analysis in terms of air quality modeling.
TECHNICAL APPROACH
Detailed models are available to estimate wind erosion as a
function of time based on consideration of site-specific conditions. In many applied dispersion modeling analyses, however,
detailed surface conditions as a function of time are not available. In these circumstances, relatively simple empirical formulas
can be used to estimate wind erosion on an annual basis, with
any subsequent temporal allocation based on surface data such as
precipitation conditions, snow cover, and wind speed relative to
a threshold value. The focus of this study was on empirical emission rate formulas, which are summarized below.
Empirical Formulas Considered
Many of the empirical formulas considered here use the
terms threshold friction velocity (u*th) or threshold wind speed
(uth) to parameterize the relationship between wind erosion and
wind conditions. Friction velocity, u* (m s−1), is related to shear
stress (Panofsky and Dutton, 1984):
u* =
t
r
[1]
where t is shear stress (g m−1 s−2) and r is air density (g m−3).
An advantage of using friction velocity to parameterize
wind erosion is that this term incorporates both wind speed and
surface roughness length into the empirical functions. Friction
velocity also has the advantage, relative to the use of wind speed,
of being approximately constant in the surface layer. For this reason, the use of a friction velocity term relative to the threshold
friction velocity is a common basis for empirical wind erosion
formulas. As wind speed and, thereby friction velocity, increases,
the force of the wind increases exponentially. This is why many of
the empirical formulas show some form of A(u* − u*th)B, where
A and B are constants. These considerations enhance the extrapolation of empirical functions based on friction velocity beyond
their direct locations of development.
SSSAJ: Volume 75: Number 4 • July–August 2011
The u*th value for any particular location may be simplified as a constant; however, it is only a simplification because
this term is a function of surface conditions. For example, as the
moisture content of an erodible surface increases, so does u*th because intercapillary forces on soil grains reinforce soil cohesion
(Fecan et al., 1999). In addition, for some surfaces the degree of
surface crusting is another variable that influences the specific
value of u*th as a function of time. Relative humidity also influences the potential for wind erosion (Park and In, 2003) and
thereby the variability of u*th as a function of time. These factors
result in significant temporal and spatial variation in u*th (Shaw
et al., 2008). Soil moisture and vegetation cover correction terms
can be used to help refine empirical formulas if sufficient input
data are available.
As an alternative, a form such as A(u − uth)B can also be
used to describe a function for wind erosion emissions as a function of wind speed. The direct applicability of this approach,
however, is limited to surfaces with comparable surface roughness. Therefore, extrapolation to other surfaces (e.g., natural surfaces, material piles, or waste piles) is limited. Table 1 provides an
overview of the empirical methods considered here. All of these
emission factors are applicable to bare, uncrusted soils. As a first
approximation, each function could be multiplied times a vegetation factor (g) ranging from 0 to 1 to account for the vegetation cover percentage (Shaw et al., 2008).
Distance Scale
Wind-generated emissions of particulate matter involve the
release of a wide range of particle sizes with greatly differing settling velocities and other plume depletion characteristics. Only a
small fraction of suspendible particles from wind erosion sources
are regionally transportable particles. The airborne particulate
distributions are variable and are a strong function of travel time
and, thereby, also of distance. In addition to gravitational settling, fine particles are depleted by filtering and electrical effects
as a function of travel distance (Pace, 2003). The regional-scale
vertical dust flux for a large-scale transport model, therefore, applies only to particles that are not deposited in the same grid cell
from which they are emitted (Countess, 2001).
The application of emission factors to local scales of analysis (e.g., <1000 m from a source area) must account for the
heavy end of the particle distribution, which can be a dominant
contributor to localized airborne exposures and surface deposition, as well as the fine particle fraction before depletion at the
regional scale.
Hypothetical sources (flat and piles) were modeled using
a nominal total suspended particulates (TSP) emission rate of
1.0 mg m−2 s−1 for the scenario of neutral stability and a wind
speed of 8.94 m s−1. A default particle size distribution based
on USEPA (1988) is listed in Table 2. We used these values for
demonstration purposes only. On a case-specific basis, actual
airborne distributions could be substantially different and can
be estimated as a function of the particle size distribution of the
source material, if known (Shaw et al., 2008).
1273
Table 1. Summary of annualized empirical wind erosion equations for total sus- and not to predict total soil erosion. An adpended particulates (TSP).
Method
Regional Specific
vs. local to storage Size range
scale
piles
addressed
TSP adjusted formula†
mm
g m−2 s−1
Wind erosion
equation
(USEPA, 1988)
regional
no
TSP
aIC K¢L¢V¢ ´ 7.12 ´ 10−6
Gillette and Passi
(1988)
regional
no
<20 mm
1.4 ´ 10−3 u*3(u* − u*th)1.25
Tegen and Fung
(1994)
regional
no
TSP
[0.7 ´ 10−6 (u2)(u − uth)
Claiborn et al.
(1998)
regional
no
PM10‡
1.2(5.6 ´ 10−3)10−2 u*3(u* − u*th)2
Draxler et al.
(2001)
regional
no
PM10
(120.8)(K)u*(u*2 − u*th2)2§
local
no
PM10
(1 ´ 10−14)u*4 (1 − u*th/u*)2¶
Shaw et al.
(2008)
ditional set of simulations was modeled with
initial dispersion set to represent a 40-m-high
hemispheric pile, with all inputs set to the
same values except for the following to represent the (hypothetical) large pile:
3
Height of pile = 40 m
8
=15 m above ground level
which is the centroid of a hemisphere, and
2
40 m
2.15
= 37.2 m
Initial vertical dispersion =
(USEPA, 1999). Figure 1 shows an example
of these hypothetical analyses for 8.94 m s−1
Limited reservoir
thresholds for flat and pile surfaces for the asmethod
local
yes
TSP
sumed particulate emissions in comparison to
(USEPA, 1988)#
an ideal gas without any loss of particles en
Nickling and
local
no
TSP
1.4 ´ 10−2 u*4.38
Gillies (1993)
route along the trajectory. As shown, the ratio
Continuous active
of near-field to regional-scale modeled conpile method
local
yes
TSP
(USEPA, 1988)
centrations is a function of the degree of ex† Bold type indicates factors used to normalize formulas to TSP. Variables are: a, fraction of
posure. The ratios of concentrations without
soil loss in the form of suspendible particulates (dimensionless); I, erodibility (U.S. tons acre−1 deposition effects to those with deposition efyr−1); C, climatic factor (dimensionless); K¢, surface roughness factor to account for surface
fects in this example were approximately 14.4
resistance to wind erosion (dimensionless); L¢, field length (m); V¢, vegetation cover factor
(flat) compared with approximately 4.4 (pile
(dimensionless); u*, friction velocity (m s−1); u*th, threshold friction velocity for continuous
wind erosion (m s−1); u, wind speed (m s−1); uth, threshold wind speed for continuous wind
scenario). This figure shows that an emission
erosion (m s−1); K, surface soil texture coefficient (dimensionless).
rate appropriate for near-scale modeling can‡ PM10, fraction of suspended particulates £10 mm.
not directly represent regional-scale impacts
§ K applicable to soils studied by Draxler et al. (2001) is 5.6 ´ 10−4 m−1. This value is
because the fraction of emitted particulates
applicable only to sandy soils (Gillette et al., 1996; Draxler et al., 2001).
available for regional-scale transport is much
¶ u* and u*th (cm s−1).
smaller than what is available for near-field
# The limited reservoir method computes the mass loss per wind erosion event based on the
daily fastest mile of wind (g m−2).
impacts and vice versa. Figure 1 demonstrates
that emission methods suitable for regional
The model-based comparisons were made using the USEPA
analysis can substantially understate localized impacts of TSP
ISCST3 dispersion model (USEPA, 1999), which accounts for
near specific sources, up to a factor of nearly 15 in this example.
gravitational settling and dry deposition loss as a function of
travel distance, wind speed, and atmospheric stability. Although
this model is representative of a large eroding dust source field, a
hypothetical portion of an erodible area was modeled as an area
source set to 100 m2 and with no initial vertical extent to represent flat source regions. A portion of the erodible area was used
only as an example to demonstrate the differences in modeling
a flat area (area source) in comparison to a pile (volume source)
Choi and Fernando
(2008)
local
no
PM10
(1 ´ 10−14)u*4 ´ 2
Table 2. Hypothetical particle size distribution for total suspended particulates before depletion (USEPA, 1988).
Aerodynamic particle diameter
Percentage of mass
mm
<2.5
2.5–9.9
10–14.9
15–30
%
20
30
10
40
1274
Fig. 1. Ratios of modeled concentrations of no-deposition treatment
to deposition treatment for flat and pile (elevated) sources at a wind
speed of 8.94 m s−1.
SSSAJ: Volume 75: Number 4 • July–August 2011
Importance of Source Exposure
(Flat vs. Dunes and Piles)
It has been widely recognized since the early work of
Bagnold (1941) that an increase in surface stress and enhanced
wind erosion is associated with perturbations to airflow.
Research has identified the importance of terrain obstructions
(e.g., dunes or piles) to modify the intensity of wind speeds and
thereby affect the assessment of wind erosion (Bagnold, 1941;
Arya and Stunder, 1988). Of equal or greater importance,
however, is the increase in the stress on surface particles that is
created by the increase in turbulent intensity near the surface
of an obstruction. Research has shown that the standard measurement of wind speed, such as that measured at 11 m above
ground level in the Arya and Stunder (1988) study, provides an
insufficient basis to evaluate the wind erosion potential across
the aerodynamically complex surfaces created by obstructions
(Neuman et al., 1997; Wiggs et al., 1996; Lancaster et al., 1996;
Frank and Kocurek, 1996; Badr and Harion, 2005; Xuan and
Robins, 1994; Xuan, 2004; Burkinshaw and Rust, 1993).
Surface stress estimates based on wind speed measurements collected at heights >1 m above the ground level of an
obstruction do not represent the surface stress that can lead to
enhanced wind erosion from the toe to the top of an obstruction to flow (Frank and Kocurek, 1996). Field and wind tunnel
studies have demonstrated that at the toe of a dune, where wind
speeds have been reduced to the point that wind erosion would
not be expected relative to the expected threshold wind speed
for flat terrain, wind erosion can still occur because of the large
increase in turbulent intensity near the obstruction (Wiggs et
al., 1996; Lancaster et al., 1996). Research has also demonstrated that wake vortices can generate sufficient surface stress to
produce intermittent wind erosion within the turbulent wake
zone in the leeward area of an obstruction to flow (Badr and
Harion, 2005).
Considering the total surface area of a dune or pile projected onto a flat surface of comparable horizontal dimension and
the enhanced wind erosion potential within the turbulent environment immediately adjacent to the exposed surface, it would
be expected that an obstruction, such as a pile or dune, would
produce substantially greater wind erosion than a comparable
source located on flat terrain. These conclusions are consistent
in principal with the “knoll factor” associated with the fundamental soil loss equation, where up to a sevenfold increase in
soil loss at the peak of a more exposed area has been recorded
relative to flat terrain (Woodruff and Siddoway, 1965).
Increases in relative wind erosion from the toe of the pile
all the way up the upwind slope of an obstruction have been
shown to be in the range of 1.5- to twofold or more. A pile
with a hemispheric shape also has twice the surface area of an
equivalent projection onto a flat base area. During subsequent
dispersion modeling of emissions from exposed piles, the increase in surface area should be considered on a case-by-case
basis to ensure that airborne exposures and deposition are not
underestimated.
SSSAJ: Volume 75: Number 4 • July–August 2011
Temporal Allocation Factors
Wind erosion is not a continuous process. The emissions of
suspended particulates by wind erosion are episodic events that
are not appropriately represented within a dispersion modeling
analysis as a constant source (Watson and Chow, 2000). A large
percentage of annual emissions generally are released within a
relatively small number of hours. For an air quality analysis of
wind erosion, the computation of emission rates is not an end
result but an input to a model-based evaluation of airborne and
deposited particulates, including toxic constituents. Proper temporal allocation of these emissions, therefore, is an essential step
in the modeling of wind erosion impacts.
Some emission factors produce total annual emissions, such
as the revised wind erosion equation (RWEQ) (USEPA, 1988),
the limited reservoir method (USEPA, 1988), and the continuous active pile method (Cowherd, 1974). In cases where the goal
is to allocate wind erosion to specific hours within a dispersion
modeling analysis, three conditions need to be satisfied:
1. Friction velocity > threshold friction velocity
2. The surface should be dry (no measurable precipitation
within the preceding 24 h)
3. The surface should not be covered with snow or ice
Li et al. (2006), for example, showed that when the soil
moisture content was 13% or greater for the soil tested, duststorm conditions did not occur.
Table 3 presents examples of wind erosion estimates where
these three conditions were met using 3 yr of meteorological data
generally representative of three locations. In other words, wind
erosion was only computed when the friction velocity exceeded
the threshold friction velocity, there was no precipitation >0.254
mm during the preceding 24 h, and there was no snow or ice cover.
Three meteorological data sets were compiled and processed
to represent the southwestern United States (Midland, TX), the
southeastern United States (Macon, GA), and the north-central
United States (Lansing, MI). Each data set included 3 yr of hourby-hour records for the following parameters: wind speed, precipitation amount (water equivalent), snow and ice cover (daily
basis), and the fastest mile of wind (actual data or by converting
the fastest minute of wind on a daily basis). The anemometer
heights were 6.7 m for Midland, 7.0 for Macon, and 6.1 m for
Lansing. It was assumed in these examples that the surfaces were
free of vegetation, were comprised of loose soil or material, and
were not crusted. These data were used as the basis for Tables 3
through 8. Using Claiborn et al. (1998), an assumed friction velocity threshold of 0.55 m s−1, and 1-cm surface roughness length
Table 3. Number of hours to attain 50th and 90th percentile
of annual mass loading.
Region
Lansing, MI
Macon, GA
Midland, TX
Time to reach percentile
50th
90th
—————————— h ——————————
66
268
4
10
119
537
1275
1276
3.52 ´ 10−6
2.84 ´ 10−7
3.08 ´ 10−8
5.91 ´ 10−8
9.88 ´ 10−7
1.84 ´ 10−9
2.05 ´ 10−8
2.70 ´ 10−9
0.69
Macon, GA
11.9
2.14 ´
3.87 ´
4.37 ´
1.98 ´
0.69
Lansing, MI
11.9
3.39 ´
2.58 ´
2.45 ´
5.54 ´
3.21 ´
10−5
10−6
10−6
6.59 ´
6.48 ´
2.64 ´
10−6
10−7
10−6
4.38 ´
10−7
0.69
Midland, TX
11.9
5.76 ´
10−6
6.49 ´
3.80 ´ 10−5
5.97 ´ 10−6
NA
10−5
10−5
1.29 ´ 10−6
3.26 ´ 10−7
10−6
10−6
2.81 ´ 10−7
1.06 ´ 10−6
10−5
10−7
2.17 ´ 10−7
10−7
0.55
Macon, GA
9.5
2.86 ´ 10−8
5.11 ´ 10−8
1.79 ´ 10−5
NA
4.40 ´ 10−5
1.42 ´ 10−5
9.38 ´ 10−6
2.13 ´ 10−6
1.82 ´ 10−6
9.45 ´ 10−6
1.24 ´ 10−6
0.55
Lansing, MI
9.5
2.92 ´ 10−5
NA
6.20 ´
2.03 ´
1.32 ´
2.84 ´
0.55
Midland, TX
9.5
1.78 ´
1.35 ´
2.97 ´
NA
5.22 ´
10−5
10−5
10−5
1.78 ´
1.25 ´
1.38 ´
10−5
10−6
1.19 ´
0.41
Macon, GA
7.1
1.56 ´
10−6
3.74 ´
NA
10−6
10−5
10−6
7.38 ´ 10−5
3.85 ´ 10−5
10−6
10−6
1.66 ´ 10−5
2.28 ´ 10−6
10−6
10−7
2.56 ´ 10−5
10−7
0.41
Lansing, MI
7.0
3.37 ´ 10−6
6.89 ´ 10−6
NA
9.68 ´ 10−5
5.15 ´ 10−5
2.16 ´ 10−5
3.03 ´ 10−5
1.00 ´ 10−5
3.42 ´ 10−5
4.50 ´ 10−6
7.1
0.41
Midland, TX
———————————————————————————————— g m−2 s−1 ————————————————————————————————
Claiborn et al. Tegen and Fung Revised wind
(1998)
(1994)
erosion equation
Gillette and
Passi (1988)
uth at 10 m
—— m s−1 ——
Local–pile
Continuously active
pile (Cowherd,
Nickling and
Limited reservoir
1974)
Gillies (1993) equation (USEPA, 1988)
u*th
To compare the results of the models using various regional
data, it is first necessary to make certain assumptions. First, surface roughness length was assumed to be 1 cm to allow for the
computation of the friction velocity (u*) based on wind speed
(referenced to the specific monitoring height above ground
level). Second, it was assumed that the roughness length at the
locations of the meteorological data and the source material are
the same (1 cm). The logarithmic wind profile equation was then
used to compute friction velocity.
For those functions that compute the emission rate as a
function of wind speed or friction velocity relative to threshold
values, only the hours that exceeded threshold wind speeds and
had dry conditions for the preceding 24 h and no snow cover
were considered as non-zero emissions.
Table 4 presents the emission rate estimates for the three
example regions for each of the emission methods. To compare
the various formulas on a common basis, the total emissions during the full 3-yr period in each formula were divided by the total number of hours in the composite periods, i.e., the emissions
were annualized for the basis of comparison. In Table 4, there
are large differences in emission rates among the three regions
reviewed. Areas that are relatively dry, windy, and with minimal
snow cover (e.g., Midland, TX) show substantially greater emissions. Hypothetical threshold friction velocities were assumed as
follows: 0.4 m s−1 (fine sand), 0.55 m s−1 (fine coal dust, sandy
soil), and 0.7 m s−1 (coal pile, scraper tracks) (USEPA, 1988).
Note that the wind erosion equation is not directly based on
threshold friction velocity. The following regression analysis was
therefore used to compute comparable soil erodibility values (I)
Region
Comparison of Emission Rates across Empirical
Emission Factors
Empirical emission rate
Local–flat
Choi and
Fernando
Shaw et al.
(2008)
(2008)
The three data sets were used, in conjunction with the emission factors summarized above, to compare annualized TSP emission rates per square meter per second, which is used for comparative purposes only. The three areas provide contrasts as follows.
Midland, TX, is a dry dusty area. Macon, GA, is a wetter environment but has relatively light wind speeds. Lansing, MI, on the other hand, has a cool climate with substantial snow cover in the winter. Collectively, these data sets provide a range of conditions with
which to compare the various empirical wind erosion formulas.
Regional–flat
CASE STUDIES
Table 4. Comparison of annualized emission rates at the regional and local scales for flat and pile (elevated) sources, with the threshold friction velocity (u*th) and the threshold
wind speed (uth) at 10 m for continuous wind erosion.
as an example, Table 3 summarizes the number of hours needed to
reach the 50th and 90th percentile annual mass loadings.
Table 3 points to the importance of accurately allocating
emissions on a temporal basis because the wind direction and
deposition velocity terms generally can be quite different during periods with high wind erosion potential than those representative of typical wind speed conditions. In other words, the
direction of transport as well as deposition velocities computed
within a dispersion model will be mischaracterized if the wind
erosion emissions are not properly allocated to account for highwind-speed periods.
SSSAJ: Volume 75: Number 4 • July–August 2011
for the assumed threshold friction velocities, where u*th is the dependent variable
and I is the independent variable:
u *th
= I m +b
where m = −0.010 and b = 2.542 (R2 [unadjusted] = 0.74). This regression analysis is based on Table 5 (USEPA, 1988;
Gillette, 1980).
The friction velocity of 0.55 to
0.56 m s−1 is representative of sandy
soils. The continuous active pile equation
(Table 1) is limited in this table to surfaces representative of sand because the
empirical factor does not include consideration of threshold wind speed or threshold friction velocity. The limited reservoir
equation is limited to threshold friction
velocities of 0.7 m s−1 or greater.
Table 5. Comparison of the soil erodibility (I) term in the revised wind erosion equation (RWEQ) and threshold friction velocity (u*th).
Typical content
Soil type
Loam
Sand
Clay loam
Clay
Loamy sand
Sandy loam
Loam
Sandy clay loam
Sandy clay
Silt loam
Silt
Silty clay loam
I†
56
220
47
86
134
86
56
38
56
47
38
38
Silt
Sand
—————— % ——————
40
60
5
100
35
65
20
80
10
90
20
80
40
60
85
15
10
50
65
35
90
10
50
50
u*th
1.9
0.6
1.8
1.6
0.9
1.3
1.9
3.4
0.9
2.7
3.6
2.3
† I values were extracted from USEPA (1988). These estimates assume that the correction factor
for nonerodible particles is zero.
Statistical Analysis of Variability and Uncertainty
Some of the differences in the constants in Table 6 can be
explained by surface roughness, soil texture, magnitude of the
wind, topography, the degree of moisture on the surface, and
vegetation cover. Other differences result from uncertainty and
should be considered when applying empirical formulas for wind
erosion and interpreting model results.
We discuss the variability found within specific models
below. Examples of uncertainty are provided to evaluate wind
erosion estimates. The emission rates computed based on these
models should not be considered as precise values, but as best
estimates within specified uncertainty ranges.
It is important to consider the difference between variability
and uncertainty in emission estimates. Variability is related to the
heterogeneity of the emission rates across time and space, an inherent property of nature. Uncertainty, on the other hand, is a lack of
knowledge of the “true” emission rates (Cullen and Frey, 1998).
The variability in emission rates can be described in these formulas as a function of surface characteristics and meteorological conditions. An expected difference between the actual emission rates and
estimates obtained from these formulas involves uncertainty.
Variability within Specific Methods
As an example of uncertainty, Table 6 provides a brief summary of the differences observed in the fitted constants for four
On a day-to-day basis, an empirical emission factor would
empirical emission formulas by soil type. Claiborn et al. (1998)
be expected to show substantial variability because of differences
and Draxler et al. (2001), for example, showed order of magin soil moisture, surface crusting (if present), organic matter
nitude differences within common soil types. Tegen and Fung
concentrations, degree of vegetation sheltering, and other fac(1994) on the other hand, showed a smaller range; however,
tors. A range of emissions (around a best estimate) more fully
the scale of their research was quite large, which may have averexpresses this variability and uncertainty rather than a single
aged out some of the differences. It should be noted that Tegen
point estimate. The most definitive basis to estimate such uncerand Fung (1994) used a global-scale model with emphasis on
tainty would be to conduct numerous field trials across sites with
sandy desert conditions. Also, the K term used in Draxler et al.
common soil and surface characteristics and then to evaluate the
(2001) was shown to be a linear function of the ratio of vertidistribution of emission estimates within each common soil catcal to total flux (F/Qtotal ). The values shown in this table show
egory. Because this degree of testing is not generally available for
the range of F/Qtotal, which provides an
indication of the degree of variability ex- Table 6. Range of constants used in the empirical formulas.
pected in the K term. The differences in
Constant in empirical
Sample
Empirical function
Soil type
formula
size
these constants are an example of the unTegen
and
Fung
(1994)
sand
0.4–1.2
certainty in both time and space that can
2
sandy loam
1.5 ´ 10−3–9.6 ´ 10−3
be observed in empirical emission rates. Claiborn et al. (1998)
Draxler et al. (2001)
sand
28
3.0 ´ 10−5–9.0 ´ 10−4
Table 6 shows large variability across
clay
7
3.0 ´ 10−5–5.0 ´ 10−5
different soil types for a given formula,
loamy sand
2
1.2 ´ 10−4–7.0 ´ 10−3
as well as substantial differences within Nickling and Gillies (1993)
sand
1.94 ´ 10−3
common soil types because of uncertainsilt
4.46 ´ 10−1
ty and other factors.
mixed agricultural
1.4 ´ 10−2
SSSAJ: Volume 75: Number 4 • July–August 2011
1277
Fig. 2. Cumulative distribution of the ratio of vertical to total flux (F/
Qtotal) for sand.
the empirical formulas investigated, a simplified procedure was
subsequently used here for demonstration purposes.
The uncertainty in a selected input value is used here as an
example to help express uncertainty in the computed emission
rates. Other inputs could be addressed in a similar fashion, if
suitable data were available, to further evaluate the sensitivity of
the emission factor to the uncertainty of various inputs.
In Draxler et al. (2001), the K term was shown to be a linear
function of F/Qtotal. The term F/Qtotal was replaced by a probability density function to provide a means of demonstrating the
variability that could be expected when applying an emissions
formula such as that of Draxler et al. (2001) within a common
source type. Gillette (1986) provided extensive data on F/Qtotal
for sand, which aids in describing the uncertainty in the K term
that is used in the empirical function that was established through
Draxler et al. (2001). The uncertainty in this “constant” in the empirical equation provides a default basis to consider the effect of
uncertainty on emission estimates. There were 28 samples shown
in Gillette (1986), which can be used to provide a default estimate of the percentile distribution of emission rates because the
computed emission rates are a linear function of K in Draxler et
al. (2001). Figure 2 shows the percentile of F/Qtotal on this basis.
Figure 3 presents an example of the expected differences
in emission rates for a sand surface based on the Lansing data
set (monitoring height of 6.1 m), assuming 8.94 m s−1 as the assumed threshold and the use of Monte Carlo sampling within
the range of the 2.5 to 97.5 percentiles of F/Qtotal for input to
the Draxler et al. (2001) emission factor. Greater than 10-fold
variability is shown. Especially on a short-term basis, such variability would be expected to lead to large differences in predicted vs. observed results. On a seasonal or annual basis, however,
much of this scatter would be averaged out.
Uncertainty among Emission Methods
The preceding demonstration addressed the expected
uncertainty with time in the application of a single emission
factor to a common surface type. The following considers the
uncertainty on an annualized basis across the range of emission factors reviewed. As demonstrated by the range in results
among the alternative empirical formulas, estimates of particu1278
Fig. 3. Comparison of best estimate emission rates and Monte Carlo
sampling of uncertainty using the Draxler et al. (2001) empirical
function (Lansing case study with threshold wind speed of 8.94 m s−1
and top-ranked 150 values during 3 yr).
late emission rates are approximations with a substantial range
of estimates. Dispersion modeling based on central tendency
values is preferred, but also quantifying the 95th percentile
range in the mean emission rates provides perspective to help
interpret the results.
The empirical emission methods in Table 1 are divided
into two major groups: a group that is directly applicable to the
local scale of analysis and another group that is directly representative of the regional scale of analysis.
Table 7 shows emission rates for data sets grouped to represent local–flat and regional–flat scenarios. Table 7 shows median emission rates based on very small sample sizes. Preferably,
8 to 10 or more direct emission factors would be available for
each scenario being evaluated. As a surrogate, the emission factors were factored to be representative of a common scale and
common exposure for the two scenarios evaluated: flat–regional and flat–local. The ratios shown in Fig. 1 and summarized
above provide a basis to factor between the local and regional
scales of analysis, with approximately a 14.4 difference between
the local and regional scales. Claiborn et al. (1998) used a factor of 4.2 to distinguish between local and regional scales based
on a 1-km grid distance and Fig. 1.
The emission rates factored to a common scale of analysis
were generally within a factor of two of the directly characterized emission rates. The direct and factored emission rates
were, therefore, combined into common sets of emission factors as an example to represent the expected confidence range
in the computed emission rates, as shown in Table 8.
More definitive best-fit values and 95% confidence ranges
could be established if more empirical functions are available in
the future to directly represent each scenario. By showing the
best fit and 95th percentile range when presenting modeling results of predicted airborne concentrations or deposition to surfaces from wind erosion of contaminated surfaces, the expected
impacts, and uncertainty range, provides greater perspective.
SSSAJ: Volume 75: Number 4 • July–August 2011
Table 7. Emission rates based on emission factors directly applicable to the scale of analysis for 0.55 m s−1 threshold friction
velocity.
Erosion rate
Method
Lansing, MI
Nickling and Gillies, 1993
Shaw et al. 2008
Choi and Fernando, 2008
Median
Tegen and Fung, 1994
Gillette and Passi, 1988
Woodruff and Siddoway, 1965 (WEQ)
Median
USEPA, 1988 (continuously active method)
Macon, GA
————— mg m−2 s−1 —————
Local exposures from flat source
4.40 ´ 10−5
1.42 ´ 10−5
9.38 ´ 10−6
1.42 ´ 10−5
Regional exposures from flat source
1.82 ´ 10−6
1.24 ´ 10−6
2.13 ´ 10−6
1.82 ´ 10−6
Local exposures from pile source
1.79 ´ 10−5
Midland, TX
1.28 ´ 10−6
3.26 ´ 10−7
2.81 ´ 10−7
3.26 ´ 10−7
6.20 ´ 10−5
2.03 ´ 10−5
1.32 ´ 10−5
2.03 ´ 10−5
5.11 ´ 10−8
2.86 ´ 10−8
1.06 ´ 10−6
5.11 ´ 10−8
2.97 ´ 10−6
1.78 ´ 10−6
2.84 ´ 10−5
2.97 ´ 10−6
5.97 ´ 10−6
2.92 ´ 10−5
Table 8. Ninety-five percent confidence intervals for emission rates based on emission factors directly applicable to the local or
regional scale of analysis at a 0.55 m s−1 threshold friction velocity; factors scaled to the scale of the analysis and computed using
directly applicable field studies and factored studies.
95% confidence level
Region
n
SD
Lansing, MI
Macon, GA
Midland, TX
7
7
7
1.42 ´ 10−5
9.49 ´ 10−7
2.02 ´ 10−5
Lansing, MI
Macon, GA
Midland, TX
7
7
7
9.87 ´ 10−7
6.60 ´ 10−8
1.40 ´ 10−6
Mean
Median
Lower bound
Upper bound
——————————————­— g m−2 s−1 ———————————————
Local exposures from flat source
2.29 ´ 10−5
1.79 ´ 10−5
9,.74 ´ 10−6
3.61 ´ 10−5
−7
−7
−7
9.90 ´ 10
7.35 ´ 10
1.12 ´ 10
1.87 ´ 10−6
3.36 ´ 10−5
2.56 ´ 10−5
1.49 ´ 10−5
5.23 ´ 10−5
Regional exposures from flat source
1.59 ´ 10−6
1.24 ´ 10−6
6.76 ´ 10−7
2.50 ´ 10−6
−8
−8
−9
6.88 ´ 10
5.11 ´ 10
7.81 ´ 10
1.30 ´ 10−7
2.34 ´ 10−6
1.78 ´ 10−6
1.04 ´ 10−6
3.63 ´ 10−6
CONCLUSIONS
Empirical wind erosion formulas need to be applied with
due consideration of the scale of analysis (e.g., near-field vs. regional) and the degree of exposure (e.g., flat surfaces vs. piles).
Both of these factors can substantially affect the representativeness of wind erosion formulas for specific applications within dispersion models. Large differences in emission rates were shown
among the three regions reviewed, with areas that are relatively
dry, windy, and with minimal snow cover (e.g., Midland, TX)
showing substantially greater emissions.
An important use of wind erosion emissions is to serve as input to subsequent dispersion modeling of airborne exposures and
surface deposition. It is essential for air quality modeling purposes
that the allocation of the wind erosion emissions be applied to hours
that: (i) have wind speeds that exceed the wind erosion threshold,
(ii) are associated with dry surface conditions (no recent or ongoing precipitation), and (iii) have no significant snow or ice cover.
Otherwise, bias in the modeled airborne concentration and deposition impacts as a function of wind direction can be anticipated.
Considering the variability and uncertainty across empirical
wind erosion emission formulas, and within the application of a
single formula to different settings, the most informative way to
present emission rates for wind erosion is in the form of a best-fit
estimate and a 95th percentile confidence range of expected values
SSSAJ: Volume 75: Number 4 • July–August 2011
rather than as a single point estimate. Furthermore, a great deal of
scatter is expected when estimating emission rates on an hourly or
daily basis because of the variability in surface conditions on a temporal basis, which are generally averaged out in the longer term.
The empirical emission factors that were compared here
converged to generally similar magnitudes in each region, with
differences in the means generally within a factor of two between
the sets of formulas that were directly used to estimate the 95%
confidence range of the mean emissions. As more directly applicable empirical emission rates are developed at the local and
regional scales, these distributions could be further refined to
represent the expected ranges in mean emission rates as a function of scale and exposure.
Review of these empirical models, and others, in the future
would be useful if measured validation data sets were used to
further evaluate the performance of each empirical method for a
range of exposure types (such as piles vs. flat terrain) and for local
vs. more regional-scale analysis.
REFERENCES
Arya, S.P.S., and B.J.B. Stunder. 1988. Windbreak effectiveness for storage pile
fugitive dust control: A wind tunnel study. J. Air Pollut. Control Assoc.
38:135–143.
Badr, T., and J.L. Harion. 2005. Numerical modelling of flow over stockpiles:
Implications on dust emissions. Atmos. Environ. 39:5576–5584.
doi:10.1016/j.atmosenv.2005.05.053
1279
Bagnold, R.A. 1941. The physics of blown sands and desert dunes. Methuen, London.
Beasley, R.P., J.M. Gregory, and T.R. McCarty. 1984. Erosion and sediment
pollution control. 2nd ed. Iowa State Univ. Press. Ames.
Burkinshaw, J.R., and I.C. Rust. 1993. Aeolian dynamics on the windward slope
of a reversing transverse dune, Alexandria Coastal Dunefield, South Africa.
p. 13–21. In K. Pye and N. Lancaster (ed.) Aeolian sediments: Ancient and
modern. Blackwell Publ., Oxford, UK.
Canada Department of Agriculture. 1943. Soil Research Laboratory, Swift
Current, Saskatchewan: Report of investigation. Can. Dep. of Agric.,
Ottawa, ON.
Chepil, W.S. 1941. Relation of wind erosion to the dry aggregate structure of the
soil. Sci. Agric. 21:488–507.
Chepil, W.S. 1945. Dynamics of wind erosion: I. Nature of movement of soil by
wind. Soil Sci. 60:305–320. doi:10.1097/00010694-194510000-00004
Chepil, W.S. 1956. Influence of moisture on erodibility of soil by wind. Soil Sci. Soc.
Am. Proc. 20:288–292. doi:10.2136/sssaj1956.03615995002000020033x
Chepil, W.S. 1958. Soil conditions that influence wind erosion. USDA Bull.
1185. Kansas Agric. Exp. Stn., Manhattan.
Choi, Y., and H.J.S. Fernando. 2008. Implementation of a windbown dust
parameterization into MODELS-3/CMAQ: Application to episodic
PM events in the US/Mexico border. Atmos. Environ. 42:6039–6046.
doi:10.1016/j.atmosenv.2008.03.038
Claiborn, C., B. Lamb, A. Miller, J. Beseda, B. Clode, J. Vaughan, L. Kang, and
C. Newvine. 1998. Regional measurements and modeling of windblown
agricultural dust: The Columbia Plateau PM10 program. J. Geophys. Res.
103(D16):19753–19767. doi:10.1029/98JD00046
Countess, R. 2001. Methodology for estimating fugitive windblown and
mechanically resuspended road dust emissions applicable to modeling
regional scale air quality. Western Governor’s Assoc., Washington, DC.
Cowherd, C., Jr. 1974. Development of emission factors for fugitive dust sources.
EPA-450/3-74-037. USEPA Office of Air and Waste Manage., Research
Triangle Park, NC.
Cullen, A.C., and H.C. Frey. 1998. Probabilistic techniques in exposure
assessment. Plenum Press, New York.
Draxler, R., D. Gillettte, J.S. Kirkpatrick, and J. Heller. 2001. Estimating PM10
air concentrations from dust storms in Iraq, Saudi Arabia, and Kuwait.
Atmos. Environ. 35:4315–4330. doi:10.1016/S1352-2310(01)00159-5
Fan, L.T., and L.A. Disrud. 1977. Transient wind erosion: A study on the
non-stationary effect on rate of wind erosion. Soil Sci. 124:61–65.
doi:10.1097/00010694-197707000-00011
Fecan, F., B. Marticorena, and G. Bergametti. 1999. Parametrization of the
increase of the aeolian erosion threshold wind friction velocity due to soil
moisture for arid and semi-arid areas. Ann. Geophys. 17:149–157.
Frank, A.J., and G. Kocurek. 1996. Airflow up the stoss slope of sand dunes:
Limitations of current understanding. Geomorphology 17:47–54.
doi:10.1016/0169-555X(95)00094-L
Gillette, D.A. 1986. Wind erosion. p. 129–162. In Soil conservation: Assessing the
National Resources Inventory. Vol. 2. Natl. Acad. Press, Washington, DC.
Gillette, D.A., J. Adams, A. Endo, D. Smith, and R. Kihl. 1980. Threshold
velocities for input of soil particles into the air by desert soils. J. Geophys.
Res. 85(C10):5621–5630. doi:10.1029/JC085iC10p05621
Gillette, D.A., G. Herbert, P.H. Stockton, and P.R. Owen. 1996. Causes
of the fetch effect in wind erosion. Earth Surf. Processes Landforms
21:641–659. doi:10.1002/(SICI)1096-9837(199607)21:7<641::AIDESP662>3.0.CO;2-9
Gillette, D.A., and R. Passi. 1988. Modeling dust emission caused by wind
erosion. J. Geophys. Res. 93(D11):14233–14242. doi:10.1029/
JD093iD11p14233
1280
Greeley, R., and J. Iversen. 1985. Wind as a geological process on Earth, Mars,
Venus, and Titan. Cambridge Univ. Press, New York.
Iversen, J.D., and B.R. White. 1982. Saltation threshold on Earth, Mars, and Venus.
Sedimentology 29:111–119. doi:10.1111/j.1365-3091.1982.tb01713.x
Lancaster, N., W.G. Nickling, C.K.M. Neuman, and V.E. Wyatt. 1996. Sediment
flux and airflow on the stoss slope of a barchan dune. Geomorphology
17:55–62. doi:10.1016/0169-555X(95)00095-M
Li, N., W. Gu, Z. Du, Z. Li, and P. Song. 2006. Observation on soil water content
and wind speed in Erlianhot, a dust-source area in northern China. Atmos.
Environ. 40:5298–5303. doi:10.1016/j.atmosenv.2006.04.019
Lu, H., and Y. Shao. 1999. A new model for dust emission by saltation
bombardment.
J.
Geophys.
Res.
104(D14):16827–16842.
doi:10.1029/1999JD900169
Lyles, L. 1977. Wind erosion: Processes and effect on soil productivity. Trans.
ASAE 20:880–884.
Neuman, C.M., and N. Lancaster, and W.G. Nickling. 1997. Relations between
dune morphology, air flow, and sediment flux on reversing dunes, Silver
Peak, Nevada. Sedimentology 44:1103–1113.
Nickling, W.G., and J.A. Gillies. 1993. Dust emission and transport in Mali,
Africa. Sedimentology 40:859–868. doi:10.1111/j.1365-3091.1993.
tb01365.x
Pace, T. 2003. A conceptual model to adjust fugitive dust emissions to account
for near source particle removal in grid model applications. Available at
cleanairinitiative.org/portal/system/files/58212_resource_5.pdf (verified
5 May 2011). USEPA, Washington, DC.
Panofsky, H.A., and J.A. Dutton. 1984. Atmospheric turbulence: Models and
methods for engineering applications. John Wiley & Sons, New York.
Park, S., and H. In. 2003. Parameterization of dust emission for the simulation
of the yellow sand (Asian dust) event observed in March 2002 in Korea. J.
Geophys. Res. 108(D19):4618. doi:10.1029/2003JD003484
Shao, Y. 2001. Physics and modeling of wind erosion. Kluwer Acad. Publ.,
Boston.
Shaw, W.J., K.J. Allwine, B.G. Fritz, F.C. Rutz, J.P. Rishel, and E.G. Chapman.
2008. An evaluation of the wind erosion module in DUSTRAN. Atmos.
Environ. 42:1907–1921. doi:10.1016/j.atmosenv.2007.11.022
Tegen, I., and I. Fung. 1994. Modeling of mineral dust in the atmosphere:
Sources, transport, and optical thickness. J. Geophys. Res. 99:22897–
22914. doi:10.1029/94JD01928
USEPA. 1988. Control of open fugitive dust sources. EPA-450/3-88-008. Office
of Air Quality Planning and Standards, Research Triangle Park, NC.
USEPA. 1999. User’s guide for the industrial source complex models. Vol. 1.
Office of Air Quality Planning and Standards, Research Triangle Park, NC.
Watson, J., and J. Chow. 2000. Reconciling urban fugitive dust emissions
inventory and ambient source contribution estimates: Summary of current
knowledge and needed research. DRI 6110.4F. Desert Res. Inst., Reno,
NV.
Wiggs, G.F.S., I. Livingstone, and A. Warren. 1996. The role of streamline
curvature in sand dune dynamics: Evidence from field and wind
tunnel measurements. Geomorphology 17:29–46. doi:10.1016/0169555X(95)00093-K
Woodruff, N.P., and F.H. Siddoway. 1965. A wind erosion equation. Soil Sci. Soc.
Am. Proc. 29:602–608. doi:10.2136/sssaj1965.03615995002900050035x
Xuan, J. 2004. Turbulent factors for threshold velocity and emission rate
of atmospheric dust. Atmos. Environ. 38:1777–1783. doi:10.1016/j.
atmosenv.2003.12.030
Xuan, J., and A. Robins. 1994. The effects of turbulence and complex terrain
on dust emissions and depositions from coal stockpiles. Atmos. Environ.
28:1951–1960. doi:10.1016/1352-2310(94)90336-0
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