3.0     Revised Formulations for Surface-to-Air Mass Flux Models

The suspension of soil particles from contaminated areas is calculated using empirical relationships based on studies of wind erosion and surface disruption. The particulate suspension models use site characteristics to provide site-specific estimates of particulate emission rates. These formulations do not apply to suspension of contamination from other surfaces.

Table 3.1 lists the particle suspension models used in the MEPAS formulations implemented in FRAMES. These models include formulations for contaminant suspension by winds, vehicular traffic (paved and unpaved roads), and other physical disturbances of the surface. The formulations for computing suspension rates given below are an adaptation of methodologies promulgated by the U.S. Environmental Protection Agency (EPA). The original version of these formulations was based on a methodology by Cowherd et al. (1985) for rapid computations of potential annual emission rates from spills of hazardous materials. Since then, EPA has released a number of revised methodologies for their regulatory applications. EPA (1988) provides models for fugitive dust control. EPA (1990) summarizes models and their applicability to various situations. In addition, EPA has released pertinent updates to AP-42 (EPA 1995, 1998, 2002).

The potential for suspension of soil particles depends on the surface cover. Vegetation cover, crusted soil, and moisture content of the soil are important factors considered in the formulations. A wet area (with saturated soil or standing water) is considered to have no potential for wind erosion. The formulations also account for the intermittent times during and after precipitation when the surfaces will be wet and no suspension is assumed to occur.

Computing the suspension of contaminants from a surface into the atmosphere requires both contaminant and site data. In the source term model, some of these data are used to define which particle suspension formulations, if any, apply to the site. If a computation is appropriate, the input data are used to compute the suspension rates.

The suspension models promulgated by EPA categorize the potential of an area for having wind suspension as either "unlimited" or "limited." Unlimited areas have the potential for the ambient winds alone to suspend particles from the local soil surfaces. Limited areas require some mechanical disturbance of the soil surface for wind erosion to occur.

In the models used, the source term release module outputs for suspension from contaminated surface areas are expressed in terms of an airborne soil concentration normalized to a unit area of contaminated surface. These airborne soil concentrations are assumed to contain the same contaminant concentrations as in the surface soil. Thus, by knowing the contaminant concentrations in the suspended particulate materials, the contaminant-specific mass or activity suspension rates can be defined.

The formulations given below represent an integration and implementation of several sources of EPA guidance to meet the objectives and constraints of the computed source term model. This process requires a number of linkage and application assumptions (as noted in these formulations). The characterization of the major mechanisms of particulate suspension formulations depends heavily on the approach proposed by Cowherd et. al. (1985). Specific models and components are updated to more recent formulations where possible and appropriate.

3.1 Emission Rates

The emissions of surface material (i.e., soil) from a site are expressed as the sum of emissions by various particle suspension processes. The output is expressed both as the mass flux in particle size ranges and as the total suspended mass. The latter is expressed as the equivalent depth of soil suspended per year.

The mass flux for each particle size range is the sum of emissions from wind and vehicular suspension over the area:

3.2 Vertical Wind Speed Profiles

Wind speed is a critical parameter in estimating the potential particle suspension from a site. Wind speed varies vertically over the surface. To make consistent estimates of suspension rates, the following formulations use a standard reference height for definition of the wind and related parameters. Near-surface vertical wind variation is recognized to vary with the local surface roughness and the stability of that air layer (i.e., the vertical temperature structure). The wind speed profile in the boundary layer for neutral atmospheric conditions can be expressed as a logarithmic wind profile,

The neutral formulation for wind variation with height alone is sufficient because the high wind conditions being considered in particle suspension computations will be at, or near, neutral atmospheric stability conditions. This relationship is used to adjust average wind speed and fastest mile wind speed to a reference height of 7 meters.

3.3 Particle Size Distribution

A major update in the formulations documented here from previous versions is the inclusion of particle size information in the emissions resulting from wind erosion (limited and unlimited areas), paved roads, and unpaved roads.

The size distribution of the suspended material is a critical input in terms of modeling the fate of the particles and estimating potential health efforts. The size distribution largely determines the environmental deposition rates. In terms of health impacts, the original Cowherd formulation estimated the total mass flux of PM₁₀ (particulate matter with diameters of 10 um or less), which is considered a respirable size range. Subsequently EPA has provided guidance on the relative contributions of mass flux in different size ranges. PM _2.5 (particulate matter with diameters of 2.5 um or less) represents particles that are more likely to be taken into the lungs. EPA also considered total suspended material (TSP) in their AP-42 revisions.

The emission and movement of particles are considered in multiple size ranges in the following formulations. The EPA guidance provides values for computing a single emission rate for one selected category of particles (i.e., PM_2.5, PM₁₀, TSP). This EPA guidance is extended to define default mass suspension fractions for different size ranges. These default values are provided in the emission rate formulations given below for situations where such specific site data on suspended size distributions are unavailable.

The particulate size distributions associated with the emissions are represented in these formulations by three model ranges of particulate sizes expressed as index d_p. Each range represents the emissions over a specified range of particulate sizes. Table 3.2 shows the properties that are used in the three particulate emission size ranges.

The particulate emission ranges in represent components of EPA particle size ranges. The "Mean Diameter" is defined to represent different components of the size distribution. The "Density" is a value selected as typical of airborne particles. The same default values are used for all the particle suspension mechanisms.

Table 3.3 shows which emission ranges will contribute to the listed particulate size classes. The concentrations for PM_2.5, PM₁₀, and TSP are computed as the sum of concentrations for the particulate emission ranges indicated with a "Yes" in the table. That is, the number for PM_2.5 is based on Particle Emission Range 1, the one for PM₁₀ is based on Particle Emission Ranges 1 and 2, etc. The emission fractions are also derived from EPA guidance. Particle emissions are reported in ranges so the output can be used in subsequent modules that account for particle size effects.

3.4 Wind Erosion and Mechanical Suspension

Particle suspension is considered the result of the action of 1) wind on a surface to break loose and suspend materials, and 2) mechanical disturbances to break loose materials that can be suspended by the wind. The formulations for these wind erosion and mechanical suspension processes are largely based on EPA regulatory modeling guidance, as noted below.

A series of EPA documents have addressed wind erosion and mechanical suspension modeling (Cowherd et al. 1985; Cowherd et al. 1988; EPA 1988, 1990, 1995). These documents, all of which use the same general approach, define steps for determining potential particulate emissions from wind erosion. The earlier models provide PM₁₀ emission rates whereas the later models provide emission rates for different particle size classes (PM_2.5, PM₁₀, etc.). The condition of the surface, apparent roughness of the site, vegetation cover, presence of a crust on the soil, and presence of nonerodible elements (e.g., large stones) are used to define the potential for suspension. Depending on the procedure results, the site is characterized as having 1) unlimited erosion potential, 2) limited erosion potential, or 3) no erosion potential.

The MEPAS source term model addresses suspension of both radionuclides and chemicals. The EPA guidance documents are mainly concerned with surface chemical contaminations. The MEPAS implementation (Whelan et al. 1987) of the original Cowherd et al. (1985) particle suspension formulations was shown to give results comparable to using resuspension factors such as are typically used in studies of the suspension of radionuclides. The comparison considered a range of surfaces from bare, unstabilized surfaces after a fire to well-stabilized surfaces with a vegetation cover (Whelan et al. 1989).

The experience with radioactive materials shows that some level of suspension of material is always occurring from natural surface disturbances (Sehmel 1984). However the guidance for the EPA models indicates that if the site has 1) no mechanical disturbances and is completely covered with vegetation, 2) a thick surface crust, or 3) a wet, saturated soil, it can be assumed that no contaminants are suspended. To allow for the fact that for certain contaminants even very small suspension rates from well-stabilized surfaces may be significant, these formulations include the assumption that some level of emissions can occur from all surfaces except those saturated with or covered by water.

The EPA models provide criteria for defining an area as having limited or unlimited erosion potential. In the source term model formulations, uncrusted areas are tested to see if unlimited erosion will occur. If not, then the entire area is treated as a candidate for limited erosion. If so, then the uncrusted area is treated as an unlimited erosion area and the remaining crusted area as a limited erosion area.

The wind/mechanical emission rate for each of the particle size ranges is computed as the sum of the unlimited and limited erosion emissions:

The model provides as output the emission rates for all defined particle ranges. These data allow users to evaluate, in subsequent air transport modules, the airborne concentrations resulting from the suspended particles over and near the source.

3.4.1 Limited Erosion Calculation

The particle suspension mechanism for an area with limited erosion potential is mechanical. That is, some mechanical disturbance breaks up some portion of the surface materials and makes them available for wind erosion. The particle suspension will thus occur when a wind event occurs that is great enough to suspend these surface materials.

A detailed approach for estimating particle suspension from limited areas based on analysis of episodic high wind-speed events has been promulgated by EPA (Cowherd 1985, EPA 1988, EPA 1995). That approach accounts for recurring conditions expected to suspend loose surface material. Within the constraints of the computed source model, the complete details of that approach could not be entirely implemented. A conservative screening approach derived from the EPA approach is used instead to estimate the limited erosion potential. That derived approach uses an assumption that suspension events occur each month of the year at a strength equivalent to the maximum monthly event. The derived approach thus provides an order-of-magnitude estimate of annual potential emission rates. For a separate, more detailed site-specific analysis that considers specific events and their occurrence frequencies, the updated EPA (1995) formulations are recommended to compute a "known flux" emission rate for a specific limited erosion area.

The potential for wind erosion is quantified in terms of a threshold friction velocity. The greater the value of the threshold friction velocity for a site, the lower the potential for particle suspension. The threshold friction velocity for the contaminated area is determined by applying the mode of the aggregate particulate size distribution (which is derived from the soil composition) in an empirical graphical relationship (represented here as a formula) given by Gillette (1980):

An approximate value for the mode of the aggregate size distribution was estimated in previous formulations using

From the viewpoint of increasing the potential for suspension, this relationship provides relatively realistic estimates for soils with greater than 75 percent sand content. For other soils, the relationship provides relatively conservative estimates that are more typical of disturbed soils than undisturbed soils.

The correction factor, f_ne, in Equation 5 allows for the effects of any non-erodible elements in the contaminated area. This correction factor depends on the fraction of surface coverage and is estimated from graphical results given by Cowherd et al. (1985), derived from wind tunnel studies by Marshall (1971). As the silhouette area of nonerodible elements increases, so does the threshold friction velocity. If the threshold friction velocity is less than 0.75 m s^-1, the area has unlimited erosion potential; otherwise, the area has only limited erosion potential (Cowherd et al. 1985).

Once the threshold friction velocity has been determined, the critical wind speed at a given height above the surface can be determined by applying Equation (3):

This relationship requires that the magnitude of reference height is enough greater than that of local surface roughness lengths that a representative horizontal wind can be defined at the reference height. The critical wind speed is one of the parameters used below to define the erosion potential. The reference height of 7 m from Cowherd et al (1985) is consistent with the critical value used above to define limited/unlimited areas based on threshold friction velocity. EPA (1995, Table 13.2.5-2) gives example threshold friction velocities and threshold wind speeds for a variety of natural surfaces. The surface roughness length of the site, z_os, is related to the size and spacing of the roughness elements in the area.

For a contaminated area having limited wind-erosion potential, the following equation from Cowherd et al. (1985) is used to predict the flux particulate mass density:

The vegetation fraction, f_v, varies from 0 for bare ground to 1 for total coverage. The Thornthwaite's PE Index, f_PE, is used as a moisture-correction parameter for wind-generated emissions. Cowherd et al. (1985) provide a map with values of f_PE for all regions in the contiguous United States.

The above equation for limited emission, E_lim, provides a method of rapidly estimating potential emission rates (Cowherd 1985). However, for estimating more realistic site-specific industrial emission rates, each erosion event must be treated separately. The non-linear nature of the erosion potential function makes this event-based analysis necessary (EPA 1988, 1995).

This mechanism of suspension represents intermittent events. Although the sum of emissions from the events over a year will estimate the annual emission rate, this value must be used as an average emission rate with some care. Although the nature of formulations (such as a sector average Gaussian model) makes the distribution of wind speeds relatively unimportant in the concentration computation, the question of wind direction is very important. This formulation uses the assumption that the wind suspension events are localized phenomena and the resulting emission rate is appropriate to estimate an annual load of suspended particles transported away by the range of ambient winds occuring at the site. Thus, this formulation uses the assumption that the particles suspended by these wind-driven events over a large number of events are transported in all directions by the local winds with a probability related to frequency of winds in each direction. This assumption ensures a wind frequency-based impact on all potential receptors in all directions. However, the approach tends to underestimate the peak concentrations for specific sets of conditions. For the latter, separate event-specific computations are recommended.

This formulation applies only for a surface where single representative values of surface roughness and frequency of disturbance exist. In general, the formulations should not be applied to areas, although reasonable estimates of emissions may be estimated by conducting separate runs to evaluate the potential emissions from the different portions of the area.

This particle suspension model for a limited area estimates the flux of PM₁₀ particulate material into the air. To estimate fluxes for distinct particle size ranges, this emission rate must be converted to an equivalent to particle-based range emissions:

3.4.2 Unlimited Erosion Calculation

The formulations for the total PM₁₀ emissions from an unlimited erosion area use the "Gillette Model" discussed in EPA (1990) and documented in Cowherd et al. (1985). Recent guidance EPA (1995) is used to define a particulate size distribution by assuming that the emissions from a limited and unlimited area will have the same size distributions.

The EPA does not currently provide guidance for modeling particle emissions from an unlimited erosion area. Instead, the analyst is directed to models developed by other agencies for special applications such as farmland. Although collaborative efforts to develop multi-agency models in this area have been undertaken over the past decade, the results of these efforts do not appear in regulatory guidance. As a result, the earlier model (Cowherd et al. 1985, EPA 1990) for an unlimited erosion area was deemed to continue to be an appropriate model to estimate particle emissions from an unlimited area in the context of applications for the computed source model.

The annual emission rate from erosion from an unlimited erosion area (Cowherd et al. 1985) is

The integration function, , comes from the cubic relationship of the vertical transport of particles and the wind speed. It is defined in graphical format by Cowherd et al. (1985). This relationship can be broken into the following discrete parts based on the values of the non-dimensional scaling parameter, :

3.5 Vehicular Suspension

Although both unpaved road surfaces and paved surfaces contribute to roadway emissions, the unpaved roads have by far the greatest potential for emissions. The original roadway suspension formulation from Cowherd et al. (1985) only included unpaved roads. The 1989 MEPAS implementation of Cowherd added an estimate for paved roads to the approach for air quality modeling. Subsequently, the formulations in the EPA AP-42 guidance for vehicular particle suspension have undergone a number of revisions. The particle suspension formulations in the computed source term model use the most recent formulations in that guidance for vehicular suspension.

For emissions resulting from mechanical disturbances by vehicle traffic on unpaved and paved roadways, the total roadway emissions for particle size ranges are computed as the sum of the unpaved and paved roadway emissions from within the source area as follows:

3.5.1 Unpaved Roads

The unpaved roadway mass flux, F_unp is computed using the relationship given in AP-42 (EPA 1998, page 13.2.2-3), which includes parameterization as a function of particle classes. The equation when expressed in metric units is

The unpaved roadway mass flux is computed on an annual basis. The emission rates for the EPA particle size classes are converted to equivalent emission rates for particle size ranges by assuming that the rates for the classes are cumulative representations of the rates for the ranges. That is, the value of F_unpr(dp) is computed for each of the three particle size ranges as follows:

For suspension of particles as a result of vehicle traffic on unpaved contaminated surfaces, the emission rate is computed from formulations recommended in AP-42, Miscellaneous Sources (EPA 1998, Section 13.2.2, version date 9-98) and summarized in Table 3.4:

Site-specific information from local sources is normally obtained for each of the parameters. When site-specific data are not available, the default values given in AP-42 (EPA 1998) may be used.

3.5.2 Paved Roads

The pollutant emissions caused by traffic on paved roads is computed using the relationships given in AP-42 (EPA 2002, Section 13.2.1). These relationships for paved roads may be expressed in a metric form as follows:

The paved roadway mass flux is computed on an annual basis. The emission rates for the EPA particle size classes are converted to equivalent emission rates for particle size ranges by assuming the rates for the classes are cumulative representations of the rates for the ranges. That is, the normalized emission rate is computed for each of the three particle size ranges as follows:

For suspension of particles as a result of vehicle traffic on paved roads, the emission rate is computed using formulations recommended in AP-42, Miscellaneous Sources (EPA 2002, Section 13.2.1, version date 10/02):

The alternative form for F_dry is based on the number of hours with reported precipitation:

The second equation for F_dry requires an estimate of the number of hours of precipitation during the annual computation time. This parameter may be obtained by analyzing an hourly surface observation dataset available from NOAA (2003). This equation includes a factor of 1.2 to account for the paved surface staying wet for some time after each precipitation event ceases.

The first equation will be appropriate for most sites. For the United States, the F_dry factor will almost always be greater than 0.9 for areas with less than 50 inches of precipitation per year. For those stations, even a factor of two change in the estimated duration of precipitation will result in a 5 percent (or less) change in the computed emission rate. As a result, the first equation normally provides more-than-adequate accuracy to estimate annual particulate emission rates.

3.6 Mass Budget for Suspended Materials

The total mass flux from the contaminated area is the sum of the mass lost from all particulate size ranges minus the amount of suspended material that re-deposits on the area. The amount of material deposited will vary with particle size range - with larger particles having much higher rates of deposition on, and nearby, the source area.

The computed source term model uses the assumption that some fraction of the suspended material will deposit in the immediate area and still be available for future suspension, leaching, runoff, etc. The model does not have formulations that allow direct computation of the amount and pattern of these deposited materials. So, as a first approximation, all material suspended in the size range greater than PM₁₀ is assumed to deposit back on the immediate area. The net mass loss from the contaminated area is assumed to be equal to the mass suspended in the PM₁₀ size ranges. Test runs using the MEPAS air transport model indicates that this assumption is reasonable but conservative in terms of estimating the mass loss from the source area. Use of this assumption avoids the possibility of artificially depleting the potential source term of material by not accounting for regional re-deposition.

The computed source term model performs an overall mass budget accounting on the source material as described in Streile et al. (1996). The relationship for computing the rate of mass lost from suspension of particles is expressed in terms of the effective depth of soil lost with time (Equation 2). The suspension of particles continues until all the mass contained in the source term is lost.

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