Measuring the flux of dust from unpaved roads John M. Veranth and Eric Pardyjak University of Utah

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1 Measuring the flux of dust from unpaved roads John M. Veranth and Eric Pardyjak University of Utah Keywords: Dust flux, fugitive dust, road dust, wind erosion, atmospheric dust measurement, US EPA AP-42. The flux of fugitive dust from sources such as storage piles, construction activities, or unpaved roads is generally measured by setting up towers with wind speed and dust concentration instruments at discrete heights. (Cowherd, Maxwell et al., 1977; EPA,1998c) Converting these discrete measurements into an integrated total flux is problematic because it is necessary to make assumptions about the conditions above the highest measurement, interpolated between the measurements, and below the lowest measurement. Frequently an arbitrary step approach has been used. The authors suggest that a much better approach is to first approximate the wind speed versus height data and the dust concentration versus height data by physically plausible functions. Then the dust flux can be calculated by integrating the product of the two functions. The preferred formulation is the combination of a power law profile for wind speed versused height and an exponential profile for dust concentration versus height. This results in an equation with an analytical solution. The following derivation has been published in a more complete form in: Veranth, J.M., G. Seshadri, and E. Pardyjak, Vehicle-generated fugitive dust transport: Analytic models and field study. Atmospheric Environment, (16): p The horizontal flux of dust is the product of the dust concentration times the wind speed integrated from ground level to the top of the dust cloud. For a line source the units are particulate matter mass per length of road per vehicle trip. Defining the coordinate axes as x perpendicular to the road, y parallel to the road and z vertical, and assuming dust concentration and wind profile do not vary parallel to the road, the mass flux per length of road passing through a plane at constant distance from the road is: z= t=tmax z=0 t=0 F dust = C(x, z, t) u(x, z,t) dt dz (1) where C is the dust concentration (mg/m 3 ) and u (m s -1 ) is the wind component perpendicular to the y,z plane, and tmax is the trip interval or other averaging time. The dust flux calculation approach recommended is to fit plausible interpolation functions to the measurements and then numerically integrate using the interpolation function values

2 evaluated at each height step. This algorithm has the advantage of being mathematically well defined and providing insight into the sensitivity of the results to wind speed and concentration vertical profiles. Wind Speed Models Several wind speed models appear in the literature. The models involved different levels of complexity for the effects of stability and roughness. The first model considered for wind speed in the stable rough surface layer was a logarithmic model given by Paulson (1970) as: u = 1 u * k ln z ' ( (3) % z o where u * is the friction velocity, k is the von Karman constant (taken to be 0.4), z o is the roughness height, and the stability function is approximated by ψ=4.7(z/l). L was estimated from the near-road sonic anemometer 1.6 m above ground, giving z/l 0.3 Within the container array the displacement distance is needed and the logarithmic profile becomes: u = 1 ) u * k ln ( z d) %, ' ( * + z o -. (4) where d is the displacement length. Stull (1988) A logarithmic wind velocity interpolation equation was obtained by a least-squares fit of equation (3) or (4) to the measured velocities at multiple heights. Although the logarithmic wind profile has a theoretical basis, Equation (4) involves four adjustable parameters that must be fit to the data or estimated from the literature. Alternatively, an empirical power law equation can give a reasonable approximation to the wind profile over a limited range of height. This gives u = u ref z % P (5) where u ref is the wind speed measured at height. The power law interpolation function has only one adjustable parameter, extrapolates to zero velocity at ground level, and is mathematically convenient.

3 Vertical Dust Concentration Models Three types of equations were considered for modeling the vertical change of particle concentration: a first-order exponential, a Gaussian distribution, and a power law. The power law equation C(z) = C ref z % 'Q (6) was derived by Goossens (1985) assuming a quasi steady-state distribution of particles where the downward flow due to gravity settling is balanced by the upward flow due to turbulent fluctuations. C ref is the dust concentration measured at height and Q is the fitting parameter. The Gaussian distribution equation can be simplified using two empirical terms as; C(z) = A exp (Bz 2 ) (7) This profile is derived based on diffusion from a source, and Gaussian models have been used in studies of vehicle-generated dust near roads. (Claiborn, Arundhati et al., 1995; Negendra and Khare, 2002) The first-order exponential decay model for dust concentration C(z) = A exp (Bz) (8) was derived by Goosens (1985) by assuming that the change in eddy diffusivity with height is a power law function. Coefficients for each of the three interpolation equations were obtained by a least-squares fit to the time-averaged field data. Stepwise expressions for wind speed and concentration were compared to the interpolation function method. For the stepwise method, the value of the bottom measurement was used for the interval from ground level to the midpoint between the bottom and second measurements where there was a discontinuous change to the new value which was used up to the midpoint between the second and third measurement, and so on. Calculation of Horizontal Flux The power law wind profile is appealing since analytical solutions exist for the integral of a power law for wind with either an exponential or Gaussian functions for dust concentration. For

4 the exponential dust concentration case F dust = C(z) u(z)dz = Ae Bz z ( ) u ref % % 0 ' ) ( P ' P *( P +1) ) dz = Au ref ( B ( P+1) (9) where Γ is the gamma function. Using a mathematical model that results in a converging definite integral avoids any uncertainty about the upper limit of integration, z max. The integral of a power law for wind times a power law for dust concentration has an analytic solution that does not converge. The horizontal dust flux can also be calculated by numerical integration of Equation (1) using alternative interpolation equations to model the time averaged wind speed and concentration as a function of height. References Claiborn, C., Arundhati, M., Adams, G., Bamesberger, L., Allwine, G., Kantameneni, R., Lamb, B. and Westberg, H., Evaluation of PM 10 emission rates from paved and unpaved roads using tracer techniques, Atmospheric Environment 29(10): Cowherd, C., Maxwell, C. M. and Nelson, D. W., Quantification of Dust Entrainment from Paved Roadways, U.S. Environmental Protection Agency. EPA, 1998a. AP-42, Compilation of Air Pollutant Emission Factors - Vol 1. Stationary, Point, and Area Sources, Chapter Unpaved Roads, Washington, D.C., U.S. Environmental Protection Agency. Goossens, D., The granulometrical characteristics of a slowly-moving dust cloud, Earth Surface Processes and Landforms 10: Paulson, C. A., The mathematical representation of wind speed and temperature profiles in the unstable atmospheric surface layer, J. Appl. Met. 9: Stull, R. B., An Introduction to Boundary Layer Meteorology, Dordrecht, The Netherlands, Kluwer Academic Publishers.

5 Veranth, J.M., G. Seshadri, and E. Pardyjak, Vehicle-generated fugitive dust transport: Analytic models and field study. Atmospheric Environment, (16): p

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