CE 397: Environmental Risk Assessment

Department of Civil Engineering

The University of Texas at Austin

Lecture Notes: Transport and Fate of Chemicals in Air, Richard Corsi, Feb 24-Mar 3, 1998

**Readings:**

- Lecture Notes on Atmospheric Transport Modeling
- Lecture Notes on Atmospheric Thermodynamics and Stability
- Benarie, M. M.,
__Editorial: The Limits of Air Pollution Modeling__,*Atmospheric Environment*, Vol. 21, No. 1, pp. 1-5, 1987. - _____,
__Accuracy of Dispersion Models__,*Bulletin of American Meteorological Society*, Vol. 59, No. 8, 1987. - Popenuck, W. W., Chang, D. P. Y.,
__Comparison of a Turbulent Shear Flow Model with the Project Prairie Grass Diffusion Data__, Air & Waste Management Association, 86^{th}Annual Meeting, Denver, CO, 1993. - Huang, C. H., A Theory of Dispersion in Turbulent Shear Flow,
*Atmospheric Environment*, Vol. 13, pp. 453-463, 1979. - Yeh, G.T., Huang, C.H.,
__Three-Dimensional Air Pollutant Modeling in the Lower Atmosphere__, Boundary-Layer Meterology, 9, 381-390, 1975.

Introduction

The atmosphere is generally defined as having four major layers. The layers are defined by their natural average temperature profiles.

The troposphere is the layer closest to the earth. Within the troposphere there are several important layers. The layer closest to the earth is the planetary boundary layer (PBL). Frictional forces and drag forces at the surface directly influence the PBL. The thickness of the PBL is determined by surface driven convection.

Atmospheric stability is defined qualitatively as a measure of the degree of vertical mixing in the atmosphere. Stable atmospheres are poorly mixed in the vertical direction. Unstable atmospheres are those that are significantly mixed in the vertical direction.

Temperature gradients in the atmosphere (characterized by the lapse rate) have a large affect on transport.

Gaussian Plume Model

The Gaussian Plume Model (GPM) is widely used to predict concentrations in the atmosphere. There are significant simplifications with the GPM. The assumptions used to derive the GPM should be understood in order to understand the uncertainties associated with modeling results. The GPM is often used as a screening calculation method for exposure assessments. The GPM is derived from the advection-diffusion equation.

The assumptions are:

1). Steady-state

2). Wind blows in x-direction and is constant in both speed and direction

3). Transport with the mean wind is much greater than turbulent transport in the x-direction

4). The source emission rate is constant (Q)

5). Eddy diffusion coefficients are constant in both time and space (this is not a good assumption)

6). The source emits chemicals of concern (COC) at a point in space x=y=0 and z=H, where H is the effective stack height

7). The COC are inert (non-decaying and non-reactive)

8). There is no barrier to plume migration (this is accounted for by using an imaginary "mirror" source)

9). Mass is conserved across the plume cross section

10). Mass within a plume follows a gaussian distribution in both the crosswind (y) and vertical (z) directions (this is a good assumption for y but not a good assumption for z).

Using the GPM the maximum concentration is found at the centerline where y=0.

The GPM is derived for continuous point sources. Line sources and area sources can be modeled as the sums of point sources.

The original experiments for dispersion coefficients were the "Project Prairie Grass" experiments. These are important because they were used to derive the dispersion coefficients (plotted as the Pasquill-Gifford curves) that are generally applied to all cases. The data collected were for ground level releases within about 1 km of the source. These data have been extrapolated to lots of other arrangements. The Briggs equations for dispersion coefficients are based on this original data and other data for different configurations. The Briggs equations are probably better relationships to use.

K-Theory Models

The k-theory models include the variability of dispersion and wind speed with vertical position. They maintain the gaussian distribution in the crosswind (y) direction. The models are usually solved numerically.

Important Definitions

Atmospheric stability - A measure of the vertical mixing in the atmosphere. Stability is characterized from unstable through neutral to stable using the letter categories A through F. The stability classes characterize the atmospheric dispersion coefficients. The dispersion coefficients are determined based on empirical relationships for the stability classes as functions of downwind distance.

Effective stack height (H) - the vertical distance used in the GPM for the emission point. The effective stack height is equal to the physical stack height plus the plume rise.

Lapse Rate - the negative of an atmospheric temperature gradient. The dry adiabatic lapse rate (G_{d}) is a reference value of 9.8 deg C/1000m. The environmental lapse rate is the measured value noted as G_{e}. An inversion occurs when the environmental lapse rate is negative. The effect of an inversion is to limit vertical mixing.

Plume rise - the vertical extent to which the centerline of an atmospheric plume rises above the emission point. Plume rise is determined based on empirical relationships derived from photographs of real plumes.

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