NRC DISPERSION MODELING SEMINAR

Roland Draxler

1994

BASIC EQUATIONS

Equivalent to that for heat conduction:

The solution, with K equal to atmospheric diffusivity:

Since the exponential term is a Gaussian distribution:

Therefore after substitution we have the well known form:

The functions for Gaussian distributions will be:

In other situations, such as continuous emissions:

Or when the vertical layer is well mixed:

PARAMETERS REQUIRED TO COMPUTE DISPERSION AND TRANSPORT

Emission Rate - Q

Wind Speed (vector) - U

Mixing Depth - Zi

Dispersion Parameters - σi or Ki

DISPERSION PARAMETERS

Eddy Diffusivity

or

Horizontal diffusivity is very difficult to obtain exactly.

Statistical Theory (Taylor's):

The functions fx and fy are usually obtained empirically by relating dispersion experiment results and measured turbulence values. The functions can also be obtained theoretically from the "spectrum" of the horizontal and vertical turbulence.

TURBULENCE CHARACTERIZATION

PASQUILL -  Measured wind fluctuations

PASQUILL/GIFFORD - Pre-determined curves and

corresponding categories (solar elev, cloud, U)

SLADE -  Categories from wind direction fluctuation

NRC - Categories from temperature difference

GOLDER - Categories from roughness and Monin-Obukhov L

Category  Pasquill  Slade     NRC (deg C/100m)

A         60        25        -1.9

B         45        20        -1.7

C         30        15        -1.5

D         20        10        -0.5

E         15        5        +1.5

F         10        2.5      +4.0

MIXING DEPTH

Turbulent mixing during the daytime reflects the amount of sensible heat that is absorbed by the atmosphere at the earth's surface.

It is a function of the solar insolation, cloud cover, wind speed, and soil moisture.

It can be computed from the intersection of the morning temperature sounding and the maximum surface temperature (Holzworth).

At night the mixing depth represents the height to which mechanical/roughness induced turbulence penetrates the stability induced by surface radiational cooling.

In the vertical:

In the horizontal:

The effect of the vertical and horizontal "shears" of the wind is that depending upon the degree of vertical mixing a single wind may not adequately represent pollutant transport.

MODELING POLLUTANT TRANSPORT AND DISPERSION

Lagrangian and Eulerian Models (from eq 1):

We expand the total derivative so that:

Gaussian Models tend to be Lagrangian Models, however Eulerian models may or may not be Gaussian, depending upon the turbulence closure scheme selected.

Some other modeling terms:

CONTINUOUS GAUSSIAN PLUME

SEGMENTED GAUSSIAN PLUME

GAUSSIAN PUFF

NON-GAUSSIAN PUFF (multi-layer modeling approach)

PARTICLE-IN-CELL MODEL

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