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Algorithms I · software · air monitoring

The mathematical model that the software uses provides options to model emissions from a wide range of sources that might be present at industrial areas and urban areas. The model is analogous to ISC3 from EPA. The basis of the model is the straight-line, steady-state Gaussian plume equation, which is used to model simple point source emissions from stacks, roads, storage piles and conveyor belts. Emission sources are categorized into three basic types of sources: point sources, line sources and area sources. The algorithms used to model each of these source types are described in detail in the following sections. The DISPER dispersion model accepts meteorological data records to define the conditions for plume rise and transport. The model estimates the concentration value for each source and receptor combination and calculates user-selected averages.

Point source emissions 

The model uses a steady-state Gaussian plume equation to model emissions from point sources, such as stacks.

The Gaussian Equation

The model for stacks uses the steady-state Gaussian plume equation for a continuous elevated source. For each source, the origin of the stack coordinate system is placed at the ground surface at the base of the stack. The x axis is positive in the downwind direction, the y axis is crosswind (normal) to the x axis and the z axis extends vertically. The fixed receptor locations are converted to each source's coordinate system. The hourly concentrations calculated for each source at each receptor are summed to obtain the total concentration produced at each receptor by the combined source emissions.

For a Gaussian plume, the hourly concentration at downwind distance x (meters) and crosswind distance y (meters) is given by:

c =(Q K V D/2 pi u_s sig_y sig_z) exp[-0.5(y/sig_y)²]  (1)

where:

Q= pollutant emission rate (mass per unit time)

K= a scaling coefficient to convert calculated concentrations to desired units (default value of 1 x 10⁶ for Q in g/s and concentration in µg/m³)

V= vertical term (See Section 1.1.6)

D= decay term (See Section 1.1.7)

sig_y,sig_z= standard deviation of lateral and vertical concentration distribution (m) (See Section 1.1.5)

u_s= mean wind speed (m/s) at release height (See Section 1.1.3) 

Downwind and Crosswind Distances

The model uses a Cartesian receptor network. All receptor points are converted to Cartesian (X,Y) coordinates prior to performing the dispersion calculations. In the Cartesian coordinate system, the X axis is positive to the east of the user-specified origin and the Y axis is positive to the north. The user must define the location of each source with respect to the origin of the grid using Cartesian coordinates. If the X and Y coordinates of the source are X(S) and Y(S), the downwind distance x to the receptor, along the direction of plume travel, is given by:

x=-[X(R)-X(S)]sin(WD)-[Y(R)-Y(S)]cos(WD)        (2)

where WD is the direction from which the wind is blowing. The downwind distance is used in calculating the distance-dependent plume rise and the dispersion parameters. The crosswind distance y to the receptor from the plume centerline is given by:

y=-[X(R)-X(S)]cos(WD)-[Y(R)-Y(S)]sin(WD)        (3)

Wind Speed Profile

The wind power law is used to adjust the observed wind speed, u_ref, from a reference measurement height, z_ref, to the stack or release height, h_s. The stack height wind speed, u_s, is used in the Gaussian plume equation. The power law equation is of the form:

u_s=u_ref(h_s/z_ref)^p     (4)

where p is the wind profile exponent. Values of p may be provided by the user as a function of stability category and wind speed class. Default values are as follows:

The stack height wind speed, u_s, is not allowed to be less than 1.0 m/s.

air monitoring