Sulfur Dioxide Pollution

Source:

Atmospheric Dispersion Modeling Compliance Guide; Karl Schnelle, Ph.D and Partha Dey, Ph.D.; McGraw-Hill 2000

Goal:

To learn how meteorological conditions and pollutant source concentrations affect pollution in a given location.

Background Reading:

Sulfur dioxide (SO₂)is a pollutant that can cause trouble breathing for asthmatic children and adults who are active outdoors. People with asthma who are exposed for a short time to elevated SO₂ levels may show symptoms of reduced lung function such wheezing, chest tightness, or shortness of breath. Longer-term exposures to high concentrations of SO₂ can cause respiratory illness, alterations in the lungs' defenses, and aggravation of existing cardiovascular disease. SO₂ is also one of the major precursors to acid rain, which is associated with acid soils, lakes, and streams, corrosion of buildings, and reduced visibility.

One source of SO₂ is burning coal, used in homes, factories, and trains. How much sulfur dioxide is in the air in a given place is determined by how much SO₂ is being produced, and how the wind blows the SO₂ in and out of the area. For example: suppose a town has a smokestack on the west edge of the city and the wind almost always comes from the east. The sulfur dioxide gets blown out of the town. But if the wind comes from the west, the SO₂ moves into the town and pollutes the center of town, even if the center of town doesn't produce any SO₂. Similarly, if the wind is only a slight breeze, the pollutant will not move as fast or as much as it would with a strong wind. Towns can figure out how much of a pollutant is in a particular area by figuring out how much is produced where, and then where it moves. To determine how much pollution is created by different areas, a town will present data in a square grid of the city, with emissions source concentrations in each grid cell.

Environmental standards give a maximum concentration for SO₂ in a three-hour average, and each city must stay within these restrictions. The average three hour concentration is calculated by:

The average hourly concentration of a pollutant is determined by

where C_ij is the concentration in any grid square, and Q_ij is the source strength for the grid square. The variables i and j denote all the places for the squares, just like a map index that says a place is in square H4 on the map.

A concentration (C_ij) grid is defined by

for the receptor square, and

for all other squares.

where f is the frequency of wind coming from that direction, u is the windspeed, x is the length of a grid square side, i is the upwind grid squares, and a and b are constants determined by the meteorological conditions.

A Sample Case Study: Grinders Switch

Grinders Switch is a small railroad town that uses coal as its main source of energy. The state enviornmental authority has required the town to make an estimate of the maximum posible three hour average sulfur dioxide concentration caused by the town's use of coal in trains, homes, and the electric plant in the center of town. The town's estimated concentration must be below the National Ambient Air Quality Standard of 1300 micrograms per cubic meter.

It has been determined that the the worst meteorological conditions are a type called Pasquill D, where a = 0.15 and b = 0.75, with a windspeed (u) of 5 m/s. The town's sulfur production is at a highest in the fall, when the power plant is generating at the highest loads, and the trains are being used the most. The wind frequencies for this time of year are as follows:

Wind Frequency Data October 5-yr Average

N	NNE	NE	ENE	E	ESE	SE	SSE
0.02	0.02	0.03	0.05	0.06	0.07	0.05	0.04
S	SSW	SW	WSW	W	WNW	NW	NNW
0.03	0.02	0.02	0.08	0.23	0.20	0.05	0.03

The concentrations of produced pollutants have already been determined and put into a grid of the town's area. Each grid cell represents an square area of the town 1000 meters on each side. Because it is a 5x5 grid, i=2 in your C_ij grid calculations (2 upwind squares from receptor square). The source strength in the hourly strength in micrograms/m²/sec

Hourly Source Strength Q_ij for Grinders Switch

1	1	2	2	3
1	1	8	7	7
2	5	15	10	2
4	8	10	4	1
2	2	4	2	1

Because the center square has the highest source, the town has decided to first determine the three hour average SO₂ concentration in using the center square as the receptor square. This calculation is the one you must carry out.

Making the Model

Use a spreadsheet application such as Excel. Alternatively, you can use the Javascript model which performs the calculations on user-entered data. Enter in all initial conditions into the spread sheet, as in the image below (click to see full scale). Information in the colored boxes in the pictures below is not necessary for the spreadsheet to work.

To work with the initial data, you must first reconcile the polar data of the wind frequencies to a grid like the Q_ij data. To do this, make a grid of (f/u)_ij. To see which frequency belongs where in the grid, simply make a 5x5 grid and draw over it the polar lines coming out from the receptor square. The cells directly north receive the North frequency, the cells north east get the NE frequency, etc. Where multiple lines exist in a single cell, add up all the frequencies. For example, the cell directly above the receptor square is a sum of NNW, N, and NNE. The receptor square is the sum of all frequencies divided by the wind speed, or simply 1/u.

Now you have a grid of (f/u). Use this data and the equations in the background reading to make a C_ij grid. Then, multiply each cell of the C_ij grid with the corresponding cell of the given Q_ij grid. This is not matrix multiplication! This new grid is C_ijQ_ij. Using this grid and the information in the background reading, determine the hourly and the three hour concentration of SO₂ in Grinders Switch. Finally, determine whether it is within the National Ambient Air Quality Standard of a 3-h average SO₂ concentration.