The Dispersion Coeficients for Flat Open Terrain

 

Students are directed to the original works for the derivations:

Pasquill F, 1961, The Estimation Of The Dispersion Of Windborne Material, Meteorological Magazine, 90,p1063.

And later modification by Gifford

Gifford 1961,Uses Of Routine Meteorological Observations For Estimating Atmospheric Dispersion, Nuclear Safety,2, (4)

Turner (1970) presents graphical distributions of dispersion coefficients with distance downwind for various stability classes. This is one of the most widely used texts on this subject but it was written before the availability of cheap computers and powerful spreadsheets.

Here we must consider a dilemma. Turner's approach using hand calculations and graphs certainly allows the investigator to avoid many of the pitfalls pointed out by Scorer in that bad science can be hidden in the computer. However writing appropriate spreadsheets can in the authors' experience help a student to gain an excellent understanding of the calculation process. Spreadsheets can also allow one to "play" very easily with the calculations to investigate the effects of certain parameters and to test the sensitivity of various parameters so that a feel for those data items, which need to be known most accurately, can be obtained.

Calculating Dispersion Coefficients According To Turners Workbook

The graphs presented by turner (1970) are inconvenient if using computer based modeling. Students should try to take a look at Turners workbook or at the summary of it presented by Masters and try to become familiar with the graphs used.

Martin (1976) presented equations which yield a reasonable fit and we will use these formulae rather than a graphical approach.:

With the values of a, d and f given as in the tables below:

1) FOR DISTANCES x is 1km OR LESS

STAB. CLASS a c d f
A 213 440.8 1.941 9.27
B 156 106.6 1.149 3.3
C 104 61.0 0.911 0
D 68 33.2 0.725 -1.7
E 50.5 22.8 0.678 -1.3
F 34 14.35 0.740 -0.35
 

2) FOR DISTANCES x is OVER 1km

STAB. CLASS a c d f
A 213 459.7 2.094 -9.6
B 156 108.2 1.098 2.0
C 104 61.0 0.911 0
D 68 44.5 0.516 -13.0
E 50.5 55.4 0.305 -34.0
F 34 62.6 0.180 -48.6

 

Task 5:

1) Using the equations above calculate the dispersion coefficients at 0.8km from the source from the source and 2km under all stability class conditions.
It may be instructive to compare this to the values you obtain using the graphs from Turner's workbook and available in Masters excellent text.

2) Using a spreadsheet plot a graph of against downwind distance for a class D situation. Assuming that the effective chimney height H is 100 m and that the plume first grounds when 3/2 = H calculate the distance at first grounding and explain the logic of the 3/2 assumption.