1. Mathematical modeling for
atmospheric dispersion of radioactive
cloud passing over Jeddah
Presented By
Dr. Najlaa D. Alharbi
Physics department - Sciences Faculty for Girls
King Abdulaziz University
December 2011

3. On March 11, 2011, at around 08:15 CET an earthquake
of magnitude 8.9 near the east coast of Honsu, Japan occurred,
followed by a tsunami.
After that the nuclear power plants at Onagawa with three
BWR reactors, at Fukushima Daichi with six BWR reactors,
at Fukushima Daini with four BWR reactors, and at Tokai
With two BWR reactors were shut down automatically and
no radiation release had been detected there.
*According to the IAEA Report on Japan Earthquake(IAEA, 2011).

6. On March 26, 2011,
the highest values of fission product radionuclides
were observed in the prefecture of Yamagata, Japan as
high as
7500 Bq.m-2 for 131I
&
1200 Bq.m-2 for 137Cs
*(IAEA, 2011).

7. On March 28, 2011,
the highest values of the above radionuclides
were observed in the prefecture of Fukushima with
23000 Bq.m-2 for 131I
&
790 Bq.m-2 for 137Cs
*(IAEA, 2011).

8. According to the Reinish Institute for Environmental Research
at the University of Cologne, Germany.
Acloud containing radioactivity formed in air over the Fukushima
nuclear power plant and moved over the Pacific Ocean,
north from Japan in the direction to the Arctic Ocean and
entered to the Atlantic Ocean over Iceland and
then diffused over the European continent.
*(Jakobs, 2011).

11. The prediction of dispersion of radionuclides to the
atmosphere is a important element of the emergency response
procedures.
 Numerical models are used in several countries around
the world .
 The dispersion models are used to estimate or to predict
the downwind concentration of air pollutants emitted from
sources such as industrial plants.

12. Atmospheric Dispersion Modeling
 A dispersion model is the mathematical simulation of how
air pollutants disperse in the ambient atmosphere.
Routinely used in:
 Environmental impact assessments
 Risk analysis
 Emergency planning
It’s parallel terms with
 Air pollution dispersion models
 Air quality models

13. Classes of Air Quality Models
 The air quality modeling procedures can be categorized into
four generic classes: Gaussian, numerical, statistical or
empirical and physical
 The emphasis is on Gaussian-plume type models for
continuous releases, which are at the core of most U.S.
Environmental Protection Agency (EPA) regulatory models
 Gaussian models are the most widely used techniques for
estimating the impact of nonreactive pollutants

14. Model Parameters
The model is based on our knowledge of the following parameters:
 Meteorological conditions (wind speed & direction, stability
class, the ambient air temperature)
 Emissions parameters (source location &height, stack diameter,
pollutants exit velocity, exit temperature, plume rise )
 Terrain (surface roughness, local topography, nearby buildings)

16. CASE STUDY
Mathematical modeling for
atmospheric dispersion of radioactive
cloud passing over Jeddah

17. Meteorological Data
The study area chosen is Jeddah city which is located on the
east coast of Kingdom of Saudi Arabia at 21.7 N and 39.2 E.
Month
Temperature Mean wind speed
(deg.c)
at elevation: 10 m
Pre.
Direction.
Sky cover
oktes mean
January
23
2.8
NNE
3.3
February
24.4
3.2
N
1.1
March
26.8
2.4
SW
0.95
April
29.2
2.8
N
2.4
May
30
2.8
N
2.45
June
31.7
2.4
W
1.15
July
33.4
2.4
N
1.25
August
32.9
2.8
NNW
1.25
September
32.3
2.4
NNW
2.35
October
29.9
2.4
N
0.65
November
27.6
2.4
N
1.7
December
25.8
2.8
ENE
1.2
The average meteorological and climatological data for Jeddah city
per month

18. Atmospheric stability
Pasquill's stability classification method is used to determine atmospheric
stability classes.
This method defines six stability classes ranging from A (extremely unstable) to
F(moderately stable) on the basis of wind speed at 10 m level,
Stability
class
A
B
C
D
E
F
sum
Repetition
Percentage
29
67
38
15
15
12
176
16.47
38.07
21.6
8.52
8.52
6.82
100

19. Wind Speed
 The predominant wind direction is North
(N)
 The mean wind speed at 10m is 2.4 m/s.

20. Dispersion Model
GAUSSIAN PLUME
MODEL (GPM)

21. The concentration distribution of a pollutant released from a continuous single
point source having emission rates Q, is expressed in the following formula :

 y2
Q
exp − 
χ ( x, y , z ) =
 2σ 2
2πU σ y σ z 
y


 
− ( z − H ) 2 
 − ( z + H ) 2 


 exp 
 + exp 

2
2
 
 2σ z

 2σ z


 
Effective Stack Height
H =hs +∆
h

22. Plume Dispersion by Gaussian Distribution and Coordinate System

23. The ground level concentration (glc) below the centerline
of the plume is obtained by setting
y=z=0 then we have:
− H 2 
Q
χ ( x, 0, 0) =
exp 
2 
π uσ y σ z
 2σ z 

24. Radioactive decay factor
 −H 
Q
−λ x
χ ( x, 0, 0) =
exp  2 2 d  exp 

b+d
π uac x
 u 
 2c x 
2

25. ACCIDENT
SCENARIO

26. It was assumed that:
 The radioactive plume passing over Jeddah city has been emitted in
an accidental conditions from a nuclear power plant.
 The reactor was assumed to operate full with its power of 10 MW. The
release scenario was assumed to occur at a stack height of 61m.
 The radionuclide activity released to the atmosphere is picked up by the
wind and transported to the receptor site (Jeddah city).
 The wind was blowing with a mean speed of 4.95 m/s at 61m height
and corrected to 2.4m/s at 10m height. The wind direction was(N) dir.
 The dominant stability class was the class B (moderately unstable).

27. Half - life for different radionuclides released to
the environment.
Radionuclide
Half-life
Rb-88
I-134
Kr-85m
Xe-135
Te-131
Xe-133
Ba-140
Sr-89
Ce-144
Cs-134
Kr-85
Sr- 90
18 min
52.5 min
4.5 h
9.1 h
30 h
5.2 d
12.8 d
50 d
285 d
754 d
10.7 yr
29 yr

28. NCD
NCD (Rb-88)
Distance
(18 min)
(km) (before decay)
NCD (I -134)
(52.5 min)
NCD (Kr-85m)
(4.5h)
NCD (Sr-89)
(50 d)
NCD (Kr-85)
(10.7y)
1
3.41145 ×10-6
2.99594 ×10-6
3.2622 ×10-6
3.38204 ×10-6
3.41134 ×10-6
3.41145 ×10-6
2
9.27778 ×10-7
7.15538 ×10-7
8.48371 ×10-7
9.11851 ×10-7
9.27717 ×10-7
9.27777 ×10-7
3
4.24299 ×10-7
2.87379 ×10-7
3.7101 ×10-7
4.1342 ×10-7
4.24258 ×10-7
4.24298 ×10-7
4
2.42588 ×10-7
1.44294 ×10-7
2.0284 ×10-7
2.34331 ×10-7
2.42556 ×10-7
2.42588 ×10-7
5
1.57022 ×10-7
8.20223 ×10-8
1.25549 ×10-7
1.50369 ×10-7
1.56996 ×10-7
1.57021 ×10-7
6
1.09992 ×10-7
5.04576 ×10-8
8.4098 ×10-8
1.04424 ×10-7
1.0997 ×10-7
1.09991 ×10-7
7
8.13804 ×10-8
3.27855 ×10-8
5.95 ×10-8
7.65948 ×10-8
8.13619 ×10-8
8.13802 ×10-8
8
6.26773 ×10-8
2.21751 ×10-8
4.38206 ×10-8
5.8483 ×10-8
6.2661 ×10-8
6.26771 ×10-8
9
4.97773 ×10-8
1.54661 ×10-8
3.32791 ×10-8
4.60459 ×10-8
4.97628 ×10-8
4.97772 ×10-8
10
4.05024 ×10-8
1.10516 ×10-8
2.58935 ×10-8
3.71432 ×10-8
4.04892 ×10-8
4.05022 ×10-8
Concentration Calculations before and after inserting Decay
Factor for different Radionuclides.

29. Conclusion

we conclude that: radioactive decay effect is clear in cases of
short lived isotopes.
 The concentration was reduce by 75% in Rb-88 radionuclide,
50% in I-134 and by 25% in Kr-85m.
 while it was reduce by 0.01% in Sr-89 and 0.00001 in Kr-85.

30. Future Vision
&
Considerations

31. Acknowledgements
The author sincerely thanks King Abdul-Aziz University Deanship of scientific research - for its support this research
of project no.(21- 007/429‫.)ح‬
Also thanks Dr. Sadah Alkhateeb for help in designing
Mathematica program.
I am grateful for Vice President for Development- Center for
teaching & learning development for give me this chance.

32. References
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33. THANK YOU
THANK YOU