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Effects of number of simulated particles on the uncertainty in simulation of dispersion of radioactive material using FLEXPART program

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Nuclear Science and Technology, Vol.9, No. 1 (2019), pp. 21-27  
Effects of number of simulated particles on the uncertainty in  
simulation of dispersion of radioactive material  
using FLEXPART program  
Nguyen Hao Quang1, Hoang Sy Than1, Duong Duc Thang2, Pham Kim Long3  
1Viet Nam Atomic Energy Institute, 59 Ly Thuong Kiet, Ha Noi, Viet Nam  
2Institute of Nuclear Science and Technology, 179 Hoang Quoc Viet, Ha Noi, Viet Nam  
3Nuclear Training Center, 140 Nguyen Tuan, Ha Noi, Viet Nam  
(Received 05 August 2019, accepted 15 September 2019)  
Abstract: FLEXPART software simulates atmospheric emissions based on wind-field movements and  
random disturbances. To simulate random processes, FLEXPART uses a certain number of simulation  
particles. Changing the number of simulation particles causes a change in the simulated results of the  
dispersion concentration of the radionuclides. The larger number of simulated particles results in the  
more accurate simulated results. However, increasing the number of simulated particles results in the  
increasing of the computational cost. The report presents an assessment of the uncertainty in the  
concentration of radionuclides in simulating dispersion of 137Cs and 131I nuclides using FLEXPART  
software according to the number of simulation particles. The number of simulation particles used in  
this study are 100, 1000, 5000, 7500, 10000, 15000, 20000, 25000 and 30000 particles / hour. Using  
the image processing software OpenCV to evaluate the uncertainties of simulated results according to  
the number of simulated particles used. Evaluation results show that the simulated results are  
acceptable with the number of simulated particles being of 20000 particles/hour.  
Keywords: FLEXPART, uncertainty, simulation particle, OpenCV.  
simulate the dispersion of radionuclides during  
the Fukushima nuclear power plant accident.  
The change in the number of simulated  
particles leads to a change in the simulation  
results of the dispersion concentrations of  
radionuclides. The larger number of simulation  
particles, the more accurate the simulation  
result we can get. However, as the number of  
particles simulated increases, the cost of  
calculation also increases. So the question is  
how we can determine the reasonable number  
of simulated particles which can produce the  
good enough result, while the computational  
cost is kept at the feasible level. In the  
published works using the FLEXPART  
program to simulate the dispersion of  
pollutants in the air environment, the used  
number of simulated particles varied in a fairly  
wide range from 5000 particles/hour [1] to  
1000000 particles/hour [2]. However, there has  
I. INTRODUCTION  
FLEXPART software is widely used in  
simulation of air dispersion. FLEXPART  
software uses the Lagrangian particle model to  
describe particle trajectories moving in the  
environment. The Lagrangian particle model is  
widely used and generally accepted as a  
powerful tool to simulate the dispersion of  
pollutants in a gaseous environment. To  
simulate random processes the FLEXPART  
program uses a certain number of simulated  
particles. They are the notional particles that do  
not represent the real aerosol particles, but the  
points moving with the ambient flows. The  
output of FLEXPART program is the  
distribution of these points in three  
dimensional space and converted into the  
distribution of pollutant concentration. In this  
study, we use the FLEXPART program to  
©2019 Vietnam Atomic Energy Society and Vietnam Atomic Energy Institute  
EFFECTS OF NUMBER OF SIMULATED PARTICLES ON THE UNCERTAINTY IN…  
not been a publication on how to choose the  
number of simulated particles to be used. In  
this study, we investigated and assessed the  
difference in the concentration of radionuclides  
in the dispersion simulation of 137Cs and 131I  
when using FLEXPART software according to  
the various numbers of simulated particles. The  
numbers of simulated particles used in this  
study to be 100, 1000, 5000, 7500, 10000,  
radionuclides according to the number of  
simulated particles being of 100, 1000, 5000,  
7500, 10000, 15000, 20000, 25000  
particles/hour with the case of simulated  
particles of 30000 particles/hour. In order to  
assess the difference in the concentration  
distribution of radionuclides between the two  
images, one is the simulation result with the  
number of simulated particles used as one of  
these cases 100, 1000, 5000, 7500, 10000,  
15000, 20000, 25000 particles/hour and  
another is the simulation result with the  
number of particles simulated being of 30000  
particles/hour, we used the quantity of  
average squared error (Mean Squared Error -  
MSE). The quantity MSE is defined as  
follows:  
15000,  
20000,  
25000,  
and  
30000  
particles/hour.  
II. CONTENT  
A. Subjects and methods  
The FLEXPART program uses the  
number of simulated particles to simulate the  
dispersion of pollutants. The program  
provides simulation results of pollutant  
concentration in the form of three-  
dimensional grid longitude, latitude and  
altitude. These output data are not easily to  
compare directly. Use the Quicklook software  
to process the three-dimensional output data  
of FLEXPART into the two dimensional  
images of distribution for radionuclide  
concentrations. In this study, in order to  
simulate the dispersion, we use the same  
source terms of 137Cs and 131I emitted during  
the Fukushima nuclear power plant accident  
from 15:00 UTC on March 11st,2011 to 0:00  
UTC on April 20th,2011 with number of  
simulated particles being of 100, 1000, 5000,  
7500, 10000, 15000, 20000, 25000, and  
30000 particles/ hour. Radioactive nuclide  
137Cs has the aerosol form and radioactive  
nuclide 131I has the gaseous form. The  
simulation results for dispersion of the  
radionuclides 137Cs and 131I with the number  
of simulated particles being of 30000 particles  
per hour are considered as the reference  
results. We assessed the difference in the  
simulation results of the concentration of  
 
        
 
∑
∑
[ (  
)
(
)]  
      
                
(1)  
    
    
    
Where m, n are the coordinate indexes of  
longitude and latitude coordinates.  
I (i, j) is the radionuclide concentration  
at the coordinate (i, j) with the number of  
simulated particles as one of these cases 100,  
1000, 5000, 7500, 10000, 15000, 20000, 25000  
particles/hour.  
K (i, j) is the concentration of  
radionuclide at the coordinate (i, j) with the  
number of simulated particles being of 30000  
particles/hour.  
To calculate MSE quantity we use a  
piece of software written in the Python  
language with the numpy library [3].  
In order to simulate the dispersion  
process of radionuclides with the number of  
simulated particles as one of these cases 100,  
1000, 5000, 7500, 10000, 15000, 20000, 25000  
and 30000 particles/hour we run FLEXPART  
on a supercomputer with configuration 24 CPU  
Intel (R) Xeon (R) X5650 @ 2.67GHz Linux  
operating system, 32Gb RAM.  
22  
NGUYEN HAO QUANG et al.  
B. Results  
With the above computer configuration, the  
calculated times with the number of simulated  
particles being of 100, 1000, 5000, 7500,  
10000, 15000, 20000, 25000 and 30000  
particles/hour are given in Table I.  
Table I. The calculated times with the number of simulated particles being of 100, 1000, 5000, 7500, 10000,  
15000, 20000, 25000, and 30000 particles/hour.  
Simulated particles  
(particles/hour)  
100  
Starting time  
Ending time  
Calculated time  
(minute)  
407  
16/01/19 3:31  
16/01/19 3:39  
12/11/18 2:32  
12/11/18 2:39  
12/11/18 4:12  
15/11/18 4:25  
15/11/18 10:06  
22/11/18 2:56  
22/11/18 8:06  
16/01/19 10:18  
17/01/19 0:48  
14/11/18 14:08  
14/11/18 23:08  
15/11/18 17:12  
20/11/18 3:12  
21/11/18 19:12  
30/11/18 8:12  
03/12/18 10:12  
1000  
5000  
1268  
3575  
7500  
10000  
4108  
5099  
15000  
20000  
7126  
9186  
25000  
30000  
11836  
15966  
From the data given in Table I, it can be  
seen that the calculated time is proportional to  
the used number of simulated particles. The  
calculated time in the case of simulated  
particles being of 30000 particles/hour is  
15966 minutes, which is about 11.1 days. This  
is a large period of time and it is often  
difficult to solve problems related to  
surveying the impact of different types of  
weather on the simulation results of a certain  
nuclear accident.  
We investigated the difference in  
concentration distribution of 137Cs and 131I  
radionuclides between the results of simulation  
calculations with the number of simulated  
particles being of 100, 1000, 5000, 7500,  
10000, 15000, 20000, 25000 particles/hour and  
the result of simulation calculation with  
simulated  
particles  
being  
of  
30000  
particles/hour. The results of investigating the  
difference in the concentration distribution of  
radionuclides 137Cs and 131I through MSE  
quantity are shown in Table II.  
Table II. MSE of the concentration distribution of radionuclides 137Cs and 131I with the number of simulated  
particles being of 100, 1000, 5000, 7500, 10000, 15000, 20000, 25000 particles/hour compared to the case of  
simulated particles being of 30000 particles/hour at 11:00 UTC on March 16th,2011.  
Simulated particles  
(particles/hour)  
MSE of the concentration distribution of 137Cs and 131I at 11:00 UTC on  
March 16th 2011  
137Cs  
473,3  
237,4  
131,3  
93,2  
131I  
182,8  
90,1  
49,7  
35,2  
34,5  
29,0  
28,1  
27,5  
100  
1000  
5000  
7500  
10000  
15000  
20000  
25000  
91,4  
77,0  
74,7  
73,0  
23  
EFFECTS OF NUMBER OF SIMULATED PARTICLES ON THE UNCERTAINTY IN…  
Table III. MSE of the concentration distribution of radionuclides 137Cs and 131I with the number of simulated  
particles being of 100, 1000, 5000, 7500, 10000, 15000, 20000, 25000 particles/hour compared to the case of  
simulated particles being of 30000 particles/hour at 18:00 UTC on April 2nd,2011.  
Simulated particles  
(particles/hour)  
MSE of the concentration distribution of 137Cs and 131I at 11:00 UTC on  
April 2nd,2011  
137Cs  
3906,4  
1264,5  
466,0  
363,2  
312,6  
248,5  
226,4  
217,2  
131I  
100  
4055,2  
1256,0  
457,6  
356,3  
306,5  
243,6  
222,2  
213,3  
1000  
5000  
7500  
10000  
15000  
20000  
25000  
Figure 1,2 show the difference in  
simulation results of radioactive nuclide  
concentration 137Cs and 131I with the  
corresponding to 100, 1000, 5000, 7500,  
10000, 15000, 20000, 25000 and 30000  
particles/hour at 11:00 UTC on March  
16th,2011.  
number  
of  
simulated  
particles  
Fig. 1. Simulation results of the radionuclide concentration of 137Cs according to the number of simulated  
particles at 11:00 UTC on March 16th,2011.  
24  
NGUYEN HAO QUANG et al.  
Fig. 2. Simulation results of the radionuclide concentration of 131I according to the number of simulated  
particles at 11:00 UTC on March 16th,2011.  
Fig. 3. Simulation results of the radionuclide concentration of 137Cs according to the number of simulated  
particles at 18:00 UTC on April 2nd,2011.  
25  
EFFECTS OF NUMBER OF SIMULATED PARTICLES ON THE UNCERTAINTY IN…  
Fig. 4. Simulation results of the radionuclide concentration of 131I s according to the number of simulated  
particles at 18:00 UTC on April 2nd,2011.  
4500  
4000  
3500  
3000  
Cs137-16-3-2011  
Cs137-2-4-2011  
I131-16-3-2011  
I131-2-4-2011  
2500  
2000  
1500  
1000  
500  
0
0
5000  
10000 15000 20000 25000 30000  
Number of simulated particles (particles/hour)  
Fig. 5. Dependence of MSE quantity on the number of simulated particles  
Figure 3,4 show the difference in  
simulation results of radioactive nuclide  
concentration of 137Cs and 131I with the number  
of simulated particles corresponding to 100,  
1000, 5000, 7500, 10000, 15000, 20000,  
25000, and 30000 particles/hour at 18:00 UTC  
on April 2nd,2011.  
Figure 5 shows the dependence of MSE  
quantities on the used number of simulated  
particles.  
26  
NGUYEN HAO QUANG et al.  
simulated particles used is greater than 10000  
particles/hour.  
C. Discussion  
From the results shown in Figure 5, it  
can be seen that the quantity of MSE decreases  
rapidly with increasing number of simulated  
particles used. But with the number of particles  
used greater than  
III. CONCLUSIONS  
The MSE quantity can be used as a  
measure of the difference in the simulation  
results of the concentration distribution of  
radionuclides when using different number of  
simulated particles. The results of the MSE  
quantity survey with different number of  
simulated particles show that with the number  
of simulated particles greater than 10000  
particles/hour the simulation results will not be  
much different from simulation results using  
the number of simulated particles being of  
30000 particles/hour. Therefore, in the case of  
limited computing resources, it is possible to  
use the number of simulated particles of 10000  
particles per hour to run the FLEXPART  
program to simulate the dispersion of  
radioactive nuclide.  
10000 particles/hour the quantity of  
MSE decreases slowly with increasing number  
of simulated particles used. Also in Figure 5, it  
can be seen that the magnitude of the MSE  
quantity for aerosol particle dispersion  
simulation (in the case of nuclide 137Cs ) is  
greater than the magnitude of the MSE  
quantity for gaseous particle dispersion  
simulation (in the case of nuclide 131I).  
However, this discrepancy decreases as the  
period of radiation release increases.  
In principle, the greater number of  
simulated particles will produce the more  
accurate simulation results of the concentration  
distribution of radionuclides. However,  
increasing the number of simulated particles  
leads to increasing the computation time and  
requires increasing computing resources. This  
poses the problem of determining the  
reasonable number of simulated particles to be  
used in such a way as to ensure the accuracy of  
the calculation results without requiring too  
much calculation resources. The MSE quantity  
can be used as a measure of the difference in  
the concentration distributions of radionuclides  
at a given time when comparing the results of  
the calculation of that distributions using  
various number of simulated particles. From  
the results shown in Figure 5, it can be seen  
that when the number of simulated particles  
used is greater than 10000 particles/hour the  
difference of MSE quantity is not much. Figure  
3,4 also show that the concentration  
distribution of radionuclides 137Cs and 131I are  
difficult to distinguish when the number of  
The authors thank the KC.05.07 / 16-20  
program for funding this research.  
REFERENCE  
[1]. [1] S. Schwere, A. Stohl, and M. W. Rotach,  
“Practical considerations to speed up  
Lagrangian stochastic particle models,”  
Comput. Geosci., vol. 28, no. 2, pp. 143–154,  
Mar. 2002.  
[2]. [2] C. Maurer et al., “International challenge  
to model the long-range transport of  
radioxenon released from medical isotope  
production to six Comprehensive Nuclear-  
Test-Ban Treaty monitoring stations,” J.  
Environ. Radioact., Mar. 2018.  
[3]. [3] “How-To:  
Python  
Compare  
Two  
Images.”  
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https://www.pyimagesearch.com/2014/09/15/p  
ython-compare-two-images/  
27  
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