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

Technology, 179 Hoang Quoc Viet, Ha Noi, Viet Nam 
3
Nuclear 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 
137
Cs 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. 
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 
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 
EFFECTS OF NUMBER OF SIMULATED PARTICLES ON THE UNCERTAINTY IN 
22 
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 
137
Cs and 
131
I 
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, 
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 
137
Cs and 
131
I emitted during 
the Fukushima nuclear power plant accident 
from 15:00 UTC on March 11
st
,2011 to 0:00 
UTC on April 20
th
,2011 with number of 
simulated particles being of 100, 1000, 5000, 
7500, 10000, 15000, 20000, 25000, and 
30000 particles/ hour. Radioactive nuclide 
137
Cs has the aerosol form and radioactive 
nuclide 
131
I has the gaseous form. The 
simulation results for dispersion of the 
radionuclides 
137
Cs and 
131
I 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 
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: 
∑ ∑ [ ( ) ( )] 
 (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. 
NGUYEN HAO QUANG et al. 
23 
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) 
Starting time Ending time Calculated time 
(minute) 
100 16/01/19 3:31 16/01/19 10:18 407 
1000 16/01/19 3:39 17/01/19 0:48 1268 
5000 12/11/18 2:32 14/11/18 14:08 3575 
7500 12/11/18 2:39 14/11/18 23:08 4108 
10000 12/11/18 4:12 15/11/18 17:12 5099 
15000 15/11/18 4:25 20/11/18 3:12 7126 
20000 15/11/18 10:06 21/11/18 19:12 9186 
25000 22/11/18 2:56 30/11/18 8:12 11836 
30000 22/11/18 8:06 03/12/18 10:12 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 
137
Cs and 
131
I 
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 
137
Cs and 
131
I through MSE 
quantity are shown in Table II. 
Table II. MSE of the concentration distribution of radionuclides 
137
Cs and 
131
I 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 16
th
,2011. 
Simulated particles 
(particles/hour) 
MSE of the concentration distribution of 
137
Cs and 
131
I at 11:00 UTC on 
March 16
th
 2011 
137
Cs 
131
I 
100 473,3 182,8 
1000 237,4 90,1 
5000 131,3 49,7 
7500 93,2 35,2 
10000 91,4 34,5 
15000 77,0 29,0 
20000 74,7 28,1 
25000 73,0 27,5 
EFFECTS OF NUMBER OF SIMULATED PARTICLES ON THE UNCERTAINTY IN 
24 
Table III. MSE of the concentration distribution of radionuclides 
137
Cs and 
131
I 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 2
nd
,2011. 
Simulated particles 
(particles/hour) 
MSE of the concentration distribution of 
137
Cs and 
131
I at 11:00 UTC on 
April 2
nd
,2011 
137
Cs 
131
I 
100 3906,4 4055,2 
1000 1264,5 1256,0 
5000 466,0 457,6 
7500 363,2 356,3 
10000 312,6 306,5 
15000 248,5 243,6 
20000 226,4 222,2 
25000 217,2 213,3 
Figure 1,2 show the difference in 
simulation results of radioactive nuclide 
concentration 
137
Cs and 
131
I with the 
number of simulated particles 
corresponding to 100, 1000, 5000, 7500, 
10000, 15000, 20000, 25000 and 30000 
particles/hour at 11:00 UTC on March 
16
th
,2011. 
Fig. 1. Simulation results of the radionuclide concentration of 
137
Cs according to the number of simulated 
particles at 11:00 UTC on March 16
th
,2011. 
NGUYEN HAO QUANG et al. 
25 
Fig. 2. Simulation results of the radionuclide concentration of 
131
I according to the number of simulated 
particles at 11:00 UTC on March 16
th
,2011. 
Fig. 3. Simulation results of the radionuclide concentration of 
137
Cs according to the number of simulated 
particles at 18:00 UTC on April 2
nd
,2011. 
EFFECTS OF NUMBER OF SIMULATED PARTICLES ON THE UNCERTAINTY IN 
26 
Fig. 4. Simulation results of the radionuclide concentration of 
131
I s according to the number of simulated 
particles at 18:00 UTC on April 2
nd
,2011. 
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 
137
Cs and 
131
I 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 2
nd
,2011. 
Figure 5 shows the dependence of MSE 
quantities on the used number of simulated 
particles. 
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 5000 10000 15000 20000 25000 30000
M
S
E
Number of simulated particles (particles/hour) 
Cs137-16-3-2011
Cs137-2-4-2011
I131-16-3-2011
I131-2-4-2011
NGUYEN HAO QUANG et al. 
27 
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 
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 
137
Cs ) is 
greater than the magnitude of the MSE 
quantity for gaseous particle dispersion 
simulation (in the case of nuclide 
131
I). 
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 
137
Cs and 
131
I are 
difficult to distinguish when the number of 
simulated particles used is greater than 10000 
particles/hour. 
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. 
The authors thank the KC.05.07 / 16-20 
program for funding this research. 
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