The document summarizes a study that used the Gaussian dispersion model AERMOD to track the spread of radioactive material released during the Fukushima Daiichi nuclear disaster. The model used meteorological data from the area and information about the explosions to determine concentration levels of iodine-131 and cesium-137 within 24 hours. The results showed higher initial concentrations declining over time, and directionality of the plume toward the northwest. This could help inform short-term evacuation planning, though the model had limitations due to assumptions where data was unavailable.

1. Gaussian Dispersion Modeling: Tracking the Effect of
the Fukushima-Daiichi Nuclear Disaster
Authors: Cedric McCall and Michael Schulz
May 6, 2011

2. Problem Statement
Reactor 1 of the Fukushima-Daiichi Nuclear facility was heavily damaged in the March, 2011
earthquake and tsunami that devastated the country of Japan. The cooling system of the reactor
failed due to power loss which allowed for the possibility of a nuclear meltdown. Over the next
few days after the earthquake, engineers and emergency personnel wrestled with the cooling of
the reactor. On March 12 near 6 am a Hydrogen explosion occurred on the reactor containment
vessel of reactor 1. This explosion resulted in the release of radioactive material into the
atmosphere. Three more subsequent Hydrogen explosions occurred to other reactors culminating
in the final explosion in reactor #4 on March 15 near 6 am [3].
This study looks at the effect of the released material on the area around the plant. A
Gaussian dispersion modeling program, AERMOD, was used to determine the 24 hour
concentration profile following the release in the form of time-averaged isopleths.
Meteorological data of the area was used along with correlations to find surface, lower
atmosphere, and upper atmosphere profiles which will be needed for the model.
Literature Review
The Fukushima-Daiichi Nuclear facility was reliant on backup diesel generators in the
case of the loss of electricity from the main power grid. The turbines powered by the nuclear
reactors were automatically shut down as the result of the earthquake. Additionally, loss of
power from the main power grid occurred. The diesel generators then began providing
electricity needed for operation of the cooling system. In its current state, the plant was in no
imminent danger [1].

3. The arrival of the tsunami led to flooding of the diesel generators and subsequent loss of
AC power which placed he plant was now in blackout. The stations cooling system was steam
driven so it only required DC power (batteries) for operation. However, if DC power was lost
before AC power could be restored the plant would be in imminent danger of meltdown. This is
because no water is being cycled in and water levels
maintained to cover the spent rods to keep them sufficiently
cooled [1].
Figure 1 shown above illustrates the Mark I
containment system used at the Fukushima-Daiichi unit 1
reactor. The vessel has both a primary and secondary
containment system. As pressure in the primary system
builds gas can be vented to the secondary system. As the
pressure in secondary system (drywell) rises, gas can be
vented through a series of filters into the atmosphere. This
venting occurs as a regular daily process in the plant. No
significant quantities of radiation are released in normal
operation during this process [2].
The reactor rods responsible for the fission process became exposed to air due to the
malfunctions and loss of power in the cooling system and decreased water levels in the fuel rod
containment vessels. This allowed the previously shut-down fission process to begin anew. The
radioactive decay of the spent fuel rods began to sensibly heat the water, eventually providing
the latent heat to turn it to steam. The decreased water levels meant that the exposed zircon-alloy
fuel rods began reacting with the steam and evolving Hydrogen. The gas began accumulating
Figure 1: Mark 1 containment system [2]

4. inside the secondary containment by leaking through bolt fittings loosened on the wall of the
primary containment system as the temperature inside that containment vessel rose. The
Hydrogen exploded in the secondary containment vessels once it reached its auto-ignition
temperature and lower flammability limit [1].
A release of a significant amount of radioactive material can come only as the result of a
partial or a complete meltdown; because of the lack of cooling water covering the fuel rods. The
contact with gas instead of cooling water allows a buildup of heat in the fuel rod due to smaller
heat transfer away from the rods. A meltdown may occur within an hour of becoming exposed
to air. When the zirconium plating of the fuel rod becomes hot enough, it will begin to burn and
the fuel rod will begin to meltdown. Significant levels of radiation will be emitted into the gas of
the containment vessel [1].
The majority of the radioactive elements released into the atmosphere were Cesium-137
and Iodine-131. These elements have a half-life of 30.23 years and 8 days respectively. This
shows that they will have a lasting effect in the affected area over the ensuing decades. There is
also evidence of several other radioactive elements such as Plutonium and Uranium from MOX
reactor #4, and Cesium-134, created as a fission product from reactor core meltdown, detected in
the area but are in insignificant amounts as compared to Cesium-137 and Iodine-131[3].
Methodology
The EPA Aermod modeling program requires three input files along with the executable
file all placed in the same subdirectory to run successfully from the Command Prompt screen.
The input Aermod run-stream file, meteorological data file, and stratospheric profile data set
each must be created as .txt files according to the format provided in the users’ manual for the

5. Aermod program and its complementary software that generates the meteorological and
stratospheric data files, respectively.
The Aermod run-stream file consists of the programming language needed to execute the
software. It was determined that it was easiest to amend the run-stream file from another test
case to our purpose to minimize programming error. The program was asked to provide
predetermined hourly maximum concentration data and data used to generate time-averaged
concentration isopleths after each run. Contour plots were then made in Matlab. Three different
excel files that held information on locations in the x and y planes, respectively, along with the
concentration at those locations are needed before entering the programming code needed to
generate the contour plot.
Aermod requires the input of specific meteorological parameters which are outlined in
the Aermet users’ manual. These can only be determined from raw meteorological data of the
appropriate time frame supplied by the weather station servicing the location under survey.
Hourly observations containing data on wind speed and direction, temperature, barometric
pressure, relative humidity, precipitation rate, and cloud cover will be the basis for the
meteorological parameter calculations needed to operate the model. NOAA does not report on
conditions in other countries, so raw data was taken from www.wunderground.com and the
meteorological parameters were calculated in Excel before being saved as .txt files. A Mathcad
program was used to calculate the frictional velocity and Monin-ubokhov length by an iterative
process as it is necessary for unstable atmospheric conditions. The net radiation was calculated
with data from NOAA website. The data was modeled over a 24 hour period beginning with the
time of the last hydrogen explosion.

6. The stratospheric profile dataset models how the upper atmosphere contributes to the
dispersion of pollutants once they rise above the mixing height of the lower atmosphere. The
group was not able to generate a stratospheric profile dataset of its own and was forced to amend
the dates of a dataset used in a different test case since the stratosphere does not behave very
differently from one location to another.
There were certain assumptions made in the creation of the Fukushima-Daiichi model test
case. The software will model pollutant dispersion over flat terrain with no buildings in the
model domain that would cause stack downwash. The Fukushima-Daiichi power plant is located
at sea level on the northeastern Japanese coastal plain in and around the town of Futaba. No
building measurements were available.
The radiation release event is modeled as a point source with the spent fuel containment
vessels of the power plant taken as the origin of the coordinate system. Some default source
parameters had to be used such as emission rate, source height, and exit velocity because those
values were not reported in the literature yet. The Fukushima disaster update website setup by
the IAEA did report that two large eight meter square holes were located on the upper wall of the
containment vessel to reactor four after it suffered the last of the hydrogen explosions that hit the
power plant [3]. This was modeled as one large circular hole of the same area. The diameter of
the area of the combined hole was then determined. The exit temperature that was used was
taken to be that of the auto-ignition temperature of Hydrogen at its lower flammability limit, both
found on a MS-data sheet, since no spark sources are located within the containment vessels.
The radioactive elements under survey for this model are Iodine-131, and Cesium-137
which are the primary elements being reported in the literature and in the news updates on the
IAEA nuclear accident update website. The team had to use data for morning and afternoon

7. mixing heights from a corresponding location in the United States that was also located on the
coast. This is because there was no isopleth data over Japan available. San Jose, California, a
coastal town of similar latitude was used as an estimate of similar conditions.
The Fukushima Daiichi nuclear disaster is in its second month of continuous radiation
emissions. The team decided to start the model on March 15, 2011 at 6 am because that is the
time when the last of four hydrogen explosions occurred at the facility and the model
subsequently carries on for only twenty-four hours afterwards.
Results
Below are tables that give values of average maximum pollutant concentration as a function
of time and distance that were generated by the software for each pollutant.
Table 1 Iodine-131 average maximum concentration, μg/m^3
Dist, m 175 350 500 1000 Dir, ̊
hr
3 0.04176 0.13048 0.16543 0.15700 120
6 0.02505 0.07829 0.09926 0.09420 120
12 0.01392 0.04349 0.05514 0.05233 120
24 0.00835 0.02610 0.03309 0.0314 120
Period 0.12527 0.39144 0.49629 0.47099 120

8. Table 2 Cesium-137 average maximum concentration, μg/m^3
Dist, m 175 350 500 1000 Dir,̊
hr
3 0.00027 0.01673 0.05650 0.21004 120
6 0.00016 0.01004 0.03390 0.12602 120
12 0.00009 0.00558 0.01883 0.07001 120
24 0.00005 0.00335 0.01130 0.04201 120
Period 0.00081 0.05018 0.16950 0.63012 120
These tables show the same general trend in both runs. The concentration is at its highest
initially and declines with increasing time, as expected. Also, the average maximum
concentration is increasing with increasing distance from the source for both irradiating species.
However, for Iodine-131, the trend reaches a maximum around 500 meters from the source
before the concentration starts declining. The average maximum concentration values in both
tables all correspond to the same direction of 120̊. This means that the fallout plume has
directionality to it instead of evenly dispersing in all directions. This means that the population
living in the direction of the plume’s advance would receive greater radiation exposure in the
short term. These affected areas should receive the highest initial evacuation priority by the
authorities. Most of the concentration data was not evenly dispersed away from the source.
Concentration data for Iodine-131 is found mostly between 80-160̊, with the highest
concentration always falling on the centerline of that range, 120̊. There is an even tighter range
for Cesium-137 with most of the data falling in the range of 90-150̊, also with a centerline at 120̊.
The difference in magnitudes of the concentration values of both irradiating species could most

9. likely be due to the amount of each present at the facility prior to the explosion and not a
function of their respective half-lives. Cesium-137 has a much longer half-life than Iodine-131
so it should be in higher concentrations if equal amounts of both species were released after the
explosions.
A contour map was generated from the output data from the Aermod program. This map is
shown below.
Figure 1: Contourmap of Iodine-131

10. The contour map for Cesium-137 was identical because the program does not take into account
molecular weights for process modeling. The numbers indicated in the contour map are
respective to the quantity released at the explosion source. The contour plot confirms the
directionality of the plume trending to the Northwest. This allows a rough short term estimate of
the area around the plant that is in most need of evacuation. The plot is not accurate enough for
regulatory purposes since it did not model stack downwash, and important variables such as
emission rate, exit velocity, concentration, and source height have not been determined and
reported in the literature.
This study recommends a 24 hour evacuation area of at least 1 kilometer away from the
blast zone. Japanese authorities had previously ordered an evacuation of anyone living within 2
kilometers and subsequent to the explosion this evacuation was enlarged to 20 kilometers from
within the blast zone [2]. US authorities issued travel advisories to US citizens travelling within
the area of larger bounds. Over 1 km2 was significantly contaminated. Steps should also be
implemented to help minimize the effects of radioactive fallout on those most affected by
supplying personal protective equipment like aspirators, protective clothing, housing people in
fallout shelters and providing medications to minimize the amount of radiation being absorbed
by the body. The group realizes that not all of these measures are possible because of the sheer
amount of people affected but no expense should be spared when it comes to mitigating disaster
and saving human lives.
Conclusions
For the purposes of this exercise, the model does provide a good indication of plume
directionality over the initial 24 hours after the last hydrogen explosion in order to determine an

11. evacuation plan; however, this model is not yet reliable for regulatory use. The accident is yet to
be contained so too many assumptions were made due to the dearth of information available.
This model could be improved by incorporating differences in the pollution species emitted. The
only input of the pollution characteristics is its half-life. Also, this exercise is limited to the last
explosion which occurred in reactor #4 for two reasons. It is the only major radiation release
event for which any data could be found to determine critical model parameters needed to
execute the program; and, there were previous vessel breaches in other reactor vessels that
happened as early as 4 days prior to the timeframe under scrutiny. We aren’t aware of the
directionality of the prior radiation release events that would be critical in forming an evacuation
plan which is the primary purpose of this exercise. As a result this is an incomplete picture of
what has actually happened. Since the radiation release is ongoing, it is also unclear how much
area needs to be evacuated to further prevent loss of life.

12. Citations
[1] Union of Concerned Scientists
http://www.ucsusa.org/nuclear_power/nuclear_power_risk/safety/nuclear-reactor-crisis-faq.html
[2] The Japan Time Online. Kanako Takahara and Kazuaki Nagata, “High Radiation Found
Outside No-go Zone.”
http://search.japantimes.co.jp/cgi-bin/nn20110401a1.html
[3] IAEA Fukushima Nuclear Accident Update Log
www.iaea.org/newscentev/news/tsunamiupdate01.html (accessed daily)
[4] Wunderground
www.wunderground.com
Weather accessed for Iwaka, Japan for the day of the last explosion
[5] AIChE
www.aiche.org
For material safety data sheets
Appendix
fukumet.sfc fukuua.pfl