# The ESTE Decision Support System for Nuclear and Radiological Emergencies: Atmospheric Dispersion Models

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Atmospheric Dispersion Models in ESTE

#### 2.1. Lagrangian Particle Model: Specific Set-Up Assumptions in ESTE

_{i}(t + ∆t) = x

_{i}(t) + U

_{i}.∆t + u

_{i}.∆t

_{i}as the i-th component of (x

_{1},x

_{2},x

_{3}) specifies the position of the particle (at the times t and t + Δt), ∆t is the time step, U

_{i}as the i-th component of (U

_{1},U

_{2},U

_{3}) is the velocity vector of the mean wind field at the given position (x,y,z), and (u

_{1},u

_{2},u

_{3}) is the turbulent component of velocity vector. The mean wind field is included in the provided numerical weather-prediction data (NWP data) directly. The LPM model of the ESTE system requires NWP data for its run. The model is able to apply various sources of NWP data; for example, data from the European Centre for Medium-Range Weather Forecasts (ECMWF), or data from the National Weather Service of the National Oceanic and Atmospheric Administration, USA (NWS/NOAA). The turbulent component of velocity vector is expressed using Langevin equation [9].

_{i}= a

_{i}(x,u,t) dt + b

_{ij}(x,u,t)dW

_{j}

_{j}is incremental components of a Wiener process, here a Gaussian random variable. The LPM implemented in ESTE is based on a theoretical description of the FLEXPART model [10], and therefore both drift and diffusion terms obtain the form as in the FLEXPART model [10].

^{17}Bq as estimated by ESTE, based on a reverse estimation from the dose rate measured in the area of the nuclear power plant (NPP), and on assumption of partial core damage or partial melting in SFP [12]). The release was modeled from March 12 to 14, 2011. The results of dispersion and radiological impacts are visualized in subsequent days, from March 15 to March 30, 2011. The control forecast of the operational archive of the ECMFW data was applied. A basic estimate resulting from the simulation is that the airborne contamination would reach the central Europe approximately on March 24, 2011. For a comparison, the first reported measurement of I-131 in the Czech Republic was on March 23 [13], which represents an acceptable result.

_{d}(in m.s

^{−1}), which is specified for various types of airborne material (e.g., gases, aerosols, iodine forms) and ground features (e.g., urban, forest, water). Deposited material in time step Δt is then calculated as:

_{d}Δt/h))

_{wo}I.

_{wo}is the coefficient of wet deposition, and is set to c

_{wo}= 1.3 × 10

^{−4}s

^{−1}for elemental iodine, c

_{wo}= 1.3 ×10

^{−6}s

^{−1}for organic iodine, and c

_{wo}= 2.6 × 10

^{−5}s

^{−1}for all radionuclides in aerosol form. The deposited material in time step Δt is assumed to follow the formula:

_{inhal}and the integral dose D

_{inhal}are calculated as:

_{inhal}(n) = C

_{0}(n) CF

_{inhal}(age,n) BR(age)

_{inhal}(n) = C

_{int}(n) CF

_{inhal}(age,n) BR(age)

_{0}is the actual air concentration, C

_{int}is the time-integrated concentration in the bottom reference layer for radionuclide n, BR is the breathing rate, depending on the age category, and CF

_{inhal}is the conversion factor for the committed effective dose for inhalation, depending on the age and nuclide.

_{depo}(n) = D

_{0}(n) CF

_{depo}(n)

_{0}(n) is the deposition of radionuclide n on the terrain, CF

_{depo}is the conversion factor for the external dose via deposition, as a function of radionuclide.

_{cloud}(n) = C

_{0}(n) CF

_{cloud}(n)

_{0}(n) is the air concentration in the bottom reference layer, and CF

_{cloud}is the conversion factor for cloudshine, and dependent on the radionuclide. The factors represent an approach of semi-infinite cloud of constant concentration, i.e., the point of interest, either a radiation monitor or a human, is immersed in the activity of the air hemisphere with constant concentration.

#### 2.2. Puff Trajectory Model

#### 2.3. Dispersion in Urban or Industrial Area

^{2}and a non-flat surface, a specific implementation of the Lagrangian Particle Model was applied in ESTE. The procedure is analogous to mesoscale calculations (see Section 2.1). Two potential examples of situations and events considered as cases for application of radiological impacts calculation in an urban area are: accidental releases within the area of a nuclear power plant, or application of a radiological dispersal device (dirty bomb) in an inhabited urban area (e.g., city centers).

_{i}is the acceleration due to gravity, and R

_{ij}is the Reynolds stress tensor, representing the turbulent fluctuations.

- Category stability, for which three cases are taken into account: unstable weather conditions (in that case, the vertical profiles on the boundaries for the calculated fields were specified by Monin–Obukhov length, L = 100 m), neutral weather conditions (L = infinity) and stable weather conditions (L = −100 m).
- Wind direction: taking into account 36 different wind directions (with a uniform step of 10°). The wind direction specifies direction of the wind entered into the meteorological field calculation as a boundary condition.
- Wind speed: taking into account 40–50 values of wind speed (depending on the stability category), ranging from low wind speed of about 0.2 m/s to 9 m/s (stable weather), to 25 m/s (neutral and unstable weather). The wind speed means the wind rate at the height of 10 m in the specification of the boundary condition for calculation of the meteorological fields.

_{i}in (1) represents the random walk term of the wind. The diffusion term in Equation (2) obtains a simple form:

_{ij}= (C ε dt)

^{1/2}δ

_{ij}

_{ij}is Kroneker delta. The drift term from Equation (2) is calculated as the Thompson’s simplest solution for diffusion in three dimensions. It is a function of the Reynolds stress tensor τ, another outcome of Equation (11), but it is more technical, therefore for more details we refer to [9,20]. This approach is implemented in several other urban dispersion models as well, e.g., the QUICPLUME model [21].

_{dd}on a surface is calculated using a similar approach as described above in (2), except for the inclusion of the surface orientation parameter c

_{so}:

_{dd}= C

_{0}ν

_{d}c

_{so}.

_{so}for aerosols is equal to 1 if the surface normal is vertical, and it is equal to 0.1 if the surface normal is oriented horizontally [22,23]. C

_{0}is the air concentration in the particular cell whose surfaces are considered as they undergo contamination by deposition. The evaluation of wet deposition takes into account all cells above the particular horizontal surface, but the vertical surfaces are assigned as zero wet deposition.

_{inhal}and the integral dose D

_{inhal}for a particular cell are calculated using Equations (5) and (6), but with C

_{0}as the actual air concentration in the given cell and C

_{int}as the time-integrated concentration in that cell.

_{cloud}(i) = ∑_j C

_{0}(j) CF

_{cloud}(i,j) SF(i,j)

_{0}(j) is the air concentration in the contributing cell, SF is shielding factor (equal to 1 if there is no building along a straight line between the cell centers of i and j, and equal to 0 if there is a building), CF

_{cloud}is the conversion factor for cloudshine, as a function of the nuclide and of the distance between cell centers i and j.

_{depo}(i) = ∑_j D

_{0}(j) CF

_{depo}(i,j) SF(i,j)

_{0}(j) is the deposit on the contributing cell. SF is shielding factor (equal to 1 if there is no building along a straight line between the cell centers of i and j, and equal to 0 if there is a building), CF

_{depo}is the conversion factor for the external dose via deposition, as a function of the nuclide and of the distance between cell centers i and j. The factors CF

_{cloud}and CF

_{depo}are prepared as a precalculated library (prepared by calculation using MCNP code version 5 [24]), for various distances between the cells and various cell sizes.

^{15}Bq of Cs-137 from the roof of the reactor building. Shown is the deposit on all surfaces (buildings and ground), the effective dose rate corresponding to this deposit, the effective dose rate from the cloud during the duration of the release, and the committed effective dose by inhalation. Doses and dose rate were calculated for ground cells.

## 3. Analysis and Discussion of Calculation Settings for LPM in Mesoscale Impacts

^{15}Bq of Cs-137, beginning at 10:00 (UTC) on November 9 and lasting 1 h. The size of the release was chosen to obtain non-negligible radiological impacts, but the choice of the size itself had no qualitative impact on the studied aspects. The southern wind was predominant during the hypothetical release, and there were slightly rainy conditions during the atmospheric transport phase, so dry and wet deposits were present in the modeled calculations. The height of the release point was set to 80 m above ground. The applied meteorological data were the numerical weather-prediction data as predicted by ECMWF for 9–16 November 2020. The dispersion in the atmosphere and the radiological impacts up to seven days from the release time were modeled.

- Point1—the village of Nižná, Slovakia, located about 4 km from the release location.
- Point2—the village of Prašník, Slovakia, located about 17 km from the release location.
- Point3—the village of Strání, Czech Republic, located about 45 km from the release location.
- Point4—the town of Valašské Meziříčí, Czech Republic, located about 110 km from the release location.
- Point5—Warsaw, Poland, located about 480 km from the release location.
- Point6—Rovno, Ukraine, located about 665 km from the release location.

#### 3.1. Total Number of Modeled Particles

#### 3.2. LPM: Initial Spatial Distribution of Released Particles

#### 3.3. LPM: Height of the Bottom Reference Layer of Air

## 4. Conclusions

## Supplementary Materials

^{15}Bq of Cs-137 from Bohunice NPP at 10:00 UTC on 9 November 2020. Evolution of total deposits over time on the map of Europe in time steps: 8 h, 16 h, 24 h, 2 days, 3 days, 4 days, 5 days, 6 days, and 7 days from the time of release; Video S2: Ground deposits of Cs-137 as a result of the release of 1 × 10

^{15}Bq of Cs-137 from Bohunice NPP at 10:00 UTC on 9 November 2020. Evolution of wet deposits over time on the map of Europe in time steps: 8 h, 16 h, 24 h, 2 days, 3 days, 4 days, 5 days, 6 days, and 7 days from the time of release; Video S3: The Fukushima Dai-ichi catastrophe, radiological impacts to Central Europe modeled by the LPM of ESTE. Time integral of air concentration (TIC) of I-131 in the bottom layer of the atmosphere up to the 16 days from the beginning of release. The blue color represents particles dispersed from Fukushima in all levels of the atmosphere—from the terrain up to >5 km above the terrain.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Example of an impact calculation for an urban environment—a release from the reactor building of the Mochovce NPP is simulated). Deposit on surfaces (

**top left**), and effective dose rate from deposition (

**top right**), from cloud (

**bottom left**), and by inhalation (

**bottom right**) are shown.

**Figure 3.**Trajectories, i.e., integrated paths, of the wind field for the initial point of the Bohunice NPP, at 10:00 UTC, 9 November 2020, for three various heights—100 m (blue line), 500 m (green line), and 1500 m (red line) above terrain. The locations of the six studied points are also shown.

**Figure 4.**Total ground deposit of Cs-137 in +7 days from the time of release. The deposit is a result of the release of 1 × 10

^{15}Bq of Cs-137 from Bohunice NPP, at 10:00 UTC on 9 November 2020.

**Figure 5.**Wet deposit of Cs-137 in +7 days from the time of release. The deposit is a result of the release of 1 × 10

^{15}Bq of Cs-137 from Bohunice NPP, at 10:00 UTC on 9 November 2020.

**Table 1.**List of isotopes significant in radiological-impact calculations in case of events in a nuclear facility and applied in ESTE models.

Kr85m | Sr89 | Zr95 | Ru105 | Te127 | I132 | Xe133 | Cs137 | Ce143 | Pu241 |

Kr85 | Sr90 | Zr97 | Ru106 | Te129m | I133 | Xe135 | Cs138 | Ce144 | |

Kr87 | Sr91 | Nb95 | Rh103m | Te129 | I134 | Xe135m | Ba140 | Np239 | |

Kr88 | Y90 | Mo99 | Rh105 | Te131m | I135 | Xe138 | La140 | Pu238 | |

Rb86 | Y91m | Tc99m | Sb127 | Te132 | Xe131m | Cs134 | Pr143 | Pu239 | |

Rb88 | Y91 | Ru103 | Sb129 | I131 | Xe133m | Cs136 | Ce141 | Pu240 |

**Table 2.**The applied Briggs sigma function σ (L) for the horizontal Gaussian model, where L is the travel length.

Stability Category | Sigma Function for Urban Condition | Sigma Function for Rural Condition |
---|---|---|

A | σ (L) = 0.32 × L × (1 + 0.0004 × L)^{−1/2} | σ (L) = 0.22 × L × (1 + 0.0001 × L)^{−1/2} |

B | σ (L) = 0.22 × L × (1 + 0.0004 × L)^{−1/2} | σ (L) = 0.16 × L × (1 + 0.0001 × L)^{−1/2} |

C | σ (L) = 0.22 × L × (1 + 0.0004 × L)^{−1/2} | σ (L) = 0.11 × L × (1 + 0.0001 × L)^{−1/2} |

D | σ (L) = 0.16 × L × (1 + 0.0004 × L)^{−1/2} | σ (L) = 0.08 × L × (1 + 0.0001 × L)^{−1/2} |

E | σ (L) = 0.11 × L × (1 + 0.0004 × L)^{−1/2} | σ (L) = 0.06 × L × (1 + 0.0001 × L)^{−1/2} |

F | σ (L) = 0.11 × L × (1 + 0.0004 × L)^{−1/2} | σ (L) = 0.04 × L × (1 + 0.0001 × L)^{−1/2} |

**Table 3.**Deposit of Cs-137, seven days from the beginning of the release of 1 × 10

^{15}Bq, in various points as a function of the number of particles modeled. (a) Dry deposit, [Bq/m

^{2}], and ratio to dry deposit in the case of 1,000,000 particles; (b) Wet deposit, [Bq/m

^{2}], and ratio to wet deposit in the case of 1,000,000 particles.

Number of Particles | Point2 | Point3 | Point4 | Point5 | Point6 |
---|---|---|---|---|---|

(a) | |||||

25,000 | 4.3 × 10^{4}/0.93 | 5.7 × 10^{4}/0.98 | 7.8 × 10^{3}/0.95 | 1.2 × 10^{3}/1.23 | 1.6 × 10^{0}/0.23 |

100,000 | 4.8 × 10^{4}/1.03 | 5.8 × 10^{4}/1.00 | 8.1 × 10^{3}/0.99 | 1.0 × 10^{3}/1.06 | 7.8 × 10^{0}/1.15 |

250,000 | 4.7 × 10^{4}/1.01 | 5.9 × 10^{4}/1.02 | 8.1 × 10^{3}/0.99 | 9.7 × 10^{2}/1.02 | 3.5 × 10^{0}/0.51 |

1,000,000 | 4.6 × 10^{4}/1.00 | 5.8 × 10^{4}/1.00 | 8.2 × 10^{3}/1.00 | 9.5 × 10^{2}/1.00 | 6.8 × 10^{0}/1.00 |

(b) | |||||

25,000 | 8.8 × 10^{3}/1.03 | 1.6 × 10^{5}/1.00 | 3.2 × 10^{4}/0.96 | 6.8 × 10^{1}/1.08 | 1.3 × 10^{0}/0.08 |

100,000 | 8.5 × 10^{3}/0.99 | 1.5 × 10^{5}/0.99 | 3.3 × 10^{4}/0.99 | 6.8 × 10^{1}/1.07 | 7.7 × 10^{0}/0.49 |

250,000 | 8.6 × 10^{3}/1.00 | 1.6 × 10^{5}/1.00 | 3.3 × 10^{4}/0.99 | 6.4 × 10^{1}/1.01 | 1.5 × 10^{1}/0.94 |

1,000,000 | 8.6 × 10^{3}/1.00 | 1.6 × 10^{5}/1.00 | 3.4 × 10^{4}/1.00 | 6.3 × 10^{1}/1.00 | 1.6 × 10^{1}/1.00 |

**Table 4.**Deposit of Cs-137, seven days from the beginning of the release of 1 × 10

^{15}Bq, in various points, as a function of initial spatial distribution of the source. Dry deposit, [Bq/m

^{2}], and ratio to dry deposit in case of point source at 80 m.

Spatial Distribution of the Source | Point1 | Point2 | Point3 | Point4 | Point5 |
---|---|---|---|---|---|

point at 80 m | 4.4 × 10^{5}/1.00 | 1.0 × 10^{5}/1.00 | 5.9 × 10^{4}/1.00 | 8.1 × 10^{3}/1.00 | 9.7 × 10^{2}/1.00 |

line with 80 ± 20 m | 3.9 × 10^{5}/0.88 | 1.0 × 10^{5}/1.01 | 5.8 × 10^{4}/0.98 | 8.1 × 10^{3}/1.00 | 9.6 × 10^{2}/0.99 |

line with 125 ± 20 m | 3.2 × 10^{5}/0.73 | 1.0 × 10^{5}/1.04 | 6.1 × 10^{4}/1.03 | 8.5 × 10^{3}/1.05 | 1.0 × 10^{3}/1.08 |

line with 35 ± 10 m | 4.3 × 10^{5}/0.97 | 1.0 × 10^{5}/1.00 | 5.7 × 10^{4}/0.97 | 8.1 × 10^{3}/1.00 | 9.4 × 10^{2}/0.97 |

**Table 5.**Deposit of Cs-137, seven days from the beginning of the release of 1 × 10

^{15}Bq, in various points, as a function of the height of the bottom layer of air. Dry deposit, [Bq/m

^{2}], and ratio to dry deposit in the case of a 100 m layer.

Bottom Layer of Air | Point1 | Point2 | Point3 | Point4 | Point5 |
---|---|---|---|---|---|

100 m layer | 4.4 × 10^{5}/1.00 | 4.7 × 10^{4}/1.00 | 5.9 × 10^{4}/1.00 | 8.1 × 10^{3}/1.00 | 9.7 × 10^{2}/1.00 |

50 m layer | 4.1 × 10^{5}/0.94 | 4.5 × 10^{4}/0.97 | 5.7 × 10^{4}/0.97 | 8.1 × 10^{3}/1.00 | 8.8 × 10^{2}/0.91 |

25 m layer | 4.2 × 10^{5}/0.95 | 4.6 × 10^{4}/0.98 | 5.6 × 10^{4}/0.95 | 8.2 × 10^{3}/1.01 | 8.5 × 10^{2}/0.88 |

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**MDPI and ACS Style**

Lipták, Ľ.; Fojcíková, E.; Krpelanová, M.; Fabová, V.; Čarný, P. The ESTE Decision Support System for Nuclear and Radiological Emergencies: Atmospheric Dispersion Models. *Atmosphere* **2021**, *12*, 204.
https://doi.org/10.3390/atmos12020204

**AMA Style**

Lipták Ľ, Fojcíková E, Krpelanová M, Fabová V, Čarný P. The ESTE Decision Support System for Nuclear and Radiological Emergencies: Atmospheric Dispersion Models. *Atmosphere*. 2021; 12(2):204.
https://doi.org/10.3390/atmos12020204

**Chicago/Turabian Style**

Lipták, Ľudovít, Eva Fojcíková, Monika Krpelanová, Viera Fabová, and Peter Čarný. 2021. "The ESTE Decision Support System for Nuclear and Radiological Emergencies: Atmospheric Dispersion Models" *Atmosphere* 12, no. 2: 204.
https://doi.org/10.3390/atmos12020204