Atmospheric dispersion modelling and dose projection under high uncertainty conditions

Understanding the overall magnitude of the deviations that may occur within the results of one or more codes allows avoiding discrepancies in decision making in the context of emergency preparedness and response. The uncertainty of the assessment input data plays a significant role in this. Currently, emergency centers around the world use a number of atmospheric dispersion modelling and dose projection tools that have the same functionality, are used for the same purpose, but may produce different results. This article reveals the problem of uncertainty in the results of atmospheric dispersion modelling and dose projection, which are laid down at the stage of input data for actual software products and decision support systems. The paper lists the main factors that can affect the uncertainty of the assessment results. On the example of the JRODOS system, possible options for describing the source for the spectrum of emergency events at NPPs are considered. Special attention is paid to assimilation of radiation monitoring results and response to hostilities.


Introduction
Modern approaches to the emergency response to radiation accidents at nuclear facilities worldwide are coherent.They aim to prevent human losses and establish control over the source of releasing radioactive substances.Mechanisms and procedures for responding to similar accidents are not designed for casualties of a terrorist or military nature, taking into account the principle of peaceful use of atomic energy.The existence of software evaluation tools and decision-making support systems for population protection during radiation accidents is no exception.These tools are the most effective if they provide the full range of input parameters to run the models [1,2].However, the response procedures require decision-making based on incomplete data or within the scope of information currently available to the decision-maker in unforeseen conditions.
Today, world emergency centers use modern assessment tools such as the European ARGOS system [3] or the American regulatory RASCAL software complex [4].The development of a complex real-time decision support system for off-site response to radiation accidents RODOS has been actively supported and coordinated since the beginning of the 90s within the framework of the European Commission's scientific programs.The Java version of this system is called JRODOS [5].Currently, the further development of this product is continued.Its improved versions are periodically presented by the leading developer of JRODOS -Forschungszentrum Karlsruhe GmbH -on behalf of the JRodos Developers Consortium.It includes 15 institutions from different European countries.Since 2013 this system has been successfully used in the emergency centers of Ukrainian NPPs and regulatory body during emergency response measures for nuclear and radiological accidents.The JRODOS system consists of several mathematical models and databases for conducting predictive calculations on the consequences of possible radiation accidents and planning urgent and early countermeasures for protecting the public.This system is increasing the technical and strategic capabilities of responding to national and cross-border emergencies.The JRODOS models and databases can be adapted for different characteristics of the NPP location and geographical, meteorological, and environmental conditions.Using this system in a state of continuous arrival of numerical weather prediction data, timely information on the chronology and activity of the release allows prompt forecasting of radiological consequences on local and global spatial scales.

Uncertainties problem
Some decision support systems (DSS) have a flexible interface and allow to specify output data of the simulation in several ways.Variability of the data entry approach facilitates prompt response to incomplete information regarding the state of the affected object.The package of the primary input data includes source term data, meteorological conditions, calculation settings, and desired results list or their format.
Figure 1 presents the impact of uncertainties regarding the release under unstable meteorological conditions.Case zoes for taking immediate countermeasures for population protection in the case of a severe accident may differ significantly depending on the release moment.
The magnitude and radionuclides mixture are distinguished in addition to the chronological uncertainty of the temporal distribution of emissions.It may also differ significantly and depend on the initial activity of the dose-forming radionuclides in inventory.Currently, various views are considered in the framework of many international projects.This type of uncertainty can be significantly leveled at the stage of emergency preparedness by comparing existing approaches, such as [6], unlike the chronological one.
The World Meteorological Organization investigates uncertainties associated with the numerical data of the meteorological forecast [7].Some modern DSS allows analyzing of consequences of cases for several variants of meteorological conditions or source terms.Such studies make it possible e to determine the influence of the forecast quality on the final result.It includes zone configuration for the adoption of urgent countermeasures for population protection.In practice, comparative analysis of the calculation results obtained by various organizations is carried out mainly within the framework of international projects and less often within the framework of special emergency exercises.The work [8] contains a list of examples and approaches for comparing results obtained using different codes or DSS.

Radionuclide vector, physical and chemical forms
Radionuclide mixes and physicochemical forms of release depend on a complex of factors such as activity of radionuclides in the reactor core and spent fuel pool, features of safety systems, phenomenological stage of fuel damage, etc. Grouping by physico-chemical classes describes the behavior of radioactive vapor-gas mixture within containment.More generalized distribution of radionuclides by physico-chemical forms is also characteristic at the modeling stages of the Several mathematical models based on the processes of heat and mass transfer and aerodynamics are used to describe radionuclides transport in the closed emergency room of nuclear enterprises.These models are part of integrated calculation software products such as MELCOR [9], MAAP, CONTAIN, etc.These codes use analytical and numerical solutions, operating with empirical and semi-empirical relations.Transport of nuclear fuel fission products is described; the power and composition of the emission of radioactive substances from the premises of emergency objects into the atmosphere are calculated with the help of such tools.The leading representatives of integral codes of this group have a similar structure and cover the main stages of modeling the transport of radioactive substances in process rooms for most design and post-design accidents that are considered during the safety analysis of nuclear power plants.
For example, MELCOR [9] is an integrated computer code at the engineering level.It stimulates the severe accident at a nuclear power plant with light water reactors.This code was developed at Sandia National Laboratories for the US regulatory body.The International Atomic Energy Agency (IAEA) member countries, including Ukraine, actively use this code.MELCOR allows the simulation of a wide range of emergency processes at a nuclear facility.The code enables modeling the transport of fission products along with such processes as the thermal-hydraulic reaction of safety systems and adjacent structures, degradation and movement of fuel masses, the interaction of core melt with concrete of building structures, generation, transportation, and combustion of hydrogen, etc.The modeling basis with this code is a nodalization scheme.It is a spatial division of the power unit objects into separate volumes according to the principle of priority of this or that equipment/room contribution to the determining parameters of the emergency process.Thermal-hydraulic parameters within the same book at a particular moment are considered the same-chemical properties group MELCOR fission products.The behavior of chemical elements and their isotopes is regarded as the same within the same class.
There are the following ways of obtaining data on the radionuclide mix in a radioactive release: 1) receiving information from actual measurement points of releases control subsystem (vent stack); 2) use of the general JRODOS library for the formation of source term; 3) analytical assessments of source term according to the phenomenological stages of fuel damage.
The other two paths are preferred but not mandatory if the information provided by the first path is sufficient for the current calculations in the JRODOS system.During the shortage of information (whole or partial), using the two named ways of data formation is necessary.
Initial data for the source term estimating are data on reactor inventory, or data on the radionuclide vector and activity of the coolant, in the absence of more than normative damage to the occupied zone [10,11].Data from the JRODOS general library can be used to generate data.It should contain source term according to defined chronological stages: • coolant release; • gas gap release; • fission products release due to partial fuel damage of the reactor core; • fission products are released due to reactor core melting (in-vessel and ex-vessel phases).
Parameters of the release during accidents with different degrees of damage to the reactor core are determined by several chemical elements and the site of their release into the coolant in case of reactor core damage.The document NUREG-1465 [12] provides information on the approximate relative share of the fission products released from reactor core into the containment air space at various stages of fuel damage for PWR and BWR-type reactors.
Special attention is paid to the distribution of iodine radionuclides during the assessment of the release parameters.This radionuclide is a dose-forming radionuclide by the physicochemical forms of the most critical pathway of exposure.It is necessary to consider the distribution of iodine according to its physical and chemical conditions to determine the rate of dry deposition and the iodine washing from the radioactive cloud.The JRODOS system makes it possible to take into account three forms of iodine: In modern approaches to realistic forecasting of the radiological consequences of accidents at water-water reactors, the following distributions are distinguished according to 2 ways of exiting the vapor-gas mixture: containment and a fast-acting reduction unit for releasing steam into the atmosphere.A higher amount of organic iodine distribution is chosen for a conservative assessment (especially for transboundary transport).

Leakage pathways
Radionuclides can bypass such a barrier as containment during an accident.They can also first enter the air space of the containment and only then enter the environment due to the leakage of the containment (figure 2).The first pathway of propagation is typical for accidents caused by the flow of the primary circuit into the second (failure of steam generator collector).At the same time, radionuclides bypass the containment, immediately entering the second circuit and entering the atmosphere without purification.Another path of propagation is characteristic of accidents associated with the rupture of pipelines of the first circuit up to the maximum design accident.It is necessary to consider the presence or absence of retenrtion to correctly assess the radionuclides released from the containment to the environment.The discharge may be subjected to various mechanisms of retention of radionuclides by safety systems (sprinkler system, bubbling) and under the influence of natural retention mechanisms (sedimentation, decay), depending on the release pathway.At the same time, the activity depends on the length of radionuclides delay before the release.The retention factor refers to the activity ratio of iodine and long-lived aerosols released into the environment to the activity created due to the accident (data from NUREG-1228 [6]).
The efficiency of the filtering system through which the vapor-gas mixture passes is considered in the case of emissions after cleaning with filtering means.It happens if their efficiency is preserved during the course of the accident.At the same time, radioiodine distribution by physicochemical forms changes dramatically.Practical calculations show that the dose-forming groups will be noble gases (Kr, Xe) and organic compounds of radioiodine during accident scenarios with operating filtered containment venting system (FCVS).At the same time, in such methods, the delay time before release into the atmosphere plays a significant role in the radiological consequences results.
Speed radionuclides entering the containment depend on a containment leakage rate.The following intensities of leakage from the containment are accepted in international practice: • 0.1 -0.3%/day (normal leakage for PWR-type reactor containments, 0.3%/day -VVER-1000); • 100% per day (failure of containment isolation valves); • 100% per hour (corresponds to the containment destruction of).
The delay time of radionuclides before the release into the atmosphere is a determining factor in the calculation of poblic exposure doses in the part of external exposure from nobel gases (dose from the cloud) and radioiodine (dose from inhalation).It is possible to find the activity at any time after the shutdown of the reactor or movement of the steam-gas mixture at any time of its exposure in the free space of the containment knowing the inventory at the end of compaign.

Effective release height
Methodological approaches to assessment of the effective release height in various literary sources are presented quite ambiguously.However, we note that all these approaches introduce the following concepts: • release from tall pipes; • release from low pipes (guideline №. 50-SG-S3 of the IAEA [13]).
The dawnwash effect can be also considered (estimation of the initial parameters of the atmospheric dispersion) in the second case to increase the realism degree of the calculation.
The plumerise as a component and as a result of the heat energy of the release according to the current parameters is defined by the pre-programmed calculation procedures (Mathcad/Excel) as a part of the real-time calculation.They are used regarding to the IAEA method № 50-SG-S3 for cases: • unstable and neutral stability class (medium and high boundary of the mixing layer); • for conditions of a stable atmosphere (low boundary of the mixing layer).
It should be noted that reducing the effective height of the release increases the degree of conservatism in the assessment results of radiological consequences in near range.
The JRODOS system allows the setting of the total release height.It considers the plume rise as a dynamic component and a result of the heat energy of the release.It uses the additional parameters: thermal power of the release, vertical flow rate, and cross-sectional area (nozzles, vent stacks, etc.).

Types of input data entry
Modern DSS have a reasonably flexible policy for entering initial data.It allows entry of the source term in terms of release fractions and reactor core inventory at the time interval or the integral release activity without reference to reactor core inventory.
Modern DSS is moving to the IRIX (International Radiological Information Exchange, [14]) format source library standard.The standard significantly facilitates data exchange between organizations and in an international context (table 1).TECDOC-955 was one of the first international documents covering the systematization of source temrs for NPP severe accidents.The source selection algorithms are based on the events tree concept according to branching criteria.It corresponds to the factors affecting the release intensity (power unit status, operation of safety systems, retention and filtration of the vaporgas mixture, etc.).Such algorithms are implemented in the International InterRAS system and its subsequent evolution as a software product, RASCAL.

Assimilation of radiation monitoring data
Application of radiation measurement data near the emergency power unit (monitoring grid, mobile vehicles, etc.) contributes to the validation of the model and the results confirmation of atmospheric dispersion modeling and dose projection.However, these systems may be partially unavailable in the case of military attacks or occupation.The reliability of the information provided by the radiation monitoring stations remains a separate issue.
Ukraine still needs an integrated automated monitoring system for detecting, analyzing, and forecasting possible radiological consequences of accidents.Accident release may spread beyond the sanitary protection zones of nuclear power plants, other atomic installations, and radiationhazardous objects in Ukraine and beyond.However, the development of an integrated automated radiation monitoring system is planned until 2024 [15].
There are currently many challenges to developing real-time radiation impact assessment tools.Now, one of the ambitious directions of DSS development is solving the inverse problem of determining coordinates and characteristics of the emission source based on the results of field measurements.The practice of calculations for a wildfirefire in the Chornobyl exclusion zone shows that it is usually possible to estimate the integral characteristics of the release quite quickly if measurement data are available in the near range.However, this procedure requires considerable time to collect and process data to provide an inversion calculation in relatively large spatial scales.
Conducting inverse modelling for events on a large spatial scale requires the involvement of specialized software tools and separate methodological approaches.In addition, the task is complicated because the format and completeness of the output data are individual in each case.Also, there currently needs to be methodical approaches regarding the consideration of radiation monitoring data in the constructed models of atmospheric dispersion of the DSS and its subsequent correction or refinement in real-time.The issue of forming universal approaches to inverse modelling remains open.

The problem of forecasting radiological consequences of military causes
The emergency preparedness and response phases are divided by the principle criteria (an announcement of the event class) according to the current IAEA classification for peacetime conditions.The classification of events as objects of the first threat category (for example, nuclear power plants) under martial law declared is not regulated by national or international regulations.It can be assumed that the situation around the Zaporizhzhia NPP is intermediate, given the repeated activation of Ukraine's crisis center's regulatory body during the first nine months of the full-scale invasion.It includes synthesizing elements of both the readiness and the response phases.Some examples of air mass movement trajectories modeling for the Zaporizhzhia NPP are presented in fig. 3. Today there is no experience in international practice on performing safety analyzes of nuclear installations under the war conditions.It includes a lack of methodology and initial data for their conduct (intensity of shelling, degree of damage to buildings and structures from the impact of various types and calibers of ammunition, action personnel, and population behavior in conditions of hostilities and extreme stress, etc.).
Several conditional reference scenarios of severe damage to the reactor core at the VVER-1000/B-320 type reactor plant were considered a representative event for NPP industrial sites considering the above.The creation of the emissions library made it possible to simulate multiunit scenarios, such as total station blackout for all power unit on-site.
Also, the accident at a spent nuclear fuel dry storage facility was considered, given the assumption of a possible mechanical destruction of spent fuel cask (as a result of hostilities or a terrorist attack), additionally for the Zaporizhzhia NPP.It was considered for one VSC-24 container containing 24 spent fuel assemblies with a minimum spending time of 5 years.
The question of the results ambiguity of atmospheric dispersion modeling and the prediction of radiation doses is based on several uncertainty factors from the input information to the endpoints report on the results.The following can be distinguished among them: • detail and completeness of input data for assessment and analysis of the situation (state of the nuclear installation, source term, pathway and effective height of the release, time resolution, physical and chemical forms, number of calculated radionuclides, etc.); • provider and completeness of parameters of numerical weather data of (spatial and temporal resolution, completeness of the list of meteorological parameters); • atmospheric dispersion model and parameterization; • dose models, number of reference groups by age, exposure routes; • model of countermeasures, form, and completeness of the final results presentation of the assessment or forecast (scale, data format, deterministic or probabilistic interpretation); • type and completeness of accompanying databases (height of roughness of the underlying ground surface, population density, land use, types of shelters, features of the infrastructure, dose coefficients, etc.); • degree of experience and qualification of the expert.  of discharges and provided detailed descriptions thereof.Furthermore, played a significant role in defining input parameters.• Andrii V. Iatsyshyn: Supported the justification of the research's relevance and played a crucial role in conducting research related to the prediction of radiation consequences in military events.Additionally, contributed to the formulation of key conclusions.
Each author's unique expertise and dedication have been instrumental in the completion of this research, enriching its depth and breadth.

Conclusions
Consequences of acts of nuclear terrorism or military attacks on nuclear facilities may significantly impact the public and environment.They are associated with high uncertainties or insufficient initial data for calculations.Modern emergency preparedness and response modeling tools (as DSS) are not designed for use under conditions of such uncertainty.
At the same time, there are many methodical approaches to the deriving source term during accidents accompanied by significant release of radioactive substances into the environment.These approaches help to approximate and sometimes re-analyze a dynamic picture of radionuclide concentrations in the air and total fallout.They also allow the conduct of comprehensive assessment on impact on the public and environment.A review of their application features showed that the development of approaches to the source term description is an effective tool for providing initial data in various variants and forms necessary for calculating radiation consequences in DSS and other software tools.
The main characteristics of the source term represent a package of initial data for modeling atmospheric dispersion and dose projection during a severe accident at a nuclear power plant.It was found that there needs to be a universal methodology and procedures for responding to events with a high degree of uncertainty, particularly in the data regarding the source term.
The problem of uncertainties requires further research and analysis from the point of view of the experience gained during the response since the beginning of the full-scale invasion of the Russian Federation, the military attack, and the seizure of the Zaporizhzhia NPP at the beginning of March 2022.

Figure 2 .
Figure 2. Leakage ways scheme of the steam-gas mixture.

Table 1 .
Types of source terms by methods of input data entry on the share/activity of the emission of modern DSS JRODOS [5].
F7Activity release rate [Bq/s or Bq/h] on the interval individually for each nuclide without reference to the reactor core inventory.
The research results presented in this publication are the culmination of the collective efforts and distinct contributions of each author:• Volodymyr O. Artemchuk : Conceived the research idea, provided the rationale for its relevance, and played a pivotal role in drafting the article.Additionally, contributed to the formulation of key conclusions.• Yurii O. Kyrylenko: Conducted extensive research on the radionuclide composition and the physical and chemical forms involved.Developed a comprehensive diagram illustrating the paths of steam-gas mixture leakage and contributed significantly to the corresponding report.• Iryna P. Kameneva: Undertook a comprehensive review of contemporary assessment tools used in global crisis centers, providing valuable insights.Focused on the intricate issues of uncertainty and conducted research related to the assimilation of emergency monitoring data.• Valeriia O. Kovach: Conducted in-depth studies aimed at determining the effective height