Novel simulation technique of radioactive aerosol substances propagation into the motionless atmosphere suddenly disseminated by wind to surrounding environment

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Abstract

Accidental discharges of radioactive aerosol into the motionless (calm) atmosphere are examined with aim to quantify ensuing radiological impact on population. This paper offers an advanced methodology that facilitates and accelerates the demanding modelling process in the calm region. The modelling simulates continuous, quite volatile, radioactive releases under strong variations of the atmospheric conditions by a chain of discrete Gaussian pulses. An original idea of insertion of the nested inner cycle enables to comprise the atmosphere state changes during individual pulse propagation. The radioactivity concentration in air at the calm end period becomes a quite non-Gaussian sum of the Gaussian puffs. The novel processing provides a simple and sufficiently precise estimate of its statistical properties. The processing approximates the sum by a single “super-puff” distribution of the Gaussian type. It remarkably facilitates analysis of the ensuing convective transport of the radioactivity package. Instead of many calculating runs of the convective transport for each individual puff, only one run realises. The approximation is based on Bayes’ paradigm (AB). The numerical experiments confirm the acceptability of the AB procedure under the inspected circumstances. The proposed way converts the laborious modelling of radiological fields into a feasible one. It supports practicability of the sampling based methods of uncertainty and sensitivity analyses, as well as the data assimilation methods, especially their inverse modelling techniques based on simulation of multiplex radiological trajectories.

Introduction

Mankind needs to reduce and minimize the impact of environmental disasters like earthquakes, volcanic eruptions, wild-land fires, sand and dust storms or biological emergencies. In the same line, the disasters from human activities have immediate impact on population. Various threats adversely influence the critical infrastructures. They concern energy generation and distribution, chemical production and distribution, transportation systems, agriculture production (pollen and odour transport, pesticide dispersion, greenhouse gases propagation) and other. Accidents connected with discharges of chemical and radioactive substance harm human health and the environment. Chemical-plant failures or traffic accident during transport of chemicals are frequently described and documented. Chlorine or ammonia gas leak from an industrial facility or spill from broken truck during transport accident threat the adjacent population. Similarly, discharges of hydrogen sulphide from a tanker or massive releases of bromine gas into the atmosphere were reported. Probably the world’s worst industrial disaster, with approximately 2500 death, caused by methyl isocyanate poisoning due to leaking from a storage tank, happened in Bhopal, India, 1984. In response to the catastrophic incidents, improvements of safety regulations for the use and distribution of the hazardous chemicals have been introduced. A similar progress in nuclear safety has been directed after the nuclear catastrophe in Chernobyl and the Fukushima accident. Disaster preparedness must also account for terroristic attacks spreading the harmful chemicals or radioactive substances into the environment. Emergency readiness plans should include management of the radiological consequences of attacks via atmospheric dispersion of contaminants originating from, for instance, ‘dirty bomb’ explosions. A special attention should be given to the accidents during worst-case meteorological conditions. We care about such particular atypical, rarely addressed, cases, of serious radioactivity spreading under very low wind speed conditions. Within this scenario, a novel technique is designed that speeds up evaluations and is applicable to other cases, too.

Hazardous effects of accidental radioactive releases during an atypical episode of the low wind speed state are examined. A hypothetic but realistic experiment is carried out with a radioactivity in the aerosol form accidentally released into the motionless atmosphere. During a few hours of the calm state, dangerous radioactivity values may locally accumulate. The calm state is immediately followed by the windy convective transport that disseminates the hazardous aerosol material. Notably, the hot spots of deposited 137Cs occur when the scenario is combined with the atmospheric precipitation. The hot spots exhibit a significantly increased radioactivity deposited on the ground. The presented modelling proposes and verifies its novel fast numerical treatment.

The topic of the paper concerns thoroughly inspected domain. Inevitably, a classical material is repeated in order to make the paper as much self-containing as possible and to explain practical important technical details.

Section 2 models the considered release scenario. The inspected realistic low wind speed and calm conditions origin from the data provided by the Czech meteorological service. The archived hourly meteorological data forecasted for a nuclear power-plant locality has served for assessing the probability of occurrence and the average duration time of the calm episode. The inspected mathematical model uses a superposition of discrete Gaussian puffs labelled by m ∈ {1,…,M} that are released from an elevated resource. The superposition approximates any continuous radioactive release. Each puff evolves during consecutive windless stages within a calm region. Afterwards, it spreads due to the ensuing convective transport initiated by the wind. Parameter changes in the calm region can account for the release source strength, isotopic composition, atmospheric stability class, rainfall, and release height. The computation scheme comprises a detailed nested propagation model of the mth puff. From its birth until the calm end, the puff propagates during adjacent time intervals. The model copes with the forthcoming changes of atmospheric stability class, e.g. in (Hanna et al., 1982), or atmospheric precipitation. The radioactivity depletion due to the radioactive decay, aerosol dry activity deposition and washout of aerosol by a prospective rain is respected. Depletion factors reflecting the radioactive decay, aerosol dry and wet radioactivity depositions are discussed for the calm episode. Section 4.2 adjusts them for the convective region.

Section 3 expands and generalizes a novel pollution processing introduced in (Pecha et al., 2020) for earlier minor release scenario and lower experiment dimensionality. It is applied just after the calm period end and initiates the convective radioactivity transport. This speeds up evaluations much and makes them widely applicable. Instead of processing all puffs further on (brute-force solution, BF), the non-Gaussian mixture of radioactivity concentrations in the air at the calm episode end is replaced by a representative Gaussian distribution. The used and recalled approximation principle is motivated by Bayesian paradigm (Bernardo, 1979). It relies on the fact that the Kullback-Leibler divergence, (Kullback and Leibler, 1951), is the adequate proximity measure between the approximated distribution and its approximant. The best Gaussian approximant is constructed. The solution is referred as the approximation based on Bayes’ paradigm (AB).

Section 4 models the convective transport in BF or AB modes. Elementary Gaussian puff dispersion model is applied over short distances. It demonstrates the main features of the scenario and its solution. It points to the dangerous accumulation of radioactivity during the calm conditions and shows of the feasibility of the AB solution. The employed relevant dry deposition and wet washout parameterisations are compiled from fields' experiments.

The approximated sum of puffs gained by BF technique is clearly non-Gaussian. Numerical results of Section 5 experimentally support the use of the fast AB solution against accurate but slow BF way. The inspected hypothetical scenario consists of five hours of the calm episode succeeded by four hours of the convective transport. The rain occurs in the last fourth hour of the convective propagation. The calm interval is split into M segments, the variants with values M ∈ {6, 10, 100, 200, 300} are examined. The source strength is assumed constant during the whole calm period. For M = 100, the scenario with a serrated shape of discharges is also inspected. Comparisons of BF and AB solutions are made in the critical rainy convective phase. The results of both processing are in a good agreement. The experiments also show that the limit of the continuous discharges (M → ∞) is well estimated.

The benefits demonstrating improved feasibility of joint uncertainty and sensitivity analyses performance of the CALM scenario are confirmed in the detailed complementary study (Pecha and Kárný, 2021) based on random sampling techniques.

Section snippets

The modelled accident conditions and the used modelling way

Potentially dangerous atmospheric dispersions at low wind speed state are inspected for a long time, see e.g., (Jones, 1996, Lines and Deaves, 1997, Okamoto et al., 2001, Hyojoon et al., 2013). Performance evaluation and comparison of modified Gaussian and Lagrangian models under low wind speed is given in (Rakesh et al., 2019). Commonly large effect of the low wind speed variability on radioactivity concentrations in air are analysed in (Pandey and Sharan, 2019). Concentration measurements

Evaluation of Radiological Quantities just at the Calm Episode Termination TENDCALM

The radioactivity accumulated in the stationary ambient atmosphere is a superposition of results of all partial puffs m until they reach end of the calm period TENDCALM. The total radioactivity concentration in the stationary package of air at the time TENDCALM is expressed as sumCnTENDCALM;r,zTOTAL=m=1m=MCm,Imnr,z

Cm,Imnr,z is concentration of the puff m (born at time tm), which reached the end of the calm period just at the moment TENDCALM (according to the scheme in Fig. 2). The puff m runs

Ensuing Convective Transport of Previous Stationary Heap of Radioactivity

By assumption, a convective movement of the atmosphere immediately follows the calm episode. The wind starts to blow. It drifts and scatters the stationary heap of the radioactivity over the terrain. A fast and sufficiently accurate estimate of dangerous radiological impact on the living environment in vicinity of the radioactive source is needed. It plays a crucial role in the early introduction of the efficient countermeasures for the protection of inhabitants. Two scenarios exploiting the

Experiments and their results

The trajectory generation of radiological fields in the low wind speed area immediately coupled with a convective transport of the accumulated radioactivity heap is described. The possible serious impact of atmospheric precipitation on incidence of dangerous “hot-spots” of deposited radioactivity on terrain is shown. Continuous release of radionuclides is treated as a sequence of discrete Gaussian puffs from the elevated source.

The experiments compare the fast calculation with the approximation

Conclusions

Discharges of the radioactivity into the motionless ambient atmosphere can cause a significant radioactivity accumulation near the source of pollution. The situation pertains to the “worst case” scenarios, which are examined within WVA (Weather Variability Assessment) analysis. Significant extent of involved uncertainties reduces credibility of the model predictions. Solution offers the data assimilation techniques accounting for the real measurements incoming from terrain. This approach

CRediT authorship contribution statement

Petr Pecha: Methodology, Software, Validation, Writing – review & editing. Miroslav Kárný: Methodology, Conceptualization, Validation.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors are grateful to the IT department of the National Radiation Protection Institute in Prague for free access to the archives of the historical meteorological data. The research of MK was partially supported by MŠMT ČR LTC18075 and EU-COST Action CA1622. Dr. T.V. Guy provided us a useful feedback on the presentation way.

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