Method for the forecasting of local radiological pollution of atmosphere using Gaussian process models

Principal investigator:

Prof. Dr. Juš Kocijan


May 1, 2017 – April 30, 2020


ARRS - Slovenian Research Agency, L2 - 8174 (B), co-financing from REODOM rešitve za odložljiva omrežja d.o.o.


The accidents in Chernobyl and Fukushima have shown that the dispersion of radioactive air pollution in the air is the critical way for this kind of danger to reach masses of inhabitants. Consequently, an innovative method for pollution-dispersion modelling is proposed in the project proposal that will show the dispersion a day or two ahead. With this model the efficiency of the population safety measures will be significantly improved. The modelling will be based on Gaussian processes (GPs).

The model based on the GP is a probabilistic and non-parametric model based on Bayes’ theorem on probability. It differs from other methods of identification based on a black box, because in the process of modelling, we do not optimize the parameters of the preselected basic functions but we are looking for links between the measured data. At the output of the models based on the GP, the prediction is obtained in the form of normal distribution, which may be expressed by its mean value and variance.

The method of modelling based on the GP is particularly suitable for complex nonlinear processes, which are defined with uncertain and missing data. The meteorological state of the atmosphere is such a complex process.

To ensure the correct action in case of a nuclear accident, we therefore need a good prediction about where the radioactive cloud would move to. In this modelling, many important steps have already been sufficiently scientifically solved. The prediction of input signals about the atmospheric variables, which are of key importance for the dispersion, is, however, still an open question. Instead of local predictions and the simultaneous improvement of the radionuclides’ concentration value this project is focused on meteorological dynamics in the assigned 3D space.

The objective of this research is to make signals' predictions that significantly improve the 3D description of the atmosphere dynamics in the vicinity of the nuclear power plant over the existing forecasting models. Consequently, a better forecast of the radionuclides' concentration in the atmosphere as a consequence of an accident with the atmospheric release will be enabled.

Since meteorological measuring stations are required in the surroundings of the nuclear plants, there are a number of measurements available. These stations describe the historical development of the weather. All this information, contained in the measurements of the history of signals, can be used for modelling and predictions of their future values. We estimate that models for precise predictions of target signals can be built with GP-based methods from the history of measurements and meteorological predictions (made by numerical weather prediction models) which will sufficiently describe the 3D condition of the atmosphere in the future, so that the appropriate air pollution dispersion model will reliably and sufficiently forecast the development of air pollution dispersion. Such forecastss of the dispersion of the radionuclide concentrations in the air are of key importance for the timely, appropriate and effective protection of the inhabitants.

We expect that the advanced methods based on the GP will significantly improve the predictions, since they have also been very successful in the related field of modelling ozone in the atmosphere. We expect that the GP-model-based identification methodology will be improved for problems where large amounts of data, signals’ periodicity and spatio-temporal modelling appear. The dynamic-system identification problem is tackled as a fusion of signals from heterogeneous data sources into the targeted prediction. A guarantee for the stability of the developed models plays an important role. The proposed method for the dispersion forecast of the radionuclide-polluted cloud based on meteorological variables is an important novelty for the assurance of safety in the case of a nuclear accident. This was confirmed by the International Atomic Energy Agency IAEA, which included this methodology proposed by us as the key element in its MODARIA II programme in the atmospheric-modelling part.

Project workpackages:
  1. Evaluation of meteorological forecasts and identification of key deficiencies in pollution dispersion modelling. (Present level of realisation: 100 %)
  2. Evaluation of different GP-based modelling methods for the identification of models useful for forecasting the variables under consideration. (Present level of realisation: 100 %)
  3. Improvements of meteorological forecasts for target areas near nuclear power plants. (Present level of realisation: 100 %)
  4. Automation of the new methodology in the Krško NPP’s user test environment. (Present level of realisation: 100 %)

Project partners:


KOCIJAN, Juš, PERNE, Matija, MLAKAR, Primož, GRAŠIČ, Boštjan, BOŽNAR, Marija. Hybrid model of the near-ground temperature profile. Stochastic environmental research and risk assessment, ISSN 1436-3240, 2019, vol. 33, no. 11/12, 2019-2032, doi: 10.1007/s00477-019-01736-5.

CRISTEA, Irina Elena, KOCIJAN, Juš, NOVAK, Michal. Introduction to dependence relations and their links to algebraic hyperstructures. Mathematics, ISSN 2227-7390, 2019, vol. 7, iss. 10, 1-14, ilustr, doi: 10.3390/math7100885.

MLAKAR, Primož, KOKAL, Dragana, GRAŠIČ, Boštjan, BOŽNAR, Marija, GRADIŠAR, Dejan, KOCIJAN, Juš. Validation of meteorological forecasts in fine spatial and temporal resolution produced as an input for dispersion models. International journal of environment and pollution, ISSN 0957-4352, 2017, vol. 62, no. 2/4, 236-246, doi: 10.1504/IJEP.2017.10010378.

Weather-variables forecast at NPP Krško location with artificial neural networks.