Uncertainty quantification by reduction of the atmospheric dispersion model applied to the Fukushima nuclear accident

In case of a nuclear accident that may imply a release of radionuclides into the environment, the French Institute of Radiation Protection and Nuclear Safety (IRSN) uses atmospheric dispersion models to infer mitigation actions and protect the population. In the post-accidental phase (after the release actually occurred), they also complement field measurements for the assessment of short- and long-term environmental and human health impacts. These atmospheric dispersion models compute, over a given domain, the concentrations of radionuclides in the atmosphere, the deposited quantities on the ground, as well as the gamma dose rates (radiation emitted by radionuclides present in the air and on the ground). The forecasts made by these simulations involve large uncertainties, due to the limited knowledge on input data (weather forecasts and source term), physical parameters of the model (deposition velocities, diffusion coefficients, scavenging factors, etc.), and numerical approximations. The aim of our study was to implement methods to assign probability density functions (PDFs) to the unknown errors on the input variables and to calibrate those PDFs using field observations. This was applied to the Fukushima nuclear disaster, using IRSN's operational dispersion model and field measurements collected during or after the disaster. In the evaluation and calibration processes, we made use of radiological observations of activity concentration in the air, deposition and gamma dose rates collected in Japan. Calibration methods require a large number of calls to the model, so that the computational time is far too high to use the physical model. To circumvent this issue, we built a metamodel, that is, a mathematical approximation of the physical model, based on statistical emulation. We used two interpolation methods : RBFs-Radial Basis Functions-and Kriging (Gaussian processes). One of the difficulties was to deal with the uncertain meteorological fields. Those are time-varying 2D or 3D variables whose uncertainties are time and space-dependent, as well as correlated between the different variables. To describe these uncertainties, we use an ensemble of 50 meteorological forecasts provided by the European Centre for Medium-Range Forecast (ECMWF) whose purpose is to sample the uncertain meteorological variables. We parameterized the set of possible meteorological fields as a convex linear combination of the ensemble of forecasts, which raised a number of difficulties in the design of experiment, in the metamodeling and the calibration. Similarly, nine credible release scenarios, compatible with the observations in the environment, were derived from the Fukushima literature and combined with random weights. A comparison study showed that the construction and execution time of RBF were rather low, with acceptable emulation of the results obtained with the physical model. Kriging was slower but showed better results, and provided in addition a standard deviation of the prediction error. This standard deviation was evaluated on an independent verification set of simulations (not used to build the emulator). The metamodels were then used in an ensemble-based calibration procedure. Firstly, a deterministic optimization was carried out. The aim was to find the best set of parameters that would minimize model-to-data scores such as the RMSE-Root Mean Square Error. Then, a probabilistic calibration was implemented in order to obtain a probability distribution for each parameter (convex combination and other parameters). The Metropolis-Hastings algorithm was applied to sample the distribution of uncertain parameters. The likelihood took into account the uncertainties in observational data. Samples obtained by Metropolis-Hastings were made of several Markov chain run in parallel. This was first applied to a simple meteorological model, using meteorological observations available on the Japanese territory during the Fukushima accident. For the full calibration of all uncertainties related to the dispersion model, difficulties arose from the high number of input parameters (19), the low sensitivity to meteorological ensemble weights, and the convex combination of the meteorological forecasts. (author)