Bayesian inverse modeling of the atmospheric transport and emissions of a controlled tracer release from a nuclear power plant

Abstract

Abstract. Probability distribution functions (PDFs) of model inputs that affect the transport and dispersion of a trace gas released from a coastal California nuclear power plant are quantified using ensemble simulations, machine-learning algorithms, and Bayesian inversion. The PDFs are constrained by observations of tracer concentrations and account for uncertainty in meteorology, transport, diffusion, and emissions. Meteorological uncertainty is calculated using an ensemble of simulations of the Weather Research and Forecasting (WRF) model that samples five categories of model inputs (initialization time, boundary layer physics, land surface model, nudging options, and reanalysis data). The WRF output is used to drive tens of thousands of FLEXPART dispersion simulations that sample a uniform distribution of six emissions inputs. Machine-learning algorithms are trained on the ensemble data and used to quantify the sources of ensemble variability and to infer, via inverse modeling, the values of the 11 model inputs most consistent with tracer measurements. We find a substantial ensemble spread in tracer concentrations (factors of 10 to 103), most of which is due to changing emissions inputs (about 80 %), though the cumulative effects of meteorological variations are not negligible. The performance of the inverse method is verified using synthetic observations generated from arbitrarily selected simulations. When applied to measurements from a controlled tracer release experiment, the inverse method satisfactorily determines the location, start time, duration and amount. In a 2 km × 2 km area of possible locations, the actual location is determined to within 200 m. The start time is determined to within 5 min out of 2 h, and the duration to within 50 min out of 4 h. Over a range of release amounts of 10 to 1000 kg, the estimated amount exceeds the actual amount of 146 kg by only 32 kg. The inversion also estimates probabilities of different WRF configurations. To best match the tracer observations, the highest-probability cases in WRF are associated with using a late initialization time and specific reanalysis data products.