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Probability distribution functions (PDFs) of model inputs that affect thetransport and dispersion of a trace gas released from a coastal Californianuclear power plant are quantified using ensemble simulations, machine-learning algorithms, and Bayesian inversion. The PDFs are constrained byobservations of tracer concentrations and account for uncertainty inmeteorology, transport, diffusion, and emissions. Meteorological uncertaintyis calculated using an ensemble of simulations of the Weather Research andForecasting (WRF) model that samples five categories of model inputs(initialization time, boundary layer physics, land surface model, nudgingoptions, and reanalysis data). The WRF output is used to drive tens ofthousands of FLEXPART dispersion simulations that sample a uniformdistribution of six emissions inputs. Machine-learning algorithms are trainedon the ensemble data and used to quantify the sources of ensemblevariability and to infer, via inverse modeling, the values of the 11 modelinputs most consistent with tracer measurements. We find a substantialensemble spread in tracer concentrations (factors of 10 to 10<sup>3</sup>), most ofwhich is due to changing emissions inputs (about 80 %), though thecumulative effects of meteorological variations are not negligible. Theperformance of the inverse method is verified using synthetic observationsgenerated from arbitrarily selected simulations. When applied to measurementsfrom a controlled tracer release experiment, the inverse methodsatisfactorily determines the location, start time, duration and amount. In a2 km × 2 km area of possible locations, the actuallocation is determined to within 200 m. The start time is determinedto 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 estimatedamount exceeds the actual amount of 146 kg by only 32 kg. Theinversion also estimates probabilities of different WRF configurations. Tobest match the tracer observations, the highest-probability cases in WRF areassociated with using a late initialization time and specific reanalysis dataproducts

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