A Bayesian Source Term inversion Method Based on Spatiotemporal Trajectory Prior and Joint Adaptive MCMC Sampling

Abstract: Determining the release source position and quantity is crucial for evaluating the consequences of atmospheric radionuclide release events, with the Bayesian method serving as the primary tool for source inversion. Reducing the impact of input data errors on inversion uncertainty and improving computational efficiency are key to developing robust and efficient inversion algorithms. To address these challenges, we developed a spatiotemporal trajectory prior (STP) distribution that effectively mitigates the influence of measurement and simulation errors on inversion results without increasing computational costs, thereby enhancing the robustness and accuracy of the inversion process. Additionally, we introduced a joint adaptive Markov Chain Monte Carlo (MCMC) sampling method that integrates the traditional parallel tempering (PT) algorithm with a novel joint adaptive transition proposal (JATP) algorithm to accelerate inversion calculations. The proposed methods were optimized and validated using data from the first release of the European Tracer Experiment (ETEX-I). After determining the hyperparameters, the JATP algorithm consistently maintained the sampling process near the theoretically optimal acceptance rate of 0.234. The PT algorithm, utilizing an optimized temperature schedule, achieved a 2.89-fold improvement in sampling efficiency compared to single-chain sampling. Under bootstrap statistical comparison, the method reduced the relative error of position, relative error of release quantity, and total relative error by 25.9%, 27.7%, and 27.8%, compared to the traditional uniform prior method, respectively. And the deviation of the estimated and true source position is within 0.25˚. The results demonstrate the accuracy and effectiveness of our method.