Using a Bayesian framework in the inverse problem of estimating the source of an atmospheric release of a pollutant has proven fruitful in recent years. Through Markov chain Monte Carlo (MCMC) algorithms, the statistical distribution of the release parameters such as the location, the duration, and the magnitude as well as error covariances can be sampled so as to get a complete characterisation of the source. In this study, several approaches are described and applied to better quantify these distributions, and therefore to get a better representation of the uncertainties. First, we propose a method based on ensemble forecasting: physical parameters of both the meteorological fields and the transport model are perturbed to create an enhanced ensemble. In order to account for physical model errors, the importance of ensemble members are represented by weights and sampled together with the other variables of the source. Second, once the choice of the statistical likelihood is shown to alter the nuclear source assessment, we suggest several suitable distributions for the errors. Finally, we propose two specific designs of the covariance matrix associated with the observation error. These methods are applied to the source term reconstruction of the ¹⁰⁶Ru of unknown origin in Europe in autumn 2017. A posteriori distributions meant to identify the origin of the release, to assess the source term, and to quantify the uncertainties associated with the observations and the model, as well as densities of the weights of the perturbed ensemble, are presented.

中文翻译：

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应用于2017年秋季106Ru事件的大气释放源评估的不确定性量化

近年来，在估计污染物大气排放源的逆问题中使用贝叶斯框架已被证明是卓有成效的。通过马尔可夫链蒙特卡罗（MCMC）算法，可以对释放参数的位置、持续时间、幅度以及误差协方差等统计分布进行采样，从而得到源的完整表征。在这项研究中，描述并应用了几种方法来更好地量化这些分布，从而更好地表示不确定性。首先，我们提出了一种基于集合预测的方法：对气象场和传输模型的物理参数进行扰动以创建增强的集合。为了解决物理模型错误，集合成员的重要性由权重表示，并与源的其他变量一起采样。其次，一旦统计可能性的选择被证明会改变核源评估，我们就会建议几种合适的误差分布。最后，我们提出了与观测误差相关的协方差矩阵的两种特定设计。这些方法应用于源项重建¹⁰⁶在欧洲待查在2017年秋季的茹 甲意味着确定所述释放的来源，以评估源项，并量化的权重的与观测和模型相关联的不确定性，以及密度分布的后验扰动的整体，呈现。