Anna Wawrzynczak

Sequential Monte Carlo in Bayesian Assessment of Contaminant Source Localization Based on the Sensors Concentration Measurements

Accidental atmospheric releases of hazardous material pose great risks to human health and the environment. In this context it is valuable to develop the emergency action support system, which can quickly identify probable location and characteristics of the release source based on the measurement of dangerous substance concentration by the sensors network. In this context Bayesian approach occurs as a powerful tool being able to combine observed data along with prior knowledge to gain a current understanding of unknown model parameters.

Approximate Bayesian Computation for Estimating Parameters of Data-Consistent Forbush Decrease Model

Realistic modeling of complex physical phenomena is always quite a challenging task. The main problem usually concerns the uncertainties surrounding model input parameters, especially when not all information about a modeled phenomenon is known. In such cases, Approximate Bayesian Computation (ABC) methodology may be helpful. The ABC is based on a comparison of the model output data with the experimental data, to estimate the best set of input parameters of the particular model. In this paper, we present a framework applying the ABC methodology to estimate the parameters of the model of Forbush decrease (Fd) of the galactic cosmic ray intensity. The Fd is modeled by the numerical solution of the Fokker–Planck equation in five-dimensional space (three spatial variables, the time and particles energy). The most problematic in Fd modeling is the lack of detailed knowledge about the spatial and temporal profiles of the parameters responsible for the creation of the Fd. Among these parameters, the diffusion coefficient plays a central role. We employ the ABC Sequential Monte Carlo algorithm, scanning the space of the diffusion coefficient parameters within the region of the heliosphere where the Fd is created. Assessment of the correctness of the proposed parameters is done by comparing the model output data with the experimental data of the galactic cosmic ray intensity. The particular attention is put on the rigidity dependence of the rigidity spectrum exponent. The proposed framework is adopted to create the model of the Fd observed by the neutron monitors and ground muon telescope in November 2004.

Algorithms for Forward and Backward Solution of the Fokker-Planck Equation in the Heliospheric Transport of Cosmic Rays

Motion of charged particles in an inhomogeneous turbulent medium as magnetic field is described by partial differential equations of the Fokker-Planck-Kolmogorov type. We present an algorithm of numerical solution of the four-dimensional Fokker-Planck equation in three-dimensional spherical coordinates system. The algorithm is based on Monte Carlo simulations of the stochastic motion of quasi-particles guided by the set of stochastic differential equations corresponding to the Fokker-Planck equation by the Ito formalism. We present the parallel algorithm in Julia programming language. We simulate the transport of cosmic rays in the heliosphere considering the full three-dimensional diffusion tensor. We compare forward- and backward-in-time solutions of the transport equation and discuss its computational advantages and disadvantages.

Approximate Bayesian Computation Methods in the Identification of Atmospheric Contamination Sources for DAPPLE Experiment

Sudden releases of harmful material into a densely-populated area pose a significant risk to human health. The apparent problem of determining the source of an emission in urban and industrialized areas from the limited information provided by a set of released substance concentration measurements is an ill-posed inverse problem. When the only information available is a set of measurements of the released substance concentration in urban and industrial areas, it is difficult to determine the source of emission. The Bayesian probability framework provides a connection between model, observational and additional information about the contamination source. The posterior distribution of the source parameters was sampled using an Approximate Bayesian Computation (ABC) algorithm. The stochastic source determination method was validated against the real data set acquired in a highly disturbed flow field in an urban environment. The datasets used to validate the proposed methodology include the dispersion of contaminant plumes in a full-scale field experiment performed within the project ‘Dispersion of Air Pollutants and their Penetration into the Local Environment in London (DAPPLE)’.

Bayesian Methodology in the Stochastic Event Reconstruction Problems

In many areas of application it is important to estimate unknown model parameters in order to model precisely the underlying dynamics of a physical system. In this context the Bayesian approach is a powerful tool to combine observed data along with prior knowledge to gain a current (probabilistic) understanding of unknown model parameters. We have applied the methodology combining Bayesian inference with sequential Monte Carlo (SMC) to the problem of the atmospheric contaminant source localization. The algorithm input data are the on-line arriving information about concentration of given substance registered by the downwind distributed sensor’s network. We have proposed the different version of the hybrid SMC along with Markov chain Monte Carlo (MCMC) algorithms and examined its effectiveness to estimate the probabilistic distributions of atmospheric release parameters.