Efficiently characterizing the origin and decay rate of a nonconservative scalar using probability theory

We present a methodology for estimating parameters which describe the source location and strength, as well as the rate of transformation, of a passive, nonconservative scalar released into (or already present in) the atmosphere. A finite number of uncertain (noisy) concentration measurements is the primary source of information for the source reconstruction, which implies that the problem is ill-posed and must be solved using a Bayesian probabilistic inferential framework. All parameters are estimated simultaneously and the model describing the forward problem (prediction of the dispersion of a contaminant given its source and rate of decay) is computationally demanding, so the capability to efficiently calculate the solution to the inverse problem is crucial. It is demonstrated how a backward Lagrangian stochastic particle model facilitates the rapid characterization of the source location and strength, while by monitoring the statistical properties of the particle travel times, the rate of transformation of the agent can be efficiently estimated. Markov chain Monte Carlo is used to sample from the multi-dimensional domain of definition of the posterior probability density function that results from applying Bayes’ theorem. The overall methodology is validated in two stages. First, the source reconstruction approach is tested using concentration data measured during an experiment in which a conservative scalar was continuously released from a point source into a statistically stationary flow in a horizontally homogeneous and neutrally stratified atmospheric surface layer (Project Prairie Grass). Next, the reconstruction approach is applied to synthetic concentration data generated using a Lagrangian stochastic model operating under the same atmospheric conditions, with decay of particle mass being modelled by a straightforward first-order mechanism.

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