Use of Reciprocity in Atmospheric Source Inversion Problems

摘要

The goal of the Event Reconstruction Project is to find the location and strength of atmospheric release points, both stationary and moving. Source inversion relies on observational data as input. The methodology is sufficiently general to allow various forms of data. In this report, the authors will focus primarily on concentration measurements obtained at point monitoring locations at various times. The algorithms being investigated in the Project are the MCMC (Markov Chain Monte Carlo), SMC (Sequential Monte Carlo) Methods, classical inversion methods, and hybrids of these. They refer the reader to the report by Johannesson et al. (2004) for explanations of these methods. These methods require computing the concentrations at all monitoring locations for a given proposed source characteristic (locations and strength history). It is anticipated that the largest portion of the CPU time will take place performing this computation. MCMC and SMC will require this computation to be done at least tens of thousands of times. Therefore, an efficient means of computing forward model predictions is important to making the inversion practical. In this report they show how Green's functions and reciprocal Green's functions can significantly accelerate forward model computations. First, instead of computing a plume for each possible source strength history, they can compute plumes from unit impulse sources only. By using linear superposition, they can obtain the response for any strength history. This response is given by the forward Green's function. Second, they may use the law of reciprocity. Suppose that they require the concentration at a single monitoring point x(sub m) due to a potential (unit impulse) source that is located at x(sub s). instead of computing a plume with source location x(sub s), they compute a reciprocal plume whose (unit impulse) source is at the monitoring locations x(sub m). The reciprocal plume is computed using a reversed-direction wind field. The wind field and transport coefficients must also be appropriately time-reversed. Reciprocity says that the concentration of reciprocal plume at x(sub s) is related to the desired concentration at x(sub m). Since there are many less monitoring points than potential source locations, the number of forward model computations is drastically reduced.