Source characterization of atmospheric releases using stochastic search and regularized gradient optimization

Abstract

In this work, an inversion technique comprising stochastic search and regularized gradient optimization is used to solve the atmospheric source characterization problem. The inverse problem comprises retrieving the spatial coordinates, source strength and the wind speed and wind direction at the source, given certain receptor locations and concentration values at these receptor locations. The Gaussian plume model is adopted as the forward model and derivative-based optimization is chosen to take advantage of its simple analytical nature. A new misfit functional that improves the inversion accuracy of atmospheric inverse-source problems is developed and is used in the solution procedure. Stochastic search is performed over the model parameter space to identify a good initial iterate for the gradient scheme. Several Quasi-Monte Carlo point-sets are considered in the stochastic search stage and their performance is evaluated against the Mersenne–Twister pseudorandom generator. Newton's method with the Tikhonov stabilizer and adaptive regularization with quadratic line-search is implemented for gradient optimization. As the forward modelling and measurement errors for atmospheric inverse problems are usually unknown, issues concerning ‘model-fit’ and ‘data-fit’ are examined. In this article, the workings and validation of the proposed approach are presented using field data from the Copenhagen tracer experiments.

Keywords:

• inverse-source problem
• Gaussian plume model
• Monte Carlo
• Quasi-Monte Carlo
• regularized Newton's method
• quadratic line-search

AMS Subject Classifications:

• 15A29
• 11K45
• 60J60