Inverse Problem Theory and Methods for Model Parameter Estimation
Inverse Problem Theory and Methods for Model Parameter Estimation
Environmental Modelling & Software
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Abstract: In this paper a method is presented which allows for estimation of the location and rate of an unknown point stationary source of passive atmospheric pollutant in a complex urban geometry. The variational formulation is used in which the cost function characterizing difference of the calculated and measured concentrations is minimized with respect to source coordinates and rate. The minimization problem is solved by a direct algorithm using a source-receptor function which is calculated by solving adjoint equation. The algorithm has been implemented in ADREA-HF computational fluid dynamics code and has been applied in complex urban geometry. Validation of the algorithm has been performed by simulation of a wind tunnel experiment on atmospheric dispersion among an array of rectangular obstacles. Good results of source parameters estimation have been achieved. The measuring sensors to be used in source estimation had been randomly selected out of 244 available sensors by a specially designed random sampling algorithm which allowed for estimation of the probability of 'good' source term estimation with the given number of sensors. In case of 'perfect model' (when synthetic measurements were used for source estimation) good results were achieved with 90% or higher probability for arbitrary measurement networks consisting of 15 or more sensors even though prior estimation of source location was not used in this case. Several tests had been performed with the use of real measurements which differed by prior estimation of source location. In all cases 90% or higher probability of obtaining good solution was reached only for measurement networks consisting of 150 or more sensors. Hence further improvement of the source estimation algorithm can be achieved first of all by improving the performance of forward model.