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Volume 9, issue 11 | Copyright
Geosci. Model Dev., 9, 4297-4311, 2016
https://doi.org/10.5194/gmd-9-4297-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Development and technical paper 25 Nov 2016

Development and technical paper | 25 Nov 2016

LS-APC v1.0: a tuning-free method for the linear inverse problem and its application to source-term determination

Ondřej Tichý1, Václav Šmídl1, Radek Hofman1, and Andreas Stohl2 Ondřej Tichý et al.
  • 1Institute of Information Theory and Automation, Czech Academy of Sciences, Prague, Czech Republic
  • 2NILU: Norwegian Institute for Air Research, Kjeller, Norway

Abstract. Estimation of pollutant releases into the atmosphere is an important problem in the environmental sciences. It is typically formalized as an inverse problem using a linear model that can explain observable quantities (e.g., concentrations or deposition values) as a product of the source-receptor sensitivity (SRS) matrix obtained from an atmospheric transport model multiplied by the unknown source-term vector. Since this problem is typically ill-posed, current state-of-the-art methods are based on regularization of the problem and solution of a formulated optimization problem. This procedure depends on manual settings of uncertainties that are often very poorly quantified, effectively making them tuning parameters. We formulate a probabilistic model, that has the same maximum likelihood solution as the conventional method using pre-specified uncertainties. Replacement of the maximum likelihood solution by full Bayesian estimation also allows estimation of all tuning parameters from the measurements. The estimation procedure is based on the variational Bayes approximation which is evaluated by an iterative algorithm. The resulting method is thus very similar to the conventional approach, but with the possibility to also estimate all tuning parameters from the observations. The proposed algorithm is tested and compared with the standard methods on data from the European Tracer Experiment (ETEX) where advantages of the new method are demonstrated. A MATLAB implementation of the proposed algorithm is available for download.

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Estimation of pollutant releases into the atmosphere is an important problem in the environmental sciences. We formulate a probabilistic model, where a full Bayesian estimation allows estimation of all tuning parameters from the measurements. The proposed algorithm is tested and compared with the state-of-the-art method on data from the European Tracer Experiment (ETEX), where advantages of the new method are demonstrated.
Estimation of pollutant releases into the atmosphere is an important problem in the...
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