Atmospheric Inverse Modeling via Sparse Reconstruction
Nils Hase1, Scot M. Miller2, Peter Maaß1, Justus Notholt3, Mathias Palm3, and Thorsten Warneke31Center for Industrial Mathematics, University of Bremen, Bremen, Germany 2Department of Global Ecology, Carnegie Institution for Science, Stanford, CA, USA 3Institute of Environmental Physics, University of Bremen, Bremen, Germany
Received: 29 Sep 2016 – Accepted for review: 10 Nov 2016 – Discussion started: 14 Nov 2016
Abstract. Many applications in atmospheric science involve ill-posed inverse problems. A crucial component of many inverse problems is the proper formulation of a priori knowledge about the unknown parameters. In most cases, this knowledge is expressed as a Gaussian prior. This formulation often performs well at capturing smoothed, large-scale processes but is often ill-equipped to capture localized structures like large point sources or localized hot spots.
Over the last decade, scientists from a diverse array of applied math and engineering fields have developed sparse reconstruction techniques to identify localized structures. In this study we present a new regularization approach for ill-posed inverse problems in atmospheric science. It is based on Tikhonov regularization with sparsity constraint and allows bounds on the parameters. We enforce sparsity using a dictionary representation system. We analyze its performance in an atmospheric inverse modeling scenario by estimating anthropogenic US methane emissions from simulated atmospheric measurements.
Different measures indicate that our sparse reconstruction approach is better able to capture large point sources or localized hot spots than other methods commonly used in atmospheric inversions. It captures the overall signal equally well, but adds details on the grid scale. This can be of great value in many research projects. We show an example for source estimation of synthetic methane emissions from the Barnett shale formation.
Hase, N., Miller, S. M., Maaß, P., Notholt, J., Palm, M., and Warneke, T.: Atmospheric Inverse Modeling via Sparse Reconstruction, Geosci. Model Dev. Discuss., doi:10.5194/gmd-2016-256, in review, 2016.