Articles | Volume 10, issue 10
Geosci. Model Dev., 10, 3695–3713, 2017
Geosci. Model Dev., 10, 3695–3713, 2017

Methods for assessment of models 10 Oct 2017

Methods for assessment of models | 10 Oct 2017

Atmospheric inverse modeling via sparse reconstruction

Nils Hase1, Scot M. Miller2, Peter Maaß1, Justus Notholt3, Mathias Palm3, and Thorsten Warneke3 Nils Hase et al.
  • 1Center 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

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 mathematics 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 (CH4) 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 feature can be of value for any inverse problem with point or spatially discrete sources. We show an example for source estimation of synthetic methane emissions from the Barnett shale formation.

Short summary
Inverse modeling uses atmospheric measurements to estimate emissions of greenhouse gases, which are key to understand the climate system. However, the measurement information alone is typically insufficient to provide reasonable emission estimates. Additional information is required. This article applies modern mathematical inversion techniques to formulate such additional knowledge. It is a prime example of how such tools can improve the quality of estimates compared to commonly used methods.