Journal cover Journal topic
Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
Geosci. Model Dev., 10, 3695-3713, 2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
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 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.

Citation: Hase, N., Miller, S. M., Maaß, P., Notholt, J., Palm, M., and Warneke, T.: Atmospheric inverse modeling via sparse reconstruction, Geosci. Model Dev., 10, 3695-3713,, 2017.
Publications Copernicus
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.
Inverse modeling uses atmospheric measurements to estimate emissions of greenhouse gases, which...