Atmospheric inverse modeling via sparse reconstruction
Atmospheric inverse modeling via sparse reconstruction
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DOI：
10.5194/gmd-10-3695-2017
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发表时间：
2016-11
影响因子：
5.1
通讯作者：
N. Hase;Scot M. Miller;P. Maass;J. Notholt;M. Palm;T. Warneke
中科院分区：
文献类型：
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作者：
N. Hase;Scot M. Miller;P. Maass;J. Notholt;M. Palm;T. Warneke
摘要。大气科学中的许多应用涉及不适定逆问题。许多反问题的一个关键组成部分是关于未知参数的先验知识的适当表述。在大多数情况下，这种知识被表示为高斯先验。该公式通常在捕获平滑的大规模过程方面表现良好，但通常不适合捕获局部结构，如大型点源或局部热点。在过去的十年中，来自不同应用数学和工程领域的科学家开发了稀疏重建技术来识别局部结构。在这项研究中，我们提出了一种新的正则化方法来解决大气科学中的病态逆问题。它基于带稀疏约束的Tikhonov正则化，允许参数有界。我们使用字典表示系统来加强稀疏性。我们通过估算模拟大气测量的美国人为甲烷（CH4）排放量来分析其在大气逆模拟情景下的性能。不同的测量结果表明，我们的稀疏重建方法比其他常用的大气逆温方法更能捕获大的点源或局部热点。它捕获的整体信号同样好，但在网格尺度上增加了细节。这一特征对于任何具有点或空间离散源的反问题都是有价值的。我们展示了巴内特页岩地层合成甲烷排放源估计的一个例子。
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.