Submitted as: methods for assessment of models
23 May 2022
Submitted as: methods for assessment of models | 23 May 2022
Status: this preprint is currently under review for the journal GMD.

Metrics for assessing Linear Inverse Problems: a case study of a Trace Gas Inversion

Vineet Yadav1, Subhomoy Ghosh2,3, and Charles E. Miller1 Vineet Yadav et al.
  • 1Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA, USA
  • 2University of Notre Dame, Notre Dame, IN, USA
  • 3National Institute of Standards and Technology, Gaithersburg, MD, USA

Abstract. Multiple metrics have been proposed and utilized to assess the performance of linear Bayesian and geostatistical inverse problems. These metrics are mostly related to assessing reduction in prior uncertainties, comparing modeled observations to true observations, and checking distributional assumptions. These metrics though important should be augmented with sensitivity analysis to obtain a comprehensive understanding of the performance of inversions and critically improve confidence in the estimated fluxes. With this motivation, we derive analytical forms of the local sensitivities with respect to the number of inputs such as measurements, covariance parameters, covariates, and forward operator or jacobian. In addition to local sensitivity, we develop a framework for global sensitivity analysis that shows the apportionment of the uncertainty of different inputs to an inverse problem. The proposed framework is applicable to any other domain that employs linear Bayesian and geostatistical inverse methods. We show the application of our methodology in the context of an atmospheric inverse problem for estimating urban GHG emissions in Los Angeles. Within its context, we also propose a mathematical framework to construct correlation functions and components of uncertainty matrices from a pre-computed jacobian that encompasses non-stationary structures.

Vineet Yadav et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on gmd-2022-89', Peter Rayner, 03 Jul 2022
  • RC2: 'Comment on gmd-2022-89', Anonymous Referee #2, 15 Jul 2022

Vineet Yadav et al.

Vineet Yadav et al.


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Short summary
Measuring the performance of inversions in linear Bayesian problems is crucial in real-life applications. In this work, we provide analytical forms of the local and global sensitivities of the estimated fluxes with respect to various inputs. We provide methods to uniquely map the observational signal to spatio-temporal domains. Utilizing this, we also show techniques to assess correlations between the jacobians that naturally translate to nonstationary covariance matrix components.