02 Jan 2024
 | 02 Jan 2024

Technical note: Posterior Uncertainty Estimation via a Monte Carlo Procedure Specialized for Data Assimilation

Michael Stanley, Mikael Kuusela, Brendan Byrne, and Junjie Liu

Abstract. Through the Bayesian lens of data assimilation, uncertainty on model parameters is traditionally quantified through the posterior covariance matrix. However, in modern settings involving high-dimensional and computationally expensive forward models, posterior covariance knowledge must be relaxed to deterministic or stochastic approximations. In the carbon flux inversion literature, Chevallier et al. (2007) proposed a stochastic method capable of approximating posterior variances of linear functionals of the model parameters that is particularly well-suited for large-scale Earth-system data assimilation tasks. This note formalizes this algorithm and clarifies its properties. We provide a formal statement of the algorithm, demonstrate why it converges to the desired posterior variance quantity of interest, and provide additional uncertainty quantification allowing incorporation of the Monte Carlo sampling uncertainty into the method's Bayesian credible intervals. The methodology is demonstrated using toy simulations and a realistic carbon flux inversion observing system simulation experiment.

Michael Stanley, Mikael Kuusela, Brendan Byrne, and Junjie Liu

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on egusphere-2023-2675', Anonymous Referee #1, 25 Jan 2024
  • RC2: 'Comment on egusphere-2023-2675', Anonymous Referee #2, 19 Feb 2024
Michael Stanley, Mikael Kuusela, Brendan Byrne, and Junjie Liu

Model code and software

GEOS-Chem Adjoint D. Henze et al.

Michael Stanley, Mikael Kuusela, Brendan Byrne, and Junjie Liu


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Short summary
To serve the uncertainty quantification (UQ) needs of data assimilation (DA) practitioners, we describe and justify a UQ algorithm from carbon flux inversion and incorporate its uncertainty into the final reported UQ. The algorithm is mathematically proved and its performance is shown on a carbon flux observing system simulation experiment. These results legitimize and generalize this algorithm’s current use and make available this effective algorithm to new DA domains.