A testbed for geomagnetic data assimilation

Gwirtz, K.; Morzfeld, Matthias; Kuang, Weijia; Tangborn, Andrew

doi:10.1093/gji/ggab327

Cited by 4 publications

(2 citation statements)

References 66 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We emphasize that Kalman-based ensemble filters, including the present work, treat the dynamical model as a black box, and only need to evaluate it at a set of samples in the forecast step. Thus, our methodology is readily applicable to a wide range of filtering problems with elliptic observations such as [5,6] in electromagnetism or [7][8][9] in incompressible fluid flows. In this paper, we focus our discussion on the representative context of incompressible fluid mechanics.…”

Section: Introductionmentioning

confidence: 99%

A low-rank ensemble Kalman filter for elliptic observations

et al. 2022

View full text Add to dashboard Cite

We propose a regularization method for ensemble Kalman filtering (EnKF) with elliptic observation operators. Commonly used EnKF regularization methods suppress state correlations at long distances. For observations described by elliptic partial differential equations, such as the pressure Poisson equation (PPE) in incompressible fluid flows, distance localization should be used cautiously, as we cannot disentangle slowly decaying physical interactions from spurious long-range correlations. This is particularly true for the PPE, in which distant vortex elements couple nonlinearly to induce pressure. Instead, these inverse problems have a low effective dimension: low-dimensional projections of the observations strongly inform a low-dimensional subspace of the state space. We derive a low-rank factorization of the Kalman gain based on the spectrum of the Jacobian of the observation operator. The identified eigenvectors generalize the source and target modes of the multipole expansion, independently of the underlying spatial distribution of the problem. Given rapid spectral decay, inference can be performed in the low-dimensional subspace spanned by the dominant eigenvectors. This low-rank EnKF is assessed on dynamical systems with Poisson observation operators, where we seek to estimate the positions and strengths of point singularities over time from potential or pressure observations. We also comment on the broader applicability of this approach to elliptic inverse problems outside the context of filtering.

show abstract

Section: Introductionmentioning

confidence: 99%

A low-rank ensemble Kalman filter for elliptic observations

et al. 2022

View full text Add to dashboard Cite

show abstract

“…Last, the Bayesian theory may help to construct new localization estimators for the future. Every year, Earth models are becoming increasingly complex, e.g., coupled atmosphere, ocean and sea ice models, or seasonal to sub-seasonal forecast models, and data assimilation is also being extended to geomagnetic models [11,14]. For all these models, traditional localization based on a single length scale parameter may no longer be appropriate.…”

mentioning

confidence: 99%

Localized covariance estimation: A Bayesian perspective

Webber¹,

Morzfeld²

2023

Preprint

View full text Add to dashboard Cite

A major problem in numerical weather prediction (NWP) is the estimation of high-dimensional covariance matrices from a small number of samples. Maximum likelihood estimators cannot provide reliable estimates when the overall dimension is much larger than the number of samples. Fortunately, NWP practitioners have found ingenious ways to boost the accuracy of their covariance estimators by leveraging the assumption that the correlations decay with spatial distance. In this work, Bayesian statistics is used to provide a new justification and analysis of the practical NWP covariance estimators. The Bayesian framework involves manipulating distributions over symmetric positive definite matrices, and it leads to two main findings: (i) the commonly used "hybrid estimator" for the covariance matrix has a naturally Bayesian interpretation; (ii) the very commonly used "Schur product estimator" is not Bayesian, but it can be studied and understood within the Bayesian framework. As practical implications, the Bayesian framework shows how to reduce the amount of tuning required for covariance estimation, and it suggests that efficient covariance estimation should be rooted in understanding and penalizing conditional correlations, rather than correlations.

show abstract

Impact of localization and inflation on geomagnetic data assimilation

Gwirtz,

Kuang,

et al. 2024

Physics of the Earth and Planetary Interiors

View full text Add to dashboard Cite

A testbed for geomagnetic data assimilation

Cited by 4 publications

References 66 publications

A low-rank ensemble Kalman filter for elliptic observations

A low-rank ensemble Kalman filter for elliptic observations

Localized covariance estimation: A Bayesian perspective

Impact of localization and inflation on geomagnetic data assimilation

Contact Info

Product

Resources

About