@article{SanchezWichtBaerenzungetal.2019,
  author    = {Sanchez, S. and Wicht, J. and Baerenzung, Julien and Holschneider, Matthias},
  title     = {Sequential assimilation of geomagnetic observations},
  series = {Geophysical journal international},
  volume    = {217},
  journal   = {Geophysical journal international},
  number    = {2},
  publisher = {Oxford Univ. Press},
  address   = {Oxford},
  issn      = {0956-540X},
  doi       = {10.1093/gji/ggz090},
  pages     = {1434 -- 1450},
  year      = {2019},
  abstract  = {High-precision observations of the present-day geomagnetic field by ground-based observatories and satellites provide unprecedented conditions for unveiling the dynamics of the Earth's core. Combining geomagnetic observations with dynamo simulations in a data assimilation (DA) framework allows the reconstruction of past and present states of the internal core dynamics. The essential information that couples the internal state to the observations is provided by the statistical correlations from a numerical dynamo model in the form of a model covariance matrix. Here we test a sequential DA framework, working through a succession of forecast and analysis steps, that extracts the correlations from an ensemble of dynamo models. The primary correlations couple variables of the same azimuthal wave number, reflecting the predominant axial symmetry of the magnetic field. Synthetic tests show that the scheme becomes unstable when confronted with high-precision geomagnetic observations. Our study has identified spurious secondary correlations as the origin of the problem. Keeping only the primary correlations by localizing the covariance matrix with respect to the azimuthal wave number suffices to stabilize the assimilation. While the first analysis step is fundamental in constraining the large-scale interior state, further assimilation steps refine the smaller and more dynamical scales. This refinement turns out to be critical for long-term geomagnetic predictions. Increasing the assimilation steps from one to 18 roughly doubles the prediction horizon for the dipole from about  tree to six centuries, and from 30 to about  60 yr for smaller observable scales. This improvement is also reflected on the predictability of surface intensity features such as the South Atlantic Anomaly. Intensity prediction errors are decreased roughly by a half when assimilating long observation sequences.},
  language  = {en}
}
@article{HolschneiderLesurMauerbergeretal.2016,
  author    = {Holschneider, Matthias and Lesur, Vincent and Mauerberger, Stefan and Baerenzung, Julien},
  title     = {Correlation-based modeling and separation of geomagnetic field components},
  series = {Journal of geophysical research : Solid earth},
  volume    = {121},
  journal   = {Journal of geophysical research : Solid earth},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {2169-9313},
  doi       = {10.1002/2015JB012629},
  pages     = {3142 -- 3160},
  year      = {2016},
  abstract  = {We introduce a technique for the modeling and separation of geomagnetic field components that is based on an analysis of their correlation structures alone. The inversion is based on a Bayesian formulation, which allows the computation of uncertainties. The technique allows the incorporation of complex measurement geometries like observatory data in a simple way. We show how our technique is linked to other well-known inversion techniques. A case study based on observational data is given.},
  language  = {en}
}
@article{BaerenzungHolschneiderWichtetal.2020,
  author    = {Baerenzung, Julien and Holschneider, Matthias and Wicht, Johannes and Lesur, Vincent and Sanchez, Sabrina},
  title     = {The Kalmag model as a candidate for IGRF-13},
  series = {Earth, planets and space},
  volume    = {72},
  journal   = {Earth, planets and space},
  number    = {1},
  publisher = {Springer},
  address   = {New York},
  issn      = {1880-5981},
  doi       = {10.1186/s40623-020-01295-y},
  pages     = {13},
  year      = {2020},
  abstract  = {We present a new model of the geomagnetic field spanning the last 20 years and called Kalmag. Deriving from the assimilation of CHAMP and Swarm vector field measurements, it separates the different contributions to the observable field through parameterized prior covariance matrices. To make the inverse problem numerically feasible, it has been sequentialized in time through the combination of a Kalman filter and a smoothing algorithm. The model provides reliable estimates of past, present and future mean fields and associated uncertainties. The version presented here is an update of our IGRF candidates; the amount of assimilated data has been doubled and the considered time window has been extended from [2000.5, 2019.74] to [2000.5, 2020.33].},
  language  = {en}
}
@article{BaerenzungHolschneiderLesur2014,
  author    = {Baerenzung, Julien and Holschneider, Matthias and Lesur, Vincent},
  title     = {Bayesian inversion for the filtered flow at the Earth's core-mantle boundary},
  series = {Journal of geophysical research : Solid earth},
  volume    = {119},
  journal   = {Journal of geophysical research : Solid earth},
  number    = {4},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {2169-9313},
  doi       = {10.1002/2013JB010358},
  pages     = {2695 -- 2720},
  year      = {2014},
  abstract  = {The inverse problem of determining the flow at the Earth's core-mantle boundary according to an outer core magnetic field and secular variation model has been investigated through a Bayesian formalism. To circumvent the issue arising from the truncated nature of the available fields, we combined two modeling methods. In the first step, we applied a filter on the magnetic field to isolate its large scales by reducing the energy contained in its small scales, we then derived the dynamical equation, referred as filtered frozen flux equation, describing the spatiotemporal evolution of the filtered part of the field. In the second step, we proposed a statistical parametrization of the filtered magnetic field in order to account for both its remaining unresolved scales and its large-scale uncertainties. These two modeling techniques were then included in the Bayesian formulation of the inverse problem. To explore the complex posterior distribution of the velocity field resulting from this development, we numerically implemented an algorithm based on Markov chain Monte Carlo methods. After evaluating our approach on synthetic data and comparing it to previously introduced methods, we applied it to a magnetic field model derived from satellite data for the single epoch 2005.0. We could confirm the existence of specific features already observed in previous studies. In particular, we retrieved the planetary scale eccentric gyre characteristic of flow evaluated under the compressible quasi-geostrophy assumption although this hypothesis was not considered in our study. In addition, through the sampling of the velocity field posterior distribution, we could evaluate the reliability, at any spatial location and at any scale, of the flow we calculated. The flow uncertainties we determined are nevertheless conditioned by the choice of the prior constraints we applied to the velocity field.},
  language  = {en}
}