Ring current pressure estimation with RAM‐SCB using data assimilation and Van Allen Probe flux data

Godinez, H. C.; Yu, Yiqun; Lawrence, Earl; Henderson, M. G.; Larsen, B.; Jordanova, V. K.

doi:10.1002/2016gl071646

Cited by 19 publications

(13 citation statements)

References 38 publications

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“…Challenges further lie in how to take full advantage of the rapidly growing massive satellite measurements and maturing physics-based models by using effective tools, such as machine learning and data assimilation. While these techniques have been widely and successfully applied in the ionosphere, they are quite limited in the inner magnetosphere field (there are only a few research groups dedicating to this area, e.g., Chu et al, 2017;Godinez et al, 2016;Kellerman et al, 2014;Shprits et al, 2013;Zhelavskaya et al, 2017). How to extend their application to other geospace regions and dynamics to achieve a full 3-D representation of the inner magnetosphere is one challenging objective.…”

Section: Future Challengesmentioning

confidence: 99%

Integration of RAM-SCB into the Space Weather Modeling Framework

Welling

Tóth

Jordanova

et al. 2018

Journal of Atmospheric and Solar-Terrestrial Physics

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The geospace inner magnetosphere, within about 10 Earth radii, contains various plasma populations with energy from a few electron volts to megaelectron volts and plays important roles in regulating the energy density of the magnetosphere, the magnetic field configuration, and wave dynamics. As an integrated part of the magnetosphere, the inner magnetosphere region also ties to other regions and can change the global geospace circulation. Therefore, understanding both internal and external cross-energy/population interactions can help further our knowledge of the inner magnetosphere dynamics and nonlinear feedback processes. In view of this, in the past 5 years (2014-2018), the Geospace Environment Modeling (GEM) Focus Group "inner magnetosphere cross-energy/population interactions (IMCEPI)" has gathered and boosted community-wide interactions among observation, simulation, and modeling studies. This commentary reports some major accomplishments of the interactive inner magnetosphere community that were advanced by the IMCEPI Focus Group discussions and layouts remaining challenges that need to be carried on.

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Section: Future Challengesmentioning

confidence: 99%

Integration of RAM-SCB into the Space Weather Modeling Framework

Welling

Tóth

Jordanova

et al. 2018

Journal of Atmospheric and Solar-Terrestrial Physics

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“…For example, in data assimilation for the interior of the Earth, such as lithospheric plates (e.g., Kano et al, 2015) and the outer core (e.g., Sanchez et al, 2019;Minami et al, 2020), the timescale of the system dynamics is so long that a sufficient length of an observation sequence is not feasible. It is also difficult to use a long sequence of observations in the Earth's magnetosphere where the amount of observations is limited (e.g., Nakano et al, 2008;Godinez et al, 2016). It is therefore an important issue to consider large uncertainties which could deteriorate the validity of the linear approximation.…”

Section: Introductionmentioning

confidence: 99%

“…Several studies have suggested that estimations in nonlinear problems can be improved by iterative algorithms in which the ensemble is repeatedly updated in each iteration (e.g., Gu and Oliver, 2007;Kalnay and Yang, 2010;Chen and Oliver, 2012;Sakov, 2013, 2014;Raanes et al, 2019). These iterative algorithms can be regarded as a S. Nakano: Ensemble variational method variant of the 4DEnVar method, based on an approximation of the Gauss-Newton method or the Levenberg-Marquardt method.…”

Section: Introductionmentioning

confidence: 99%

Behavior of the iterative ensemble-based variational method in nonlinear problems

Nakano

2021

Nonlin. Processes Geophys.

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Abstract. The behavior of the iterative ensemble-based data assimilation algorithm is discussed. The ensemble-based method for variational data assimilation problems, referred to as the 4D ensemble variational method (4DEnVar), is a useful tool for data assimilation problems. Although the 4DEnVar is derived based on a linear approximation, highly uncertain problems, in which system nonlinearity is significant, are solved by applying this method iteratively. However, the ensemble-based methods basically seek the solution within a lower-dimensional subspace spanned by the ensemble members. It is not necessarily trivial how high-dimensional problems can be solved with the ensemble-based algorithm which employs the lower-dimensional approximation based on the ensemble. In the present study, an ensemble-based iterative algorithm is reformulated to allow us to analyze its behavior in high-dimensional nonlinear problems. The conditions for monotonic convergence to a local maximum of the objective function are discussed in a high-dimensional context. It is shown that the ensemble-based algorithm can solve high-dimensional problems by distributing the ensemble in different subspace at each iteration. The findings as the results of the present study were also experimentally supported.

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“…For example, in data assimilation for the interior of the Earth such as lithospheric plates (e.g., Kano et al, 2015) and the 20 outer core (e.g., Sanchez et al, 2019;Minami et al, 2020), time scale of system dynamics is so long that a sufficient length of an observation sequence is not feasible. It is also difficult to use a long sequence of observations in the Earth's magnetosphere where the amount of observations is limited (e.g., Nakano et al, 2008;Godinez et al, 2016). It is therefore an important issue to consider large uncertainties which could deteriorate the validity of the linear approximation.…”

Section: Introductionmentioning

confidence: 99%

Behavior of the iterative ensemble-based variational method in nonlinear problems

Nakano¹

2020

Preprint

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The behavior of the iterative ensemble-based data assimilation algorithm is discussed. The ensemble-based method for variational data assimilation problems, referred to as the 4-dimensional ensemble variational method (4DEnVar), is a useful tool for data assimilation problems. Although the 4DEnVar is derived based on a linear approximation, highly uncertain problems, where system nonlinearity is significant, are solved by applying this method iteratively. However, it is not necessarily trivial how the algorithm works in highly uncertain problems where nonlinearity is not negligible. In the present study, an 5 ensemble-based iterative algorithm is reformulated to allow us to analyze its behavior in nonlinear problems. The conditions for monotonic convergence to a local maximum of the objective function are discussed in nonlinear context. The findings as the results of the present study were also experimentally supported. https://doi.org/10.5194/npg-2020-9 Preprint. Discussion started: 17 April 2020 c Author(s) 2020. CC BY 4.0 License.Several studies have suggested that estimation in nonlinear problems can be improved by iterative algorithms in which 25 the ensemble is repeatedly updated in each iteration (e.g., Gu and Oliver, 2007;Kalnay and Yang, 2010; Chen and Oliver, 2012; Sakov, 2013, 2014;Raanes et al., 2019). These iterative algorithms can be regarded as a variant of the 4DEnVar method based on an approximation of the Gauss-Newton method or the Levenberg-Marquardt method. The Gauss-Newton and the Levenberg-Marquardt methods are variants of the Newton-Raphson method for solving nonlinear least squares problems by using the Jacobian of a nonlinear function. Thus, when the Gauss-Newton or the Levenberg-Marquardt framework 30 is strictly applied to data assimilation problems, the tangent linear of the system model is required. Indeed, if the tangent linear of the system model is obtained, 4-dimensional variational data assimilation problems can be solved with the incremental formulation (Courtier et al., 1994) which can be regarded as an instance of the Gauss-Newton framework (Lawless et al., 2005). The ensemble-based methods avoid computing the Jacobian of a nonlinear system model by a low-rank linear approximation using the ensemble. This ensemble-based approximation is justified if linearity can be assumed over the range where the 35 ensemble members are distributed. However, it has not necessarily been clarified how the algorithm works in highly uncertain problems where nonlinearity is not negligible.The present study aims to reformulate an ensemble-based iterative algorithm in order to analyze its behavior in nonlinear problems. We then explore the conditions for achieving monotonic convergence to a local maximum of the objective function in nonlinear context. The monotonic convergence means that the discrepancies between estimates and observations are reduced 40 in each iteration. It is thus ensured that the algorithm would attain a satisfactory result in nonlinear problems. This study is originally moti...

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Ring current pressure estimation with RAM‐SCB using data assimilation and Van Allen Probe flux data

Cited by 19 publications

References 38 publications

Integration of RAM-SCB into the Space Weather Modeling Framework

Integration of RAM-SCB into the Space Weather Modeling Framework

Behavior of the iterative ensemble-based variational method in nonlinear problems

Behavior of the iterative ensemble-based variational method in nonlinear problems

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