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Ryosuke Nakashima, Shigeo Yoshida, [プレプリント] Two-dimensional ideal magnetohydrodynamic waves on a rotating sphere under a non-Malkus field: I. Continuous spectrum and its ray-theoretical interpretation, *arXiv / EarthArXiv*, 10.48550/arXiv.2310.01341, 10.31223/X5Z67T, 2023.10, Two-dimensional (2D) ideal incompressible magnetohydrodynamic (MHD) linear waves at the surface of a rotating sphere are studied as a model imitating the outermost Earth's core or the solar tachocline. This thin conducting layer is permeated by a toroidal magnetic field whose magnitude depends only on the latitude. The Malkus background field, which is proportional to the sine of the colatitude, gives two well-known groups of branches on which Alfvén waves gradually become fast or slow magnetic Rossby (MR) waves as the field amplitude decreases. For non-Malkus fields, we show that the associated eigenvalue problems can yield a continuous spectrum instead of Alfvén and slow MR discrete modes. Critical latitudes attributed to the Alfvén resonance wipe out these discrete eigenvalues and produce an infinite number of singular eigenmodes. The theory of slowly varying wave trains in an inhomogeneous magnetic field shows that a wave packet related to this continuous spectrum propagates toward a critical latitude corresponding to the wave and is eventually absorbed there. The expected behaviour that the retrograde propagating packets which pertain to the continuous spectrum approach the latitudes from the equatorial side and that the prograde ones approach there from the polar side is consistent with the profiles of their eigenfunctions shown by our numerical calculations. Further in-depth discussions of the Alfvén continuum would progress the theory of ``wave-mean field interaction'' in the MHD system and one's understanding of the dynamics in such thin layers.. |

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Takuto Minami, Shin’ya Nakano, Vincent Lesur, Futoshi Takahashi, Masaki Matsushima, Hisayoshi Shimizu, Ryosuke Nakashima, Hinami Taniguchi, Hiroaki Toh, A candidate secular variation model for IGRF-13 based on MHD dynamo simulation and 4DEnVar data assimilation, *Earth, Planets and Space*, 10.1186/s40623-020-01253-8, 72, 1, 2020.09, Abstract
We have submitted a secular variation (SV) candidate model for the thirteenth generation of International Geomagnetic Reference Field model (IGRF-13) using a data assimilation scheme and a magnetohydrodynamic (MHD) dynamo simulation code. This is the first contribution to the IGRF community from research groups in Japan. A geomagnetic field model derived from magnetic observatory hourly means, and CHAMP and Swarm-A satellite data, has been used as input data to the assimilation scheme. We adopt an ensemble-based assimilation scheme, called four-dimensional ensemble-based variational method (4DEnVar), which linearizes outputs of MHD dynamo simulation with respect to the deviation from a dynamo state vector at an initial condition. The data vector for the assimilation consists of the poloidal scalar potential of the geomagnetic field at the core surface and flow velocity field slightly below the core surface. Dimensionless time of numerical geodynamo is adjusted to the actual time by comparison of secular variation time scales. For SV prediction, we first generate an ensemble of dynamo simulation results from a free dynamo run. We then assimilate the ensemble to the data with a 10-year assimilation window through iterations, and finally forecast future SV by the weighted sum of the future extension parts of the ensemble members. Hindcast of the method for the assimilation window from 2004.50 to 2014.25 confirms that the linear approximation holds for 10-year assimilation window with our iterative ensemble renewal method. We demonstrate that the forecast performance of our data assimilation and forecast scheme is comparable with that of IGRF-12 by comparing data misfits 4.5 years after the release epoch. For estimation of our IGRF-13SV candidate model, we set assimilation window from 2009.50 to 2019.50. We generate our final SV candidate model by linear fitting for the weighted sum of the ensemble MHD dynamo simulation members from 2019.50 to 2025.00. We derive errors of our SV candidate model by one standard deviation of SV histograms based on all the ensemble members.. |