著者

菖蒲迫 健介 吉田 茂生 川田 佳史 中島 涼輔

雑誌

日本地球惑星科学連合2022年大会

巻号頁・発行日

2022-03-24

著者

中島 涼輔 吉田 茂生

雑誌

日本地球惑星科学連合2022年大会

巻号頁・発行日

2022-03-24

著者

南 拓人 中野 慎也 高橋 太 松島 政貴 中島 涼輔 清水 久芳 谷口 陽菜実 藤 浩明

雑誌

JpGU-AGU Joint Meeting 2020

巻号頁・発行日

2020-03-13

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The thirteenth generation of International Geomagnetic Reference Field (IGRF-13) was released by International Association of Geomagnetism and Aeronomy (IAGA) in December, 2019. Prior to the release, we submitted a secular variation (SV) candidate model for IGRF-13 using a data assimilation scheme and a magnetohydrodynamic (MHD) dynamo simulation code (Minami et al. submitted to EPS special issue for IGRF-13). Our candidate SV model was evaluated by IAGA Division V Working Group V-MOD and contributed to the final IGRF-13SV model with the optimized weight. This became the first contribution to the IGRF community from research groups in Japan. This was enabled by bilateral corroboration between Japan and France; in our data assimilation scheme, we used the French main field model (Ropp et al. 2020), which was developed from magnetic observatory hourly means, and CHAMP and Swarm-A satellite data. We adopted an iterative assimilation algorithm based on four-dimensional ensemble-based variational method (4DEnVar) (Nakano 2020), which linearizes outputs of our MHD dynamo simulation (Takahashi 2012; 2014) 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 Earth’s core surface, and flow velocity field slightly below the core surface, which was calculated by presuming magnetic diffusion in the boundary layer and tangentially magnetostrophic flow below it (Matsushima 2020). Dimensionless time of numerical geodynamo was adjusted to the actual time by comparison of secular variation time scales. For estimation of our IGRF-13SV candidate model, we first generated an ensemble of dynamo simulation results from a free dynamo run. We then assimilated the ensemble to the data with a 10-year assimilation window from 2009.50 to 2019.50 through iterations, and finally forecasted future SV by linear combination of the future extension parts of the ensemble members. We generated our final SV candidate model by linear fitting for the best linear combination of the ensemble MHD dynamo simulation members from 2019.50 to 2025.00. We derived errors of our SV candidate model by one standard deviation of SV histograms based on all the ensemble members. In the presentation, we plan to report our IGRF project through the bilateral corroboration with France, and describe our SV candidate model.

著者

松島 政貴 清水 久芳 高橋 太 南 拓人 中野 慎也 中島 涼輔 谷口 陽菜実 藤 浩明

雑誌

JpGU-AGU Joint Meeting 2020

巻号頁・発行日

2020-03-13

---

The International Geomagnetic Reference Field (IGRF) is a standard mathematical description in terms of spherical harmonic coefficients, known as the Gauss coefficients, for the Earth’s main magnetic field and its secular variation. On December 19, 2019, the working group V-MOD of the International Association of Geomagnetism and Aeronomy (IAGA) released the 13th generation of IGRF, which consists of three constituents; a Definitive IGRF (DGRF) for 2015, an IGRF for 2020, and a secular variation (SV) model from 2020 to 2025. We submitted a candidate model for SV from 2020 to 2025, relying on our strong points, such as geodynamo numerical simulation, data assimilation, and core surface flow modeling.We can estimate core flow near the core-mantle boundary (CMB)from distribution of geomagnetic field and its secular variation. Such a flow model can be obtained for actual physical parameters of the Earth. However, numerical simulations of geodynamo were carried out for physical parameters far from actual ones. Therefore, a core flow model to be used for data assimilation had to be obtained on a condition relevant to the numerical simulations. To obtain the candidate model for SV, we adjusted time-scale of a geodynamo model (Takahashi 2012, 2014) to that of actual SV of geomagnetic field as given by Christensen and Tilgner (2004).In this presentation, we first investigate temporal variations of geomagnetic field due to the magnetic diffusion only. Next, we investigate temporal variations of geomagnetic field due to the motional induction caused by some core flow models as well as the magnetic diffusion. Then we compare secular variations of geomagnetic field forecasted by these methods.

著者

高橋 太 中野 慎也 南 拓人 谷口 陽菜実 中島 涼輔 松島 政貴 清水 久芳 藤 浩明

雑誌

JpGU-AGU Joint Meeting 2020

巻号頁・発行日

2020-03-13

---

Secular variation (SV) of the Earth's magnetic field is governed by the advection and diffusion processes of the magnetic field within the fluid outer core. The IGRF (International Geomagnetic Reference Field) offers the average SV for the next five years to come, which has been estimated in various methods. In general, forecasting the evolution of a non-linear system like the geodynamo in the Earth's core is an extremely difficult task, because the magnetic field generation processes are controlled by the complex interaction of the core flows and the generated magnetic field. Data assimilation has been a promising scheme forecasting the geomagnetic SV as demonstrated in literatures (Kuang 2010, Fournier et al. 2015), where time dependency is controlled by a numerical dynamo model. While Ensemble Kalman Filter (EnKF) has been a popular method for data assimilation in geomagnetism, we apply a different data assimilation procedure, that is, four-dimensional, ensemble-based variational scheme, 4DEnVar. Applying the 4DEnVar scheme iteratively, we have derived a candidate SV model for the latest version of the IGRF. In evaluating SV, two forecasting strategies are tested, in which core flows are assumed to be steady or time-dependent. The former approach is favored in Fournier et al. (2015), where the magnetic field evolves kinematically by the flows prescribed to be time-independent in the initialization step. On the other hand, we have adopted linear combination of magnetohydrodynamic (MHD) models to construct a candidate as the best forecast (Minami et al. 2020). It is likely that which strategy is more suitable to forecasting SV depends on assimilation scheme and/or numerical dynamo model. However, we have little knowledge on the issue at present. In this study, we investigate results of MHD and kinematic dynamo runs with a 4DEnVar scheme in order to have a grasp of the properties of the scheme in the 5-year forecast process. Also, MHD and kinematic runs are compared to infer internal dynamics responsible for SV in the geomagnetic field.

著者

中島 涼輔 吉田 茂生

雑誌

JpGU-AGU Joint Meeting 2020

巻号頁・発行日

2020-03-13

---

Magnetohydrodynamic (MHD) shallow water linear waves are investigated over a rotating sphere with an imposed equatorially antisymmetric toroidal magnetic field: B0Φ=B0sinθcosθ, where B0 is a constant, θ is the colatitude and Φ is the azimuth. This system can imitatively represent the dynamics of a liquid metal within a stably stratified layer at the top of the Earth's core, which was detected through seismological surveys (e.g. Helffrich & Kaneshima, 2010[1]) and also has been deduced from geophysical and geochemical knowledge (e.g. Buffett & Seagle, 2010[2]; Pozzo et al., 2012[3]; Gubbins & Davies, 2013[4]; Brodholt & Badro, 2017[5]). Because slowly propagating waves in the liquid core can result in geomagnetic secular variations, comparison between exhaustive studies of MHD waves in a rotating stratified fluid and observations of geomagnetic fluctuations should provide constraints on the obscure stratified layer in the outermost core (e.g. Braginsky, 1993[6]; Buffett, 2014[7]).The adopted configuration of the background field complicates solving the eigenvalue problem of linear waves due to the emergence of an Alfvén continuum and critical latitudes unless dissipation effects are taken into account. These result from non-dissipative Alfvén resonance, which occurs only when B0Φ/sinθ depends on θ, that is, regular singular points appear in the differential equation of linear problems. The solutions of the continuum are required to express the transient evolution of an arbitrary initial disturbance (e.g. Case, 1960[8]; Goedbloed & Poedts, 2004[9]). We can confirm numerically and analytically that introducing magnetic diffusion eliminates these Alfvén continuous modes and their singular structures around critical latitudes (Nakashima, Ph.D. thesis, 2020[10]).For the Earth's core-like parameter (B0≃0.5—5mT and magnetic diffusivity η≃1m2/s), westward polar trapped modes are obtained as eigenmodes, which have a period of around from several to 1000 years. We may be able to observe these modes as geomagnetic secular variations in high latitude regions, if the strength of stratification in the stratified layer is close to the estimate of Buffett (2014)[7]. The analyses of recent geomagnetic models and paleomagnetic data in terms of such waves could confirm the robustness of previous estimates of the properties of the layer.[ Reference ][1] Helffrich, G., Kaneshima, S. (2010) Nature, 468, 807. doi: 10.1038/nature09636[2] Buffett, B. A., Seagle, C. T. (2010) J. Geophys. Res., 115, B04407. doi: 10.1029/2009JB006751[3] Pozzo, M., Davies, C., Gubbins, D., Alfè, D. (2012) Nature, 485, 355. doi: 10.1038/nature11031[4] Gubbins, D., Davies, C. J. (2013) Phys. Earth Planet. Inter., 215, 21. doi: 10.1016/j.pepi.2012.11.001[5] Brodholt, J., Badro, J. (2017) Geophys. Res. Lett., 44, 8303. doi: 10.1002/2017GL074261[6] Braginsky, S. I. (1993) J. Geomag. Geoelectr., 45, 1517. doi: 10.5636/jgg.45.1517[7] Buffett, B. (2014) Nature, 507, 484. doi: 10.1038/nature13122[8] Case, K. M. (1960) Phys. Fluids, 3, 143. doi: 10.1063/1.1706010[9] Goedbloed, J. P., Poedts, S. (2004) Principles of magnetohydrodynamics: with applications to laboratory and astrophysical plasmas, Cambridge Univ. Press, Cambridge.[10] Nakashima, R. (2020) Ph.D. thesis, Kyushu University. http://dyna.geo.kyushu-u.ac.jp/HomePage/nakashima/pdf/doctoral_thesis.pdf

著者

中島 涼輔 吉田 茂生

雑誌

JpGU-AGU Joint Meeting 2020

巻号頁・発行日

2020-03-13

---

Magnetohydrodynamic (MHD) shallow water linear waves are examined on a rotating sphere with a background toroidal magnetic field expressed as B0Φ=B0sinθ, where B0 is constant, θ is the colatitude and Φ is the azimuth. The MHD shallow water equations are often used in studying the dynamics of the solar tachocline (e.g. Gilman & Dikpati, 2002[1]; Márquez-Artavia et al., 2017[2]) and sometimes the outermost Earth's core (Márquez-Artavia et al., 2017[2]; Nakashima, Ph.D. thesis, 2020[3]) and exoplanetary atmosphere (e.g. Heng & Workman, 2014[4]). In this poster, we especially focus on the propagation mechanisms and the force balances of polar trapped waves and unstable modes (Márquez-Artavia et al., 2017[2]; Nakashima, Ph.D. thesis, 2020[3]).Comprehensive searches for eigenmodes yield two polar trapped modes when the main magnetic field is weak (the Lehnert number α=VA/2ΩR2<0.5, where VA is the Alfvén wave velocity, Ω is the rotation rate and R is the sphere radius). One is the slow magnetic Rossby waves, which propagate eastward for zonal wave number m≧2 (Márquez-Artavia et al., 2017[2]). As the Lamb's parameter ε=4Ω2R2/gh→0 (where g is the gravity acceleration and h is the equivalent depth), these branches asymptotically approach the eigenvalues of two-dimensional slow magnetic Rossby waves. Another is newly discovered westward polar trapped modes (Nakashima, Ph.D. thesis, 2020[3]).In the case when α>0.5 (the background field is strong), these novel westward modes merge with the westward-propagating fast magnetic Rossby waves. In addition, only when m=1, polar trapped unstable modes appear due to the interaction between these fast magnetic Rossby waves and westward-propagating slow magnetic Rossby waves. These growth modes are believed to be the polar kink (Tayler) instability (Márquez-Artavia et al., 2017[2]).In order to easily understand the propagation mechanisms and the force balances of polar trapped modes, we investigate a cylindrical model around a pole with an artificial boundary condition. This model provides the approximate dispersion relations and eigenfunctions of polar trapped modes, and indicates that stable polar trapped modes are governed by magnetostrophic balance and that the metric magnetic tension force causes the difference between the slow magnetic Rossby waves and the novel westward modes. For m=1 and α>0.5, the balance between Coriolis and Lorentz forces is disrupted and the part of magnetic tension with which Coriolis force can not compete induces kink instability.[ Reference ][1] Gilman, P. A., Dikpati, M. (2002) Astrophys. J., 576, 1031. doi: 10.1086/341799[2] Márquez-Artavia, X., Jones, C. A., Tobias, S. M. (2017) Geophys. Astrophys. Fluid Dyn., 111, 282. doi: 10.1080/03091929.2017.1301937[3] Nakashima, R. (2020) Ph.D. thesis, Kyushu University. http://dyna.geo.kyushu-u.ac.jp/HomePage/nakashima/pdf/doctoral_thesis.pdf[4] Heng, K., Workman, J. (2014) Astrophys. J. Sup., 213, 27. doi: 10.1088/0067-0049/213/2/27

著者

中島 涼輔 吉田 茂生

出版者

日本地球惑星科学連合

雑誌

日本地球惑星科学連合2019年大会

巻号頁・発行日

2019-03-14

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Magnetohydrodynamic (MHD) waves in a thin layer on a rotating sphere with an imposed toroidal magnetic field are investigated. The system is often considered as a model of the stably stratified outermost Earth's outer core or the tachocline of the Sun. The stratification of the outermost core is suggested on the basis of seismological evidence (e.g. Helffrich and Kaneshima, 2010; Kaneshima, 2018) and interpretations of the geomagnetic variations with MHD waves (e.g. Braginsky, 1993; Buffett, 2014; Chulliat et al., 2015). In order to provide constraints on the obscure stratified layer by comparing with wavy variations in the geomagnetic field, we studied the linear waves of the two-dimensional MHD and the MHD shallow water system over a rotating sphere.We adopt an azimuthal equatorially antisymmetric field (BΦ(θ) = B0 sinθcosθ, where θ is colatitude, Φ is azimuth) as a background magnetic field. On the other hand, an equatorially symmetric field (BΦ(θ) = B0 sinθ) was assumed in Márquez-Artavia et al.(2017), whose results we replicated and reported in JpGU 2018.Compared with previous results, the dispersion diagrams obtained with the toroidal equatorially antisymmetric field show that some fast magnetic Rossby branches remain, while slow magnetic Rossby waves disappear. Besides, a continuous spectrum is found in the range where an azimuthal phase velocity is coincident with a local Alfvén velocity divided by sinθ. Similar continuous spectra are also seen in various physical situations, including inviscid shear flow (e.g. Case, 1960; Balmforth and Morrison, 1995; Iga, 2013) and plasma oscillations (e.g. Van Kampen, 1955; Case, 1959; Barston, 1964; Sedláček, 1971). The continuous spectra are accompanied by a singular eigenfunction, which is physically meaningful only when they are integrated over the continuous spectra. Its integrated solutions generally decay with time, which is referred to as phase mixing. Unlike exponentially damped discrete modes, this decaying is proportional to negative powers of time.In the case of the shallow water system with the antisymmetric field, discrete eigenvalues buried in the continuous spectrum is found, which include unstable modes. For the Earth-like parameters, polar trapped modes with decadal period and equatorial trapped Rossby waves with a few years period are found when the stratification is weak.

著者

中島 涼輔 吉田 茂生

出版者

日本地球惑星科学連合

雑誌

日本地球惑星科学連合2018年大会

巻号頁・発行日

2018-03-14

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We investigated waves in a stably stratified thin layer in a rotating sphere with an imposed magnetic field. This represents the stably stratified outermost Earth's core or the tachocline of the Sun. Recently, many geophysicists focus on the stratification of the outermost outer core evidenced through seismological studies (e.g. Helffrich and Kaneshima, 2010) and an interpretation of the 60-year geomagnetic secular variations with Magnetic-Archimedes-Coriolis (MAC) waves (Buffett, 2014).Márquez-Artavia et al.(2017) studied the effect of a toroidal magnetic field on shallow water waves over a rotating sphere as the model of this stratified layer. On the other hand, MAC waves are strongly affected by a radial field (e.g. Knezek and Buffett, 2018). We added a non-zero radial magnetic perturbation and magnetic diffusion to Márquez-Artavia et al.(2017)'s equations. Unlike their paper's formulation, we applied velocity potential and stream function for both fluid motion and magnetic perturbation, which is similar to the first method of Longuet-Higgins(1968).In the non-diffusive case, the dispersion relation obtained with the azimuthal equatorially symmetric field (Bφ(θ) ∝ sinθ, where θ is colatitude) is almost the same as Márquez-Artavia et al.(2017)'s result, which includes magneto-inertia gravity (MIG) waves, fast magnetic Rossby waves, slow MC Rossby waves and an unexpected instability. In particular, we replicate the transition of the propagation direcition of zonal wavenumber m=1 slow MC Rossby waves from eastward to westward with increasing Lamb parameter (ε=4Ω2a2/gh, where Ω, a, g and h is the rotation rate, the sphere radius, the acceleration of gravity and a equivalent depth, respectively) and Lehnert number (α=vA/2Ωa, where vA is Alfvén wave speed). As a consequence, fast magnetic Rossby waves and slow MC Rossby waves interact, and the non-diffusive instability occur.Next, we are examining the case with an equatorially antisymmetric background field, which is more realistic in the Earth's core. In this case, if the magnetic diffusion is ignored, the continuous spectrums appear owing to Alfvén waves resonance (similar to the continuous spectrums in inviscid shear flow, e.g. Balmforth and Morrison, 1995). To solve this difficulty, our numerical model includes the magnetic diffusion term.