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A case for variational geomagnetic data assimilation: insights from a one-dimensional, nonlinear, and sparsely observed MHD system
A. Fournier,C. Eymin,T. Alboussière
Nonlinear Processes in Geophysics (NPG) , 2007,
Abstract: Secular variations of the geomagnetic field have been measured with a continuously improving accuracy during the last few hundred years, culminating nowadays with satellite data. It is however well known that the dynamics of the magnetic field is linked to that of the velocity field in the core and any attempt to model secular variations will involve a coupled dynamical system for magnetic field and core velocity. Unfortunately, there is no direct observation of the velocity. Independently of the exact nature of the above-mentioned coupled system – some version being currently under construction – the question is debated in this paper whether good knowledge of the magnetic field can be translated into good knowledge of core dynamics. Furthermore, what will be the impact of the most recent and precise geomagnetic data on our knowledge of the geomagnetic field of the past and future? These questions are cast into the language of variational data assimilation, while the dynamical system considered in this paper consists in a set of two oversimplified one-dimensional equations for magnetic and velocity fields. This toy model retains important features inherited from the induction and Navier-Stokes equations: non-linear magnetic and momentum terms are present and its linear response to small disturbances contains Alfvén waves. It is concluded that variational data assimilation is indeed appropriate in principle, even though the velocity field remains hidden at all times; it allows us to recover the entire evolution of both fields from partial and irregularly distributed information on the magnetic field. This work constitutes a first step on the way toward the reassimilation of historical geomagnetic data and geomagnetic forecast.
A case for variational geomagnetic data assimilation: insights from a one-dimensional, nonlinear, and sparsely observed MHD system  [PDF]
Alexandre Fournier,Céline Eymin,Thierry Alboussière
Physics , 2007, DOI: 10.5194/npg-14-163-2007
Abstract: Secular variations of the geomagnetic field have been measured with a continuously improving accuracy during the last few hundred years, culminating nowadays with satellite data. It is however well known that the dynamics of the magnetic field is linked to that of the velocity field in the core and any attempt to model secular variations will involve a coupled dynamical system for magnetic field and core velocity. Unfortunately, there is no direct observation of the velocity. Independently of the exact nature of the above-mentioned coupled system -- some version being currently under construction -- the question is debated in this paper whether good knowledge of the magnetic field can be translated into good knowledge of core dynamics. Furthermore, what will be the impact of the most recent and precise geomagnetic data on our knowledge of the geomagnetic field of the past and future? These questions are cast into the language of variational data assimilation, while the dynamical system considered in this paper consists in a set of two oversimplified one-dimensional equations for magnetic and velocity fields. This toy model retains important features inherited from the induction and Navier-Stokes equations: non-linear magnetic and momentum terms are present and its linear response to small disturbances contains Alfv\'en waves. It is concluded that variational data assimilation is indeed appropriate in principle, even though the velocity field remains hidden at all times; it allows us to recover the entire evolution of both fields from partial and irregularly distributed information on the magnetic field. This work constitutes a first step on the way toward the reassimilation of historical geomagnetic data and geomagnetic forecast.
Four decades of European geomagnetic secular variation and acceleration
Giuliana Verbanac,Monika Korte,Mioara Mioara Mandea
Annals of Geophysics , 2009, DOI: 10.4401/ag-4605
Abstract: Geomagnetic secular variation, the generally slow, continuous change in the core magnetic field, is characterized by occasional rapid variations known as geomagnetic jerks. Recent studies on magnetic data obtained by satellites with a good global coverage suggest that more rapid and smaller scale features than previously thought occur in the field change. We have taken advantage of the comparatively high density of geomagnetic observatories in Europe and have derived a regional model for the detailed study of secular variation and acceleration over the past four decades from 1960 to 2001 by means of improved and regularized spherical cap harmonic analysis. We show the improvements to our regional model over a global model. All the known jerks are seen in our model, but further times with rapid changes in secular variation exist. Moreover, times of zero acceleration in general do not occur simultaneously in all magnetic field components, although this nearly is the case in 1969.6 and 1982.2. Secular variation and acceleration show very dynamic patterns indicating rapid and complex causal processes in the Earth’s fluid core.
Secular trends in storm-level geomagnetic activity
J. J. Love
Annales Geophysicae (ANGEO) , 2011,
Abstract: Analysis is made of K-index data from groups of ground-based geomagnetic observatories in Germany, Britain, and Australia, 1868.0–2009.0, solar cycles 11–23. Methods include nonparametric measures of trends and statistical significance used by the hydrological and climatological research communities. Among the three observatory groups, German K data systematically record the highest disturbance levels, followed by the British and, then, the Australian data. Signals consistently seen in K data from all three observatory groups can be reasonably interpreted as physically meaninginful: (1) geomagnetic activity has generally increased over the past 141 years. However, the detailed secular evolution of geomagnetic activity is not well characterized by either a linear trend nor, even, a monotonic trend. Therefore, simple, phenomenological extrapolations of past trends in solar and geomagnetic activity levels are unlikely to be useful for making quantitative predictions of future trends lasting longer than a solar cycle or so. (2) The well-known tendency for magnetic storms to occur during the declining phase of a sunspot-solar cycles is clearly seen for cycles 14–23; it is not, however, clearly seen for cycles 11–13. Therefore, in addition to an increase in geomagnetic activity, the nature of solar-terrestrial interaction has also apparently changed over the past 141 years.
Secular evolution of a satellite by tidal effect. Application to Triton  [PDF]
Alexandre C. M. Correia
Physics , 2009, DOI: 10.1088/0004-637X/704/1/L1
Abstract: Some of the satellites in the Solar System, including the Moon, appear to have been captured from heliocentric orbits at some point in their past, and then have evolved to the present configurations. The exact process of how this trapping occurred is unknown, but the dissociation of a planetesimal binary in the gravitational field of the planet, gas drag, or a massive collision seem to be the best candidates. However, all these mechanisms leave the satellites in elliptical orbits that need to be damped to the present almost circular ones. Here we give a complete description of the secular tidal evolution of a satellite just after entering a bounding state with the planet. In particular, we take into account the spin evolution of the satellite, which has often been assumed synchronous in previous studies. We apply our model to Triton and successfully explain some geophysical properties of this satellite, as well as the main dynamical features observed for the Neptunian system.
Aerodynamic Stability of Satellites in Elliptic Low Earth Orbits  [PDF]
Matthew Bailey,Brian Ladson,Stefan C. Mancas,Bogdan Udrea,Uchenna Umeadi
Physics , 2013,
Abstract: Topical observations of the thermosphere at altitudes below $200 \, km$ are of great benefit in advancing the understanding of the global distribution of mass, composition, and dynamical responses to geomagnetic forcing, and momentum transfer via waves. The perceived risks associated with such low altitude and short duration orbits has prohibited the launch of Discovery-class missions. Miniaturization of instruments such as mass spectrometers and advances in the nano-satellite technology, associated with relatively low cost of nano-satellite manufacturing and operation, open an avenue for performing low altitude missions. The time dependent coefficients of a second order non-homogeneous ODE which describes the motion have a double periodic shape. Hence, they will be approximated using Jacobi elliptic functions. Through a change of variables the original ODE will be converted into Hill's ODE for stability analysis using Floquet theory. We are interested in how changes in the coefficients of the ODE affect the stability of the solution. The expected result will be an allowable range of parameters for which the motion is dynamically stable. A possible extension of the application is a computational tool for the rapid evaluation of the stability of entry or re-entry vehicles in rarefied flow regimes and of satellites flying in relatively low orbits.
Chaos in navigation satellite orbits caused by the perturbed motion of the Moon  [PDF]
Aaron J. Rosengren,Elisa Maria Alessi,Alessandro Rossi,Giovanni B. Valsecchi
Physics , 2015, DOI: 10.1093/mnras/stv534
Abstract: Numerical simulations carried out over the past decade suggest that the orbits of the Global Navigation Satellite Systems are unstable, resulting in an apparent chaotic growth of the eccentricity. Here we show that the irregular and haphazard character of these orbits reflects a similar irregularity in the orbits of many celestial bodies in our Solar System. We find that secular resonances, involving linear combinations of the frequencies of nodal and apsidal precession and the rate of regression of lunar nodes, occur in profusion so that the phase space is threaded by a devious stochastic web. As in all cases in the Solar System, chaos ensues where resonances overlap. These results may be significant for the analysis of disposal strategies for the four constellations in this precarious region of space.
On the Orbits of Infalling Satellite Halos  [PDF]
Andrew R. Wetzel
Physics , 2010, DOI: 10.1111/j.1365-2966.2010.17877.x
Abstract: The orbital properties of infalling satellite halos set the initial conditions which control the subsequent evolution of subhalos and the galaxies that they host, with implications for mass stripping, star formation quenching, and merging. Using a high-resolution, cosmological N-body simulation, I examine the orbital parameters of satellite halos as they merge with larger host halos, focusing primarily on orbital circularity and pericenter. I explore in detail how these orbital parameters depend on mass and redshift. Satellite orbits become more radial and plunge deeper into their host halo at higher host halo mass, but they do not significantly depend on satellite halo mass. Additionally, satellite orbits become more radial and plunge deeper into their host halos at higher redshift. I also examine satellite velocities, finding that most satellites infall with less specific angular momentum than the host halo virial value, but that satellites are `hotter' than the host virial velocity. I discuss the implications of these results to the processes of galaxy formation and evolution, and I provide fitting formulas to the mass and redshift dependence of satellite orbital circularity and pericenter.
Bifurcations of lunisolar secular resonances for space debris orbits  [PDF]
Alessandra Celletti,C?t?lin Gale?,Giuseppe Pucacco
Mathematics , 2015,
Abstract: Using bifurcation theory, we study the secular resonances induced by Sun and Moon on space debris orbits around the Earth. In particular, we concentrate on a special class of secular resonances, which depends just on the debris' orbital inclination. This class is typically subdivided into three distinct types of secular resonances: those occurring at the critical inclination, those corresponding to polar orbits and a third type resulting from a linear combination of the rates of variation of the argument of perigee and the longitude of the ascending node. The model describing the dynamics of space debris includes the effects of the geopotential, as well as Sun's and Moon's attractions, and it is defined in terms of suitable action-angle variables. We consider the system averaged over both the mean anomaly of the debris and those of Sun and Moon. Such multiply-averaged Hamiltonian is used to study the lunisolar resonances which depend just on the inclination. Borrowing the technique from the theory of bifurcations of Hamiltonian normal forms, we study the birth of periodic orbits and we determine the energy thresholds at which the bifurcations of lunisolar secular resonances take place. This approach gives us physically relevant information on the existence and location of the equilibria, which help us to identify stable and unstable regions in the phase space. On the other hand, beside their physical interest, the study of inclination dependent resonances offers interesting insights from the dynamical point of view, since it sheds light on different phenomena related to bifurcation theory.
analysis of the geomagnetic secular variation in the 20th century.
20世纪地磁长期变化场分析

WANG Tan Wen Institute of Geophysics,China Seismological Bureau,Beijing,China Lab of Space Weather,Chinese Academy of Sciences,Beijing,China,
王亶文

地球物理学报 , 2004,
Abstract: Using IGRF(International Geomagnetic Reference Field) workout by IAGA (International Association of Geomagnetism and Aeronomy), this paper investigates the geomagnetic field in the 20th century. The quadrupole field ( n =2) is the most significant one of the geomagnetic secular variation in the 20th century. The Gauss series of the geomagnetic secular variation is converged slower than that of the main field. Using the method of tracing the change of the position of the anomaly focus, it is found that there are 5 anomalies in the chats of Z (vertical component) of the secular variation of the non dipole field. Their drifting is not consolidate in a few degrees. But they are drifting westward basically. This inconsistency of the westward drifting of the geomagnetic secular variation proves the Wang's geomagnetic model in some degrees. Different from the geomagnetic main field, the power spectra of the dipole, quatrupole and the eighthpole field of the secular variation have significant changes.
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