A spectral decomposition in vector spherical harmonics for Stokes equations

2016 ◽  
pp. 237-241
Author(s):  
M Tran ◽  
T Nguyen
Keyword(s):  
Spherical Harmonics ◽  
Spectral Decomposition ◽  
Stokes Equations ◽  
Vector Spherical Harmonics

Algorithm 1018: FaVeST—Fast Vector Spherical Harmonic Transforms

2021 ◽  
Vol 47 (4) ◽  
pp. 1-24
Author(s):  
Quoc T. Le Gia ◽  
Ming Li ◽  
Yu Guang Wang
Keyword(s):  
Spherical Harmonics ◽  
Spherical Harmonic ◽  
Fourier Coefficients ◽  
Computational Cost ◽  
Tangent Vector ◽  
Tangent Vector Field ◽  
Vector Spherical Harmonics ◽  
Numerical Examples ◽  
Vector Spherical Harmonic ◽  
Tangent Fields

Vector spherical harmonics on the unit sphere of ℝ 3 have broad applications in geophysics, quantum mechanics, and astrophysics. In the representation of a tangent vector field, one needs to evaluate the expansion and the Fourier coefficients of vector spherical harmonics. In this article, we develop fast algorithms (FaVeST) for vector spherical harmonic transforms on these evaluations. The forward FaVeST evaluates the Fourier coefficients and has a computational cost proportional to N log √ N for N number of evaluation points. The adjoint FaVeST, which evaluates a linear combination of vector spherical harmonics with a degree up to ⊡ M for M evaluation points, has cost proportional to M log √ M . Numerical examples of simulated tangent fields illustrate the accuracy, efficiency, and stability of FaVeST.

scholarly journals Vector spherical harmonics and their application to magnetostatics

1985 ◽  
Vol 6 (4) ◽  
pp. 287-294 ◽  
Author(s):  
R G Barrera ◽  
G A Estevez ◽  
J Giraldo
Keyword(s):  
Spherical Harmonics ◽  
Vector Spherical Harmonics

scholarly journals Active compensation of magnetic field distortions based on vector spherical harmonics field description

AIP Advances ◽  
2017 ◽  
Vol 7 (3) ◽  
pp. 035216
Author(s):  
G. Wyszyński ◽  
K. Bodek ◽  
S. Afach ◽  
G. Bison ◽  
Z. Chowdhuri ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Spherical Harmonics ◽  
Vector Spherical Harmonics ◽  
Active Compensation

Global estimation of ionospheric drivers during extreme storms

2021 ◽  
Author(s):  
Aurora Lopez Rubio ◽  
Seebany Datta-Barua ◽  
Gary Bust
Keyword(s):  
Kalman Filter ◽  
Geomagnetic Storm ◽  
Electric Fields ◽  
Spherical Harmonics ◽  
Space Weather ◽  
Basis Function ◽  
Geomagnetic Storms ◽  
Vector Spherical Harmonics ◽  
Neutral Winds ◽  
Global Estimation

<p>During geomagnetic storms, the space environment can be drastically altered as the plasma in the upper atmosphere, or ionosphere, moves globally. This plasma redistribution is mainly caused by storm-time electric fields, but another important driver of the velocity of the ions in the plasma is the neutral winds. These winds refer to the movement of the neutral particles that are part of the thermospheric layer of the atmosphere, that can drag the plasma. Geomagnetic storms increase the neutral winds, due to the heating of the thermosphere that comes from the storm. In this study we want to understand how these ionospheric drivers affect the ionosphere behavior because, among other reasons, during geomagnetic storms the plasma can refract and diffract trans-ionospheric signals and, consequently, can cause problems in the navigation systems such as GNSS (Global Navigation Satellite System)/GPS (Global Positioning System) that use the information from the signals.</p><p>In this work, our objective is to estimate the electric fields and neutral winds globally during a geomagnetic storm. Global GNSS TEC (total electron content) measurements are ingested by the Ionospheric Data Assimilation 4-Dimensional (IDA4D) algorithm [1], whose output is the electron density rate over a grid at different time steps during a geomagnetic storm. The density rates are treated as “observations” in EMPIRE (Estimating Model Parameters from Ionospheric Reverse Engineering), which is a data assimilation algorithm based on the plasma continuity equation [2,3,4]. Then, the EMPIRE “observations” are used to estimate corrections to the electric field and neutral winds by solving a Kalman filter. To study these drivers with EMPIRE, basis functions are used to describe them. For the global potential field, spherical harmonics are used.</p><p>To have a global estimation of the neutral winds, we introduce vector spherical harmonics as the basis function for the first time in EMPIRE. The vector spherical harmonics are used to model orthogonal components of neutral wind in the zonal (east-west) and meridional (north-south) directions. EMPIRE’s Kalman filter needs the error covariance of the vector spherical harmonics decomposition. To calculate it, the basis function is fitted to the model HWM14 (Horizonal Wind Model) values of the neutral winds and the error between the fitting and the model is studied. Later, we study the global potential field and global neutral winds over time to understand how much each driver contributes to the plasma redistribution during the geomagnetic storm on October 25<sup>th</sup> 2011. We compare the results to FPI (Fabry-Perot Interferometer) neutral winds measurements to validate the results.   </p><p>[1] G.S.Bust, G.Crowley, T.W.Garner, T.L.G.II, R.W.Meggs, C.N.Mitchell, P.S.J.Spencer, P.Yin, and B.Zapfe, Four-dimensional gps imaging of space weather storms, Space Weather, 5 (2007),  doi:10.1029/2006SW000237.</p><p>[2] D.S.Miladinovich, S.Datta-Barua, G.S.Bust, and J.J.Makela, Assimilation of thermospheric measurements for ionosphere-thermosphere state estimation, Radio Science, 51 (2016).</p><p>[3] D.S.Miladinovich, S.Datta-Barua, A.Lopez, S. Zhang, and G.S.Bust, Assimilation of gnss measurements for estimation of high-latitude convection processes, Space Weather, 18 (2020).</p><p>[4] G.S.Bust and S.Datta-Barua, Scientific investigations using ida4d and empire, in Modeling the Ionosphere-Thermosphere System, J. Huba, R. Schunk, and G. Khazanov, eds., John Wiley & Sons, Ltd, 1 ed., 2014.</p>

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