Decomposing the geomagnetic field: oscillation modes and characteristics

2020 ◽  
Author(s):  
Cristiana Stefan ◽  
Venera Dobrica ◽  
Crisan Demetrescu
Keyword(s):  
Geomagnetic Field ◽  
Field Model ◽  
Empirical Orthogonal Functions ◽  
Time Span ◽  
Eof Analysis ◽  
Detailed Structure ◽  
Orthogonal Functions ◽  
Oscillation Modes ◽  
Field Oscillation

<p>Using the COV-OBS.x1 (Gillet et al., 2015) main geomagnetic field model, covering the time span 1840–2020, respectively IGRF-13 (1900-2020), we decomposed the geomagnetic field at Earth’s surface in oscillation modes by means of empirical orthogonal functions (EOF) as well into a long term and a cyclic component using HP filtering (Hodrick and Prescott, 1997). Further, the long term component is filtered using a Butterworth filter (1930) with different cut-off periods in order to obtain oscillation at inter-centennial (> 100 years) and sub-centennial (60-90 years) timescales. The EOF analysis shows that the first three oscillation modes are characterized by periodicities of >100 years while modes 4 and 5 are characterized by dominant periodicities of 70-90 year. Although the variance of the modes 4 and 5 is rather small compared to that of the first three modes, these two modes are responsible for the detailed structure of the geomagnetic field. A comparison between the results of both methods is done as well.</p>

scholarly journals Eddy Trains and Striations in Quasigeostrophic Simulations and the Ocean

2016 ◽  
Vol 46 (9) ◽  
pp. 2807-2825 ◽  
Author(s):  
Changheng Chen ◽  
Igor Kamenkovich ◽  
Pavel Berloff
Keyword(s):  
North Pacific ◽  
Empirical Orthogonal Functions ◽  
Eof Analysis ◽  
Sea Level Anomaly ◽  
Orthogonal Functions ◽  
The North ◽  
Temporal Averaging ◽  
Low Pass ◽  
The Relationship ◽  
The North Pacific

AbstractThis study explores the relationship between coherent eddies and zonally elongated striations. The investigation involves an analysis of two baroclinic quasigeostrophic models of a zonal and double-gyre flow and a set of altimetry sea level anomaly data in the North Pacific. Striations are defined by either spatiotemporal filtering or empirical orthogonal functions (EOFs), with both approaches leading to consistent results. Coherent eddies, identified here by the modified Okubo–Weiss parameter, tend to propagate along well-defined paths, thus forming “eddy trains” that coincide with striations. The striations and eddy trains tend to drift away from the intergyre boundary at the same speed in both the model and observations. The EOF analysis further confirms that these striations in model simulations and altimetry are not an artifact of temporal averaging of random, spatially uncorrelated vortices. This study suggests instead that eddies organize into eddy trains, which manifest themselves as striations in low-pass filtered data and EOF modes.

scholarly journals Using Lomb–Scargle Analysis to Derive Empirical Orthogonal Functions from Gappy Meteorological Data

2018 ◽  
Vol 57 (10) ◽  
pp. 2217-2229
Author(s):  
Christopher Dupuis ◽  
Courtney Schumacher
Keyword(s):  
Time Series ◽  
Meteorological Data ◽  
Tropical Rainfall Measuring Mission ◽  
Empirical Orthogonal Functions ◽  
Eof Analysis ◽  
Complex Topography ◽  
Sampled Data ◽  
Orthogonal Functions ◽  
Hard Limit ◽  
Irregularly Sampled Data

AbstractThe Lomb–Scargle discrete Fourier transform (LSDFT) is a well-known technique for analyzing time series. In this study, a solution for empirical orthogonal functions (EOFs) based on irregularly sampled data is derived from the LSDFT. It is demonstrated that this particular algorithm has no hard limit on its accuracy and yields results comparable to those of complex Hilbert EOF analysis. Two LSDFT algorithms are compared in terms of their performance in evaluating EOFs for precipitation observations from the Tropical Rainfall Measuring Mission satellite. Both are shown to be able to capture the pattern of the diurnal cycle of rainfall over the complex topography and diverse land cover of South America, and both also show other consistent features in the 0–12-day frequency band.

Analysis of Geomagnetic Variability by Empirical Orthogonal Functions

2020 ◽  
Author(s):  
Chi-Hua Chung ◽  
Benjamin Fong Chao
Keyword(s):  
Geomagnetic Field ◽  
Empirical Orthogonal Functions ◽  
Spatial Structures ◽  
Orthogonal Functions ◽  
Core Mantle Boundary ◽  
The Core ◽  
Orthogonal Function ◽  
Secular Variations ◽  
Complex Eof ◽  
Westward Drift

<p>We examine the secular variations of global geomagnetic field on long temporal scales using the IGRF model given in Gauss coefficients for 1900 - 2020. We apply the Empirical Orthogonal Function (EOF) analysis to the geomagnetic field truncated at degree 6 and downward continue it to the core-mantle boundary (CMB) under the assumption of an insulating mantle. The first three EOF modes show the periods around 120, 75 and 60 years with corresponding spatial structures. These oscillational modes potentially support the manifestation of magnetic, Archimedes and Coriolis (MAC) waves in the stably stratified layer near CMB (Buffett, 2016). We also model and decompose the geomagnetic field to standing and drifting components according to trajectories of the Gauss coefficients similarly to Yukutake (2015). We then use the Complex EOF (CEOF) analysis on the drifting field. The results indicate the presence of the westward drift phenomenon but only weakly given the fact that the westward drift has only completed a fraction of a cycle during this time.</p>

scholarly journals On polar daily geomagnetic variation

2015 ◽  
Vol 58 (5) ◽  
Author(s):  
Paola De Michelis ◽  
Giuseppe Consolini
Keyword(s):  
Magnetic Field ◽  
Geomagnetic Field ◽  
Empirical Orthogonal Functions ◽  
Activity Level ◽  
Geomagnetic Variation ◽  
Orthogonal Functions ◽  
Equivalent Current ◽  
Dominant Component ◽  
Magnetospheric Currents ◽  
Current Representation

<p style="-qt-block-indent: 0; text-indent: 0px; margin: 0px;">The aim of this work is to investigate the nature of the daily magnetic field perturbations produced by ionospheric and magnetospheric currents at high latitudes. We analyse the hourly means of the X and Y geomagnetic field components recorded by a meridian chain of permanent geomagnetic observatories in the polar region of the Northern Hemisphere during a period of four years (1995-1998) around the solar minimum. We apply a mathematical method, known as natural orthogonal component (NOC), which is capable of characterizing the dominant modes of the geomagnetic field daily variability through a set of empirical orthogonal functions (EOFs). Using the first two modes we reconstruct a two-dimensional equivalent current representation of the ionospheric electric currents, which contribute substantially to the geomagnetic daily variations. The obtained current structures resemble the equivalent current patterns of DP2 and DP1. We characterize these currents by studying their evolution with the geomagnetic activity level and by analysing their dependence on the interplanetary magnetic field. The obtained results support the idea of a coexistence of two main processes during all analysed period although one of them, the directly driven process, represents the dominant component of the geomagnetic daily variation.</p>

Empirical Orthogonal Functions: The Medium is the Message

2009 ◽  
Vol 22 (24) ◽  
pp. 6501-6514 ◽  
Author(s):  
Adam H. Monahan ◽  
John C. Fyfe ◽  
Maarten H. P. Ambaum ◽  
David B. Stephenson ◽  
Gerald R. North
Keyword(s):  
Dimensionality Reduction ◽  
Data Compression ◽  
Empirical Orthogonal Function ◽  
Degrees Of Freedom ◽  
Empirical Orthogonal Functions ◽  
Eof Analysis ◽  
Orthogonal Functions ◽  
Entire Domain ◽  
Orthogonal Function

Abstract Empirical orthogonal function (EOF) analysis is a powerful tool for data compression and dimensionality reduction used broadly in meteorology and oceanography. Often in the literature, EOF modes are interpreted individually, independent of other modes. In fact, it can be shown that no such attribution can generally be made. This review demonstrates that in general individual EOF modes (i) will not correspond to individual dynamical modes, (ii) will not correspond to individual kinematic degrees of freedom, (iii) will not be statistically independent of other EOF modes, and (iv) will be strongly influenced by the nonlocal requirement that modes maximize variance over the entire domain. The goal of this review is not to argue against the use of EOF analysis in meteorology and oceanography; rather, it is to demonstrate the care that must be taken in the interpretation of individual modes in order to distinguish the medium from the message.

Empirical Orthogonal Functions

2011 ◽  
Author(s):  
Gidon Eshel
Keyword(s):  
Missing Values ◽  
Original Data ◽  
Empirical Orthogonal Functions ◽  
Basis Set ◽  
Data Matrix ◽  
Multidimensional Data ◽  
Data Sets ◽  
Eof Analysis ◽  
Orthogonal Functions ◽  
Multidimensional Data Sets

This chapter focuses on empirical orthogonal functions (EOFs). One of the most useful and common eigen-techniques in data analysis is the construction of EOFs. EOFs are a transform of the data; the original set of numbers is transformed into a different set with some desirable properties. In this sense the EOF transform is similar to other transforms, such as the Fourier or Laplace transforms. In all these cases, we project the original data onto a set of functions, thus replacing the original data with the set of projection coefficients on the chosen new set of basis vectors. However, the choice of the specific basis set varies from case to case. The discussions cover data matrix structure convention, reshaping multidimensional data sets for EOF analysis, forming anomalies and removing time mean, missing values, choosing and interpreting the covariability matrix, calculating the EOFs, projection time series, and extended EOF analysis.

Empirical Orthogonal Function Analysis of 2D Current Transects in the Fehmarn Belt

2013 ◽  
Author(s):  
Maziar Golestani ◽  
Jacob Tornfeldt Sørensen
Keyword(s):  
Time Series ◽  
Degrees Of Freedom ◽  
Function Analysis ◽  
Spatial Coherence ◽  
Three Dimensional ◽  
Empirical Orthogonal Functions ◽  
Eof Analysis ◽  
Orthogonal Functions ◽  
Relative Contribution ◽  
Adcp Measurements

Describing spatial coherence of hydrodynamic conditions typically includes analysis of long time series of model results and site specific bathymetric and hydrodynamic features. This complex task often involves a time-consuming qualitative analysis to identify the critical physical processes for normal and extreme conditions. A methodology for skillful reduction of the system dimensions and determination of the most important current patterns can provide a more quantitative analysis of the coherence and variability of complex spatial time series. The objective of this study is to decompose transects of velocity in the hydrodynamically complex Fehmarn Belt area into Empirical Orthogonal Functions (EOF) and determine their relative contribution to the total variance. This will help marine engineers and contractors to gain a more quantitative and accessible picture of the changes in the current transects and to obtain an overview of current shear pattern while performing complex and exquisite operations. 18 years of hindcast data from a three-dimensional flow model are used for performing the EOF analysis. After performing the EOF analysis, the most important and dominant current patterns are extracted. The analysis reveals that the first eigenmode explains about 89 % of the variance and resembles the barotrpic flow at the cross-section while other EOF modes represent various modes of the baroclinic flow. The results are compared to EOF analysis of two ADCP measurements installed on the seabed and comparisons with similar analysis of model output are performed. It is shown that the whole time series can be reconstructed with much fewer degrees of freedom and almost no data loss by using only the first five EOF modes.

scholarly journals On the terms of geomagnetic daily variation in Antarctica

2009 ◽  
Vol 27 (6) ◽  
pp. 2483-2490 ◽  
Author(s):  
P. De Michelis ◽  
R. Tozzi ◽  
A. Meloni
Keyword(s):  
Geomagnetic Field ◽  
Daily Variation ◽  
Empirical Orthogonal Functions ◽  
High Latitudes ◽  
Orthogonal Functions ◽  
Modes Of Variability ◽  
Magnetospheric Currents ◽  
Geomagnetic Data ◽  
Magnetic Perturbations ◽  
The Magnetic Field

Abstract. The target of this work is to investigate the nature of magnetic perturbations produced by ionospheric and magnetospheric currents as recorded at high-latitude geomagnetic stations. In particular, we investigate the effects of these currents on geomagnetic data recorded in Antarctica. To this purpose we apply a mathematical method, known as Natural Orthogonal Composition, to analyze the magnetic field disturbances along the three geomagnetic field components (X, Y and Z) recorded at Mario Zucchelli Station (IAGA code TNB; geographic coordinates: 74.7° S, 164.1° E) from 1995 to 1998. Using this type of analysis, we characterize the dominant modes of the geomagnetic field daily variability through a set of empirical orthogonal functions (EOFs). While such mathematically independent EOFs do not necessarily represent physically independent modes of variability, we find that some of them are actually related to well known current patterns located at high latitudes.

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