533

# Earth’s Magnetic Field

Authored by: Nils Olsen

# Space Weather Fundamentals

Print publication date:  September  2016
Online publication date:  November  2016

Print ISBN: 9781498749077
eBook ISBN: 9781315368474

10.1201/9781315368474-3

#### Abstract

3.1 Introduction

3.2 Magnetic Observations

3.3 Sources of Earth’s Magnetic Field

3.4 Describing Earth’s Magnetic Field in Space and Time: Geomagnetic Field Models

3.5 Dipole Approximation of Earth’s Magnetic Field

3.6 Geomagnetic Field Models Including the Nondipole Field

;3.6.1 The International Geomagnetic Reference Field

3.6.2 High-Resolution Models of the Recent Geomagnetic Field

3.7 Time Changes of the Earth’s Main Field

References

#### Contents

 3.1 Introduction 35 3.2 Magnetic Observations 35 3.3 Sources of Earth’s Magnetic Field 36 3.4 Describing Earth’s Magnetic Field in Space and Time: Geomagnetic Field Models 37 3.5 Dipole Approximation of Earth’s Magnetic Field 41 3.6 Geomagnetic Field Models Including the Nondipole Field 42 ;3.6.1 The International Geomagnetic Reference Field 42 3.6.2 High-Resolution Models of the Recent Geomagnetic Field 43 3.7 Time Changes of the Earth’s Main Field 43 References 45

#### 3.1  Introduction

The Earth has a strong magnetic field that varies both in space and time. Its major part is produced by a selfsustaining dynamo operating in the fluid outer core (at depths greater than 2900 km). But what is measured on ground or in space is the sum of this core field and of fields caused by magnetized rocks in the Earth’s crust, by electric currents flowing in the ionosphere, magnetosphere, and oceans, and by currents induced in the Earth by the time-varying external fields. The separation of these various field contributions and the determination of their spatial and temporal structure based on observations of the magnetic field requires advanced modelling techniques (see, e.g., Hulot et al., 2015, for an overview).

“Space weather” concerns the rather rapid variations of the magnetic field due to electric currents in the Earth’s ionosphere and magnetosphere (including secondary fields due to electromagnetic induction in the Earth’s interior). However, the processes that result in these “external” sources (in the ionosphere and magnetosphere, i.e., external to Earth’s surface) depend heavily on the Earth’s “internal” field (primarily the sources in the core). The electrical conductivity in the ionosphere is for instance anisotropic: conductivity in the direction of the ambient magnetic field is several orders of magnitude higher than conductivity perpendicular to the field. Knowledge of Earth’s own magnetic field and how it varies in space and time is therefore of fundamental importance for a physical understanding of space weather. Providing such information is the aim of this chapter.

#### 3.2  Magnetic Observations

The strength of the magnetic induction B, in following for simplicity denoted as “magnetic field,” varies at Earth’s surface between about 25,000 nT near the equator and about 65,000 nT near the poles (1 nT = 10−9 T, with 1 T = 1 tesla = 1 Vs−1 m−2). The magnetic vector B is completely described by three independent numbers (also called magnetic elements). B is typically given in a local topocentric (geodetic) coordinate system (i.e., relative to a reference ellipsoid as approximation for the geoid), shown in Figure 3.1. The magnetic elements X, Y, Z are the components of the field vector B in an orthogonal right-handed coordinate system, the axes of which are pointing toward geographic North, geographic East, and vertically down. Derived magnetic elements are the angle between geographic North and the (horizontal) direction in which a compass needle is pointing, denoted as declination D = arctan Y/X (for the numerical calculation it is recommended to use D = atan2(Y, X), to avoid the π ambiguity of the arctan function); the angle between the local horizontal plane and the field vector, denoted as inclination I = arctan Z/H; horizontal intensity $F = X 2 + Y 2$; and total intensity $F = X 2 + Y 2 + Z 2$ . The latter is simply the strength of the magnetic field, also called magnetic field intensity.

Figure 3.1   The magnetic elements in the local topocentric coordinate system, seen from the Northeast.

Providing the three components of B in the geodetic frame, B = (X, Y, Z) with X, Y, Z as defined above, is useful for describing the magnetic field on the Earth’s surface. However, when dealing with satellite data, it is often more appropriate to use a spherical coordinate system, also called North-East-Center (NEC) local Cartesian coordinate frame, with BNEC = (BN, Be, BC), where BC is the component toward the center of the Earth (as opposed to Z which is approximating the plumb line direction), BE is the component toward geographic East (and thus is identical to Y), and BN is the component toward geographic North. Equations for transforming coordinates and magnetic field components between the geodetic and the geocentric frame can be found in Section 5.02.2.1.1 of Hulot et al. (2015). However, the difference between components in the geodetic and the geocentric frame is small (at Earth’s surface it is below 160 nT in an ambient field of up to 60,000 nT) and can be ignored for most space-weather-related purposes, in particular as it manifests as a static offset.

When measuring the magnetic field at ground, it is common to distinguish geomagnetic observatories, where the magnetic field is monitored absolutely, and variometer stations, where only its temporal variation is measured, which means that the absolute level (the baseline) of the magnetic field measurements is not known, and may even vary with time. Data from variometer stations are therefore mainly used for studying temporal variations of the external field at periods (between seconds and days) shorter than that of the variability of the (unknown) baseline. Studying the slow variation of Earth’s magnetic core field requires, however, knowledge of the absolute level of the magnetic field, as monitored by geomagnetic observatories. Presently, the Earth’s magnetic field is measured at about 150 geomagnetic observatories, the majority of which is located in the Northern Hemisphere and on continents. The filled circles of Figure 3.2 show their spatial distribution. Observatory data are provided through the INTERMAGNET network (www.intermagnet.org) and through the World Data Center (WDC) system (e.g., www.wdc.bgs.ac.uk). In contrast, the open circles of Figure 3.2 represent the location of variometer stations as given by the SuperMAG repository of magnetic variometer data (see http://supermag.uib.no/). Presently about 450 variometer stations measure fluctuations of the geomagnetic field, mainly at polar latitudes (where ionospheric and magnetospheric processes have largest impact on the Earth’s magnetic field).

#### 3.3  Sources of Earth’s Magnetic Field

Several sources contribute to the magnetic field at or above Earth’s surface. An overview is presented in Figure 3.3. By far the largest part of the geomagnetic field is due to electrical currents generated via induction by fluid motions in the Earth’s fluid outer core. This socalled core field is responsible for more than 93% of the observed magnetic field at ground.

Magnetized material in the crust (which consists of the uppermost few kilometers of Earth) causes the crustal field; it is relatively weak and accounts on an average only for a few percentage of the observed field at ground (but can exceed several thousands of nT in certain regions, for instance in the area around Kiruna in Northern Sweden where one of the world’s largest known iron ore deposits exist). Core and crustal fields together make the internal field (since their sources are internal to the Earth’s surface). External magnetic field contributions are caused by electric currents in the ionosphere (at altitudes between 90 and 1000 km) and magnetosphere (at altitudes of several Earth radii). Finally, electric currents induced in the Earth’s crust and mantle by the time-varying fields of external origin cause magnetic field contributions that are also of internal origin; however, since they are driven by external sources, typically only the core and crustal fields are understood when one refers to “internal sources.” The crustal field is static (at least on the timescales shorter than a few centuries that are interesting for space weather applications) but the core field changes significantly with time, a process called secular variation.

Figure 3.2   Geographical distribution of geomagnetic observatories (filled circles) and variometer stations (open circles). Location of the magnetic poles in 2015 is shown by the black squares. Dashed lines show magnetic latitude in steps of 10°.

#### 3.4  Describing Earth’s Magnetic Field in Space and Time: Geomagnetic Field Models

A geomagnetic field model is a set of coefficients that describes the Earth’s magnetic field vector B(t, r, θ, ϕ) for a given time t and position (r, θ, ϕ) in spherical coordinates, with r being the distance from the Earth’s center, θ = 90° – δ the geographic colatitude (δ is geographic latitude) and ϕ the geographic longitude. The magnetic field vector B = ‒∇V can be derived from a scalar potential V = Vint + Vext which is the sum of a potential, Vint, describing sources internal to the Earth’s surface (e.g., in the Earth’s core and crust) and a potential, Vext, describing sources external to the Earth’s surface (e.g., due to electric currents in the Earth’s ionosphere and magnetosphere). At or above Earth’s surface, the magnetic field Bint = −∇Vint due to internal (core and crust) sources can be derived as the negative gradient of the scalar potential Vint which can be expanded in terms of spherical harmonics:

3.1()$V int = a ∑ n = 1 N int ∑ m = 0 n ( g n m cos m ϕ + h n m sin m ϕ ) ( a r ) n + 1 P n m ( cos θ )$

where:

• a = 6371.2 km is a reference radius (Earth’s mean radius)
• $P n m$ are the associated Schmidt seminormalized Legendre functions
• ${ g n m , h n m }$ are the Gauss coefficients describing internal sources
• Nint is the maximum degree and order of the spherical harmonic expansion

The expansion starts at degree n = 1 (representing a dipole); the zero-degree coefficient $g 0 0$ (which represents a monopole) vanishes because of the nonexistence of magnetic monopoles. Low-degree coefficients of the expansion (terms $g n m , h n m$ with n ≤ 14) represent wavelengths of the magnetic field that are dominated by the core field, while higher degrees n > 14 are dominated by the crustal field. Due to the core field changes with time (i.e., secular variation), the Gauss coefficients $g n m ( t ) , h n m ( t )$ for n ≤ 14 depend on time although terms with n < 14 are often assumed to be static.

Figure 3.3   Sketch of the various sources contributing to the near-Earth magnetic field. FAC: Field Aligned Currents; IHFAC: Inter-hemispheric Field Aligned Currents; PEJ: Polar Electrojet; Sq: solar-driven daily variation; EEJ: Equatorial Electrojet.

The magnetic field components follow from the expansion Equation 3.1 of the potential as

3.2()$X ≈ − B θ = + ∂ V r ∂ θ = + ∑ n , m ( g n m cos m ϕ + h n m sin m ϕ ) ( a r ) n + 2 d P n m d θ$

3.3()

3.4()$Z ≈ ∼ = B r = + ∂ V ∂ r = − ∑ n , m ( n + 1 ) ( g n m cos m ϕ + h n m sin m ϕ ) ( a r ) n + 2 P n m$

The approximations $X ≈ − B θ$ and $X ≈ − B r$ become exact if the Earth’s surface is assumed to be a sphere rather than an ellipsoid, that is, if the difference between geodetic and geocentric components is ignored. Note the radial dependence $∝ r − ( n + 2 )$ of the magnetic field vector (as opposed to the radial dependence $∝ r − ( n + 1 )$ of the scalar potential V, cf. Equation 3.1). Figure 3.4 shows the strength of the magnetic field, F, at ground (top) and at 6000 km altitude (bottom). In both cases, the field is about twice as strong near the poles compared to the equator, but the field strength at 6000 km altitude (which roughly corresponds to a radius of r = 2a) is only about (1/2)3 = 1/8 of its value at Earth’s surface (r = a). This is the expected decrease with radius for a dipole field (for which n = 1, i.e., (1/2)n+2 = (1/2)3 = 1/8), thereby indicating the dominance of the dipole terms.

Figure 3.4   Map of the magnetic field strength F at ground (top), resp. at 6000 km altitude (bottom). The dashed curve represents the location of the dip equator (where the field lines are horizontal) at the respective altitude; the dash-dotted line shows the location of the dipole equator (defined as the equatorial plane of the dipole frame).

Terms with higher degrees—for example, coefficients describing a quadrupole (n = 2) or octupole (n = 3)— attenuate more rapidly with radius. As a consequence, the Earth’s magnetic field becomes increasing dipolar with increasing altitude. As an example: 93% of Earth’s magnetic field energy at ground is described by the dipole (higher degrees account for the remaining 7%), but at 6000 km altitude the dipole accounts for as much as 98.7% of the total magnetic energy.

It is also of interest to consider the difference between the dipole equator (defined as the equatorial plane of the dipole frame, shown as the dash-dotted line in Figure 3.4) and the dip equator (which is the line where the magnetic field is strictly horizontal, shown by the dashed line). Nondipole contributions are the cause of the difference between the dipole equator and the dip equator, and the fact that they differ more at ground (by up to 15° in latitude at longitudes of about 20° W) compared to 6000 km altitude (where the difference is less than 7° in latitude) indicates the fact that Earth’s magnetic field is more dipolar at higher altitudes.

Geomagnetic spectrum. The spatial power spectrum of the geomagnetic field, often called geomagnetic spectrum or Lowes–Mauersberger spectrum (e.g., Lowes (1966) is a useful way of characterizing the spatial behavior of the Earth’s magnetic field. The spectrum of the field of internal origin, Rn, is defined as the mean square magnetic field at a sphere of radius r (e.g., at Earth’s surface, with r = a = 6371 km) due to core and crustal contributions with horizontal wavelength $λ n ∼ 2 π r / n$ corresponding to spherical harmonic degree n. Rn (r) at radius r can be determined from the Gauss coefficients $g n m , h n m ,$ by means of

3.5()$R n ( r ) = ∑ m = 0 n ( n + 1 ) [ ( g n m ) 2 + ( h n m ) 2 ] ( a r ) 2 n + 4$

Figure 3.5 shows Rn (r) at different altitudes. The spectrum on the Earth’s surface decreases rapidly with increasing degree n for n < 14 but is “flat” (i.e., independent on degree) for higher degrees. The rather sharp “knee” at about degree n = 14 marks the transition from dominance of the core field contributions (at spatial scales larger than 3000 km corresponding to degrees n < 14) to dominance of the crustal field at smaller spatial scales (n > 14).

The steeper the decrease of power with increasing degree n, the more important the low-degree terms. As mentioned above, the Earth’s magnetic field becomes more dipolar with altitude, a fact that is confirmed by the altitude dependence of the spectra shown in Figure 3.5.

Figure 3.5   Power spectrum Rn(r) of Earth’s magnetic field in dependence on spherical harmonic degree n (bottom axis), resp. horizontal wavelength λn at surface (top axis). Left axis shows power (squared amplitude) while right axis shows amplitude.

#### 3.5  Dipole Approximation Of Earth’s Magnetic Field

When analysing data taken at altitudes of several thousand kilometers where nondipole contributions to the geomagnetic field become less important, it is often sufficient and convenient to approximate Earth’s internal field by means of a dipole. This approximation is often in particular valid for studying magnetospheric processes.

The first coefficient, $g 1 0$ of the expansions of Equations 3.1 through 3.4 represents the magnetic field of a dipole at the Earth’s centre that is aligned with its rotation axis; such a dipole is called an axial dipole. The other degree-1 coefficients $g 1 1$ and $h 1 1$ correspond to dipoles at Earth’s center located in the equatorial plane and pointing toward the Greenwich meridian (in the case of $g 1 1$), resp. the 90° E meridian ($h 1 1$). The superposition of these three terms represent the magnetic field of a centered but tilted dipole. Its dipole axis intersects the Earth’s surface at the dipole poles, also known as the geomagnetic poles; geocentric co-latitude θ0 and longitude ϕ0 of the North geomagnetic pole is thus given by

3.6()$θ 0 = 180 ° − arccos ( g 1 0 m 0 )$

3.7()$ϕ 0 = − 180 ° + a tan 2 ( h 1 1 , g 1 1 )$

where $m 0 = | g ˜ 1 0 |$ is the dipole strength and

3.8()$g ˜ 1 0 = − ( g 1 0 ) 2 + ( g 1 1 ) 2 + ( h 1 1 ) 2$

is the Gauss coefficient of an axial dipole in the dipole frame (the negative sign accounts for the fact that the magnetic pole in the Northern Hemisphere is actually a South pole, which is often ignored for simplicity). Using the Gauss coefficients $g 1 0 = − 29442 nT ,$ $g 1 1 = − 1501 nT ,$ $h 1 1 = 4797 nT$ of the most recent version of the International Geomagnetic Reference Field (IGRF) for epoch 2015 (IGRF-12, see Section 3.6.1 and Thebault et al., 2015b) gives as geocentric coordinates of the North geomagnetic pole: θ0 = 9.63°, ϕ0 = –72.63° with $g ˜ 1 0 = 29868$ nT.

Dipole coordinates and components. A coordinate system with pole at (θ0, ϕ0) is referred to as a dipole or geomagnetic coordinate system (cf. Figure 3.6). Dipole (or geomagnetic) co-latitude and longitude are defined as

3.9()$θ d = arccos [ cos θ cos θ 0 + sin θ sin θ 0 cos ( ϕ − ϕ 0 ) ]$

3.10()$ϕ d = a tan 2 [ sin θ sin ( ϕ − ϕ 0 ) , cos θ 0 sin θ cos ( ϕ − ϕ 0 ) − sin θ 0 cos θ ]$

The dipole poles are then the points for which θd = 0°, resp. 180°. Dipole equator (also known as geomagnetic equator, shown by the dash-dotted curve in Figure 3.4) is defined as the line for which θd = 90°.

Figure 3.6   Relationship between spherical geocentric coordinates θ, ϕ, dipole (geomagnetic) coordinates θd, ϕd, and the spherical geocentric coordinates of the North dipole (geomagnetic) pole, θ0, ϕ0. G is the North geographic pole, D is the North dipole pole, and P is the location of the point in consideration, given by (θ, ϕ) in the geographic frame and by (θd, ϕd) in the geomagnetic (dipole) frame.

When working in the dipole approximation it is convenient to rotate, in addition to the coordinates (which define the location of the point in consideration), also the horizontal vector magnetic field components from the geographic to the dipole frame. Rotation of the spherical geographic components Br, Bθ, Bϕ, to the dipole frame, $B r ′ , B θ ′ , B ϕ ′$ is done by means of

3.11()$( B r ′ B θ ′ B ϕ ′ ) = ( 1 0 0 0 + cos ψ + sin ψ 0 − sin ψ − cos ψ ) ( B r B θ B ϕ )$

where

3.12()$ψ = atan2 ( sin θ 0 sin ( ϕ − ϕ 0 ) , cos θ 0 sin θ − sin θ 0 cos θcos ( ϕ − ϕ 0 )$

is the angle between the geographic and the dipole meridian at the location in consideration (cf. Figure 3.6).

In terms of the Gauss coefficients $g 1 0 , h 1 1 , h 1 1$ of a centered dipole the magnetic vector components are given by

3.13()$( X Y Z ) ≈ ( − B θ + B ϕ − B r ) = ( − g 1 0 sin θ − ( g 1 1 cos ϕ + h 1 1 sin ϕ ) cos θ h 1 1 cos ϕ − g 1 1 sin ϕ − 2 g 1 0 cos θ − 2 ( g 1 1 cos ϕ + h 1 1 sin ϕ ) sin θ ) ( a r ) 3$

or, as components in the dipole frame,

3.14()$\left(\begin{array}{c}{X}^{\prime }\\ {Y}^{\prime }\\ {Z}^{\prime }\end{array}\right)\approx \left(\begin{array}{c}-{B}_{\text{θ}}^{\prime }\\ +{B}_{\varphi }^{\prime }\\ -{B}_{r}^{\prime }\end{array}\right)=\left(\begin{array}{c}-{\stackrel{˜}{g}}_{1}^{0}\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}{\text{θ}}_{d}\\ 0\\ -2{\stackrel{˜}{g}}_{1}^{0}\text{\hspace{0.17em}}\mathrm{cos}{\text{θ}}_{d}\end{array}\right){\left(\frac{a}{r}\right)}^{3}$

where, similar to Equations 3.2 through 3.4, the approximation (X, Y, Z) = (–Bθ, + Bϕ, – Br) is exact if the ellipticity of the Earth is neglected.

#### 3.6  Geomagnetic Field Models Including the Nondipole Field

Describing Earth’s magnetic field by an inclined dipole, as in the previous section, is valid at altitudes greater than several Earth radii. It is, however, a rather crude approximation at altitudes below a few thousands of kilometers. For those regions, more advanced descriptions of Earth’s magnetic field have to be used.

#### 3.6.1  The International Geomagnetic Reference Field

The IGRF is the de facto standard description of the Earth’s magnetic field and its secular variation. It describes the large-scale part (spatial scales larger than 3000 km at ground) of internal contributions, a part that is also referred to as main field. IGRF does not describe the crustal field (which becomes dominant for spherical harmonic degrees n > 13 that are not included in IGRF) or external (e.g., large-scale magnetospheric) sources, nor the Earth-induced magnetic field produced by external sources despite of the fact that they are large scale and of internal origin.

The IGRF model is produced by an international team of scientists under the auspices of the International Association of Geomagnetism and Aeronomy (IAGA). Due to the time changes of the Earth’s core field, the IGRF has to be updated regularly, presently every fifth year. The most recent (i.e., 12th) version of the model, called IGRF-12 (Thebault et al., 2015b), is valid until 2020 and consists of definitive field models (DGRFs) for the years 1900 to 2010, a main field model for epoch 2015, and a predictive linear secular variation model for the years 2015 to 2020. The maximum spherical harmonic degree is Nint = 13 for models after 2000 (and Nint = 10 for models between 1990 and 2000), with a linear secular variation in time for coefficients$g n m , h n m$ of degree up to n = 8 for 2015 to 2020.

The IGRF is used in a wide variety of studies, including space weather activities, and as a source of orientation information. Thebault et al. (2015a) give an overview about how the IGRF is used for science and applications.

Quasidipole (QD) coordinates. Earth’s magnetic field affects the motion of charged particles. As a consequence, processes in the Earth’s ionosphere and magnetosphere are naturally organized with respect to the geomagnetic field. Ionospheric conductivity is for instance highly anisotropic, resulting in values that are so high in the direction to the magnetic field that its field lines are practically electric equipotential lines. It is therefore often convenient to work in a coordinate frame that follows the morphology of the Earth’s main magnetic field. The use of the dipole- approximation (Equations 3.9 through 3.11) is too crude an approximation at altitudes lower then a few thousand kilometers where the nondipole contributions to the geomagnetic field are important. An example coordinate frame that accounts for nondipole contributions is the QD system of coordinatesq, ϕq) proposed by Richmond (1995) (see also Emmert et al., 2010). The basic idea is to trace a field line (given by IGRF of a specific epoch) from the point under consideration outward to the highest point of the field line (i.e., its apex). The longitude of that point defines QD longitude ϕq. QD colatitude θq is found by following an axial dipole field line from the Apex downward to the ionospheric E-layer (typically assumed to be at an altitude of 115 km); the colatitude of the intersection of the dipole field line and that altitude defines QD co-latitude θq. The points at the surface where the magnetic field lines are vertical are called dip poles or magnetic poles and are given by the points for which θq = 0°, resp. θq = 180°. The dip equator (or magnetic equator) is the line where the magnetic field lines are horizontal, that is, inclination I = 0° is given by θq = 90°. Finally, magnetic local time (MLT) is defined as the difference between the magnetic longitudes of the subsolar point and the point under consideration.

In contrast to the dipole frame, which is an orthogonal coordinate system, the QD coordinate system is not orthogonal and therefore mathematical differential operations (like curl, grad, and div) are nontrivial in QD coordinates. Efficient algorithms for calculating QD coordinates and their basis vectors (necessary for rotating components in the QD frame) are provided by Emmert et al. (2010).

Other magnetic coordinate systems that are based on IGRF are Altitude Adjusted Corrected Geomagnetic Coordinates (AACGM) (e.g., Gustafsson et al., 1992), Apex Coordinates (VanZandt et al., 1972), and Modified Apex Coordinates (Richmond, 1995).

#### 3.6.2  High-Resolution Models of the Recent Geomagnetic Field

The IGRF model describes the temporal evolution of the geomagnetic field using a linear time dependence within five years. This is enough to capture slow changes in the geomagnetic field but fails to describe more rapid variations that occur on shorter timescales of less than five years. Sudden changes in the second time derivative of the Earth’s magnetic field, so-called geomagnetic jerks, are an example of such a short timescale phenomenon that occur in irregular intervals. Prominent examples are the jerks that happened in 1969, 1978, 1991, and 1999 and, more recently, in 2003, 2007, 2011, and in 2014. These events are not captured by IGRF since their description requires a temporal description of the Gauss coefficients $g n m ( t ) , h n m ( t )$ on an annual or even subannual timescales. Geomagnetic jerks presently hamper a more precise prediction of the future evolution of the geomagnetic field.

A continuous monitoring of the Earth’s magnetic field from space began in 1999 with the launch of the Danish Ørsted satellite. It was followed by the German CHAMP satellite (2000–2010), the United States/Argentinian/Danish SAC-C satellite (2000–2006) and ESA’s 3-satellite constellation mission Swarm (since 2013). In particular, the combination of data from all these satellite missions allows for a determination of the Earth’s magnetic field with high resolution in space and time. Prominent examples of such high-resolution models of the recent geomagnetic field are: the CHAOS series (e.g., Olsen et al., 2006, 2014; Finlay et al., 2015), the GRIMM model series (e.g., Lesur et al., 2008, 2010, 2015), and the POMMME models (e.g., Maus et al., 2005, 2006).

The core field part of the comprehensive model series (e.g., Sabaka et al., 2002, 2004, 2015) is an example of a model that describes the evolution of the Earth’s magnetic field over the last 50 years (roughly covering the satellite era).

Models describing the Earth’s magnetic field on even longer timescales are based on historical magnetic observations. The gufm1 model (Jackson et al., 2000), for instance, describes how the Earth’s magnetic field has changed over the past four centuries.

#### 3.7  Time Changes of the Earth’s Main Field

Many space weather phenomena are affected by the geometry and strength of the Earth’s magnetic field, and thus time-changes of the geomagnetic field have impact on the space weather. A prominent example is the evolution of the South Atlantic Anomaly (SAA), a region of particularly low magnetic field intensity.

The geomagnetic field is an effective shield against charged particles impinging from outer space onto the Earth. Radiation damage to spacecraft and radiation exposure to humans in space is a matter of increasing concern. On a global scale, the dipole part of the geomagnetic field (cf. Equation 3.8) has weakened by 7% during the last century. Weakening of the geomagnetic field is, however, much stronger in certain areas on Earth, for instance in the Southern Atlantic. Since this is the region of lowest field intensity on Earth, any further weakening is of particular concern.

In 1900, the lowest field intensity on Earth was F = 25,460 nT close to the East coast of Brazil. The bottom panel of Figure 3.7 shows how this point moved westward by roughly 20 km/year, with field strength decreasing to F = 24,590 nT in 1940 and further down to F = 22,400 nT in 2015. In addition to this deepening, the spatial size of the SAA also increase: The region where F is below 25,000 nT, shown in Figure 3.7, almost doubled its size every 25 years over the last 60 years, increasing from 5.6 · 106 km2 in 1960 to 29 · 106 km2 in 2015.

Another prominent feature of the geomagnetic field is the dip equator, that is, the line where the field is strictly horizontal. This is the location of the Equatorial Electrojet, an electric horizontal current in the dayside lower ionosphere. During the last century, the dip equator moved westward by 350 km/decade, with slightly increasing speed.

Looking at polar regions, the dipole poles (defined in Equations 3.9 and 3.10 and shown in the top panel of Figure 3.7) have moved, with a speed of about 1 km/year between 1900 and 1940, since then accelerating to 7 km/year in 2015.

The position of the dip poles (the location where B is vertical) moved too, although much faster, with a typical speed between 10 and 20 km/year. Since 1980, the movement of the Northern dip pole accelerated and topped around 2005 with a speed of 55 km/year. It is presently located northward of Canada, is expected to be closest to the geographic pole around 2020 and will thereafter continue its journey toward Siberia.

The magnetic field is of primary importance for the external environment of the Earth. It acts as a shield against high-energy particles from the Sun and from outer space. It controls the radiation belts, and also the trajectories of incoming cosmic ray particles. The movement of regions of low magnetic intensity and hence high radiation, such as the SAA, is a direct consequence of the changing core field. These high radiation environments cause radiation damage to spacecraft and enhanced radiation exposure to humans in space. Recent instrument failures on some low-Earth-orbiting spacecraft confirm that the SAA has shifted to the Northwest. Continuous spacecraft monitoring of the magnetic field at low Earth orbit, and the derivation of field models, plays therefore an important role in predicting radiation hazards within the space environment.

Figure 3.7   Top: Movement of the dipole-poles and of the dip-poles between 1900 (light gray symbols) and 2020 (black symbols). Bottom: Location of the dip equator (the line where the magnetic field is strictly horizontal), of the location of weakest field intensity, and of the 25,000 nT contour interval of field intensity. All values are given at ground level.

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