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geomagnetic jerk

the Earth. These interactions can generate large current sheets in the magnetosphere and ionosphere, whose associated magnetic ﬁelds can have direct effect on power transmission systems because of the continental scale of those systems.

geomagnetic elements The geomagnetic ﬁeld intensity, F, can be characterized at any point by its geomagnetic elements. These may be expressed as the magnitudes of three perpendicular components, or by some other set of three independent parameters. Several different sets are used, depending on context. Generally, the preferred set is (X, Y, Z) where X is the component of the geomagnetic ﬁeld measured to the geographic north direction; Y is the component of the geomagnetic ﬁeld measured to the geographic east direction; and Z is the component of the geomagnetic ﬁeld measured in the vertical, with the positive sign directed downwards (so the geomagnetic Z component is positive in the northern hemisphere). Other elements are H, D, and I where H is the horizontal component of the geomagnetic ﬁeld measured in the direction of the north geomagnetic pole; D, the magnetic declination, is the angle between the direction of the geomagnetic ﬁeld, the direction a compass needle points, and true geographic north, reckoned positive to the east; and the inclination, I, or dip angle, is the angle that the geomagnetic ﬁeld dips below the horizontal. See geomagnetic ﬁeld, nanotesla.

geomagnetic ﬁeld The magnetic ﬁeld intensity measured in and near the Earth. This is a vector, with the direction deﬁned such that the north-seeking pole of a compass points toward the geomagnetic north pole and in the direction deﬁned as positive ﬁeld. Thus, the magnetic ﬁeld lines emerge from the Earth’s South Pole and point into the North Pole. The surface intensity of the Earth’s magnetic ﬁeld is approximately 0.32 × 10−4 tesla (T) at the equator and 0.62 × 10−4 T at the North Pole. Above the Earth’s surface, the ﬁeld has the approximate

form of a magnetic dipole with dipole moment 7.9 × 1015 Tm−3. Many earth-radii away, this

dipole is distorted into a teardrop with its tail pointing anti-sunward by the magnetized solar wind plasma ﬂow. The principal sources of

the geomagnetic ﬁeld are convective motions of the Earth’s electrically conducting ﬂuid core, magnetization of the crust, ionospheric currents, and solar wind perturbations of the geomagnetic neighborhood.

geomagnetic indices Geomagnetic indices give a very useful descriptive estimate of the extent of geomagnetic disturbances. Most common indices of the Earth’s magnetic ﬁeld are based on direct measurements made at magnetic observatories. Local indices are calculated from these measurements and then global indices are constructed using the local indices from selected, standard locations. These global indices are often referred to as planetary indices. Commonly used indices are the K index (a local index) and the Kp index (the associated planetary K index, which depends on a speciﬁc number of magnetic observatories); the A index (essentially a linear local index) and Ap index (the associated planetary index). Other important indices are the AE index, which gives a measure of the currents ﬂowing in the auroral region, and the Dst index, which gives a measure of the currents ﬂowing in the Earth’s magnetosphere. See Ap, K, Kp indices.

geomagnetic jerk It has been observed that there are on occasion impulses in the third time derivative of the geomagnetic ﬁeld (i.e., “jerks” in the ﬁeld, which appear as an abrupt change in the gradient of the secular variation). These appear to be global phenomena of internal origin, with recent examples around 1969, 1978, and 1991, and claims of several earlier examples. The effect appears to be most notable in the eastward component of the magnetic ﬁeld, and the phenomenon appears to take place over a timescale of perhaps 2 years. Unless the mantle behaves as a complicated ﬁlter causing slow changes in the core to be revealed as relatively rapid variation at the Earth’s surface, the sharpness of this phenomenon places a constraint on mantle conductivity: it must be sufﬁciently low so that the magnetic diffusion timescale of the mantle (over which sharp changes in the ﬁeld at the core’s surface would be smoothed out when observed at the Earth’s surface) is at most the same order of magnitude as that of the jerk. It is not entirely clear what causes geomagnetic

geomagnetic potential

jerks, although one proposal has been sudden unknotting of ﬁeld loops within the core, and there have been claims that they are associated with jumps in the Chandler wobble.

geomagnetic potential An auxiliary function, denoted γ or V, used for describing the internally generated magnetic ﬁeld of the Earth. See harmonic model.

geomagnetic storm A geomagnetic storm is said to occur when the geomagnetic indices exceed certain thresholds. At these times, a worldwide disturbance of the Earth’s magnetic ﬁeld is in progress. There are categories of geomagnetic storm. In one form of classiﬁcation, a minor geomagnetic storm occurs when the Ap index is greater than 29 and less than 50; a major geomagnetic storm occurs when the Ap index is greater than 49 and less than 100; and a severe geomagnetic storm occurs when the Ap index exceeds 100. A geomagnetic storm arises from the Earth’s magnetic and plasma environment response to changes in the solar wind plasma properties. A key factor is a change in the solar wind interplanetary magnetic ﬁeld from north to south, facilitating easier access to the Earth’s magnetic domain. The geomagnetic storm can be described by various phases. During the initial phase of a storm there may be an increase in the observed middle-latitude magnetic ﬁeld as the solar wind plasma compresses the Earth’s magnetosphere. This is then followed by the main phase of the storm when the magnetic ﬁeld at middle latitudes decreases below normal levels and can exhibit large, sometimes rapid, changes. This phase is associated with the formation of large-scale current systems in the magnetosphere caused by the solar wind interactions. Finally, during the recovery phase the geomagnetic ﬁeld gradually returns to normal levels. A storm may last for one or more days. Statistically, there is a greater likelihood of larger geomagnetic storms during the equinoxes. See also coronal mass ejection, geomagnetic indices, gradual commencement storm, solar wind.

geometrodynamics A particular interpretation of general relativity in which the geometry of the 3-space (see ADM form of the Einstein–

Hilbert action) is treated as a dynamical object (along with matter ﬁelds) which evolves according to the spatial components of Einstein equations and satisﬁes the Hamiltonian and (super-) momentum constraints. The full set of physical ﬁelds forms the so-called superspace with a ﬁnite number of degrees of freedom at each space point. It can also be restricted so as to have a ﬁnite total number of degrees of freedom. See minisuperspace, Hamiltonian and momentum constraints in general relativity, superspace.

geophysics The subdiscipline of geology which deals with the application of physics to geologic problems. Some of the major areas of geophysical analysis are vulcanology, petrology, hydrology, ionospheric and magnetospheric physics, geochemistry, meteorology, physical oceanography, seismology, heat ﬂow, magnetism, potential theory, geodesy, and geodynamics. The aims of geophysics are to determine a body’s interior composition and structure, and the nature of the processes that produce the observed features on the body’s surface.

geopotential The sum of the Earth’s gravitational potential and the centrifugal potential associated with the Earth’s rotation. Geopotential is sometimes given in units of the geopotential meter (gpm) deﬁned by

1 gpm = 9.8m2s−2 = 9.8 Jkg−1 ,

so that the value of the geopotential in geopotential meters is close to the height in meters. Alternatively, the geopotential height or dynamic height is deﬁned by the geopotential divided by acceleration due to gravity, so that the geopotential height in meters is numerically the same as the geopotential in geopotential meters.

geopotential surface If the sea were at rest, its surface would coincide with the geopotential surface. This geopotential surface is called sea level and is deﬁned as zero gravitational potential.

geospace One of several terms used to describe the totality of the solar-terrestrial environment. It is the domain of sun-Earth interactions and comprises the particles, magnetic and electric ﬁelds, and radiation environment

geothermal gradient

that extend from the sun to Earth and includes the Earth’s space plasma environment and upper atmosphere. Geospace is considered to be the fourth physical geosphere (after solid earth, oceans, and atmosphere).

geostrophic adjustment A process in which the pressure and ﬂow ﬁelds adjust toward the geostrophic balance. The upper panel shows such an example, where the shallow water system is initially at rest but its surface level has a discontinuous jump. In a non-rotating system, the water surface will become ﬂat at the average of the initial levels (middle). In a rotating system, in contrast, the water level difference is sustained by ﬂows in geostrophic balance with the surface slope (lower panel). The discontinuous jump in water level deforms into a smooth slope whose horizontal scale is the radius of deformation.

t=0

Non-rotating

Rotating

counter-clockwise in the Northern Hemisphere. The resulting ﬂow from this balance is called the geostrophic ﬂow and the resulting transport from this balance is called the geostrophic transport.

geostrophy See geostrophic balance.

Geosynchronous Operational Environmental Satellites (GOES) A series of meteorology observing satellites operated by the National Oceanic and Atmospheric Administration (NOAA). GOES also monitors space weather via its onboard Space Environment Monitor (SEM) system. The three main components of space weather monitored by GOES at 35,000 km altitude are X-rays, energetic particles, and magnetic ﬁeld.

geosynchronous orbit A prograde circular Earth-satellite orbit at a radius of 42,300 km above the equator. At this distance from Earth, the orbital period of a satellite is 1 day, i.e., equal to the rotational period of Earth. The satellite thus remains above the same point on the ground. Such orbits have extreme commercial value for broadcast and communications.

geotherm Because the Earth is losing heat to its surface, the interior of the Earth is hot. The temperature of the Earth’s interior as a function of depth is the geotherm. Typically the increase in temperature with depth is about 25 K/km.

geostrophic approximation	The assump-
tion of geostrophic balance.

geostrophic balance A balance between the pressure gradient and Coriolis forces: f u×k = − p/ρ, where f is the Coriolis parameter, u the horizontal velocity, k the unit vertical vector, p the pressure, and ρ the water density. For large-scale ocean-atmospheric motion, it provides a good approximate relation between ﬂow and pressure ﬁelds. In the Northern (Southern) Hemisphere, pressure increases toward the right (left) for an observer facing downstream in a geostrophic ﬂow. Thus, geostrophic winds associated with a circular low pressure system rotate

geothermal energy The energy contained in heat below the surface of the Earth or the development of this energy for commercial purposes. The dominant form of use is natural hot water from subsurface formations, but other approaches, such as pumping water underground to heat it, can be carried out. Though in some places (Iceland) hot geothermal water is used to heat buildings, in most cases it is used to generate electricity or in dual (cogeneration) use. The worldwide installed geothermal electrical production in 1998 was about 8000 MW electrical, equivalent to several large nuclear plants.

geothermal gradient The vertical gradient of temperature in the Earth. Downward increase

Geroch group

(about 25 K/km near the surface) is usually taken to be positive.

Geroch group In general relativity, an inﬁnite-parameter symmetry group of stationary axisymmetric vacuum space-times. It is generated by two noncommuting 3-parameter symmetry groups; one is the group of constant linear combinations of the space-like and timelike Killing vectors. The other generating group (called the Ehlers group) acts on the gravitational potentials and is isomorphic to O(2,1).

Geroch–Hansen moments (1974) Gravitational multipole moments of stationary and axisymmetric isolated sources in the theory of general relativity. They form a complex inﬁnite series. The real parts are the mass (or gravielectric) moments and the imaginary parts are the current or gravimagnetic moments. The Schwarzschild spacetime has a mass monopole moment equal to the mass m, and all other moments vanish. The nth moment of the Kerr spacetime with rotation parameter a is m(ia)n. See Kerr black hole, Schwarzschild black hole.

Gershun’s law The conservation of energy equation obtained by integrating the monochromatic radiative transfer equation (for a medium with no inelastic scattering or other sources) over all directions; it states that the depth derivative of the net plane irradiance equals the negative of the absorption coefﬁcient multiplied by the scalar irradiance.

Gershun tube A tube used to limit the ﬁeld of view of a radiometer to a small solid angle; used in measuring radiances.

GeV Giga electronvolt; a unit of energy equal to a billion (109) electronvolts.

giant branch The collection of stars in which a contracting helium core heats an overlying hydrogen shell, accelerating hydrogen burning. Stars develop a large hydrogen envelope and occupy a speciﬁc region in the HR diagram, with K to M spectral type (B − V = 1.0 − −1.8, absolute magnitude 2 to -2). The Red Giant phase ends when the temperature of the core reaches

108K, and helium ignites explosively in its core (the “helium ﬂash”).

giant cells The largest of the discrete scales governing convective motions on the sun; the other three being granulation, mesogranulation, and supergranulation. The existence of giant cells is less conclusive than the other scales of convection. However, they are believed to have a dimension comparable with that of the depth of the convection zone ( 300,000 km), surface velocities of as little as 0.03 to 0.1 kms−1 and lifetimes of 14 months.

giant planet One of Jupiter, Saturn, Uranus, and Neptune in the solar system, or a similar extrasolar planet. Typically much more massive than terrestrial planets, giant planets are composed of volatiles (hydrogen, helium, methane, ammonia) with small solid cores, if any.

Gibbs free energy (Gibbs Potential) An extensive thermodynamic potential H given by

H = U − ST − P V ,

where U is the internal energy, S is the entropy, T is the temperature, P is the pressure, and V is the volume of the system. For a reversible process at constant T and P , work stored as Gibbs Potential can be recovered completely.

gilvin See colored dissolved organic matter.

Ginzburg temperature In quantum (or classical) systems with multiple minima in some potential, separated by a barrier, the minimum temperature needed to induce thermal jumps from one minimum of the potential to another. Applications include magnetism, superconductivity, and the mechanism of formation of topological defects in the early universe. See correlation length, cosmic topological defect, Kibble mechanism.

glacial Referring to processes or features produced by ice.

glaciation A geologic epoch when 30% of the Earth’s land surface is covered with moving ice. The most recent glaciation began in the