Introduction to linear and nonlinear programming

After a brief review of magnetospheric and interplanetary phenomena for intervals with enhanced solar wind-magnetosphere interaction, an attempt is made to define a geomagnetic storm as an interval of time when a sufficiently intense and long-lasting interplanetary convection electric field leads, through a substantial energization in the magnetosphere-ionosphere system, to an intensified ring current sufficiently strong to exceed some key threshold of the quantifying storm time Dst index. The associated storm/substorm relationship problem is also reviewed. Although the physics of this relationship does not seem to be fully understood at this time, basic and fairly well established mechanisms of this relationship are presented and discussed. Finally, toward the advancement of geomagnetic storm research, some recommendations are given concerning future improvements in monitoring existing geomagnetic indices as well as the solar wind near Earth.

/pdf/what-is-a-geomagnetic-storm-28nleury90.pdf

What is a geomagnetic storm

We present a new estimate of the Earth's heat loss based on a new global compilation of heat flow measurements comprising 24,774 observations at 20,201 sites. On a 5 o x 5 o grid, the observations cover 62% of the Earth's surface. Empirical estimators, ref- erenced to geological map units and derived from the observations, enable heat flow to be estimated in areas without measurements. Corrections for the effects of hydrothermal circulation in the oceanic crest compen- sate for the advected heat undetected in measurements of the conductive heat flux. The mean heat flows of continents and oceans are 65 and 101 mW m -2, re- spectively, which when areally weighted yield a global mean of 87 mW m -2 and a global heat loss of 44.2 x 10 2 W, an increase of some 4-8% over earlier esti- mates. More than half of the Earth's heat loss comes from Cenozoic oceanic lithosphere. A spherical hat- monic analysis of the global heat flow field reveals strong sectoral components and lesser zonal strength. The spectrum principally reflects the geographic dis- tribution of the ocean ridge system. The rate at which the heat flow spectrum loses strength with increasing harmonic degree is similar to the decline in spectral strength exhibited by the Earth's topography. The spectra of the gravitational and magnetic fields fall off much more steeply, consistent with field sources in the lower mantle and core, respectively. Families of con- tinental and oceanic conductive geotherms indicate the range of temperatures existing in the lithosphere under various surface heat flow conditions. The heat flow field is very well correlated with the seismic shear wave velocity distribution near the top of the upper mantle.

Heat flow from the Earth's interior: Analysis of the global data set

The 12th generation of the International Geomagnetic Reference Field (IGRF) was adopted in December 2014 by the Working Group V-MOD appointed by the International Association of Geomagnetism and Aeronomy (IAGA). It updates the previous IGRF generation with a definitive main field model for epoch 2010.0, a main field model for epoch 2015.0, and a linear annual predictive secular variation model for 2015.0-2020.0. Here, we present the equations defining the IGRF model, provide the spherical harmonic coefficients, and provide maps of the magnetic declination, inclination, and total intensity for epoch 2015.0 and their predicted rates of change for 2015.0-2020.0. We also update the magnetic pole positions and discuss briefly the latest changes and possible future trends of the Earth’s magnetic field.

/pdf/international-geomagnetic-reference-field-the-12th-4g4mwr9etv.pdf

International Geomagnetic Reference Field: the 12th generation

A worldwide network of receivers tracking the transmissions of Global Positioning System (GPS) satellites represents a new source of ionospheric data that is globally distributed and continuously available. We describe a technique for retrieving the global distribution of vertical total electron content (TEC) from GPS-based measurements. The approach is based on interpolating TEC within triangular tiles that tessellate the ionosphere modeled as a thin spherical shell. The high spatial resolution of pixel-based methods, where widely separated regions can be retrieved independently of each other, is combined with the efficient retrieval of gradients characteristic of polynomial fitting. TEC predictions from climatological models are incorporated as simulated data to bridge significant gaps between measurements. Time sequences of global TEC maps are formed by incrementally updating the most recent retrieval with the newest data as it becomes available. This Kalman filtering approach smooths the maps in time, and provides time-resolved covariance information, useful for mapping the formal error of each global TEC retrieval. Preliminary comparisons with independent vertical TEC data, available from the TOPEX dual-frequency altimeter, suggest that the maps can accurately reproduce spatial and temporal ionospheric variations over latitudes ranging from equatorial to about ±65°.

https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/97RS02707

A global mapping technique for GPS‐derived ionospheric total electron content measurements

A best current model of the main geomagnetic field is presented as a response to a need for an “International Geomagnetic Reference Field”. This model is described by a series of 120 spherical harmonic coefficients and their first and second time derivatives from an epoch 1960.0. It was derived from a sample of all magnetic survey data available from the interval 1900-1964 plus a recent global distribution of preliminary total field observations from the OGO-2 (1965-81A) spacecraft for epoch 1965.8. A duplicate data selection was made and the resulting field model compared with the first to help evaluate the minimum error. It was noted that the root —mean—square difference between the two models was about 30γ in the force components, 0.04 degrees in dip and 0.3 degrees in declination at the earth's surface for 1965.0.

A Proposed Model for the International Geomagnetic Reference Field-1965

A spherical harmonic model of the earth's internal magnetic field of degree and order 23 is derived from selected Magsat data, and its power spectrum, computed with terms developed by Mauersberger (1956) and Lowes (1974), is found to exhibit a change of a slope at n = 14 which is interpreted as an indication that the core field dominates at values lower than 13 while the crust field dominates above a value of 15. The representations of the two portions of the spectrum obtained can be used to establish order-of-magnitude inaccuracies due to both crustal fields and the inability to observe core field wavelengths beyond n = 13, at which point they are obscured by the crustal field, in core field models.

/pdf/a-geomagnetic-field-spectrum-5ua01foab2.pdf

A geomagnetic field spectrum

Data from the MAGSAT spacecraft for November 1979 through April 1980 and from 91 magnetic observatories for 1978 through 1982 are used to derive a spherical harmonic model of the Earth's main magnetic field and its secular variation. Constant coefficients are determined through degree and order 13 and secular variation coefficients through degree and order 10. The first degree external terms and corresponding induced internal terms are given as a function of Dst. Preliminary modeling using separate data sets at dawn and dusk local time showed that the dusk data contains a substantial field contribution from the equatorial electrojet current. The final data set is selected first from dawn data and then augmented by dusk data to achieve a good geographic data distribution for each of three time periods: (1) November/December, 1979; (2) January/February; 1980; (3) March/April, 1980. A correction for the effects of the equatorial electrojet is applied to the dusk data utilized. The solution included calculation of fixed biases, or anomalies, for the observation data.

/pdf/the-near-earth-magnetic-field-at-1980-determined-from-magsat-22tfwc5csf.pdf

The near‐Earth magnetic field at 1980 determined from Magsat data

SUMMARY The near-Earth magnetic field is caused by sources in the Earth’s core, ionosphere, magnetosphere, lithosphere and from coupling currents between the ionosphere and the magnetosphere, and between hemispheres. Traditionally, the main field (low degree internal field) and magnetospheric field have been modelled simultaneously, with fields from other sources being modelled separately. Such a scheme, however, can introduce spurious features, especially when the spatial and temporal scales of the fields overlap. A new model, designated CM3 (Comprehensive Model: phase 3), is the third in a series of efforts to coestimate fields from all of these sources. This model has been derived from quiet-time Magsat and POGO satellite and observatory hourly means measurements for the period 1960‐1985. It represents a significant advance in the treatment of the aforementioned field sources over previous attempts, and includes an accounting for main field influences on the magnetosphere, main field and solar activity influences on the ionosphere, seasonal influences on the coupling currents, a priori characterization of the influence of the ionosphere and the magnetosphere on Earth-induced fields, and an explicit parametrization and estimation of the lithospheric field. The result is a model that describes well the 591 432 data with 16 594 parameters, implying a data-to-parameter ratio of 36, which is larger than several popular field models.

A comprehensive model of the quiet‐time, near‐Earth magnetic field: phase 3

In August 1991 the International Association of Geomagnetism and Aeronomy revised the International Geomagnetic Reference Field (IGRF) for the fifth time. This Sixth Generation IGRF now consists of 10 spherical harmonic models of the main geomagnetic field at five year intervals from 1945 through 1990 and a secular variation model extending the main field model of 1990 through 1995. For the interval 1945-1985 the models are definitive (DGRFs), in that it is unlikely that the underlying data sets will be significantly improved so there is no plan for future revision of the models. The present revision consists of adoption of a definitive main field model for 1985, DGRF 1985, a main field model for 1990 with secular variation coefficients for 1990-1995, IGRF 1990, and a provisional model, PGRF 1985, for 1985-1990 defined as the linear interpolation between DGRF 1985 and IGRF 1990. All main field models are of degree and order 10. The secular variation model is of degree and order 8. The models were derived from five candidate main field models at 1985, five at 1990, and three candidate secular variation models at epoch 1992.5. Weighted averages of the candidate models were specified to arrive at the final models. A brief description of the development of the IGRF is given, useful formulae are reviewed, and contour maps of the geomagnetic elements D, I, H, X, Y, Z, and F at 1990 are included. The nature of and philosophy behind the IGRF are discussed and a new procedure for deriving the IGRF is proposed.

https://www.jstage.jst.go.jp/article/jgg1949/44/9/44_9_679/_pdf

Robert A. Langel

Papers

A Proposed Model for the International Geomagnetic Reference Field-1965

A geomagnetic field spectrum

The near‐Earth magnetic field at 1980 determined from Magsat data

A comprehensive model of the quiet‐time, near‐Earth magnetic field: phase 3

International geomagnetic reference field : the sixth generation