Gary A Glatzmaier

The GeodynamoPaleomagnetic records indicate that the geomagnetic field has existed for at least three billion years. However, based on the size and electrical conductivity of the Earth's core, the field, if it were not continually being generated, would decay away in only about 20,000 years since the temperature of the core is too high to sustain permanent magnetism. In addition, paleomagnetic records show that the dipole polarity of the geomagnetic field has reversed many times in the past, the mean time between reversals being roughly 200,000 years with individual reversal events taking only a couple thousand years.

These observations argue for a mechanism within the Earth's interior that continually generates the geomagnetic field. It has long been speculated that this mechanism is a convective dynamo operating in the Earth's fluid outer core, which surrounds its solid inner core, both being mainly composed of iron. The solid inner core is roughly the size of the moon but at the temperature of the surface of the sun. The convection in the fluid outer core is thought to be driven by both thermal and compositional buoyancy sources at the inner core boundary that are produced as the Earth slowly cools and iron in the iron-rich fluid alloy solidifies onto the inner core giving off latent heat and the light constituent of the alloy. These buoyancy forces cause fluid to rise and the Coriolis forces, due to the Earth's rotation, cause the fluid flows to be helical. Presumably this fluid motion twists and shears magnetic field, generating new magnetic field to replace that which diffuses away.

However, until now, no detailed dynamically self-consistent model existed that demonstrated this could actually work or explained why the geomagnetic field has the intensity it does, has a strongly dipole-dominated structure with a dipole axis nearly aligned with the Earth's rotation axis, has non-dipolar field structure that varies on the time scale of ten to one hundred years and why the field occasionally undergoes dipole reversals. In order to test the convective dynamo hypothesis and attempt to answer these longstanding questions, the first self-consistent numerical model, the Glatzmaier-Roberts model, was developed that simulates convection and magnetic field generation in a fluid outer core surrounding a solid inner core (Figure 1) with the dimensions, rotation rate, heat flow and (as much as

possible) the material properties of the Earth's core [1-5]. The magnetohydrodynamic equations that describe this problem are solved using a spectral method (spherical harmonic and Chebyshev polynomial expansions) that treats all linear terms implicitly and nonlinear terms explicitly [4]. These equations are solved over and over, advancing the time dependent solution 20 days at a time.

Fig.1 A snapshot of the region (yellow) where the fluid flow is the greatest. The core-mantle boundary is the blue mesh; the inner core boundary is the red mesh. Large zonal flows (eastward near the inner core and westward near the mantle) exist on an imaginary "tangent cylinder" due to the effects of large rotation, small fluid viscosity, and the presence of the solid inner core within spherical shell of the outer fluid core. (click on image to download, 0.15 Mb)

The resulting three-dimensional numerical simulation of the geodynamo, run on parallel supercomputers at the Pittsburgh Supercomputing Center and the Los Alamos National Laboratory, now spans more than 300,000 years. The simulated magnetic field has an intensity and a dipole dominated structure that is very similar to the Earth's (Figure 2) and a westward drift of the non-dipolar structures of the field at the surface that is essentially the same as the 0.2 degrees/year measured on the Earth. Our solution illustrates how the influence of the Earth's rotation on convection in the fluid outer core is responsible for this magnetic field structure and time dependence [1].

Fig.2 A snapshot of the 3D magnetic field structure simulated with the Glatzmaier-Roberts geodynamo model. Magnetic field lines are blue where the field is directed inward and yellow where directed outward. The rotation axis of the model Earth is vertical and through the center. A transition occurs at the core-mantle boundary from the intense, complicated field structure in the fluid core, where the field is generated, to the smooth, potential field structure outside the core. The field lines are drawn out to two Earth radii. Magnetic field is rapped around the "tangent cylinder" due to the shear of the zonal fluid flow (Fig. 1). (click on image to download, 0.15 Mb)

In addition, about 36,000 years into the simulation the magnetic field underwent a reversal of its dipole moment (Figure 3), over a period of a little more than a thousand years. The intensity of the magnetic dipole moment decreased by about a factor of ten during the reversal and recovered immediately after, similar to what is seen in the Earth's paleomagnetic reversal record. Our solution shows how convection in the fluid outer core is continually trying to reverse the field but that the solid inner core inhibits magnetic reversals because the field in the inner core can only change on the much longer time scale of diffusion [2]. Only once in many attempts is a reversal successful, which is probably the reason why the times between reversals of the Earth's field are long and randomly distributed.

Fig.3 Like in Fig. 2, but 500 years before the middle of a magnetic dipole reversal,

at the middle of the reversal, and

500 years after the middle of the reversal. (click on images to download, 0.15 Mb each)

After the first magnetic reversal, we continued our simulation on two different branches: one by continuing to prescribe a uniform heat flux out of the core at the core-mantle boundary and the other by prescribing a heterogeneous heat flux there that is similar to the Earth's present pattern. The former has not reversed again; the latter underwent two more reversals, roughly 100,000 years apart. This demonstrates the influence the thermal structure in the lower mantle has on the style of convection and magnetic field generation in the fluid core below.

One part of this numerical solution is the rotation rate of the solid inner core relative to the surface, which evolves according to the torque applied on the inner core by the generated magnetic field. Our solution shows how the field couples the inner core to the eastward flowing fluid above it (Figure 4a), keeping it in co-rotation [5]. This mechanism is analogous to a synchronous electric motor for which the field, carried eastward by the fluid, acts like the rotating field in the stator and the inner core acts like the rotor.

Fig.4 (a) A snapshot of the simulated magnetic field structure within the core, with lines blue where outside the solid inner core and yellow where inside. Again, the rotation axis is vertical. (click on image to download, 0.24 Mb) (b) A schematic image illustrating the super-rotation of the inner core relative to the Earth's surface.

The inner core in our simulation initially rotated between 2 and 3 degrees longitude per year faster than the solid mantle and surface [1, 5]. This prediction in 1995 [1] for the Earth motivated two seismologists from Columbia University in early 1996 to search for evidence of this super-rotation in 30 years of seismic data. They found evidence that supports our prediction and published it in July 1996

[6], (Figure 4b). More recent simulations of ours that now include a simple parameterization for the gravitational coupling that may exist between the mantle and the inner core have a much smaller inner core rotation amplitude; however, this rotation is still predominantly eastward relative to the model Earth's surface.

For more about the Geodynamics, visit these links: "Analyses of simulated magnetic dipole reversals" "Computer simulations of the Earth's mantle and core" "Institute of Geophysics and Planetary Physics" "Studies of the Earth's Deep Interior" Geodynamo Computations at the Pittsburgh

Supercomputing Center 1996 Computerworld-Smithsonian Award in Science

NASA HPCC Grand Challenge in Geophysics

References:

[1] G.A. Glatzmaier and P.H. Roberts, "A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle," Phys. Earth Planet. Inter., 91, 63-75 (1995).

[2] G.A. Glatzmaier and P.H. Roberts, "A three-dimensional self-consistent computer simulation of a geomagnetic field reversal," Nature, 377, 203-209 (1995).

[3] G.A. Glatzmaier and P.H. Roberts, "On the magnetic sounding of planetary interiors," Phys. Earth Planet. Inter., 98, 207-220 (1996).

[4] G.A. Glatzmaier and P.H. Roberts, "An anelastic evolutionary geodynamo simulation driven by compositional and thermal convection," Physica D, 97, 81-94 (1996).

[5] G.A. Glatzmaier and P.H. Roberts, "Rotation and magnetism of Earth's inner core," Science, 274, 1887-1891 (1996).

[6] X. Song and P. Richards, "Seismological evidence for differential rotation of the Earth's inner core," Nature, 382, 221-224 (1996).

"The Magnetic Compass

The magnetic compass has been used for navigation for hundreds of years. At one time, it was the only reliable means of direction-finding on days when the sun and stars were not visible. Nowadays, sophisticated equipment is available that enables users to

determine their bearing accurately and to pinpoint locations to within a few metres. However, such equipment has not made the compass obsolete. It is still a very practical tool for navigation for many small craft and for people on foot. Even airplanes and ships equipped with more sophisticated equipment often carry compasses as backups. Compasses come in a variety of shapes and sizes depending on their intended use. The type of compass used on a ship or aircraft is a complex device capable of compensating for both the motion of the craft and its metallic structure. At the other extreme are small

pocket compasses of low precision intended for casual use. Regardless of their intended purpose or the complexity of

their construction, most compasses operate on the same basic principle. A small, elongated, permanently magnetized needle is placed on a pivot so that it may rotate freely in the horizontal plane. The Earth's magnetic field which is shaped approximately like the field around a simple bar magnet exerts forces on the compass needle, causing it to rotate until it comes to rest in the same horizontal direction as the magnetic field. Over much of the Earth, this direction is roughly true north, which accounts for the compass's importance for navigation. Area of Compass Unreliability The horizontal force of the magnetic field, responsible for the direction in which a compass needle is oriented, decreases in strength as one approaches the North Magnetic Pole, where it is zero. Close to the pole, an area is reached where the frictional forces in the pivot are comparable to the horizontal forces of the magnetic field. The

compass starts to behave erratically, and eventually, as the horizontal force decreases even more, the compass becomes unusable. Magnetic Reference Field Models Since magnetic observations are neither uniformly nor densely distributed over the Earth, and since the magnetic field is constantly changing in time, it is not possible to obtain up-to-date values of declination directly from a database of past observations. Instead, the data are analyzed to produce a mathematical routine called a magnetic reference field "model", from which magnetic declination can be calculated. Global models are produced every five years. These constitute the series of International Geomagnetic Reference Field (IGRF) models. The latest IGRF was produced in 1995, and is valid until 2000. The Canadian Geomagnetic Reference Field (CGRF) is a model of the magnetic field over the Canadian region. It was produced using denser data over Canada than were used for the IGRF, and because the analysis was carried out over a smaller region, the CGRF can reproduce smaller spatial variations in the magnetic field than can the IGRF. The latest CGRF was also produced in 1995 and is valid until 2000. The accompanying declination chart is based on the CGRF. Since magnetic field models such as the IGRF and CGRF are approximations to observed data, a value of declination computed using either of them is likely to differ somewhat from the "true" value at that location. It is generally agreed that the IGRF achieves an overall accuracy of better than

1° in declination; the accuracy is better than this in densely surveyed areas such as Europe and North America, and worse in oceanic areas such as the south Pacific. The accuracy of the CGRF, in southern Canada, is about 0.5°. The accuracy of all models decreases in the Arctic near the North Magnetic Pole. Magnetic field models are used to calculate magnetic declination by means of computer programs such as the Magnetic Information Retrieval Program (MIRP), a software package developed by the Geomagnetism Program of the Geological Survey of Canada. The user inputs the year, latitude and longitude and MIRP calculates the declination. MIRP is able to compute

values for any location on the Earth in the time period 1960 to 2000. For locations within Canada, MIRP computes values using the CGRF. Outside Canada, values are calculated using the IGRF. True North?Many people are surprised to learn that a magnetic compass does not normally point to true north. In fact, over most of the Earth it points at some angle east or west of true (geographic) north. The direction in which the compass needle points is referred to as magnetic north, and the angle between magnetic north and the true north direction is called magnetic

declination. You will often hear the terms "variation", "magnetic variation", or "compass variation" used in place of magnetic declination, especially by mariners. The magnetic declination does not remain constant in time. Complex fluid motion in the outer core of the Earth (the molten metallic region that lies from 2800 to 5000 km below the Earth's surface) causes the magnetic field to change slowly with time. This change is known as secular variation. As an example, the accompanying diagram shows how the magnetic declination has changed with time at Halifax. Because of secular variation, declination values shown on old topographic, marine and aeronautical charts need to be updated if they are to be used without large errors. Unfortunately, the annual change corrections given on most of these maps cannot be applied reliably if the

maps are more than a few years old since the secular variation also changes with time in an unpredictable manner.

The position of the Magnetic North PoleA pole position was [next] determined by Canadian government scientists shortly after World War II. Paul Serson and Jack Clark, of the Dominion Observatory, measured a dip of 89° 56' at Allen Lake on Prince of Wales Island. This, in conjunction with other observations made in the vicinity, showed that the pole had moved some 250 km northwest since the time of Amundsen's observations. Subsequent observations by Canadian government scientists in 1962, 1973, 1984, and most recently in 1994, showed that the general northwesterly motion of the pole is continuing, and that during this century it has moved on average 10 km per year . Diurnal Motion of the Pole

It is important to realize that when we talk about the location of the pole, we are referring to an average position. The pole wanders daily in a roughly elliptical path around this average position, and may frequently be as much as 80 km away from this position when the Earth's magnetic field is disturbed. The diagram shows the average path on a magnetically quiet day (inner ellipse) and on a magnetically disturbed day (outer ellipse). Why is the Pole Moving?If, as Gilbert believed, the Earth acts as a large magnet, the pole would not move, at least not as rapidly as it does. We now know that the cause

of the Earth's magnetic field is much more complex. We believe that it is produced by electrical currents that originate in the hot, liquid, outer core of the Earth. As a simple analogy, consider an electromagnet, in which we can produce a strong magnetic field by passing an electric current through a coil of wire. In nature, processes are seldom simple. The flow of electric currents in the core is continually changing, so the magnetic field produced by those currents also changes. This means that at the surface of the Earth, both the strength and direction of the magnetic field will vary over the years. This gradual change is called the secular variation of the magnetic field. The position of the North Magnetic Pole is strongly influenced by the secular variation in its vicinity. For example, if the dip is 90° at a given point this year, that point will be the North Magnetic Pole, by definition. However, because of secular variation, the dip at that point will change to 89°58' in about two years, so it will no longer be the pole. However, at some nearby point, the dip will have increased to 90°, and that point will have become the pole. In this manner, the pole slowly moves across the Arctic. The more rapid daily motion of the pole around its average position has an entirely different cause. If we measure the Earth's magnetic field continually, such as is done at a magnetic observatory, we will see that it changes during the course of a day, sometimes slowly, sometimes rapidly. The ultimate cause of these fluctuations is the Sun. The Sun constantly emits charged particles that, on encountering the Earth's magnetic field, cause electric currents to be produced in the upper atmosphere. These electric currents disturb the magnetic field, resulting in a temporary shift in the pole's position. The distance and speed of these displacements will, of course, depend on the nature of the disturbances in the magnetic field, but they are occurring constantly. When scientists try to determine the average position of the pole, they must average out all of these transient wanderings."

How do racing pigeons "average out all these transient wanderings" in determining the location of the pole in their minds to be available as a reference useful for navigating their way home? The secular variation is not expected to present much of a problem to racing pigeons because it happens gradually over a long period of time but a different

situation exists with the more rapid daily motion of the pole, especially when the earth's magnetic field is disturbed at which time the pole can move rapidly distances of up to 80 km. This may have dire consequences for our racing pigeons as their point of reference has moved enough to cause them to pass by their home loft.Consider the eruption of Mount St Helen which disturbed the geomagnetic forces enough to move the pole suddenly causing the birds to "locate" their loft where it is not and thus creating difficulties for them. Many racing pigeon clubs all over North America experienced terrible returns from their organized races on that weekend.High sunspot numbers resulting in high geomagnetic disturbances and a high K factor will also result in rapid movement of the magnetic pole. A "smash" toss need not necessarily occur when the K-factor (a 3 hourly local index of geomagnetic activity) is high. It is the unreliability of the position of the magnetic pole which will not inspire confidence regarding the bird's homing ability and consequently lead to poor orientation in years of high solar activity, not necessarily on days of geomagnetic disturbances. Consider the K factor on August 4, 2000. There was little geomagnetic activity and yet we had a catastrophic toss. A toss from the same location on August 12, 2000 at the time of a geomagnetic storm resulted in an excellent return.

Of course we need to mention that the birds participating in this second toss were the ones who succeeded in navigating during the previous attempt. We therefore had already selected for the birds better adapted to navigating in this year of high geomagnetic activity.In spite of factors such as these similar to "moving the goal posts", there are thus always some birds much less affected than the majority. Racing pigeons have many tools at their disposal for finding their way home and it is the ones who can use most of them effectively who will succeed. Perhaps we should not lament the loss of inferior ones but welcome nature's method of helping us with the selection which must be done.

Main Magnetic Field:

The Main Magnetic Field originates from a dynamo process in the fluid outer core of the Earth. It strongly dominates over the various other contributions to the geomagnetic field, accounting for over 95% of the field strength observed at the Earth's surface.

Fig. 1: Strength of the magnetic field at the Earth's surface in 2006, as given by the main field model POMME-3.0.

The main field changes slowly with a time scale of years. Accurate measurements of the magnetic field, provided by satellites and magnetic observatories, can be used to estimate the present changes in the field. The first time derivative is called the secular variation (Fig. 2). It shows that the field strength is decreasing in most parts of the World. The strongest decrease is seen the Caribbean. But there are also areas of increasing field strength, such as in the Indian Ocean.

Fig. 2: Secular variation of the strength of the magnetic field in 2006

The 2nd time derivative is called the secular acceleration (Fig. 3). Comparing the maps in Figures 2 and 3 reveals some interesting behavior of the magnetic field. For instance, the increasing field strength in the Indian Ocean (in Fig. 2) is decreasing in the East and increasing in the West (Fig. 3). Thus, this region of increasing field is moving westward. Similarly, the decreasing strength over the Americas (Fig. 2) is increasing in the East and decreasing in the West (Fig. 3). Hence, this feature is also moving westward. The general tendency of magnetic field features to move westward is called the westward drift. However, this is not a strict rule, as there are features in the Pacific which are moving eastward.

Fig. 3: Secular acceleration of the magnetic field in 2006

Using these time derivatives, the core field can be predicted for the upcoming couple of years. For example, the World Magnetic Model (WMM) provides a predicted value of the magnetic field vector at any desired location, up to 5 years into the future, based on the estimated mean secular variation. The International Geomagnetic Reference Field (IGRF) provides the historical core field, starting in 1900, including a similar prediction 5 years into the future. Finally, scientific geomagnetic field models, like POMME-3 provide the core field, including the secular acceleration, together with contributions from the lithospheric magnetization and magnetospheric currents.

4b. Where are they? Magnetic Poles

The geomagnetic poles or geocentric dipole, can be computed from the first three Gauss coefficients from a main field model, such as the WMM or IGRF. Based on the current WMM model, the 2005 location of the geomagnetic north pole is 79.74°N and 71.78°W and the geomagnetic south pole is 79.74°S and 108.22°E.

The magnetic poles or dip pole are computed from all the Gauss coefficients using an iterative method. Based on the current WMM model, the 2005 location of the north magnetic pole is 83.21°N and 118.32°W and the south magnetic pole is 64.53°S and 137.86°E.

The location of the center of the eccentric dipole, sometimes known as the magnetic center, computed using the first eight Gauss coefficients for 2005.0, is at approximately (r, φ´, λ) = (552 km, 22.2°N, 141.6°E).

The task of locating the principal magnetic pole by instrument is difficult for many reasons; the large area over which the dip or inclination (I) is nearly 90 degrees, the pole areas are not fixed points, but move tens to hundreds of kilometers because of daily variations and magnetic storms, and finally, the polar areas are relatively inaccessible to survey crews (map of North and South polar wander - courtesy of Dr. John Quinn, U.S. Geological Survey retired). The Geological Survey of Canada keeps track of the North Magnetic Pole, which is slowly drifting across the Canadian Arctic, by periodically carrying out magnetic surveys to redetermine the Pole's location. The most recent survey, completed in May, 2001, determined an updated position for the Pole and established that it is moving approximately northwest at 40 km per year. The observed position for 2001 and estimated positions for 2002 to 2005 are:

Year Latitude (°N) Longitude (°W)

2001 81.3 110.8

2002 81.6 111.6

2003 82.0 112.4

2004 82.3 113.4

2005 82.7 114.4

Observed position of the South Magnetic Pole

2001 64.7° S138.0° E

Source: Canadian Geologic Survey