How to actually label a geomagnetic field diagram without confusing your readers
I spent about three weeks last year trying to get a clean, publication-ready magnetic field diagram for a geophysics methods paper. The core problem wasn't understanding the physics — it was figuring out which conventions to follow and which labels were actually necessary versus decorative. Most people who ask about this just want a quick answer, but the labeling choices you make depend heavily on who's going to look at the diagram and what you're trying to communicate. The first decision is what kind of diagram you're working with. There are really three categories that show up in practice: the dipole approximation diagram (useful for intro courses), the actual multipole field with inclination and declination angles, and the vector field plot with field lines. Each one demands a different set of labels. I kept making the mistake of treating them interchangeably, which made my figures look wrong to reviewers who actually work in this field. For a proper geomagnetic field diagram, you need to label the magnetic north pole and magnetic south pole clearly — but don't call them N and S without clarification, because the geographic North Pole and the magnetic North Pole are about 400 kilometers apart right now and moving roughly 10 to 15 kilometers per year. If you're drawing field lines, show the direction arrows on at least half the lines around the diagram, not all of them, because that creates visual clutter without adding information. I used to put arrows on every single line, and one of my co-authors pointed out that it looked like a children's textbook illustration.
The inclination angle — sometimes called magnetic dip — is another label people forget to include or include incorrectly. Inclination is the angle between the magnetic field vector and the horizontal plane. At the magnetic equator it's zero, at the magnetic poles it approaches 90 degrees. If you're showing a cross-section of the Earth with field lines emerging from one hemisphere and entering the other, draw a small right-angle triangle at a mid-latitude point and label the inclination angle I. Don't use the Greek letter theta without defining it, because different textbooks use different conventions for that symbol in geomagnetism. Declination, or magnetic variation, is the horizontal angle between true north and magnetic north. This one matters most if your diagram is meant to be used for navigation purposes. Label it with a curved arrow from the geographic North direction toward the magnetic North direction, and include the value in degrees east or west. I learned this the hard way when a reviewer rejected my figure because I showed declination as a simple angle without indicating the east-west convention. The workaround was straightforward: I added a small compass rose in the corner and labeled both true north and magnetic north with their respective directions, then showed the declination angle between them with a curved arrow and a value like "12°W".
What most people get wrong about magnetic field labels
Here's something counter-intuitive that beginners usually miss: the Earth's magnetic field is not symmetric around the geographic axis. The magnetic poles are offset, and the dipole axis doesn't pass through the center of the Earth exactly. If you're drawing a textbook-style symmetric dipole diagram, that's fine for illustration, but you should note in the caption that it's an approximation. Real geomagnetic field models like IGRF — the International Geomagnetic Reference Field — use spherical harmonics up to degree and order 13 or higher for accurate predictions, and the resulting field lines look noticeably asymmetric if you plot them carefully. Another common pitfall: labeling the magnetic field strength units incorrectly. The standard unit is the nanotesla, abbreviated nT. One tesla is a very strong field — the Earth's surface field is roughly 25,000 to 65,000 nT depending on where you are. I've seen diagrams label this as "Tesla" with values like 0.00005, which is technically correct but practically useless for readers. Put the value in microtesla or nanotesla, and include a color bar or contour labels if you're showing field strength distribution. A typical range on the surface is about 30,000 nT at the equator to 60,000 nT near the poles. There's also the question of whether to label the core-generated field separately from the crustal field. The main geomagnetic field is about 95% generated by processes in the Earth's outer core, with the remaining 5% coming from magnetized rocks in the crust and mantle. If your diagram is meant to represent the total field, you don't need to decompose it, but if you're showing a model or simulation, label which component you're displaying. I ran into a situation where my figure showed a synthetic field that included only the core contribution, and a collaborator thought it was the total measured field, which led to a misunderstanding about why the values didn't match what she expected from satellite data.
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Tools and practical workflow
For actually creating these diagrams, Python with Matplotlib and the Cartopy library is the most straightforward approach for most people. You can generate field lines by integrating the magnetic field vector along a path, which is computationally simple but takes about 5 to 10 minutes for a high-resolution plot depending on your machine. The trick is getting the coordinate system right — use geographic coordinates (latitude, longitude) and make sure your field line integration respects the spherical geometry rather than treating the surface as flat. I wasted about two days on my first attempt because I was using a Cartesian projection for a global field plot, which distorted the line spacing near the poles. If you need publication-quality figures and don't want to code, GM Smith's Magnetic Field Plotter or the NOAA NGDC tools can export vector field diagrams, but the labeling is minimal and you'll still need to add annotations by hand in Illustrator or Inkscape. I usually spend about 30 to 45 minutes on post-processing each figure to add the inclination triangles, declination arrows, and proper axis labels. The total time from raw data to final labeled diagram is typically 2 to 3 hours for a first draft, down to about 45 minutes once you have a template set up. One limitation you should be aware of: most free tools don't include the time-dependent variation of the magnetic field unless you explicitly pass the epoch date. The IGRF model updates every five years, and the current version (IGRF-14, valid through 2025) predicts that the magnetic north pole is moving from northern Canada toward Siberia at roughly 55 kilometers per year. If you're generating a diagram for a paper that will be read in five years, the pole positions will be off by about 275 kilometers if you don't account for this drift. The workaround is to specify the observation epoch in your model call and document it in the figure caption.
When standard labeling fails
There are scenarios where a conventional magnetic field diagram simply doesn't work well. During a magnetic storm or when the magnetosphere is highly compressed, the field line configuration near the Earth changes significantly, and a static diagram becomes misleading. If you're studying space weather effects, you need time-series field line plots or multiple snapshots rather than a single representative figure. I encountered this when trying to illustrate auroral oval expansion during a G3-level geomagnetic storm — a standard dipole diagram looked completely wrong compared to what the ground magnetometer network was actually measuring. Another edge case: near the magnetic poles, the field lines become nearly vertical and the concept of "north" and "south" on a 2D map breaks down. If your diagram includes polar regions, use a polar stereographic projection and label the field direction with 3D cues or color coding rather than relying on horizontal arrows. I found that using a color scale from blue (field lines pointing up, away from Earth) to red (field lines pointing down, into Earth) made the polarity unambiguous even in the polar cap region where traditional arrow labels become confusing. If you need the field values rather than a schematic diagram, the NOAA National Centers for Environmental Information website provides downloadable grids from the IGRF model, and you can extract values at any latitude, longitude, and epoch. The data comes in spherical harmonic coefficients, so you'll need a small script to convert those to field components, but it takes about 15 to 30 seconds to generate a global grid at resolution 0.5 degrees on a modern laptop. For most people who just need a labeled diagram for a presentation or paper, the approximate dipole model with corrected pole positions is sufficient and saves considerable time compared to running the full harmonic synthesis.
