The World Magnetic Model

The WMM is invisible infrastructure: every consumer compass app, every commercial aircraft's magnetic-based instruments, and most military navigation systems quietly apply it to convert raw magnetometer readings into useful bearings. This article goes deeper than the /learn/magnetic-declination-explained pillar on the model itself — the mathematics, the data, the production cycle, the 2019 anomaly, and the comparison with IGRF.

What the WMM produces

Given inputs:

• Latitude (degrees, ±90°)
• Longitude (degrees, ±180°)
• Altitude (meters above WGS 84 ellipsoid)
• Date (within the 5-year validity period)

The WMM outputs:

• X (north), Y (east), Z (down) components of the magnetic field vector, in nanoteslas (nT).
• Horizontal intensity H = √(X² + Y²), in nT.
• Total intensity F = √(X² + Y² + Z²), in nT.
• Declination D = atan2(Y, X), in degrees east of true north.
• Inclination (dip) I = atan2(Z, H), in degrees below horizontal.
• Secular variation — the time rates of change of all the above.

Plus the error estimates (95% confidence) for each: ~150 nT for total intensity, ~1° for declination at mid-latitudes, growing toward the magnetic poles.

The output covers the full Earth surface (including poles, where declination becomes ill-defined), at any altitude from sea level to several Earth radii out (though accuracy degrades far from the surface).

The mathematics

The WMM represents the magnetic field as the gradient of a scalar potential V:

B = -∇V

Where V is expanded in spherical harmonics:

V(r, θ, λ, t) = a · Σ_n Σ_m (a/r)^(n+1) [g_n^m(t) cos(mλ) + h_n^m(t) sin(mλ)] · P_n^m(cos θ)

Where:

• r is the radial distance from Earth's center.
• θ is the geocentric colatitude (90° - geographic latitude, approximately).
• λ is the longitude.
• a is the reference radius (6,371.2 km — a standard geomagnetic value).
• g_n^m(t) and h_n^m(t) are the time-varying Gauss coefficients of degree n and order m.
• P_n^m are the Schmidt semi-normalized associated Legendre functions.

The summation runs from n = 1 to n = 12 (the WMM's maximum degree). For each n, m runs from 0 to n. Total coefficient count: 12 × 13 = 156 g coefficients, 12 × 12 = 144 h coefficients (h_n^0 are zero by symmetry), for about 168 active coefficients.

The time dependence in the WMM is linear within the 5-year validity:

g_n^m(t) = g_n^m(t_0) + ġ_n^m · (t - t_0)
h_n^m(t) = h_n^m(t_0) + ḣ_n^m · (t - t_0)

Where t_0 is the model epoch (e.g., January 1, 2025 for WMM2025), and the dotted values are the secular variation coefficients. So the full coefficient set includes both the main field (g, h) and the secular variation (ġ, ḣ), totaling ~340 numbers.

Data sources

The coefficients are fitted to:

Satellite measurements

Modern WMM iterations rely primarily on satellite magnetometer data. Key missions:

• MagSat (NASA, 1979): the first dedicated magnetic satellite mission. Operated for ~7 months. Provided reference data for WMM iterations through the 1980s.
• Ørsted (Denmark, 1999–2014): low-altitude polar orbit; provided dense coverage during a long mission life.
• CHAMP (Germany, 2000–2010): another low-altitude mission, providing high-resolution data.
• Swarm (ESA, 2013–present): three identical satellites in different orbits, providing the most precise contemporary measurements. Swarm is the dominant data source for WMM2025 and is expected to continue operating through the late 2020s.

Satellite measurements have the advantage of global coverage including ocean regions where ground stations don't exist.

Ground observatories

Approximately 150 ground magnetic observatories report data through the International Real-time Magnetic Observatory Network (INTERMAGNET). Observatory data provides:

• High-cadence temporal coverage (typical sampling every second or minute) — important for capturing the short-timescale variations.
• Absolute reference — observatory measurements are calibrated against absolute standards, providing the reference for satellite-data calibration.
• Regional density — Europe, North America, Japan, Australia have particularly dense networks.

Major contributing institutions include USGS (US observatories), BGS (UK and overseas), GFZ Potsdam (German), IPGP (French), CNES, and many national geomagnetism programs.

The 5-year cycle

The WMM is produced on a regular 5-year schedule:

| Version | Released | Valid | | -------- | -------- | ------------------ | | WMM1990 | 1990 | 1990–1995 | | WMM1995 | 1995 | 1995–2000 | | WMM2000 | 2000 | 2000–2005 | | WMM2005 | 2005 | 2005–2010 | | WMM2010 | 2010 | 2010–2015 | | WMM2015 | 2014 | 2015–2020 | | WMM2015v2 | 2019 | 2015–2020 (revised)| | WMM2020 | 2019 | 2020–2025 | | WMM2025 | 2024 | 2025–2030 |

Each version is fitted to data through the year before release (so WMM2025 used Swarm and observatory data through 2023, plus selected 2024 data for validation).

Production timeline within a 5-year cycle:

1. Data collection (years 1–3): satellite and observatory data accumulates.
2. Model fitting (year 4): NCEI and BGS independently fit candidate models, compare, and reconcile.
3. Coefficient finalization (year 4 end): the official coefficients are agreed.
4. Validation (early year 5): test against held-out data.
5. Release (year 5 mid): coefficients, software, documentation, charts, and online calculator made public.
6. Validity period (years 5+0 through 5+5): the released model is the standard.

The model becomes increasingly inaccurate near the end of the validity period as the actual field drifts from the linear secular-variation extrapolation. Typical end-of-period error is ~2× the start-of-period error.

The 2019 emergency update

WMM2015 was released in late 2014 and valid through 2019. The model fitted the available data well at release and predicted continued slow drift of the Magnetic North Pole.

By 2017–2018, the actual pole drift had accelerated to ~55 km/year — faster than the WMM2015 secular variation had captured. Arctic declination errors grew beyond the WMM's 1° accuracy spec.

NCEI and BGS responded with an out-of-cycle update, sometimes called WMM2015v2. Released February 4, 2019, about ten months before WMM2020 was due. The 2019 update used additional Swarm data through late 2018 to capture the accelerated pole motion.

This was the first emergency update in WMM history. It demonstrated:

• The model is genuinely needed, not vestigial — without it, every smartphone compass in the Arctic would have been wrong by > 1°.
• The 5-year cycle has limits when core dynamics surprise us.
• The coordination between NCEI and BGS works under pressure (the update went from need-identification to release in <6 months).

WMM2020 then released on the normal schedule. WMM2025 in late 2024.

WMM vs IGRF

The International Geomagnetic Reference Field (IGRF) is the parallel research-focused model, produced by the International Association of Geomagnetism and Aeronomy (IAGA) — a working group of the International Union of Geodesy and Geophysics (IUGG).

| Feature | WMM | IGRF | | ------- | --- | ---- | | Production | NOAA NCEI + BGS | IAGA international consortium | | Cycle | 5 years (regular) | 5 years (regular) | | Current version | WMM2025 (2024) | IGRF-14 (2024) | | Main-field degree | 12 | 13 | | Secular variation degree | 8 | 8 | | Validity | Strict 5 years | 5 years + retrospective updates | | Use | Navigation, defense | Scientific research | | Mandated by | DoD spec, NATO STANAG | IAGA recommendation | | Distribution | NCEI public domain | IAGA public domain |

The two models typically agree within ~0.1° in declination predictions. The differences arise from:

• Slightly different data weighting between the two production teams.
• Higher degree in IGRF (degree 13 vs WMM's 12) captures somewhat smaller spatial features.
• Retrospective updates in IGRF (the “DGRF” — Definitive Geomagnetic Reference Field — replaces IGRF for past epochs as more data accumulates) vs WMM which doesn't retrospect.

For navigation, WMM is the choice (its 5-year cycle is locked-in and the model is mandated by spec). For research, IGRF is preferred (slight precision advantage and retrospective DGRF for historical work).

Use and distribution

MIL-STD-3034

U.S. DoD spec MIL-STD-3034C mandates WMM for all U.S. military magnetic navigation applications. The standard specifies:

• WMM version (most recent)
• Update procedures
• Validation requirements
• Accuracy specifications

Compliance is required across the U.S. military and contractor base. NATO STANAGs reference WMM similarly.

Aviation

The FAA uses WMM for:

• Airport runway numbering decisions (when to renumber due to declination drift)
• VOR / VORTAC / NDB station ground-magnetic references
• Flight charts (magnetic-vs-true direction)
• Magnetic compass certification testing

Air traffic control software and aircraft FMS systems typically embed WMM coefficients to handle magnetic heading computations.

Consumer electronics

Every modern smartphone with a magnetometer applies WMM internally:

• iOS Core Location: CLHeading.trueHeading computed by applying WMM to the magnetometer reading for the device's location.
• Android: GeomagneticField class implements WMM and provides getDeclination().
• Embedded GPS receivers: most include WMM coefficients to provide magnetic heading alongside true heading.

The WMM is updated on smartphone OSes within months of a new model release. Old smartphones with stale WMM data gradually become inaccurate; major OS updates refresh the coefficients.

Marine

The International Hydrographic Organization (IHO) recommends WMM (or IGRF) for marine chart compass roses. National hydrographic offices (NOAA, UKHO) use WMM data for chart updates and re-issues.

Distribution

NCEI distributes the WMM as:

• Coefficient files: WMM.COF text file with the Gauss coefficients.
• Reference software: C, Fortran, Python, MATLAB implementations of the spherical-harmonic evaluation.
• Online calculator: https://www.ngdc.noaa.gov/geomag/calculators/magcalc.shtml
• Printed charts: PDF maps of declination, inclination, and total intensity for the validity period.
• Technical report: detailed documentation of the methodology and fitting.

All distribution is public domain — no licensing restrictions.

Limitations

The WMM is excellent within its design scope but has known limitations:

Main field only

WMM models only the main field generated by the Earth's liquid outer core. It does not include:

• Crustal field: anomalies from magnetic rocks in the upper ~30 km. Can be ±5°+ in declination locally (e.g., iron-ore districts in northern Sweden).
• External field: ionospheric and magnetospheric contributions, which vary on minute-to-day timescales.
• Magnetic storms: solar-driven disturbances, up to several degrees of declination perturbation during major storms.

Applications needing better-than-WMM accuracy in specific regions need supplementary models (Enhanced Magnetic Model EMM, regional crustal models) or real-time observatory data.

Polar accuracy

Near the magnetic poles, the spherical-harmonic representation becomes ill-conditioned. WMM accuracy degrades within ~1,000 km of either magnetic pole. Smartphone compasses near the magnetic poles routinely show large errors.

Linear secular variation

Within the 5-year validity, the WMM assumes the field changes linearly. Real changes are nonlinear; errors accumulate quadratically with time-since-release. End-of-period errors are typically 2–3× start-of-period errors. The 2019 emergency update was triggered when the linear extrapolation grew unacceptably wrong mid-cycle.

No prediction beyond 5 years

The published WMM is valid only for the 5-year window. Beyond that, use the next WMM version (released near the end of the previous validity period). Don't extrapolate older WMMs forward — they get progressively wronger.

Common misconceptions

“WMM is the same as the actual magnetic field.” It's a model — a mathematical fit to data. The actual field can differ by ~1° in declination at any point, and by more in regions of strong crustal anomaly or near the magnetic poles.

“The WMM coefficients are secret.” They're fully public. Anyone can download them from NCEI and apply the spherical-harmonic evaluation to compute the field at any point.

“WMM is updated continuously.” It's updated every 5 years on the regular cycle, with one emergency update in 2019. The coefficient file changes only at these releases; between releases the model is static. The illusion of continuous updates comes from the model's internal secular-variation extrapolation.

“WMM accuracy is sub-arcminute.” It's specified at ~1° in declination at mid-latitudes (95% confidence). Sub-arcminute precision is available from real-time observatory data, regional models, or high-degree research models — not from WMM.

“WMM requires internet to use.” The model is a static coefficient file plus deterministic math. Once the coefficient file is loaded (e.g., in a smartphone OS), no internet is needed to evaluate the field at any location and time within the validity period.

“The 2019 update fixed a bug.” It addressed an empirical shortfall — the actual pole drift was faster than the linear extrapolation captured. Not a bug in the math; a limitation of linear extrapolation against nonlinear physical behavior.

“WMM applies to all altitudes.” WMM is fitted primarily to surface and low-altitude observations; it's accurate from sea level to several Earth radii out (declining accuracy with altitude as crustal and external effects dominate). For very-high-altitude applications (satellites in high orbit), more sophisticated models are used.

“WMM and IGRF disagree significantly.” They typically agree within 0.1° in declination — well within the WMM's own 1° accuracy spec. For practical purposes the two are interchangeable; the choice between them is driven by use case (navigation vs research) and institutional mandate rather than technical superiority.

“WMM tracks magnetic storms.” It doesn't. Storms are external-field disturbances on minute-to-day timescales; WMM models only the slowly varying main field. Real-time observatory data is the source for storm-tracking; products like NOAA Space Weather Prediction Center provide forecasts and nowcasts.