The World Magnetic Model High Resolution (WMMHR) is an advanced geomagnetic field model that provides a more detailed, accurate depiction of the geomagnetic field than the World Magnetic Model (WMM). WMMHR2025 includes core field and secular variation coefficients for degrees n = 1 to 15. This model also covers the crustal field (from n=16 through n=133). As a result, it has more coefficients ((18,210 non-zero coefficients instead of 336) and more digits (4 instead of 1) in each coefficient.
The National Geospatial-Intelligence Agency (NGA) highly recommends that all DoD systems use the WMMHR instead of the WMM. See the Software Download section for more information about the WMMHR COF file format.
The WMMHR model was sponsored by NGA and the United Kingdom’s Defence Geographic Centre (DGC). NCEI and the British Geological Survey (BGS) jointly developed the WMMHR.
Product Details
The core field and secular variation of WMMHR2025 were developed using the same method and data as the WMM2025. The coefficients for WMMHR2025 are identical to the WMM2025 coefficients up to spherical harmonic degree n=12, but WMMHR2025 coefficients have more significant digits.
WMMHR2025 also includes core field and secular variation coefficients for degrees n=13 to 15. The WMMHR2025 crustal field component is derived from the MF7 model, which covers degrees 16 to 133 and is based on data acquired during the final two years of the Challenging Mini-satellite Payload (CHAMP) mission (Maus et al., 2008).
Software Download
| File | Release Date | Product Description |
|---|---|---|
| WMMHR2025 Coefficients (zip file) | December 2024 | WMMHR2025 Coefficient file valid for 2025.0 - 2030.0, test values and instructions to update your software. See the Documentation tab on the WMM for more information. |
| WMM2025 Software with Windows Graphical User Interface (GUI) | ||
| WMMHR2025_Windows.zip | December 2024 | World Magnetic Model High Resolution (WMMHR 2025) with C software and executables for Windows environment. |
| WMMHR2025_Linux.tar.gz | February 2025 | World Magnetic Model High Resolution (WMMHR 2025) with C software and executables for Linux environment. |
| WMMHR2025GUI.zip | February 2025 | World Magnetic Model High Resolution (WMMHR 2025) with Stand-alone Graphical User Interface (GUI) for Windows. |
| WMM2025 Software | February 2025 | WMM2025 Software is available on the WMM Webpage |
| Mobile Apps | ||
| iOS | December 2024 | WMMHR calculator as part of "CrowdMag" app (uses the WMMHR2025) |
Citation
NOAA NCEI Geomagnetic Modeling Team; British Geological Survey. 2024: World Magnetic Model High Resolution 2025. NOAA National Centers for Environmental Information. https://doi.org/10.25921/qb1c-vn52. Accessed [date].
Magnetic Model Comparisons
Table 2 compares important WMMHR features with other geomagnetic models hosted at NCEI:
- World Magnetic Model High resolution (WMMHR)
- World Magnetic Model (WMM)
- International Geomagnetic Reference Field (IGRF) and Definitive Geomagnetic Reference Field (DGRF)
- High Definition Geomagnetic Model (HDGM)
- Enhanced Magnetic Model (EMM)
| WMMHR | WMM | IGRF / DGRF | HDGM /EMM | |
|---|---|---|---|---|
| Max Degree & Order, Main Field | 133 | 12 | 13 | 790 |
| Max Degree & Order, Secular Variation | 15 | 12 | 8 (IGRF) 13 (DGRF) | 15 |
| Approx. resolution at the equator | 300 Km | 3330 Km | 3074 Km | 51 Km |
| Time Step (Years) | 5 | 5 | 5 | 1 (HDGM) 5 (EMM up to 2017) |
| Retrospective Update | No | No | Yes | Yes (HDGM) Yes (EMM) |
Error Model
The WMMHR error model was estimated using the same approach as the WMM error. The model development team used trackline survey, observatory, and repeat station data to infer the WMMHR crustal field error for each magnetic field component. The team combined crustal and external field errors to calculate the total omission errors for each component, and with the core field and secular variation errors to obtain the total errors.
We found that WMMHR slightly reduces the crustal field (omission) error when averaged over the entire Earth's surface. However, it significantly reduces error in certain regions, such as continents (see the additional comparison maps between WMM and WMMHR in the Maps section).
| Component | Uncertainty |
|---|---|
| X | 135 nT |
| Y | 85 nT |
| Z | 134 nT |
| H | 130 nT |
| F | 134 nT |
| I | 0.19° |
| D | √(0.252+(5205/H)2) |
WMM/WMMHR Comparison
Figure 1 and 2 show the differences between WMMHR and WMM at 2020.0. The large-scale magnetic field from the core is removed to reveal the magnetic signatures of the crustal field. The upper figure is the difference in the total field, F. The crustal magnetic field from WMMHR is most prominent over continental regions. Magnetic fields are weaker over the oceanic regions, However, the magnetic signatures associated with the sea floor spreading are clearly visible. The differences in the Declination component (lower) are prominent closer to the geomagnetic dip locations due to the geometric effect. However, there are a few large declination anomalies in the south-eastern European region.
Significant Digits and Accuracy
The current WMM.COF file uses coefficients with only one decimal place. However, the WMMHR needs more precision to achieve sufficient accuracy due to the increase in degree from 12 to 133. To accommodate this increased precision, the WMMHR has a new coefficient format with 58 character lines (compared to 48-character lines for the WMM).
The WMMHR coefficients are written to this file in a specific format. If implemented correctly, the WMMHR.COF file format updates to a new WMMHR by replacing the old “WMMHR.COF” file with the new one without any changes to the software. The coefficient file is in ASCII format with one header line, 9044 lines of coefficients data, and two terminating lines. Each data line has 58 characters, ending with a carriage return and a linefeed (\n\r).
WMMHR format
Line 1: "Header"
2025.0 WMMHR-2025 11/13/2024
^ ^ ^
Epoch Model-name Date of release
Example code to read the header data
fscanf(fp, "%lf %s %s", &epoch, &model_name, &release_date);
Lines 2 to 9045: "Coefficients"
1234512345123456789012123456789012123456789012123456789012 (line length 58)
1 0 -29351.7976 0.0000 11.9581 0.0000
....
133 133 0.0100 -0.0005 0.0000 0.0000
Lines 9046 to 9047: "File terminators"
999999999999999999999999999999999999999999999999 (line length 48)
999999999999999999999999999999999999999999999999
Example code to read the coefficients
fscanf(fp,"%5d%5d%12.4f%12.4f%12.4f%12.4f", &n, &m, &g_nm, &h_nm, &g_dot_nm, &h_dot_nm);
While the WMM uses 336 non-zero coefficients, the WMMHR needs 18,210 non-zero coefficients to operate. The data increases the file size; WMM files are 5 KB, while WMMHR files are 534 KB.
The existing official WMM software implementations are compatible with the WMMHR coefficients file. However, custom-implementations of the WMM software may need additional testing and modifications.