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The World Magnetic Model - Accuracy, limitations, magnetic poles and error model

Accuracy of the WMM2015

Changes of the fluid flow in the Earth's outer core lead to unpredictable changes in the Earth's magnetic field. Fortunately, the system has large inertia, so that these changes take place over time scales of many years. By surveying the field for a few years, one can precisely map the present field and its rate of change and then linearly extrapolate it out into the future. Provided that suitable satellite magnetic observations are available, the prediction of the WMM is highly accurate on its release date (Fig. 1) and then subsequently deteriorates towards the end of the 5 year epoch (Fig. 2), when it has to be updated with revised values of the model coefficients.

Limitations of the WMM2015

It is important to recognize that the WMM and the charts produced from this model characterize only the long-wavelength portion of the Earth's internal magnetic field, which is primarily generated in the Earth's fluid outer core. The portions of the geomagnetic field generated by the Earth's crust and upper mantle, and by the ionosphere and magnetosphere, are largely unrepresented in the WMM. Consequently, a magnetic sensor such as a compass or magnetometer may observe spatial and temporal magnetic anomalies when referenced to the WMM. In particular, certain local, regional, and temporal magnetic declination anomalies can exceed 10 degrees. Anomalies of this magnitude are not common but they do exist. Declination anomalies of the order of 3 or 4 degrees are not uncommon but are usually of small spatial extent. See EMM home page for a model which includes crustal fields down to 50 km wavelength.

map of declination uncertainty 2015
Fig. 1. Estimated WMM2015 declination inaccuracy without considering crustal and disturbance field contributions. Click for high-resolution image.

Error model for the WMM2015

The WMM2015 software and online calculator include an error model providing uncertainty estimates for every geomagnetic element (X, Y, Z, H, F, I and D) and every location at the Earth's surface. This model is built upon the results of the error analysis (subsection 3.3 of the WMM2015 report), while taking into account the geometrical relationships between the various components. It includes both the commission error (due to inaccuracies in model coefficients) and the omission error (due to missing contributions to the total geomagnetic field such as crustal and external fields). The error values (Table 1) may be interpreted as one standard deviation difference between a hypothetical measurement and the calculator result for a location.

Component Uncertainty
X138 nT
Y89 nT
Z165 nT
H133 nT
F152 nT
D0.242+(5432/H)2 °
Table 1. Uncertainty estimates provided by the WMM2015 error model for the various field components. H is expressed in nT in the formula providing the error in D.

A global map of the magnetic declination error is provided in Fig. 2. As can be seen on this map, the error is lower at mid- to low-latitudes, while it is larger near the magnetic poles and in an area close to South Africa where the horizontal field is very low.

map of declination uncertainty 2020
Fig. 2. Global distribution of the declination error provided by the WMM2015 error model Click for high-resolution image.

Magnetic Poles and Magnetic Center

Based on the WMM2015 coefficients for 2015.0 the geomagnetic north pole is at 72.62°W longitude and 80.37°N latitude, and the geomagnetic south pole is at 107.38°E longitude and 80.37°S latitude. The axis of the dipole is currently inclined at 9.69° to the Earth's rotation axis.The WMM can also be used to calculate dip pole positions. These model dip poles are computed from all the Gauss coefficients using an iterative method. In 2015.0 the north dip pole computed from WMM2015 is located at longitude 159.18°W and latitude 86.27°N and the south dip pole at longitude 136.59°E and latitude 64.26°S. More information about geomagetic poles here.

Details of the model derivation are described in the NOAA Technical Report: The US/UK World Magnetic Model for 2015-2020 (pdf).