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My question is about World Magnetic (WMM) and International Geomagnetic Reference Field (IGRF) models. It is well known that to a first approximation, earth magnetic field is a field of dipole. It corresponds to the first term in the Gaussian series. Is it possible to estimate the error of such an approximation? I am interested only in dipole approximation, i. e. is it possible to obtain an error of given (first) Gauss coefficient, or is there any studies where the dipole model investigated, with estimation of uncertainties?

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I am most familiar with IGRF. One simple way is to evaluate IGRF using only the dipole terms, and compare that to the field that you get from the quadrupole and higher order terms.

There is publicly available software and coefficients of IGRF:

https://www.ncei.noaa.gov/products/international-geomagnetic-reference-field

You could also try using WMM, which is nearly identical to IGRF: https://www.ngdc.noaa.gov/geomag/WMM/soft.shtml

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  • $\begingroup$ This is a very practical solution and will show how much of the field from Earth's core, which these models represent, is contributed by the dipole part. You could also compare what the dipole part of a model predicts for a given time and location to observations which will also include other sources of natural magnetic field, such as that from the crust, magnetosphere and ionosphere. During a magnetic storm for example, this can be thousands on nano-Tesla additional "error". $\endgroup$
    – WJB
    Jan 8, 2023 at 18:08

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