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