A more realistic estimate of the variances and systematic errors in spherical harmonic geomagnetic field models

Abstract

Most modern spherical harmonic geomagnetic models based on satellite data include estimates of the variances of the spherical harmonic coefficients of the model; these estimates are based on the geometry of the data and the fitting functions, and on the magnitude of the residuals. However, the accuracy of these estimates depends on the correctness of various assumptions, some of which are in practice not valid. Using the Ørsted OSVM model as an example, we show that ignoring the serial correlation of the magnetospheric ‘noise’ in the data, and not solving separately for the ionospheric field, led to quite inaccurate variance estimates. We estimate correction factors which range from 1/4 to 20, with the largest increases being for the zonal, m= 0, and sectorial, m=n, terms. With no correction, the OSVM variances give a mean-square vector field error of prediction over the Earth's surface at sea level of 1.5 nT2 (for the field of degrees n= 1–13); applying our correction increases this to 3.5 nT2. The leakage of the ionospheric field into the solution also gave a large systematic error field, of magnitude about 6 nT. We discuss how our approach is applicable to other similar modelling approaches.