The International Geomagnetic Reference Field (IGRF) is the internationally agreed model of the main field: the potential, on and above the surface,
V(r,θ,φ)=an=1∑N(ra)n+1m=0∑n(gnmcosmφ+hnmsinmφ)Pnm(cosθ),
with a=6371.2km, B=−∇V, and Gauss coefficients gnm, hnm (in nT) given every five years since 1900, together with their rate of change over the next five years.