where a is the radius of the Earth’s surface, ϑ is the co-latitude, λ is the east longitude, Pm
n (cos ) are the spherical harmonic Smith functions, and the coefficients gm n and hm n are the Gauss coefficients. This equation is important because a similar mathematical approach has been used to represent ionospheric characteristics over a sphere in order to obtain global ionospheric maps, as described in Chap. 6. See Fig. 2.12 for an example of a global map of the total magnetic field F in nT for the year 2005.