Stokes’s Theorem, Data, and the Polar Ice Caps

Geographers and climate scientists alike sometimes need to estimate the area of a large region on the surface of the Earth, such as the polar ice caps. Doing so using only a sequence of latitude–longitude data points along a piecewise-linear approximation of the boundary of the region can be accomplished via a novel use of Stokes’s theorem that generalizes classical and contemporary applications of Green’s theorem to data. The polar ice caps are seen to hide a complication that makes their estimation from data singularly interesting.