The starting point for the Blatter-Pattyn model is the full Stokes equations
where P is the pressure and τ is the deviatoric stress tensor. The latter is given by
where σ is the full stress tensor.
There are a number of ways to argue that because of the "shallowness" of ice sheets - that is because the ratio of H/L, where H is the thickness and L is a relevant horizontal length scale, is small - the equations above can be reduced to the following "first-order approximation"