1. A method for modeling a distribution of a tire footprint boundary, comprising: inputting into a finite element analysis system a finite element model of a tire rolling against a road surface described by discrete road surface coordinates; performing a finite element analysis simulation of the model of the tire rolling against the road surface for a first plurality of time increments; generating a plurality of tire footprint boundary data, each of the tire footprint boundary data having road surface coordinates on which a footprint boundary overlaps corresponding to a unique one of a second plurality of time increments of the finite element analysis, wherein the second plurality of time increments is a subset of the first plurality of time increments; and determining for each of a plurality of the discrete road surface coordinates a number of the second plurality of time increments during which the footprint boundary overlaps the each of the plurality of the discrete road surface coordinates.