A definition of earth surface modeling is proposed on the basis of discussing the concept of earth surface.Studies on earth’s surface topography modeling and climate system modeling are reviewed

which indicates that it is eagerly necessary to develop simulation methods with high speed

high accuracy and low memory requirement.Introduction of methods for high accuracy and high speed surface modeling（HASM）

developed by means of the fundamental theorem of surfaces

might be an efficient way to characterize the states of earth-surface and changes in those states.