TOWARD GEOMORPHOMETRIC MODELING ON A SURFACE OF A TRIAXIAL ELLIPSOID (FORMULATION OF THE PROBLEM)

Geomorphometric modeling is widely used to study multiscale problems of the Earth and planetary sciences. Existing algorithms of geomorphometry can be applied to terrain models given by plane square grids or spheroidal equal angular grids on a surface of an ellipsoid of revolution or a sphere. Computations on spheroidal equal angular grids are trivial for modeling the Earth, Mars, the Moon, Venus, and Mercury. This is because: (a) forms of the abovementioned celestial bodies can be described by an ellipsoid of revolution or a sphere; and (b) for these surfaces, this is well-developed theory and computational algorithms for solving direct and inverse geodetic problems, as well as for determining spheroidal trapezium areas. It is advisable to apply a triaxial ellipsoid for describing forms of small moons and asteroids. However, there are no geomorphometric algorithms intended for such a surface. In this paper, we have formulated the problem of geomorphometric modeling on a surface of a triaxial ellipsoid. Let a digital elevation model of a celestial body or its portion be given by a spheroidal equal angular grid using geodetic or planetocentric coordinate systems of a triaxial ellipsoid. To derive models of local morphometric variables, one should: (1) turn to the elliptical coordinate system, and (2) determine linear sizes of spheroidal trapezoidal moving window elements by the Jacobi solution. To derive models of nonlocal morphometric variables, one may determine areas of spheroidal trapezoidal cells by similar way. Related GIS software should be developed.