General approach to conformal mappings used in atmospheric modeling Original Research Article

A class of conformal separable variable mappings is introduced to generalize different conformal projections used in atmospheric modeling and cartography for representation of spherical regions. It is shown that conformal stereographic, conic and cylindrical projections are special cases of this class of mappings. A second approach based on composition of conformal mappings is used to describe the set of all conformal transformations from a sphere onto a plane. Under a natural assumption about the independence of the map factor from longitude a theorem of equivalence between the two above classes of conformal mappings is proved. A problem of minimization of the map factor variation within the constructed set of mappings is considered. A comparison of the map factor for different kinds of mappings (polar and oblique stereographic, conic and cylindrical) is performed based on analytical and numerical evaluations.