Optimising 2-parameter Lambert Conformal Conic projections for ground-to-grid distortions

Abstract

[EN] A Lambert Conformal Conic (LCC) projection with two true-scale parallels of latitudes phi(l)and phi(u)can be recast in a LCC projection with one standard parallel of latitude phi(0)and scalek(0), having the practical advantage that the same type of definition can be used for the two conformal projections universally used: LCC and Transverse Mercator (TM). While equations giving phi(0)andk(0)in terms phi(l)and phi(u)can be found in the literature, inverse relationships are not readily found. They are derived in the present paper. These may be necessary in views of the planned future definition of the United States State Plane Coordinate System (SPCS) 2022 for the users of particular mapping software requiring to specify the two latitude values instead of the central latitude and central scale. While map projection parameters are customary selected to minimise ellipsoid-to-grid distortions for a region, in some cases it could be more convenient to study and minimise ground-to-grid distortions. Also bearing in mind the design of SPCS 2022, we discuss the advantages and disadvantages of working with each type of distortion definition.