Fibonacci lattices for the evaluation and optimization of map projections

Abstract

Latitude-longitude grids are frequently used in geosciences for global numerical modelling although they are remarkably inhomogeneous due to meridian convergence. In contrast, Fibonacci lattices are highly isotropic and homogeneous so that the area represented by each lattice point is virtually the same. In the present paper we show the higher performance of Fibonacci versus latitude-longitude lattices for evaluating distortion coefficients of map projections. In particular, we obtain first a typical distortion for the Lambert Conformal Conic projection with their currently defined parameters and geographic boundaries for Europe that has been adopted as standard by the INSPIRE directive. Further, we optimize the defining parameters of this projection, lower and upper standard parallel latitudes, so that the typical distortion for Europe is reduced a 10% when they are set to 36° and 61.5°, respectively. We also apply the optimization procedure to the determination of the best standard parallels for using this projection in Spain, whose values remained unspecified by the National decree that commanded its official adoption, and obtain optimum values of 37° and 42° and a resulting typical distortion of 828 ppm.