Fast approximate Barnes interpolation: Illustrated by Python-Numba implementation fast-barnes-py v1.0

Abstract

Barnes interpolation is a method that is widely used in geospatial sciences like meteorology to remodel data values recorded at irregularly distributed points into a representative analytical field. When implemented naively, the effort to calculate Barnes interpolation depends on the product of the number of sample points N and the number of grid points W×H, resulting in a computational complexity of O(Ng..Wg..H). In the era of highly resolved grids and overwhelming numbers of sample points, which originate, e.g., from the Internet of Things or crowd-sourced data, this computation can be quite demanding, even on high-performance machines. This paper presents new approaches of how very good approximations of Barnes interpolation can be implemented using fast algorithms that have a computational complexity of O(N+Wg..H). Two use cases in particular are considered, namely (1) where the used grid is embedded in the Euclidean plane and (2) where the grid is located on the unit sphere.