  Spatially embedded networks have attracted increasing attention in the last
decade. In this context, new types of network characteristics have been
introduced which explicitly take spatial information into account. Among
others, edge directionality properties have recently gained particular
interest. In this work, we investigate the applicability of mean edge
direction, anisotropy and local mean angle as geometric characteristics in
complex spherical networks. By studying these measures, both analytically and
numerically, we demonstrate the existence of a systematic bias in spatial
networks where individual nodes represent different shares on a spherical
surface, and describe a strategy for correcting for this effect. Moreover, we
illustrate the application of the mentioned edge directionality properties to
different examples of real-world spatial networks in spherical geometry (with
or without the geometric correction depending on each specific case), including
functional climate networks, transportation and trade networks. In climate
networks, our approach highlights relevant patterns like large-scale
circulation cells, the El Ni\~{n}o--Southern Oscillation and the Atlantic
Ni\~{n}o. In an air transportation network, we are able to characterize
distinct air transportation zones, while we confirm the important role of the
European Union for the global economy by identifying convergent edge
directionality patterns in the world trade network.
