We present a framework to characterize terrestrial functions—surficial and bottom topographic regions that are represented, respectively, as raster digital elevation models (DEMs) and digital bathymetric models (DBMs)—through analysis of flow fields that are simulated via geodesic morphology. Characterization of such functions is done via a new descriptor. Computation of this new descriptor involves the following steps: (i) basin in digital form representing topographic fluctuations as an input, (ii) threshold decomposition of basin—that consists of channelized and nonchannelized regions—into sets, (iii) proper indexing of these sets to decide the marker set(s) and its (their) corresponding mask set(s), (iv) performing geodesic propagation that provides basic flow field structures, and (v) finally providing a new basin descriptor—geodesic spectrum. We demonstrated this five-step framework on five different synthetic and/or realistic DEMs and/or DBMs. This study provides potentially invaluable insights to further study the travel-time flood propagation within basins of both fluvial and tidal systems.