Directional landscape connectivity as a predictor of water and material fluxes and indicator of system dynamics in both aquatic and terrestrial landscapes

The spatial arrangement of landscape elements into nonrandom patches reflects internal dynamics and external forcing and is itself a critical component of a system's internal dynamics. Metrics such as connectivity that quantify the configuration of landscape elements thus have the potential to indicate a system's key dynamics as well as provide understanding of how that system might respond to changes in hydrologic inputs or other forcing. Consequently, connectivity metrics for hydrologic systems may also advance understanding of large-scale hydroecologic and geomorphic feedback processes. Typically, studies have focused on achieving local-scale understanding of the effects of roughness elements or vegetation patches on flow, but understanding of the effects of landscape-scale configurations of channel networks and vegetation patches on water and sediment throughput remains a research frontier and is a prime focus of this study. In systems forced by gradient-flux dynamics, directional measures of connectivity yield the most insight and provide the most information for characterizing and comparing landscapes. For example, the graph theory-based Directional Connectivity Index has shown sensitivity in the Everglades to specific trajectories of landscape evolution and is a first responder to events triggering catastrophic shifts in landscape state. On hillslopes directional connectivity of channel networks provides a measure of slope coherence and new insight into erosional feedbacks. When used in combination with other metrics such as fractal dimension and anisotropy, directional connectivity is also a powerful predictor of hydrologic fluxes. Modifying an approach initially developed for modeling groundwater fluxes, we developed an analytical spatial averaging scheme for predicting hydrologic fluxes through heterogeneously rough surface-water landscapes. Analysis of the equation's partial derivatives suggests that hydrologic fluxes exhibit the highest sensitivity to the Directional Connectivity Index, followed by fractal dimension and finally by the aerial coverage of the roughness elements.