How Important Is Connectivity for Surface Water Fluxes? A Generalized Expression for Flow Through Heterogeneous Landscapes

Abstract

How important is hydrologic connectivity for surface water fluxes through heterogeneous floodplains, deltas, and wetlands? While significant for management, this question remains poorly addressed. Here we adopt spatial resistance averaging, based on channel and patch configuration metrics quantifiable from aerial imagery, to produce an upscaled rate law for discharge. Our model suggests that patch coverage largely controls discharge sensitivity, with smaller effects from channel connectivity and vegetation patch fractal dimension. However, connectivity and patch configuration become increasingly important near the percolation threshold and at low water levels. These effects can establish positive feedbacks responsible for substantial flow change in evolving landscapes (14–36%, in our Everglades case study). Connectivity also interacts with other drivers; flow through poorly connected hydroscapes is less resilient to perturbations in other drivers. Finally, we found that flow through heterogeneous patches is alone sufficient to produce non‐Manning flow–depth relationships commonly observed in wetlands but previously attributed to depth‐varying roughness.

Ecogeomorphic Feedbacks that Grow Deltas

“…Olliver and Edmonds (), for instance, found evidence supporting the hypothesis that intertidal (the elevation range from SAV and up to, but not including, Colocasia ) and subaerial (the elevation range from Colocasia to Salix nigra ) elevation platforms are alternative stable states, which self‐organize to remarkably consistent elevations. This self‐organization, in the face of local variability in the strength of ecogeomorphic feedbacks, may reflect larger‐scale ecogeomorphic feedbacks, such as those arising from the effect of landscape configuration on regional flow fields (Larsen et al, ) or on the sediment (Nardin & Edmonds, ) or particulate nutrient supply (Bouma et al, ) delivered to vegetated platforms. Prediction of delta evolution will ultimately require understanding of both the large‐scale and local‐scale ecogeomorphic feedbacks, with spatial transfer entropy providing efficient means of identifying and quantifying local‐scale feedbacks and interactions.…”

Connectivity as an emergent property of geomorphic systems

“…Investigations of connectivity and disconnectivity in geomorphic systems can focus on fluxes of different types of materials, such as water (Bracken et al, 2013;Larsen et al, 2017) or sediment (Fryirs et al, 2007a;Bracken et al, 2015;Li et al, 2016). Investigations can emphasize features that enhance or limit connectivity, such as landforms that create physical thresholds which must be exceeded before material can move between compartments (Kondolf et al, 2006;Fryirs et al, 2007a).…”

Biophysical Interactions in Fragmented Marine Canopies: Fundamental Processes, Consequences, and Upscaling

“…These can then be explored to elicit mechanistic understanding of the cross-scale relationships. They can also be used to infer correlative relationships between patch/gap-scale causes and landscape-scale effects of the type described above that are underpinned by that mechanistic understanding (e.g., Luhar and Nepf, 2013;Larsen et al, 2017). However, such models require detailed understanding, not only of the nature of processes at the smaller scale, but also of ways in which these interact with each other as spatial complexity and scale are increased.…”

“…To address this type of problem, scale transition theory (Chesson et al, 2005;Benedetti-Cecchi et al, 2012;Chesson, 2012) quantifies the non-linear scale-dependence of interactions between parameters in terms of the variances and co-variances of their patch/gap-scale values across whole landscapes. Larsen et al (2017) provide an illustration of how the problems of non-linearity and spatial distribution effects in upscaling are addressed in a hydrological context in a study of the flow through the vegetated ridge-and-slough landscape of the Florida Everglades. Following approaches that have been used previously in the groundwater literature (Cushman et al, 2002;Farmer, 2002), they calculate the landscape-scale average flow resistance as a non-linear spatial average of small scale roughness, using an approach based on the ergodic hypothesis (Lumley and Panofsky, 1964).…”

“…They conceptualize the landscape as binary -being made up purely of patches and gaps of 'matrix' between them. The landscape-scale average of a parameter (flow resistance in the case of Larsen et al, 2017), H land , is then calculated from values of the same parameter for the patches, h p , and the gaps, h g , and the fractional cover of patches, p, across the whole landscape as…”