Geometric Constraints on Long-Term Barrier Migration: From Simple to Surprising

Abstract

Considerations of mass conservation, sediment budgets, and geometry lead to insights regarding how barriers respond to sea-level rise. We begin with relatively simple insights, which facilitate more surprising conclusions as more complicated cases are considered. The simplest case assumes: (1) a constant depth beyond which sediment transport is negligible; (2) a lack of gradients in net long-term alongshore sediment flux that add or remove sediment; (3) shoreface erosion into a substrate that produces sediment which is all sufficiently coarse to remain in the nearshore system; and (4) a spatially uniform slope across which a barrier migrates (i.e., the substrate slope). In this case, the migration trajectory for the barrier shorelines—the ratio between the rates of sea-level rise and landward transgression—parallels the average slope of the barrier and shoreface profile (the surface over which active sediment transport occurs). In the next simplest case, substrates composed partly of fine sediment (which is lost to the nearshore system when the substrate is eroded) cause a reduction of the slope of the migration trajectory, because more landward migration is required for each increment of sea-level rise in this case. Gradients in net alongshore sediment transport also cause adjustments to the migration trajectory (although the adjustment depends on the rate of relative sea-level rise). Analysis shows that even with a gradient in net alongshore sediment transport, in the long term, barrier geometry adjusts until the trajectory parallels the (spatially uniform) slope of the substrate. When a barrier is eroding into material that was deposited in back-barrier bay or marsh environments, surprising results come from considerations of geometry and conservation of mass. In this case, the effects of substrate slope on barrier migration trajectory become indirect and time-lagged. In addition, depending on the relative compositions of marsh and bay deposits, feedbacks tend to either produce a stable bay/marsh width and barrier geometry, or a runaway widening or narrowing of the back-barrier environment. When substrate slope (or alongshore-transport gradients or substrate composition) varies as the barrier migrates landward, numerical investigation is required to determine how the migration trajectory varies with time.