Parallel scaling of tidal channel length and surface area with marsh area for 1st through Kth-ranked channels and their tributaries: Application for tidal marsh restoration

Abstract

Scaling relationships in landforms are a signature of locally stable, self-organized critical states, which in tidal marshes result from the interaction of hydrodynamics, sediment dynamics, and biota. Empirical scaling relationships for tidal channel planform were developed for reference tidal marshes in four of the largest river deltas in Puget Sound to explore the potential underlying generative process of the observed patterns and to provide design guidance for restoration of estuarine rearing habitat for juvenile salmon. The length, surface area, and drainage basin area of the largest, 2nd-largest, 3rd-largest, etc., up to 15th-largest tidal channels that drain a marsh island, as well as the lengths of the largest through 5th-largest tributaries to the largest and 2nd-largest channels scaled with marsh area. Additionally, regression of the scaling relationship y-intercepts against channel rank for each delta showed that the rate of channel size decrease from one rank to the next was well fit by a power function, with R2 values approaching 1. These relationships reveal predictable structure in many aspects of tidal channel planforms and allow engineers to design channel excavation in considerable detail. A simulation model of channel formation through recursive marsh island conglomeration in river deltas reproduced the scaling behavior of the empirically observed marsh channels, thereby linking observed patterns to the underlying generative process. Previous allometric modeling has provided predictions of the number of tidal channels a marsh restoration site should have; this study provides a method to predict the size distribution of those channels so that engineers, planners, and restoration scientists can better plan, design, and monitor marsh restoration.