Beyond Regime: A Stochastic Model of Floods, Bank Erosion, and Channel Migration

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Abstract
Equilibrium or regime models based on a single formative (channel‐forming) discharge have been instrumental in developing a quantitative understanding of river channel dynamics. However, alternative paradigms can be used to ask fundamentally different questions about river channel behavior. In this paper, we present the Stochastic Channel Simulator (STOCHASIM), a simple biogeomorphic model that models the interplay between erosion and vegetation encroachment through changes in channel geometry. Results for a range of flood distributions are compared to predictions from a similar model based upon a traditional regime approach. Flood variability strongly influences the mean channel geometry and channel stability; the regime model and the stochastic model predict the same channel width when flow variability is low but diverge as flow variability increases. The return period of the formative flow required to match the geometry generated by a traditional regime approach increases systematically, from about 2 years for flow regimes in humid regions to nearly 8 years for more variable flow regimes, like those typical of arid regions. While the traditional regime approach provides a reasonable simplification for streams with little variability in the flood distribution, stochastic modeling may provide more realistic estimates of channel size as flood variability increases (e.g., in arid streams or small watersheds). The success of STOCHASIM in replicating realistic patterns of erosion, as well as the historical contingency often observed in natural streams, suggests that adopting a stochastic dynamics paradigm could advance geomorphology, just as it has done in hydrology, ecology, and other natural sciences.

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