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

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.

Channel stability in steep gravel–cobble streams is controlled by the coarse tail of the bed material distribution

“…Deterministic models of channel response that are based on the role of dominant discharge only approximate the channel response if the effect of geomorphic history is small. Work by Davidson and Eaton (2018) has shown that channel response is highly sensitive to the geomorphic history of a channel and is thus important to include.…”

Floods and rivers: a circular causality perspective

“…When trying to understand the linkage with flooding, an important parameter to focus on is the bankfull hydraulic geometry, which provides information on the channel's morphology and storage capacity 40 . This concept emerges from the field evidence that rivers are in a perpetual state of flux and constantly adapt to recent floods (2020) 10:5175 | https://doi.org/10.1038/s41598-020-61533-x www.nature.com/scientificreports www.nature.com/scientificreports/ and changing sediment loads 101 . The study of hydraulic geometry has been prominent starting from the 1960s and highlighted how channel capacity and widths scale with bankfull discharge, the latter typically being the discharge with a one to two-year recurrence interval 40,47,[102][103][104][105][106][107][108] .…”

“…The study of hydraulic geometry has been prominent starting from the 1960s and highlighted how channel capacity and widths scale with bankfull discharge, the latter typically being the discharge with a one to two-year recurrence interval 40,47,[102][103][104][105][106][107][108] . While regime models based on a single flood discharge yield meaningful predictions of average conditions in many systems, formative flow and effective discharge diverge in some circumstances 101,[109][110][111] , calling into question the veracity of the underlying assumption of equilibrium between a single discharge (however, it is defined) and the reach-average channel dimensions. Differences across watersheds regarding flow regimes, catchment size, regional climatic and physiographic factors, geological characteristics, the responsiveness of the catchment, and human activities 40,47,[102][103][104][105][106][107][108] can be described observing adjustment of hydraulic geometry as power-law functions (Hydraulic Scaling Function HSF) relating bankfull properties and flows in the downstream direction along the river profile.…”

A decadal‐scale numerical model for wandering, cobble‐bedded rivers subject to disturbance

“…In MAST‐1D, we make the simplifying assumption that channel narrowing only occurs during relatively low flows. We assume that the magnitude of vegetation encroachment is proportional to the area of unvegetated point bar surface (this is the similar to the approaches of Konrad [] and Davidson and Eaton []). The rate of encroachment is treated as a constant, α n : where B min is a constant user‐defined minimum width and B c − B min represents the unvegetated point bar.…”

“…Eke et al, 2014;Higson and Singer, 2015), but normally on the scale of a single bend. Others rely on regime relations (Davidson and Eaton, 2018) or optimality criterion (Tunnicliffe and Church, 2015), whose assumptions of equilibrium break down for cases where streams are adjusting to disturbance. A 2D model incorporating both bank erosion and vegetation encroachment has been applied to large, lowland rivers on decadal timescales (Nicholas et al, 2013), but it uses only two grain size classes, which is not appropriate for cobble-bed mountain streams where bed armoring is an important control on sediment transport.…”