Trends in width, bed elevation, and area in river channel cross sections and implications for equilibrium channel theories

Alluvial river channels are often assumed to maintain an equilibrium between the supply of water and sediment from the upstream catchment and their cross-sectional geometry. Since they are self-formed, they have degrees of freedom to adjust their width, bed elevation, and overall channel area. Thus, cycles of scour/fill and widening/narrowing under stationary boundary conditions of hydrology and sediment supply would be expected to produce mere fluctuations in channel area as dynamic equilibrium, rather than long term channel expansion/contraction. Under nonstationary conditions (changes to upstream flow and/or sediment supply), equilibrium theory suggests that a channel will adjust its capacity to maximize the efficiency of flow and sediment conveyance (e.g., higher flows will produce a larger channel for the same sediment supply). This theory has been used to inform management paradigms and is widely used as the basis for river engineering, river restoration, and flood prediction. Despite the ubiquity of equilibrium theory in river science, the timescales over which alluvial channels adjust, as well as the direction of the adjustment (vertical v. horizontal), have not been assessed systematically. Previously we identified unidirectional decadal trends in channel geometry across the continental USA, many of which are independent of streamflow nonstationarity. These trends suggest equilibrium channel adjustment theories are incomplete or even inappropriate for many fluvial systems, and therefore raise many questions. We present the results of the first systematic investigation of trends in area, width, and bed elevation using publicly accessible USGS stream measurements at 2600 gauges across the USA between 1950 and 2012. We find a predominance of erosional trends, particularly in humid regions and at low elevations. Shifts in channel area tend to support equilibrium theory, with erosional trends (widening, degradation, and channel expansion) where flows have increased, and accretional trends (narrowing, aggradation, and channel contraction) at sites where they decreased. We assessed the proportion of change in area occurring through shifts in bed elevation v. width and find that bed-dominant trends are most numerous (64% v 36%). These bed-dominant trends in area occur disproportionately at sites with large drainage areas (>100km²), while width-dominant trends tend to occur at sites with small drainage areas (<100km²). These trends can either be additive or offsetting in terms of their effect on channel area, and we find that additive effects dominate over offsetting ones throughout the US (63% of sites where both occur), but that the magnitude and direction of these effects appear to be modulated by drainage area and climatic regime.