A comparison of 1D and 2D bedload transport functions under high excess shear stress conditions in laterally constrained gravel-bed rivers: a laboratory study

Abstract

Abstract. Channel processes under high-magnitude flow events are of central interest to river science and management as they may produce large volumes of sediment transport and geomorphic work. However, bedload transport processes under these conditions are poorly understood due to data collection limitations and the prevalence of physical models that restrict feedbacks surrounding morphologic adjustment. The extension of mechanistic bedload transport equations to gravel-bed rivers has emphasised the importance of variance in both entraining (shear stress) and resisting (grain size) forces, especially at low excess shear stresses. Using a fixed-bank laboratory model, we tested the hypothesis that bedload transport in rivers collapses to a more simple function (i.e. with mean shear stress and median grain size) under high excess shear stress conditions. Bedload transport was well explained by the mean shear stress (1D approach) calculated using the depth–slope product. Numerically modelling shear stress to account for the variance in shear stress (2D) did not substantially improve the correlation. Critical dimensionless shear stress values were back-calculated and were higher for the 2D approach compared to the 1D. This result suggests that 2D critical values account for the relatively greater influence of high shear stresses, whereas the 1D approach assumes that the mean shear stress is sufficient to mobilise the median grain size. While the 2D approach may have a stronger conceptual basis, the 1D approach performs unreasonably well under high excess shear stress conditions. Further work is required to substantiate these findings in laterally adjustable channels.

An Attempt to Take Into Account Natural Variability in 1D Bedload Prediction

“…One can see that the addition of variability consistently leads to higher estimated volumes, and that the increase differs from one equation to another. This result is consistent with results obtained when considering variability at the scale of the cross‐section (Adams & Eaton, 2022; Bertoldi et al., 2009; Chen & Stone, 2008; Monsalve et al., 2020; Recking, 2013b) and is directly linked to the nonlinearity of the equation. When a time series is considered, a random Shields stress τ *(t) is selected at each time step that is not the mean value.…”

“…Finally, despite the topic of the paper was the use of 1D models, a huge potential of improvement also exists when coupling the investigation with multidimensional numerical models (Francalanci et al., 2012), which can be used for building the appropriate spatial distribution of shear stress (Adams & Eaton, 2022) or for accounting for the complex feedbacks that exist between shear stress distribution, erosion, and morphology (Eaton et al., 2006).…”

“…This “missing dimension” (Ferguson, 2003) is not without consequences: smoothing the river by averaging both the data and the models gives a biased representation of a natural process (the bedload response to shear stress), which is by nature strongly nonlinear (Chen & Stone, 2008; Ferguson, 2003; Recking, 2013b). Not only does it limit the validity of 1D flume equations to 1D field computation, but the local cross‐section average parameters are morphology‐dependent, which suggests that different computational settings could be required for each morphology (Adams & Eaton, 2022; Francalanci et al., 2012; Monsalve et al., 2020; Recking et al., 2016).…”

“…Previous papers have analyzed the effect of replacing the local shear stress with a cross‐section‐averaged shear stress and concluded that, without taking variability into account, bed load equations tend to under‐predict, particularly for low to moderate transport (Adams & Eaton, 2022; Bertoldi et al., 2009; Chen & Stone, 2008; Monsalve et al., 2020; Recking, 2013b). The approach proposed here is different in that, instead of comparing the effect of replacing local (i.e., on each vertical) values with an average across a section (cross‐sectional average), we consider how the spatial and temporal variability of cross‐sectional average values affects bedload prediction.…”

Improving predictions of critical shear stress in gravel bed rivers: Identifying the onset of sediment transport and quantifying sediment structure

“…Such an approach seems to be appropriate when sediment transport is also being measured in a reach‐averaged way, or where the location of the mobile grains within the reach is unknown. However, unless the channel is unusually uniform, τ and hence sediment transport are likely to be spatially variable, and so the reach‐average shear stress will be an underestimate of the higher local shear stress in the areas of the bed where sediment first starts to move (Adams & Eaton, 2022; Ferguson, 2003; Lisle et al, 2000; Monsalve et al, 2016; Nelson et al, 2010; Segura & Pitlick, 2015). Conversely, the reach‐averaged shear stress can be an overestimate of the local shear stress acting on sediment when part of the stress is borne by significant large roughness elements (e.g.…”