A physically-based estimation of the length parameter in river bifurcation models

The morphological trajectory of river bifurcations is commonly investigated through one-dimensional models. In this approach, the two-dimensional topographic effects exerted by the bifurcation are simply accounted for by a nodal point relation, which quantifies the amount of sediment that is transported towards each downstream branch. The most widely-adopted nodal point relation is based on considering two computational cells located just upstream the bifurcation node, which laterally exchange water and sediments. The results of this approach strongly depend on a dimensionless parameter that represents the ratio between the bifurcation cell length and the main channel width, whose value needs to be empirically estimated. An interesting possibility is the calibration of this parameter on the basis of the analysis of existing  two-dimensional linear models, which directly solve the momentum and mass conservation equations. Following this idea, I demonstrate that a full consistency between the one-dimensional approach and the two-dimensional models can be directly achieved by adopting different scaling for the bifurcation cell length, which results in a theoretically-defined and constant dimensionless cell length parameter. Comparison with experimental observations reveals that this physically-based scaling yields more accurate predictions of bifurcation stability and discharge asymmetry. This constitutes  a starting point for incorporating other factors that are typically observed in natural settings, such as flow variability and non-trivial plainform configuration. In conclusion, this work provides a physically-based method for parameterizing one-dimensional bifurcation models, easily incorporable in existing models of braided networks, channel deltas or individual channel loops.