Defining the length parameter in river bifurcation models: a theoretical approach

One-dimensional models for river bifurcations rely on a nodal point relation that determines the distribution of sediments between the downstream branches. The most widely-adopted nodal point relation describes the two-dimensional topographic effects exerted by the bifurcation by introducing two computational cells, located just upstream the bifurcation node, that laterally exchange water and sediments. The results of this approach strongly depend on a dimensionless parameter that represents the ratio between the cell length and the main channel width, whose value needs to be empirically estimated. Previous works proposed calibrating this parameter on the basis of more complete two-dimensional linear models, which directly solve the momentum and mass conservation equations. This study demonstrates 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 length parameter. Comparison with experimental observations reveals that this physically-based scaling yields more accurate predictions of bifurcation stability and discharge asymmetry. This indicates that the proposed method may provide a more reliable and precise estimation of the cell length, potentially improving the performance of one-dimensional models for bifurcation processes in rivers.