Evidence of tipping of a fluvial system?

Abstract

We assess whether an observed sudden change in trend of the flow partitioning over the downstream branches of a bifurcation system in the Dutch Rhine River, following two consecutive peak flow events, is evidence of system tipping. For this purpose, we analyze field data of the bifurcation region and relate observed sudden and subsequent slow system changes to the stability properties of equilibrium solutions of a low complexity river bifurcation model. In particular, the two peak flow events led to sediment deposition at the upstream end of one bifurcate. As the resulting larger flow rate toward the other bifurcate enhanced channel bed erosion, that bifurcate has attracted an ever larger portion of the flow rate since. This presumably unstable state of the bifurcation region is of concern, as flood risk management and freshwater supply within the system are based on a certain agreed flow partitioning ratio between the bifurcates. Based on the river bifurcation model, we illustrate that there exist several paths in which a sudden decrease in flow depth in one bifurcate leads to a transition from one stable state with two open branches to another stable state with one closed branch. As the bifurcation model is a heavily schematized one, we cannot prove that the observed bifurcation system change agrees with one of these theoretical trajectories. There are indications that some natural systems are able to prevent tipping behavior, provided that their response is characterized by sufficient degrees of freedom. The fact that the river system is a heavily engineered system with fixed planform and banks (and hence limited degrees of freedom of channel response) may have prevented the system from evading tipping behavior.