Determining the correct river incision mechanism under different climatic and lithological conditions using disorder metrics

Fluvial incision patterns help us understand the role of precipitation in river formation and evolution. Incision is generally thought to be a function of channel gradient and either discharge or drainage area. Many studies use drainage area as a proxy for discharge, but incision could potentially be related to area rather than discharge because area determines sediment fluxes. Assumptions about discharge or drainage area control on incision impact the calculations of chi profiles and steepness indices, which are indicators of the erosional and tectonic history of the landscape. Here we use numerical modelling and topographic analysis to determine if spatially varied precipitation leads to distinctive patterns of channel profiles that can be used to differentiate if a discharge or drainage-area driven incision rule is appropriate for a given landscape.  

We use the modelling framework Fastscape to set up two scenarios: one including an incision rule with drainage area and another with discharge (rainfall). We evolve them to steady state and extract from the resultant topography a disorder metric, which measures the relation between the tributaries and the main river in chi space. To simulate a blind test of the incision conditions, we calculate the disorder metric under the two incision case assumptions. We find that scenarios in which incision is discharge-driven cases are statistically distinguishable from those in which incision is driven by drainage area alone. 

We repeat these analyses with variable rainfall gradients, simulating those found in real landscapes. The results are in agreement: in a sandbox model with homogeneous lithology, it is possible to distinguish the incision case based on the disorder metric under all rainfall conditions. Real landscapes are not sandboxes, however, so we run further simulations to quantify the impact of heterogeneous lithology under different rainfall scenarios. This reveals that it is not possible to distinguish the incision case, as the distortions to channel profiles driven by lithology masks evidence of discharge dominance. 

We complete the analysis by testing the hypothesis in 10 real landscapes across the globe, with different lithological and climatic regimes. Some study areas, such as the Pyrénées or the Alburz Mounts, show a weak trend towards discharge dominance, although there is no conclusive statistical evidence of the preference of one incision rule, hinting at the dominance of lithology over rainfall as shown in the models.