4.1 Case 1: Spatially Uniform Decrease in Rainfall
The modelled catchment response to a spatially uniform decrease in rainfall is characterized by adjustment to uniformly higherksn and an increase in steady state fluvial relief. For this model run, rainfall is decreased from 2 to 1 m/yr, causing discharge to decrease similarly by 50% (Movie S1).
Erosion rate decreases across the entire channel network following the change in rainfall, driven by a decrease in erosional efficiency directly proportional in magnitude (i.e., 50%; recall m = 1). The resulting disequilibrium, with E < U , drives surface uplift and upstream migration of a convex-up slope-break knickpoint, and eventually a ~40% increase in fluvial relief.
In ksn–Eavg space (Figure 4a), the decrease in erosional efficiency driven by the change rainfall causes the trunk river and tributary network to shift uniformly onto a different erosional efficiency curve that describes the expected relationship between ksn and erosion rate for a given erosional efficiency at steady state. Specifically, both shift from K=2 ·Kp to K=Kp(Kf = 0.5·Ki ). Following this initial shift, the trunk river and individual tributaries approximately follow this new curve (K=Kp ) during adjustment toward higher erosion rates and ksn to return to steady state, although in detail they deviate slightly. This deviation is a result of averaging segments above and below the migrating knickpoint into mean (upstream-averaged)sn and erosion rate values. Insofar as the relationship between channel steepness and erosion rate implies a given erosional efficiency, these deviations imply an apparent erosional efficiency different, albeit minor in this case, from the modelled value.
In ksn-qEavg space (Figure 4b), both the initial and final steady state conditions plot in the same location on the K=Kp curve. Here, the initial decrease in erosional efficiency causes the trunk and tributaries to shift uniformly along this curve to lowerksn-q and erosion rate rather than shifting onto a different curve. During adjustment both generally follow this curve to return to steady state, minor transient deviations as seen forksn notwithstanding.