4.2 Case 2: Spatially Uniform Increase in Rainfall
The modelled catchment response to a spatially uniform increase in rainfall is characterized by adjustment to uniformly lowerksn and a decrease in steady state fluvial relief. To compare responses, we invert the change in rainfall from the previous example, and rainfall is increased from 1 to 2 m/yr, resulting in a 100% increase in discharge (Movie S2).
We observe a broadly symmetrical response to Case 1, where the twofold increase in rainfall leads to an initial twofold increase in erosion rate (E > U ) and a ~30% decrease in steady state fluvial relief. The transient knickpoint is concave-up in this case and it broadens as it migrates upstream, as is expected for a concave-up knickpoints where n > 1 (Royden & Perron, 2013). The signal of transient adjustment communicated to tributaries is consequently protracted, making adjustments more diffuse.
Responses reflected inksn โ€“Eavg andksn-q โ€“Eavg relationships also mirror Case 1. As is characteristic for ksn , the initial change in erosional efficiency causes the trunk and tributary network to shift onto a different steady state erosional efficiency curve; in this case, from K =Kp to K = 2ยทKp , and they generally follow this curve during adjustment (Figure 4a). Minor deviations from this curve exhibit a convex-up pattern (inverted from Case 1) due to the opposite knickpoint shape. Meanwhile inksn-q โ€“Eavg space (Figure 4b), the initial and final equilibrium conditions for both the trunk and tributary network plot in the same location, as in Case 1. The change in rainfall again causes a shift only along the K=Kpcurve, but to uniformly higher ksn-q and erosion rate in this case, and they generally follow this curve during adjustment back to steady state.