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 โEavg andksn-q โEavg 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 โEavg 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.