4.4.1 Case 4: Trunk Response
In this case, the trunk river experiences a 33% initial decrease in erosional efficiency and erosion rate at the outlet, and a 50% increase in the headwaters following the change in rainfall pattern (Figure 6). This range is significantly narrower than the range of variations in rainfall because of the buffering effect that concentrating rainfall in the headwaters has on downstream changes in discharge (e.g., Figure 2b inset). Like Case 3, because this scenario also exhibits a complex transient response, the transition between decreases in erosion rate downstream and increases upstream is initially at positionxsc . Unlike Case 3, knickpoint shape does not invert during transient adjustment and is always convex-up. Interestingly, combined with observations from Case 3, this suggests that complex responses generally are more likely to exhibit convex-up knickpoints. Retention of the knickpoint shape is accommodated by over-adjustment upstream of xsc , specifically by progressively more rapid upstream adjustment (higher erosional efficiency) toward gentler slopes that outpaces downstream adjustment. By the time that the migrating trunk knickpoint reaches positions upstream of xsc , the profile has incised below its equilibrium elevation and is shallower than its equilibrium slope. Thus, the profile is forced to uplift and steepen to reach steady state, preserving the convex-up knickpoint shape (Movie S4).