4.3.3 Case 3: ksn–Eavg and ksn-q–Eavg
Plots of ksnEavg andksn-q–Eavg clarify some additional features of the transient response (Figure 5). The trunk profile exhibits higher ksn andksn-q values and spans a relatively narrower range in erosion rates than tributaries during transient adjustment, reflecting the fundamentally different ways they experience the modelled rainfall gradient. This behavior illustrates that the network of tributaries (isolated catchments that individually experience relatively uniform rainfall but collectively span a range of conditions) inherently incorporates a more direct signal of the change in rainfall patterns compared to the trunk, which averages upstream rainfall variations. This is consistent with findings by Han et al. (2015) for steady state landscapes exposed to orographic rainfall and is important for designing an effective sampling strategy in the field – discussed further in section 5.3.
In ksnEavg space (Figures 5a, 5b), shifts onto different erosional efficiency curves occur as in Cases 1 & 2, but here the spatial rainfall variability causes different positions along the trunk and individual tributaries shift by different amounts. The trunk profile response spans fromK = 0.5·Kp to ~1.8·Kp , while the network of tributaries spans from K = 0.5·Kp to 4·Kp . To first order, points representing a given location along the trunk or a given tributary move along these curves reflecting local erosional efficiency during adjustment toward steady state as in Cases 1 & 2, but again deviate in detail. Trajectories are more complex in this case because of the interplay between changes in erosional efficiency and baselevel variations in modulating tributary channel steepness and the over-adjustments mentioned previously (c.f. , Figures 4 & 5). Finally, we note an interesting feature where the range of erosional efficiency values that correspond to upstream mean ksn at steady state for the trunk profile (K = 0.5·Kp to ~1.8·Kp ) are lower than that implied by mean rainfall (i.e., K = ~2.7·Kp ; Figures 1b, 5a) – discussed further in section 5.2.
In ksn-qEavg space (Figures 5c, 5d), differences between trunk and tributary responses andksn vs. ksn­-q are readily apparent. Initial and final steady state conditions plot in the same position, as is characteristic of ksn-q where uplift rate is constant. Following the change in rainfall, the trunk profile expands slightly obliquely to the K=Kpcurve, where downstream locations are systematically shifted toward higher erosional efficiency. This shift reflects systematic slope adjustments that must occur along the trunk to bring it into equilibrium with the non-uniform rainfall pattern and decreases with time as these adjustments take place. Apart from this minor shift, different positions along the trunk profile generally follow the K=Kpcurve during adjustment back to steady state. In tributaries, on the other hand, the change in rainfall causes expansion precisely along theK=Kp curve because they experience no along-stream variations in rainfall. Tributaries again generally evolve along the K=Kp curve toward steady state (as with cases 1 and 2). Transient morphological adjustments affect this trajectory in detail and deviations, which affect apparent erosional efficiency, are more significant in drier tributaries near the headwaters. Overadjustment is also evident for both the trunk and tributaries in this space, but because transient evolution is generally along the steady state curve, it does not significantly affect the apparent erosional efficiency. As a final note, dispersion around the steady state erosional efficiency curve inksn-qEavg space is minor over the duration of the transient adjustment compared to dispersion inksnEavg space – we expand on implications from this point in section 5.3.