4.3.3 Case 3: ksn–Eavg and
ksn-q–Eavg
Plots of ksn –Eavg 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 ksn –Eavg 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-q –Eavg 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-q –Eavg space is minor
over the duration of the transient adjustment compared to dispersion inksn –Eavg space – we
expand on implications from this point in section 5.3.