Figure 9. Plot illustrating how rainfall gradients
systematically influence correlation between mean rainfall andksn at steady state, and consequences for
relationship between channel steepness and erosion rate (inset). A
common symbology is used in both the main figure and the inset. Expected
SPM relationship based on uniform climate (uniform erosional efficiency,K ) is shown in solid back line. Grey long-dashed lines represent
changes in K =Kp \(\overset{\overline{}}{P}\)m .
Circles colored by mean rainfall reflect scenarios shown in Figure 1 –
uniform rainfall of 1, 1.5, and 2 m/yr, and bottom- and top-heavy
gradients (also used in Cases 3 & 4). While Kpis equivalent for all scenarios, rainfall gradients cause dispersion
(apparent differences in erosional efficiency) from the expected
relationship (solid black line) equivalent to differences inKp of approximately a factor of two (inset). For
instance, the bottom-heavy case where mean rainfall is
~2.7 m/yr exhibits an apparent ~50%
reduction in erosional efficiency based on meanksn (plots onK ≈0.5Kp curve in main figure) and thus
plots where one would expect a catchment that experiences half as much
rainfall to plot in the inset. Dotted line in main figure illustrates,
conceptually, how this dispersion could distort inferred relationships
between mean rainfall and channel steepness (weaker and quasi-linear in
this case), even at steady state and in systems where the SPM is a
complete description of the controls on channel profile form. Where
uplift rates are unknown, this systematic bias in apparent erosional
efficiency due to rainfall gradients is a potential source of dispersion
in relationships between ksn and erosion rate
(inset).