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Supplementary Information 1 The analytical model presented in the manuscript text (Equation 5) employs a model to describe surface topography that relates soil flux and slope linearly. Alternatively, a nonlinear relationship between soil flux and slope, following Roering et al. 1999, can be used to arrive at an analytical expression that describes the thickness of the weathered zone (or the ratio of bedrock relief to surface relief, Zb0/Zs0) as a function of geomorphic and hydraulic parameters. Following the non-linear model, the 1-D analytical expression for the steady state relief of the ridge top (Zs0) is given by −
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where $ = (- ⁄- ). and Sc is the critical slope (Roering et al., 2001). Dh, in the nonlinear case, is the soil diffusivity [L2/T]. The boundary conditions used to arrive at this solution are the same as those employed to arrive at Equation 1 in the manuscript text: There is no soil flux across the ridge top (x=0) and the channel elevation (z=0) occurs at x=L where L is the hillslope length. The ratio of bedrock relief to surface relief at the ridge top (Zb0/Zs0), is then given by /01
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−
=
Submission PDF ln
+
( ⁄ )
!"
"
+ (2$%⁄&' ) −
ln (
)( (
*⁄ ) )
⁄ )
+,
(i)
where $ = (- ⁄- ). and Sc is the critical slope (Roering et al., 2001). Dh, in the nonlinear case, is the soil diffusivity [L2/T]. The boundary conditions used to arrive at this solution are the same as those employed to arrive at Equation 1 in the manuscript text: There is no soil flux across the ridge top (x=0) and the channel elevation (z=0) occurs at x=L where L is the hillslope length. The ratio of bedrock relief to surface relief at the ridge top (Zb0/Zs0), is then given by /01
/21 343563789
=
=
>
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=
@A
B (?⁄> )
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: ; " 4 (* )
