Figure 3 . Sensitivity analysis of a river profile to different spatial gradients in rainfall. a) Defines general domains of behavior described in the sensitivity analysis shown in (b) – see text for descriptions of different fields. Black star in (a) marks the initial condition; note, initial conditions in panels (a) and (b) are different. Top-heavy and bottom-heavy domains are separated by the 1:1 line. The primary influence of different h values in Hack’s Law is on the slope of Qf /Qi , as indicated. b) Same as (a) but where the initial profile is adjusted to spatially uniform P = 1.5 m/yr, and grey fields in (a) are colored by magnitude of Δzsc ­ (e.g., Figure 2). White stars show rainfall gradient scenarios explored in section 3 – Cases 3 & 4. Contours of Qf/Q are shown in grey dashed lines, and contours ofRf /Ri in black dotted lines.