The Role of Bed Coverage in Reducing the Area Dependence of Fluvial Incision: Implications for the Maximum Relief of Mountains.

Analytical models of the coupled behavior between fluvial incision and wedge tectonics predict that the dependence of fluvial incision on drainage area is an important factor for understanding how climate (through precipitation) affects the height of active mountain belts. These models use a stream-power formulation I=KA^{mS^n} to represent fluvial incision, but this equation is only an approximation of the many processes that control fluvial incision. Although stream power is widely applied, it is not well tested. Using first principles and scaling laws for channel flow, the value of m in the stream-power equation is derived to be between 0.3 and 1.0. Our contribution here is to consider empirical estimates of m and n, which we will refer to as μ and ν . These estimates are made by fitting a power-law function to slope, area, and incision rate data and are independent from assumptions about the incision process. We use data from both natural settings (the Clearwater River, Washington State, USA, and the Lachlan River, SE Australia) and synthetic examples obtained using the CHILD landscape-evolution model. In both of the natural settings, all estimates of μ are less than 0.2 and sometimes negative. Likewise for the simulated landscapes, when sediment load is included in the incision model and uplift varies spatially, power-law estimates produce a wide range of μ values and also include negative values. The CHILD model demonstrates that the estimated μ is quite different from the value of m used in the model calculation. The reason seems to be that the bed-coverage effect is correlated with drainage area for these examples. The results raise the question of what parameter values should be used in coupled analytical models. If the empirical estimates are relevant, then the low-area dependence of incision rate (as indicated by estimates of μ ) suggests that climate plays a very weak role in controlling the height of mountains.