An empirical stream power formulation for knickpoint retreat in Appalachian Plateau fluviokarst

Abstract

Summary Hydrologically abandoned caves on tributaries of the Upper Cumberland River, Tennessee, USA record a wave of river incision that advanced up the drainage basin in the Late Pliocene and Early Pleistocene. Geomorphic and geologic evidence suggests that incision occurred as a migrating knickpoint generated by sudden base-level lowering. The passage of a knickpoint up the Cumberland River tributaries was modeled as a perturbation to steady-state incision according to the stream power law E = kQ m S n and tested using dated incision events recorded in cave sediments. Knickpoint migration rates generated by this model were 0.1–0.18 m/yr over the entire stream network, and 4.0 m/yr for the mainstem Cumberland River channel. The ratio m / n = 0.79 was consistent with previously published parameters; however, the values of m = 1.91 and n = 2.39 were much higher than those reported in previous field studies. These results suggest the stream power model may be used to model knickpoint migration in the study area, provided values for the constants m and n are larger. This may be due to the influence of fluviokarst, where surface drainage is interrupted due to diversion into the underlying karst aquifer. Field measurements of channel and basin geometry in fluviokarstic tributaries to the Upper Cumberland River show (1) a stronger variance between channel slope and discharge; (2) a nonlinear relationship between discharge and drainage area; and (3) stream width to be nearly invariant, as opposed to non-karst watersheds. Because the stream power model relies heavily on the substitution of discharge for drainage area, the behavior of channel incision and knickpoint migration in fluviokarst may differ substantially from that of non-karst channels.