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Abstract : Long-term bedrock incision is driven by daily discharge events of variable magnitudeand frequency, with ineffective events below an incision threshold. We exploretheoretically how this short-term stochastic behavior controls long-term steady stateincision rates and bedrock channel profiles, combining a realistic frequency-magnitudedistribution of discharge with a deterministic, detachment-limited incision model in whichincision rate is a power function of basal shear stress above a critical shear stress. Ourmodel predicts a power law relationship between steady state slope and drainage areaconsistent with observations. The exponent of this power law is independent of dischargemean and variability, while the amplitude factor, which controls mountain belt relief, is apower law function of mean runoff with an exponent of 0.5 and a complex functionof runoff variability. In accordance with evidence that incision occurs between 6 and20% of time in rapidly incising rivers >1 mm-yr our model predicts that channelsteepness is virtually insensitive to runoff variability. Runoff variability can only decreasechannel steepness for very slow incision rates and-or weak lithologies. The relationshipbetween channel steepness and incision rate is always a power law whose exponentdepends on the channel cross-sectional geometry and runoff variability. This contradictsmodels neglecting discharge stochasticity in which the steepness-incision scaling is setby the incision law exponent. Our results suggest that changes in climate variabilitycannot explain an increase in bedrock incision rates during the Late Cenozoic within thecontext of a detachment limited model.





Author: Dimitri Lague Niels Hovius Philippe Davy

Source: https://hal.archives-ouvertes.fr/



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