Discharge, discharge variability, and the bedrock channel profile
Résumé
Long-term bedrock incision is driven by daily discharge events of variable magnitude
and frequency, with ineffective events below an incision threshold. We explore
theoretically how this short-term stochastic behavior controls long-term steady state
incision rates and bedrock channel profiles, combining a realistic frequency-magnitude
distribution of discharge with a deterministic, detachment-limited incision model in which
incision rate is a power function of basal shear stress above a critical shear stress. Our
model predicts a power law relationship between steady state slope and drainage area
consistent with observations. The exponent of this power law is independent of discharge
mean and variability, while the amplitude factor, which controls mountain belt relief, is a
power law function of mean runoff (with an exponent of 0.5) and a complex function
of runoff variability. In accordance with evidence that incision occurs between 6 and
20% of time in rapidly incising rivers (>1 mm/yr) our model predicts that channel
steepness is virtually insensitive to runoff variability. Runoff variability can only decrease
channel steepness for very slow incision rates and/or weak lithologies. The relationship
between channel steepness and incision rate is always a power law whose exponent
depends on the channel cross-sectional geometry and runoff variability. This contradicts
models neglecting discharge stochasticity in which the steepness-incision scaling is set
by the incision law exponent. Our results suggest that changes in climate variability
cannot explain an increase in bedrock incision rates during the Late Cenozoic within the
context of a detachment limited model.
Domaines
Géomorphologie
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