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Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Whether or not steady-state topography and denudation are probable states depends on the timescale of system response to tectonic and climatic perturbations relative to the frequency of those perturbations. This paper presents analytical derivations of algebraic relations for the response time of detachment-limited fluvial bedrock channel systems both to tectonic and climatic perturbations. Detachmentlimited fluvial erosion is described by the stream-power incision model, and the derivations are limited to the applicability of that model. All factors likely to influence system response time that are not adequately captured by the stream-power incision model will tend to increase the response time. The calculations presented thus provide minimum estimates of landscape response time and therefore over-predict the probability of attaining and sustaining steady-state topography and denudation. The Central Range of Taiwan is used as a case study to estimate response times in a landscape often argued to be in steady state. Model parameters are fit to modern stream profiles by assuming that the topography represents a quasi-steady-state form. Estimated response times generally range from 0.25 to 2.5 Ma, depending on the non-linearity of the incision rule and the magnitude and type of perturbation. Thus it may be reasonably argued that steady-state topography and denudation are likely to prevail during periods of climatic stability (response time is sufficiently short compared with plate tectonic timescales). However, rapid climatic fluctuation in the Quaternary appears to preclude the attainment of steady-state conditions in modern orogens.
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