Erosional dynamics, flexural isostasy, and long‐lived escarpments: A numerical modeling study

Abstract

Erosional escarpments are common features of high‐elevation rifted continents. Fission track data suggest that these escarpments form by base level lowering and/or marginal uplift during rifting, followed by lateral retreat of an erosion front across tens to hundreds of kilometers. Previous modeling studies have shown that this characteristic pattern of denudation can have a profound impact upon marginal isostatic uplift and the evolution of offshore sedimentary basins. Yet at present there is only a rudimentary understanding of the geomorphic mechanisms capable of driving such prolonged escarpment retreat. In this study we present a nonlinear, two‐dimensional landscape evolution model that is used to assess the necessary and sufficient conditions for long‐term retreat of a rift‐generated escarpment. The model represents topography as a grid of cells, with drainage networks evolving as water flows across the grid in the direction of steepest descent. The model accounts for sediment production by weathering, fluvial sediment transport, bedrock channel erosion, and hillslope sediment transport by diffusive mechanisms and by mass failure. Numerical experiments presented explore the effects of different combinations of erosion processes and of dynamic coupling between denudation and flexural isostatic uplift. Model results suggest that the necessary and sufficient conditions for long‐term escarpment retreat are (1) incising bedrock channels in which the erosion rate increases with increasing drainage area, so that the channels steepen and propagate headward; (2) a low rate of sediment production relative to sediment transport efficiency, which promotes relief‐generating processes over diffusive ones; (3) high continental elevation, which allows greater freedom for fluvial dissection; and (4) any process, including flexural isostatic uplift, that helps to maintain a drainage divide near an escarpment crest. Flexural isostatic uplift also facilitates escarpment retreat by elevating topography in the vicinity of an eroding escarpment, thereby increasing channel gradients and accelerating erosion which in turn generates additional isostatic uplift. Of all the above conditions, high continental elevation is common to most rift margin escarpments and may ultimately be the most important factor.

Cenozoic river profile development in the Upper Lachlan catchment (SE Australia) as a test of quantitative fluvial incision models

“…Therefore the detachment-limited stream power model may be useful to study incision on a local scale [e.g., Kirby and Whipple, 2001;Snyder et al, 2000] but its use on regional scales [e.g., Finlayson et al, 2002;Royden et al, 2000] appears problematic. In numerical SPMs the problem may be circumvented by combining detachment-limited and transport-limited stream power algorithms, with the one that predicts the lowest incision being taken as the rate-limiting process [e.g., Densmore et al, 1998;Tucker and Slingerland, 1994;Whipple and Tucker, 2002]. Alternatively, ''hybrid'' formulations such as the undercapacity model implicitly predict transitions from one to the other behavior to take place along the streams.…”

“…The stream power incision law has been widely used to numerically model landscape development [e.g., Anderson, 1994;Tucker and Slingerland, 1994;Willett, 1999] as well as to infer rock uplift rates directly from fluvial profile forms [Finlayson et al, 2002;Kirby and Whipple, 2001;Snyder et al, 2000].…”

A stochastic approach to modeling the role of rainfall variability in drainage basin evolution

“…Most quantitative landscape models solve this problem by devising a "steady runoff" coefficient that is assumed to encapsulate the average effect of many floods over many years. For models that assume a linear drainage area-discharge relation, this runoff coefficient has dimensions of length per time and can be thought of as a "geomorphically effective" precipitation rate [e.g., Beaumont et al, 1992; Anderson, 1994;Tucker and Slingerland, 1994]. In some cases an "intermittency factor" is included as a simple approximation for the degree of runoff variability [Paola et [1991a] argued that flood variability could be parameterized on the basis of mean peak discharge but did not attempt to draw an explicit connection with climate properties.…”

Mathematical Analysis of a Model of River Channel Formation

“…Nonlinear studies of channel development and topographic evolution focussed on catchment scale problems, such as that of WILLGOOSE et al (1991), however such efforts were unable to compute the solution of the governing models directly, essentially because of the stiffness of the system. WILLGOOSE et al (1991) reverted to an artificial channel indicator variable, and KRAMER and MARDER (1992) used cellular lattice models, a development which has formed the thrust of simulation models since, e.g., those of HOWARD (1994) and TUCKER and SLINGERLAND (1994). There have been efforts to solve the Smith-Bretherton model directly (e.g., SMITH et al, 1997;BIRNIR et al, 2001), although these are problematical, unsurprisingly since the original Smith-Bretherton model is actually ill-posed.…”