Implications of the shear stress river incision model for the timescale of postorogenic decay of topography

Abstract

[1] The reason for the survival of mountainous topography in ancient orogenic belts is a long-standing problem in geomorphology and geodynamics. We explore the geomorphologic controls on the timescale for the postorogenic decay of topography to address the question of whether there is a viable geomorphologic explanation for the persistence of topography in ancient orogenic belts or whether alternative geodynamic explanations must be sought. Using both approximate analytical solutions and numerical simulations, we show that the standard detachment-limited stream power river incision model predicts, for reasonable initial topographies, relatively short postorogenic decay times of 1-10 Myr. Additional layers of complexity are introduced to this simplest model including isostasy and flexural strength, a transition to transport-limited conditions during decline, and the incorporation of the combined effects of a critical threshold for erosion and the stochastic variability of flood magnitudes. Each of these additional factors acts to lengthen the decay timescale. Pure Airy isostatic rebound of a thick crustal root results in decay times that are at most a factor of 6 longer than the detachmentlimited result. The transition to transport-limited conditions involves partial protection of the bed by a thin layer of alluvium, which inhibits erosion and therefore increases decay times by a factor of 2-3 in our analysis. Finally, including critical shear stress results increases decay time by approximately a factor of 20 for the parameter values in our example calculation. More importantly, however, a significant portion of topography remains after predicted lowering rates have dropped to values less than measured rates of denudation in weathering-limited, low-relief environments. Thus a model combining isostasy, a transition to transport-limited conditions, and a critical shear stress for erosion could account for the presence of residual topography for hundreds of million years. All three of these factors can be expected to play a role in natural settings. INDEX TERMS:1815 Hydrology: Erosion and sedimentation; 1824 Hydrology: Geomorphology (1625); 8110 Tectonophysics: Continental tectonics-general (0905); KEYWORDS: topography, erosion, relief, postorogenic, geomorphology Citation: Baldwin, J. A., K. X. Whipple, and G. E. Tucker, Implications of the shear stress river incision model for the timescale of postorogenic decay of topography,

Numerical modelling of landscape and sediment flux response to precipitation rate change

“…13). These slopes are in agreement with the approximate analytical solutions of Whipple (2001) and numerical models of Baldwin et al (2003); i.e. the stream power response time τ sp has a proportionality,…”

“…Lague, 2014;Croissant and Braun, 2014;Rudge et al, 2015) and likewise within the transport model it is plausible that the slope exponent γ > 1. The response time for the stream power model for various values of n has been explored within Baldwin et al (2003). Here we expand on this by exploring the equivalent response times for the transport model.…”

“…Whittaker et al, 2007;Cowie et al, 2008;Whittaker and Boulton, 2012), although the precise appropriateness of any time-integrated erosion law to specific field sites is not always easy to establish. Sediment flux response times for the advective stream power law have been previously characterized by Whipple (2001) and Baldwin et al (2003), and for the transport model they have been studied by Armitage et al (2011) and Armitage et al (2013), but not systematically or using 2-D models. Furthermore, to our knowledge no comparison between the transport models has been previously made.…”

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

“…[60] Our conclusion that a threshold for incision is not resolvable in the Lachlan catchment may be influenced by our implementation of a linear form of the excess stream power model (equations (2b) and (3)), although Tomkin et al [2003], who use the fully nonlinear formulation (2a), note a similar vanishingly small threshold. In contrast, Baldwin et al [2001] and Snyder et al [2003] suggest that a threshold shear stress may play a major role controlling river incision, and may notably explain the observed extreme variations in incision rates between actively uplifting and tectonically quiet regions, without similarly large differences in relief [see also Pazzaglia et al, 1998]. The approach of these authors is somewhat different, however, in that they express the erosion coefficient K of the stream power model as a product of three factors encompassing hydraulic, climatic, and threshold shear stress parameters respectively.…”

“…It has been argued that transport-limited behavior should be favored in geomorphic systems that are in a declining state [Baldwin et al, 2001;Pazzaglia et al, 1998;Whipple and Tucker, 2002], such as is the case in the stable postrift setting of the SE Australian highlands. Moreover, it has been argued that mixed bedrock-alluvial rivers such as the Lachlan should be transportlimited systems [Howard, 1998;Whipple and Tucker, 2002].…”