Landscape form and millennial erosion rates in the San Gabriel Mountains, CA Roman A. DiBiase a, ⁎, Kelin X. Whipple a , Arjun M. Heimsath a , William B. Ouimet b a School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287, USA b Department of Geology, Amherst College, Amherst, MA 01002, USA abstract article info Article history: Received 28 May 2009 Received in revised form 16 October 2009 Accepted 26 October 2009 Available online 22 November 2009 Editor: Dr. R.W. Carlson Keywords: erosion landscape evolution topographic metrics cosmogenic radionuclides San Gabriel Mountains It has been long hypothesized that topography, as well as climate and rock strength, exert first order controls on erosion rates. Here we use detrital cosmogenic 10 Be from 50 basins, ranging in size from 1 to 150 km 2 , to measure millennial erosion rates across the San Gabriel Mountains in southern California, where a strong E–W gradient in relief compared to weak variation in precipitation and lithology allow us to isolate the relationship between topographic form and erosion rate. Our erosion rates range from 35 to 1100 m/Ma, and generally agree with both decadal sediment fluxes and long term exhumation rates inferred from low temperature thermochronometry. Catchment-mean hillslope angle increases with erosion rate until ∼ 300 m/Ma, at which point slopes become invariant with erosion rate. Although this sort of relation has been offered as support for non-linear models of soil transport, we use 1-D analytical hillslope profiles derived from existing soil transport laws to show that a model with soil flux linear in slope, but including a slope stability threshold, is indistinguishable from a non-linear law within the scatter of our data. Catchment-mean normalized channel steepness index increases monotonically, though non-linearly, with erosion rate throughout the San Gabriel Mountains, even where catchment-mean hillslope angles have reached a threshold. This non-linearity can be mostly accounted for by a stochastic threshold incision model, though additional factors likely contribute to the observed relationship between channel steepness and erosion rate. These findings substantiate the claim that the normalized channel steepness index is an important topographic metric in active ranges. © 2009 Elsevier B.V. All rights reserved. 1. Introduction Modern surface topography reflects the competition and interac- tion between climatic and tectonic forcing. Whereas climatic and tectonic variables are often difficult to quantify, surface topography can be readily obtained for much of the Earth's land surface from spaceborne sensors and aerial photography. However, extracting quantitative understanding of the interactions among climate, topography, and tectonics requires the unraveling of the relative contributions of a complicated suite of surface processes. Conse- quently, a central theme in modern geomorphology involves linking surface processes and their rates to observed landforms (e.g., Dietrich et al., 2003). Such quantitative knowledge is required before we can fully exploit the archive of climatic and tectonic history that is encoded in landforms. The importance of probing current topography for clues to process rates and mechanics is well recognized, and many have proposed that erosion rate increases with hillslope angle and local relief (e.g., Gilbert, 1877; Ahnert, 1970; Montgomery and Brandon, 2002). Basic observations support this, and the concept of slope-dependent soil flux on hillslopes has been around for over 100 years (Davis, 1892). Similarly, decadal sediment yield measurements were widely used to infer quantitative relationships between erosion rate and precipita- tion, uplift, and relief (e.g., Langbein and Schumm, 1958; Schumm, 1963; Judson and Ritter, 1964; Ahnert, 1970). Much uncertainty remains, however, regarding interrelationships among channel steepness, hillslope gradients, relief measured at various scales, and erosion rate even within a single climate zone. In addition, data of sufficient quality and distribution to allow rigorous testing of existing theory are sparse. Cosmogenic radionuclide (CRN) dating of surfaces and inference of erosion rates, in conjunction with the widespread availability of digital elevation models, affords an opportunity to make significant progress on this problem. Beginning with Granger et al. (1996), there have been a number of comparisons of hillslope gradients with millennial erosion rates determined with CRN (e.g., Safran et al., 2005; Vanacker et al., 2007; Binnie et al., 2007; Stock et al., 2008; Ouimet et al., 2009), as well as studies comparing erosion rates with various measures of local relief (e.g., Burbank et al., 1996; Schaller et al., 2001; Montgomery and Brandon, 2002; Wittmann et al., 2007). As initially noted by Penck (1953) and Strahler (1950), and later recast by Burbank et al. (1996), Schmidt and Montgomery (1995), and Montgomery and Brandon (2002), meso-scale rock strength limitations result in hillslopes reaching threshold angles wherever erosion rate exceeds a critical Earth and Planetary Science Letters 289 (2010) 134–144 ⁎ Corresponding author. E-mail address: roman.dibiase@asu.edu (R.A. DiBiase). 0012-821X/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.epsl.2009.10.036 Contents lists available at ScienceDirect Earth and Planetary Science Letters journal homepage: www.elsevier.com/locate/epsl