Quantifying rock uplift rates using channel steepness and cosmogenic nuclide–determined erosion rates: Examples from northern and southern Italy Andrew J. Cyr1,†, Darryl E. Granger1, Valerio Olivetti2, and Paola Molin2 1DEPARTMENT OF EARTH AND ATMOSPHERIC SCIENCES, PURDUE UNIVERSITY, 550 STADIUM MALL DRIVE, WEST LAFAYETTE, INDIANA 47907, USA 2DIPARTIMENTO DI SCIENZE GEOLOGICHE, UNIVERSITÀ DEGLI STUDI “ROMA TRE,” LARGO SAN LEONARDO MURIALDO 1, 00146 ROME, ITALY ABSTRACT Rock uplift rates can be diffi cult to measure over 103–105 yr time scales. If, however, a landscape approaches steady state, where hillslope erosion and rock uplift rates are steady and locally similar, then it should be possible to quantify rock uplift rates from hillslope erosion rates. Here, we test this prediction by comparing channel steepness index values and 10Be catchment-averaged erosion rates to well-constrained rock uplift rates in two landscapes in Italy. The fi rst fi eld area is the Romagna Apennines, northern Italy, where rock uplift rates are relatively uniform, between 0.2 and 0.5 mm/yr (regional mean 0.40 ± 0.15 [SE] mm/yr), and have been steady since 0.9 Ma. The second area is the region around northeastern Sicily and the southernmost Italian peninsula, where rock uplift rates are higher and exhibit a strong spatial gradient, from ~0.7 to ~1.6 mm/yr (regional mean 1.09 ± 0.13 [SE] mm/yr). In both regions, channel steepness indices and 10Be erosion rates vary directly with rock uplift rates. Although there is considerable variability in erosion rates, regionally averaged rates in both the northern (0.46 ± 0.04 [SE] mm/yr) and southern (1.21 ± 0.24 [SE] mm/yr) areas accurately measure rock uplift rates. Although channel steepness indi- ces do not quantify rock uplift rates, they are useful for (1) identifying regional patterns of rock uplift, (2) identifying areas where uplift rates might be expected to be uniform, and (3) informing 10Be sampling strategies. This study demonstrates that, together, channel steepness and hillslope erosion rates can provide a powerful tool for determining rock uplift rates. LITHOSPHERE; v. 2; no. 3; p. 188–198, Data Repository 2010137. doi: 10.1130/L96.1 INTRODUCTION races require the assumption that river incision cators of rock uplift rates in a place where uplift is equilibrated with rock uplift, yet strath forma- rates are known independently. Knowing the distribution of rock uplift tion is often attributed to climatic fl uctuations, In the following section, we briefl y intro- rates across a landscape is important for iden- making it diffi cult to distinguish climatic from duce the use of channel steepness index and tifying and understanding active tectonic struc- tectonic causes of river incision (e.g., Pazza- erosion rate to determine rock uplift rates, with tures, and for establishing the pace and pattern glia and Gardner, 1993; Merritts et al., 1994; an emphasis on the assumptions and conditions of mountain growth. Rock uplift rates can be Hancock et al., 1999; Wegmann and Pazzaglia, necessary for their success. Channel steepness determined geodetically over short (100–102 yr) 2002; Pan et al., 2003). index is a measure of stream-channel gradi- time scales, or inferred from thermochrono- Alternative methods for inferring local- to ent normalized to drainage area (see Wobus et meters over much longer (106 yr) time scales. regional-scale rock uplift rates, such as stream- al., 2006), and it has been shown to be directly Over intermediate (103–105 yr) time scales, channel morphometry and catchment-averaged proportional to rock uplift rates in a variety of rock uplift rates can be inferred from uplifted erosion rates, have become increasingly used to landscapes (e.g., Snyder et al., 2000; Lague and geomorphic markers such as marine or fl uvial measure relative differences in rock uplift rates Davy, 2003; Duvall et al., 2004). We measured terraces, provided that their ages can be deter- across a region (Lague et al., 2000; Kirby and erosion rates using cosmogenic 10Be in quartz, mined. Each of these methods provides impor- Whipple, 2001; Kobor and Roering, 2004; Fer- which is produced in proportion to the residence tant constraints but also suffers from limitations. rier et al., 2005; Wobus et al., 2005, 2006; Kirby time of mineral grains in the uppermost few Geodetic measurements only incorporate a frac- et al., 2007). These methods are widely applica- meters of Earth’s surface. We then applied both tion of the seismic cycle and are limited to sites ble; however, they implicitly assume a landscape of these methods to two different landscapes in with existing surveys and where uplift rates are in steady state or dynamic equilibrium, in which Italy, where rock uplift rates are known indepen- rapid enough to be measured precisely. Thermo- erosion and river incision are equal to rock uplift. dently from marine terrace stratigraphy. chronology indicates the time taken to exhume This assumption is diffi cult to test. Nevertheless, rocks by kilometers and cannot typically resolve both channel steepness index, a proxy for river Channel Steepness Index shorter-term patterns. Uplifted fl uvial strath ter- incision rate, and cosmogenic nuclide–deter- mined erosion rates have become widely used Bedrock river channel steepness index can †Present address: U.S. Geological Survey, 345 with at least qualitative success. What remains be used to infer relative differences in rock uplift Middlefi eld Road, Menlo Park, California 94025, USA; to be demonstrated is a quantitative test of both rates across a landscape, given uniform lithol- e-mail: [email protected]. channel steepness index and erosion rate as indi- ogy and climatic forcing. River incision, E, is 188 For permission to copy, contact [email protected] | |Volume © 2010 2 Geological | Number Society3 | LITHOSPHERE of America Downloaded from http://pubs.geoscienceworld.org/gsa/lithosphere/article-pdf/2/3/188/3044578/188.pdf by guest on 02 October 2021 Quantifying rock uplift rates using channel steepness and erosion rates | RESEARCH often cast as a function of basal shear stress, and 1999) and empirical (Howard and Kerby, 1983; ~80% of rock uplift, and in an orogen main- can be expressed as (Howard and Kerby, 1983; Tarboton et al., 1991; Snyder et al., 2000) argu- taining a constant elevation, erosion must equal Howard et al., 1994), ments, their ratio (θ) should be between 0.35 rock uplift (Molnar and England, 1990). In these and 0.6. cases, a measure of spatially averaged erosion E = KAmn S , (1) Channel steepness index can be obtained by rates over time scales of 103 to 105 yr should either surveying stream channels or by regres- closely correspond to the regionally averaged where S is local channel slope, A is the contrib- sion of local channel slopes and drainage areas rock uplift rate. uting drainage area that serves as a proxy for obtained from digital elevation models (e.g., Spatially averaged erosion rates can be esti- local discharge, K is a variable that incorpo- Wobus et al., 2006). Provided that K and n are mated using cosmogenic nuclides such as 10Be rates incision process–, substrate-, climate-, and uniform across the region of interest, then varia- in quartz-bearing alluvial sediment (Brown et hydrology-dependent variables (see Whipple, tions in ks among channels or channel segments al., 1995; Bierman and Steig, 1996; Granger et 2004), and m and n are positive constants that will track variations in uplift rate (Whipple and al., 1996). Beryllium-10 accumulates in quartz are functions of basin hydrology, channel geom- Tucker, 1999; Snyder et al., 2000). It is diffi cult near Earth’s surface proportional to its local etry, and specifi c incision process (Howard et to solve for rock uplift rates directly, because K production rate and inversely proportional to the al., 1994; Whipple and Tucker, 1999; Whipple is poorly constrained. For example, Stock and surface erosion rate. The cosmogenic nuclide et al., 2000a). Montgomery (1999) suggested that K may vary method averages erosion rates over the time The change in channel bed elevation at any over several orders of magnitude due to spatial required to erode a catchment by about one point along the longitudinal profi le with respect differences in rock properties, as well as due to secondary cosmic-ray penetration length, or to time, dz/dt, refl ects a competition between the frequency of discharge events signifi cant ~60 cm in rock of density 2.6 g/cm3 (Masarik the rates of rock uplift and channel incision with enough to initiate bedrock incision. Addition- and Reedy, 1995). In most landscapes, this is 3 5 respect to base level. This can be expressed as, ally, in order for ks to indicate relative changes in anywhere from 10 to 10 yr. rock uplift rates, the channel longitudinal profi le Several conditions must be met for cosmo- dz =−=− mn dt UEUKAS, (2) must be in steady state and refl ect the current genic nuclides to accurately indicate catch- climatic and tectonic conditions. Both U and K ment-averaged erosion rates. Quartz must be where U is the rock uplift rate. For a steady-state must be uniform along the entire channel length. distributed evenly throughout the catchment, landscape, where river incision rate is equal to Empirical support for a correlation between or else erosion rates will be biased to areas of the rock uplift rate, dz/dt = 0, and Equation 2 can channel steepness index and rock uplift rates higher quartz content. Sediment samples must be solved for equilibrium channel slope, S, at a is emerging from multiple landscapes around be representative of the entire watershed, rather given drainage area, A, the globe. In two regions of coastal Califor- than be dominated by a single landslide.