Rock uplift rates can be difficult 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 first field 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 indices 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.
Knowing the distribution of rock uplift rates across a landscape is important for identifying and understanding active tectonic structures, and for establishing the pace and pattern of mountain growth. Rock uplift rates can be determined geodetically over short (100–102 yr) time scales, or inferred from thermochronometers over much longer (106 yr) time scales. Over intermediate (103–105 yr) time scales, rock uplift rates can be inferred from uplifted geomorphic markers such as marine or fluvial terraces, provided that their ages can be determined. Each of these methods provides important constraints but also suffers from limitations. Geodetic measurements only incorporate a fraction of the seismic cycle and are limited to sites with existing surveys and where uplift rates are rapid enough to be measured precisely. Thermochronology indicates the time taken to exhume rocks by kilometers and cannot typically resolve shorter-term patterns. Uplifted fluvial strath terraces require the assumption that river incision is equilibrated with rock uplift, yet strath formation is often attributed to climatic fluctuations, making it difficult to distinguish climatic from tectonic causes of river incision (e.g., Pazzaglia and Gardner, 1993; Merritts et al., 1994; Hancock et al., 1999; Wegmann and Pazzaglia, 2002; Pan et al., 2003).
Alternative methods for inferring local- to regional-scale rock uplift rates, such as stream-channel morphometry and catchment-averaged erosion rates, have become increasingly used to measure relative differences in rock uplift rates across a region (Lague et al., 2000; Kirby and Whipple, 2001; Kobor and Roering, 2004; Ferrier et al., 2005; Wobus et al., 2005, 2006; Kirby et al., 2007). These methods are widely applicable; however, they implicitly assume a landscape in steady state or dynamic equilibrium, in which erosion and river incision are equal to rock uplift. This assumption is difficult to test. Nevertheless, both channel steepness index, a proxy for river incision rate, and cosmogenic nuclide–determined erosion rates have become widely used with at least qualitative success. What remains to be demonstrated is a quantitative test of both channel steepness index and erosion rate as indicators of rock uplift rates in a place where uplift rates are known independently.
In the following section, we briefly introduce the use of channel steepness index and erosion rate to determine rock uplift rates, with an emphasis on the assumptions and conditions necessary for their success. Channel steepness index is a measure of stream-channel gradient normalized to drainage area (see Wobus et al., 2006), and it has been shown to be directly proportional to rock uplift rates in a variety of landscapes (e.g., Snyder et al., 2000; Lague and Davy, 2003; Duvall et al., 2004). We measured erosion rates using cosmogenic 10Be in quartz, which is produced in proportion to the residence time of mineral grains in the uppermost few meters of Earth's surface. We then applied both of these methods to two different landscapes in Italy, where rock uplift rates are known independently from marine terrace stratigraphy.
Channel Steepness Index
Channel steepness index can be obtained by either surveying stream channels or by regression of local channel slopes and drainage areas obtained from digital elevation models (e.g., Wobus et al., 2006). Provided that K and n are uniform across the region of interest, then variations in ks among channels or channel segments will track variations in uplift rate (Whipple and Tucker, 1999; Snyder et al., 2000). It is difficult to solve for rock uplift rates directly, because K is poorly constrained. For example, Stock and Montgomery (1999) suggested that K may vary over several orders of magnitude due to spatial differences in rock properties, as well as due to the frequency of discharge events significant enough to initiate bedrock incision. Additionally, in order for ks to indicate relative changes in rock uplift rates, the channel longitudinal profile must be in steady state and reflect the current climatic and tectonic conditions. Both U and K must be uniform along the entire channel length.
Empirical support for a correlation between channel steepness index and rock uplift rates is emerging from multiple landscapes around the globe. In two regions of coastal California, Snyder et al. (2000), working in the King Range, and Duvall et al. (2004), working in the Santa Ynez Range, found that the steepness index values of small bedrock channels were higher at higher rock uplift rates as inferred from the elevations of marine terraces (Merritts and Bull, 1989; Metcalf, 1994; Gurrola et al., 1998; Trecker et al., 1998). Multiple studies have demonstrated a similar relationship in the Siwalik Hills of central Nepal (Kirby and Whipple, 2001; Lague and Davy, 2003; Wobus et al., 2006) and in the northern Apennines, Italy (Wilson et al., 2009), where systematic changes in steepness index have been correlated with rock uplift rate across a fault-bend fold (Lavé and Avouac, 2001) and a fault-propagation fold (Wilson et al., 2009), respectively.
It is commonly assumed that over tectono-geomorphic time scales (104–106 yr), landscapes approach a condition of dynamic equilibrium, in which erosion and river incision rates roughly balance rock uplift rates (e.g., Hack, 1960; Schumm and Lichty, 1965). A perfect match between rock uplift and erosion may never be achieved, because erosion rates will vary with climate change (e.g., Whipple et al., 1999). Nevertheless, isostasy alone dictates that in compensated orogens, erosion drives at least ∼80% of rock uplift, and in an orogen maintaining a constant elevation, erosion must equal rock uplift (Molnar and England, 1990). In these cases, a measure of spatially averaged erosion rates over time scales of 103 to 105 yr should closely correspond to the regionally averaged rock uplift rate.
Spatially averaged erosion rates can be estimated using cosmogenic nuclides such as 10Be in quartz-bearing alluvial sediment (Brown et al., 1995; Bierman and Steig, 1996; Granger et al., 1996). Beryllium-10 accumulates in quartz near Earth's surface proportional to its local production rate and inversely proportional to the surface erosion rate. The cosmogenic nuclide method averages erosion rates over the time required to erode a catchment by about one secondary cosmic-ray penetration length, or ∼60 cm in rock of density 2.6 g/cm3 (Masarik and Reedy, 1995). In most landscapes, this is anywhere from 103 to 105 yr.
Several conditions must be met for cosmogenic nuclides to accurately indicate catchment-averaged erosion rates. Quartz must be distributed evenly throughout the catchment, or else erosion rates will be biased to areas of higher quartz content. Sediment samples must be representative of the entire watershed, rather than be dominated by a single landslide. If erosion occurs primarily by landsliding, then the watershed should be large enough that a sediment sample is likely to contain grains from many different landslides (Niemi et al., 2005; Yanites et al., 2009). The catchment should not be glaciated, since glaciation may disrupt sediment transport paths, making stream sediment unrepresentative of the catchment as a whole (von Blanckenburg, 2005; Wittmann et al., 2007; Stock et al., 2009). Finally, erosion must occur at a nearly constant rate over the time taken to erode several secondary cosmic-ray penetration lengths (a few meters). If erosion rates change through time, cosmogenic nuclide concentrations will provide an average erosion rate (Schaller and Ehlers, 2006).
Empirical data from a variety of landscapes suggest a correlation between cosmogenic nuclide–determined erosion rates and rock uplift inferred by different methods. In both tectonically quiescent and tectonically active mountain ranges, cosmogenic nuclide–determined, millennial erosion rates are similar to longer-term (106 yr) exhumation rates as inferred from low-temperature thermochronometry (e.g., Kirchner et al., 2001; Matmon et al., 2003; Vance et al., 2003; Safran et al., 2005; Stock et al., 2009). Although rock exhumation does not necessarily equal rock uplift, these results are compelling when considered in the context of two recent studies in which cosmogenic nuclide erosion rates were compared directly to uplift rates determined by geodetic methods. Wittmann et al. (2007) and Champagnac et al. (2009) documented erosion rates in the Swiss central Alps that were locally similar to decadal-scale uplift rates determined by Global Positioning System (GPS) and re-leveling. In a similar study in the northern and central Apennines, Italy, erosion rates were similar to both short-term rock uplift determined by geodetic methods and long-term (105 yr) rock uplift rates determined from marine deposits and fluvial terrace stratigraphy (Cyr and Granger, 2008). On the other hand, Ferrier et al. (2005) found that two catchments on the northern California coast are eroding substantially slower than uplift rates and river incision rates determined from marine terraces, indicating an increasing mean elevation across the area or that erosion by landslides is under-represented. While these studies suggest that erosion rates may equal rock uplift rates, at least in some settings, a test of the sensitivity of erosion rates to a wide range of independently determined, long-term rock uplift rates has yet to be performed.
To test the accuracy and sensitivity of bedrock channel steepness index and catchment-averaged erosion rates as indicators of rock uplift rates, we chose two landscapes in Italy (Fig. 1) where rock uplift rates are known from marine and fluvial terrace stratigraphy. The Romagna Apennines, northern Italy, have relatively low and uniform rock uplift rates (Cyr and Granger, 2008; Picotti and Pazzaglia, 2008; Wegmann and Pazzaglia, 2009), whereas the Peloritani Mountains, northeastern Sicily, and the Aspromonte Massif, southern Italy, have higher and spatially variable rock uplift rates (Cosentino and Gliozzi, 1988; Miayuchi et al., 1994; Bordoni and Valensise, 1998; Ferranti et al., 2006).
The Romagna Apennines have developed as a result of collision between the Adriatic promontory of the African plate and the southern margin of the European plate. They emerged above sea level ca. 4 Ma after the northern Apennines accretionary wedge overrode thicker, more buoyant Adriatic continental crust (Castellarin et al., 1985; Ricci-Lucchi, 1986; Zattin et al., 2002; Bartolini, 2003; Picotti and Pazzaglia, 2008). Presently, the Romagna Apennines expose a Miocene-aged, uniform sequence of quartz-rich, shaly-arenaceous sandstone (Ricci Lucchi, 1986; Zattin et al., 2000; Feroni et al., 2001). River channels have either bedrock or mixed alluvial-bedrock cover (Simoni et al., 2003; Spagnolo and Pazzaglia, 2005), indicating that channel incision is likely detachment-limited. Hillslopes in the Romagna Apennines are mantled by thin (<1 m) soil (Simoni et al., 2003; Spagnolo and Pazzaglia, 2005) and hillslope erosion is dominated by shallow landsliding (Simoni et al., 2003; Del Maschio et al., 2005).
Short- and long-term rock uplift rates in the Romagna Apennines have been constrained by a recent geodetic re-leveling survey and by marine deposit and fluvial terrace stratigraphy. D'Anastasio et al. (2006) used geodetic re-leveling of a network of benchmarks in place since 1870 to measure rock uplift rates within major river valleys and along the crest of the northern and central Apennines. Relative to a benchmark at Genoa (sea level), mean rock uplift rates in the Reno River valley, at the northern edge of the Romagna Apennines, are 1.0 ± 0.2 mm/yr, and those in the Marecchia valley, at the southern edge of the Romagna Apennines, are 0.41 ± 0.26 mm/yr since 1870. The stated uncertainties reflect the standard deviation of all D'Anastasio et al.’s (2006) uplift rate determinations along a given re-leveling transect. We refer the interested reader to D'Anastasio et al. (2006) for a detailed description of how they handled uncertainties in each re-leveling measurement. Higher rock uplift rates in the Reno River valley likely reflect actively growing structures at the mountain front (Picotti and Pazzaglia, 2008). Longer-term (103–105 yr) rock uplift rates can be inferred from the ages and elevations of uplifted fluvial-deltaic/nearshore deposits exposed along the northern and central Apennines mountain front, and from fluvial strath terrace stratigraphy upstream of the mountain front. Paleomagnetic, biostratigraphic, and electron spin resonance (ESR) data constrain the age of the Sabbie Gialle, an uplifted fluvial-deltaic/nearshore sequence of sandstones and mudstones exposed along the mountain front (Marabini et al., 1995) to between 0.78 and 1.0 Ma (Colalongo et al., 1979; Gagnepain et al., 1996; Falguères, 2003). Assuming a deposition age of ca. 0.9 Ma and the modern elevation of the Sabbie Gialle (200–300 m; Marabini et al., 1995), the rock uplift rate of the Romagna Apennines front since 0.9 Ma is between 0.22 and 0.36 mm/yr. Beginning ∼3–5 km upstream of the mountain front, strath terraces in the Reno River valley (Picotti and Pazzaglia, 2008), on the northern edge of the Romagna Apennines, and in the Bidente and Musone River valleys (Wegmann and Pazzaglia, 2009), on the southern edge of the study area, both dated using radiocarbon, indicate uplift rates between 0.2 and 0.5 mm/yr between 900 and 140 ka in the area where 10Be samples were collected.
Peloritani Mountains and Aspromonte Massif
The Peloritani Mountains and Aspromonte Massif expose Mesozoic sedimentary cover rocks and late Paleozoic–aged quartzo-feldspathic, crystalline igneous, and metamorphic rocks (Amodio-Morelli et al., 1976; Catalano and D'Argenio, 1978; Bonardi et al., 1980; Nigro, 1996) that were exhumed to within a few kilometers of the surface (temperatures between 250 °C and 70 °C) between ca. 35 and 15 Ma due to a combination of accelerated surface erosion (Thomson, 1994, 1998) and localized late-orogenic extension (Platt and Compagnoni, 1990). They attained their geographic position and elevation due to a pulse of rapid rock uplift during the late Pliocene to early Pleistocene (between 1.0 and 0.8 Ma), likely in response to a change in the axis of backarc spreading in the Tyrrhenian Sea (Hippolyte et al., 1994) and/or delamination and rollback of the subducting Ionian slab (Faccenna et al., 2001, 2004). These mountain ranges support a deeply dissected, generally high-relief landscape that has small patches of low-relief, relict landscape preserved at the highest elevations, generally greater than ∼1800 m above sea level. These patches of relict landscape typically display deep weathering profiles, with saprolite between 5 and 10 m thick, mantled by organic soils (Ietto et al., 2007). The flanks of the Peloritani and Aspromonte are drained by small catchments characterized by steep channel and hillslope gradients (Le Pera and Sorriso-Valvo, 2000). Channels are floored by either bedrock or coarse sand– to cobble-sized sediment, but they are typically incising their beds and undercutting hillslopes (Le Pera and Sorriso-Valvo, 2000; Ietto et al., 2007). Hillslope erosion occurs primarily by shallow landsliding (Le Pera and Sorriso-Valvo, 2000; Ietto et al., 2007), although deep-seated bedrock landslides have been observed in the steepest upper reaches of some drainages during either heavy rainfall or large seismic events (Pellegrino and Prestininzi, 2007).
Long-term rock uplift rates in the Peloritani and Aspromonte are constrained by marine terraces, the most extensive of which have been attributed to the marine isotope stage (MIS) 5e highstand (ca. 125 ka) based on the presence of a unique and short-lived faunal assemblage, and radiometric and electron spin resonance ages (see Ferranti et al., 2006). Rock uplift rates vary spatially, with the highest rates of 1.63 mm/yr near the Messina Strait, decreasing to ∼0.6 mm/yr at the eastern end of our study area (Cosentino and Gliozzi, 1988; Miayuchi et al., 1994; Bordoni and Valensise, 1998; Ferranti et al., 2006).
Channel Morphologic Analysis
Channel longitudinal profiles were extracted from 3 arc-second (∼90 m) shuttle radar topography mission (SRTM) data and analyzed in MatLab using the Stream Profiler codes developed by Snyder et al. (2000) and Kirby and Whipple (2001), and detailed in Wobus et al. (2006) and Whipple et al. (2007). These codes are publicly available at http://geomorphtools.org. Channel longitudinal profiles derived from SRTM data contain several segments with zero slope, which are the result of nonphysical artifacts in the SRTM data and the ArcGIS pit-filling routine. These artifacts mean that some smoothing of the original SRTM data must be applied. Channel profiles were smoothed using a moving window average of ∼11 pixels (1000 m). This method effectively minimizes noise in the SRTM data while maintaining the form of the longitudinal profile. It has been shown that longitudinal profiles extracted from digital elevation data according to these methods are similar to profiles determined by digitizing topographic maps (e.g., Snyder et al., 2000) and from detailed surveys of channel elevations (e.g., Snyder et al., 2000; Kirby and Whipple, 2001). Local channel gradients were calculated over a constant vertical interval of 10 m from the smoothed elevation data (Snyder et al., 2000; Kirby and Whipple, 2001; Wobus et al., 2006), and linear regressions of these local channel slopes and their respective drainage areas in log-log space were used to determine the values of the channel concavity (θ, the slope of the regression) and channel steepness (ks, the y-intercept of the regression) index values (Eq. 3). A recent review by Wobus et al. (2006) provides a detailed description of data handling and processing procedures, as well as analytical techniques.
Slope-area relationships described by Equation 3 are only valid for detachment-limited, bedrock fluvial channels. The transition from unchannelized headwaters or debris flow–dominated channels to those characterized by fluvial processes has been identified from digital elevation data by many workers (e.g., Dietrich et al., 1993; Montgomery and Foufoula-Georgiou, 1993; Stock and Dietrich, 2003; Wobus et al., 2006), where the slope-area data of unchannelized or debris flow–dominated reaches have local slopes that do not vary as a function of increasing drainage area. This transition is well defined in all of the catchments examined in the Romagna Apennines and Peloritani and Aspromonte, and it typically occurs in drainage areas between 1 and 10 km2 (Fig. 2). It is likely that this is actually a gradual transition and that many upper reaches of our fluvial channels may periodically be better characterized by debris-flow processes (e.g., Stock and Dietrich, 1998); however, differences in channel longitudinal profile form along the observed spatial gradient in rock uplift rate are not likely to significantly alter these analyses (Kirby et al., 2007). Regressions of slope-area data were not extended beyond the downstream transition to alluvial-fan and coastal-plain deposits in the lower reaches of Romagna Apennines and Peloritani-Aspromonte rivers, respectively.
Direct comparisons of the ks values of one channel to another can be problematic because of the autocorrelation between ks and θ (e.g., Sklar and Dietrich, 1998). In order to compare the channel steepness index values of drainages that have different concavities, a normalized channel steepness index, ksn, is calculated using a reference concavity, θref (e.g., Snyder et al., 2000; Kirby et al., 2003; Wobus et al., 2006). Typically, θref is taken as the mean of observed θ values in a given field area; however, relative differences in ks should be maintained regardless of the specific choice of θref (Wobus et al., 2006). We calculated ksn values using θref = 0.45. While this θref is different from the average concavities for the Romagna Apennines and Peloritani-Aspromonte (Table 1), it allows immediate direct comparisons to ksn values determined in other studies (e.g., Snyder et al., 2003; Duvall et al., 2004; Wobus et al., 2006; Kirby et al., 2007; Ouimet et al., 2009) and does not change the results of our analysis (Table DR2; Fig. DR4).1
We calculated catchment-averaged erosion rates from cosmogenic 10Be in quartz-bearing stream sediments (Brown et al., 1995; Bierman and Steig, 1996; Granger et al., 1996). Samples for 10Be analysis were collected from either the active channels or overbank deposits of both main-stem and tributary channels of three catchments in the Romagna and five catchments in the Peloritani and Aspromonte. Samples were collected from upstream of the mountain front in the Romagna Apennines, whereas in the Peloritani and Aspromonte, they were collected upstream of the observed downstream transition to completely alluviated channels. In addition to minimizing the potential for older fluvial sediments to affect cosmogenic 10Be concentrations, this sampling strategy ensures that catchment-averaged erosion rates are being compared over the channel segments where ksn values were calculated. Catchments upstream of sampling locations drain either a single, lithologically uniform formation (Romagna Apennines) or lithology (Peloritani and Aspromonte), which should minimize the effects of nonuniform quartz concentrations on our calculated erosion rates. In both regions, hillslope erosion is dominated by shallow landsliding; however, the sampled catchments are sufficiently large that landslide-derived sediment should be well mixed and representative of long-term catchment-wide erosion rates (Niemi et al., 2005; Yanites et al., 2009). Hillslope erosion rates calculated from the 10Be concentrations of sediment from some catchments draining the Aspromonte Massif could potentially be biased by quartz enrichment in the soils and saprolite present on the relict landscape (Granger et al., 2001; Riebe et al., 2001). However, these areas are small and are not sampled by the selected drainage basins. The procedures used to physically separate quartz and chemically isolate 10Be are detailed in Appendix DR1 (see footnote 1).
Normalized channel steepness index values were determined for seven channels in the Romagna Apennines, and five channels in the Peloritani and Aspromonte. The results of the channel morphologic analyses are presented in Table 1, Figure 3, and Figures DR1–DR3 (see footnote 1). Normalized channel steepness index values in the Romagna Apennines fall within a narrow range between 46.0 ± 1.0 and 63.7 ± 1.5 m0.9, with a regional mean of 57.5 ± 2.4 (SE) m0.9. Channel steepness values of the lower-elevation channel segments are slightly higher than higher-elevation segments, although the observed variability is not different from similar studies where rock uplift rates are uniform (e.g., Snyder et al., 2000; Duvall et al., 2004). In the Peloritani and Aspromonte, ksn values are all higher than those in the Romagna Apennines, ranging from 75.3 ± 1.0 to 108.4 ± 5.4 m0.9, with a regional mean of 97.6 ± 14.5 (SE) m0.9, and increase in proportion to rock uplift rates (Figs. 3 and 4).
Millennial-scale, catchment-averaged hillslope erosion rates determined from the 10Be concentrations of stream sediments from the Romagna Apennines and Peloritani-Aspromonte are presented in Table 2 and Figures 3 and 4. Erosion rates in the Romagna Apennines range from 0.36 ± 0.04 to 0.72 ± 0.14 mm/yr and have a regional mean of 0.46 ± 0.04 (SE) mm/yr. These erosion rates are slightly higher than those reported in Cyr and Granger (2008) because of the muogenic contribution to 10Be concentrations, which was not accounted for in their calculations. Catchment-averaged erosion rates in the Romagna Apennines do not show any pattern with respect to elevation within watersheds or location within the mountain range. Two samples collected from the same location (Table 2, samples 3A and 3B), but at different times of the year, yield erosion rates of 0.36 ± 0.04 mm/yr and 0.57 ± 0.12 mm/yr. This degree of variability is not unexpected with cosmogenic nuclide–based erosion rates, particularly in catchments where hillslope erosion is dominated by mass wasting and where sediments may not be fully mixed (e.g., Granger et al., 1996; Niemi et al., 2005; Yanites et al., 2009). Erosion rates in the Peloritani-Aspromonte are higher than those in the Romagna Apennines and have greater variability, ranging from 0.62 ± 0.06 to 2.01 ± 0.27 mm/yr with a regional mean of 1.21 ± 0.23 (SE) mm/yr. Erosion rates are higher in catchments closest to the Messina Strait, where rock uplift rates are highest (Fig. 3).
Both the ksn values of stream channels and 10Be hillslope erosion rates in the Romagna Apennines and Peloritani-Aspromonte increase as a function of increasing rock uplift rates (Fig. 4). The correlation of both ksn values and 10Be erosion rates with rock uplift rates (1) validates our assumption that the Romagna Apennines and Peloritani-Aspromonte landscapes approach steady state, and (2) indicates that both ksn indices and catchment-averaged erosion rates might be useful for quantifying rock uplift rates. However, while both ksn values and catchment-averaged erosion rates increase with increasing rock uplift rates, the nature of these relationships warrants further discussion.
Channel Steepness Values and Rock Uplift Rates
Normalized channel steepness index values in the Romagna Apennines and Peloritani-Aspromonte are compared to long-term rock uplift rates in Figure 4A. In general, ksn values in the Romagna Apennines, which have been uplifting at 0.2–0.5 mm/yr since ca. 0.9 Ma (Picotti and Pazzaglia, 2008; Wegmann and Pazzaglia, 2009), are lower than ksn values in the Peloritani-Aspromonte, where rock uplift rates are between 0.69 and 1.63 mm/yr since at least 125 ka (Cosentino and Gliozzi, 1988; Miayuchi et al., 1994; Bordoni and Valensise, 1998; Ferranti et al., 2006). This relationship is consistent with both theoretical predictions (e.g., Whipple and Tucker, 1999), as well as previous field studies (e.g., Snyder et al., 2000; Kirby and Whipple, 2001; Lague and Davy, 2003; Duvall et al., 2004; Wobus et al., 2006), which all document higher ksn values at increasingly rapid rock uplift rates.
In the Romagna Apennines (46.0 ± 1.0 ≤ ksn ≤ 63.7 ± 1.5 m0.9), ksn values are generally higher in downstream channel reaches closest to the mountain front. Systematic downstream increases in ksn values could be the result of a variety of factors (e.g., Whipple, 2004), including (1) downstream increases in grain size, bed load, and/or channel width, (2) orographically enhanced precipitation, or (3) higher rock uplift rates, U, in the downstream portions of the analyzed channels. In the case of either downstream increases in sediment caliber or channel width, or of orographically enhanced precipitation at higher catchment elevations, ksn values would decrease downstream, whereas if U increases downstream, ksn values should also increase (e.g., Whipple and Tucker, 1999; Snyder et al., 2000; Kirby and Whipple, 2001; Lague and Davy, 2003; Duvall et al., 2004; Whipple, 2004; Wobus et al., 2006). Although it is likely that the Romagna Apennines approach steady state (Cyr and Granger, 2008), fluvial terrace stratigraphy elsewhere in the northern and central Apennines indicates that rock uplift rates are higher at the mountain front and have accelerated since ca. 140 ka due to active fold growth (Picotti and Pazzaglia, 2008; Wegmann and Pazzaglia, 2009). While variations in bed state or channel width cannot be ruled out as a possible cause for the observed variation in ksn across the Romagna Apennines and Peloritani-Aspromonte, it is more likely that the observed ksn values reflect actively growing structures at the Apennines mountain front (e.g., Picotti and Pazzaglia, 2008; Wegmann and Pazzaglia, 2009). In the Peloritani-Aspromonte region, ksn values increase as a function of rock uplift rate (Figs. 3 and 4; Tables 1 and 2). This is consistent with both the relationship between U and ksn predicted by Equation 3, as well as empirical studies conducted in landscapes where rock uplift rates are known.
It is also possible that the patterns of ksn values observed in both landscapes are the result of the chosen value of θref. Normalized channel steepness index values calculated using a range of θref between 0.2 and 0.7 are presented in Table DR2 and Figure DR4 (see footnote 1). Although the absolute values of ksn vary over several orders of magnitude depending on the selected value of θref (Table DR2 [see footnote 1]), the relationship between ksn and rock uplift rates is maintained (Fig. DR4 [see footnote 1]).
Regardless of the chosen value of θref, our data indicate that the ksn values of detachment-limited stream channels in the Romagna Apennines and Peloritani-Aspromonte do increase as a function of increasing rock uplift rates, which is consistent with both theoretical predictions and field observations. It also appears that the relationship between ksn and rock uplift rate is nonlinear, with ksn reaching a threshold at rock uplift rates greater than ∼1 mm/yr. The small number of our ksn data points makes a quantitative relationship between ksn and rock uplift rates in the Romagna Apennines and Peloritani and Aspromonte Massif difficult to define. However, if we assume a linear relationship between ksn values and rock uplift rate, the threshold ksn required to initiate channel incision is 43.15 ± 12.20 m0.9 (assuming θref = 0.45).
Erosion Rates and Rock Uplift Rates
Erosion rate data from both the Romagna Apennines and Peloritani-Aspromonte suggest a correlation with local rock uplift rates as determined from fluvial and marine terrace stratigraphy (Figs. 3 and 4; Table 2). In both of these landscapes, catchment-averaged hillslope erosion rates are similar to local rock uplift rates to within a factor of ∼2. This variability might be related to either (1) the stochastic nature of hillslope landsliding and insufficient mixing of landslide-derived sediment in the sampled stream channels (e.g., Granger et al., 1996; Niemi et al., 2005; Yanites et al., 2009), and/or (2) the observed spatial pattern of Quaternary rock uplift rates. This variability makes it unlikely that any one erosion rate from a single drainage basin will accurately quantify millennial-scale rock uplift rates. However, in catchments where hillslope erosion is dominated by shallow landsliding, determinations of erosion rates from 10Be concentrations of sediment samples collected from multiple non-nested catchments should converge on the long-term average concentration of 10Be and reflect true millennial-scale catchment-averaged erosion rates (Niemi et al., 2005; Yanites et al., 2009).
In this case, the data can be considered as two groups of catchments representing landscapes where rock uplift rates are relatively slow (the Romagna) and relatively rapid (the Peloritani-Aspromonte). If the data are treated in this way, the regional mean hillslope erosion rates are indistinguishable from the regional mean rock uplift rates within one standard error of the mean (Fig. 4). This result is perhaps not surprising, given the predictions of various conceptual and numerical landscape evolution models that have described a similar functional relationship between hillslope erosion rates and rock uplift rates, and it demonstrates the potential for 10Be-determined, catchment-averaged hillslope erosion rates to be used as a proxy for millennial-scale rock uplift rates.
Steady-State Assumption in the Romagna Apennines and Peloritani-Aspromonte
Our use of ksn values and 10Be catchment-averaged erosion rates to quantify absolute rock uplift rates depends on the underlying assumption that the Romagna Apennines and Peloritani-Aspromonte landscapes approach steady state. Some studies have demonstrated that a variety of landscapes around the world may approach steady-state conditions by demonstrating that erosion rates are similar to long-term exhumation rates (e.g., Matmon et al., 2003; Vance et al., 2003; Safran et al., 2005), or that one or both ksn values and 10Be erosion rates are sensitive to spatially variable tectonic forcing (e.g., Wobus et al., 2005, 2006). However, it has also been suggested that steady-state conditions may never be reached, since the adjustment time scales of hillslope and channel systems may be longer than either the climatic (e.g., Zhang et al., 2001) or tectonic fluctuations to which they respond.
Despite the argument that steady state may be difficult to achieve and/or maintain over geologic time scales (>104 yr), there is evidence that some of our field areas do approach steady state. In a comparison of 10Be erosion and paleoerosion rates to long- and short-term erosion, channel incision, and rock uplift rates, Cyr and Granger (2008) demonstrated that the Romagna Apennines approach steady state. In this case, erosion and paleoerosion rates were similar to (1) short-term (decadal) sediment yield determined from reservoir sedimentation, (2) long-term (106 yr) sediment yield determined from basin sedimentation, (3) fluvial incision rates determined from terrace stratigraphy (over 105 yr), (4) mountain uplift rates from geodetic re-leveling (over 102 yr), (5) coastal uplift rates from uplifted shorelines (over 105 yr), and (6) long-term (106 yr) exhumation rates from thermochronometry, indicating steady-state conditions in the Romagna Apennines since at least 0.9 Ma.
There are no similar data indicating that the Peloritani-Aspromonte approach steady state, besides making the qualitative argument that the channel morphology exhibits no clear sign of disequilibrium over the examined portions of channel longitudinal profiles. Regardless, the fact that both ksn values and catchment-averaged erosion vary in proportion to rock uplift rates in the Peloritani-Aspromonte, as well as in the Romagna Apennines, both tests and confirms our initial steady-state assumption. This sort of integrated approach, combining both ksn analysis and 10Be erosion rate determinations, may be useful for identifying possible steady-state conditions in landscapes where the degree of steady state is unknown.
Comparing Channel Steepness and Erosion Rates
Individually, both calculated ksn values and 10Be-determined hillslope erosion rates have limitations as tools for describing absolute rock uplift rates. Determinations of the ksn values of channels draining the Romagna Apennines and Peloritani-Aspromonte, while broadly indicative of relative differences in rock uplift rates across a given area, do not appear to increase indefinitely with increasing rock uplift rates. This potentially limits the utility of ksn for quantifying spatial variations in rock uplift rates in rapidly uplifting landscapes. Catchment-averaged hillslope erosion rates, on the other hand, are locally similar to long-term (105 yr) rock uplift rates in both relatively slowly and relatively rapidly uplifting landscapes. Erosion rates appear to increase roughly linearly with rock uplift rates in all cases. However, based on repeat erosion rate determinations at one sampling location (Table 2), any single erosion rate measurement is different from the local rock uplift rate by up to a factor of ∼2, making it unlikely that any single determination of an erosion rate in an individual catchment can be used to reliably quantify rock uplift rate. The combination of detachment-limited channel profile analysis and determinations of catchment-averaged hillslope erosion rates using 10Be might be a more effective way to (1) establish that a landscape approaches steady state with tectonically driven rock uplift; (2) identify landscapes where rock uplift rates might be similar; and (3) quantify rock uplift rates by using the erosion rates of several catchments across a region and averaging those rates together.
Lithologically uniform drainage basins that approach steady state should exhibit uniform ksn values and catchment-averaged erosion rates. Catchments where all segments of the drainage network have similar ksn values suggest spatially uniform K and U (Eq. 1). In these cases, channel incision rates should scale with rock uplift rates, and an average of 10Be erosion rates in these catchments should equal the regional average rock uplift rate. The distributions of ksn values and catchment-averaged hillslope erosion rates might also be useful for distinguishing landscapes with different tectonic forcing. In addition to determining whether channel incision rates approach steady state with rock uplift rates, channel steepness analyses could be used to identify where changes in tectonic forcing might occur. Catchments with internally similar ksn values in one landscape that are different from those in another landscape, such as those between the Romagna Apennines and Peloritani-Aspromonte, suggest that the two drainage networks have equilibrated to different sets of K and/or U values. Assuming steady-state conditions, the spatial pattern of ksn values could be used to inform cosmogenic nuclide sampling strategies with the goal of using the average erosion rates of several catchments across a region to quantify regional average rock uplift rates.
The Romagna Apennines, northern Italy, and the Peloritani Mountains and Aspromonte Massif, southern Italy, are landscapes that have broadly similar climate and lithologic resistance to erosion, but that record markedly different rock uplift rates over at least the past 125 k.y., as indicated by fluvial and marine terrace stratigraphy. We calculated normalized channel steepness index (ksn) values and cosmogenic 10Be erosion rates in eight catchments where rock uplift rates inferred from fluvial and marine terrace stratigraphy increase from 0.40 ± 0.15 mm/yr to 1.35 ± 0.03 mm/yr. We find that:
(1) ksn values increase with rock uplift rates up to ∼1 mm/yr, above which they appear to reach a threshold value; and
(2) 10Be erosion rates increase linearly with increasing rock uplift rates. Based on repeat measurements, individual determinations of erosion rate are only similar to local rock uplift rates to within a factor of ∼2. However, regional average erosion rates in each of our landscapes are indistinguishable from the regional mean rock uplift rates.
Collectively, our ksn and erosion rate data indicate that these methods can be combined as a tool to quantify rock uplift rates. Channel steepness index calculations could be used to inform field mapping in order to assess the effects of changes in channel width, bed cover, rock resistance to erosion, etc., and sediment sampling for the determination of erosion rates using cosmogenic nuclides. This would allow the determination of regionally (≥100 km2) averaged rock uplift rates using catchment-averaged erosion rates by maximizing the effects of tectonically driven rock uplift rates on the sampled catchments, while simultaneously minimizing the complications inherent in both methods.
This project was supported by National Science Foundation Continental Dynamics Program grant EAR-0208169 (RETREAT), PRIME Laboratory at Purdue University, and the U.S. Geological Survey Mendenhall Postdoctoral Fellowship program. This manuscript benefited from comments by Thomas Hanks, Stephen DeLong, reviews by Brian Yanites and an anonymous reviewer, and editorial guidance from Jon Pelletier.