The formation of inner gorges cut into bedrock has been explained as relief rejuvenation by fluvial incision in response to rapid base level drop, repeated glaciations, frequent pore pressure–driven landsliding focused at hillslope toes, or catastrophic outburst flows from natural dam failures. Prominent inner gorges occur in soft Mesozoic Bündner schist and lower Tertiary flysch units of the formerly glaciated Alpenrhein catchment, eastern Swiss Alps. Their channel and hillslope morphologies differ from basins characterized by strong glacial or landslide imprints, while formally resembling the theoretically predicted transient response of detachment-limited bedrock rivers to rapid base level fall by headward knickpoint migration. Assuming a postglacial onset of fluvial bedrock incision into a Last Glacial Maximum surface in response to base level drop induced by downwasting of trunk valley glaciers requires downcutting rates E > 20 mm yr−1 and requires hillslopes to adjust by frequent landsliding toward development of a threshold state. We test this scenario using data on surface uplift, geomorphometry, geomorphic hillslope coupling, and probabilistic slope stability models. We find that adjustment of inner gorge walls through landsliding is mainly strength limited and structurally controlled, and threshold conditions are restricted to the lower 25% of local hillslope relief. Mass movement processes on upper hillslopes remain largely decoupled from channel incision despite inferred postglacial specific sediment yields of 104 m3 km−2 yr−1 from the studied basins. Conversely, several constraints imposed by fluvial bedrock detachment, postglacial sediment yields, and bedrock landsliding argue for a pre-Holocene origin for at least some of the inner gorges in the area. This implies partial protection of fluvial gorge topography by subglacial sediment fill during the last (Würm) extensive glaciation and implies that glaciers were insufficient to fully eradicate fluvially sculpted bedrock topography. This leads us to conclude that lithology and major climate oscillations should be considered as further alternative controls on inner gorge formation.
 Inner gorges are landform elements that form at the interface between hillslopes and river channels. They are characterized by a convex break in hillslope gradient, and lined, often symmetrically, by hillslope toes significantly steeper than those of upper valley flanks [Kelsey, 1988]. This distinctive “valley-in-valley” topography [Baillie and Norbu, 2004] may occur in bedrock or debris slopes alike. There are at least four processes that favor the formation of inner gorges: (1) relief rejuvenation by fluvial incision in response to rapid base level drop [Ahnert, 1988; Densmore et al., 1997; Bonnet et al., 2001; Stock et al., 2005]; (2) repeated glaciations of differing erosion potential [Mitchell et al., 1999]; (3) frequent pore pressure-driven landsliding that preferentially undermines hillslope toes [Kelsey, 1988; Densmore and Hovius, 2000]; and (4) catastrophic and highly erosive outburst flows from natural dam failures [Knudsen and Marren, 2002; Rudoy, 2002]. Despite these different mechanisms of formation and their possible superposition, inner gorges are commonly interpreted as transient landforms of relief rejuvenation [e.g., Whipple et al., 2000], which may be eventually be removed by slope-clearing landslides [Densmore et al., 1997]. The age of an inner gorge may thus record a marked change in process rates of both hillslope and channel systems [Stock et al., 2005]. However, the rates of geomorphic coupling, simply regarded here as the exchange of mass and energy, between hillslopes and channels, are rarely quantified [Schlunegger et al., 2002], although recent modeling advances have been made for soil-mantled landscapes [Mudd and Furbish, 2005]. Persisting research gaps for bedrock-dominated landscapes derive from the many unknowns of how sudden rate changes in bedrock channel incision are communicated to hillslope systems. In tectonically active mountain belts, for instance, frequent landsliding on threshold hillslopes is one of the purported means of relief adjustment to fluvial bedrock incision [Burbank et al., 1996]. However, the preservation of continuous inner gorges, slot canyons, or high-level bedrock strath terraces in these areas is seemingly at odds with the notion of hillslope gradients being maintained by, albeit spatially variable, threshold landsliding. This is because, although these landforms attest to efficient fluvial incision, they also document the limited response of hillslopes to this process [Tinkler and Wohl, 1998]. Obviously, rock mass properties, which can be subsumed as strength and incision limits to hillslope stability and relief [Schmidt and Montgomery, 1995], become important controls on dictating the rates of local hillslope relief adjustment to channel processes.
 Impressive inner gorges occur in many parts of the European Alps, where they, beheld intuitively, resemble landforms of both rejuvenation and high process activity, though little is known about their ages or the geomorphic processes that formed them. This motivates an enquiry on the underlying causes of and controls on their formation, which we wish to elucidate in a study area of the eastern Swiss Alps as a simple field test of previously proposed models [e.g., Kelsey, 1988; Densmore et al., 1997]. More specifically, our objective is to use the combined results from field observations, geomorphometry, surface uplift data, and probabilistic slope stability modeling to derive first-order quantitative constraints on the dominant processes, rates, and timing of gorge incision with respect to glacial-interglacial cycles during the Quaternary. In the first part of this paper, we present results from a morphometric analysis that we augment with geomorphic field evidence to bracket the time of inception and rates of inner gorge incision in the study area. In the second part, we use a simplistic slope stability model to probabilistically test for the likelihood of threshold-landsliding and lithological controls of inner gorge cutting. We build the discussion of our results around two contrasting scenarios, which argue for either a postglacial or a pre-Holocene onset of gorge cutting, and conclude with several implications of fluvial relief inheritance and rejuvenation for models of inner gorge formation.
2. Study Area
 Major continuous bedrock gorges occupy >10% of the channel network of the Alpenrhein catchment in eastern Switzerland, which drains 4470 km2 above the town of Sargans (Figure 1a). The exact proportion is likely to be much higher, but difficult to assess, partly because many gorges were infilled by reservoirs for hydropower generation. The regional geology comprises a broad range of rock types with marked differences in erodibility [Kühni and Pfiffner, 2001]. The northern parts are made up of crystalline basement covered by metasediments of the European continental plate, which are overlain by a stack of Penninic and Austroalpine nappes that partly originated from the African continental plate. The Penninic nappes (Figure 1b) comprise high-grade basement rocks and a medium- to low-grade metasedimentary cover, encompassing a suite of metacarbonates and highly erodible shales and arenites several thousands of meters thick, including the Bündner (calc-)schists and flysch units [Kühni and Pfiffner, 2001]. In the southeast, the Austroalpine units are composed of a sequence of basement rocks covered by Mesozoic carbonates.
 The Alpenrhein was covered by an extensive ice stream network as part of the 1.6 × 104 km2 Rhine-Linth glacier during the last (=Würm) glaciation, which in trunk valleys has caused glacial overdeepening roughly down to sea level [Persaud and Pfiffner, 2004]. Only the highest peaks remained as nunatakker. Locally, hillslopes are mantled by glacial tills several tens of meters thick, and many of the major valley trains host postglacial sediment fills several hundreds of meters thick [Hinderer, 2001]. Impressive inner gorges with local relief of >100 m occur in many trunk and tributary basins (Figures 2 and 3). They predominantly occur in soft Cretaceous Bündner schist and lower Tertiary flysch lithology. The Bündner schists mainly comprise calc-schists of highly varying degrees of metamorphism. They are interbedded with shales and quartzites, and lithologically similar to the younger flysch deposits [Bousquet et al., 1998]. Both rock types are strongly folded with inclusions of sheared and broken shale and sandstone layers containing variable amounts of swelling clay minerals, and weather rapidly to produce platy to flaky fragments [Huder, 1976], which in places can readily be dislodged from outcrops by hand. Gorges of comparable size occur in other calcareous and dolomitic rocks, while they are less frequent and less prominently incised in harder crystalline rocks of, e.g., the Silvretta nappe (Figure 1b). The dendritic network and sinuosity of the gorges excludes any preferential incision along tectonic fault zones or other lineaments of low rock mass strength. Contemporary rates of surface uplift measured by geodetic surveys of first-order leveling benchmarks relative to the benchmark at Aarburg between ∼1905 and 1990 contain effects of postcollisional exhumation and isostatic rebound, and amount to Uh = 0.8–1.4 mm yr−1 [Kahle et al., 1997] (Figure 1c). The study area has also experienced some of the highest exhumation rates in the Alps in the recent geological past as indicated by apatite fission track ages <5 Ma [Schlunegger and Willett, 1999].
 To quantify our initial qualitative observations of differing drainage basin response in general, and the geomorphic properties of basins featuring inner gorges in particular, we conducted a morphometric analysis of 28 basins with catchment areas 3 < A < 20 km2 (Figure 1 and Table 1). We focused on small tributary basins to capture bedrock channel morphologies on the assumption of short response times to tectonic or climatic forcing or other forms of intrinsic transience, such as significant changes to sediment flux [Schlunegger et al., 2002]. At least three general types of drainage basin morphologies can be distinguished by visual inspection: (1) glacial trough basins featuring characteristic u-shaped cross sections, mostly deglaciated cirques, patchy moraine cover, rock knobs and steps, hanging valley outlets drained by minor gorges or waterfalls, and generally little postglacial fluvial modification; (2) basins perched on top of large, deep-seated, and slow-moving landslides of the sackung type, involving the gradual collapse of valley flanks on a 101-km2 scale; and (3) basins that show typical glacially smoothed features above steep and deeply (>100 m) incised v-shaped inner bedrock gorges that flank most of the channels (Figure 2). The concurrence of these basin-scale morphological differences clearly points to transient landscape conditions with respect to geological time.
Table 1. Hillslope and Channel Metrics Stratified by Basin Type, Alpenrhein Catchment, Swiss Alpsa
Tilde means knickpoint at major bedrock-sediment contact.
0.08 ± 0.004
−0.63 ± 0.09
0.05 ± 0.01
0.44 ± 0.05
0.08 ± 0.01
−0.77 ± 0.10
cas, ph, bt
0.18 ± 0.02
−1.92 ± 0.19
0.11 ± 0.01
−0.47 ± 0.06
0.09 ± 0.004
0.54 ± 0.06
0.07 ± 0.01
0.39 ± 0.05
0.12 ± 0.01
−0.89 ± 0.10
0.15 ± 0.02
−0.92 ± 0.11
0.09 ± 0.01
0.33 ± 0.03
0.07 ± 0.01
0.73 ± 0.09
0.03 ± 0.003
0.50 ± 0.04
0.01 ± 0.004
0.58 ± 0.04
0.06 ± 0.01
0.56 ± 0.03
0.05 ± 0.01
0.59 ± 0.04
0.03 ± 0.01
0.43 ± 0.04
ca, cas, ph
0.03 ± 0.01
0.52 ± 0.06
0.07 ± 0.01
0.45 ± 0.05
ca, cas, ph
0.05 ± 0.005
0.40 ± 0.02
0.04 ± 0.004
0.44 ± 0.04
0.05 ± 0.01
−0.57 ± 0.09
0.08 ± 0.01
−0.47 ± 0.07
ls, ca, cas, ph
0.04 ± 0.004
0.40 ± 0.04
0.07 ± 0.01
−0.86 ± 0.09
ls, cs, ph
0.03 ± 0.004
0.28 ± 0.04
cas, ph, ca
0.04 ± 0.004
0.27 ± 0.04
0.08 ± 0.01
−0.88 ± 0.11
ls, cs, ph
0.07 ± 0.01
−0.46 ± 0.05
ls, cs, ph
Mean of 1–28
9.8 ± 4.7
1.7 ± 0.2
0.07 ± 0.04
0.36 ± 0.11
0.81 ± 0.18
−0.04 ± 0.68
0.53 ± 0.18
0.24 ± 0.27
0.33 ± 0.36
Mean of 12–20
11.2 ± 5.1
1.8 ± 0.2
0.04 ± 0.02
0.46 ± 0.06
0.72 ± 0.28
0.50 ± 0.07
0.45 ± 0.08
0.50 ± 0.31
0.22 ± 0.13
Mean of 1–11; 21–28
9.1 ± 4.5
1.6 ± 0.2
0.08 ± 0.04
0.32 ± 0.09
0.85 ± 0.01
–0.29 ± 0.70
0.57 ± 0.21
0.12 ± 0.12
0.39 ± 0.43
3. Methods and Assumptions
 We used a 25-m DEM to compute a range of hillslope and channel metrics that are commonly employed to infer process relationships in tectonic geomorphology. From slope area regression we obtained the indices of concavity θc and steepness kc for bedrock channels [Whipple and Tucker, 2002]. We used kc, fixed for a concavity θc′ = 0.45, as a proxy for specific stream power or, more generally, fluvial erosion potential for comparison between channels of differing θc [e.g., Safran et al., 2005; Korup, 2006]. We adapted this approach for computing hillslope steepness kh corrected for the effects of catchment position, for all cells with contributing areas smaller than the channelization threshold Ach determined from high-resolution orthophotos and fieldwork, and using the regional mean of θh′ = 0.07 as a reference. To characterize the relationship between channel and hillslope morphology for each basin, we defined a dimensionless concavity ratio,
We expect high values of Rθ to indicate concave channels bounded by rectilinear hillslopes, whereas low or negative values should characterize convex channels with more concave hillslopes.
 To further identify the inner gorges at the basin scale, we adapted the method of relating local hillslope gradient Sh to normalized hillslope position xs [Densmore and Hovius, 2000],
where xd and xu are the distances from each cell to the local channel and hillcrest, respectively. For bins of width Δxs = 0.05, we calculated the probability density
where Sa is an arbitrary slope gradient, for which we appointed values of 0.47, 0.58, 0.70, and 1, i.e., 25°, 30°, 35°, 40°, and 45°, respectively. Here, we use the relative deviation from the mean 〈P(a)〉,
to assess trends in the probability of encountering steep gradients at a given hillslope position.
 The extent of inner gorges was mapped for each basin (Figure 1), and complemented by measurements from other basins not studied in further detail; the heights and mean slope gradients of the gorge walls, Hg and 〈S〉, were manually recorded at each intersection of the 20-m contours with the valley bottom, and complemented by local measurements of A and kc. We did not sample at tributary junctions or where the upper edges of the gorges were found to be poorly defined. In order to quantify the volume of material eroded from the inner gorges, Ve, we used a tension spline (TS) interpolation between elevation points recorded at their upper edges. The resulting artificial surfaces do not necessarily represent any actual past geomorphic surfaces. By subtracting the present-day topography from these model surfaces, however, we obtain first-order estimates of Ve for each basin, assuming that none of the gorges are structural in origin.
4. Morphometric Characteristics of Inner Gorges
4.1. Basin Types
 The distribution of eight basin-averaged terrain variables stratified by basin type show different characteristic ranges. We find that glacial basins have the highest mean basin elevation 〈E〉 (Figure 4), whereas the basins perched on top of large landslides have the lowest relief, as their channels often drain only the lower parts of hillslopes. Basins with inner gorges have the lowest values of the hypsometric integral, but are also have the steepest slopes on average. Their hillslopes tend to be the most rectilinear (mean θh = 0.04), and stand out against the more concave glacial basins (Figure 4). Basins with inner gorges also have the highest values of Rθ = 12.9, whereas basins without inner gorges are characterized by a negative Rθ. On average, channels appear to be steepest in glacial basins, although much of this effect needs to be attributed to convex long profiles with a large degree of glacial landform inheritance. In summary, however, we find that these differences in the ranges of terrain variables formally support our initial qualitative distinction between three basin types.
4.2. Inner Gorge Channels
 The inner gorges in the study basins are characterized by steep (〈Sc〉 > 0.16) and deeply incised (Hg > 50 m) channels flanked by rectilinear and occasionally subvertical bedrock cliffs (Figures 2 and 5 and Table 2). In the basins studied, inner gorges extend over ∼70% of the lower trunk channels (Figure 3a), and occupy the lower 25% of local hillslope relief, and 10% of total basin relief H, on average (Table 2). Some of the channel beds have an alluvial cover, especially in reaches with torrent control measures such as sediment retention basins, yet we find from high-resolution orthophotos that larger patches of valley floor sediment are absent. Long profiles show distinctive channel knickpoints, some of which form waterfalls, while channels above most knickpoints are bounded by more gentle banks and hillslopes. These bedrock knickpoints are only rarely related to major lithologic contacts (Figure 6 and Table 1). Most inner gorges extend up into major tributaries, locally via hanging outlets or bedrock slots of tributary ravines (Figure 2d). In some headwaters, the gorges are linked to active dendritic gully networks. The upper edges of the inner gorges roughly mark concave long profiles similar to those of the modern river profiles (Figure 6). The profile of the upper edge of the inner gorge and the profile of the modern river appear to join at their upstream ends at major channel knickpoints, marked by the highest values of kc along a given profile. Channel concavity in the inner gorges is well developed with a mean θc = 0.50 (Table 1). In contrast, basins with pronounced glacial and landslide imprint have much more convex to straight channel long profiles (Figure 4). We find that the spatial pattern of channel steepness index kc in basins with inner gorges is independent of that of short-term surface uplift rate Uh (R2 < 0.25; Figure 7a). Similarly, no correlation can be observed with the pattern of long-term apatite fission track ages in the area [Persaud and Pfiffner, 2004].
Table 2. Morphometric Properties of Selected Inner Gorges in the Study Area
Normalized by gorge area and assuming age of LGM surface of 15 and 10 ka, respectively.
88 ± 40
4 ± 2
169 ± 73
8 ± 4
154 ± 37
9 ± 2
168 ± 44
9 ± 2
206 ± 108
12 ± 6
117 ± 29
7 ± 2
79 ± 29
5 ± 2
316 ± 84
22 ± 6
205 ± 68
13 ± 4
4.3. Inner Gorge Hillslopes
 In catchments with inner gorges, distinctive convex hillslope knickzones define the upper edges of the gorge walls, which are significantly steeper than the soil-mantled hillslopes of the upper basin (Figure 5). Field observations reveal that dry raveling, rockfall, topple and slide, debris flows, and gully erosion are the dominant processes of erosion of the gorge walls, which are on average ∼60% forest covered (Figure 3b). However, geomorphic hillslope-channel coupling is limited to episodic slope failures along the gorge walls and to steep tributaries, which transfer sediment directly into the gorges [Schlunegger et al., 2002]. In contrast, processes on upper slopes such as solifluction, gullying or shallow soil sliding are largely decoupled from trunk channel processes (Figure 3a). When averaged over a given catchment, the average incision depth of gorges is unrelated to both channel steepness kc and drainage basin size A (Figures 7b and 7c), hence gorges appear to be prominent regardless of their catchment position. In individual basins, the local height of the gorge walls, Hg, increases with catchment area (Figure 8); that is, gorges become seemingly deeper downstream. Where alluvial cover is absent Hg can be used to estimate the total incision depth. The mean slope gradients of hillslopes and gorge walls vary little with A, and indicate the dominance of rectilinear slope profiles, which are slightly more concave for the gorge walls, while the spatial distribution of slope gradient with slope position varies considerably (Figure 9). Moreover, the data do not show any significant control of fluvial erosion potential, approximated by kc, over Hg or 〈Sh〉 (Figure 8).
5. Geomorphic Constraints on the Formation of Inner Gorges
 The range of values of several geomorphic hillslope and channel metrics, i.e., mean elevation and slope gradient, basin relief, hypsometric integral, concavity and steepness, as well as concavity ratio, differ noticeably between the types of study basins (Figure 4), and quantitatively support earlier notions of transient landscape conditions in the eastern Swiss Alps [e.g., Schlunegger and Hinderer, 2003]. Similar results were presented by Brardinoni and Hassan  for the postglacial landscape of coastal British Columbia. Our main interest here, however, is the limited geomorphic coupling of hillslope with channel processes in the basins with inner gorges (Figures 4, 5, 7, and 8). In the following, we augment our morphometric results with several other independent lines of geomorphic evidence to further explore the role of inner gorges within the postglacial landscape disequilibrium.
5.1. Fluvial Detachment of Bedrock
 The river long-profile geometries of many of the studied inner gorges formally resemble the transient response of bedrock channels to base level fall by headward knickpoint migration [Whipple and Tucker, 2002], assuming that the upper edges of the gorges aptly record the geomorphic surface before downcutting commenced (Figure 6). The continuity of the inner gorges along trunk and tributary channels points to a propagating, and not a randomly distributed, adjustment process. Importantly, the concavity of the gorge channels is well defined and close to θc = 0.45, a value typically observed for bedrock rivers in mountain belts (Table 1). This attests to a strong fluvial imprint, which is poorly defined or absent in similar-sized basins of a pronounced glacial or landslide legacy (Figure 4). There, long profiles show marked convexity, caused by hanging valley mouths, glacially scoured bedrock knobs and steps, and deep-seated landsliding.
 Supposing that gorge cutting indeed was limited to the Holocene exclusively requires average bedrock incision rates of E > 20 mm yr−1 to explain the present height of most of the gorge walls (Table 2). These tentative rates are extremely high for the European Alps, and rival those in tectonically more active mountain belts [Burbank et al., 1996], although pulses of elevated bedrock incision are also documented in regions of low uplift [Reusser et al., 2004]. De Graaff  reported values of E < 5 mm yr−1, measured on stream boulders and bedrock surfaces over five years in nearby Austrian basins underlain by flysch and crystalline rocks. Jäckli  noted rates of up to 8 mm yr−1 on the basis of historic abrasion of torrent control structures mantled by calc-schists similar to those in the Bündner schist units. Although high in their own right, they are most likely not representative of the mean postglacial erosion rates of <2 mm yr−1 [Hinderer, 2001]. Also, none of the historically observed high rates match those required for cutting the gorges during the Holocene exclusively.
5.2. Postglacial Sediment Yields
 The volume of material removed from the inner gorges necessitates estimated specific basin yields Qś = 2.8–4.2 × 103 m3 km−2 yr−1 during the Holocene on average (Table 2 and Figure 7d). These yields are of the same order of magnitude as mean erosion rates back calculated from the volumes of perialpine lake sediment storage, i.e., 1–2 mm yr−1 [Hinderer, 2001], especially when considering that historic Qś from basins underlain by Bündner schist and flysch is amongst the highest in the Alps. Where steep torrents undercut large schist sackung-type landslides, Qś may attain up to >3 × 104 m3 km−2 yr−1, dominantly transported during large debris flows [Huder, 1976; Ziegler, 1982]. Jäckli  estimated that individual sackungen delivered to the drainage network an annual average lateral input between 0.6 and 15 m2 of sediment per unit length of basal channel. For comparison, denuding a cross section of 300-m-high inner gorge walls inclined at 45° by parallel slope retreat, at a rate of 20 mm yr−1, would produce 6 m2 per unit channel length. Large postglacial alluvial and debris flow fans sourced from small tributary basins in Bündner schists prograde onto the broad Vorderrhein valley floor, and provide a means to interpolate sediment yields over the Holocene. We estimated the volumes of these fans spanning most of the present valley floor width, and covering trunk-river alluvium that lies discordantly over hummocky debris of the 9-ka-old Flims rockslide [Von Poschinger, 2005] (Figure 1b). The inferred rates range from 0.04 to 2.5 × 104 m3 km−2 yr−1, and most likely apply to bed load only. Considering a more conservative immediate post-LGM onset of fan formation still requires average basin denudation rates of D = 5–13 mm yr−1.
 The question is whether these high rates of postglacial sediment yields have been facilitated mainly by bedrock erosion or by removal of valley fills. The latter possibility is indicated by pockets of tentative glacial and fluvioglacial deposits preserved along parts of some gorge walls and several debris-filled and deeply incised slot gorges [Cadisch, 1926; Jäckli, 1957]. In the Landquart valley, we found that the 1.5-km2 postglacial alluvial fan of the Ariesch torrent (immediately south of basin 19, Figure 1a) is perched on top of its tributary junction cut in bedrock; what appears to be fanhead trenching is actually incision of at least 20 m into Bündner schist bedrock. The presence of such sediment fills in gorges >100 m deep constrains any preceding bedrock incision to the early Holocene, and it is thus likely that a number of gorges existed prior to this period. Unfortunately, neither contemporary sediment yields nor the present degree of alluvial cover in some of the gorge floors can be taken as an indication of any long-term transport conditions because of extensive torrent control in many small basins in the study area. This includes afforestation measures, which may partly explain the forest stands on some of the gorge walls.
5.3. Bedrock Landsliding
 Rapid postglacial fluvial bedrock incision with active headward knickpoint migration of the rates sketched above would strongly promote, if not require, the formation of threshold hillslopes. DEM-derived slope area data yield values of θh ∼ 0 that formally resemble the theoretically predicted 〈Sh〉–A plots for threshold hillslopes (Figure 9) [Tucker and Bras, 1998]. Also, the correlation between kc and mean hillslope gradients 〈Sh〉 along the inner gorges is weak (Figure 8). A comparable situation was noted, for example, by Safran et al.  in the Bolivian Andes, who argued for a threshold state in hillslope development, which, because of frequent landsliding, was insensitive to varying fluvial incision rates. The amount of average vertical incision is independent of catchment area A (Figure 7c), although the inferred rates of postglacial denudation decrease with increasing kc. If kc is indeed acceptable as a proxy for fluvial erosion potential, this seemingly counterintuitive instance can be explained by the transient state of steeper channels that have not yet managed to achieve their full incision potential, all other influences such as erodibility or sediment flux being constant.
 Another important observation is that these tentative threshold conditions are largely limited to the lower 25% of local hillslope relief. In terms of geomorphic hillslope-channel coupling, the inner gorge walls thus essentially form most of the active hillslopes. Mass movement processes such as shallow landsliding, debris flow, or solifluction on the upper, more gently inclined, and larger portions of the hillslopes are largely decoupled from the channels, and may have undergone climatically driven activity phases during the Holocene [Dapples et al., 2003] without any fluvial forcing. Only where steep ravines deliver sediment from the hillslopes directly into the channel, or where large (>106 m3) and slope-clearing failures have in places obliterated inner gorge walls (“Ri” in Figure 10), is the geomorphic coupling of hillslopes and channels more pronounced. We point out that this spatially limited development of threshold hillslopes is not evident from slope histograms (Figure 5). Large postglacial, catastrophic bedrock landslides that have been emplaced into existing bedrock gorges provide further age constraints. For example, the removal of excessive landslide debris of up to 400 m thickness that blocked the Vorderrhein and several major tributaries near Flims around 9 ka (Figure 1b) has since impeded bedrock gorge cutting over large upstream reaches [Von Poschinger, 2005; Korup, 2006]. The neighboring giant (109 m3) Tamins rockslide–rock avalanche, which is believed to have occurred shortly after the Flims event, has truncated small bedrock gorges, which therefore must predate catastrophic detachment of the rock mass (Figure 2b). These observations support the notion of a pre-Holocene onset of gorge cutting.
 A number of presumably Holocene slow-moving landslides commonly involving 108–109 m3 on dip slopes also maintain hillslope adjustment to fluvial incision. These sackung failures effectively counteract fluvial incision by horizontal rock mass advection documented by historically measured rates of differential slope deformation of 100–103 mm yr−1 [Ziegler, 1982], clearly outpacing regional rates of surface uplift. This close geomorphic coupling has created asymmetric valley cross sections, and prevented the formation of continuous inner gorges. From a regional kinematic analysis we find that slope adjustment of inner gorge walls by landsliding is strongly controlled by the orientation of the schist bedding planes. Even hillslopes with low bedding-dip angles (i.e., 15–25°) may be prone to large slow-moving landslides [Jäckli, 1957]. Conversely, inner gorges appear to be preferentially cut normal to the strike of major bedding planes on counterdipping opposite valley walls (Figures 2c and 10). Geometrically, this requires that toppling combined with sliding are important processes for fluvial bedrock detachment, whereas small-scale wedge failures mobilize rock from the inner gorge walls (Figure 3b). This complements the findings of Miller , who observed a consistent alignment of channel slope with the dip of carbonate strata in bedrock rivers of south-central Indiana.
5.4. Postglacial Versus Pre-Holocene Age of Inner Gorges
 In summary, we find that field observations and geomorphometry support two plausible, yet contrasting scenarios, which postulate either a postglacial or a pre-Holocene onset of gorge cutting. The first scenario explains the origin of the inner gorges by headward knickpoint migration in response to changes in base level fall rate. Bedrock incision theory predicts a kinematic wave response to changes in uplift under detachment-limited conditions. As the base level signal propagates upstream, migrating knickpoints separate downstream reaches adjusted to base level fall from upstream reaches subject to further slope replacement [Whipple and Tucker, 2002], while adjacent hillslopes are oversteepened by elevated erosion rates [e.g., Ahnert, 1988]. Because the Alpenrhein catchment was almost fully glaciated during the LGM, this scenario of relief rejuvenation requires postglacial fluvial bedrock incision into a glacially shaped geomorphic surface [Schlunegger and Hinderer, 2003]. Gorge incision would thus have been caused climatically, with decaying glaciers in overdeepened trunk valleys driving local base level falls that were communicated upstream from tributary junctions, and possibly enhanced by meltwater discharge through proglacial gorges from degrading cirque glaciers [e.g., McEwen et al., 2002; Meigs et al., 2006].
 The second scenario argues for a pre-Holocene onset of gorge cutting, as most of the basins with inner gorges are tributaries of valleys that have been repeatedly glacially scoured during the Pleistocene. The occurrence of hanging tributaries and waterfalls along some of the gorges suggests a subglacial phase in their evolution, although Stock et al.  pointed out the possibility of fluvial hanging valleys. Nevertheless there may have been subglacial mechanisms conducive to gorge incision [Shreve, 1972]. Although tunnel valleys are known to have developed under continental ice sheets [e.g., Hooke and Jennings, 2006], little is known about the preservation of larger subglacial bedrock channels in alpine terrain, let alone representative rates of subglacial or postglacial bedrock incision [Brocard et al., 2003]. Eyles et al.  found that several of the glacial overdeepened lake basins in the interior plateau of British Columbia featured massive sediment fills above a v-shaped bedrock topography with depths of ∼650 m below sea level, and followed that Wisconsinan glaciers had accentuated bedrock relief along preglacial and structurally controlled drainage lines. Conversely, several studies argued for a protective effect of large-scale glaciations [Garwood, 1910], on the basis of the limited occurrence of glacial deposits in some inner gorges. With few absolute age constraints, this lends limited support to the notion that incision of at least a number of inner gorges had begun prior to the Holocene [Cadisch, 1926; Tricart, 1960; De Graaff, 1996]. This requires the preservation of gorge relief beneath a protective sediment fill. Such fill could have been contributed in parts by ice-marginal deposits following tributary blocking by trunk glaciers, and subsequent burial by proglacial deposits from growing tributary cirque glaciers [De Graaff, 1996].
6. Constraints From Slope Stability Modeling
6.1. Model Rationale
 In the following, we further explore the possibility of rapid postglacial cutting of the inner gorges in the study area. We surmise that the required high rates of fluvial bedrock incision should prompt the formation of threshold hillslopes (Figure 8). Here we used a simplistic slope stability model as a test of whether the inner gorge walls in the study area are indeed in a state conducive to frequent landsliding in concert with rapid gorge cutting. The literature is almost devoid of mechanistic approaches to explicitly test the concept of threshold hillslopes [Montgomery, 2001]. Schmidt and Montgomery  argued that, at the landscape scale, hillslope relief is limited by either rock mass strength or fluvial incision. They used the Culmann wedge failure criterion for dry soil cliffs to derive the maximum stable hillslope height Hc,
where c is cohesion, β is mean hillslope angle, ϕ is the angle of internal friction, and γr is the mean unit weight of the slope material.
 On the basis of our observations of failure processes on inner gorge walls, we chose a limit-equilibrium approach more applicable to an oversteepened rock slope. This model assumes planar sliding of a trapezoidal block below a vertical tension crack (Figure 3c). The ratio of hillslope strength to effective shear stress is expressed as
where FS is the factor of safety, c′ is the cohesive strength of the failure plane, As is the area of the failure plane, ψ is the angle of the failure plane, w is the weight of the rock block above the failure plane, u is the uplifting water force along the failure plane, and v is the driving water force along the tension crack [e.g., Wyllie and Mah, 2004]. Equation (6) can be written in dimensionless groups as
where γw is the unit weight of water, z is the depth of the vertical tension crack, zw is the depth of water in the tension crack, Hg is the height of the inner gorge wall, b is the horizontal distance of the crack from the crest of the gorge wall, and α is the slope angle of the upper hillslope above the gorge (Figure 3c). For cohesionless slopes (c′ = 0), stability thus depends only on slope geometry, but not on slope size. This makes it applicable to small block slides as well as large slope-clearing failures. For all other cases, we expect FS to decrease nonlinearly with slope height Hg, for a given slope geometry.
Equations (9) and (10) allow inclusion of transient loading due to cleft water pressures along the tension crack and the potential sliding plane. Another advantage of the trapezoidal model is that it states a general form of a series of special cases for which the critical hillslope height Hc at limit equilibrium (i.e., FS = 1) may be derived. For example, we find that, for shallow failures on a fully drained slope (z, b → 0),
This is equal to the expression for planar rock slides on a dip slope where ψ < β [Selby, 1992],
Simplifying further for the limit case of a fully drained vertical gorge wall with daylighting potential failure planes [e.g., Cruden, 1976], where β = 90°, and α = ψ, we obtain
as a simple model of parallel slope retreat. Values of ψ are usually difficult to predict. However, the angle of the critical failure plane ψc in a dry rock slope can be approximated by computing for which value of ψ limit equilibrium is most readily reached, i.e., setting ∂FS/∂ψ = 0 in equation (7) [Wyllie and Mah, 2004], thus obtaining
 Planar rock slope failures described by equation (6) require tight geometric preconditions [Wyllie and Mah, 2004]. These are not met everywhere along the gorge walls, particularly where rock parcels detach by other mechanisms such as fall, topple, rotational sliding, or along two intersecting sliding planes. Factors of safety for more common wedge failures (Figure 3b) are usually higher than those predicted by equation (6) by a wedge shape factor Kw, assuming that ϕ and ψ are equal for both failure planes. Wyllie and Mah  suggest that 1 < Kw < 5 for most cases. They argue that, for FSw > 2, dry cohesionless rock slopes are generally stable over a wide range of dynamic loading conditions. Therefore equation (6) is a practical and conservative first-order approximation of a variety of failure scenarios.
6.2. Mechanistic-Probabilistic Approach to Threshold Hillslopes
 The few published values of the apparent cohesive strength c′ of Bündner schist range between 6 and 120 kPa for fragmented samples, for a unit weight of 19–22 kN m−3, and an angle of internal friction of 23–30° [Huder, 1976; Ziegler, 1982]. Following the method of Marinos and Hoek , our field estimates of the Geological Strength Index (GSI) are between 15 and 40, suggesting a range of c′ = 300–800 kPa, and ϕ = 16–33°. Because of these substantial ranges, and our interest in potential threshold conditions at the regional scale, we performed a Monte Carlo simulation on equation (6). Together with the rock mass properties, we varied Hg such that we assigned a random value between 0 and 300 m (Table 3). This covers most of the relief of inner gorges, while also allowing for failures of portions of the gorge walls where failure planes dip out of the slope. The Monte Carlo method is a probabilistic first-order test of threshold conditions along the inner gorge walls. Statistically speaking, the majority, i.e., >50%, of gorge walls should be inclined at an angle conducive or close to failure [Burbank et al., 1996]. We used a coefficient of reliability rc that states the percentage of simulations where FS < 1; the probability of failure is given by 1–rc. Thus rc = 1 implies that all gorge walls are theoretically stable under the conditions chosen. It follows that a possible criterion for threshold hillslopes is rc = 0.5, which implies that half of the gorge walls that the model readily applies to are potentially unstable. In other words, we suggest a median FS = 1 as a quantitative indicator of the presence of threshold hillslopes, while fully allowing for any spatial variability of their occurrence. We ran the model for four slope conditions, i.e., fully drained (fd); fully saturated (fs); fully drained with undercut toe (α = 0, fdc); and fully saturated with undercut toe (α = 0, fsc; Figure 11a). We determined the coefficient of reliability rc as a function of c′ at intervals Δc′ = 10 kPa. For each interval, we ran 5,000 simulations of equation (6), varying all parameters within field- and DEM-derived distributions (Table 3).
Table 3. Field- and DEM-Derived Parameter Ranges Used for Monte Carlo Simulation of Planar Rock-Slope Stability Along Inner Gorges
field observations of typical slope-failure depths
α = 0
field observations on typical overhang angles at undercut gorge walls
 Simulation results show that dry slopes attain rc = 1 at c′ = 175 kPa, while fully saturated slopes do so at c′ = 275 kPa (gray vertical lines in Figure 11). We term these two values the strength limits. Any decrease in c′ below these limits because of weathering will result in an increase in the probability of failure due to loss of hillslope strength, so that the maximum stable gorge wall height is mainly strength limited. Increases in c′, conversely, will not affect this probabilistic stability, although it will raise FS on average and hence “excess” stability. In other words, without any changes to rock mass properties, instability above these strength limits is only possible, if the slope geometry is altered by fluvial incision. Hence the maximum gorge wall height is mainly incision limited. The simulation suggests that toe undercutting does little to increase the probability of failure near the strength limits, but substantially contributes to destabilizing slopes at lower values of c′ (Figure 11a). The worst-case scenario is given by the curve that is a fully saturated slope with toe undercut (fsc). Assuming a probabilistic threshold hillslope state (rc = 0.5), we obtain apparent cohesive strengths of about 20 kPa and 120 kPa for fully drained, and fully saturated slopes, respectively (Figure 11a). We term these values the threshold hillslope strengths. Because median FS ∝ c′ (equation (6)), any alternative criterion for the presence of threshold hillslopes based on the median FS must also be a function of cohesive strength.
 We used the strength limits derived from Figure 11a to compute the critical height a given gorge wall is able to sustain before planar failure (equations (15) and (16)). We also plotted curves for potential circular failure planes, which we derived from slope stability charts [Wyllie and Mah, 2004]. We test the applicability of these model curves by comparing them to the heights and mean gradients of gorge walls derived from the DEM (Figure 11b). The plot suggests that most slopes can be considered stable when using a simple dip slope model under fully drained conditions (Dd, equation (15)). With regard to circular failure planes (Rd), about 10% of the gorge walls plot above the theoretically possible height limit, indicating potential failure by slumping. We infer that the model simulation either underestimates the rock mass properties, or that conditions for rotational failure are not fully met at these sites, while other failure models might be more adequate. The probability of failure roughly doubles for fully saturated conditions (Rs, Figure 11b). Back calculations for a rotational landslide that affected 2.5 km2 of the northern part of basin 14 (“Ri”, Figure 10) indeed suggests that the valley flank would have been stable under fully drained conditions, whereas fully saturated conditions could have triggered failure. The landslide toe has been further trimmed to slope angles that now appear more stable with respect to rotational failure (arrowed triangles in Figure 11b). The largest theoretical instability is predicted by the model of parallel-retreat slopes undercut by a vertical cliff (cDd, equation (16)), though in this case the Hc solely applies to the cliff section. Because we did not find vertical portions of gorge walls in excess of about 20 m in the field, we regard this model to be rather conservative.
6.3. Strength and Incision Limits
 The Monte Carlo approach provides conservative probabilistic limits of planar rock slope stability set by cohesive strength (Figure 11). Frequent wetting and drying, freeze-thaw cycles, and rapid weathering of soft Bündner schist and flysch rocks play important roles in reducing slope stability. Conversely, fluvial incision leads to release of tectonic strain energy [Huder, 1976], causing slope dilatation and further destabilization. We therefore use equation (15) as an example to anticipate the relative importance of strength limitation over incision limitation through time, as weathering reduces c′, while fluvial downcutting into bedrock increases Hg. Both processes contribute to reducing FS, and gradually attaining the critical slope height Hc. Equations (15) and (16) imply that with slope geometry and internal friction angle remaining constant, Hc is a linear function of c′. Howard  modeled gradual loss of cohesion through weathering as
where c0 is the initial cohesion at initial time t0, and λ is the mean weathering rate, and which in this case does not alter ϕ. From equations (15) and (16) we obtain for t0 = 0:
for weathering-induced, and incision-induced rock slope failure, respectively, where H0 and Hc′ are gorge relief, and critical (strength-limited) gorge relief, at time t0, respectively, and Λ is a dimensionless coefficient describing the slope geometry and its internal friction. We can thus estimate the time theoretically required for a gorge wall to fail by attaining the strength limit (Figure 12).
 This simple model neglects any climatic variability that may affect λ over the timescales considered. Also, assuming E to be constant throughout excludes effects of knickpoint migration, and requires that incising rivers remain below capacity as to maintain detachment-limited conditions despite increasing rates of hillslope sediment yields, as gorge relief and hillslope lengths grow. Moreover, maintained exposure of fresh bedrock by landsliding in response to high rates of fluvial incision may effectively limit weathering. Nevertheless, the model is, to our best knowledge, the first approach to depict within a framework of field data the relationship between rock strength, fluvial incision rate, weathering rate, and inner gorge relief along a bedrock river flanked by oversteepened rock slopes.
 We stress that the limit-equilibrium model used is a simplistic and first-order approach to probabilistically testing the presence of threshold hillslopes at the regional scale, bearing several caveats. First, the anisotropic rock mass properties of Bündner schist and flysch violate the model assumption of uniform slope materials [Margielewski, 2006]. However, this is a common problem in many slope stability assessments, and not confined to this study. The Monte Carlo method and back calculation of c′ is one way of overcoming and quantifying some of this uncertainty through a coefficient of reliability. We are under no illusion that this probabilistic approach goes much beyond a crude regional estimate, which is what we intended in the first place. It is not a surrogate of site-specific slope stability, especially as many other controls on rock mass strength, among others, vegetation, weathering (besides the ones sketched above), and neotectonics, are not included. It is, however, a consequential extension of earlier attempts to model thresholds and limits in hillslope response to fluvial incision [Schmidt and Montgomery, 1995; Burbank et al., 1996; Montgomery, 2001]. Second, the kinematic requirements for the plane-strain model are not met everywhere along the inner gorge walls. In fact, large-scale sackung-type landslides that slowly reduce slope angles at the scale of whole valley flanks have developed on most dip slopes (Figures 4 and 10). Ziegler  showed that several slopes subject to such deep-seated creep failure should be considered metastable, as back calculations have returned values of 1 < FS < 1.5. Nonetheless, Figure 11 covers basic scenarios for rotational landslides, and sets lower bounds for wedge failures; our findings on strength and incision limitation are strictly valid for these failure modes, and within the specified parameter spaces (Table 3). Third, we point out that our analysis did not touch upon other possible mechanisms of hillslope adjustment toward a threshold state, such as gullying or debris flow on weathered rock slope portions (Figure 2c).
 Despite these limitations, slope stability modeling provides two important insights, albeit for a set of special cases. First, it offers a mechanistic rationale to quantitatively define a threshold state in hillslope development expressed by a probabilistic coefficient of reliability (Figure 11a). Second, it provides estimates of strength and incision limits that are averaged over a range of possible conditions. These can be used to estimate the critical gorge wall height as a function of its mean gradient, thus making comparison of model with field data possible. The theoretically derived strength limits (Figure 11a) seem unduly high for fragmented Bündner schist and flysch rocks exposed in many gorge walls. Lower, and possibly more realistic, values of c′ imply that parts of the inner gorge walls are intrinsically unstable as a result of inner gorge cutting (Figure 11b). Field observations support the notion that the Bündner schists and flysch rocks most inner gorges are cut into are strength limited, thus prone to a variety of threshold slope failure mechanisms. The morphologically most pronounced is that of slow hillslope-scale sliding along dip slopes.
 In summary, we infer that the constraints on the age of inner gorges set by fluvial bedrock incision, postglacial sediment yields, and bedrock landsliding are ambiguous. Morphometric characteristics of inner gorges indicating profile adjustment and threshold hillslope formation due to sudden base level adjustment, intuitively guiding as they may be, must be treated with care, as there is the possibility of an unquantifiable amount of inheritance preserved in these landforms. This inheritance of fluvial sculpted topography cannot be resolved sufficiently by morphometric analysis alone, although the seemingly contradictory field evidence can be reconciled by postulating that the present morphology of inner gorges in the study area bears imprints of both rejuvenation and inheritance. This leads us to speculate that a combination of the two scenarios is most likely, i.e., that many bedrock gorges in the study area have been cut in pre-Holocene times, and have been protected and rejuvenated during glacial and interglacial conditions, respectively. If this notion is realistic, one corollary is that the denudation by an extensive ice stream network was insufficient to obliterate the fluvial character of these gorges.
 We stress that, even without a specific date for the onset of gorge cutting, the associated erosion rates are high, outpacing the decadal-scale surface uplift rate by an order of magnitude. Judging from thermochronologic constraints [Schlunegger and Willett, 1999], the possibility that gorge incision responded to dramatic changes in postcollisional uplift is remote; however isostatic rebound or neotectonics may have played a significant role. On shorter timescales, e.g., repeated glacial-interglacial cycles, we propose a delayed hillslope response to fluvial bedrock incision modulated by climatic oscillations, i.e., repeated glacial-interglacial cycles.
 We refine the model of Kelsey  by noting that weak and highly anisotropic rocks may also be subject to inner gorge formation, without invoking the need for solely parallel retreat of gorge walls. Moreover, the inner gorges we studied are contiguous, and not randomly dispersed, landforms, so that we can infer a systematic response to a forcing mechanism instead of a stage in normal hillslope development [Densmore et al., 1997]. Finally, because large slope-clearing landslides mainly involve persistent deep-seated creep, it is possible that inner gorges could have never fully developed at the toes of sackungen instead of having been removed episodically by catastrophic failures.
 Future research on inner gorges in the eastern Swiss Alps will need to better confine the absolute ages of the LGM geomorphic surfaces, as well as many of the undated sedimentary fills in the gorges themselves. This should be complemented by physical rate measurements of channel incision and gorge wall retreat. Finally, regional inventories of major inner gorges in the European Alps and other mountain belts could help further refining their relationship to lithology, rates of uplift and erosion, Quaternary climate cycles, and large-scale hillslope stability.
 Three distinctive types of tributary basins variably dominated by either glacial, fluvial, or landslide morphologies indicate a postglacial landscape transience in the Alpenrhein catchment. Prominent inner bedrock gorges cut into highly erodible Cretaceous Bündner schist and lower Tertiary flysch units underlying many of the “fluvial-type” basins attest to geomorphic decoupling of hillslopes from bedrock channels. Inner gorge long and cross profiles show a high morphometric resemblance to detachment-limited bedrock rivers rapidly adjusting to base level fall through incision and headward knickpoint migration. The assumption of postglacial incision in response to decaying trunk glaciers fits well with very high postglacial sediment yields of up to 104 m3 km−2 yr−1, derived from soft calc-schists subjected to mainly strength-limited threshold landsliding in response to channel incision, limited to the lower 25% of local hillslope relief. This transient state, in which hillslopes lag behind channel adjustments, is a further characteristic of a postglacial landform and process disequilibrium. Moreover, historic sediment yield attains 104 m3 km−2 yr−1, thus locally outpacing short-term surface uplift rate Uh obtained over a comparable (i.e., 101 year) timescale by an order of magnitude. Likewise, both hillslope and channel metrics are independent of the contemporary pattern of surface uplift. Any tectonic forcing on gorge incision is thus considered remote.
 For some bedrock gorges, a pre-Holocene onset of formation is plausible. Subglacial preservation, if not enlargement or formation, of the inner gorges, requires that glacial erosion either (1) is limited in its efficiency to fully remove landforms of fluvial erosion most likely because the gorges were filled with sediment or (2) locally contributes to enhancing selective linear erosion. The strong fluvial overprint in inner gorges shows that the concavity index θc, contrary to previous notions, does record transient adjustments in mountain rivers. We propose that lithology and Quaternary glacial-interglacial cycles are the primary controls on the formation of inner gorges in the Alpenrhein catchment. Clearly, long-term trends in landscape evolution in the eastern Swiss Alps cannot be readily extracted from the present-day relief without clearly resolving the effect of inheritance and rejuvenation. We therefore caution against the sole use of topographic data when inferring the rates of landscape response to tectonic or climatic forcing. Finally, there is the possibility that gorge incision could have been similarly inherited in other formerly glaciated mountain belts.
drainage basin area, L2.
contributing catchment area at channel head, L2.
area of inner gorge, L2.
area of sliding plane, L2.
angle of upper slopes above inner gorge, deg.
horizontal distance of tension crack from top of inner gorge, L.
hillslope angle, deg.
cohesion, ML−1 T−2.
cohesive strength of failure plane, ML−1 T−2.
critical cohesive strength for planar failure, ML−1 T−2.
initial cohesive strength, ML−1 T−2.
mean basin denudation rate, L T−1.
bedrock channel incision rate, L T−1.
mean basin elevation, L.
angle of internal friction, deg.
factor of safety for plane failure model.
factor of safety for wedge failure model.
unit weight of rock, ML−2 T−2.
unit weight of water, ML−2 T−2.
total basin relief, L.
height of slope undercut, L.
maximum stable slope height for strength-limited rock slopes, L.
initial strength limit to gorge relief, L.
height of inner gorge wall, L.
inner gorge relief at model time t = t0, L.
steepness index of channel, L2θc.
steepness index of hillslopes, L2θh.
mean weathering rate, T−1.
coefficient of slope geometry and internal friction.
length of inner gorge, L.
specific sediment yield, L3 L−2 T−1.
angle of failure plane, deg.
critical angle of failure plane, deg.
coefficient of reliability of FS.
mean channel gradient.
mean hillslope gradient.
concavity index of channel; reference value θc′ = 0.45.
concavity index of inner gorge walls.
concavity index of hillslopes; reference value θh′ = 0.07.
uplifting water force along failure plane, ML T−2.
contemporary rate of surface uplift, L T−1.
driving water force along vertical tension crack, ML T−2.
apparent volume eroded from inner gorge, L3.
weight of rock block above an inclined sliding plane, ML T−2.
distance to basal channel, L.
normalized hillslope position (0 = channel, 1 = divide).
distance to hillcrest, L.
depth of vertical tension crack, L.
height of water column in vertical tension crack, L.