It has been proposed that debris flows cut bedrock valleys in steeplands worldwide, but field measurements needed to constrain mechanistic models of this process remain sparse due to the difficulty of instrumenting natural flows. Here we present and analyze measurements made using an automated sensor network, erosion bolts, and a 15.24 cm by 15.24 cm force plate installed in the bedrock channel floor of a steep catchment. These measurements allow us to quantify the distribution of basal forces from natural debris-flow events that incised bedrock. Over the 4 year monitoring period, 11 debris-flow events scoured the bedrock channel floor. No clear water flows were observed. Measurements of erosion bolts at the beginning and end of the study indicated that the bedrock channel floor was lowered by 36 to 64 mm. The basal force during these erosive debris-flow events had a large-magnitude (up to 21 kN, which was approximately 50 times larger than the concurrent time-averaged mean force), high-frequency (greater than 1 Hz) fluctuating component. We interpret these fluctuations as flow particles impacting the bed. The resulting variability in force magnitude increased linearly with the time-averaged mean basal force. Probability density functions of basal normal forces were consistent with a generalized Pareto distribution, rather than the exponential distribution that is commonly found in experimental and simulated monodispersed granular flows and which has a lower probability of large forces. When the bed sediment thickness covering the force plate was greater than ∼ 20 times the median bed sediment grain size, no significant fluctuations about the time-averaged mean force were measured, indicating that a thin layer of sediment (∼ 5 cm in the monitored cases) can effectively shield the subjacent bed from erosive impacts. Coarse-grained granular surges and water-rich, intersurge flow had very similar basal force distributions despite differences in appearance and bulk-flow density. These results demonstrate that debris flows can have strong control on rates of steepland evolution and contribute to a foundation needed for modeling debris-flow incision stochastically.
 Networks of high-gradient, relatively straight valleys commonly dissect steeplands worldwide. In map view, these networks resemble those carved by fluvial processes, but they differ from lower-gradient channels in that they often convey debris flows. As debris flows travel down valley, they can entrain large quantities of sediment (up to 20 m3m−1) and scour valley bottoms clean to bedrock [e.g., Dietrich and Dunne, 1978; Suwa and Okuda, 1980; Meyer and Wells, 1997; Cannon and Reneau, 2000; Fannin and Wise, 2001; Hungr et al., 2005; Stock and Dietrich, 2006; Breien et al., 2008; Santi et al., 2008; Berger et al., 2011; Schurch et al., 2011; McCoy et al., 2012]. Evidence of debris flow-related bedrock incision, caused primarily by flow particles impacting the bed, has been observed at slopes as low as 3–10% [Stock and Dietrich, 2003, 2006]. Additionally, drainage area-slope scaling in these valleys commonly departs from that predicted by models of fluvial bedrock incision, which has led to the suggestion that debris flows may in fact be the primary erosional process [e.g., Seidl and Dietrich, 1992; Sklar and Dietrich, 1998; Montgomery and Foufoula-Georgiou, 1993; Stock and Dietrich, 2003, 2006]. Valleys with gradients greater than ∼ 10% can compose a dominant portion of valley network relief and network length in many steepland environments. Hence, understanding the mechanics of bedrock incision by debris flows and encoding these processes in geomorphic transport laws are important for discerning controls on rates and patterns of steepland evolution [e.g., Howard, 1998; Lancaster et al., 2003; Dietrich et al., 2003; Stock and Dietrich, 2003; Tucker and Hancock, 2010].
 As a first step to quantify dominant controls on valley incision by debris flows, Stock and Dietrich  proposed a geomorphic transport law motivated by field observations. They hypothesized that bedrock lowering rates should depend on the integral of rock-breaking, bed-normal stress excursions caused by flow particles impacting the bed, frequency of debris-flow events, length of the coarse-grained granular front, and rock strength. The model of Stock and Dietrich  was formulated in terms of the bed-normal component of impact stress because this component is primarily responsible for fracture and erosion of brittle materials by impacting particles. Cutting wear, which depends on the tangential component, is relatively ineffective for brittle materials [e.g., Bitter, 1963; Head and Harr, 1970; Engle, 1978; Rabinowicz, 1995; Sklar and Dietrich, 2004]. Although the resulting formulation could reproduce longitudinal profiles of debris-flow dominated valleys, the parameterization between stress excursions likely responsible for eroding bedrock and field-measurable bulk flow properties remains largely untested. This is partly because the manner in which these large excursions scale with bulk flow properties and the form of their frequency-magnitude distribution remain poorly quantified, especially in natural debris flows with wide grain-size distributions.
 Experiments, simulations, and field measurements with debris flows and related granular flows demonstrate that basal stresses and forces are inherently variable. When bed-normal flow accelerations are small, the time-averaged mean basal force is simply equal to the bed-normal weight of the flow [e.g., Berti et al., 2000; McArdell et al., 2007; Hsu, 2010; Iverson et al., 2010]. Yet, large fluctuations, occasionally up to an order of magnitude greater than the time-averaged mean, have been measured, beneath steady, uniform granular flows [e.g., Miller et al., 1996a; Iverson, 1997; Silbert, 2005; Behringer et al., 2008; Hsu, 2010]. The cause of these fluctuations is related to the fact that granular materials are composed of macroscopic, discrete particles. In static or slowly sheared granular materials, fluctuations result largely from distributed loads being localized on filamentary structures called force chains [e.g., Liu et al., 1995; Majmudar and Behringer, 2005]. At the higher shear rates characteristic of debris flows, force chains form infrequently, and single-particle impacts, rather than multiparticle contacts, are the dominant cause of large fluctuations [Silbert et al., 2001; Yohannes et al., 2012; McCoy, 2012]. Discrete-element simulations of these more rapid flows demonstrate that the largest impact forces scale as the square of the grain diameter and the particle impact velocity to the 6/5 power, as predicted from the grain-scale, Hertzian contact mechanics underlying the simulations [Yohannes et al., 2012]. Thus, variability in force fluctuations in more rapid flows should be strongly controlled by variability in the size and velocity of impacting particles.
 The influence of the full distribution of force fluctuations on bedrock incision is illustrated in Figure 1. The curves represent two alternate probability density functions, one with a small mean and variance, the other with a large mean and variance. The vertical line represents a threshold value below which force is insufficient to wear rock; it is analogous to thresholds for bed sediment entrainment via fluid friction [e.g., Tucker and Bras, 2000]. This threshold could represent the force required to fracture bedrock, the force required to pluck fracture-bounded blocks, or the force for fracture due to fatigue. If the bedrock of interest has a nonnegligible threshold, then narrow distributions result in a low cumulative probability of effective impacts, whereas broad distributions, even if the mean remained unchanged, are likely to have effective impacts and higher incision rates. If the statistics of force fluctuations can be determined, then probability density functions of impact force can be combined with suitable wear laws to determine average incision rates. In other words, knowledge of the probability distribution of basal force would allow one to develop a stochastic wear law analogous to stochastic models of long-term river erosion and transport [e.g., Tucker and Bras, 2000; Tucker, 2004; Lague et al., 2005; Molnar et al., 2006; Turowski, 2009; DiBiase and Whipple, 2011].
 Laboratory experiments with monodispersed granular material under various gravity-driven and shear-driven flows [e.g., Howell et al., 1999; Longhi et al., 2002; Ferguson et al., 2004; Jalali et al., 2006; Gardel et al., 2009; Kheiripour Langroudi et al., 2010] as well as calculations using discrete element models [e.g., Bardenhagen et al., 2000; Antony, 2000; O'Hern et al., 2001; Lois et al., 2007; Wang and Zhou, 2010] have shown that probability density functions of particle-bed contact forces measured over the duration of an experiment have an exponential tail and that these distributions commonly scale linearly with the time-averaged mean force. Exponentially distributed forces have also been measured at the base of static granular assemblies [e.g., Liu et al., 1995; Radjai et al., 1999].
 Some experiments, however, deviate from this exponential behavior. Corwin et al.  showed that the force distribution above the mean either decayed faster or more slowly than an exponential, depending on shear rate and flow thickness. In laboratory experiments with an annular Couette cell, Jalali et al.  found that when monodispersed spheres where replaced with bidispersed spheres, distributions of force fluctuations under different vertical compressive loads no longer collapsed onto a single exponential distribution when normalized by the mean force. Working with wide grain-size distribution natural debris-flow mixtures in a large rotating drum, Hsu  found that forces greater than the mean decayed more slowly than exponentially and were best fit by generalized Pareto distributions with shape factors as large as ∼ 0.3. As the grain-size distribution was broadened to include larger and larger grains, the shape factor increased, indicating an increased probability of larger impacts. In contrast to the strong effect the grain-size distribution had on the force distributions, Hsu  found that the variance of basal force was only weakly affected by changes in interstitial fluid viscosity, even when viscosity ranged over four orders of magnitude. These differences in observed force distributions, given departures from idealized monodispersed material, raise some questions. For example, what aspects of these experiments and simulations apply to full-scale debris flows in natural settings? What is the force distribution from natural debris-flow mixtures flowing over realistic bed topography? How does this force distribution change with different bulk flow properties?
 In this work, we use a well-monitored natural debris-flow catchment to answer these questions and to bridge the gap between experimental work and full-scale natural debris flows. We first document the total amount of bedrock lowering that occurred over approximately a 4 year monitoring period (May 2008 through March 2012) and the mechanisms by which bedrock was removed during the passage of debris flows. Although the bedrock incision measurements lack time resolution needed to examine controls on per-event lowering rates, they demonstrate that the monitored debris-flow events were, on average, erosive. We then investigate characteristics of these erosive debris flows, with particular emphasis on the basal normal force. We present measurements from five different flow events (15 September 2009, 12 June 2010, 28 June 2010, 26 July 2011, and 3 August 2011), analyze these measurements in both the time and frequency domain, and determine some basic characteristics of probability density functions of basal force.
2 Field Site and Monitoring
 Our field site is located at Chalk Cliffs, Colorado, USA, in a steep 0.3 km2 basin, adjacent to the range-bounding Sawatch normal fault. Hydrothermally altered and fractured quartz monzonite bedrock composes ∼ 60% of the basin area, the other ∼ 40% is covered by sparsely vegetated colluvium. Loose sediment accumulates in valley bottoms following rockfall and dry ravel. This sediment is subsequently entrained by rainfall-related surface water runoff to form a debris flow [Coe et al., 2008]. A typical debris-flow event at Chalk Cliffs consists of multiple fluid-poor, steep-fronted, coarse-grained granular surges separated by water-rich, intersurge flow [McCoy et al., 2010, 2011]. Granular surges generally have densities between 1700 and 2100 kg m−3. The surface of intersurge flows lack coarse clasts characteristic of granular surges; instead, the surface has waves and splashes. Densities of intersurge flows are generally less than that of granular surges, but commonly remain above 1300 kg m−3, which implies solids concentrations greater than 20% [McCoy et al., 2010, 2011, 2012]. Flows with similar properties are sometimes referred to as hyperconcentrated flows [e.g., Pierson, 2005], debris floods [Hungr et al., 2001], or watery surge tails. We refer to the coarse-grained, fluid-poor surge fronts as granular surges, the water-rich flows between surges as intersurge flows or as watery tails, and the entire event, composed of both granular surges and intersurge flow, as a debris-flow event.
 At our Chalk Cliffs monitoring site, debris flows occur at the extremely high rate of one to five times per year. To study various debris-flow processes, we developed an automated sensor network composed of three instrumented cross sections (upper, middle, and lower stations) [Coe et al., 2010; McCoy et al., 2011]. All instrumentation to study basal force is located at the upper station, which is ∼ 590 m downstream from the drainage divide and in a straight bedrock reach with a reach-averaged slope of 13° and length of ∼50 m (Figure 2). The bedrock channel floor is rough at multiple scales. It has meter-scale bed forms (Figure 3), centimeter-scale ledges (Figures 2a and 2b), and grain-scale texture with no apparent fluvial polishing. A more complete description of the geologic setting, debris-flow initiation mechanisms and the high frequency of occurrence, characteristics of measured storms and debris-flow events, site selection, and monitoring system can be found in earlier work [Coe et al., 2008, 2010; McCoy et al., 2010, 2011, 2012].
2.1 Sediment Characteristics
 Grain-size distributions of hillslope sediment, fresh debris-flow deposits (lateral levees), and channel deposits composed of material previously mobilized by debris flows, watery tails, and dry ravel, are all characterized by wide distributions that span over five orders of magnitude (Figure 4). The grain-size distribution of sediment smaller than cobbles has been characterized using standard sieve and hydrometer methods [Coe et al., 2008; McCoy et al., 2012]. Samples collected over a 4 year period and from different locations within the study basin were composed of ∼ 40–60% gravel, ∼ 35–50% sand, and less than ∼ 10% silt and clay, although debris-flow levees were coarser than other channel or hillslope sediments (Figure 4). The grain-size distribution of sediment coarser than sand has been characterized using random-walk point counts of clasts found on freshly deposited debris-flow levees [McCoy et al., 2012]. The grain-size distribution from a point-count of a lateral levee formed during a small debris flow with a maximum flow depth of less than 0.35 m was significantly finer than that from a lateral levee at the same location formed during a separate debris flow with flow depths greater than 1 m (Figure 4).
2.2 Measuring Basal Normal Force
 We measured basal normal force with a force plate cemented in the bedrock channel floor (Figures 2 and 5). The force plate consisted of a 2.54 cm thick metal plate, with surface dimensions of 15.24 cm by 15.24 cm (232 cm2), attached to a shear-compensating, shear-web type, single-axis load cell made by Tovey Engineering (product number: SWS10). The force plate and load cell were placed in a sealed enclosure. The load cell was rated to approximately 45 kN and had a full-scale manufacturer-reported accuracy of ±25 N. The noise at zero load was less than ±5 N. As a result of the shear-compensating design, measurement uncertainty of the normal force only increased as ±0.4% of the applied shear force.
 We determined the in situ natural frequency of the force plate to be 200–250 Hz by striking the plate with a hammer while sampling at 1 kHz (Figure 6). Single impacts, generated by dropping a cobble onto the plate, were recorded as one, or at most two, elevated force measurements when sampling at 1 kHz, indicating that impacting particles remained in contact with the plate for 1 to 2 ms. Because each individual measurement was the result of a 0.25 ms analog integration of the signal, which is a fraction of a typical contact time, we assume each force measurement approximates an instantaneous measure of the force on the plate surface. The automated data-logging system had limited write speed, which, depending on the number of sensors sampled, set the maximum sampling rate. We sampled the force plate at 100 Hz until 2011 when we decreased the rate to 33 Hz for the 26 July 2011 event and to 50 Hz for the 3 August 2011 event.
 To install the force plate, we excavated a hole in the bedrock channel floor slightly larger than the enclosure using a rock saw and chisel. We then placed the force plate and enclosure into the hole such that the top surface of the force plate was flush to the surface of the bedrock channel (Figure 2c). We filled around the plate with concrete and then smoothed and flushed the concrete to the plate and surrounding rock. Because the bedrock surrounding the force plate was lowered during the study period (discussed below), we repeated the concrete and screeding procedure after each event that directly overran the force plate to ensure the force plate surface remained flush to the surrounding bedrock. In May 2011, a new force plate surface was installed to repair damage and the bedrock hole in which the force plate sat was deepened to decrease the amount of concrete required to bring the force plate surface flush to the surrounding channel.
 Measurements of time-averaged mean normal force and amplitudes of fluctuations about that mean depend on force plate area. In diverse experimental flows, fluctuation amplitude relative to the time-averaged mean decreases as plate area increases [Iverson, 1997; Miller et al., 1996a; Howell et al., 1999; Jalali et al., 2006]. As plate area increases, the total mass supported by the plate increases, which in turn increases the time-averaged mean normal force on the plate. A larger plate area also permits more particles to contact the plate. If particle-plate contact forces are spatially uncorrelated, then fluctuation amplitude relative to the time-averaged mean force will decrease as contact forces are spatially averaged. When measuring bulk flow properties, plates that are large relative to flow particles are used to take advantage of this spatial averaging effect [Iverson, 1997; McArdell et al., 2007]. In contrast, plate sizes that permit interaction with only a single particle are used to measure maximum fluctuation amplitude [e.g., Longhi et al., 2002; Ferguson et al., 2004; Gardel et al., 2009]. We chose a plate size (15.24 cm × 15.24 cm) close to the diameter of large particles in the flow. Although this plate size allows simultaneous contacts with small particles, simultaneous contacts with large particles should be limited, and the measured fluctuations should approximate the maximum fluctuation amplitude measured with zero spatial averaging.
 Granular flow dynamics are particularly sensitive to whether boundaries have particle-scale roughness or are completely smooth [Silbert et al., 2002; Iverson et al., 2010]. Flows over rough boundaries are more agitated and lack coherent structures or crystallized zones that are common in flows over smooth beds [Silbert et al., 2002; Iverson et al., 2010]. Here debris flows travel over naturally rough boundaries before encountering our smooth force plate. Plate dimensions are small relative to channel dimensions and are comparable to the largest particles in the flow. Given the limited number of sequential particle-plate interactions, the plate is likely too small to cause flows to transition from an agitated state of a rough bed to a less agitated state of a smooth bed. Hence, flow dynamics measured by the plate should be representative of those developed over naturally rough beds.
2.3 Measuring Flow Stage and Bed-Sediment Height
 We measured flow stage using a laser-stage sensor (sampled at 10 Hz) suspended ∼ 2 m above the bedrock channel from an aluminum bridge (Figure 2), except in 2009 when an ultrasonic distance meter was used. The datum for the stage measurements was the surface of the force plate. Thus, when no bed sediment covered the force plate, flow stage equaled bed-normal flow depth. We measured bed sediment height with an in situ erosion sensor described by McCoy et al. . This sensor allowed us to determine when the force plate was exposed to the base of a debris flow.
2.4 Bedrock Incision Resulting From Monitored Debris Flows
 To determine the mechanisms by which bedrock was removed from the channel floor and walls, we inspected the channel after each debris-flow event with particular attention to areas of exposed bedrock. Fresh-looking wear marks were classified as resulting from sliding if grooves were obvious, abrasion if bedrock was lowered at mineral-grain scale, impact fracturing if shattered fresh faces were apparent, or plucking of fracture-bounded blocks if fracture-bounded volumes had fresh faces [Stock and Dietrich, 2003, 2006].
 Fresh wear marks were observed after each monitored event. The primary process by which bedrock was removed from the channel floor was by plucking of fracture-bounded blocks and by point load impact fracturing of intact rock. Bedrock reaches lacked any fine-scale features such as flutes or potholes that are typical of fluvial abrasion. Plucked blocks encompassed a range of sizes but were typically of centimeter-scale thickness. After a single debris-flow event, the initially polished force-plate surface was roughened by millimeter-scale indentations (Figure 5). Superimposed on this roughened surface were larger and deeper indentations indicative of point loads. Evidence for prominent wear due to sliding, such as long grooves, was not commonly found on bedrock surfaces or on the force plate surface.
 In the reach around the upper station, we installed 13 expansion bolts along the centerline of the bedrock channel to measure the total bedrock incision that occurred during the monitoring period from May 2008 through March 2012 (Figure 2). The 130 mm long, 10 mm diameter bolts provided a record of the preflow channel surface; a similar design was used by Stock et al.  in which he installed nails and hollow-wall anchors in bedrock channels to measure fluvial bedrock incision. After installation, we measured the length of exposed bolt. At the end of the monitoring period, we measured the length of the bolt's centerline from its head to the bedrock channel floor and took the difference between the initial and final exposed lengths to calculate the total erosion that occurred. Due to the large forces at the base of the monitored flows, the bolts were commonly bent over in the downstream direction (Figure 2). Total incision measurements must be considered a maximum because we assume that increases in exposed bolt length were due only to incision of the surrounding bedrock and were not a result of debris flows simply pulling the bolt out of the bedrock. This assumption is reasonable given that we tested the bolts and found them to be secure during periodic visits to the site during the 4 year monitoring period.
 To estimate the rock compressive strength, we took 10 Schmidt Hammer measurements at each erosion bolt location. No systematic trends were observed along the reach. The mean of the 130 measurements was 24 (on a unitless scale from 10 to 100), while the range was 10 to 44, confirming the weak, hydrothermally altered, and highly fractured nature of the rock. For comparison, the rock type chalk can give readings of ∼ 20, whereas unweathered granite can give readings of ∼ 70 [Katz et al., 2000].
 Erosion-bolt measurements confirmed our observations that the monitored debris flows were erosive and demonstrated that 36–64 mm of bedrock incision occurred along the monitored reach during the 4 year monitoring period (Figure 2a). Of the 13 bolts originally installed, four bolts were missing and could not be used to measure incision. All bolts that remained were tightly in place, and none of the expansion sleeves that give the bolt its holding strength were exposed. Occasional sediment cover and time constraints prevented collection of a per-event time series of bedrock lowering from the erosion bolts.
2.5 Data Processing and Analysis
2.5.1 Basal Normal Force
 We analyzed the basal normal force data to characterize forces accompanying bedrock incision. The basal normal force signal Fn(t) can be separated into a time-averaged mean and a fluctuating component about that mean . is set largely by bulk flow properties, while is set by grain-scale processes. Because 0.5 Hz was a typical maximum frequency of changes in bulk flow properties, we used a low-pass filter with a cutoff frequency of 0.5 Hz to isolate from Fn(t). Filtering visibly smoothed but did not remove changes in force due to the arrival of small surges. Similar results, albeit with less precision in the frequency domain, could be achieved with a time-domain moving-window-mean filter [Smith, 1997]. We used a fourth-order digital Butterworth filter, applied in both forward and backward directions to get zero-phase shift, because this filter produced no ripple in the passband and had high attenuation over the stopband (∼350 dB), while still providing a narrow transition bandwidth of 0.2 Hz. We calculated as .
 We calculated the power spectra of Fn(t) for each event to quantify the frequency-domain characteristics of the force signal. To determine whether the power spectra of (i.e., the high-frequency components of Fn(t)) changed with time as flows transitioned between granular surges and water-rich, intersurge flow, we calculated a spectrogram of for each event. A moving Hamming window with a width of 128 points, and window overlap of 50%, was used for the short-time Fourier transform of the spectrogram. This window width resulted in better than 1 Hz resolution in the frequency domain. We report the power spectral density relative to the mean of the medians of spectral density from all calculated spectrograms.
2.5.2 Basal Normal Force Statistics
 We analyzed the statistics of measured basal normal force to understand how the probability density functions of force changed across debris-flow events and with measurable flow properties. Our goal in this analysis was to determine whether certain flows had greater probability of large magnitude forces, and hence were more likely to incise bedrock. We separated the force data into populations based on date of occurrence of each event and then removed all measurements that were made while the force plate was covered by bed sediment. A single master population was also created by combining measurements from the uncovered force plate from all events. We separated this master population of Fnmeasurements into subpopulations based on flow properties. To investigate the role of flow composition, we grouped measurements into granular-surge and water-rich, intersurge populations using the video footage taken at the upper station. Intersurge populations contained measurements made during water-rich flows that lacked coarse particles on the surface of the flow and were characterized by turbulence, waves, and splashes. Granular-surge populations only included measurements made during times when a high concentration of coarse-grained particles (cobbles and boulders) was present on the surface of the flow and the flow was many grain diameters deep. We also separated the master population of Fninto subgroups based on a measurement's concurrent flow depth using the 10 Hz flow-stage time series linearly interpolated up to the sampling frequency of the force measurements (with group edges at 0.0, 0.25, 0.5, 0.75, and 1.0 m) as well as based on concurrent measurements (with group edges of 0.0, 100, 200, 300, and 1000 N). To remove the influence of variability in on the distribution of Fnand to isolate the influence of grain-scale processes, we normalized each force measurement Fn by its concurrent before calculating the probability density function (pdf) for each population (note that ).
 To aid quantitative comparison between pdfs from different flows, flow types, and studies, we estimated the parameters for the Generalized Pareto Distribution (GPD) using maximum likelihood estimators. The GPD has the advantage that it encompasses both the exponential distribution, when the shape parameter k=0, and the Pareto distribution, when k>0. We estimated distribution parameters based on data above a lower bound xmin, equal to the mean of a given population. The probability density for the GPD can be written as
in which k is the shape parameter, μis the scale parameter, and xmin is the location or the threshold parameter. If k=0, then the density is described by an exponential distribution
The corresponding mean EGPDand variance VGPDare the following
for k<1 and for k<0.5, respectively [e.g., Castillo and Hadi, 1997]. Equations (1) and (3) highlight that for a given μ, which for will always be ∼ 1, an increasing k indicates an increasing probability of observing large magnitude forces.
 During the monitoring period from May 2008 through March 2012, 15 debris-flow events occurred. Of these 15 events, four flowed exclusively over bed sediment and did not scour bedrock in the monitored reach. Seven entrained all bed sediment at the upper station and spent some portion of the event directly scouring bedrock, and four occurred days to weeks after a bedrock-scouring event and hence spent the entire event scouring bedrock. Our instruments recorded basal force during five of the 11 bedrock-scouring events. These events occurred on 15 September 2009, 12 June 2010, 28 June 2010, 26 July 2011, and 3 August 2011 (see Table 1 for summary of event characteristics). Comparison of the flow-stage time series, which were recorded during all 15 events, revealed that these five events had flow depths and durations typical of all but the smallest events recorded at Chalk Cliffs. The continuous monitoring revealed that no clear water runoff events occurred at the upper station during the monitoring period.
Table 1. Storm Characteristics and Flow Properties Measured at the Upper Station
15 Sept 2009
12 June 2010
28 June 2010
26 July 2011
3 Aug 2011
Peak 5 min rain intensity (mm hr−1)
Peak flow depth during event (m)
Mean flow depth (m)
Event volume (m3)
GPD shape parameter
0.21 ± 0.02
0.2 ± 0.02
0.32 ± 0.01
0.33 ± 0.03
0.41 ± 0.02
3.1 Basal Normal Force Time Series
 Basal normal force measurements made during debris flows had a very different character when the force plate was covered with static bed sediment compared to when it was free of sediment. This difference is exemplified by the event on 12 June 2010 (Figure 7). Other events for which basal force was measured are shown in the Supporting Information. When the force plate was covered by a thickness of static bed sediment greater than ∼ 20 times the median bed sediment grain size, no significant fluctuations about the time-averaged mean force were measured (Figure 7), the magnitude of high-frequency force components was not much larger than measurement uncertainty (Figure 7b), and there was little spectral density above 0.5 Hz (Figure 7c). Given that the bed sediment acted as a very effective low-pass filter, shielding the bed from high-frequency force components, we focus on measurements made while flows directly overran the force plate.
 While flows directly overran the force plate, force measurements revealed large-magnitude, high-frequency fluctuations about . Figure 8 concatenates data from all five events, for periods during which the force plate was not covered by bed sediment. Results demonstrate that the force signal was characterized by a significant fluctuating component about , and that often had a magnitude many times (Figure 8b). Above 0.5 Hz, power spectra from each event decreased with frequency f as f−β with β ranging from 0.2–0.6 (Supporting Information). The general pattern of higher spectral density at lower frequencies is apparent in spectrograms of (Figures 7c and 8c) and is superimposed by instances when the measured frequency band saturates with high spectral density. As shown in Figure 6, the latter is the spectral signature of a large impulse [Percival and Walden, 1993] and is more apparent on plots that span a shorter time window (Figure 7c). Bins with large and uniform spectral density across all frequencies align with large positive deviations from the mean force. These large fluctuations generally elevated the measured force for only a single measurement. Changes in bulk flow properties occurred much more slowly and persisted over longer durations, which eliminates them as a cause of these short-duration, large-magnitude fluctuations, but the specific particle bed interactions responsible are difficult to determine from the force time series alone.
 Although granular surges were visually distinct from water-rich, intersurge flows, and the spectra of from each flow type shared similar characteristics (Figures 7, 9, and 10). Granular-surge fronts commonly had distinct rapid increases in both stage and , but the transition from granular surge to watery intersurge flow was difficult to determine by these nonvisual methods (Figures 10a and 10b). Particularly indistinct were and its spectrogram for each flow type (Figures 7 and 10). Both flow types had similarly large and exhibited instances in which the measured frequency band was saturated by large impulses.
3.2 Influence of Bed Topography on Basal Normal Force
 Meter-scale bedrock bed forms perturbed the time-averaged mean force from that expected from the static weight of the flow. Although the monitored reach at the upper station was selected for its particularly smooth bedrock character (Figure 2a), a close look (Figures 2b and 3) reveals meter-scale bed forms, as well as centimeter-scale ledges surrounding the force plate. When bedrock bed forms were covered by bed sediment, scaled with flow depth (Figure 7a). Assuming a lithostatic state, bulk flow densities ranged from 1500 to 2100 kg m−3when calculated from measurements made while the force plate was covered. Once all bed sediment had been entrained by the flow and bedrock exposed, a linear relationship between and flow depth was not always observed and calculated densities ranged from 500 to 3000 kg m−3. The persistent nature of disproportionately large or small values of relative to flow depth can be observed in the scaled time series data during times with exposed bedrock (Figures 7a, 8a, and Supporting Information). At low flow depths, was up to two times greater than that expected from the static weight of the flow with the bulk flow density equal to 1800 kg m−3, while at higher flow depths, was up to three times smaller. Video footage revealed that when a flow encountered bedrock bed forms persistent dynamics in the form of standing waves and jets developed. Video footage also documented that the location of the standing waves and jets relative to the force plate changed as a function of flow depth. Thus, depending on flow depth, these flow features either increased or decreased by locally redirecting some fraction of the down-channel flow momentum normally incident to, or away from, the force plate.
3.3 Statistics of Basal Normal Force
 Probability density functions (pdfs) of normalized basal normal force, , for each measured debris-flow event were right skewed and decayed more slowly than an exponential distribution (Figure 11). Estimates of the generalized Pareto distribution (GPD) shape parameter ranged from 0.2–0.41 across events (here and elsewhere denotes estimated parameter values) and showed a weak positive correlation with measures of event magnitude such as event-averaged flow depth and peak rainfall intensity (Table 1). Values of indicate that the mean and variance of the distributions are defined and that the distributions are not heavy tailed.
 Probability density functions of normalized basal normal force from granular surges and intersurge flows overlapped and had the same within error (Figure 12). Despite their obvious visual distinction from surface flow characteristics, granular surges and intersurge flows appeared to have very similar force distribution shapes and hence were not treated separately in the remainder of the analysis.
 When force measurements Fnwere separated into groups based on contemporaneous flow depth or measurements, the spread of Fnmagnitudes in each group increased with increasing flow depth and (Figures 13a and 14a). We attribute the poor separation of distributions for each flow-depth group (Figure 13a to the fact that flow depth was an imperfect predictor of basal force when persistent accelerations were incited by bed topography. When each force measurement was normalized by the corresponding , distributions from each flow-depth or mean-force group collapsed towards a single common distribution (Figures 13b and 14b). Such a collapse indicates that the fluctuating component responsible for the observed force variability scales with the time-averaged mean force. The estimated remained relatively constant and showed no trend with increasing flow-depth or mean-force group (Figures 13b and 14b). Thus, as the time-averaged mean force increased, the distribution simply stretched to accommodate the increasing mean and dispersion about that mean, but did not experience large changes in shape (Figures 13 and 14).
4.1 Debris Flows as Effective Geomorphic Agents
 Over the course of 4 years, the bedrock channel floor surrounding the upper station was lowered by 36 to 64 mm. Through the use of continuous-automated monitoring, we can attribute this lowering to scour of the bedrock channel by debris flows. Our observations and data add to the mounting evidence that debris flows are not only effective in entraining loose channel sediment, but also at eroding bedrock [Stock and Dietrich, 2003, 2006]. These data are also consistent with earlier work proposing that impact-related wear during the passage of a debris flow can play a primary role in eroding bedrock in steep valleys [Stock and Dietrich, 2006; Hsu, 2010]. In total, we add to the small but growing body of field evidence that debris flows incise bedrock via granular impacts.
4.2 Normal Force at the Base of Debris Flows
 The basal normal force during these erosive debris flows was characterized by large variability. Force fluctuations occasionally exceeded 10 times the time-averaged mean normal force (Figures 7 and 8). The magnitudes of these large fluctuations were composed almost exclusively of high-frequency components (>0.5 Hz), frequencies higher than concurrent fluctuations in flow depth and flow density. The high-frequency nature of large-magnitude fluctuations indicates that they resulted from grain-scale momentum exchange processes operating within the flow. We interpret these grain-scale processes to be particle-bed impacts as observed at the flow front in video recordings and in simulations of rapid granular flows [Drake, 1991; Silbert et al., 2001; Yohannes et al., 2012; McCoy, 2012]. But our force measurements alone cannot discriminate between particle impacts and other grain-scale processes known to cause force fluctuations such as force chains interacting with the bed [e.g., Estep and Dufek, 2012], or more persistent particle-bed contacts such as rolling. A sediment thickness of ∼ 20 times the median grain size was sufficient to dissipate all but the largest of these fluctuations. These measurements provide direct instrumental evidence that only a thin layer of loose sediment (∼ 5 cm in the monitored cases) is needed to shield the bed from impacting particles with diameters at least as large as cobbles. This finding is consistent with hypotheses of workers from Gilbert  to Sklar and Dietrich  that thin bed cover negates the effectiveness of particle impacts in damaging subjacent bedrock.
 Probability density functions of normalized basal normal force were broad and decayed slowly with increasing force magnitude due to the large variability induced by grain-scale processes. Generalized Pareto distributions with estimated shape parameters between 0.2–0.41 captured much of the observed variability. In rotating drum experiments with natural debris-flow mixtures, Hsu  also found that distributions of basal force were well described by generalized Pareto distributions with between ∼0.0–0.3. In contrast to these results, laboratory experiments and simulations with monodispersed granular flows find that contact forces in the tail are distributed in an exponential manner [e.g., Howell et al., 1999; Longhi et al., 2002; Ferguson et al., 2004; Jalali et al., 2006; Gardel et al., 2009; Kheiripour Langroudi et al., 2010; Bardenhagen et al., 2000; Antony, 2000; O'Hern et al., 2001; Lois et al., 2007; Wang and Zhou, 2010]. Exponential distributions estimated from our field measurements under-predict the probability of large magnitude fluctuations by orders of magnitude (Figure 11). Such discrepancy highlights the greater variability in force magnitude present in natural debris flows with wide grain-size distributions flowing over rough boundaries.
 Variability in the magnitude of the fluctuating basal force component increased with (Figure 14). Groups with larger magnitude had broader force distributions and as a result had a larger likelihood of a containing a large magnitude force fluctuation. Figure 1 portrays this behavior schematically with the addition of an erosion threshold to highlight that flows with large mean forces, and hence flows with large force variability, will likely be more erosive due to the higher frequency of erosive impacts. Thus, the time-averaged mean force encodes information needed to estimate the actual distribution of force resulting from grain-scale processes.
 Rough bedrock topography consisting of centimeter-scale ledges and meter-scale bedrock bed forms caused flow features (standing waves and jets) that locally perturbed from that expected due to the bed normal weight of the flow. two times larger and three times smaller than the expected lithostatic value were observed. Whether was enhanced or suppressed relative to the expected lithostatic value depended on the location of dynamic flow features relative to the force plate. Iverson et al.  also measured force enhancement of two to three times the expected lithostatic values when large-scale experimental debris flows overrode 5 mm gaps in the otherwise smooth flume bed. These gaps were located 0.18 m upstream of their force plates. When flows encountered these gaps, small standing waves formed that locally enhanced the normal basal force by redirecting down-channel flow momentum normal to the force plate [Iverson et al., 2010]. This mechanism for local and persistent enhancement of the mean force matches well with our observations from natural debris flows. These observations indicate that bed-normal flow accelerations caused by bed topography can change by amounts comparable to, or in excess of, that possible through changes in bulk flow properties. A factor of three change in from that expected due to the bed normal weight of the flow. two times larger and three times smaller than the expected lithostatic value were observed. Whether was enhanced or suppressed relative to the expected lithostatic value depended on the location of dynamic flow features relative to the force plate. Iverson et al.  also measured force enhancement of two to three times the expected lithostatic values when large-scale experimental debris flows overrode 5 mm gaps in the otherwise smooth flume bed. These gaps were located 0.18 m upstream of their force plates. When flows encountered these gaps, small standing waves formed that locally enhanced the normal basal force by redirecting down-channel flow momentum normal to the force plate [Iverson et al., 2010]. This mechanism for local and persistent enhancement of the mean force matches well with our observations from natural debris flows. These observations indicate that bed-normal flow accelerations caused by bed topography can change by amounts comparable to, or in excess of, that possible through changes in bulk flow properties. A factor of three change in requires a large change in flow depth, while changes in flow density simply cannot account for such a change.
4.3 Granular Surges Versus Water-Rich Intersurge Flow
 Normalized force distributions for both intersurge flow and granular-surge populations collapsed toward the same distribution (Figure 12). The similarity in distributions, once the effect of different time-average mean forces was removed, is surprising. Granular surges had densities around 2000 kg m−3and grains visible on the flow surface commonly ranged from cobbles to boulders in size. In contrast, intersurge flows had a large component of water, densities generally ranged between 1300 and 1700 kg m−3, and coarse-grained material was absent on the surface of the flows. Why do the distributions we measured for granular surges and intersurge flows appear similar? One hypothesis is that grain-scale dynamics are similar for both granular surges and intersurge flow and that the grain-size distribution contacting the channel bed is similar across flow types.
 Granular surges transfer momentum to the bed primarily through particle-bed interactions such as impacts and rolling. Hydrodynamically driven bed load transfers momentum to the bed through very similar particle-bed interactions [Gao, 2008]. At high transport stages, uninterrupted bed load saltation gives way to stratified flow that is commonly called sheet flow (not to be confused with overland sheet flow): a basal flowing layer of grains, multiple grain diameters thick, with concentrations that approach those of granular flows [e.g., Hanes and Bowen, 1985; Asano, 1992; Sumer et al., 1996; Gao, 2008]. Although fluid drag and buoyancy forces play an important role in mobilizing the bed load layer, within the layer itself, grains are supported primarily through particle-particle interactions, as is typical in granular flows [Armanini et al., 2005; Gao, 2008]. In fact, accurate simulations of sheet flow use the same equations to model the basal flowing layer as are commonly used for rapid granular flows [e.g., Hanes and Bowen, 1985; Drake and Calantoni, 2001; Hsu et al., 2004] and properties of the dense flowing layer, such as the velocity profile, match those of granular flows [Armanini et al., 2005; Larcher et al., 2007]. Based on field observations, other workers have hypothesized that bed load layers do indeed reach such high concentrations that the flow vertically stratifies into a granular flow submerged beneath a lower density near-surface layer [e.g., Scott and Gravlee, 1968; Cronin et al., 2000; Manville et al., 2000; Manville and White, 2003]. Thus, the similarity in force distributions measured during both granular surges and intersurge flows could indicate that despite having different compositions in the near-surface layer, both flow types have a dense, basal layer composed of coarse-grained granular material, which can generate large-magnitude impact forces.
 In a recent paper, McCoy et al.  showed that the rate of bed sediment entrainment was quite steady over the course of a debris-flow event, even though some portions of event were dominated by granular surges, and others were dominated by water-rich, intersurge flow. Similarity in basal force distributions between these visually distinct flows might explain these observations. In addition, similarity in the force distributions for granular surges and intersurge flows implies that in steep headwaters where high transport stages and mobile coarse grains are present throughout the length of the flow, significant bedrock incision is not limited only to the surge front.
5 Summary and Conclusions
 Debris flows are effective geomorphic agents that not only entrain and transport sediment in steep valleys but also erode bedrock. Over a 4 year monitoring period at the Chalk Cliffs monitoring site, the bedrock channel floor was lowered by 36 to 64 mm due to debris-flow scour. The basal normal force during these erosive debris-flow events had a large-magnitude, high-frequency fluctuating component. This fluctuating component was the result of grain-scale processes and particle-bed impacts, not fluctuations in bulk flow properties. Generalized Pareto distributions with estimated shape parameters between 0.2–0.41 described the wide basal force distributions that resulted from large variability in the fluctuating component. Although variability was large and force fluctuations over an order of magnitude larger than the concurrent time-averaged mean force were observed, distributions always had well-defined means and variances. With increasing force magnitude, probability density declined more slowly than an exponential distribution, which contrasts with the exponential behavior found in many simulations and experiments using idealized (often monodisperse) mixtures. Our measurements demonstrate that natural debris-flows with wide grain-size distributions have much broader distributions of basal force and thus are more likely to have a higher frequency of erosive impacts than predicted from experiments with monodispersed mixtures. When the force plate was covered by sediment thicker than ∼ 20 times the median bed sediment grain size, no fluctuating component was measured, indicating that a thin layer of bed sediment can act as a very effective low-pass filter, shielding the bed from erosive particle impacts.
 As a result of the fluctuating component of basal force, force variability and the probability of large-magnitude forces increased with increasing time-averaged mean force. Despite increases in the spread of the distribution with increasing time-averaged mean force, distribution shape parameters remained relatively constant as a function of time-average mean force, as well as across events, which suggests that there might be a characteristic distribution shape for the monitored basin. If particular rock types only produce small particles with a narrow grain-size distribution, then the probability of effective impacts could dramatically decrease and with it the incision rate.
 Despite the visual distinction between granular surges and water-rich, intersurge flows based on surface flow characteristics, both flow types appear to have a similar basal force signature. Intersurge flows have frequency domain characteristics similar to granular surges, as well as similarly broad basal force distributions. As a result, high erosive potential is not strictly limited to the visually coarse-grained surge front in the monitored flows. Rather, erosive potential likely exists during the majority of a debris-flow event. In total, these results indicate that debris flows are important agents of landscape change and move us closer to a defensible stochastic approach to steepland evolution by debris flows.
 This research was supported by the National Science Foundation (NSF) Graduate Fellowship, NSF grants EAR 0643240 and EAR 0952247, and the USGS Landslides Hazards Program. Randy Amen provided invaluable guidance during the design and construction of the force plate. The Associate Editor D. Lague and reviewers R. M. Iverson, B. W. McArdell, and J. D. Stock all provided thorough and critical reviews that improved the manuscript. Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the U.S. government.