Data Processing and Analysis

4.4.2.1 Stage data

To smooth high-frequency noise associated with small splashes and waves and to highlight more persistent changes in flow depth we filtered the 10 Hz laser stage data with two filters. First, we used a 3-point moving-window-median filter centered on the current point. This filter preserved the complex structure of the time series, but removed anomalously high and low readings due to missed returns or returns from very large splashes. We then used a moving-window-mean filter centered on the current point with a window width of 1 s, which acted as a low-pass filter with a

cutoff frequency (the frequency at which amplitude gain equals p1/2) of ∼ 0.5 Hz [Smith, 1997].

We filtered the 2 s ultrasonic stage data based on echo return strength to remove low-strength inaccurate returns. These ultrasonic-stage data were only used in 2009 and for the debris-flow event that occurred on 30 June 2011.

4.4.2.2 Stress data

To smooth the stress data in the time domain and highlight the low-frequency, long-wavelength components we also filtered the stress data. Before filtering, we converted the raw force data (100

Hz or 33 Hz) to stress by dividing the time series by the force plate area (232 cm2). We then filtered

73 current data point. This procedure acted as a low-pass filter with a cutoff frequency of ∼0.5 Hz.

The mean state of stress on the force plate was non-stationary due to entrainment and removal of the static bed sediment and due to large changes in flow depth as deep surges passed the station. To determine how stress measurements were distributed relative to this non-stationary mean stress, we calculated probability density functions (pdfs) of scaled stress in which each stress measurement was normalized by the median of a 1 s centered moving window. The window width was chosen to be a fraction of the average surge duration (∼ 5 s).

4.4.2.3 Pore-fluid pressure data

We measured p using unvented, temperature-compensated pressure transducers. To remove the atmospheric pressure component from the measured gauge pressure we subtracted the pre-storm dry-bed pressure (assumed to be purely atmospheric) from all subsequent pressure measurements. This procedure produced similar results, within error, compared with when we independently and concurrently measured atmospheric pressure and then subtracted this time series from the time series of gauge pressure. Hence, we discontinued use of the separate barometric pressure sensor. To quantify the degree to which pore-pressure signals generated in the near-surface bed sediment by the overriding flow experienced frequency-dependent attenuation during propagation to deeper depths, we calculated power spectra of the signals from each bed-sediment pressure transducer. The power spectra were calculated from short segments (7 seconds) of the time series directly preceding each erosion-sensor-element-removal event. Amplitude attenuation was reported as gain, which is the ratio of amplitude at depth to the amplitude at the near-surface transducer.

4.4.2.4 Average erosion rates

Average erosion rates and initiation of erosion were determined from direct measurements of bed sediment height for events when they were available. To determine average erosion rates for events in which direct measurements of bed sediment height were not made, we used two separate indirect methods. For both methods we assumed that bed-sediment erosion began when a large

74 surge front arrived. This assumption is supported by events for which initiation of erosion was directly measured with the erosion sensor. In the first method, we used the temperature sensor onboard the basal pressure transducer to determine the timing of complete removal of bed sediment. We observe that complete removal of bed sediment is indicated by an abrupt drop in temperature when the sensor first makes contact with cold flow water. We determined the uncertainty in response time of the temperature sensor to be ±3.5 s during laboratory and field tests. In the second method, we used the timing of the first occurrence of a large-magnitude (>1.5 times the current mean stress) high-frequency stress signal to determine the timing of complete removal of bed sediment. This approach was developed after the combined analysis of the erosion sensor and stress data demonstrated that thin layers of bed sediment rapidly damped the effect of impulsive loading through frictional interaction (see analysis of the effects of stress damping below).

4.4.2.5 Video

We used the spatially referenced video imagery at the upper station, taken at 2 frames per

second, to calculate flow-front velocity ¯u for each surge as it passed the upper station and to

separate events into granular surges and inter-surge flow (auxiliary material Videos 1, 2, 3, 4 and 5 ). Inter-surge flows were water-rich flows that lacked coarse particles on the surface of the flow, and were characterized by turbulence, waves, and splashes. Despite the watery appearance, inter-surge

flows generally had bulk densities > 1300 kg m−3. Shallow flows that transported thin sheets of

granular material, approximately a grain diameter thick, were also designated as inter-surge flow. Granular surges were defined as those having a distinctly high concentration of coarse-grained particles (cobbles and boulders) on the surface of the flow, and flow depths many grain diameters deep.

4.4.2.6 Discharge and total event volume estimate

To create a continuous time series of flow velocity at the upper station, needed for discharge and volume estimates, we developed a rating curve. The rating curve relates surge-front velocity

75 ¯

u, calculated from the video footage at the upper station from all events, to flow depth h using ¯

u = 1.4√gh (root-mean-squared error equals 0.7 m s−1), in which g is the gravitational acceleration.

We calculated the time series of flow depth as the difference between the stage time series and the average bed sediment height time series, determined from the temperature perturbation method described above.

For each debris-flow event, we estimate the total event volume passing the upper station, V (sediment plus water), using

V = te X tb ¯ u(h(t))A(t)∆t (4.1)

in which the summation was taken from the beginning of a flow event tb to the end te, ¯u(h(t))

is the mean cross-sectional velocity from the rating curve, ∆t is the length of time between two stage measurements, and A(t) is the active cross-sectional area at a given time, calculated using the surveyed bedrock cross section, the corresponding bed height and flow depth.

4.4.2.7 Bulk density and factor of safety

We calculated the wet bulk density of a flow ρf(t) by assuming a one-dimensional static stress

state and by using

ρf(t) = σf(t)/(gh(t) cos(α)) (4.2)

in which h(t) is the time series of measured flow depth and σf(t) is the time series of total nor-

mal stress due to the flow only, g is gravitational acceleration, and α is the bed and force plate

inclination. We calculated σf(t) as the difference between the total normal stress measured at the

sediment bedrock interface σ(t) and the total normal stress due to the weight of the bed sediment

covering the force plate σs (σf(t) = σ(t) − σs(t)). Accurate bulk densities can only be determined

from this method when the assumption of a static stress state is valid. This assumption was most closely approximated when meter-scale bedrock bedforms near the force plate were covered by a graded layer of bed sediment. Such a state was present at the beginning of each event, before

76 bounds that present for all events and accounts for the uncertainty in flow depth and stress.

To assess the stability of the total thickness of bed sediment, we calculated a factor of safety F OS at the bedrock-sediment interface by assuming cohesionless sediment and by using the measured time series of total normal stress σ(t) and pore-fluid pressure p(t), and the measured friction angle of the bed sediment φ in

F OS = (σ(t) − p(t)) tan φ/(σ(t) tan α). (4.3)

4.4.2.8 Bed Sediment Characterization

Prior to the monitored flows, we collected 3 kg samples of channel-bed sediment at the upper station to analyze the fine fraction (< 5 cm) using standard sieve and hydrometer methods [Coe et al., 2008]. We used a a random-walk point count at the upper station to select 100 rocks from the channel-bed surface and levee deposits and measured the length of the three axes to characterize the coarse fraction. To measure the internal angle of friction φ we excavated 30 kg of bed sediment,

oven dried the sample at 105◦C for 24 hours, and used a tilt table with dimensions of 60 cm by 37

cm by 6 cm deep, by methods described in Iverson et al. [2010].

Sieve and hydrometer results from two samples collected in 2008 show that the sieved channel sediment was ∼60% gravel, ∼35% sand ∼3% silt and ∼2% clay. These results are very similar to results obtained previously by Coe et al. [2008]. The median grain sizes of these two samples were 10 mm and 8 mm. The median values of the A, B, and C axes of the coarse fraction present on the bed-sediment and levee-deposit surfaces were 100 mm, 70 mm, and 40 mm, respectively. The liquid and plastic limits for both samples were nearly equal and < 20%, which places them in the cohesionless soils category according to the Unified Soil Classification System plasticity chart. Coe et al. [2008] determined that field-saturated hydraulic conductivity of recently deposited channel sediments, as well as older, consolidated channel and levee deposits, ranged from 0.014 to 0.024 cm

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