E3S Web of Conferences 415, 01024 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341501024

Inferring spatial variations in velocity profiles and bed geometryof natural debris flows based on discharge estimates from highfrequency 3D LiDAR point clouds; Illgraben, Switzerland
Raffaele Spielmann1,2*, Jordan Aaron1,2, and Brian W. McArdell2
1ETH Zürich, Department of Earth Sciences, Engineering Geology, 8092 Zurich, Switzerland
2Swiss Federal Institute for Forest, Snow and Landscape Research WSL, 8903 Birmensdorf, Switzerland

Abstract. More detailed field measurements are required for a better understanding of surging debris flows.
In this work, we analyze a debris flow at the field-scale using timelapse point clouds from a high-resolution,
high-frequency 3D LiDAR sensor, which has been installed over a check dam on the fan of the Illgraben
catchment in Switzerland. In our investigations, we manually measured the front velocity and tracked
individual features such as large boulders and woody debris over a 25 m long channel segment. We observed
a change in the front velocity as well as a difference in the velocity of large boulders and woody debris(vboulder ≈ 0.6 vwood) during the second surge of the event. We also estimated the discharge for different
closely spaced channel sections based on automated measurements of the cross-sectional area and thesurface velocity, which enabled us to infer spatial variations in the bed geometry and the velocity profile.
From the discharge estimates, we then derived the volume of this event. Over the course of the next year,
the amount of field-scale LiDAR data from the Illgraben will increase substantially and allow for an evenmore detailed analysis of fundamental debris-flow processes.

1 Introduction
The destructiveness of debris flows is strongly
controlled by their surging behavior, which manifests as
peak discharge values being order of magnitudes larger
than floods [1, 2]. This surging behavior is not fully
understood at present and more detailed fieldmeasurements are needed to clarify this process [3, 4].
In particular, high temporal and spatial resolution
measurements of front and surface velocity as well as
event discharge are needed to better understand debrisflow destructiveness. In the present work, we quantify
the following of these hazard-related parameters in
unprecedented detail at the field scale using a newly
installed 3D timelapse LiDAR scanner: (i) front
velocity, (ii) surface velocity, (iii) cross-sectional area,(iv) discharge and (v) event volume.
In the past, debris-flow front velocity has been
quantified using time-distance methods, video sequence
analysis or high-frequency radar measurements [5].
Other researchers have studied the velocity profile
present in debris-flow material and have shown that it
can vary from block sliding to simple shear [6, 7].
Furthermore, debris-flow discharge has been
investigated at many locations worldwide [5]. Thesestudies have revealed that discharge can vary strongly
through time due to the surging nature of these flows.
In the present study, we use a high-resolution, highfrequency (10 Hz), multi-beam LiDAR scanner (OusterOS1-64, Gen. 1; see also [8]), which has the distinct* Corresponding author:

advantage – especially over the abovementioned,
conventional monitoring techniques – of capturing an
undistorted, truly 3D representation of the surroundings,
even in the absence of light or during rainfall. Such a
LiDAR scanner has been installed in Switzerland’s
Canton of Valais at the Illgraben, one of the most active
debris-flow catchments in the Alps [9]. The monitoring
station is located roughly 500 m downstream of the fanapex, and the sensor is suspended in the middle of thechannel above a check dam (Fig. 1). On 19 September
2021, the LiDAR scanner recorded a first debris-flow
event, which will be analyzed herein.

Fig. 1. LiDAR scanner (Ouster OS1-64, Gen. 1) and video
cameras at the monitoring station “Gazoduc”, which islocated on the fan of the Illgraben next to a check dam, ca.
500 m downstream of the apex.

raffaele.spielmann@erdw.ethz.ch© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0(https://creativecommons.org/licenses/by/4.0/).

E3S Web of Conferences 415, 01024 (2023)
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https://doi.org/10.1051/e3sconf/202341501024

2 Methods

In addition to these manual measurements, analgorithm for automated surface velocity measurement
was developed. The algorithm provides the (mean)surface velocity as 3D vector field, which covers theentire investigated channel segment (Fig. 2b) at any time
during the event and is based on fusing video camera
and LiDAR data, as described in detail in [8].

The first step was pre-processing the raw point clouds,
i.e. all point-cloud frames of the 19 Sept. 2021 event. In
this step, the point clouds were rotated around the meanslope of the channel segment upstream of the sensor(3.70°) to a bed-parallel coordinate system. Afterwards,
the point clouds were cropped to a 50 m x 20 m x 8 m
box to omit reflections from objects outside of thechannel bed (e.g. trees).
Because the shape of the channel bed during thedebris-flow event is unknown (erosion or deposition),
we prepared different channel geometry scenarios toaccount for this uncertainty when measuring the crosssectional area (cf. also [10]). For each section, a preevent and post-event channel geometry was defined
based on LiDAR scans recorded immediately before andafter the event, respectively. Furthermore, we specified
a third, intermediate channel geometry which served as“mean” scenario for these measurements (Fig. 2a).

2.2 Cross-sectional area
The cross-sectional area of the flow was determined atseveral locations along the channel (Fig. 2b) considering
three different basal channel geometry scenarios (Fig.
2a). In the upstream sections (upstream of sensor
distances y = 25 m and 20 m), the cross section could bemeasured in the LiDAR data directly by fitting abounding area (using Matlab’s alphaShape function)
between the current debris-flow surface and the base of
the flow. For the more downstream sections (y = 15 m,10 m, 5 m and 0 m), point clouds acquired fromphotogrammetric drone flights prior and after the event
were used as basal channel geometry because theLiDAR’s field of view does not cover the entire channel
width (Fig. 2b). For the same reason, the debris-flow
surface had to be extrapolated from the middle of thechannel to the banks for these four sections before fitting
the bounding area. The errors introduced by theextrapolation are small because the flow surface waslargely horizontal in this event (cf. also Fig. 2a).
2.3 Discharge and event volume
The discharge was estimated by multiplying the surface
velocities by the cross-sectional area. For the surface
velocity we used the mean value across a channel
section (Fig. 2b), while for the cross-sectional area weconsidered the value derived from the intermediatechannel geometry (Fig. 2a). We note that this approachassumes a constant bed geometry and plug-flow velocity
profile, which are important assumptions and will be
discussed in Section 4. If there are spatial variations in
bed geometry and/or the velocity profile, we expect thatthe estimated discharge through these cross sections will
not be the same. To quantify this, we further calculated
the ratio between the discharge estimates obtained forthe various cross sections.
The event volume was derived by integrating thedischarge over the entire duration of the event. Because
our discharge values are not continuous but discrete intime, the volume was calculated as Riemann sum oversubintervals of 1 s.

Fig. 2. a) Channel section ca. 25 m upstream of the LiDARsensor (cf. Fig. 2b) with basal channel geometries (averageover 1 m long slice) as well as flow surface and measured
cross-sectional area for the intermediate scenario.
b) Investigated channel segment with approximate locationsof the analyzed cross-sections (upstream of sensor distance yin meters). The red dots indicate the LiDAR point cloud
projected on the camera image. Only cross-sections y = 15 m
and y = 5 m will be analyzed in detail herein (Fig. 4).

2.1 Front and surface velocity
The high-resolution timelapse point clouds allowed us
to identify features in the moving debris flow such as theflow front as well as large rolling boulders and woody
debris. These features were labelled manually by fitting
cuboids around them in every fifth point cloud frame(i.e. at a frequency of 2 Hz) using Matlab’s groundTruthLabeler. From the 3D Euclidean distance between
subsequent cuboid positions and the correspondingtimespan (i.e. 0.5 s), we calculated the 3D velocity of
the front as well as of rolling boulders and woody debris.

3 Results
3.1 Front and surface velocity
As indicated in Figure 3, the velocity of the debris-flow
front changes within the investigated channel segment.
In a first phase (01:47–01:54) the front is moving at
1.2 m/s, whereas in a second phase (01:54–02:04),

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Fig. 3. Trajectory of the flow front from the 19 Sept. 2021
event, manually identified in the LiDAR point-cloud frames.
The slopes of the linear trendlines indicate the change in front
velocity from 1.2 m/s in a first phase (01:47–01:54) to0.8 m/s in a second phase (01:54–02:04).

Fig. 4. Discharge estimates for the 19 Sept. 2021 debris flowat sections 15 m and 5 m upstream of the sensor (cf. Fig. 2b).
The ratio Q(y=5)/Q(y=15) is also indicated to highlightspatial variations in bed geometry and/or velocity profile.

which begins roughly 5 m upstream of the sensor (cf.
Fig. 2b), the front decelerates to 0.8 m/s.
We also manually measured the mean velocity ofdifferent surface features. During the first surge of theevent (02:04–07:00), rolling boulders and floating
woody debris were moving at similar velocities, ranging
from 1.2 m/s to 1.9 m/s. However, in the second surge(07:00–13:00), the velocity of the rolling boulders was
substantially slower (1.5 m/s–2.2 m/s) than the velocityof the woody debris (2.6 m/s–3.6 m/s). The ratio of these
two feature velocities during the second surge wasapproximately 0.6 (i.e. vboulder ≈ 0.6 vwood). Manualmeasurements later in the event could not be performed
due to a lack of identifiable surface features.
Spatially and temporally much more detailed
measurements of the surface velocity were obtained in
the automated analysis, which is described in detail in[8]. The automated measurements follow the generaltrend over time, which was already observed in the
manual measurements, i.e. the surface velocities wereslower (1.2 m/s–2.3 m/s) during the first surge (up to07:00) than in the second surge of the event (1.5 m/s–
3.1 m/s). Furthermore, the automated analysis also
revealed a spatial variation in the surface velocity along
the investigated channel segment.

3.3 Discharge
The discharge shown in Figure 4 was estimated for thesections at 15 m and 5 m upstream of the sensor, basedon the automated surface velocity measurements(assuming a plug-flow velocity profile) and theintermediate channel geometry scenario (cf. Sect. 2).
The discrepancy between the calculated discharge forthe two different channel sections is roughly 5 m3/s(Fig. 4) and is mainly related to the abovementioned
decrease in cross-sectional area towards the check dam.
The underlying assumptions and the implications of thisobservation will be discussed in Section 4.
Figure 4 also shows the ratio between the more
downstream (y = 5 m) and the more upstream (y = 15 m)discharge estimates. Over the first 15 minutes of theevent, this ratio is between 0.7 and 0.8 before slightly
dropping to 0.5–0.6. As will be discussed in Section 4,
this indicates that the channel bed and/or velocity profile
are spatially and temporally variable.
3.4 Event volume
Based on the two discharge estimates shown in Figure
4, we calculated the volume of the 19 Sept. 2021 debrisflow (cf. also Sect. 2.4). For the section at y = 15 m we
calculated a volume of 17 500 m3, whereas for thesection at y = 5 m we obtained 12 500 m3. It is important
to note that this volume range is most likely a maximum
estimate because we assumed a plug-flow velocity
profile, i.e. a maximal depth-averaged velocity value(see also Sect. 4).

3.2 Cross-Sectional areaThe cross-sectional area in the more upstream sections(i.e. y = 25 m, 20 m and 15 m; cf. Fig. 2b) was between
10 m2 (post-event channel geometry) and 13 m2 (preevent channel geometry) during the passage of the front.
Afterwards, the cross-sectional area slightly decreased
to 7 m2–10 m2, before increasing again after 07:00 tovalues between 9 m2 and 12 m2. Then, the crosssectional area started decreasing relatively steadily andfell below 1 m2 at around 25:00.
In the sections closer to the check dam (i.e. y = 5 mand 0 m), the cross-sectional area shows a similar trend
over time. However, all values are generally between
3 m2 and 5 m2 smaller than in the more upstream
sections., i.e. we observed a general decrease in crosssectional area towards the check dam, which will bediscussed below (Sect. 4).

4 Discussion
The observed decrease in the front velocity (Fig. 3) by
ca. 0.4 m/s could be explained by a change in thechannel slope and a widening of the channel crosssection. The mean channel slope in the segment 10 m to20 m upstream of the sensor is 4.2° and the channel
width is 7 m–9 m, whereas in the segment from 0 m to10 m the slope reduces to 1.9° and the channel width
increases to 12 m–14 m.

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The spatial changes of surface velocity along thechannel are most likely related to the presence of thecheck dam. The decrease in flow depth (cross-sectionalarea) towards the check dam is also likely caused by thecheck dam, which is analogous to the hydraulicdrawdown upstream of a critical flow section observed
in river flow (e.g. [11]).
The uncertainty of the cross-sectional area caused by
the unknown shape of the channel bed during the flow
is about 3 m2 (difference in cross section assuming preevent and post-event channel geometry). Nevertheless,the differences in the cross-sectional area between theupstream and downstream sections (e.g. y = 25 m andy = 0 m differ by 3 m2–5 m2 over most of the event)exceed this qualitatively-assessed uncertainty value,indicating that topographic uncertainties alone cannot
explain the observed decrease in cross-sectional area
towards the check dam.
Based on our calculations, the discharge in theinvestigated channel section decreases towards thecheck dam (Fig. 4), which would imply deposition of alarge amount of material, not observed in the LiDAR
and video data. As mentioned in Section 2.3, thisdiscrepancy could be due to either a change in thevelocity profile along the channel and/or a change in theheight of the channel bed during the event. In the firstcase, the depth-averaged velocity of the upstream
section (y = 15 m) would have to be reduced by a factorof 0.6–0.8 (i.e. the discharge ratio shown in Fig. 4) andwould no longer be characterized by a plug-flow
velocity profile. In the second case, the cross-sectional
area at y = 15 m would be reduced by the same factor(cf. Fig. 4), which could be caused by sedimentdeposition during (an early phase of) the event. At
present, it is difficult to separate these two effects, butthey will be investigated in future events.
As mentioned in Section 3.4, our volume estimates
represent maximum values because we assumed a plugflow velocity profile for the calculation of the discharge.
Therefore, the actual event volume might be smaller
than our estimates. Furthermore, the volume range of ca.
5 000 m3 provides an uncertainty assessment of ourvolume estimates related to the variable bed geometry
and velocity profile, and it underlines the importance ofinvestigating and better understanding these spatial
variations in order to further reduce this uncertainty inthe future.

tracked individual features such as large rolling boulders
and woody debris and showed that the former feature
was moving at roughly 0.6 the velocity of the latter
during the second surge of the event (i.e. vboulder ≈ 0.6vwood). In addition, we analyzed the discharge in various
sections (assuming plug-flow and a mean channel bedgeometry) upstream of a check dam and observed adecreasing discharge (3 m3/s–5 m3/s) towards the checkdam. This “discharge paradox” could potentially beexplained by an along-channel change in the velocityprofile and a changing channel bed elevation during theevent.
In order to better understand the fundamental
mechanisms and to quantify spatial variations invelocity profiles as well as bed geometry, further
investigations are necessary and will be carried out overthe course of the next year based on additional fieldscale LiDAR data from the Illgraben.
We are grateful to Christoph Graf and Stefan Boss, Swiss
Federal Research Institute WSL, for their support in the fieldinstallation. We also would like to thank Dr. Tjalling de Haas,
Utrecht University, for the processing of photogrammetricdata. This research project is part of an Ambizione project
funded by the Swiss National Science Foundation (grantnumber 193081).

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5 Conclusions and outlook
In this study, hazard-related debris-flow parameters
were measured with unprecedented detail at the fieldscale using a novel high-resolution, high-frequency 3Dtimelapse LiDAR sensor. The sensor was installed at theIllgraben catchment and recorded point clouds during
one debris-flow event (19 Sept. 2021), which wereanalyzed using both manual as well as automatedmethods. In our velocity measurements, we documented
a decrease in the front velocity by 0.4 m/s over a ca.
25 m long channel segment and observed changes in thesurface velocity during the event. Furthermore, we4