E3S Web of Conferences 415, 03016 (2023)
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https://doi.org/10.1051/e3sconf/202341503016

Volume, Peak discharges and Froude Number of Debris-Flow
Surges: 10 Years of Monitoring on the Réal Torrent (France)
Suzanne Lapillonne1,*, Firmin Fontaine1, Guillaume Piton1, Vincent Richefeu2 and Frédéric Liébault1
1 Univ. Grenoble Alpes, INRAE, CNRS, IRD, Grenoble INP, IGE, 38000 Grenoble, France
2 Univ. Grenoble Alpes, 3SR, 38000 Grenoble, FranceAbstract. This work presents a summary of data on debris-flow monitoring stations focusing on the surge
scale rather than full-scale debris-flow event (several fronts and surges with intermediate diluted flows). Surgescale debris-flow data are not easily accessible for modellers but would be very beneficial for the community.
A summary of the data processing protocol is offered, and its application to the monitoring station of the Réal
Torrent is described (drainage area: 2 km², SE France). Investigated bulk surge features are volume, front
height, peak discharge, and Froude number. This investigation leads to statistical distributions of theseparameters on 34 surges gathered from 2011 to 2020. Their volumes are typically a few thousand cubic metres,
their peak flow height is 1 to 2 m, their peak discharge is a few dozens of cubicmetres per second and their
Froude number is near critical. Results drawn from this work will be a great asset for modellers to better feed
their numerical experiments with realistic, field-driven features.

1 Introduction
Debris-flow monitoring has attracted increasing
attention in the past twenty years [1]. Thanks to debrisflow monitoring efforts, a wide range of torrent
catchments are now equipped to record a variety of data.
Although these measurements are being recorded, very
few data has yet been made available, especially at thesurge scale. The most basic features of debris-flow
surges remain unclear: worldwide debris-flow volumes
can vary from a few hundreds to a few millions of cubic
metres; peak discharges, front depth and velocity arepoorly known. Discharge, grain sizes, rheologicalfeatures of the bulk surges and interstitial fluid are alsovariable and rarely reported in the literature [but see 1,2, 4]. Some datasets have been shared, like for instancereported volumes of full-scale debris-flow events in theIllgraben catchment [5] and ful hydrographs of debris
flow events in the Moscardo catchment [6]. This paves
the way to international collaboration for an easy to use
database.
Numerical modellers as well as physical modelling
initiatives need such data ranges to better design theirsimulations. Due to this lack of dataset, wide ranges ofparameters are explored, for example wide ranges of
Froude numbers [7–9 among others]. Exploring suchwide ranges requires huge amounts of effort, which
could be redirected towards better understanding thephysics of debris-flow surges if a narrower range wasused. On the contrary, there is a habit of using very
simple flow hydrographs, with narrow ranges ofdischarge, when the variability of real flow hydrographs

has shown to have a significant impact on the flow
behaviour [4]. Providing a complete database, including
multiple sites in different geomorphological contexts
would allow modellers to design experiments closer tofield reality. Understanding the high variability of
Nature is complex, and takes both financial andtemporal
resources. Providing a public data set would allow
debris-flow research to focus on deeper questions. The
present work is a proof of concept. It aims to quickly
present a protocol to be implemented in order to build
such a complete database and shows preliminaryresultson the monitoring site of the Réal Torrent [1,10,11].
This database contains data on representative surge
volumes, Froude numbers, maximum height andpeak discharge of the surges.

2 Methods
2.1 Overview of an event analysis
Debris-flow monitoring stations have several types ofmeasurement strategies [12,1]. In Figure 1, a conceptual
sketch of the essence of the protocol implemented in theRéal is displayed. Overall, several types of sensors arenecessary to feed the database regarding velocity, depth
and wetted cross-section (Fig. 1a):(i) flow stage measurements with a frequency thatallows catching the peak flow;(ii) accurate hypothesis on the cross-section at themonitoring station (Fig. 1b), which can include
hypotheses on channel erosion / deposition or detailed
geometry of the cross-section (e.g. a check dam);* Corresponding author: suzanne.lapillonne@inrae.fr© 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, 03016 (2023)
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https://doi.org/10.1051/e3sconf/202341503016

𝐹=𝑢√𝑔⋅ℎ𝑚𝑎𝑥(3)

2.2 Surge identification
Detecting a debris-flow surge is not a trivial task.
Monitoring stations record all the continuum of flowtypes encountered in steep headwaters, anddifferentiating debris-flow surges from debris flood andrunoff with high sediment transport can sometimes betricky. This is especially true for continuous monitoring
stations where the harsh conditions lead to measurement
setups focused on being reliable and light in datatransfer, meaning camera recordings of the events canbe scarce.
Similarly, because debris flows are generallycomposed of several surges and eventually have liquid
diluted flows, defining the end of the surge front and thebeginning of the diluted flows is important. Indeed, thesurge front is a very complex and the most destructive
part of the flows. Focusing data analysis on this front
goes hand in hand with the intention for this database to
be used for modelling the surge behaviour. This work is
thus different from previous initiatives where the full
event, sometimes with multiple surges and more diluted
flows, was aggregated (as provided in [5]). The
applicability of Eq. (2) also relies on high solid
concentration, meaning diluted flows cannot be taken
into account.
By experience, identifying debris-flow surges using
exclusively the flow stage sensor is quite unreliable,
especially in catchments where after-flows are very
intense. Another criterion may be used and preferably
one that can be cross-controlled. Having a rational andprecise threshold for differentiation and definition ofsurges is vital to the rigour of this database project.

Fig. 1. Overview of a debris-flow event analysis: a) typicallocation and types of sensors, b) cross section
approximations: real cross sections are approximated to a
virtual equivalent to estimate wetted areas for discharge andvolume calculations, c) velocity estimation by travel timeanalysis

2.3 Application to the Réal Torrent (France)
For the purpose of illustration of the protocol, data fromthe Réal Torrent monitoring stations are used
[10,11,13,14]. This catchment is monitored by threestations, one on a check dam and two on natural crosssections further downstream (drainage areas of 1.3 km²,1.7 km² and 2.0 km², respectively). Each station isequipped with a rain gauge, a flow stage sensor andseveral geophone sensors. The geophone sensors record
seismic activity near the flow stage sensor location, as
well as upstream and downstream of this location.
Distance between the sensors makes the physicalintegrity hypothesis to be sensible. Stations are also
equipped with cameras that allow both to confirm
hypotheses on debris-flow surge identification anddifferentiation from debris floods, and to have access toa cross-control of the velocity measurement by image
analysis.
The identification of debris flow is done using theseismic sensors by visual interpretation. Indeed, they
provide a data-driven criterion for debris-flow detection
because they capture the sediment transport activity. It
has been shown that mature debris flows have acharacteristic seismic signature where (i) the seismic
signal shows a sudden increase when the front passes at(iii) access to the flow velocity either via direct
measurements (LS-PIV or image processing) or using
the travel time of the surge between a pair of sensors(Fig. 1c).
These measurements must be available at a location
at which it is reasonable to assume that: (i) the measured
velocity can be safely assumed to be the velocity of thesurge caught by the flow stage sensors; (ii) the surges
keep their physical integrity between the two sensors,i.e., the surge does not stop, is not divided into multiple
surges or merged with other surges, and the surge shape
between the two sensors has not drastically changed.
If these assumptions are valid, it will be possible toaccess the main properties of interest, i.e., the velocityof the surge u, the peak discharge Qp, the volume V, thepeak flow stage hmax and the Froude number F. These
key parameters describing the surges are then computed
using the time series from the sensors where Δt = 1/f, f
is the sampling frequency of the signal and Q(t) is theinstantaneous discharge:
Q(t) = u · A(t)(1)
V = Σt Q(t) · Δt(2)

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the level of the sensor, and (ii) the seismic activity ishigh and does not drop to zero for the whole duration of
the surge [15]. On the contrary, immature debris flows,debris floods and bedload-laden flows may trigger
seismic activity which are instantaneously high, butwhich do drop to zero, appearing as a very strong andnoisy signal, characterized by a low signal-to-noise
ratio. The characteristic seismic signal of a debris-flow
surge is, in essence, a prolonged and consistent seismic
activity. A more thorough description of this method,
including discussion on aggregated signals for volume
estimation is available in [16].
The delay between the geophone sensors catching
the debris-flow signature signal is computed throughcross-correlation. Velocity of the front surge is thencomputed from that delay (Fig. 1c).
For natural cross-sections, different hypotheses areused to assume a relationship between hmax and thewetted area, using both the expertise on local geometry
from [15] and hypotheses on the erosion / deposition
profiles, including results from [17] (Fig. 1b).
The gathered data come from 10 years of recording(2011 - 2020). For this paper only surges with hmax
> 1 m have been kept, considering them as maturesurges.
If multiple surges happen on the same event but do haveseismic signatures clearly separated by a diluted phase, thetwo surges are considered separately.Conversely, if twosurges appear to be almost continuous regarding thecharacteristic seismic signature but keep their two-peaks
shape on all sensors, they are taken as a single surge.
This case remains marginal (one surge). These criteria
sum to have 34 surges for the Réal Torrent, 26 of which
are from the upstream station, located on a 8 m-widecheck-dam; four at the intermediate station (7 m-widenatural channel) and two at the lowest station (12 mwide natural channel).

Fig. 2. Cumulative density functions of four hydraulicproperties of debris-flow surges of the Réal Torrent: a)volume, b) maximal flow stage, c) peak discharge and d)
Froude number.

Surge volumes range from 200 to 4500 m³ (Fig. 2a quantiles 25%, 50%, 75%: 390 m³, 640 m³, 1460 m³).
Surges are relatively small, typically from 300 to2000 m³/km² (recall that this is surge scale and an event
may comprise several of them and some after-flows).
Maximal flow stage is most of the time lower than 2 m(Fig. 2b - quantiles 25%, 50%, 75%: 1.1 m, 1.25 m, 1.6m). The peak discharge range between 6 and 92 m³/s
(Fig. 2c - quantiles 25%, 50%, 75%: 11 m³/s, 18 m³/s,
28 m³/s). Comparison of these features to features ofother debris flow prone catchments can be found in [16].
The unit peak discharge is thus typically 1 to
8 m³/s.m. Finally, Froude numbers range from 0.25 and1.6 (Fig. 2d - quantiles 25%, 50%, 75%: 0.48, 0.65,0.95), i.e. are typically near critical, i.e. between 0.5 and1.5. Interestingly, this is consistent with laboratory
observations on debris flood processes [18].
Froude numbers used in the literature for debris-flow
modelling are usually much higher than these values. A
wider dataset could help to confirm if the measurements
made on the Réal Torrent are consistent with other sites
or if this trend is site-specific. We should then findfeatures that can be cross-compared between different
sites as for instance specific sediment yield (m³/km²),
unit discharge (m³/s.m) and Froude numbers. Thispermits modellers to have a first idea of the ranges ofhydraulic properties of debris flows. If more monitoring

3 Results
3.1 Database structure
Results from processing the surges are gathered into a
database in HDF5 format and stored by surges. Froudenumbers, maximal flow stage, peak discharge, flow
volume and front velocity are stored, as well as raw datafrom the monitoring (rainfall measurements, seismicsignals, flow height, location of the sensors and versionof the data logger). For each computed property,
uncertainties on the measurements and error estimationfrom the hypotheses are also saved. This is especiallycritical for natural cross-sections where the hypotheses
on wetted areas is a major component of the global
uncertainty.
3.2 Ranges of hydraulic properties of debris
flow surges
Such data points allow us to study ranges of thedifferent properties. In Figure 2, the cumulative
distribution functions are plotted for Froude numbers,
maximal flow stage, peak discharge and volumes.

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stations were to get associated with this project, not only
would more statistically representative data beavailable, but also new relationships between theseproperties could be explored. The interpretation of thecurrent content of the database might not be exploitable
as is - 34 events on one site is too specific to be able toretrieve global behaviours - but a rich dataset would
allow to explore deeper scientific questions, and benefit
the community.

2.

4 Discussion
Choosing to segment the event at surge scale isserving the purpose of surge scale modelling but does
present drawbacks concerning the study ofmorphological changes associated to whole events.
Complete sediment balance as well as temporal andupstream-downstream transfers are not described.
Indeed, bed-load, wash-load and small debris flood
events are not included in the database, meaning that thefull catchment sediment export is not described.
Several hypotheses would be unreasonable if applied
to non-debris flow processes: (i) Eq. (1) assumes that thesurge velocity is a relevant proxy of the flow velocity.
This surge velocity if applied to hydrographs would not
be relevant. (ii) Eq. (2) is only applicable if the solid
concentration is very high. For diluted flows, the solid
phase and the liquid phase should be consideredseparately which is difficult, as the solid concentration
cannot be directly measured easily.

5 Conclusion
This work is a proof of concept for data processing ofdebris-flow surges from monitoring stations. Bulk surgefeatures are investigated including volume, front height,
peak discharge and Froude number. This investigation
leads to statistical distributions of these parameters on
34 surges gathered from 2011 to 2020 on the Réal
Torrent. Their volumes are typically a few thousands
cubic metres, their peak flow height is 1 to 2 m, theirpeak discharge is a few dozens of cubic metres per
second and their Froude number is near critical.
These results show the potential of an international,
collaborative database. We believe debris-flowmonitoring has reached sufficient maturity to makerepresentative hydraulic properties available for themodelling community. We clearly intend to complete
this database using collaborative approaches and we arelooking for monitoring sites and experts willing to shareeither their raw or pre-processed data to feed thedatabase. The database will be made available and will
come with a descriptive note for each monitoring site.
This project is funded by the LabEx Tec21 Investissements
d'avenir - agreement n°ANR-11-LABX-0030.

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