Debris-flow surges of a very active alpine torrent : a field database

. This paper presents a protocol to analyze debris flow focusing on the surge scale rather than the full scale of the debris flow event, as well as its application to a French site. Providing bulk surge features like volume, peak discharge, front height, front velocity and Froude numbers allows for numerical and experimental debris flow investigations to be designed with narrower physical ranges and thus, for deeper scientific questions to be explored. We suggest a method to access such features at surge scale that can be applied to a wide variety of monitoring stations. Requirements for monitoring stations for the 5 protocol to be applicable include (i) a flow stage measurements, (ii) a cross section hypothesis and (iii) a velocity estimation. Raw data from three monitoring stations on the Réal torrent (drainage area: 2 km 2 , South-East France) are used to illustrate an application on 34 surges measured from 2011 to 2020 on the three monitoring stations. Volumes of debris-flow surges on the Réal Torrent are typically sized at a few thousand cubic meters. Peak flow height of surges range from 1 to 2 m. Peak discharge range around a few dozens cubic meters per second. Finally, we show that Froude numbers of such surges are near critical. 10

experiments. There is, for instance, a habit of exploring very large ranges of Froude numbers in numerical studies of impact forces, typically 1 -8 (e.g., Albaba et al., 2015;Ceccato et al., 2018;Ng et al., 2020, among others). Performing such extensive parameter studies is a prudent approach that ensure to cover the poorly known variability of Nature. However, it creates huge needs regarding experimental effort, computational power and time. These efforts are a high price to pay as they mean that more complicated scientific questions are not explored due to a lack of resources. In addition, in both experimental and numerical 40 simulations, Froude numbers used are usually high, namely typically > 2 -4 (e.g., Ng et al., 2020;Chen et al., 2020;Goodwin and Choi, 2022). Meanwhile, various regimes of impacts and flow behavior emerge depending on the Froude number (Faug et al., 2012), but the transition seem to occur for lower Froude values, typically near critical (Laigle and Labbe, 2017). Whether it makes sense to study each regime highlighted in laboratory experiments for field application should be decided in the light of field measurements. Thus, a database would ensure using features that are more representative of field reality, saving time 45 to focus on deeper scientific questions. Now that monitoring stations have been installed for a reasonable period of time, raw data processing is possible in order to build a common and open data base on flow characteristics of debris-flow surges. Such a database would aim to give access to the scientific community to values of typical flow features such as volume, maximal flow height, peak discharge and Froude numbers of real debris flows. A protocol for debris-flow surges data processing is described in the present paper to focus on 50 the surge scale rather than full scale debris-flow event (several fronts and surges with intermediate diluted flows).
The end goal of this paper is to define a common protocol that is sufficiently simple to apply to make it widely usable to any debris flow monitoring stations. Using it will then permit gathering characteristics of debris-flow surges in a homogeneous, easy to access database. Surge identification, velocity computation and volume determination methods are more thoroughly described in this paper. The protocol we used to process monitoring data is first presented in this paper. Its application to the  Each monitoring station has different types of sensors and different strategies to measure flow characteristics (Hürlimann et al., 2019). To apply the protocol, the following measurements are required ( Fig. 1): flow stage measurements with representative frequency f (> 2Hz), sufficient to detect maximum height of the flow, known cross section where the flow is measured, or , a hypothesis on the relationship between flow height and wetted area, a way to access directly the velocity of the surge, typically by estimating the travel time between a pair of sensors (eventually of different type) at sensible distance from one another, or , more accurate but rarely available, by direct velocity measurement (e.g. image processing or large scale particle image velocimetry, see Theule et al., 2017).

70
These measurements must be done at sufficiently close locations to reasonably assume that the measured flow stage is associated with the measured surge velocity.

Surge identification
A debris flow is generally composed of one or several surges, with eventual intermediate flows that are more diluted (called "diluted runoff" hereafter). The strongest complexity, destructive power, and interest in debris flows is most probably the surges and their fronts. As a consequence, the database aims at gathering measurements focusing on the surge fronts and their main 85 body, rather than the full scale of the debris-flow event including several surges ( e.g. as provided in McArdell and Hirschberg, 2020). In addition, it is arguable that diluted runoff have a lower sediment concentration and contribute much less significantly to the bulk event volume than the main, mature debris-flow surges. As a matter of fact, the applicability of Eqs. (1) and (2) rely on a hypothesis of high solid concentration, constant throughout the surge. Focusing data processing at the surge scale goes hand in hand with the intention for this database to be used to explore scientific question on the surge front behavior. This 90 approach is different from other initiatives in the literature where the full scale of the event was considered.
Clearly defining the surges is thus a prerequisite to the data processing as the volume of the surge is integrated over the surge duration (Eq. 2), not the full event duration. If several surges in a single event are identified, each surge is taken separately as a data-point of the database.
The most basic identification of the surges is performed on the flow stage time-series by identifying surges on the flow 95 hydrograph. Doing so without cross control based on other information is however doubtful on catchments where diluted runoff and debris floods are frequent and intense. By experience, when available, images of the front can be used to define this separation. Geophones data proved to enable more reliable and data-driven criteria because they capture the solid transport intensity Chmiel et al., 2022). Bel (2017) showed that when mature debris flows travel at the levels of the geophones, the seismic activity is high and does not drop to zero. Conversely, immature debris-flow surges or debris floods 100 may trigger seismic signal, instantaneously high, but still dropping to zero. The existence of a prolonged period of consistently high seismic activity can be chosen to differentiate debris-flow events from immature debris flows and debris floods. Diluted runoff are also easily differentiated from the surge using geophone signal. surge : geophone actiity decreases before a sharp increase due to a second surge; t3 marks the end of the second surge : seismic activity is negligible even though the flow height is still high: those are the diluted runoff flows, t4 marks the start of the third surge. Note that even though the second surge has two peaks on the flow level, it is seen as one surge due to continuous seismic activity On Fig. 2, the concept of the identification is described. The onset of a surge is detected by a sharp increase in both flow level and seismic activity, followed by a consistently non-zero seismic activity. The end of a surge is either determined by a seismic 105 activity dropping to zero or by the onset of a second surge that can clearly be separated from the first one. Indeed, at the end of the first surge of the figure, a drop in seismic activity is clearly observed and a second sharp increase announces a second surge. On the other hand, the second surge displays two peaks in the flow level but as the seismic activity stays consistently high, those two peaks are considered part of one single surge.

Velocity calculation 110
In the proposed approach, as shown in Eq. (1), a single velocity value is considered for each surge. By doing so, the authors knowingly assume that the velocity is uniform within the surge. This is a crude simplification of the complex rheology of debris flows. The assumption is however required due to the lack of more precise data on most monitoring sites (see an exception in Nagl et al., 2020). This surge average velocity is a relevant proxy of the front velocity. Carefully defining the surge main body and consistently not including diluted runoff is a pivot point of this approach, as this approximation on the velocity is more 115 relevant if the surge is only restricted to its front and main body (see section 2.1.2).
The velocity is generally computed using the lag ∆t between the signals of two sensors and the known inter-distance ∆L between those sensors. Once the lag is determined, the velocity is computed as u = ∆L ∆t . Accessing the value of this lag is done by comparing the two signals and their time-scale characteristics. Choosing two sensors that are at a sensible distance one from 5 https://doi.org/10.5194/egusphere-2022-1297 Preprint. Discussion started: 3 January 2023 c Author(s) 2023. CC BY 4.0 License. another is important: choosing two sensors too close to each other will induce significant uncertainty in the lag measurement.
Due to the direct comparison of signals, the approach assumes that the source of the signal is the same that was propagating between the two different locations; in other words, the same surge is detected at both location. This approach thus also assumes that the surge does not significantly change between the two sensors e.g., no massive deposition or erosion, no strong change in surge duration, no merging between surges. However, the travel distance should be sufficiently longer than the uncertainty on the lag to provide an accurate estimate. Two methods were used to estimate velocities : cross-correlation of signals if they 125 were good enough and a visual identification method otherwise. For more information, the detailed protocol is presented in supplementary data.

Wetted area
From raw data, flow height and wetted area are determined at each time step. This requires assumptions on the channel bed level. Two examples will be presented in this section : assumptions that are reasonable on a check dam, and assumptions on a 130 natural cross-section.
On controlled cross-sections, e.g., on a check dam crest, it is assumed that there is neither erosion, nor deposition. Consequently, the bed level and cross section shape are assumed constant and known. Flow height and wetted area can then easily be estimated. This configuration is preferable. Practically this means Erosion and deposition occurring during debris-flow events may change the channel geometry. Not only does this mean that h ef f ective ̸ = z measured − z bed where z bed would be the bed level before the flow [m], but it also means the cross-section shape will change during the event. The erosion-deposition process has two consequences : uncertainty on the channel shape and uncertainty on the channel bed level at a given time during the surge.

140
Accounting for the variability of the channel is necessary (e.g. width, bed level, shape). Cross-wise profile shape is sensitive to the event. Simplifying assumptions are necessary for cross-section shape : the simplest being the rectangular shape. Other, more precise, assumptions are to be made when information is available (e. g. trapezoidal, including knowledge of a nonerodible level on one side).
Bed level change throughout the surge is explored using different hypothesis (Fig. 3). With z low,min the minimal bed level 145 through the event, three hypothesis are made, when relevant : -The whole depth of the flow is sheared (effective ) until z low,min during the whole surge (hypothesis max), -The flow isn't sheared in depth, this is less likely but allows to compute a minimal possible volume (hypothesis min), -In the case of an erosion process, the bed level is assumed to follow a fitted logarithmic law following Kaitna and Hübl (2021)   The Réal Torrent, located in south of France, has been instrumented since September 2010 (Navratil et al., 2011). Three monitoring stations are distributed along the channel. Fig. 5 shows the station locations. The first one S 1 is located on a 20m wide check dam as seen on Figure 8a and is the most upstream. Station S 2 and S 3 are located in the middle reach and at the outlet of the torrent, and are both on natural cross-sections. In Table 2, a summary of the main physical features of the stations 155 is shown (drawn from Bel et al., 2017). The purpose of the installation is to monitor the flow stage, rainfall and seismic activity during sediment activity from bedload to debris flow. A thorough study of the station can be found in Fontaine et al. (2017) and in Bel (2017). The protocol presented above has been applied to these three stations and the results are presented further in this paper.
In essence, each station is equipped with : (i) a tipping bucket rain gauge with 0.201mm resolution (Campbell), (ii) an 160 ultrasonic or radar flow stage sensor (Paratronic), (iii) a set of three vertical geophones (GS20DX0 Geospace) each spaced out ≈ 100m apart from each other, upstream, midstream and downstream of the flow stage sensors.
Images of the channel and flow proved to be useful to facilitate the interpretation of the signals (Piton et al., 2017). Two cameras have been added to stations S 1 and S 2 (CC640 Campbell, replaced in 2018 by a PC900 Reconyx and EOS1200D Canon, respectively). Data are recorded using an environmental datalogger (CR1000 Campbell) powered by a solar panel, and 165 are stored in a compact flash module (CFM100 Campbell).   low correlation coefficient or inconsistent velocity when compared to a first quick manual computation). This visual method was used marginally, i.e. for one surge in our case, and was confirmed using image processing.
These sensors and post-processing allow to have for each event the followings : (i) seismic activity at three different points 180 around the station with a frequency of 5 or 10Hz, (ii) rainfall data every 5mn, (iii) flow stage with a frequency of 5 or 10Hz, and (iv) imagery of the event (when possible) with a 0.2 or 1Hz frequency,

Summary of available data
For the construction of the database, only significant events were considered to ensure the analysis of mature debris flows: a 185 threshold of flow stage above 1 m was selected for this catchment. Overall, 34 events were considered for the Réal station for the period 2011-2020. Table 2 show when those events occurred, the number of surges passing at each station and the availability of the describing parameters. Over the 34 surges, most, i.e. 26, are recorded in the upstream station S 1 , while only four surges reached S 2 and only two reached S 3 , the most downstream station. The lack of events on the period 2014 -2018 is partially due to the natural variability of event sizes but also due to faulty sensors during that time period.  Table. 2, and some diluted runoff). Maximal flow stage is most of the time lower than 2m ( Fig. 6a -quantile 25%, 50%, 75%: 1.1m, 1.25m, 1.6 m). The peak discharge range between 6.2 and 91.8 m 3 /s (Fig. 6b 200 -quantile 25%, 50%, 75%: 10.8 m 3 /s, 17.5 m 3 /s , 27.9 m 3 /s). The unit peak discharge is thus typically 0.775 to 7.65 m 3 /s.
Finally, Froude numbers range from 0.25 to 1.6 ( Fig. 6d - Table S1. Finally, relationships between these hydraulic values may be explored with a wider dataset, and a more thorough description of each event. Fig. 7 shows for instance the relationship between a few key variable (Froude numbers, volume of each surge   normalized by the catchment area, front height and velocity). To cross-compare measurements performed at different stations, but also to help transferring these results to other catchments, the surge volume was normalized by the catchment area. A slight trend can be seen on Fig. 7a with increasing Froude number for increasing specific surge volume. Maximum flow stage is quite variable with surge volume (Fig. 7b). Similarly, no clear correlation seems to appear between front velocity and flow stage (Fig. 7c). Litterature data has been displayed, drawing from Comiti et al. (2014) We interpret these lack of trend as evidences of varying surge viscosity between events. The sample size remains however relatively small and site-specific, calling for prudent interpretation of these data. We believe it will be of high interest if several other sites could be added to a similar analysis. Fitting a relationship between Froude numbers and surge volume could be a very interesting asset for numerical and experimental modeling. 156m 3 /km 2 to 3342m 3 /km 2 . In comparison to specific volumes given by McArdell and Hirschberg (2020), which range from 171m 3 /km 2 to 7690m 3 /km 2 , these are much smaller. One of the key reason why there is such a difference -apart from 220 differences in geological and rheological makeup-is the method employed : classically, available volumes can contain multiple surges and diluted tails and thus, volumes are not as restrictive as in the method employed in this paper. Specific volumes of the Réal catchment being much smaller is consistent with the difference in hypothesis in each methods. In Comiti et al. (2014), the Gadria catchment monitoring is described and the method employed is much more comparable. In that case, specific volumes for the two events are 380m 3 /km 2 and 1500m 3 /km 2 , which show similar range to our dataset.  The absence of subcritical Froude numbers can be seen as such heavy and large surges requiring a strong inertial input to flow.
On the other hand, smaller surges can flow more easily and do not need strong inertial inputs to maintain steady flow. The catchment, so the surges with high volume that are passing at the stations meet the "minimum requirements" to flow. One surge with supercritical Froude number and high volume is still detected.
For smaller specific volumes (< 1000m 3 /km 2 ), Froude numbers range from 0.2 to 1.2 with most surges being clearly 240 subcritical with Froude < 0.8. Flow conditions for smaller volumes require less inertial input. For a same specific volume, a wide range of subcritical Froude numbers are found, showing that volume is not the main driver to flowing conditions, and that surge viscosity vary widely in surges with low volume, i.e. < 1000m 3 /km 2 .
The initial expectation for Figure 7b would be that surges of higher volume render higher maximal flow stage. This would be the case if hydrograph shape was consistent on all events. The lack of clear relationship between the two features highlights 245 the complexity of debris flow surges : surges with the highest volumes can be caused by short very high flows or longer more moderate flows. There is a great variety of hydrograph shapes at surge scale. Figure 7c shows no definitive relationship between witnesses of inertial and potential inputs in the flow. This is yet another argument to point out that surge granular content and viscosity might differ widely from one event to another on the same catchment. The idea that composition of the debris flow surges changes between events is supported by Hürlimann et al. 250 (2003). A study of the surge content in boulders and coarse grain (Takahashi, 2014) and of their interstitial fluid rheology (Bardou et al., 2003) would be complementary to support this idea, but is at the moment not possible with the available data.

Evidence of the erosion/deposition cycles
On Fig. 5b and d, the valley bottom landforms bear the footprint of high morphological activity due to debris flows. More specifically in the reach between S 1 and S 2 where landforms such as abandonned channels, levees and lobes can be seen 255 (Fig. 1b-c). Fig. 8 exemplifies these changes in the channel morphology directly downstream of station S 1 at five different dates. An erosion/deposition cycle of the channel incising and refilling is highlighted over six years of field pictures. Such processes explain why many debris flows are measured at station S 1 while much less are observed further downstream.
In Figure 9, volumes of all events are shown along time. If the geomorphic cycle exemplified in Figure 8 was detectable by this method, pseudo-cycles of cumulated volumes surges at station S 1 would be less frequently exported as surges of 260 higher volume at station S 2 (or as many small volume surges at S 2 in the following years). It can be seen that the two surges reaching station S 3 are indeed of relatively high volume but the data lacking between 2015 and 2019 prevent us to draw further observations. With the current data, we can simply conclude that higher volumes of debris flows pass station S 1 than further downstream. The system is thus either or both storing sediment in the valley through aggradation and/or also exporting sediment volume through another process than mature debris flows. The applicability of this approach to study the sediment

Upstream-downstream transfers of debris-flow surges along the channel
A key interest of having three different monitoring stations on the same torrent is the possibility to study cascading sediment transfers. Fig. 10 shows the analysis of volumes, flow rates, Froude numbers and flow height of each events that could be found on more than one of the station. One could expect to see consistent relationships between upstream and downstream 275 characteristics but results are more complicated.
Volumes passing stations S 1 , S 2 and S 3 are generally very different at a same date (Fig. 10). In some cases, the debrisflow surges were growing, recruiting sediment from the bed (V 2 > V 1 and / or V 3 > V 2 ) showing the profound morphological changes debris flow passage can lead to. In other cases, some deposition occurred (V 2 < V 1 ) but erosion might still appear downstream. For the subset of events happening on the same date at the three stations, no particular relationship between the 280 four parameters studied in Fig. 7 was identified.
On Fig. 10a and b, volumes and peak discharge should consistently grow if the surges were consistently eroding from upstream to downstream of the reach. Events like the 2012-04-30 surges show increasing volumes, with a potential agglomeration of the surges between S 1 and S 2 (accumulated volumes at S 1 are smaller than the volume at S 2 ). This shows deep erosion is possible between the two stations, which is consistent with the morphological changes shown on Figure 5b. Nonetheless, on 285 this event, peak discharge is not increasing between the two stations.
Similarly, maximum surge depth can also either be lower upstream (2013-03-30 of Fig. 10c) or higher at the first station (events of summers 2011 and 2014, Fig. 10c). The Froude number also varies from upstream to downstream with some events a b c d having lower downstream Froude number and others not (Fig. 10d). Froude numbers could be expected to be consistent from upstream to downstream : the ability to flow of the surge would be driven by the interplay between kinetic and potential inputs.

290
Erosion and deposition processes of the surge along the reach will influence the Froude number both by changing the volume and the composition (and viscosity) of the surge.
The observation on volumes, discharges and surge heights, as well as the much stronger frequency of mature debris flow passing S 1 against those passing S 2 or S 3 (26, 4 and 2, respectively), highlight that strong processes of erosion and deposition occur in the catchment.

295
While analysing data from three different stations located on such a small and active catchment is interesting, events detected on multiple stations are scarce : most surges detected upstream tend to deposit or to attenuate while travelling such that they are not detected as a mature surge downstream. On the opposite end of this spectrum, a surge that was under the detection threshold on the upstream station might have become fully formed in the downstream stations (see the events of June 10, 2014 and October 28, 2018 that were detected at S 1 , not at S 2 and again detected at S 3 , Tab. 2).

300
On the other hand, surges that are detected on multiple stations are also difficult to rely to each other, and although volume comparison could be interesting, actual quantitative comparison relies on the hypothesis that the exact same surge between upstream and downstream stations is comparable, i.e. that along the journey, only marginal changes in process occurred, which is known to be a crude hypothesis of this first work. In essence, the data shown in this paper are interesting because they are actual field observations with quantitative measurements but the analysis of the catchment sediment transfers is not 305 possible. However, the dataset does demonstrate how strong and intense the processes of erosion and deposition in debris flow prone catchments are. An analysis seeking to determine rainfall triggering conditions of debris flows would for instance draw different conclusions depending on which station is used (but see Bel et al., 2017, which partially addresses this issue). We believe that further effort should be put on better understanding not only debris-flow triggering factor but also propagation through headwaters and intermediate reaches.

Analysis of the physical ranges of the events
Comparing the present data to the literature shows the ranges found in the Réal torrent to be consistent with empirical fits proposed in previous works (Bovis and Jakob, 1999;Rickenmann, 1999;Mizuyama et al., 1992), even though the measurements of volumes were done with debris-flow levees in these previous works rather than direct measurements as our contribution.
According to Fig. 11, the peak discharge of the Réal catchment for various volumes of debris-flow surges seems closer from 315 the empirical fit related to granular debris flows of Bovis and Jakob (1999) or the fit proposed by Rickenmann (1999). Peak discharges associated with muddy debris flows are lower than those measured at the Réal catchment for equivalent volumes.
These results are consistent with the work of Bel (2017) who already showed this concordance using an analysis considering the full debris-flow event with a former version of this protocol.
This work is a proof of concept for data processing of debris-flow surges from monitoring stations. A full and simple protocol on debris-flow data processing is presented. The clear goal of this paper is not only to make a first dataset available but also to call for collaboration on a common database for debris-flow surge features.
Bulk surge features are investigated including volume, front height, peak discharge and Froude number. This investigation allowed to access these hydraulic features on 34 surges gathered from 2011 to 2020 on the Réal torrent catchment (South-East 325 France, catchment size 1.3 -2 km 2 ). Surge volumes are typically a few thousand cubic meters, peak flow heights range from one to two meters, peak discharge is usually of the order of magnitude of a few dozens of cubic metres per second and their Froude number is near critical.
Access to representative field data will ensure accurate representation of these natural flows. This database is meant to be extended to other monitoring stations to strongly gain in impact on the scientific community. Open access to field data 330 for numerical research can be the bridge needed to close any gaps between the field-driven approaches and the numerical investigations. Research on debris flow behaviour is growing and we hope that this initiative will allow more projects to be born, and allow field observations and numerical computations to evolve conjointly. On top of this, experiences drawn from the post processing of such data can allow for better, more effective data monitoring in the future (e.g. what type of cross section to choose, where to install successive stations).