E3S Web of Conferences 415, 02014 (2023)
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Statistical Modelling of Sediment Supply in Torrent Catchmentsof the Northern French Alps
Maxime Morel1,2,*, Guillaume Piton2, Damien Kuss3, Guillaume Evin² and Caroline Le Bouteiller2
1Office National des Forêts - service de Restauration des Terrains en Montagne des Hautes-Alpes, 5 rue des Silos, 05000 Gap, France
2Univ. Grenoble Alpes, INRAE, CNRS, IRD, Grenoble INP, IGE, Grenoble, France
3 Syndicat Mixte des Bassins Hydrauliques de l’Isère, 9 rue Jean Bocq, 38022 Grenoble, FranceAbstract. The ability to understand and predict sediment transport in torrent catchments is a key element
for the protection and prevention against the associated hazards. In this study, we collected data describing
sediment supply at 100 torrential catchments in the Northern French Alps. These catchments have longrecords of past events and sediment supply due to debris deposition basin management enabling estimationof sediment supply frequency. The mean annual, the 10-year return period and the reference volume (i.e.
the 100-year return level or the largest observed volume) of sediment supply were derived for studied
torrents. We examined the relationships between sediment supply volumes and several explanatory variables
using multivariate statistical analyses. Several predictive models were developed in order to estimate thesediment supply in torrents that are not equipped with sedimentation structures.

1 Introduction
In mountain areas, the knowledge of the mean annualand event-driven sediment supply potential is important
for the assessment of torrential hazards and themanagement of torrent catchments. Empirical methods,
relating volume to descriptive catchment characteristics(for example, [1-3]), are a relatively simple approach toestimate the material supply of a torrent and arecommonly used in engineering projects.
These approaches have generally been calibrated ona limited number of torrents and/or with shortobservation periods. Some of these approaches are
specifically focused on debris flows and/or have beencalibrated on "specific" torrents, i.e. particular, very
active torrents producing large amounts of sediment.
Since most empirical equations were derived fromsamples of very active torrents, these equations maylead to overestimations when applied to catchments withfew or small sediment sources. On the contrary, the lessactive, dormant torrents produce very erratically large
amounts of sediment and their low background sedimentproduction is usually unknown. Luckily, some of theserarely active catchments in the French Alps were also
equipped with debris deposition basins.
This study aims to present a new prediction approachbased on multivariate statistical models calibrated froman original dataset covering 100 torrents catchments in
the Northern French Alps for which sediment supply
records have been documented over a period of 5 to 40years and have a wide spectrum of active erosion areaand several order of magnitude of sediment specificyield.

2 Materials and method
In this study, we analysed 100 torrents with sedimentsupply data in the Northern French Alps (Fig. 1). The
dataset is varied and includes debris-flow-prone,bedload-prone, and mixed torrents. For example,
catchment areas range from 0.06 to 77.8 km² (median:2.7 km²), the Melton index ranges from 0.09 to 2.8(median: 0.77), and the ratio Rzp of connected eroding
areas in the catchment defined as the ratio between thecumulated area of bare soil and rock connected with thetorrent bed, divided by the catchment area ranges from
0.1% to 98% (median: 4%).
Data on sediment supply volumes were collectedfrom the monitoring of debris deposition basin dredging
and historical records from the catchment managers. For
the studied torrents, the records on sediment supply
covered periods ranging from 5 to 40 years (mean: 25years).
These data were used to estimate the average annual
volumes for all the torrents studied. For the torrents
where long enough records were available, individual
frequency analyses for each torrent were performed toestimate the quantile representing the sediment supply
volume for a 10-year return period, as well as thereference volume, i.e. the 100-year return level or thelargest observed volume (Fig. 2). The latter refers to thevolume of the largest known and documented event or atheoretical 100-year return period event, if higher as wasthe case for 15 catchments. Generalized Pareto
distribution GPD or exponential type adjustment were* Corresponding author: maxime.morel@onf.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/).

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performed depending on the number of observations(GPD if n > 10 non-null observations were available).

catchment, Melton index, alluvial fan slope, etc.). Fig. 3shows the distribution of some of the calculated
explanatory variables.
Based on this database, multivariate statisticalanalyses using Random Forests (RF) and multiple linear
regression (LR) were performed to relate theexplanatory variables to the sediment supply variablesof the studied torrents.

Fig. 1. Spatial distribution of the studied sites. The colours
represent the different data providers (State (ONF-RTM):
state torrent control service; AS: Isère river tributaries
manager in Isère department; METRO Grenoble:
intercommunality of Grenoble; SFTRF: Fréjus tunnel
motorway manager; SM3A: Arve river catchment manager).

Vref = 62823 m3;
Method: GPD

V10 = 26169 m3;

Gumbel variable u
Fig. 2. Statistical adjustment performed from theobservations to estimate the volumes: example on the Ebron
torrent (Isère, France). The monitoring period covers 35 years
and presents 19 years with non-null observations. A GPD
distribution was adjusted.

Fig. 3. Distributions of the main characteristics of the studied
torrents: a) catchment area; b) ratio of connected areas; c)stream slope; d) Melton index; e) proportion of the of thesample classified according to [5] into debris flows, debris
flood or floods. The colours represent the different dataproviders.

On the studied catchments, several morphologicalandhydrometeorologicalcharacteristics
weredetermined (for example, sediment connectivity indices[4], proportion of connected eroded areas in the2E3S Web of Conferences 415, 02014 (2023)
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3 Results and concluding remarks
Multivariate statistical analyses were used to select themost relevant variables to predict the specific annual
sediment yield (m3/km²/year) and the event specificsediment yield (m3/km²/event) for the 10-year return
period and the reference event.
Results showed that the ratio Rzp of connected
eroding areas was the most important predictor of thesediment production volumes (eg. Fig. 4). Other
variables such as the Melton index or the indices ofsediment connectivity have also an influence.

Fig. 4. Relationship between the specific sediment yield forthe 10-year return period and the ratio of connected eroding
areas; colours refer to the classification into debris flows,debris flood or floods according to [5].

Several statistical models were then calibrated basedon several selected explanatory variables and theirperformance was then assessed. For example, Equations(1-3) show the most simple predictive models derived
from the LR involving the catchment area and the ratioof connected eroding areas.
Vm/A=52 Rzp0,81(1)V10/A=168 Rzp0,88(2)
Vref/A=475 Rzp0,94(3)where Vm, V10 and Vref are the mean annual volume, the10-year return period volume and the reference volume(m3), respectively; A is the catchment area (km²) and Rzp
is the ratio of connected eroding areas in the catchment(%).
To assess the performance of the different models,we performed a leave-one-out cross-validation
procedure, and we used several criteria: the coefficientof determination R2, the percentage bias, the RMSEstandard deviation ratio of observations. In general, theselected models predict satisfactory sediment supplyvolumes, even with very simple empirical equations
such as Eq. (1-3). The predictive models lead to R2
coefficients ranging from 0.62 to 0.75. Contrary to what
was expected, the RF models do not bring
improvements compared to the LR models (e.g. Fig. 5).
All the details regarding both the material and methods,
and the results can be found in the research report of theproject [6], as well as in a preprint paper [7] (includingthe full dataset).

Fig. 5. Predicted against observed values of sediment supply
for the Vm, V10 and Vref. The grey squares et and dark circles
represent the values predicted by LR (Eq. 1-3) and RF
respectively. Solid black line refers to the perfect agreement.
Dashed and grey lines refer to [Vpred./2 ; 2Vpred.] and[Vpred../5 ; 5Vpred.], respectively.

Performance was also assessed by measuring theproportions of the ratio of predicted to observed values
within the intervals [2/3; 3/2]; [1/2; 2] and [1/5; 5]. We
noticed that about 30 % of the predictions fall in the first3

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interval, about 50 % in the second and a very highproportion in the third which is very large. Thisdemonstrates the limitations of these methods thatprovide at most orders of magnitude of sediment supply.
This study is part of the HYDRODEMO project which isfinanced by the European Union through the FEDER POIA
program and by state funds through the FNADT-CIMA
program. The authors would like to thank the French torrent
control service (ONF-RTM) and the many catchment
stakeholders who provided dredging data on the torrents.

References
1.

2.
3.

4.
5.
6.

7.

A. Takei, in International SymposiumInterpraevent (pp. 35-48), June 1984, Villach,
Austria (1984).
L. Marchi, V. D’Agostino, Earth Surface
Processes and Landforms, 29(2), 207–220 (2004)
C. Peteuil, F. Liébault, O. Marco, in 12th Congress
Interpraevent (pp. 293-304), April 2012, Grenoble,France (2012)
M. Cavalli, S. Trevisani, F. Comiti, L. Marchi,Geomorphology, 188, 31–41 (2013)
D.J. Wilford, M.E. Sakals, J.L. Innes, R.C. Sidle,
W.A. Bergerud, Landslides, 1, 61–66 (2004)
M. Morel, G. Piton, G. Evin, C. Le Bouteiller.
Projet HYDRODEMO : Évaluation de l’aléa
torrentiel dans les petits bassins versants desAlpes du Nord - Action 3 : Caractériser laproduction sédimentaire. INRAE [online]
Available from: https://hal.archivesouvertes.fr/hal-03549827 (2022)
M. Morel, G. Piton, D. Kuss, G. Evin, C. Le
Bouteiller. EGUsphere DOI: 10.5194/egusphere2022-1494, (2023)

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