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To cite this version: Douinot, Audrey and Roux, Hélène and Garambois, Pierre-André and Dartus, Denis Using a multi-hypothesis framework to improve the understanding of flow dynamics during flash floods. (2018) Hydrology and Earth System Sciences, 22 (10). 5317-5340. ISSN 1027-5606

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Hydrol. Earth Syst. Sci., 22, 5317–5340, 2018https://doi.org/10.5194/hess-22-5317-2018© Author(s) 2018. This work is distributed underthe Creative Commons Attribution 4.0 License.

Using a multi-hypothesis framework to improve the understandingof flow dynamics during flash floodsAudrey Douinot1, Hélène Roux1, Pierre-André Garambois2, and Denis Dartus1

1Institut de Mécanique des Fluides de Toulouse (IMFT), University of Toulouse, CNRS – Toulouse, France2Laboratoire des Sciences de l’ingénieur, de l’informatique et de l’imagerie (ICUBE) – INSA Strasbourg, Strasbourg, France

Correspondence: Audrey Douinot ([email protected])

Received: 4 December 2017 – Discussion started: 8 December 2017Revised: 14 September 2018 – Accepted: 18 September 2018 – Published: 16 October 2018

Abstract. A method of multiple working hypotheses wasapplied to a range of catchments in the Mediterranean areato analyse different types of possible flow dynamics insoils during flash flood events. The distributed, process-oriented model, MARINE, was used to test several repre-sentations of subsurface flows, including flows at depth infractured bedrock and flows through preferential pathwaysin macropores. Results showed the contrasting performancesof the submitted models, revealing different hydrological be-haviours among the catchment set. The benchmark study of-fered a characterisation of the catchments’ reactivity throughthe description of the hydrograph formation. The quantifi-cation of the different flow processes (surface and intra-soilflows) was consistent with the scarce in situ observations,but it remains uncertain as a result of an equifinality issue.The spatial description of the simulated flows over the catch-ments, made available by the model, enabled the identifica-tion of counterbalancing effects between internal flow pro-cesses, including the compensation for the water transit timein the hillslopes and in the drainage network. New insightsare finally proposed in the form of setting up strategic moni-toring and calibration constraints.

1 Introduction

1.1 Flash flood events: an issue for forecasters

Flash floods are “sudden floods with high peak discharges,produced by severe thunderstorms that are generally of lim-ited areal extent” (IAHS-UNESCO-WMO, 1974; Garam-bois, 2012; Braud et al., 2014). They are often linked to

localised and major forcings (greater than 100 mm; Gaumeet al., 2009) at the heads of steep-sided, mesoscale catch-ments (with surface areas of 10–250 km2).

The large specific discharges and intensities of precipita-tion lead to the flash floods being classified as extreme. Nev-ertheless, those events are not scarce nor unusual, since onaverage, there were no fewer than five flash floods a year inthe Mediterranean Arc between 1958 and 1994 (Jacq, 1994),and they tend to be amplified against a background of climatechange (Llasat et al., 2014; Colmet Daage et al., 2016). Flashfloods constitute a significant hazard and are therefore a con-siderable risk for populations (UNISDR, 2009; Llasat et al.,2014). They are particularly dangerous due to their charac-teristics, namely that (i) the suddenness of events makes itdifficult to warn populations in time, and this can lead topanic, thus increasing the risk when a population is unpre-pared (Ruin et al., 2008), (ii) the traditional connected mon-itoring systems are not adapted to the temporal and spatialscales of the flash floods (Borga et al., 2008; Braud et al.,2014), and (iii) the magnitude of floods implies significantamounts of kinetic energy, which can transform transitoryrivers into torrents, resulting in the transport of debris rang-ing from fine sediments to tree trunks as well as the scouringof river beds and the erosion of banks (Borga et al., 2014).

A major area of interest for flash floods is, therefore, betterrisk assessment, which enables them to be forecasted and therelevant populations to be pre-warned. Greater knowledgeand understanding is required to better identify the determin-ing factors that result in flash floods. In particular, in orderto implement a regional forecasting system, the properties ofthe catchments and the climatic forcing and linkages betweenthem that lead to flash flood events need to be characterised.

Published by Copernicus Publications on behalf of the European Geosciences Union.

5318 A. Douinot et al.: Using a multi-hypothesis framework to improve the understanding of flash flood dynamics

1.2 Flash flood events: understanding flow processes

Due to the challenges involved in forecasting flash floods,there has been considerable research done on the subjectover the last 10 years. Examples include the HYDRATE (Hy-drometeorological data resources and technologies for effec-tive flash flood forecasting, 2006–2010; Gaume and Borga,2013), which enabled the setting up of a comprehensive Eu-ropean database of flash flood flash events as well as the de-velopment of a reference methodology for the observation ofpost-flood events, the EXTRAFLO (EXTreme RAinfall andFLOod estimation, 2009–2013; Lang et al., 2014) to estimateextreme precipitation and floods for French catchments, theHYMEX project (HYdrological cycle in the MediterraneanEXperiment, 2010–2020; Drobinski et al., 2014) focusingon the meteorological cycle at the Mediterranean scale andparticularly on the conditions that allow extreme events todevelop, the FLASH project (Flooded Locations and Simu-lated Hydrographs, 2012–2017; Gourley et al., 2017) assess-ing the ability and the improvement of a flash flood forecast-ing framework in USA on the basis of real-time hydrologi-cal modelling with high-resolution forcing, or the FLOOD-SCALE project (Multi-scale hydrometeorological observa-tion and modelling for flash floods understanding and sim-ulation, 2012–2016; Braud et al., 2014), based on a multi-scale experimental approach to improve the observation ofthe hydrological processes that lead to flash floods.

In the northwestern Mediterranean context – especiallyconcerned with specific autumnal convective meteorologi-cal events – the European cited research particularly demon-strates the importance of cumulative rainfall (Arnaud et al.,1999; Sangati et al., 2009; Camarasa-Belmonte, 2016), theprevious soil moisture state (Cassardo et al., 2002; Marchan-dise and Viel, 2009; Hegedüs et al., 2013; Mateo Lázaroet al., 2014; Raynaud et al., 2015) and the storage capac-ity of the area affected by the precipitation (Viglione et al.,2010; Zoccatelli et al., 2010; Lobligeois, 2014; Garamboiset al., 2015a; Douinot et al., 2016). The combined influenceof the spatial distribution of precipitation and event-relatedstorage capacities, reported in the study of a number of par-ticular events (Anquetin et al., 2010; Le Lay and Saulnier,2007; Laganier et al., 2014; Garambois et al., 2014; Facciniet al., 2016), suggests that there is a hydrological reaction insome areas of the catchments that arises from localised soilsaturation. This statement surmises that there is little directHortonian flow, but rather that there is a production of runoffthrough excess soil saturation or lateral fluxes in the soil re-sulting from the activation of preferential pathways.

The geochemical monitoring of eight intense precipitationevents over a 3.9 km2 catchment area (Braud et al., 2014)underlined the dominance of the intra-soil dynamic. First, ananalysis of the water from the first 40 cm of the soil layerrevealed a flushing phenomenon, the water present at thestart being replaced by so-called new rainwater (Braud et al.,2016a; Bouvier et al., 2017). In addition, even if the peaks of

the floods mainly consisted of new water, with a proportionvarying between 50 % and 80 %, it appears that over the en-tire period of the events, old water accounts for between 70 %and 80 % of the total volume of water discharged, which sup-ports the dominance of the water pathways in the soil.

Finally the geological properties themselves appear tobe markers of the storage capacities available over thetimescales involved in flash floods (that are of the orderof a day). From simple flow balances of flash flood events(Douinot, 2016), studies of the diverse hydrological re-sponses of several catchments over the same precipitationepisode (Payrastre et al., 2012) or the application of re-gional hydrological models dedicated to flash flood sim-ulation (Garambois et al., 2015b), the literature tends todemonstrate the low storage capacity of non-karst sedimen-tary catchments and marl-type catchments, and, conversely,the potential for storing large volumes of water in the alteredrocks of granitic or schist formations.

1.3 Applying a multi-hypothesis framework forimproving the hydrological understanding of theflash flood events

The knowledge gained about the development of the flowprocesses (for example, the tracing of events carried out dur-ing the FLOODSCALE project; Braud et al., 2014) relates tostudies on a number of specific sites where flash floods couldbe observed while they were taking place. However, beingable to generalise the knowledge gained is limited by the spe-cific nature of each study (McDonnell et al., 2007) and by thegap between the spatial scale of forecasts (mesoscale) com-pared with that of the in situ observations (<10 km2) (Siva-palan, 2003). Hydrological modelling work can be consid-ered as a means of extrapolating knowledge to an extendedgeographical area, possibly covering catchments with differ-ing physiographic properties.

Moreover, hydrological models viewed as ”tentative hy-potheses about catchment dynamics” are interesting tools fortesting hypotheses about hydrological functioning using asystematic methodology. A considerable amount of recentlypublished works has involved comparative studies, using nu-merical models to develop or validate the hypotheses aboutthe type of hydrological functioning that is most likely toreproduce hydrological responses accurately (Buytaert andBeven, 2011; Clark et al., 2011; Fenicia et al., 2014, 2016;Coxon et al., 2014; Ley et al., 2016). Using the same model’sstructure but differing solely in terms of the hypotheses testedin the form of modules, the comparison is then focused andrestricted to the hydrological assumptions tested. Doing thisavoids the limitations on interpretation that are often en-countered in comparative studies of models (Van Esse et al.,2013), where numerical choices can influence results inde-pendent of the underlying assumptions.

The multiple working hypotheses framework is usually ap-plied using a flexible conceptual and lumped model frame-

Hydrol. Earth Syst. Sci., 22, 5317–5340, 2018 www.hydrol-earth-syst-sci.net/22/5317/2018/

A. Douinot et al.: Using a multi-hypothesis framework to improve the understanding of flash flood dynamics 5319

Figure 1. Locations of the catchments studied, with a topo-graphic visualisation at a resolution of 25 m (Source – IGN; MNTBDALTI).

work, such as FUSE (Framework for Understanding Struc-tural Errors, Clark et al., 2008) or SUPERFLEX (Flexibleframework for hydrological modeling, Fenicia et al., 2011).However, Clark et al. (2015a, b) have also proposed a uni-fied structure to test multiple working hypotheses within adistributed modeling framework. To our knowledge, the casestudies using the aforementioned frameworks are related tocontinuous hydrological studies in order to assess hydrolog-ical hypotheses through the overall hydrological signature ofthe catchments. In this work, we extend the method of multi-ple working hypotheses to the assessment of an event-basedhydrological model framework.

The objective is to test a number of proposed hydrologi-cal mechanisms that occur during flash flood events in a setof contrasting catchments in the French Mediterranean area.While the proportion of flows passing through the soil ap-pears to be significant, questions arise about how they form:

– Are they subsurface flows that take place in a restrictedarea of the root layer as a result of preferential path ac-tivation? Or are they lateral flows taking place at greaterdepth, comparable to those seen in some aquifers?

– Does the geological bedrock or an altered substratumplay a role limited to that of mere storage reservoir, oris it actively involved in flood flows formation?

– Which are the flow processes proportions, according tothe events and the catchments?

The aim of this article is to attempt to answer these ques-tions using a multi-model approach that tests different typesof hydrological dynamics. The study was based on MA-RINE (Modélisation de l’Anticipation du Ruissellement etdes Inondations pour des évéNements Extrêmes), a phys-ically based, distributed hydrological model (Roux et al.,

2011; Garambois et al., 2015a), which was developed specif-ically to model flash floods in the catchments of the FrenchMediterranean Arc. Several new representations for the soilcolumn and underground flows were proposed (Douinot,2016) and included in the MARINE model in the form ofmodules that can be used to test different hydrological func-tions (Sect. 3). Those different hydrological dynamics wereapplied to a set of catchments, presented in Sect. 2, withphysiographic properties representative of the whole of theFrench Mediterranean Arc. The performance of each modelwas then examined and subjected to a comparative study(Sects. 4 and 5). The contributions of the results for improv-ing the hydrological functioning understanding are lastly dis-cussed in Sect. 6 before concluding.

2 Catchments and data used in the study

2.1 Study catchment set

We studied the behaviour of four catchments and eight nestedcatchments in the French Mediterranean Arc (Fig. 1). Thecatchments (in the order they are numbered in Fig. 1) werethose of the Ardèche, Gard, Hérault and Salz rivers. Thesewere selected for the following reasons; (i) they are represen-tative of the physiographic variability found in areas whereflash floods occur, (ii) numerous studies of flash floods havealready been carried out on the Gard and Ardèche (Ruinet al., 2008; Anquetin et al., 2010; Delrieu et al., 2005;Maréchal et al., 2009; Braud et al., 2014) that could guide theinterpretation of the modelling results (Fenicia et al., 2014),and (iii) a considerable number of observations of flash floodevents are available for these catchments.

The main physiographical and hydrological properties ofthe catchments are presented in Table 1. Figure 2 showsthe contrasting geological properties of the studied area; thecatchments are marked by a clear upstream–downstream dif-ference. The Ardèche catchment upstream of Ucel essentiallysits on a granite bedrock with some sandstone on its edges,while downstream the geology changes to predominantlyschist and limestone formations. Similarly, the upstream partof the Gard catchment consists of schistose bedrock, whiledownstream the bedrock is impermeable marl-type and gran-ite formations. The Hérault catchment is split into mostlyschist and granitic head watersheds (the Valleraugue andla Terrisse sub-catchments) and is a predominantly lime-stone plateau (Saint-Laurent-le-Minier sub-catchment). Fi-nally, the Salz is characterised by sedimentary bedrock com-prised of sandstone and limestone (Fig. 2).

The Ardèche and the Gard catchments have been subject tointensive monitoring and studies (see later references, https://deims.org/site/czo_eu_fr_024, last access: 10 May 2018),leading to prior knowledge on hydrological understanding.Both the local in situ experiments (Ribolzi et al., 1997; Braudand Vandervaere, 2015; Braud et al., 2016a, b) and the mod-

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https://deims.org/site/czo_eu_fr_024


Table1.Physiographic

propertiesand

hydrologicalstatisticsof

the12

catchments.H

ere,IDis

thecoding

name

ofthe

catchments

usedatFig.1

andTable

2,andthe

following

arerepresented:area

(km2),m

eanslope

(–),soilpropertiesof

mean

soildepth(m

)and

main

soiltexture(T

x),sandyloam

texture=

(Ls),loam

texture=

(L),silty

loamtexture

=(L

si).In

terms

ofgeology,the

following

arerepresented:percentage

ofbedrock

geology(%

),includingsubcategories

ofsandstone

(Sa),limestone

(Li),granite

andgneiss

(GG

),marl(M

a)and

schists(Sc).

(i)Bold

valuesrepresentthe

dominantgeology.M

eanannualprecipitation

isP(m

m).In

terms

ofhydrometry,period

isthe

dischargetim

e-seriesavailability,the

mean

inter-annualdischargeisQ

(m3

km−

2s−

1),the2

yearreturnperiod

ofmaxim

umdaily

dischargeisQ

D2

(m3

km−

2s−

1),andthe

10yearreturn

periodofm

aximum

hourlydischarge

isQ

H10

(m3

km−

2s−

1).Hydrom

etricstatistics

arecalculated

fromH

ydroFrancedatabank

(http://ww

w.hydro.eaufrance.fr/,lastaccess:10

May

2018),andthe

pluviometric

onesusing

rainfalldataare

fromthe

raingauge

network

oftheFrench

floodforecasting

services.

IDR

iverO

utletSoilproperties

Geology

(i)H

ydrometry

Area

SlopeD

epthT

xSa

Li

GG

Ma

ScP

QQ

D2

QH

10Period

(km2)

(−)

(m)

(−)

(%)

(%)

(%)

(%)

(%)

(mm

)(m

3km−

2s−

1)Period

no.1aL’A

rdècheVogüé

6220.17

0.47L

s10.5

5.771.9

0.011.9

15870.041

0.622.25

00–15no.1b

Ucel

4770.20

0.45L

s13.7

0.084.5

0.01.8

15770.046

0.792.30

05–15no.1c

Pont-de-la-Beaum

e292

0.220.39

Ls

14.00.0

86.00.0

0.01690

0.0560.75

2.5300–15

no.1dM

eyras99

0.240.32

Ls

5.40.0

94.60.0

0.01720

0.0360.72

2.9200–15

no.2aL

eG

ardonA

nduze543

0.160.25

L7.2

1.518.0

12.161.2

13700.026

0.481.82

94–15no.2b

Corbès

2200.16

0.27L

9.30.0

34.29.0

47.51460

0.0220.57

2.2894–15

no.2cM

ialet Roucan

2400.17

0.22L

2.00.6

2.99.4

85.11407

0.0230.62

2.5402–15

no.3aL’H

éraultL

aroque912

0.140.26

Lsi

6.754.5

11.73.2

24.01160

0.0190.39

1.2100–15

no.3bL

aV

isSaint-L

aurent-le-Minier

4990.10

0.26L

si4.0

83.01.0

3.28.8

9300.018

0.421.10

00–15no.3c

L’Arre

La

Terrisse155

0.190.25

L19.5

12.327.2

6.234.8

11300.027

0.612.0

00–15no.3d

L’Hérault

Valleraugue

460.27

0.25L

0.00.0

0.00.0

100.01920

0.0491.13

4.008–15

no.4L

aSalz

Cassaigne

1440.13

0.37L

si33.5

56.50.0

5.14.9

7000.008

0.201.31

01–15


http://www.hydro.eaufrance.fr/


Figure 2. The geology of the Ardèche catchment (a), the Gard and Hérault catchments (b), and the Salz catchment (c) (sources: BD Million-Géol, BRGM).

elling studies focused on this area (Garambois et al., 2013;Vannier et al., 2013) tend to support a hydrological classifica-tion according to those contrasting geological properties, inagreement with the usual hydrogeological signature found inthe literature (Sayama et al., 2011; Pfister et al., 2017a). Marl,sandstone and limestone without karst are characterised bylimited storage capacities, resulting in higher runoff coef-ficients and high sensitivity to the initial soil moisture (Ri-bolzi et al., 1997; Braud et al., 2016a). In contrast, in graniteand schist transects located on the hillslope of the Ardèchecatchment, infiltration tests and analyses of electrical resis-tivity signals show the high permeability of the geologicalsubstratum in depth (measured up to 2.5 m in depth); highstorage capacities reach up to 600 mm in 7 out of 10 as-sessments with artificial forcing and the three remaining testssuggest local unaltered bedrock (Braud et al., 2016a, b). Thenatural resistivity profile suggests a regular soil bedrock in-terface when the latter consists of schist, while the graniteone presents a more chaotic structure. Finally, the continuouscomparative study of two experimental sites over surface ar-eas of the order of 1 km2 – one located on the schist upstreampart of the Gard catchment and the other one on the down-stream granite part – suggests that there is rapid subsurfaceflow processing on the schist area, while flow formation ap-pears to be controlled by the extension of the saturated zonerelated to the river on the granitic site (Ayral et al., 2005;Maréchal et al., 2009, 2013).

2.2 Forcing inputs and hydrometric data

The hydrometric data were derived from the network of oper-ational measurements (HydroFrance databank, http://www.hydro.eaufrance.fr/, last access: 10 May 2018). Eight totwenty years of hourly discharge observations were avail-able, according to the dates when the hydrometric stationswere installed (Table 1).

Flood events with peak discharges that had exceeded the2 year return period for daily discharge (QD2 in Table 1,which corresponds to the alert threshold for flood forecast-

ing centres in France) were selected as events to be includedin the study. Thus, only one criterion for hydrological re-sponse was considered. This led to a selection of precipita-tion events of varying origins (for instance, rainfall inducedby mountains, stagnant convective cells and rainfall occur-ring in different seasons, mainly in autumn and early spring).Such a selection risked complicating the study because flowprocesses can vary from one season to another. Nevertheless,it allowed us to test the ability of the model to deal with dif-ferent (non-linear) flow physics regimes. Note also that mod-erate or intense rainfall events without respective hydrologi-cal responses might be taken out of the analysis. Neverthelessthe first alert threshold used here is small enough to have aselection of flood events with contrasting runoff coefficients(see Table 2).

Precipitation measurements were taken from MétéoFrance’s ARAMIS (Application Radar à la Météorolo-gie Infra-Synoptique) radar network (Tabary, 2007), whichprovides precipitation measurements at a resolution of1 km× 1 km every 5 min. The French flood forecasting ser-vice (SCHAPI – Service central d’hydrométéorologie etd’appui à la prévision des inondations) then used the CALA-MAR patented software (Badoche-Jacquet et al., 1992) toproduce rainfall depth data by combining these radar mea-surements with rain gauge data. This processed dataset isused here as inputs for the model. Each rainfall product isfirstly assessed through an individual sensitivity analysis ofthe standard MARINE model (DWF model; see Sect. 3.1).When presenting an atypical sensitivity to the soil depth pa-rameter, the rainfall event is discarded in the study, as it sug-gests questionable measurements. Depending on the avail-ability of the results of rainfall and hydrometric measure-ments, 7 to 14 intense events were selected for each catch-ment (Table 2). Each set is finally split into calibration andvalidation subsets as follows; the extreme events were keptfor validation, and a minimum of three calibration events arechosen in order to cover the wide range of initial soil mois-ture conditions.





E

Figure 3. The MARINE model structure, parameters and variables. The Green–Ampt infiltration equation contains the following parameters:infiltration rate i (m s−1), cumulative infiltration I (mm), saturated hydraulic conductivityK (m s−1), soil suction at the wetting front9 (m),and saturated and initial water contents, θs and θi (m3 m−3), respectively. Subsurface flow contains the following parameters: soil thickness(m), lateral saturated hydraulic conductivity K (m s−1), local water depth h (m), transmissivity decay with depth mh (m) and bed slope S(m m−1). The kinematic wave contains the following parameters: surface water depth h (m), time t (s), space variable x (m), rainfall rate r(m s−1), infiltration rate i (m s−1), bed slope S (m m−1) and Manning roughness coefficient n (m−1/3 s). Module 2 described in this figurecorresponds to the standard definition applied in the MARINE model.

As the MARINE model is event-based, it must be ini-tialised to take into account the previous moisture state ofthe catchment, which is linked to the history of the hydro-logical cycle. This was done using spatial model outputsfrom Météo-France’s SIM (Safran-Isba-Modcou, Habets etal., 2008) operational chain, including a meteorological anal-ysis system (SAFRAN; Vidal et al., 2010), a soil–vegetation–atmosphere model (ISBA; Mahfouf et al., 1995) and a hydro-geological model (MODCOU; Ledoux et al., 1989). Basedon the work of Marchandise and Viel (2009), the spatial dailyroot-zone humidity outputs (resolution of 8 km× 8 km) sim-ulated by the SIM conceptual model were used for the sys-tematic initialisation of MARINE.

3 The multi-hypothesis hydrological modellingframework

3.1 The MARINE model

The MARINE model is a distributed mechanistic hydrologi-cal model especially developed for flash flood simulations. Itmodels the main physical processes in flash floods: infiltra-tion, overland flow and lateral flows in soil and channel rout-ing. Conversely, it does not incorporate low-rate flow pro-cesses such as evapotranspiration or base flow.

MARINE is structured into three main modules that arerun for each catchment grid cell (see Fig. 3). The first mod-ule allows for the separation of surface runoff and infiltra-tion using the Green–Ampt model. The second module rep-resents the subsurface downhill flow. It was initially based

on the generalised Darcy’s law used in the TOPMODEL(TOPography-based) hydrological model (Beven and Kirby,1979), but it was developed in greater detail as part of thisstudy (see Sect. 3.2). Lastly, the third module representsoverland and channel flows. Rainfall excess is transferred tothe catchment outlet using the Saint-Venant equations sim-plified with kinematic wave assumptions. The model distin-guishes grid cells with a drainage network, where channelflow is calculated on a triangular channel section (Maubour-guet et al., 2007) from grid cells on hillslopes and where theoverland flow is calculated for the entire surface area of thecell.

The MARINE model works with distributed input datasuch as (i) a digital elevation model (DEM) of the catchmentto shape the flow pathway and distinguish hillslope cells fromdrainage network cells according to a drained area threshold,(ii) soil survey data to initialise the hydraulic and storageproperties of the soil, which are used as parameters in theinfiltration and lateral flow models, and (iii) vegetation andland-use data to configure the surface roughness parametersused in the overland flow model.

The MARINE model requires parameters to be calibratedin order to be able to reproduce hydrological behaviours ac-curately. Based on sensitivity analyses of the model (Garam-bois et al., 2013), five parameters are calibrated: soil depth,represented as Cz, the saturation hydraulic conductivity usedin lateral flow modelling, Ckss, the hydraulic conductivity atsaturation that is used in infiltration modelling, Ck , and fric-tion coefficients for low and high-water channels, nr and np,respectively, with nr and np being uniform throughout the



Table 2. Properties of the flash flood events as an average on the event set (± standard deviation). ID is the coding name of the concernedcatchments (See Fig. 1: no. 1 for the Ardèche, no. 2 for the Gard, no. 3 for the Hérault and no. 4 for the Salz); Nevt is the number of observedflash flood events; P (mm) is the mean precipitation; Imax (mm h−1) is the maximal intensity rainfall per event; Qpeak is the specific floodpeak (m3 km−2 s−1); Hum is the initial soil moil moisture according to SIM output (Habets et al., 2008); CR is the runoff coefficient (%).

ID Outlet Nevt P (mm) Imax Qpeak Hum (%) CR (–)(mm h−1) (m3 km−2 s−1)

no. 1a Vogüé 10 192 (±93) 17.3 (±6.2) 1.33 (±0.57) 58 (±6) 0.50 (±0.16)no. 1b Ucel 10 208 (±105) 19.1 (±7.1) 1.41 (±0.70) 56 (±5) 0.47 (±0.17)no. 1c Pont-de-la-Beaume 10 222 (±122) 20.5 (±6.2) 1.79 (±0.82) 56 (±5) 0.51 (±0.22)no. 1c Meyras 10 235 (±141) 25.6 (±10.6) 2.15 (±1.15) 56 (±4) 0.51 (±0.20)

no. 2a Anduze 13 182 (±69) 26.9 (±12.6) 2.10 (±1.67) 53 (±7) 0.31 (±0.13)no. 2b Corbès 14 196 (±73) 31.4 (±11.6) 1.90 (±0.93) 55 (±7) 0.32 (±0.15)no. 2c Mialet Roucan 14 177 (±72) 30.9 (±13.2) 1.85 (±0.85) 51 (±7) 0.33 (±0.15)

no. 3a Laroque 7 188 (±95) 16.0 (±8.1) 0.82 (±0.43) 59 (±8) 0.45 (±0.16)no. 3b Saint-Laurent-le-Minier 7 153 (±95) 18.4 (±8.9) 1.14 (±0.31) 56 (±9) 0.47 (±0.16)no. 3c La Terrisse 7 193 (±103) 22.1 (±12.1) 1.63 (±0.87) 52 (±8) 0.60 (±0.23)no. 3d Valleraugue 7 156 (±110) 16.4 (±8.7) 2.14 (±1.33) 48 (±6) 0.62 (±0.22)

no. 4 Cassaigne 8 136 (±47) 17.8 (±6.2) 1.48 (±0.64) 57 (±7) 0.55 (±0.24)

drainage network. Ckss, Ck and Cz are the multiplier coeffi-cients for spatialised, saturated hydraulic conductivities andsoil depths. In this study, modifications of Module 2 (i.e. sub-surface downhill flow) were tested for assessing several pos-sible ways to represent the intra-soil hydrological function-ing. Consequently, instead of Cz and Ckss, new parametersof calibration were introduced, as described in the followingsection.

3.2 Modelling lateral flows in the soil: the developmentof a multi-hypothesis framework

We proposed several modifications to Module 2 – the subsur-face downhill flow submodel – covering the three hypothesesof hydrological functioning:

– The deep water flow model (DWF) assumed deep infil-tration and the formation of an aquifer flow in highlyaltered rocks. In hydrological terms the pedology–geology boundary was transparent. The soil columncould be modelled as a single entity of depth Dtot(m),which is at least equal to the soil depth DBDsol(m)(see Fig. 4). Given the lack of knowledge and avail-able observations, a uniform calibration was appliedto the depth of altered rocks, represented as DWB(m),which is rapidly accessible to the scale of a rain event.Groundwater flow was described using the generalisedDarcy’s law (qdw, Eq. 1). The exponential growth of thehydraulic conductivity at saturation as the water table(hdw) rises assumed an altered rock structure where hy-draulic conductivity at saturation decreases with depth

(the TOPMODEL approach).

qdw = Kdw ·Dtot exp(hdw−Dtot

mh

)· S, (1)

with hdw(m) as the water depth of the unique water ta-ble, mh(m) as the decay factor of the hydraulic conduc-tivity at saturation with soil depth, S[-] as the bed slope,Kdw = Ckdw ·KBDsol(ms−1) as the simulated hydraulicconductivity at saturation and Dtot =DBDsol+DWB asthe soil column depth. Calibrated parameters are inbold.

– The subsurface flow model (SSF) assumed that the for-mation of subsurface lateral flows was due to the activa-tion of preferential paths, like the in situ observations ofKatsura et al. (2014) and Katsuyama et al. (2005). Thealtered soil–rock interface acts as a hydrological bar-rier. The rapid saturation of shallow soils results in thedevelopment of rapid flows due to the steep slopes ofthe catchments and the existence of rapid water flowscirculating through the macropores as the soil becomessaturated. The soil column was thus represented by atwo-layer model (see Fig. 5), with the depth of an up-per layer equal to the soil depth DBDsol (m) and a lowerlayer of uniform depthDWB (m). The lateral flows in theupper layer were described by the generalised Darcy’slaw. However, variations in hydraulic conductivity wereexpressed as a function of the mean water content of thelayer (θsoil) and not of the height of water (hsoil) thatwould form a perched water table (Eq. 2). Expressingthe variability in hydraulic conductivity as a functionof the saturation rate indeed appears to be a more ap-propriate choice for representing the activation of pref-



erential paths in the soil by the increase in the degreeto which the soil is filled. The decay factor of the hy-draulic conductivity as a function of the saturation rate,mθ , was set according to the linearised empirical rela-tions developed by Van Genuchten (1980) between thehydraulic conductivity and soil water content for the dif-ferent classes of soil textures. Flows in the lower soillayer (qdw; Eq. 3) in the form of a deep aquifer werelimited by setting the hydraulic conductivity of the sub-stratum as being equivalent to that of the soil dividedby 50 (this choice being guided by the orders of magni-tude generally observed in the literature; Le Bourgeoiset al., 2016; Katsura et al., 2014). The altered rockswere thus assumed to mainly play a storage role. In-filtration occurring between the two layers was initiallyrestricted by the Richards equations, which were incor-porated using the set hydraulic properties of the sub-stratum (Eq. 4). When the upper layer is saturated, thisallows the filling through a piston effect. The depth ofthe soil layer,DBDsol, was set according to the soil data,while the depth of the substratum, DWB, was calibratedin the same way as in the DWF model.

qss = Kss ·DBDsol exp(θsoil− 1mθ

)· S, (2)

qdw = Kdw ·DWB exp(hWB−DWB

mh

)· S, (3)

qinf =−KdwδH(θsoil,θWB)

δz, (4)

where hsoil and hWB (m) represent the soil water depthin the upper and lower layer, respectively, θsoil andθWB (−) represent the soil water content of the upperand lower layer, respectively, mθ (−) represents the de-cay factor of the hydraulic conductivity with soil watercontent θsoil, Kss = Ckss ·KBDsol and Kdw = 0.02 ·Kss(m s−1) represents the simulated hydraulic conductivityat saturation of the upper and lower layer in the SSFmodel, respectively.

– The subsurface and deep water flow model (SSF-DWF)assumed that the presence of subsurface flow was duenot only to local saturation of the top of the soil col-umn, but also to the development of a flow at depth, asa result of significant volumes of water introduced byinfiltration and a very altered substratum whose appar-ent hydraulic conductivity was already relatively high.This hypothesis of the process led to a modelling ap-proach analogous to the SSF model (Fig. 5), where thehydraulic conductivity at substrate saturation,Kdw, wasno longer simply imposed, but instead was calibratedusing an additional coefficient, Ckdw. In the SSF-DWFmodel,

Kdw = Ckdw ·KBDsol. (5)

Figure 4. DWF model of flow generation by infiltration at depthand support of a deep aquifer qdw(hdw) (Eq. 1).

Figure 5. SSF and SSF-DWF models of flow generation by the satu-ration of the upper part of soil column and activation of preferentialpaths (qss), with support flow at depth (qdw) and water exchangesfrom the upper layer to the lower one according to both soil watercontent, represented by qinf(θsoil, θWB). See Eqs. (2), (3) and (4)for the definition of the flows.

The soil water content prior to simulation was similarlyinitialised for each model in order to ensure that, for a fixeddepth of altered rock, the same volume of water was allocatedfor all models. The SIM humidity indices (Sect. 2.2) wereused to set an overall water content for all groundwater flowmodels for a given flood.

4 Methodology for calibrating and evaluating themodels

4.1 Calibration method

The three hydrological models studied, DWF, SSF and SSF-DWF, were calibrated for each catchment by weighting 5000randomly drawn samples from the parameter space for eachmodel (the Monte Carlo method). The weighting was doneusing the DEC (Discharge Envelope Catching) score (Eq. 6;discussed by Douinot et al., 2017) in order to integrate thea priori uncertainties of modelling

((σmod, i

), i = 1. . .n

), as

represented by Eq. (7), and those related to the flow mea-surements

((σyi

), i = 1. . .n

), as represented by Eq. (8). The

choice of DEC is justified by the desire to adapt the evalua-tion criterion to the modelling objectives (for example, by fo-cusing calibration on the reproduction of the rise and peaks



of floods in order to be able to forecast flash floods) whilealways being aware of the uncertainties in the reference flowmeasurements.

Given the lack of information, these uncertainties((σyi

), i = 1. . .n

)were set at 20 % of the measured dis-

charge, which is in line with the literature on discharge mea-surements from operational stations (Le Coz et al., 2014),and increased linearly with the 10-year hourly discharge,beyond which, as a general rule, the observed flow is nolonger measured but is derived by extrapolation from a dis-charge curve, making it less accurate (Eq. 8). The envelope((yi±2σyi

), i = 1. . .n

)consequently defines the 95 % con-

fidence interval of the observed flows.The modelling uncertainties

((σmod, i

), i = 1. . .n

)were

set at a minimum value (as a function of the basic catchmentmodule), thus ensuring that the evaluation of the hydrographswould not be unduly affected by the reproduction of rela-tively low flows, which were strongly dependent on initiali-sation using previous moisture data that were not the subjectof this study. In addition, it was assumed that a modelling un-certainty of 10 % around the confidence interval of observedflows was acceptable (Eq. 7). Finally, the overall overarchingenvelope

((yi±2σyi±2σmod, i

), i = 1. . .n

)defines hereafter

the acceptability zone, that is to say the interval in which anysimulated flow would be considered as acceptable, accordingto the modelling and measurement uncertainty definitions.

DEC=1n

n∑i=1

εDECi =

1n

n∑i=1

di

σmod, i, (6)

σmod, i = 0.5 ·Q+ 0.025 · yi, (7)

σyi = 0.05 · yi ·(

1+yi

QH10

), (8)

with εDECi as the DEC modelling error at time i, yi and σyi as

the observed discharge and the uncertainty of measurementat time i, di as the discharge distance between the model pre-diction at time i (yi) and the confidence interval of observedflow at time i (yi±2σyi ), σmod, i as the simulated uncertaintyat time i, andQ andQH10 as the mean inter-annual dischargeand the 10 year maximum hourly discharge of the relatedcatchment, respectively.

4.2 Metrics and key points in model evaluation andcomparison

Results of the models were first assessed and benchmarkedusing performance scores (Sect. 5.1). The evaluation focusedon the performance of the models in reproducing the hydro-graphs in overall terms but also more specifically on theirability to reproduce the characteristic stages of floods: ris-ing flood waters, high discharges and flood recession. Thesestages were defined as follows:

– The period of rising flood waters is between the momentwhen the observed flow rate exceeds the mean inter-annual discharge of the catchment and the date of thefirst flood peak.

– The stage of high discharges includes the points forwhich the observed flow was greater than 0.25 times themaximum flow during the event.

– The stage of flood recession begins after a period oftc, which is the catchment concentration time accord-ing to Bransby’s formula (Pilgrim and Cordery, 1992),represented by tc = 21.3 ·L/(A0.1

· S0.2) after the peakof the flood, and ends when discharge is rising again (or,where appropriate, at the end of the event, which is thetime of peak flooding+ 48 h).

The DEC score has provided a standard assessment of themodelling errors, enabling a reasonable weighting of the sim-ulations. However, for a sake of easy understanding, the per-centage of acceptable points of the simulated median timeseries, Qmed_INT [%] (Douinot et al., 2017), was chosen toevaluate the ability of the models to reproduce overall flows,rising flood waters and high discharges. A point is definedas acceptable when the median simulated value stands withinthe modelling acceptability zone

((yi±2σyi±2σmod, i

), i =

1. . .n)

.Conversely, Qmed_INT was not relevant for the evalua-

tion of the capacity to reproduce recessions, because the cal-culation of this score during the recession interval stronglydepends on performance at high discharges. Instead, we usedthe Aslope score defined in Eq. (9). It calculates the averagestandard error in simulating the decreasing rate of the dis-charge during the flood recession interval. Through the con-sideration of the Aslope score here, it was assumed that therecession rate is a relevant feature of the catchment’s hydro-logic properties (Troch et al., 2013; Kirchner, 2009).

Aslope =

∑li=k|

dyidt −

dyidt |∑l

i=kdyidt

, (9)

where dyidt and dyi

dt are the observed and the simulated reces-sion rates, respectively, at a time step i that belongs to theflood recession interval

(i = k. . .l

).

The evaluation was completed through the descrip-tion of the modelling errors (Sect. 5.2) in order toidentify those that were inherent in the choice ofmodel structure, regardless of the calibration methodol-ogy adopted (Douinot et al., 2017). Attention was paidto the a priori and a posteriori confidence interval of themodel simulations defined by

([y

prior−5thi , y

prior−95thi

], i =

1. . .n)

and([yDEC−5thi , yDEC−95th

i

], i = 1. . .n

), respec-

tively, where yprior−5thi and yprior−95th

i are the 5th and the 95th



percentile of the 5000 model simulation values at time i, andwhere yDEC−5th

i and yDEC−95thi are the 5th and the 95th per-

centile of the same but weighted series according to the DECcalibration criterion.

Those confidence intervals were standardised according tothe DEC modelling error definition (Eq. 6), defining the apriori and a posteriori confidence intervals of the modellingerrors;

εα−xthi =

0 if | yα−xth

i |≤ 2 · σyiyα−xthi ± 2 · σyi

2 · σmodiotherwise

(− if yα−xthi >0 ; + if yα−xth

i ≤ 0 )

(10)

where εα−xthi is the xth percentile of the α modelling errors

distribution at time i.The latter definition allows for an informative transla-

tion of the prior and posterior confidence intervals (Douinotet al., 2017); a value of εα−xth

i equal to 0 indicates that theyα−xthi bound lies within the discharge confidence interval. If

0<εα−xthi ≤ 1, the yα−xth

i bound lies within the acceptabilityzone. If εα−xth

i is larger than 1, the errors of modelling are de-tected or remain. In addition, the benchmark of both a prioriand a posteriori confidence intervals allows for highlighting,which was the remaining modelling errors that were inducedby the model’s assumptions and those that were induced bythe calibration.

5 Results

5.1 Performance of the models

5.1.1 Overall performances of the models

Assessment of the performances by catchment. Fig. 6 showsthe average and standard deviations of the Qmed_INT scoresobtained after the calibration of the DWF, SSF and SSF-DWF models for each catchment studied. The DWF model,assuming deep infiltration and the formation of an aquiferflow in altered bedrock, showed better performance in theArdèche catchment (no. 1), while in the Gard (no. 2) andthe Salz (no. 4) catchments, the SSF and SSF-DWF models,assuming the formation of subsurface flows due to the ac-tivation of preferential flow paths by local saturation (SSF)with development of flow at depth (SSF-DWF), producedthe most accurate results. On the Hérault catchment (no. 3),the modelling results obtained with each model in termsof Qmed_INT were less obvious, although the SSF-DWFmodel seemed to stand out to some extent. The differencesin model performance were more pronounced for the valida-tion events. The better-performing models tended to be moreconsistent, with equivalent Qmed_INT scores on calibrationand validation events, for example, the DWF model on theArdèche (no. 1) or the SSF and SSF-DWF models on the

Even

ts o

f cal

ibra

tion

no. 1

ano

. 1b

no. 1

cno

. 1d

no. 2

ano

. 2b

no. 2

cno

. 3a

no. 3

bno

. 3c

no. 3

dno

. 4M

ean

Qm

ed_I

NT

(%)

050

100

Assessment of all the hydrographs

DWFSSFSSF−DWF

Mean valueQ5th − Q95th

Even

ts o

f val

idat

ion

no. 1

ano

. 1b

no. 1

cno

. 1d

no. 2

ano

. 2b

no. 2

cno

. 3a

no. 3

bno

. 3c

no. 3

dno

. 4M

ean

Qm

ed_I

NT

(%)

050

100

(a)

(b)

Figure 6. Qmed_INT scores, with mean Qmed_INT scores ob-tained for the calibration (a) and validation (b) events, by model andcatchment. The Qmed_INT scores were calculated for the wholehydrograph. The x axis refers to the ID number of each catchment(Fig. 1). Finally, the mean attribute refers to the average results overall the catchments obtained with each model.

Gard (no. 2). There was also a deterioration in performancein several models that had already been judged as less ef-fective, for example, the SSF and SSF-DWF models on theArdèche (no. 1) or the DWF model on the two catchments ofthe Hérault, no. 3c and no. 3d.

SSF model versus SSF-DWF model. As a reminder, the dif-ference between the SSF and SSF-DWF models is that thelatter has an extra calibration parameter, Ckdw, which is ableto initialise a significant lateral flow in the subsoil horizonsof the soil column (see Eq. 3). The lateral hydraulic conduc-tivity in the deep layer is configured using the hydraulic con-ductivity from BDsol; Kdw = Ckdw ·KBDsol, with Ckdw setto 0.02 ·Ckss in the SSF model and calibrated in the SSF-DWF model. The small differences between the SSF andSSF-DWF models showed that this flexibility does not pro-duce any significant improvement, with the exceptions of theArdèche catchment at Meyras and the Hérault catchment atValleraugue. These two areas have a number of common fea-tures that could explain the similar modelling results; they areat the heads of high elevation catchments with steep slopes(Table 1) and are subject to considerable annual meteorolog-ical forcing. The calibration of Ckdw consistently tended tosimulate a significant flow at depth for these two catchments,



Mod

ule

Q

0.01

0.05

no. 1

ano

. 1b

no. 1

cno

. 1d

no. 2

ano

. 2b

no. 2

cno

. 3a

no. 3

bno

. 3c

no. 3

dno

. 4

Ckd

w (−

)0.

010.

05

(a)

(b)

.

Figure 7. (a): Mean inter-annual discharge (m3 km−2 s−1) for thecatchments. (b): a posteriori distribution of the calibration of thesubsoil horizon hydraulic conductivity in the SSF-DWF model (theCkdw parameter; Eq. 3)

with exclusively higher values from the prior confidence in-terval having been selected (Fig. 7). In general, the calibra-tion of the Ckdw parameter of the SSF-DWF model correlateswith the more or less sustained, annual hydrological activityof the catchments; the confidence interval of the Ckdw coef-ficient is restricted to low values for the catchments with lowmean inter-annual discharges (no. 2a, no. 2b, no. 2c, no. 3a,no. 3b and no. 4) and inversely for the catchments with highmean inter-annual discharges (no. 1, no. 3c and no. 3d).

5.1.2 Detailed performances: assessment of the modelsto simulate the different stages of an hydrograph

Figure 8 shows the detailed assessments according to thespecific stages of the hydrographs. It highlights whether theoverall performances (Fig. 6) reflect uniform results alongthe hydrographs or if they actually hide the contrasting like-lihood of the simulations over the course of different hydro-graphs’ stages.

Uniform results are observed on the Gard catchment atCorbès and Anduze (no. 2a and no. 2b) and on the Salzcatchment (no. 4); the SSF and SSF-DWF models demon-strated clearly superior performances for all stage-specificassessments of those catchments. For the Gard catchment atMialet (no. 2c), the detailed assessment (Fig. 8) shows thatthe overall superiority of the SSF and SSF-DWF models ismainly due to a better simulation of the rising limb. Never-theless, for any score, the SSF and SSF-DWF models simi-larly both present the best modelling results compared to theDWF model.

On the Ardèche catchments (no. 1a, no. 1b, no. 1c andno. 1d), the overall performances reflect the simulation ofthe high discharges and of the flood recessions. There, theDWF model gives the best results for simulating those hydro-graphs’ stages. Conversely, it deals slightly less well with thesimulation of the rising flood waters. As shown in Sect. 5.2,

all the models tend to underestimate initial flows prior to theevent and during the onset of a flood. The DWF model, inparticular, exhibits this modelling weakness; for example,see the onset of floods in the hydrographs for the 18 Octo-ber 2006 and 1 November 2014 events in Ucel (no. 1b) asdepicted in Fig. 10, which explains the poorer performance.It can be noticed that the SSF-DWF model clearly better sim-ulated the rising flood waters of the Ardèche head watershed(no. 1d), explaining the overall good performance as well ofthis model on this catchment (Fig. 6).

On the Hérault, the detailed evaluation enabled us to dis-tinguish the performance of the different models. On the onehand, for the two larger catchments (no. 1a and no. 1b), theDWF model performed slightly better for rising flood wa-ters simulations, while the SSF model gave more clearly bet-ter simulations of the flood recessions. On the other hand,the SSF-DWF model generated the best simulations of therising flood waters and of the high flows on the upstreamcatchments of La Terrisse (no. 3c) and Valleraugue (no. 3d),while the DWF model simulated a better flood recession.These contrasting results explained why there is not a spe-cific model that stands out on this catchment. In addition, itsuggests a marked influence of the physiographic propertieson the development of flow processes, because they are cor-related with the differences in the geological and topograph-ical properties of the Hérault (no. 3; see Fig. 2 and Table 1).The hydrological behaviours simulated for the Valleraugueand La Terrisse sub-catchments, which are predominantlygranitic and schistose and where slopes are very steep, canbe distinguished from those of Laroque and Saint-Laurent-le-Minier, which are mainly sedimentary and in the form oflarge plateaus.

5.1.3 Summary of the assessment

Figure 9 sums up the highlighted models according to theassessed hydrograph’s stage. It shows when one’s model hasa clearly higher performance according to the following defi-nition; a model is assessed as clearly superior when the lowerbound of the confidence interval of its score is higher than themedian values of the scores obtained with the other models.It reveals that the catchments set might be divided into fourgroups:

– A first group of catchments is where the SSF and SSF-DWF models uniformly perform either similar or bet-ter than the DWF models. This is the case for the Gard(no. 2) and the Salz (no. 4) catchments.

– A second group of catchments is where the DWF modelgives the best results according to all the scores, exceptfor the rising flood waters assessment. This is the casefor the downstream Ardèche catchments (no. 1a, no. 1band no. 1c).


5328 A. Douinot et al.: Using a multi-hypothesis framework to improve the understanding of flash flood dynamicsEv

ents

of c

alib

ratio

n

no. 1

ano

. 1b

no. 1

cno

. 1d

no. 2

ano

. 2b

no. 2

cno

. 3a

no. 3

bno

. 3c

no. 3

dno

. 4M

ean

Qm

ed_I

NT

(%)

050

100

(a) Assessment of the rising limbs

DWFSSF

SSF−DWFMean value

Q5th − Q95th

Mea

n

Qm

ed_I

NT

(%)

050

100

(b) Assessment of the high flows

Mea

n

A slo

pe (

−)

#1a #1b #1c #1d #2a #2b #2c #3a #3b #3c #3d #4

1.0

0.8

0.6

0.4

0.2

(c) Assessment of the recessionsEv

ents

of v

alid

atio

n

Mea

n

Qm

ed_I

NT

(%)

050

100

Mea

n

Qm

ed_I

NT

(%)

050

100

Mea

n

A slo

pe (

−)1.

00.

80.

60.

40.

2

no. 1

ano

. 1b

no. 1

cno

. 1d

no. 2

ano

. 2b

no. 2

cno

. 3a

no. 3

bno

. 3c

no. 3

dno

. 4

no. 1

ano

. 1b

no. 1

cno

. 1d

no. 2

ano

. 2b

no. 2

cno

. 3a

no. 3

bno

. 3c

no. 3

dno

. 4

no. 1

ano

. 1b

no. 1

cno

. 1d

no. 2

ano

. 2b

no. 2

cno

. 3a

no. 3

bno

. 3c

no. 3

dno

. 4

no. 1

ano

. 1b

no. 1

cno

. 1d

no. 2

ano

. 2b

no. 2

cno

. 3a

no. 3

bno

. 3c

no. 3

dno

. 4

no. 1

ano

. 1b

no. 1

cno

. 1d

no. 2

ano

. 2b

no. 2

cno

. 3a

no. 3

bno

. 3c

no. 3

dno

. 4

Figure 8. Assessment of the models by catchment in the different stages of the hydrographs. (a): Qmed_INT scores calculated over therising flood waters stage. (b): Qmed_INT scores calculated over the high discharges stage. (c): Aslope scores. High Qmed_INT scores andconversely low Aslope values indicate good performances of the model.

Figure 9. Summary of the models’ benchmark. A colour is at-tributed for each score and each catchment when one model gives aclearly superior performance, or two colours are attributed for eachscore and each catchment when two models give clearly superiorperformances: the score of a model is defined as clearly superiorwhen the lower bound of its confidence interval is higher than themedian values obtained with the other models. The superiority of amodel might be half attributed if the criteria is only respected forthe calibration processes. Colour attribution: orange for the DWFmodel, blue for the SSF model, green for the SSF-DWF model andgrey when the superiority of one’s model is undetermined.

– A third group is where the models’ results are not reallydiscernible. For those catchments, the DWF model ap-pears to simulate the rising flood and the high dischargeslightly better, while the recession is better representedby the SSF model. This is the case for the downstreamHérault catchments (no. 3a and no. 3b).

– A last group is where the SSF-DWF model generatesthe rising flood and the high discharge slightly better,while the recession is better represented by the DWF

model. The head watersheds of the Hérault (no. 3c andno. 3d) and of the Ardèche (no. 1d) catchments are inthis group.

5.2 Modelling errors inherent in the models’ structures

For the sake of conciseness, only the simulation over onecatchment is presented. Figure 10 shows the simulation re-sults of the three models over the Ardèche catchment at Ucel(no. 1b). It shows the simulated hydrographs and their con-fidence intervals compared with the observed flows as wellas the inherent errors in the simulations. This highlights themodelling errors due to the choice of model structure (DWF,SSF or SSF-DWF models). When the a priori confidence in-terval (grey colour) at a time i does not cross the acceptabilityregion (green colour), it means that no parameter set givesan acceptable simulation, and modelling errors due to thestructure (or assumptions) of the model are consequentiallydetected. When the posterior confidence interval (salmoncolour) is outside the acceptability zone, the modelling errorremains. Finally whether the prior (posterior) interval is largeor small, the model’s structure allows for reaching a larger orless large range of simulated values (the model prediction ismore or less uncertain, respectively).

Representing the soil column with either one compartment(the DWF model) or two compartments (SSF or SSF-DWFmodels) leads to a distinct a priori confidence interval ofmodelling errors (grey). The DWF model constrains the sim-ulated flows at the beginning of the event, before the onset ofprecipitation, because the width of the confidence interval of



Figure 10. Calibration of the three models for the Ardèche catchment at Ucel (no. 1b). The results of the simulation of five flood hydrographsand the inherent modelling errors (Eq. 10) for each model (a: DWF, b: SSF and c: SSF-DWF). The median simulation and the posteriorconfidence interval are shown in red and salmon, respectively. The confidence intervals of the measured flows and the acceptability zone areshown in green and blue, respectively. The a priori confidence intervals for each model (i.e. with no calibration) are shown in grey. Denotedare events of calibration (∗) and events of validation (∗∗).



the modelling errors is low at that point. More specifically, ittends to underestimate the initialisation discharges, becausethe variation interval of the errors over this period is predom-inantly negative. This may explain this model’s relative diffi-culty in reproducing the onset of floods, since the calibrationof the parameters did not allow the acceptability zone in thispart of the hydrograph to be reached. A resulting interpreta-tion applicable to the catchment sets is that good results inmodelling the rising flood waters with the DWF model meanthat the observed rising flow is relatively slow and could bereached in spite of the restrictive modelling structure (for ex-ample, no. 3a and no. 3b).

Likewise, it can be noted that the one-compartment struc-ture (i.e. the DWF model) allows for flexibility in the mod-elling of high discharges and flood recessions, because theconfidence interval of the modelling errors is quite large overthese periods in the hydrograph. However, it also led to theunderestimation of high discharges and flood recessions. Infact, the prior modelling error interval (in grey) has a negativebias with respect to the acceptability zone. The calibration fi-nally allows the simulations to be selected at the intersectionof the acceptability zones and the a priori confidence in mod-elling errors. This generally corresponds to the calibration ofa low-depth altered rock, DWB, in order to make the modelmore sensitive to soil saturation and more responsive via thegeneration of early runoff. From that resulting low DWB, thesimulated water storage capacity is limited, which might ex-plain the inadequacy of the DWF model for a catchment withsmall runoff coefficients (no. 2, Table 2).

Conversely, the two-compartment structure (the SSF andSSF-DWF models) offers flexibility in modelling the begin-ning of events, flood warnings and high discharges, but theability to model flood recessions is more constrained. SSFand SSF-DWF models simulate fast flood recessions in com-parison to the DWF model, suggesting that good results inmodelling the flood recession with the SSF model that mightbe interpreted as a fast return to normal or low discharge areobserved on the related catchments (as example, no. 2, no. 4).

In the SSF and SSF-DWF models, the addition of a fluxcalibration parameter in the subsoil horizons not surprisinglyleads to wider variations in the a priori modelling errors. Asurprising finding, however, is that the calibration of the lat-eral conductivity of the deep layer,Ckdw, seems to affect onlythe simulation at the beginning of the hydrographs (see theevents of 1 November 2011 and 13 November 2014, Fig. 10)and has a very little effect on flood recessions. The highsimilarities of the prior modelling intervals of the SSF andSSF-DWF models explain the similar performances of thosemodels. In the same way, when there is improvement in theperformance through the SSF-DWF, it concerns the early ris-ing of the flood; as the detailed performances have alreadyshown, the SSF-DWF enables the fast and early start of theflood events.

5.3 Analysis of relevance of the internal hydrologicalprocesses simulated

5.3.1 Characterisation of the hydrological processessimulated

The proportional volumes of the water making up the hydro-graphs, which arise from the three main simulated paths (onthe surface, through the top or through the deep layer of thesoil), were calculated. Figure 11 shows the simulated runoffcontribution, i.e. the water that has not passed through thesoil at any point. The contributions of these surface flows onthe whole of the hydrograph (Fig. 11, left) and those that sup-port high discharges (Fig. 11, right) are distinguished. Notethat the other contributions are not detailed, being correlatedto the runoff assessment and therefore leading to a similaranalysis.

The runoff contribution simulated by the DWF model evenfurther discredits that model for representing the hydrologi-cal behaviour of the Gard (no. 2) and Salz (no. 4) catchments.Really high proportion of runoff contribution over the entirehydrograph were simulated, ranging from 40 % to 98 %. Incontrast, the few experimental measurements made on theGard (Bouvier et al., 2017; Braud et al., 2016a) provide evi-dence of the proportions of new water, which might be seenas an upper bound for runoff contribution volume, rangingfrom 20 % to 40 % of the volumes in the hydrograph. TheSSF and SSF-DWF model conversely gave a more reason-able runoff contribution, although it remained high, rangingfrom 19 % to 62 %.

The assessment of the flow contributions through the mostsuitable model’s simulations for each catchment revealed inSect. 5.1 is consistent with the catchment set’s diversity. Con-sidering the DWF model for the Ardèche catchment andthe SSF and SSF-DWF models for the Gard catchment, therunoff contributions to the high flows of the hydrographswere slightly lower in the three downstream Ardèche catch-ments (no. 1a, no. 1b and no. 1c, with runoff contributions in-cluded between 17 % and 57 %) compared to the runoff con-tributions in the Gard catchment (no. 2a, no. 2b and no. 2c)and in the upstream part of the Ardèche (no. 1d, with runoffcontributions between 20 % and 78 %). It is consistent withboth the properties of the catchments and the rainfall forcing,with the first catchment subset (no. 1a, no. 1b and no. 1c)having deeper soil cover, a more permeable soil texture (seeTable 1), and being forced by rainfall with lower maximal in-tensities (see Table 2), which is in contrast to the second one(no. 2a, no. 2b and no. 2c).

On the downstream catchments of the Hérault (no. 3a,no. 3b), the variation intervals of the surface flows estimatedby the three models overlap. It may explain why the threemodels can achieve good reproductions of the hydrologicalsignal; the calibration step makes it possible from that inte-grated point of view to obtain an analogous distribution ofthe flow processes.



(a) Flow proportion of the whole hydrograph (b) Flow proportion in the high flows

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Figure 11. Proportion of surface runoff in the flows at the outlet. Left: The proportion over the whole hydrograph. Right: the proportion athigh discharges (observed flow greater than 0.25 times the maximum flow during the event).

Table 3. Realistic models and parameter sets for the Hérault catchment at Saint-Laurent-le-Minier (no. 3b). Csoil: the contribution to thehydrograph of flows passing through the soil. Ckdw/C

∗kss: the value of the parameter Ckdw for model DWF (Eq. 1) or the value of the

parameter C∗kss for the model SSF (Eq. 2).

ID NSE DWB (m) Ck (–) Ckdw/C∗kss (–) nr (–) np (–) Csoil (%)

DWF1 0.82 0.15 17.3 8711 19.6 19.11 61DWF2 0.84 0.11 2.34 4416 19.16 7.63 39SSF1 0.89 0.40 15.81 45284 15.96 5.86 68SSF2 0.89 0.34 2.08 22543 14.06 6.42 53

Notwithstanding the uncertainty related to the choice ofthe model when any model has been identified most suit-able through the performances, the largest uncertainties arerelated to the parameterisation of the models, a consequenceof the equifinality of the solutions when calibrating a hydro-logical model against the sole criterion of the reproduction ofthe hydrological signal. While in terms of plausibility, sev-eral sets of parameters may be equivalent, even for the samemodel, these sets of parameters are likely to lead to a differ-ent hydrological functioning.

5.3.2 Detailed study of four plausible simulations onthe Hérault watershed at Saint-Laurent-le-Minier

Spatialised and integrated changes in moisture levels andflow velocities generated within the catchments have beenconsidered in order to give new details on the different im-pacts of the models’ structure, but also to explain the re-sulting uncertainty when assessing the flow processes’ dis-tribution. Next, the results of four simulations are describedand are equally considered to be plausible according to theDEC criterion obtained from the DWF and SSF models (twosimulations per model, see Table 3). The Hérault catchmentat Saint-Laurent-le-Minier (no. 3b) has been considered be-cause of the equivalence of the models in representing that

catchment. Figure 12 compares the changes over time in thestate of soil saturation and the different simulated flow veloc-ities of the four model+ parameter set configurations (Ta-ble 3). Figure 13 compares the spatial distributions of thesevariables at a given moment.

In terms of hydrographs, which is quite logical given thesimilar likelihood scores, the simulations differed very little.The notable difference in the generation of hydrographs is thecontribution of the different simulated flow paths. The pro-portions of water passing through the soil column (via sub-or surface-soil horizons) were highly variable, with an aver-age of 39 % for the DWF2 model, 53 % for the SSF2 model,61 % for the DWF1 model and 68 % for the SSF1 model (Ta-ble 3). This is both due to (i) the structural choices (DWF andSSF) that involved a different saturation dynamics and the in-corporation of different types of flow, and to (ii) the choiceof the parameters that involved flow velocities of differentorders of magnitude.

The choice of a model’s structure (DWF and SSF) implieddifferences in soil moisture spatial distribution and dynam-ics, which in turn impacted the timing of the flow processes.In the DWF structure, the soil moisture distribution is sensi-tive to the soil depth spatial distribution as a result of the de-crease in the simulated intra-soil flows as a function of watertable height (cf. Sect. 3.2, Eq. 1). Consequently, the DWF



(a) Hydrograph at Saint-Laurent-le-Minier

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Upper soil compartmentSoil column

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040

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Figure 12. Comparison of the results of four equally plausible simulations for the Hérault at Saint-Laurent-le-Minier (Table 3). (a) Floodhydrographs (solid lines) and outlet flows transiting via the soil (dashed lines). (b) Evolution in the overall moisture content of the soilcolumn. (c) Evolution in simulated mean velocities in the subsoil horizon (DWF model) and in the upper part of the soil column (SSF model).(d) Average runoff velocities on the hillslopes. (e) Average runoff velocities in the drainage network. Denoted are events of calibrations (∗)and events of validation (∗∗).



Figure 13. Spatialised outputs for a given moment during the event of 18 October 2009 for the Hérault at Saint-Laurent-le-Minier (duringthe development of the flood, where Q= 74 m3 s−1). (a, d, g, j) soil moisture conditions simulated, respectively, by the configurationsDWF1, DWF2, SSF1, SSF2. (b, e, h, k) discharges in the soil simulated, respectively, by the configurations DWF1, DWF2, SSF1, SSF2(NB: different colour scheme). (c, f, i, l) surface flow velocities simulated, respectively, by the configurations DWF1, DWF2, SSF1, SSF2.



model produced a greater contrast in saturation levels be-tween different areas of the catchment (Fig. 13a and d). Withthe SSF model, the overall catchment saturation level wasmore related to the topography; saturated cells were observedclose to the drainage network, and, lower water content wasconversely observed in the upper reaches of the catchments.In fact, for the SSF model, rainfall forcing is mainly involvedin the saturation of the upper soil layer (the dashed lines inFig. 12b), which reacts very rapidly to precipitation.

As a result of the contrasting soil moisture dynamic, theflow velocities simulated in the soil showed consecutive dif-ferences. At the start of flooding, the SSF structure resultedin an early increase in flow velocities due to a higher andmore homogeneous saturation level of the upper soil layer(Fig. 12c). Conversely, in the DWF model that simulated amore heterogeneous spatial saturation of the catchment, thesimulated velocities increase was delayed, and the maximumvalues reached were 2 to 4 times lower.

The dynamics in the drainage network were impacted bythe choice of the structure as well. The runoff velocities’ av-erage reflected the earlier inlet of the subsurface flow pro-cesses through the fast saturation of the upper compartmentwith the SSF model (Fig. 12e). The DWF model yields amore contrasting variation in the runoff velocities in thedrainage network, mirroring variations in soil saturation lev-els.

The choice of parameters mainly implied different rangesof values for the velocities simulated in the soil, on the sur-face of the hillslope and in the drainage network. The cal-ibration of the Ckss and Ckdw parameters controlled the or-der of magnitude in the subsurface velocities (Table 3 andFig. 13b, e, h and k). The calibrated Ck (infiltration capacitycontrol) and DWB (depth of the subsoil horizon) parameterscontrolled the infiltration as well, leading to a higher or lesshigh number of cells with excess saturation or the infiltrationcapacity being reached (Fig. 13c, f, i, l) and consequently toa higher or less high proportion of runoff over the hillslope(Fig. 12d).

Several orders of magnitude were actually allowed whilerespecting the calibration objective, because the transit timesof the different water pathways compensate each other. Asforeshadowed by those four configurations, the selection ofplausible parameter sets for any model in any catchmentshows (i) a positive correlation between the parameters Ckand nr and np, suggesting the necessity of slowing downflows in the drainage network when a larger proportion ofrunoff from the catchments is simulated (i.e low Ck wouldimply low nr and np and vice versa) and (ii) a positive cor-relation between Ck , Ckss and Ckdw parameters, suggestingthe necessity of accelerating the intra-soil flows when highinfiltration rate is allowed and, consequentially, when largerproportion of subsurface flow is simulated. Thus, a degree ofcompensation occurs in the simulated transfer times betweenthe various water paths from the hillslopes to the drainagenetwork and from the drainage network towards the outlet.

6 Discussion

6.1 On the hydrological functioning of the catchmentsstudied

The benchmark of the models’ performance on the catch-ment set leads to reveal four subsets, suggesting four dis-tinct hydrological behaviours. According to the modellingassumptions (Sect. 5.1), the resulting errors in simulating thedifferent stages of the hydrographs (Sect. 5.2) and the catch-ment properties (Sect. 2.1), the hydrological behaviour of thecatchment can be interpreted by each subset as follows:

– The SSF and SSF-DWF models showed better overallperformance (with no particular pattern) in the first sub-set, the Gard (no. 2) and Salz (no. 4) catchments. Thissuggests, on the one hand, rapid catchment reactivitywith fast rising flood waters as well as a fast flood reces-sion, and on the other hand, the formation of the flowsin the soil through local saturation tied to the climateforcing. Although the models exhibited similar perfor-mances, the contrasting physiographic characteristics ofthese catchments suggest that there are different expla-nations for this better fit of the SSF-DWF model. On theGard, the very high intensities of the observed events(Table 2) and/or the low soil depth (Table 1) may ex-plain the limitations on vertical infiltration due to theproperties of the soil and/or geological bedrock. As aresult, the rapid formation of a saturated zone at the topof the soil column favours runoff and a subsurface fluxby activating preferential paths in the soil. This interpre-tation is in agreement with the field studies achieved ona schist upstream sub-catchment of the Gard, the schistsubstratum being the predominant geology of the Gardcatchment (see Sect. 2.1, Ayral et al., 2005; Maréchalet al., 2009, 2013). On the one hand, on the Salz (no. 4),the soil is deeper and the precipitation intensities lower.On the other hand, the geological bedrock composed ofmarl, sandstone and limestone is assumed to have lowpermeability, and the soil is less conductive due to itspredominantly silt-loam texture. As a result, despite thelower forcing intensities, the surface soil can reach sat-uration, which might explain why the SSF model offersthe best fit.

– The considerable hydrological responses in terms ofvolume on the Ardèche second subset appear to belinked to hydrological activity at depth, including thatwhich takes place during intense floods, as suggested bythe better fit of the DWF model. Here, in particular, themodel gave a better representation of the relatively slowand uniform hydrological recessions from one eventto the next, reflecting an aquifer-type flow whose dis-charge properties are only governed by the propertiesof the catchment bedrock only. This interpretation isenforced by the field studies achieved at the time in



a granite experimental sub-catchment localised in thedownstream part of the Gard (Sect. 2.1, Ayral et al.,2005; Maréchal et al., 2009, 2013), the Ardèche catch-ment being granitic. The somewhat delayed flood tim-ing that the structure of the one-compartment model im-posed seems to indicate that there are more rapid flowsat the beginning of an event, which this model structureis not able to represent. A plausible explanation is thedefault calibration, which uses a uniform depth of ac-tive subsoil horizons, DWB, during a flood. This mightmask the appearance of local saturation zones and thesubsequent runoff due to shallow soil and discontinu-ities in the permeable base layer (for example, in thedownstream sedimentary layers, where infiltration testshave shown the appearance of runoff; see Sect. 2.1). Incontrast, the SSF and SSF-DWF models did not displaythis weakness because the varying nature of soil depths(DBDsol, which determines the depth of the upper com-partment) allowed for the rapid development of flowsvia preferential paths in the soil blocks, thus enablingthe simulation of such local dynamics.

– The third subset consists of the downstream part of theHérault (no. 3a and no. 3b). The models’ performancescontrasted with the Hérault catchment heads (no. 3c andno. 3d), suggesting hydrological behaviours related tothe contrasting geological properties. An interpretationof hydrological functioning is nevertheless not possible,given the similar overall results offered by the modelsand that no distinctions can be drawn according to othercriteria.

– The last subset consists of the catchment heads (no. 1d,no. 3c, and no. 3d). We observed superior performancesfrom the DWF and SSF-DWF models, with a particu-lar improvement in the forecasting of rising flood wa-ters when using the SSF-DWF model. This suggests thepresence of several types of flow in the soil with strongsupport from flows at depth, which corroborates thehigh mean inter-annual discharges associated with thesecatchments, and additionally the presence of rapidlyformed flows, providing a good simulation of the risingflood waters. The fact that the model SSF-DWF, whichprecisely alleged to represent the simultaneous settingup of shallow and deep subsurface flows, did not com-pletely outperform the two other models is interesting.From our point of view, it points out the limit of theirartificial implementation, using a threshold infiltrationfrom the top layer to the deep one. In reality, the simul-taneous setup of the two fluxes more likely refers to thespatial heterogeneity of the soil properties, especially inthe head watersheds within a catchment cell (2.5 km2),which might allow either deep infiltration or fast topsoilsaturation.

6.2 Overcoming the remaining uncertainty

The submitted multi-hypothesis test classically faced theequifinality issue related to the parameter uncertainty andhighlighted the uncertainty related to the model’s structure.The comparative and detailed description of the simulationrevealed the model’s structure controls, thus giving almostdirect guidelines to overcome the equifinality issue.

One of the objectives of the study, the assessment ofthe flow contributions to the hydrographs, is not com-pletely reached, mainly because of the parameter uncertainty(Sect. 5.3.1). The benchmark of modeling configurations,scanning the different simulated processes (Sect. 5.3.2),showed how the calibration lead to that uncertainty. The widerange of values that has been allowed through the parame-ter setup enabled counterbalancing effects between the inter-nal velocities simulated. As a direct consequence, variableflow contributions could be simulated while finally produc-ing similarly likely hydrographs. This points out direct fur-ther objectives for improving and better restraining the cali-bration of the models. While several ranges of value for theinternal flow velocities have been simulated, a reasonablerestriction based on the velocity likelihood could be fore-seen. This further perspective should also shift experimentalstudies toward a better assessment of the water transit timealong the different pathways at the hillslope scale, either us-ing direct methods such water isotope tracing (Tetzlaff et al.,2018), developing imaginative indirect ones such as the di-atom tracing (Pfister et al., 2017b), or taking advantage ofsuspended particles and water turbidity measurements.

The equifinality of the models in several catchmentsmostly points out the limit of the assessment of hydrologicalmodel through the sole use of the hydrological discharge timeseries at the outlet. Leading up to a multi-criteria calibration,the detailed comparative description outlined the discrepan-cies of the simulations and thus provided guidelines for inte-grating judicious information to differentiate the models’ ad-equacy. The distinguished saturation spatial patterns gener-ated by the DWF and SSF structures suggest the relevancy ofthe soil moisture distribution assessment along hillslopes andsoil heterogeneities, as the first structure implied a soil mois-ture dynamic related to local soil properties, while the latterimplied a soil moisture pattern related to the distance to thedrainage network. In addition, the description of the a priorimodelling errors (Sect. 5.3.2) points the way towards an op-timal consideration of the early rising limb and the flood re-cession, when calibrating the models over the discharge timeseries. Indeed, the model’s structure appeared to mostly con-trol these particular stages, especially the simulated timing ofthe first stage and the simulated dynamic of the latter one. Aconsequential need to accurately discharge benchmarks, par-ticularly during these stages, should further direct the rivermonitoring toward the high temporal resolution of the riverlevel, with the rising and receding flood stages being shortperiods during flash floods and efforts for reducing the uncer-



tainty of the rating curve at low and moderate flows, ratherthan getting extreme discharge measurements, including, forexample, the hysteresis of the discharge curves (Le Coz et al.,2014).

7 Conclusions

7.1 Summary of the study’s objectives andmethodology

The objective of the study was to improve our understandingof flash flooding in the French Mediterranean Arc. In partic-ular, attention was paid to the dynamics of soil saturationin catchments during these events and their possible rela-tionship with the physiographic diversity encountered. Themethod used consisted of the consideration of hydrologicalmodels as a diagnostic tool to test hypotheses about the func-tioning of catchments.

Based on the structure of the MARINE model, a hydrolog-ical model with a physical and distributed basis, three typesof dynamic of soil saturation were postulated and tested. Inthe first case (the DWF model), we assumed an aquifer dy-namic with an infiltration at depth and the generation of astrong base support according to the volume of infiltratedwater. In the second case (the SSF model), it was the acti-vation of preferential paths at the soil–altered-rock interfacethat generated the majority of the flows passing through thesoil, with the lower part of the soil column serving only asa storage reservoir. In the third case (the SSF-DWF model),there was flow generation via both the activation of prefer-ential pathways, initially by the saturation of the top of thesoil column, and a significant increase in the base flux viathe subsequent infiltration of water present at deeper levels.

The same calibration strategy was used for the three mod-els on a set of 12 catchments, which are representative of thediverse characteristics of the Mediterranean Arc. Whether amodel offers a good fit was evaluated on the basis of scoresrepresenting overall or partial model performance in terms ofsimulating the hydrographs, the proportions of the processessimulated, and the timing and form of flood recession.

7.2 Conclusions on our understanding of the processesinvolved

The specific use of a multi-hypothesis framework supports aclear comparison of the hydrological behaviours, which hasin turn provided the main basis of the insights of this study.From the application and validation of the three hydrologicalmodels, the 12 catchments of the study could be classifiedinto four categories, including (i) the Gard and Salz catch-ments, for which the SSF model is better suited to reproduc-ing the hydrological signal, highlighting the importance oflocal and surface soil dynamics in the generation of flowsespecially at the beginning of a flood, (ii) the Ardèche catch-ments, for which the DWF model most accurately reproduces

the observed flows, which indicates more regular and inte-grated hydrological functioning at the catchment level, withthe flows generated being directly related to the moisturehistory and rainfall volumes, (iii) the Hérault catchments atValleraugue and La Terrisse and the Ardèche catchment atMeyras, which have steep-sloped catchment heads where theSSF-DWF model stands out, suggesting both sustained andsignificant hydrological activity at depth during flash floodsand surface activity in the establishment of early flows atthe beginning of events, and (iv) the Hérault catchments atLaroque and Saint-Laurent-le-Minier, for which no modelshows any significant difference.

The modelling results help to draw consistent assumptionsof hydrological behaviours, which corroborate, when avail-able, the knowledge and observations on the overall hydro-logical functioning of the catchments or the experimental es-timations of flow processes. The results suggest that the be-haviour of catchments under extreme forcing is a continua-tion of the hydrological functioning normally encountered.

The assessment of the flow processes in the catchments re-mains uncertain, owing to the equifinality issue. The analysisof the internal processes enabled the explanation of the com-pensation effects between the simulated flow pathways andthe resulting uncertainty of the calibrated parameter sets onthe sole basis of the discharge time series. In addition, otherdetailed descriptions of the simulations, such as the spatialdynamic of the soil moisture distribution or the modellingerrors, highlighted the actual impacts of the model’s assump-tions on the simulations. The revealed discrepancies betweenmodels, namely the range of values of the flow velocities,the spatial pattern of the soil moisture, the early rising limbtiming and the recession rate of the hydrographs, finally de-fined pertinent milestones for improving the assessment ofthe model’s adequacy.

Data availability. Hydrometric data come from the network of op-erational measurements (HydroFrance databank, http://www.hydro.eaufrance.fr/, SPC Grand Delta et al., 2018). Rainfall data are pro-vided by the rain gauge network of the French flood forecastingservices and Météo-France (radar data).

Author contributions. AD developed Module 2 of the MARINEcode. AD performed model simulations and prepared the paper. Allauthors discussed the results and contributed to the text.

Competing interests. The authors declare that they have no conflictof interest.

Acknowledgements. This work was partly funded by the Euroré-gion Pyrénées-Méditerranée (PGRI-EPM project) and the FrenchCentral Service for Flood Forecasting (SCHAPI).





Edited by: Markus HrachowitzReviewed by: two anonymous referees

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https://doi.org/10.1002/wat2.1241

https://doi.org/10.1002/met.1469

https://doi.org/10.1016/S1251-8050(97)83983-3






https://doi.org/10.1175/WAF1004.1


https://doi.org/10.1002/wrcr.20407

https://www.unisdr.org/we/inform/terminology

https://www.unisdr.org/we/inform/terminology



https://doi.org/10.1002/joc.2003



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Open Archive Toulouse Archive Ouvertecal events – the European cited research particularly demon-strates the importance of cumulative rainfall (Arnaud et al., 1999; Sangati et al.,