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Measuring surface flow concentrations using a cellular automaton metric: a new way of detecting potential impacts of flash floods in sedimentary context

Mesurer les zones de concentration des écoulements de surface en utilisant un automate cellulaire : une approche originale pour détecter les dommages possibles en cas de crues rapides en milieu sédimentaire
Johnny Douvinet, Daniel Delahaye et Patrice Langlois
p. 27-46

Résumés

Dans cet article, une nouvelle méthode pour détecter les dommages possibles en cas de crues rapides est expérimentée. Les zones de concentration théorique des écoulements de surface sont cartographiées en utilisant l’automate cellulaire RuiCells, puis comparées aux dégâts observés suite à des crues rapides avérées sur 5 « vallons secs » localisés dans le nord de la France (Bassin parisien). L’automate a été conçu et développé en implémentant trois règles hydrologiques simplifiées guidant la dynamique des écoulements de surface. Les simulations numériques permettent d’étudier les relations entre l’organisation des réseaux de talweg et les surfaces au sein d’une forme donnée. Un indice de concentration (IC) fait émerger toutes les confluences en amont desquelles le réseau et les surfaces sont structurellement bien organisés. Les cartes de l’IC, les observations de terrain, la connaissance locale et la localisation à échelle fine des dommages apparaissent corrélées puisque les simulations mettent au jour les endroits où les crues rapides ont causé d’importants dommages (matériels et parfois humains) et les zones où les concentrations des eaux de surface ont entraîné des incisions majeures (ravines). Dans de rares cas, les cartes de l’IC n’ont pas été validées car personne n’a pu confirmer l’existence de dégradations lors d’événements passés. Ces investigations méthodologiques amènent à discuter de la place de l’occupation du sol et de l’utilité de tels outils pour mieux comprendre la genèse des crues rapides dans ces « vallons secs ». Les expérimentations réalisées dans d’autres bassins du nord de la France offrent aussi des perspectives intéressantes : les gestionnaires du risque pourraient utiliser les cartes de l’IC afin de prévenir les dommages probables en cas de futures crues rapides, mais également s’y référer pour définir les territoires sensibles au ruissellement sur un grand nombre de bassins afin de répondre aux premiers objectifs de la Directive Cadre Européenne sur l’Eau (2007/60/CE).

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Notes de la rédaction

Article soumis le 3 octobre 2011, accepté le 28 février 2012.

Texte intégral

Introduction

1The origin and the prediction of flash floods in small basins is getting increasing attention (Borga et al., 2008; Gaume et al., 2009; Douvinet and Delahaye, 2010) and the last decades have seen an increase in forecasting of such events in numerous countries (Montz and Grunfest, 2002; Estupina-Borell et al., 2005; Balmforth and Dibben, 2006; Ruin et al., 2007). Such natural hazards threaten people, cause increasing losses of buildings and infrastructures and occur in a short time-duration. Flash floods are generated during or shortly following high rainfall intensities, and are characterised by sudden onset, rapid rising time and a surge that rushes down the main valley just a few minutes after rainfall has peaked (Reid, 2004; Schmitz and Cullmann, 2008; Ortega and Heydt, 2009; Morin et al., 2009; Douvinet and Delahaye, 2010). Differences observed in sediment transport rates are explained by the travel distance of materials from different source areas and the lag between water and sediment waves (Martin-Vide et al., 1999). To address the lack of available information, various models and approaches have been carried out. By necessity, investigations on recent flash floods generally are event-based and opportunistic as they enhance the information content (Hazenberg et al., 2011). While meteorological observations provide relevant details on the timing and location of convection in the storm environment (Neppel, 2006; Anquetin et al., 2009), hydrological and physical processes remain difficult to assess for several reasons: i) flow measurements and classical field-based experimentations (as the reconstitution of maximum peak discharges thanks to slack water deposits; Gaume et al., 2009) are rarely collected in basins of small-size; ii) these floods are insufficiently documented and are difficult to monitor in real time as they produce destructive effects to measuring devices (Reid, 2004); iii) the infrequency of these events makes the statistical analysis and calibration of models delicate (Ferraris et al., 2002).

2In this study, our objectives are to use a cellular automaton (CA) approach using the CA RuiCells (Delahaye et al., 2001; Langlois and Delahaye, 2002; Douvinet et al., 2008) in order to: i) promote further understanding of the effects of runoff concentration which is influenced by basin form, slope and the drainage network during flash floods, and ii) to better assess the potential of flow concentration since local to global scales. RuiCells is based on a framework common to other CAs and respect two main properties: a CA is a model simplifying the reality to a group of automates dealing with information and inducing cellular actions; CA use finite state, homogeneous, interconnected and regularly organised cells. In a more format aspect, a CA model is defined by a certain number of cells (with states) and by transition rules (Wolfram, 2004). The guiding principle of RuiCells follows the idea that mechanical rules of flow based on topography can be combined with a CA representation of spatial processes to better assess the complex relations between basin structures and surface flow pathways (Tarboton, 1997; Delahaye et al., 2001). While numerous distributed hydrological models have been realised with Digital Elevation Maps (Moussa and Bocquillon, 1996; Cudennec et al., 2002; Kirkby et al., 2005), none of them allow for the estimation of potential surface flow concentration in all parts within a basin. Previous studies have typically focused on the relation between the global catchment morphology and its hydrological response measured at the final outlet. These studies underlined difficulties encountered when linking local responses (sub-basins or hillslopes) to this global behaviour and this aim has been one of the main issues for geomorphologists since the 1970s (Veltri et al., 1996; Rodriguez-Iturbe and Rinaldo, 1997; Schmidt et al., 1998). A few studies have successfully shown that the drainage network organisation plays a key role on hydrological functionality (Dietrich et al., 1993; Vogt et al., 2003). Others recently defined the global response as the result of linear system (with a linear relation between mean discharges and the basin sizes) and show that global catchment response can be summarised by an Instantaneous Unit Hydrograph (IUH; Lopez et al., 2005), evolving in a Geomorphologic Instantaneous Unit Hydrograph (Cudennec et al., 2002). However, in this study we use a CA approach to better link local hydrological rules to the emergence of global hydrological responses. Our goal is to identify all sub-basins in which high surface flow concentrations can be hidden at larger scales and this approach is applied on small-size basins where flash floods occurred in order to create prevention maps (Douvinet et al., 2010). One major but unsolvable problem remains the calibration of simulations for realistic modelling and validation (Gaume et al., 2009). Assuming that this tool is relevant to the planning of and protection from such types of events, it could also be useful for the understanding of floods in ungauged valleys. Moreover, definition of flood potential in temporary streams is required in the design of bridges and culverts and is also needed to assess the extent of probable flooding in the future.

3We begin by presenting the study sites. We then describe the structure and the challenges supported by the numerical simulations based on the CA RuiCells. A specific “IC index” is created to quantify the potential of surface flow concentration from local scales. The simulations made on the five studied areas enable identification of the links between basin form, slope and the drainage networks on hydrological properties observed since local to global scales. This information is also aligned with known instances of damage registered on roads and houses after previous events. If similarities are observed between simulations and reality, we should be able to predict possible damages in the five basins in case of future thunderstorms or in other basins where high potentials are detected. Simulations finally confirm the key role of morphology on dynamics of flash floods at local scales and prevention maps could be supported by the CA RuiCells as high potential are now well-known for more than 300 small-size basins (< 20 km²).

Study sites

4In a previous study (Douvinet, 2008), 189 basins in northern France were identified in which damage due to flash floods was observed over the period 1983-2005 (fig. 1B). All these basins contain differences in morphology, land use or degree of urbanisation but have common morpho-structural features as they belong to the Parisian Basin. Landscapes consist of successive sub-horizontal to slightly undulating plates (Mathieu et al., 1997) which are incised by ‘dry valleys’ inherited from Quaternary, periglacial periods (Lahousse et al., 2003; Larue, 2005). Dominant soils are luvisols and the latter are highly vulnerable to erosion due to low contents of organic matter (< 2%) and clay (< 15%), and high contents of silt (> 70%). The sensitivity of these soils has been well demonstrated in several previous works (Auzet et al., 1995; Souchère, 1995; Mathieu et al., 1997; Le Bissonnais et al., 2002): 67% of the 189 basins (fig. 1B) present high sensitivity to erosion during summer and 58% during spring. In these areas, surface degradation under raindrop effects induces a strong reduction of water infiltration capacity and a progressive disappearance of soil roughness which provide important concentrated runoff waters (Delahaye, 2002). For this reason, soil erosion has first been studied in the context of land-use dynamics, agricultural practices and long-duration rains in this region (Souchère et al., 2005).

5To test, compare and discuss the simulations obtained with the CA RuiCells, we focus on five basins (fig. 1C) in which knowledge of local actors and field experiments provide relevant information on local erosion, damage and inundated areas during flash-flood events. The Aizelles basin (2.8 km²) has an elevation ranging from 240 m to 76 m (fig. 1C) over a distance of 1.2 km. Its geology is comprised of Eocene rocks in upstream slopes and Cretaceous calcareous rocks throughout most of the basin. Forests of broad-leaved trees exist on the upper and middle slopes and interact with vineyards, maize and potatoes in downstream parts (tab. 1). On July 28th, 2001, following an event in which 50 mm of rain fell in one hour, the main inundated areas were located at the outlet, where the river passes through the small village of Aizelles (fig. 1C). The L’Eaunette basin (15.8 km²) presents the lowest slopes with an elevation ranging from 60 m at the final outlet to 141 m in the plate known as La Haute Borne (fig. 1C2). Due to gentle slope gradients, cultivated areas (corn, potatoes and wheat) dominate the basin land cover and forests exist in the upper part (0.3 km²). The town of Villers-Plouich was the most heavily impacted (one person died and water levels were ranging from 1 to 2.3 meters in the main thalweg) following the flash flood event of September 8th, 2008, in which 56 mm fell in 6 h. The Saint-Martin basin (14.3 km²) has an elevation of 4 m above the town of the same name, located at the outlet (fig. 1C3), where the ‘dry valley’ joins the Seine River, and 154 m on the drainage limit near the plate knows as La Vaupalière. The basin land cover comprises forests on the upper and middle slopes with intensive farming (corn and wheat) and urbanised areas on the gentle slopes of the plateau, and urbanisation and other cultivated areas on the floodplain. This basin experienced heavy convective rainfalls on June 16th, 1997, during which 80 mm fell in 6 h, leading to the deaths of three people near the village of La Vaupalière (fig. 1C). The Warnette basin (25.8 km²) has an elevation of 117 m, ranging from 17 m above the city of Raye-sur-Authie to 134 m on the plate of Artois (fig. 1C). The land cover comprises grasslands and forests in the middle and upper slopes with intensive farming (corn, flax and potatoes) on the plate as in the floodplain. A flash flood occurred on May 20th, 2000 in this basin. In that day, 35 mm were recorded in less than 1 h (tab. 1). The most important damages were located at the outlet and near the Fond Beharel, in the south of the village of Guigny (fig. 1C). Local knowledge completes our field experiment as other material losses were also located at the outlet of two small valleys (Fond Madame and Wancourt). The Aunette basin (45.9 km²) has the highest elevation (178 m) going from 56 m above the village of Trie-le-Château to the drainage basin limit located on the front of a structural embankment named The cuesta of Therain (fig. 1C). The land cover presents numerous forests in the upper and middle slopes which interact with cultivated areas (corn, potatoes and beetroot) and grasslands on the floodplain and in the heads of a few small ‘dry valleys’. Several floods were registered on July 1st, 1993 (after 100 mm in 2 h), July 11th, 1997 or August 5th, 1997. Minor material damages were observed in Labosse (fortunately, nobody died) and material damages on roads were registered within some rare parts of this basin (fig. 1C).

6Given that the dynamics of water flows and kinematics of the surges seem to be controlled by topography the main question addressed is the following: can estimating a potential of surface flow concentration using morphological features improve knowledge on potential damage in case of flash floods? The decision to study this question using model simulations is due to the fact that i) installing a monitoring network is difficult to justify as a flash flood may not occur in a period of 20 years and ii) the likelihood of a station getting destroyed during a single event.

Fig. 1 – Presentation of the five studied basins.
Fig. 1 – Présentation des cinq basins étudiés.

Fig. 1 – Presentation of the five studied basins. Fig. 1 – Présentation des cinq basins étudiés.

A: Location map at the French national scale. B: Regional map of the northern Parisian Basin. 1: main cities; 2: 187 basins where flash floods have been observed during the period 1983-2005 (Douvinet, 2008); 3: the five basins studied in this article; 4: limits of ‘department’; 5: name of ‘department’. C: Average land-use cover. 1: equal level lines (10 m); 2: main equal level lines (50 m); 3: altitude of several level lines (in m); 4: altitude numbers (in m); 5: outlet; 6: permanent stream rivers; 7: drainage basin limit; 8: year of the land-use cover mapping linked to previous flash-flood events; 9: name of the villages and cities within the basin; 10; local name of plates or valleys; 11: Used Cultivated Areas (SAU in French); 12: urbanised areas; 13: forests; 14: permanent grasslands.
A : Carte de localisation à l’échelle de la France. B : Carte de localisation à l’échelle du nord du Bassin parisien. 1 : villes principales ; 2 : 187 bassins versants où des crues rapides ont été précédemment observées sur la période 1983-2005 (Douvinet, 2008) ; 3 : les cinq bassins étudiés dans cette étude ; 4 : limites des départements ; 5 : nom des départements. C : Caractéristiques de l’occupation du sol (moyenne). 1 : courbes de niveau (équidistance : 10 m) ; 2 : principales courbes de niveau (équidistance : 50 m) ; 3 : altitude des courbes de niveau ; 4 : points côtés (en m) ; 5 : exutoire ; 6 : écoulement permanent ; 7 : limite des bassins versants ; 8 : année de la cartographie réalisée pour l’occupation du sol en lien avec la date de la crue passée ; 9 : nom des principaux villages/villes au sein du bassin ; 10 : noms des plateaux ou vallées citées dans le texte ; 11 : Surface Agricole Utile (SAU) ; 12 : surfaces urbanisées ; 13 : forêts ; 14 : prairies permanentes.

Tab. 1 – Information collected for the five studied basins.
Tab. 1 – Informations collectées sur les 5 bassins versants étudiés.

Name of the five studied basins

Aizelles

L’Eaunette

Saint-Martin-de-Boscherville

Warnette

Aunette

Date of events A

2001/07/26

2008/08/09

1997/06/16

2000/06/03

1993/07/01

Basin size (in km²)

4.6

14.3

14.3

25.7

30.1

Elevation (in m)

123

121

132

117

178

Average altitude (in m)

138

107

111

95.2

168.9

Slope STTD B

34.2

19.8

25.8

24.5

45.6

Main talweg length (in m)

3.1

5.3

7.9

9.6

16.5

Gravelius index C

1.15

1.45

1.19

1.24

1.61

Morton Sprawl index D

1.45

5.11

2.17

4.52

5.16

Rainfall inputs (in mm)

70

56

80

35

100

Rainfall duration (in min)

210

360

360

60

120

Urban areas (in %)

12.7

5.1

15.8

3.1

3.0

Grasslands (in %)

11.2

11.9

17.1

18.1

11.2

Cultivated areas (in %)

45.1

82.6

22.1

71.7

63.7

Forests (in %)

31.0

0.4

45.0

7.1

22.1

A This information has been extracted from the files related to the French recognition of the “state of natural disaster” (CATNAT database).
B Standard Threshold Deviation (STTD) for the slope systems (automatically calculated by ESRI ®Arc Gis 9.8).
C This Gravelius index represents the fraction between the perimeter of one basin and the perimeter of a circle having the same surface.
D The Morton sprawl index represents the fraction between the perimeter and the square root of its area (Douvinet, 2008, p. 196).

Material and method

Recent advances in geomorphology using CA

7Before presenting the structure, functionality, inputs and outputs of RuiCells, we provide a brief overview of how CA models have significantly contributed to hydrological and geomorphological studies over the past decade (e.g., Fonstad, 2006; Ménard and Marceau, 2006; Coulthard et al., 2007; Van de Wiel et al., 2007). CA is supported by an array of advances in fields outside hydro/geomorphology such as physics, computer sciences and mathematics. In these dynamic models, global properties arise from local and spatial interactions of many cellular entities (Wolfram, 2002; Fonstad, 2006). CA is often characterised by a lattice where each cell possesses a state. The time is discrete and the state of cells is updated through the application of a set of predefined transition rules (Phipps and Langlois, 1997). These rules (expert rule-based, deterministic or probabilistic) dictate how the different cell states will react to state configurations present in the neighbourhood of each cell. This approach is decades old, first introduced by Von Neumann in 1951 (Gardner, 1970) and devised for the famous Game of Life by Conway (1970). The first CA model including hydrology and geomorphology was developed by A.B. Murray and C. Paola (1994) but the representations of river processes did not include explicit time and real physical scaling in the model (Parsons and Fonstad, 2007). N. Thomas and A.P. Nicholas (2002) extended this model in order to simulate more realistic water flow dynamics in braided river systems. Other CA models of water flow aim at simulating the growth of small rills in response to hillslope erosion (Favis-Mortlock, 1998), at measuring soil erosion at microscopic scales in SoDa (Valette et al., 2006) or at simulating basin responses using a wave approximation for in-channel flows (De Roo et al. 1996). T.J. Coulthard et al. (2007) and M.J. Van de Wiel et al. (2007) recently introduce a gradually-varied CA for catchment response modelling that produces sediment transport dynamics in spite of not including unsteady catchment hydrology. A few applications are currently used to study aeolian ripples (Anderson, 1990), forest-fires (Clarke et al., 1994), debris-flows (Di Gregorio et al., 1998), debris-laden floods (Bursik et al., 2003), lava dynamics (Avolio et al., 2006), channel meandering (Coulthard and Van de Wiel, 2006), the evolution of coasts (Dearing et al., 2005) and the analysis of superimposed bed forms (Narteau et al., 2009) for example. Smoothed-particles can also be linked with CA models (Drogoul, 1993) to better assess generic dynamics or hydrological fluxes. Since a few years, agent-based modelling has also been tested in hydrology and geomorphology after first initiatives in ecology, sociology or human geography. Modules of CATCHSCAPE allow simulating the hydrological system with its distributed water balance or to irrigate schemes management, crop and vegetation dynamics (Bécu et al., 2003). Agent-based modelling can also be used in alluvial plains where processes between independent interacting entities behave according to the local environment (Teles et al., 1998). But these agent-based modelling applications remain less used than CA in the field of geomorphology as the attention is more drawn on interactions between physic components than on relations with human relationships.

Framework and structure of the specific CA model RuiCells

8Previous experimentations in CA modelling for surface water flow provide several advices and recommendations. The main difficulty in these models is generally to establish a link between topographic variables, such as the elevation and its derivative, and hydraulic variables as water fluxes (Crave and Davy, 2001). Furthermore, from a numerical perspective, square lattices induce problems for simulating the runoff routing (Palacio-Vélez et al., 1998; Mita et al., 2001) as surface flows do not follow the real drainage. Different studies also highlighted the critical influence of the DEMs cells size on the accuracy of extracted networks (O’Callaghan and Mark, 1984; Vogt et al., 2003). Consequently, in the CA model RuiCells, we choose to use a lattice based on triangular, regular and interconnected cells based on a Digital Elevation Model (DEM) and we define simple rules to simulate the interactions between basin form, slope and the drainage network.

9The structure of RuiCells is basically summarised as follows. The first step permits to create a topological mesh in triangular finite elements. In this, the direction of the steepest slope gives the downstream direction of flow and this information available in each cell is draped over the Digital Elevation Model (fig. 2A). The lowest diagonal was chosen to obtain more realistic surface flows. Each cell contains the pointer to its lowest downstream neighbour and such a procedure resembles the Local Drain Direction Network (LDDN) used in models such as PcRaster (Karssenberg et al., 2001). The second step assigns one hydrological rule for each cell. The triangular facets represent elementary cells on hill-slopes; the linear portions the thalwegs; and several nodes the local closed depressions. Combining these rules in the third step, we aim to simulate the interactions between these various surface-water flows (Murray and Paola, 1994; Palacios-Velez et al., 1998). Each cell is linked to upstream/downstream cell(s) by a flow graph to form a cellular unit (fig. 2B1). The connectivity between those cells is directed predominantly by the morphological link structured by the mesh (or lattice) as well as the neighbourhood topology of cells. There, contrary to other CA classical models, flow pathways are not only guided by the neighbourhood or vicinity conditions. Although two kinematics cascades were proposed by O.L. Palacios-Velez et al. (1998), this approach assumes that linear runoffs and spatial runoffs are dependent. A synchronous advection operator also avoids the problem of order in calculi. Indeed, process is iterative in RuiCells. It means that surface, flows or other values used during the simulation flow in each cell at the same moment.

10This summary enables us to see that RuiCells is based on a generalised CA model, in which cells have different facets and in which flow pathways represent real effects of the morphological structure and not only its topology (fig. 2B3). Finally, the structure of the CA used here is different from classical CA models. Indeed, we respect several guidelines (a spatial lattice, a small number of states, one iterative process) but we also adapt it to answer to one hydrological problem (hence, important changes appear for transition or neighbouring rules). So it can be considered as a Geographical Cellular Automata (GCA; Ménard and Marceau, 2006).

Fig. 2 – Structure and originality of the cellular routing scheme of Ruicells.
Fig. 2 – Structure et spécificités des règles de fonctionnement de Ruicells.

Fig. 2 – Structure and originality of the cellular routing scheme of Ruicells. Fig. 2 – Structure et spécificités des règles de fonctionnement de Ruicells.

A: The framework necessary to create the cellular mesh using a Digital Elevation Map. B: Presentation of the cellular unit. 1: triangulation and exposition of cells; 2: slopes accorded on each surface; 3: distinction between the deterministic hydrological rules; 4: theoretical flowing links and equal level lines observed on the cellular unit.
A : Les étapes nécessaires pour passer d’un modèle numérique de terrain à l’unité cellulaire sur laquelle repose le maillage utilisé ensuite dans les simulations. B : Présentation du maillage utilisé. 1 : triangulation et exposition des surfaces des cellules ; 2 : pentes associées à chaque cellule ; 3 : les trois types d’écoulement dissociés ; 4 : ligne d’écoulement théorique et courbes de niveau qui peuvent être affichées sur le maillage cellulaire par le logiciel RuiCells.

The cellular routing scheme

11At the beginning of the simulations, the cells are initialised with their own surface and the automaton handles the advection operator moving each surface between each cell simultaneously. We conserve the main property defined as locality in classical CA (Fonstad, 2006): the transition rules operate on cells directly based on local neighbourhood. But in this case, we do not use the Moore (4) or Von Neumann (8) neighbourhood (for example) because the surface flow follows the downstream direction as defined previously. Here, the Cellular Routing Scheme (CRS) depends both on the surface flow from each cell and on the updating of the values of all the sub-states. Surface flow is routed downstream via each row of cells until the downstream boundary is reached. The main difficulty rises when two neighbouring cells exist. Several studies have shown that a flow partitioning into multiple directions is better (Depraetere and Moniod, 1991; Palacio-Vélez et al., 1998; Thomas and Nicholas, 2002) and the flow dispersion is classically deduced by dividing the flow between a maximum of two neighbouring downstream grid cells (Tarboton et al., 1991). However, here, the routing scheme is proportionally partitioned according to the slope angle and such a procedure improves the diffusion of surfaces on each cell (fig. 3). The triangular mesh also gives satisfactory results, particularly in floodplains and thalwegs.

Fig. 3 – Distribution of the surface flows in case of a flat terrain.
Fig. 3 – Répartition des écoulements arrivant sur un terrain plan.

Fig. 3 – Distribution of the surface flows in case of a flat terrain. Fig. 3 – Répartition des écoulements arrivant sur un terrain plan.

1: slope direction; 2: part (in %) of the decanted surface flow; 3: links in surface on each cell; 4: elevation of nodes (in m); 5: thalweg; 6: triangular cell; 7: planar cell existing in a flat terrain or within a floodplain.
1 : direction de la pente ; 2 : part (en %) de l’écoulement transvasé ; 3 : liens en surface entre chaque cellule ; 4 : altitude des nœuds (en m) ; 5 : talweg ; 6 : cellule triangulaire ; 7 : cellule plane existant sur un terrain plan ou dans un fond de vallée.

Simulation outputs

12Graphs obtained at the end of the simulation process (fig. 4C) show the sum of surfaces at interaction and not only the number of cells as a function of distance n from the outlet. Steps are not time but rather length-steps because the surface flow diffusion depends on the spatial lattice size. These surface flow graphs give a picture of the theoretical spatial behaviour of a given basin in two dimensions and improve previous methods. The width-function defined by R.L. Shreve (1966) informed on the number of links in the network at a flow distance x to the outlet but the graphs obtained with RuiCells are not only based on the distance along permanent networks (fig. 4A). The Link Frequency Distribution or the area-distance-function (fig. 4B) proposed by M.J. Kirkby (1976) also gave different results because the distribution of pixels covering the drainage area was always used (Rodriguez-Iturbe and Rinaldo, 1997) while the surface flowing in RuiCells follows three deterministic rules (differences between surface, linear or node transition) and is based on a triangular lattice. For the same reasons, this CA modelling approach offers more realistic results than those obtained with the area-distance-function and differs from those using a surface flow travel time probability distribution through networks (Cudennec et al., 2002; Lopez et al., 2005) as time is not integrated during the CA iterative process.

Fig. 4 – Three different methods to measure the spatial behaviour of a basin.
Fig. 4 – Trois méthodes différentes pour mesurer le comportement spatial d’un bassin-versant.

Fig. 4 – Three different methods to measure the spatial behaviour of a basin. Fig. 4 – Trois méthodes différentes pour mesurer le comportement spatial d’un bassin-versant.

A: “Witdth-function” of R.L. Shreve (1966), taking into account the number of links from the outlet. 1: link; 2: networks. B: “Area-distance-function” using the pixels distribution covering the drainage basin. 1: studied area is equal to the area represented in the graph. C: surface-flow graph proposed with the CA RuiCells, taking into account surfaces, their links with network and hydrological rules as defined in fig. 2.
A : « Fonction-largeur » de R.L. Shreve (1966) tenant compte du nombre de liens dans le réseau depuis l’exutoire. 1 : liens ; 2 : réseaux. B : « Fonction-aire-distance » basée sur la distribution des pixels au sein de la surface drainée. 1 : la surface du bassin sur la carte est la même que celle traduite sur le graphique. C : Graphique des écoulements de surface proposé à partir de l’automate cellulaire RuiCells utilisant les surfaces, leurs liens avec les réseaux et les trois règles hydrologiques présentées sur la fig. 2.

A specific index to measure the links between surfaces and networks

13To quantify the surface flow concentrations at local scales, we propose to divide the highest peak of surfaces (Smax) observed on the surface flow graphs by the square root of the basin area (A’) located upstream (fig. 5). Smax is equal to the highest line of cells located at a distance n from the outlet and is measured at a given iteration (ItMax). In previous works (Delahaye et al., 2001; Douvinet et al., 2008), we call it Qmax but this value does not have any link with discharge, so we prefer recall it. However, we divide Smax by the square root of upstream in following the well-shown relation between discharges and square root of basin areas (Llamas, 1993). We multiply the ratio by 100 to render the analysis easier: the value obtained for Smax is equal to a percentage of the average diameter of the studied basin (fig. 5). This index of concentration (IC) enables us to survey the increase of basin width with the cumulative distance of surfaces from the outlet and it offers a new metric to encapsulate the intensity of surface flows. In a previous research (Douvinet et al., 2008), we called this index IE (for Index of Efficiency) but confusions were observed during discussions with local actors. Indeed, high values for IE correspond to areas where the risk managers observed weak hydraulic efficiency of networks (it gives the same result in reality but the sense of this index requires further clarification). To avoid such type of mistakes, we prefer to recall it as IC. Values automatically calculated during the simulation process are available in each cell and have same significance regardless of the basin area if the numerical model never changes. The results should be interpreted differently if the resolution evolves. Even if indexes do not present a scalar dependence, a numerical model with higher resolution naturally gives lower values for the peak of surfaces (Smax) and consequently for the IC. In this study we always use a DEM of 50-m long. When ICs are equal to 50, it indicates a medium surface flow concentration; i.e., the peak of surfaces (Smax) corresponds to the half of the average diameter. When ICs exceed 55 (this arbitrary threshold was validated during our first field investigations), networks and surfaces appear really well-structured. Points or linear with IC up to 55 are potential points of important concentration of surface flows on a short distance. Next, we investigate whether these simulations capture what is occurring in reality and whether they are linked to instances of damage after previous flash-flood events on the five studied basins.

Fig. 5 – Interpretation of the IC.
Fig. 5 – Interprétation de l’IC.

Fig. 5 – Interpretation of the IC. Fig. 5 – Interprétation de l’IC.

A: Presentation of the values required to calculate the IC. 1: division of the studied area in a triangular spatial grid; 2: point of measurement; 3: line of maximum cells located at the same distance from the outlet; 4: Smax equals to this maximum peak of surfaces; 5: A’ equals to the surface area upstream of the point of measurement. B: IC formula with values used in this example; C: Graphic explanation of the result. 1: theoretical network from Smax to the outlet; 2: square form representing the same surface than those for the real basin in the point 5A; 3: Dmoy equals to the average diameter.
A : Présentation des valeurs nécessaires pour calculer l’IC. 1 : traduction de la surface étudiée en un maillage triangulaire ; 2 : point de mesure ; 3 : bande de cellules situées à égale distance de l’exutoire ; 4 : Smax désigne le pic de surface ; 5 : A’ désigne la surface située en amont du point de mesure. B : La formule de l’IC reprenant les valeurs de l’exemple présenté ici. C : Explication graphique du résultat. 1 : réseau théorique reliant les cellules de Smax à l’exutoire ; 2 : forme carrée qui a une surface équivalente à celle du bassin étudié dans la fig. 5A ; Dmoy désigne le diamètre moyen du bassin étudié.

Simulation results

14The presentation of results first focuses on the spatial behaviours observed at the global scale (studying results obtained at the final outlets), and second by analysing the contributions of sub-basins. The IC is thus measured and discussed in the studied basins regarding field experiments and local knowledge in order to validate or not simulations. Authors assume to not discuss their results with elementary metrics of basin morphometry as in previous reviews (Douvinet, 2008; Douvinet et al., 2008), they have shown that such indexes do not permit to translate dynamics of morphological systems and cannot be linked to hydrological functionality.

Various morphological signatures detected at global scales

15Several indexes based on the surface-flow graphs obtained at the final outlets (i.e., points “1”) are used to explore the global spatial behaviour of the studied basins (tab. 2). It is important to remind here that the simulations account surfaces as input data. Maximum peaks of surfaces (Smax) and the number of iteration necessary to raise this peak (ItMax) generally increase as the drainage area increases. The smallest basin (Aizelles) has the lowest peak formed by the sum of surfaces (10.58 ha) located at a distance of 53 cells from the outlet (fig. 6) while the peak of 27.68 ha, achieved at the 163th iteration, is the largest for the Aunette basin. Other values are 17.07 ha. at a distance of 129 cells for the Saint-Martin basin, 20.75 ha. in 70 cells in the L’Eaunette basin, and 24.14 ha achieved in 189 cells for the Warnette basin (tab. 2). This relation between Smax vs. basin size was clearly demonstrated in a previous study (Douvinet, 2008) on 189 studied areas (fig. 1). The correlation coefficient equals to 0.83 (fig. 6). Such a result suggests a scaling effect due to the internal morphological organisation. The relation given by the equation A = = αSmaxβ indicates that parameters α and β are respectively equal to 5.65 and 0.45. These results support the findings on log-log linearity yet proven by J.Y. Hack (1957) and confirmed by V.K. Gupta et al. (1996). We obtain here similar exponent coefficients using a CA approach. However the scaling effect does not exist for the lengths-to-peak (ItMax) vs. the basin size (fig. 6). This value informs on distances required to reach the peak of surfaces but does not ever increase proportionally as the area becomes larger. The elongated form of Saint-Martin basin strongly enlarges its spatial behaviour (fig. 7) and lengthens the distance for rising Smax from 24 (point 4) to 126 iterations at the point 1. In comparison, in L’Eaunette basin (of similar size), ItMax is achieved at the 70th iteration at the final outlet. So, the more the surfaces and the networks within a basin are well organised, the higher is the peak of surfaces. This result confirms the key role of the spatial organisation within a basin. Next, as the surface flow graphs were only studied at the final outlets, we focus on the evolution of the spatial behaviour through scales (since the drainage limit) and on interactions between contributions of sub-basins and their spatial distance from the outlet.

Fig. 6 – Relations between the maximum peak of surfaces, time-duration of the simulations, the mean surface flows, the distance to raise the peak of surface flows, and the basin size.
Fig. 6 – Relations entre le pic maximum de surfaces, la durée des simulations, les apports moyens en surface, la distance pour atteindre le pic de surface depuis l’exutoire et la taille des bassins versants.

Fig. 6 – Relations between the maximum peak of surfaces, time-duration of the simulations, the mean surface flows, the distance to raise the peak of surface flows, and the basin size. Fig. 6 – Relations entre le pic maximum de surfaces, la durée des simulations, les apports moyens en surface, la distance pour atteindre le pic de surface depuis l’exutoire et la taille des bassins versants.

1: Aizelles basin; 2: Saint-Martin de Boscherville basin; 3. L’Eaunette basin; 4. Warnette basin; 5. Aunette basin (all the points results from the simulations obtained on the 187 basins presented in fig. 1; for more details, see Douvinet, 2008).
1 : bassin de l’Aizelles ; 2 : bassin de Saint-Martin de Boscherville ; 3 : Bassin de L’Eaunette ; 4 : bassin de Warnette ; 5 : bassin de l’Aunette (tous les autres points montrent les résultats obtenus sur les 187 bassins présentés sur la fig. 1 ; pour plus de détails, voir Douvinet, 2008).

Fig. 7 – Morphological features in the five studied basins.
Fig. 7 – Comportements morphologiques des 5 bassins étudiés.

Fig. 7 – Morphological features in the five studied basins. Fig. 7 – Comportements morphologiques des 5 bassins étudiés.

A: Maps of surface flow crossed in each cell, with the percentage of global basin area in upstream parts. 1: points of measurement (in relation with tab. 2 and tab. 3); 2: altitudes numbers (in m); 3: confluences where the final Smax measured at the global scale is yet obtained in the basin; 4: drainage basin limits; 5; limits of sub-basin; 6: urbanised areas. B: Surface flow graphs for each basin to facilitate the comparison.
A : Carte des écoulements de surface passés dans chaque cellule, avec le pourcentage de surface par rapport à la surface totale du bassin. 1 : points de mesure (associés aux tab. 2 et tab. 3) ; 2 : points côtés (en m) ; 3 : confluences où la valeur Smax mesurée à l’échelle globale est déjà atteinte à l’échelle intra-bassin ; 4 : limite du bassin-versant ; 5 : limites de quelques sous-bassins ; 6 : surfaces urbanisées. B : Graphiques des écoulements de surface pour chaque bassin avec une échelle commune pour faciliter l’analyse comparative.

Tab. 2 – Simulation results obtained at the final outlet (point 1) on the five basins.
Tab. 2 – Résultats des simulations réalisées aux exutoires (points 1) des cinq bassins étudiés.

Name of the five studied basins

Aizelles

L’Eaunette

Saint-Martin

Warnette

Aunette

Points of measurement

1

1

1

1

1

Basin size (in km²)

4.6

14.3

14.3

25.7

30.1

Time required for the simulation (iterations)

84

143

179

256

246

Smoy = average surface flow per iteration

Smax = maximum peak of surfaces (in ha)

5.22

10.58

10.00

20.75

8.25

17.07

10.03

24.14

12.21

27.68

Iteration of Smax (ItMax)

53

70

129

186

163

Index of concentration (IC)

49.32

54.87

45.40

47.61

50.45

Importance of internal organisation

16The place and characteristics of the spatial behaviours simulated at the outlet of several sub-basins are compared with the global properties observed before. In the Aizelles basin (fig. 7), the two main sub-basins (upstream part of the point 2) support together the SMax measured at the final outlet (point 1). In the Warnette basin, constant contributions of the three main upstream sub-basins (upstream part of the point 2) explain the final Smax (point 1). Networks and surfaces are well organised and such observation explains why the peak of surfaces (Smax) becomes higher in the southern part of the village of Guigny. In these two basins, Smax measured at the final outlet is achieved within the basin and not at the final outlet. On the other hand, this cascading surface flow system becomes inefficient when the contributions of sub-basins are shifted in space. In the Aunette basin (tab. 3), upstream areas of points 2 and 4 present a efficient organisation but their contribution are not combined at the final outlet, explaining the flat response and the gentle increase of the final peak of surfaces. A similar discrepancy induces on the Saint-Martin basin the global and long out-flow (fig. 7). Downstream contribute to the beginning of the final surface flow graph during the first 63 iterations but upstream sub-basins strongly enhance SMax at the end of the simulation. Obviously, SMax in upstream point 1 is the same that those obtained in upstream point 2 (7.8 km²) and upstream point 3 (tab. 3) explains 68% of the final peak whereas its size only represents 23% of the global basin size (13.4 km²).

17Effects of concentration and their progressive evolution through the scales are well depicted by the simulations. RuiCells allow us to follow the sudden increase or the regular decrease of the maximum peak of surfaces since the drainage limit. In several cases, continuous contributions of sub-basins (Aizelles, Warnette or L’Eaunette) explain why SMax measured at the final outlet does not change. Our approach permits better assessment of the effects of form and structure, but also the influence of local supply in the variability of the morphological responses across scales. If the simulations improve the evolution of the “basin-width” as many authors proposed several decades ago, surface flow graphs obtained with RuiCells better account for the hydrological functionality on a cellular lattice. Results also confirm previous findings on the peak of surface which exhibits an asymptotic scaling feature as areas become larger (Menabde et al., 2001; Mantilla et al., 2006).

Tab. 3 – Results obtained on the other points of measurement within the five studied basins.
Tab. 3 – Résultats obtenus aux autres points de mesure dans les cinq bassins étudiés.

Other points of measurement

Name of the basin

Basin size (in km²)

Time for the simulation (in iterations)

Smax (peak of surfaces)

ItMax (Iteration needed to Smax)

IC (index of concentration)

Point 2

Aizelles

2.9

70

10.17

39

59.72

Point 2

L’Eaunette

2.8

68

8.35

34

50.01

Point 3

L’Eaunette

3.1

90

7.28

66

41.41

Point 2

Saint-Martin

8.9

114

17.07

64

56.31

Point 3

Saint-Martin

3.71

96

10.88

46

56.43

Point 4

Saint-Martin

3.77

85

8.44

24

40

Point 2

Warnette

15.0

140

24.14

69

62.31

Point 3

Warnette

7.2

125

12.11

54

45.17

Point 4

Warnette

4.4

97

10.64

43

50.61

Point 2

Aunette

8.1

144

14.66

58

51.66

Point 3

Aunette

7.1

113

12.12

87

45.35

Point 4

Aunette

4.1

74

12.12

48

59.85

Potential of concentration and emergence of local efficiencies

18The maximum surface flow concentration emerges mapping the IC in the five study basins. The Saint-Martin basin presents high value (IC = 56.3) at point 2 as networks and surfaces are well organised in upstream (fig. 7). Values greatly increase from points 3 to 2 but gradually decrease downstream from point 2: the maximum peak of surfaces never changes while upstream area increases (fig. 8A). In the Aizelles and Warnette basins, the same concentration patterns are observed (high values and compact forms) but IC is not as important as areas present a gentle compactness (tab. 1). In L’Eaunette, the concentration suddenly increases in the main channel due to cumulative and constant contributions of the sub-basins into point 2 (tab. 3). The Aunette basin presents specific internal homothetic behaviour (as it was defined by I. Rodriguez-Iturbe and Rinaldo, 1997) due to several concentrations measured at the outlet of four upstream small-basins (fig. 8A). Values decrease between confluences but the surface flow concentration increases again at local points (2, 3) and at the final outlet. In these basins, we observe that the IC index remains high when the peak of surfaces and the average diameter of a basin proportionally increase. Concentric organisation of surfaces within compact forms, regular contributions of sub-basins and self-organised networks explain such high values. On the other hand, elongated shapes, contributions of sub-basins shifted in space and non-hierarchical networks flatten this IC. This result explains why indexes are unrelated to the basin scale and it joins results obtained by R. Mantilla et al. (2006) who has shown that the drainage area is convenient for investigating the spatial behaviour of a given basin in self-similar basins but not in non-self similar areas.

19To better understand the origin of high IC values, the line of cells explaining the maximum peak of surfaces has been mapped fig. 7). Distances between final outlets, networks and this line of cells and the role played by the basin form are well highlighted. High values result from different internal organisations: IC ranging from 63 to 65 is obtained at the outlet of numerous sub-basins presenting various downstream networks. The maximum size with IC exceeding 55 never exceeds 10 km². High concentration tends to disappear when the basin size increases as upstream areas increase more quickly than the peak of surfaces. These results are now qualitatively aligned with observed and known instances of damage caused by flash floods.

Fig. 8 – Maps of IC and links with instances of damage.
Fig. 8 – Comparaison entre les cartes des IC et la localisation des dommages.

Fig. 8 – Maps of IC and links with instances of damage. Fig. 8 – Comparaison entre les cartes des IC et la localisation des dommages.

A: Potential of concentration in each basin. 1: points of measurement; 2; high IC values; 3; maximum IC value per basin; 4: maximum water levels observed after flash-floods events; 5: drainage-basin limits; 6: water-flooding problems. B: Instances of damage realised just after flash-flood events. 1: equal level lines (10 m); 2: main equal level lines (50 m); 3: altitude of several level lines (in m); 4: altitude numbers (in m); 5: outlet; 6: high-water levels in flooded areas; 7: inundation width in the floodplain; 8: drainage-basin limits; 9: material damage in houses; 10: human losses; 11: major erosion on roads; 12: cars carried out; 13: water-levels estimated by tachometer; 14: flowing problems in pipelines; 15: flooded surface; 16: urbanised areas; 17: forests (similar in fig. 1).
A : Potentiel de concentration des écoulements de surface. 1 : points de mesure ; 2 : valeurs élevées de l’IC ; 3 : valeur maximale de l’IC pour chaque bassin ; 4 : hauteur d’eau mesurée après une crue ; 5 : limite du bassin-versant ; 6 : problèmes d’écoulement. B : Carte des dommages réalisée à échelle fine après les crues rapides observées. 1 : courbes de niveau (équidistance : 10 m) ; 2 : principales courbes de niveau (équidistance : 50 m) ; 3 : altitude des courbes de niveau ; 4 : points côtés (en m) ; 5 : exutoire du bassin ; 6 : hauteur d’eau maximale atteinte ; 7 : largeur des zones inondées ; 8 : limite du bassin-versant ; 9 : dommages matériels recensés dans les maisons ; 10 : pertes en vie humaine ; 11 : incision remarquable sur les routes ; 12 : voitures emportées ; 13 : niveaux d’eau estimés à l’aide d’un tachéomètre ; 14 : problèmes d’évacuation recensés dans les canalisations ; 15 : zones inondées ; 16 : zones urbanisées ; 17 : zones boisées (identique sur la fig. 1).

Links between high concentrations and real damage

20Field observations were conducted in the five basins just a few days after flash flood events (fig. 8B). In the Saint-Martin basin, high IC values matched exactly sections where most of the damages were registered after the event of June 16th, 1997. The section with IC > 50 between points 3 to 2 (going upstream to downstream) presented erosion forms in the road along a distance of 500 m with an average depth ranging from 1 m to 2 m. Several cars were dragged resulting in the death of 3 people. In this section high concentrations induced high level of risk for urbanised areas: the sudden rising peak occurred in less than 15 min (fig. 8) taking people outside by surprise. Sediments, stones and round ballers were also transported up to the outlet (point 1) located 2.1 km full downstream (fig. 8B). Extensive financial costs (3 M€) and losses in human life were finally directly linked in this section to high surface flow concentration which were aggravated by farming upstream areas (Douvinet, 2008). Other damage was located at the final outlet, where urbanisation faced to flood. In the L’Eaunette basin, inundated areas and damage were also correlated to simulation results (fig. 8B). Inhabitants, field measurements and videos confirm that the water levels reached 1 m to 2.3 m in the Villers-Plouich centre where gravels, sediments (clay and limestones) and straw deposits in several houses exceed 50 cm in thickness. Collective water networks were quickly saturated in the western part of Gouzeaucourt (fig. 8B) but the sudden peak wave appeared clearly along the D917 road, arriving from the Bois Gaucher sub-basin just after the confluence identified as the first upstream point with IC > 55. The water-treatment plant located near the D917 road was also affected, resulting in water pollution. Forests downstream reduced the effects of flow accumulation, thus flooding decreased where the river joined the town of Marcoing (located 3.1 km in the north). The other points with high IC values in the Aizelles and Aunette basins sustained less damage. In rare cases as in the L’Eaunette basin (fig. 8B), high IC values exist in grasslands or in uninhabited areas. As nobody lives near these sites, correlation between simulation results and material losses is difficult to evaluate. However, in any case, hydrological problems have been observed due to surface flow concentration, particularly along roads which enhance flow velocity. In summary, mapping the IC values appears to be a good indicator of what is taking place on the ground, and intersecting numerical simulations, morphological process and damage due to flash flooding offers promising prospects, as we will discuss next.

Discussion

Mapping dynamics and potentials of the spatial behaviour

21Numerous reviews have focused on the impacts of morphological features on hydrological responses over the past forty years (e.g., Rodriguez-Iturbe and Valdès, 1979; Abrahams, 1984; Zavoianu, 1985; Beven et al., 1988; Font, 2002; Luo and Harlin, 2003; Delcaillau, 2004). But assessing dynamics and potentials of spatial behaviours remains challenge. Traditionally, “width-function” or “distance-area function” provided methods to characterise the catchment response as a function of its geomorphologic properties (Rodriguez-Iturbe and Rinaldo, 1997). But these methods present important drawbacks (Douvinet et al., 2008): they describe morphological features in a planar dimension (Tricart, 1991; Lambert, 1996) or do not consider the dynamical impacts of topography on surface flow concentration (Delahaye et al., 2001). Some reviews indicated other limitations such as scale dependency (Bardossy and Schmidt, 2002) or fractal properties which can falsify the results of compactness or circulatory indexes (Bendjoudi and Hubert, 2002). Here, with a CA approach, we propose a new metric to account for the interactions between networks, forms and surfaces. Hortonian systems present a regular increase of the spatial behaviour and of the surface flow concentration due to regular contributions from tributaries. It clearly conveys internal homothetic behaviours when several high surface concentrations are observed at several outlets. In addition, simulations show original patterns such as a decrease of surface concentration due to non-hierarchical organisation of networks, or various internal efficiencies. The IC permits to calculate and quantify this concentration in all parts of a given basin. In summary, this study confirms that more than the basin size, the morphological structure and the spatial organisation of networks determine the distribution of surface flow concentration and the potential accuracy of runoff processes.

Interactions between land use and upstream points with high IC

22The majority of flash floods occurring in ‘dry valleys’ belonging to the Parisian Basin (northern France) have classically been related to land use, agricultural practices and/or soil erosion. These relationships are obvious as soils provide materials which explain the turbidity of stream flows (Delahaye, 2002). Such floods have been linked to extensive soil erosion appearance (Auzet et al., 1995; Le Bissonnais et al., 2002; Poesen et al., 2003), but fewer researches have focused on the effects of morphology on surface-flow dynamics in the context of gentle slopes and of oceanic climate without extreme rains. Nevertheless, recent works (Delahaye, 2002; Douvinet et al., 2008) as well as this study demonstrate the importance of topography which controls the surface-flow concentrations and potential damage. Cultivated areas in upstream points of high IC values play also a key role on dynamics of flash floods that were studied. In the Saint-Martin basin (fig. 8A), cultivated areas and urbanisation aggravate the effects of the surface-flow concentration because they represent 74% upstream point 3 and only 19% at the global scale (point 1). In the Aunette and Warnette basins, runoff surfaces represent respectively 64% and 74% upstream point 3 (fig. 8A). In the L’Eaunette basin, cultivated areas are more important: 84% upstream point 2 but only 54% upstream point 1. But percentage of cultivated areas measured at the global scale present weak values (e.g., less than 30% for the Saint-Martin basin). So the “basin scale” usually used in hydrology is not relevant in these cases. Therefore, as in other basins, this surface-flow concentration can be reduced by the presence of forests or grasslands and can explain why instance of damage is not observed (fig. 1C). Hence, the dominant runoff processes are influenced by first of all local topography, followed by land-use cover, crust of loamy soils and the intensities of rains at local scales. This observation joins previous studies (Poesen et al., 2003; Kirkby et al., 2005).

Surface-flow concentration and flash-flood prevention

23Flash-flood prevention in these areas becomes urgent because they induce rare but violent and sudden impacts on the population located at sensitive outlets. None of the runoff and erosion models developed earlier such as STREAM, LISEM or WATEM (De Vente and Poesen, 2005) permits the prevention of damage due to such flash floods. So we propose to use numerical simulations based on morphological dynamics to improve actual risk prevention without taking into account rainfall frequency. This approach consists of combining surface-flow concentrations with the location of houses or roads. This comparison is thus discussed with local actors to verify whether these morphological potentials have resulted in previous problems. Simulations obtained in basins of different sizes with high points of surface flow concentration have been carried out (tab. 4). This table confirms the importance of damage in the case of high IC values. Sometimes, the roads were just incised (e.g., Pourville and Surdon basins); in other cases, water level achieved 1.5 m (Val-de-Saâne basin) up to 2 m (Jaulgonne) or violent onset occurred (Les Ouis and Varnette basins). Differences in instances of damage can be explained by differences in human settlement, their perception on risk, and by rainfall intensity. These preliminary investigations give promising results. We hope that this kind of work will serve not only to help farmers reducing soil losses, but also to help risk managers to define places or roads where potential high-level damage can be expected. There is a need to protect people if time to react does not exceed a few minutes, as was the case in the Saint-Martin basin.

Tab. 4 – Investigations on other 25 basins also affected by previous flash floods in northern France.
Tab. 4 – Résultats pour 25 autres bassins touchés par des crues rapides dans le Nord de la France.

Name of other studied basins

Points of measurement

Basin size (in km²)

Time for the simulations

Smax (in ha)

ItMax (in iterations)

Values for IC

Correlation between IC and types of damage

Pourville

1

1.37

53

6.68

29

56.91

Incision on roads

Algot

2

1.93

58

8.61

25

61.89

Lack of knowledge

Fond des Mares

1

2.51

76

8.98

28

56.98

Runoff on cultures

Ru d’Orval

3

2.60

69

9.83

31

60.89

Lack of damage

Vallon Quérelle

4

2.93

53

10.94

27

63.82

Inundated roads

Surdon

2

3.08

66

10.61

42

60.42

Incision on roads

Rue des Vaux

1

3.51

92

10.90

51

58.14

Inundated roads

Haramont

1

3.96

74

14.09

32

70.75

Incision and flooded roads

Bellefontaine

1

5.80

90

15.81

42

65.61

Lack of knowledge

Jaulgonne

3

5.85

110

13.92

62

57.50

Water level up to 2 m

Ru de Milleville

2

6.16

107

13.84

36

55.73

Turbid deposits

Val-de-Saâne

1

8.07

122

16.14

73

56.81

Water level up to 1.5 m

Les Ouis

1

8.29

123

16.36

57

56.80

Violent sudden onset

Sélens

1

8.45

120

16.71

64

57.47

Water level up to 1 m

Ru du Moulin

5

8.47

120

17.84

58

61.29

Inundated roads

Maresquel

1

9.13

111

19.00

68

62.87

Incision and flooded roads

Lézarde

3

9.45

116

16.68

78

54.25

Water level up to 1 m

Gergonne Macla

3

9.49

138

19.44

69

63.08

Incision and flooded roads

Auchy-les-Hesdin

1

9.68

154

18.44

61

59.24

Incision and flooded roads

Domptin

1

13.41

134

20.35

67

55.56

Turbid deposits

Essômes

1

21.32

185

25.75

94

55.76

Incision and flooded roads

Nesles-Pierrecourt

1

27.42

222

31.93

143

60.97

Water level up to 1 m

Varnette

1

28.70

236

29.48

110

55.02

Violent sudden onset

Kilienne

1

43.72

250

34.51

120

52.18

Incision and flooded roads

Ordrimouille

1

59.37

321

43.13

184

55.97

Violent sudden onset up to 3 m

Conclusions

24The understanding of flash floods in small ‘dry valleys’ in northern France is hampered by a lack of hydrological and geomorphological data. The rareness and violence of such events do not render the measurement of the role played by the topography easy. In this study, we propose to use numerical simulations based on the cellular automaton RuiCells as a new metric of measuring dynamics of spatial behaviours across scales. The IC also allows both measurement and quantification of the dynamic effects of morphological components from local (cellular) to global (outlet) scales on surface-flow concentrations. The morphological system, defined by the relationship between the basin form, network, surface and its distance to the outlet, appears of prime importance compared to basin size. This information has been suggested theoretically for a long time but this cellular application helps to better assess such systems. Some basins such as L’Aunette basin present internal homothetic behaviour but others present local concentration which remains hidden if we stay at the global scale (Saint-Martin). Using the IC, we can detect where the surface flow concentrations can suddenly appear and induce damage on houses and/or roads. Validation with real losses, local knowledge and field measurements in these five study basins gives satisfying results even if damage in some places remain unknown due to the lack of people to confirm such observations. In addition, the strong interaction between land-use cover and topography requires important attention at local scale: high percentage of cultivated areas upstream points of concentrations in the Saint-Martin and L’Eaunette basins explain violent onsets despite these areas representing a small part at the global scale. Work is in progress to identify other basins in which cultivated areas are dominant upstream concentration. This work is being carried out in 60 basins in the Nord-Pas-de-Calais and 180 basins in Seine-Maritime. Our hope is to be able to help risk managers to locate areas with high exposure to flash floods in order for them to plan structural measures to reduce such sensibility to violent hazards.

The authors would like to thank CNRS and the French Research Ministry for financial funding to the project SYMBAD (2004-2007) “Complex system in human and social sciences”, permitting improvement of the CA Ruicells. Moreover, thanks are due to the different persons helping in field experimentations and information on the five studied flash-flood events: Antoine Guilleux, Matthieu Bernard, Gregory Douvinet, Florian Michel. Sincere thanks to Aurélie Dubray, Jérome Guillaume, Matthieu Flourez (DREAL Nord-Pas-de-Calais) and to Emma Desette and Eric Masson (University of Lille 1) who improved preliminary observations and accepted to discuss simulation results. The authors are also grateful to Aurélie Escudier, Bruno Janet et André Bachoc (SCHAPI) for financial grants in order to test numerical investigations in other small basins. A sincere thank is dedicated for the corrections in English on this paper to Marco Van de Wiel, Marjorie Ambrosio, Julie Josas, Louise Purdue and Jagannath Ayral, and for the three reviewers who strongly improve this paper.

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Annexe

Version abrégée en français

Les crues rapides représentent une réelle menace sur la vie des personnes et sur leurs biens tant elles se manifestent avec sévérité et rapidité. Ces phénomènes apparaissent suite à des pluies de forte intensité et s’accompagnent souvent d’une « vague de boue » (ou mur d’eau) qui déferlent en quelques minutes dans les principaux fonds de vallon. Afin de mieux comprendre la dynamique des processus hydrologiques associés à ces inondations, tout en fournissant des éléments pour en prédire la survenue, différentes approches sont souvent proposées. Les retours d’expérience post-événement visent à estimer les débits de pointe à partir des laisses de crue, pour pouvoir ensuite mieux reconstituer la cinétique des écoulements (Gaume et al., 2009), tandis que les observations météorologiques fournissent des informations sur la nature et la localisation des systèmes pluvieux convectifs (Anquetin et al., 2009 ; Neppel et al., 2010). Toutefois, plusieurs inconnues demeurent car : 1) les mesures classiques telles que l’évaluation des débits de pointe restent difficiles à collecter dans des bassins de petite taille ; 2) les rares stations de mesure ne permettent pas d’établir des courbes de tarage pertinentes compte tenu des effets de remous et des changements incessants de vitesse au cours de l’épisode ; 3) comment également justifier ce type d’instrumentation dans des bassins où les crues se produisent une fois tous les 20 ans ? ; 4) la rareté de ces événements rend par ailleurs utopiques les analyses statistiques et la calibration des modèles (Ferraris et al., 2002).

Dans cette étude, nous proposons d’utiliser une approche spatialisée simplifiée en ayant recours à un automate cellulaire (RuiCells) afin 1) de mieux comprendre les effets de concentration des écoulements de surface qui sont influencés de façon préférentielle par la forme du bassin-versant, le système de pente et l’organisation des réseaux de talwegs durant la crue ; 2) d’évaluer le potentiel de concentration de ces écoulements à travers les échelles, depuis les têtes de bassin-versant (échelle locale) jusqu’aux exutoires (échelle globale). RuiCells est un automate cellulaire qui respecte en partie le formalisme traditionnel car il se base sur un maillage régulier et intègre des règles de transition déterministes et non modifiables au cours de la simulation. Cet automate a cependant été modifié pour pouvoir modéliser la structure variable des éléments de terrain et la connectique entre les cellules. Les liens d’écoulement ne sont plus guidés uniformément par la topologie de voisinage du réseau cellulaire mais par les liens structurant la surface. La démarche s’appuie finalement sur un automate cellulaire dont les cellules sont de forme et de dimension variables (point, ligne, surface) et dont les liens traduisent directement la structure morphologique de la surface (Delahaye et al., 2001 ; Langlois et Delahaye, 2002). La principale difficulté est de relier les variables topographiques (l’altitude et ses dérivées) aux variables hydrauliques telles que la direction et le sens des écoulements sur le maillage triangulaire.

L’automate cellulaire RuiCells a été utilisé dans le cadre de cette étude pour mieux associer les règles hydrologiques locales à l’émergence des réponses observées à l’échelle globale (exutoire). L’un des objectifs est d’identifier les sous-bassins ayant une efficacité morphologique marquée (avec une rapide concentration des écoulements de surface) mais dont les effets peuvent devenir masqués si on reste justement à l’échelle globale du bassin. Pour cela, a été créé un indice de concentration IC, qui s’appelait dans nos publications précédentes l’indice IE mais qui a été clarifié pour éviter de confondre l’efficacité morphologique avec l’efficacité hydraulique. Cet indicateur fait appel à deux valeurs : le pic de surface (Smax) et la racine carrée de la surface amont (A’). La valeur Smax correspond à la surface maximum arrivant à une certaine itération (ItMax) au point de mesure, ou autrement dit à la plus grande bande de cellules situées à même distance de ce point de mesure. Cette valeur Smax est récupérée sur toutes les cellules à partir des graphiques des écoulements de surface qui traduisent le comportement spatial d’un bassin. Cette réponse théorique avait déjà fait l’objet de plusieurs travaux. Cependant, la fonction de distribution des drains (Kirkby, 1976), la « fonction-largeur » de Shreve (1966) ou la « fonction aire-distance » (Rodriguez-Iturbe et Rinaldo, 1997) ont été améliorées ici grâce aux trois règles d’écoulements dissociés et à l’utilisation d’un maillage triangulaire régulier qui limite les effets de bordure, contrairement à un maillage carré (Mita et al., 2001). Ensuite, la valeur Smax est rapportée à la racine carrée de la surface amont en s’appuyant sur des lois hydrologiques bien établies, à savoir que le débit d’un bassin augmente proportionnellement à la racine carrée de la surface (Llamas, 1993). Pour finir, nous avons multiplié cette valeur par 100 ; cela permet de comparer la valeur Smax obtenue avec le diamètre moyen du bassin étudié. Cet indice de concentration IC est calculé en tout point du bassin (sur toutes les cellules) et son évolution est suivie depuis les zones sources jusqu’à l’exutoire final. Ce calcul dépend fortement de la résolution du modèle numérique de terrain (MNT) choisi initialement. Plus le MNT aura une résolution fine, plus les valeurs obtenues seront faibles car la valeur Smax se retrouve fortement diminuée. Dans le cadre de ce travail, un MNT au pas de 50 m a toujours été utilisé. Lorsque l’indice IC a une valeur de 50, cela indique que Smax équivaut à la moitié du diamètre moyen d’un bassin. Après plusieurs expérimentations, les valeurs IC supérieures à 55 semblent indiquer une concentration élevée des écoulements de surface, avec des réseaux de talwegs bien structurés au sein d’une forme donnée. Toutes les confluences identifiées avec une valeur IC équivalents à 55 deviennent alors des points névralgiques où les flux peuvent se concentrer de manière rapide et violente.

Les résultats obtenus avec l’indice IC sont présentés et discutés sur cinq vallons secs, sur lesquels des cartes de dommages ont été réalisées post-événement à échelle fine et où les connaissances locales doivent permettre de valider ou non les simulations numériques. Dans le bassin de Saint-Martin (fig. 8B), les valeurs IC > 55 identifient exactement la zone la plus sinistrée lors de la crue du 16 juin 1997 (qui avait donné lieu à des incisions majeures, sur plus de 2 m de profondeur et sur une distance de plus de 500 m). Le risque est élevé dans cette section car le pic de crue est apparu moins de 15 min après le pic des pluies, prenant les personnes mobiles par surprise (c’est d’ailleurs dans cette partie amont du bassin que 3 personnes ont trouvé la mort). Dans le bassin de l’Eaunette (fig. 8B), les zones inondées et les dommages sont aussi corrélés aux simulations. Les habitants, les mesures de terrain (à partir des laisses de crue et des dépôts de limons et d’argiles) et les vidéos confirment que les niveaux d’eau ont soudainement atteint entre 1,5 m et 2,3 m de haut à partir du village de Villers-Plouich, situé au sein du bassin, et que la vague de boue est survenue le long de la route D917 (juste après la confluence identifiée par les cartes de l’indice IC ayant une valeur supérieure à 55). Les réseaux collectifs d’assainissement ont aussi été saturés dans la partie ouest de Gouzeaucourt (fig. 8B). Dans la partie aval, les zones boisées semblent avoir diminué les impacts de la concentration des écoulements de surface, les niveaux d’eau ayant fortement diminué à l’exutoire et jusqu’à la ville de Marcoing située à une distance de 3,1 km. Sur les autres bassins, on remarque les mêmes corrélations mais avec des dommages moindres. Dans de rares cas, les valeurs élevées de l’indice IC existent dans des zones pâturées ou inhabitées, ce qui limite toute possibilité de validation (aucune déclaration de dommages = aucune connaissance locale).

Dans tous les exemples étudiés, des problèmes hydrologiques ont toujours été observés. Dès lors, les cartes de l’indice IC pourraient 1) être de bons indicateurs des dommages potentiels liés à la concentration des écoulements de surface, 2) servir de cartographie prédictive dans des bassins où les simulations ont été validées (comme c’est le cas pour les cinq bassins étudiés ici) et 3) être testées sur un plus grand nombre de bassins afin de valider (ou non) cette démarche.

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Table des illustrations

Titre Fig. 1 – Presentation of the five studied basins. Fig. 1 – Présentation des cinq basins étudiés.
Légende A: Location map at the French national scale. B: Regional map of the northern Parisian Basin. 1: main cities; 2: 187 basins where flash floods have been observed during the period 1983-2005 (Douvinet, 2008); 3: the five basins studied in this article; 4: limits of ‘department’; 5: name of ‘department’. C: Average land-use cover. 1: equal level lines (10 m); 2: main equal level lines (50 m); 3: altitude of several level lines (in m); 4: altitude numbers (in m); 5: outlet; 6: permanent stream rivers; 7: drainage basin limit; 8: year of the land-use cover mapping linked to previous flash-flood events; 9: name of the villages and cities within the basin; 10; local name of plates or valleys; 11: Used Cultivated Areas (SAU in French); 12: urbanised areas; 13: forests; 14: permanent grasslands.A : Carte de localisation à l’échelle de la France. B : Carte de localisation à l’échelle du nord du Bassin parisien. 1 : villes principales ; 2 : 187 bassins versants où des crues rapides ont été précédemment observées sur la période 1983-2005 (Douvinet, 2008) ; 3 : les cinq bassins étudiés dans cette étude ; 4 : limites des départements ; 5 : nom des départements. C : Caractéristiques de l’occupation du sol (moyenne). 1 : courbes de niveau (équidistance : 10 m) ; 2 : principales courbes de niveau (équidistance : 50 m) ; 3 : altitude des courbes de niveau ; 4 : points côtés (en m) ; 5 : exutoire ; 6 : écoulement permanent ; 7 : limite des bassins versants ; 8 : année de la cartographie réalisée pour l’occupation du sol en lien avec la date de la crue passée ; 9 : nom des principaux villages/villes au sein du bassin ; 10 : noms des plateaux ou vallées citées dans le texte ; 11 : Surface Agricole Utile (SAU) ; 12 : surfaces urbanisées ; 13 : forêts ; 14 : prairies permanentes.
URL http://geomorphologie.revues.org/docannexe/image/10112/img-1.png
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Titre Fig. 2 – Structure and originality of the cellular routing scheme of Ruicells. Fig. 2 – Structure et spécificités des règles de fonctionnement de Ruicells.
Légende A: The framework necessary to create the cellular mesh using a Digital Elevation Map. B: Presentation of the cellular unit. 1: triangulation and exposition of cells; 2: slopes accorded on each surface; 3: distinction between the deterministic hydrological rules; 4: theoretical flowing links and equal level lines observed on the cellular unit.A : Les étapes nécessaires pour passer d’un modèle numérique de terrain à l’unité cellulaire sur laquelle repose le maillage utilisé ensuite dans les simulations. B : Présentation du maillage utilisé. 1 : triangulation et exposition des surfaces des cellules ; 2 : pentes associées à chaque cellule ; 3 : les trois types d’écoulement dissociés ; 4 : ligne d’écoulement théorique et courbes de niveau qui peuvent être affichées sur le maillage cellulaire par le logiciel RuiCells.
URL http://geomorphologie.revues.org/docannexe/image/10112/img-2.png
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Titre Fig. 3 – Distribution of the surface flows in case of a flat terrain. Fig. 3 – Répartition des écoulements arrivant sur un terrain plan.
Légende 1: slope direction; 2: part (in %) of the decanted surface flow; 3: links in surface on each cell; 4: elevation of nodes (in m); 5: thalweg; 6: triangular cell; 7: planar cell existing in a flat terrain or within a floodplain.1 : direction de la pente ; 2 : part (en %) de l’écoulement transvasé ; 3 : liens en surface entre chaque cellule ; 4 : altitude des nœuds (en m) ; 5 : talweg ; 6 : cellule triangulaire ; 7 : cellule plane existant sur un terrain plan ou dans un fond de vallée.
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Titre Fig. 4 – Three different methods to measure the spatial behaviour of a basin. Fig. 4 – Trois méthodes différentes pour mesurer le comportement spatial d’un bassin-versant.
Légende A: “Witdth-function” of R.L. Shreve (1966), taking into account the number of links from the outlet. 1: link; 2: networks. B: “Area-distance-function” using the pixels distribution covering the drainage basin. 1: studied area is equal to the area represented in the graph. C: surface-flow graph proposed with the CA RuiCells, taking into account surfaces, their links with network and hydrological rules as defined in fig. 2.A : « Fonction-largeur » de R.L. Shreve (1966) tenant compte du nombre de liens dans le réseau depuis l’exutoire. 1 : liens ; 2 : réseaux. B : « Fonction-aire-distance » basée sur la distribution des pixels au sein de la surface drainée. 1 : la surface du bassin sur la carte est la même que celle traduite sur le graphique. C : Graphique des écoulements de surface proposé à partir de l’automate cellulaire RuiCells utilisant les surfaces, leurs liens avec les réseaux et les trois règles hydrologiques présentées sur la fig. 2.
URL http://geomorphologie.revues.org/docannexe/image/10112/img-4.png
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Titre Fig. 5 – Interpretation of the IC. Fig. 5 – Interprétation de l’IC.
Légende A: Presentation of the values required to calculate the IC. 1: division of the studied area in a triangular spatial grid; 2: point of measurement; 3: line of maximum cells located at the same distance from the outlet; 4: Smax equals to this maximum peak of surfaces; 5: A’ equals to the surface area upstream of the point of measurement. B: IC formula with values used in this example; C: Graphic explanation of the result. 1: theoretical network from Smax to the outlet; 2: square form representing the same surface than those for the real basin in the point 5A; 3: Dmoy equals to the average diameter.A : Présentation des valeurs nécessaires pour calculer l’IC. 1 : traduction de la surface étudiée en un maillage triangulaire ; 2 : point de mesure ; 3 : bande de cellules situées à égale distance de l’exutoire ; 4 : Smax désigne le pic de surface ; 5 : A’ désigne la surface située en amont du point de mesure. B : La formule de l’IC reprenant les valeurs de l’exemple présenté ici. C : Explication graphique du résultat. 1 : réseau théorique reliant les cellules de Smax à l’exutoire ; 2 : forme carrée qui a une surface équivalente à celle du bassin étudié dans la fig. 5A ; Dmoy désigne le diamètre moyen du bassin étudié.
URL http://geomorphologie.revues.org/docannexe/image/10112/img-5.png
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Titre Fig. 6 – Relations between the maximum peak of surfaces, time-duration of the simulations, the mean surface flows, the distance to raise the peak of surface flows, and the basin size. Fig. 6 – Relations entre le pic maximum de surfaces, la durée des simulations, les apports moyens en surface, la distance pour atteindre le pic de surface depuis l’exutoire et la taille des bassins versants.
Légende 1: Aizelles basin; 2: Saint-Martin de Boscherville basin; 3. L’Eaunette basin; 4. Warnette basin; 5. Aunette basin (all the points results from the simulations obtained on the 187 basins presented in fig. 1; for more details, see Douvinet, 2008).1 : bassin de l’Aizelles ; 2 : bassin de Saint-Martin de Boscherville ; 3 : Bassin de L’Eaunette ; 4 : bassin de Warnette ; 5 : bassin de l’Aunette (tous les autres points montrent les résultats obtenus sur les 187 bassins présentés sur la fig. 1 ; pour plus de détails, voir Douvinet, 2008).
URL http://geomorphologie.revues.org/docannexe/image/10112/img-6.png
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Titre Fig. 7 – Morphological features in the five studied basins. Fig. 7 – Comportements morphologiques des 5 bassins étudiés.
Légende A: Maps of surface flow crossed in each cell, with the percentage of global basin area in upstream parts. 1: points of measurement (in relation with tab. 2 and tab. 3); 2: altitudes numbers (in m); 3: confluences where the final Smax measured at the global scale is yet obtained in the basin; 4: drainage basin limits; 5; limits of sub-basin; 6: urbanised areas. B: Surface flow graphs for each basin to facilitate the comparison.A : Carte des écoulements de surface passés dans chaque cellule, avec le pourcentage de surface par rapport à la surface totale du bassin. 1 : points de mesure (associés aux tab. 2 et tab. 3) ; 2 : points côtés (en m) ; 3 : confluences où la valeur Smax mesurée à l’échelle globale est déjà atteinte à l’échelle intra-bassin ; 4 : limite du bassin-versant ; 5 : limites de quelques sous-bassins ; 6 : surfaces urbanisées. B : Graphiques des écoulements de surface pour chaque bassin avec une échelle commune pour faciliter l’analyse comparative.
URL http://geomorphologie.revues.org/docannexe/image/10112/img-7.png
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Titre Fig. 8 – Maps of IC and links with instances of damage. Fig. 8 – Comparaison entre les cartes des IC et la localisation des dommages.
Légende A: Potential of concentration in each basin. 1: points of measurement; 2; high IC values; 3; maximum IC value per basin; 4: maximum water levels observed after flash-floods events; 5: drainage-basin limits; 6: water-flooding problems. B: Instances of damage realised just after flash-flood events. 1: equal level lines (10 m); 2: main equal level lines (50 m); 3: altitude of several level lines (in m); 4: altitude numbers (in m); 5: outlet; 6: high-water levels in flooded areas; 7: inundation width in the floodplain; 8: drainage-basin limits; 9: material damage in houses; 10: human losses; 11: major erosion on roads; 12: cars carried out; 13: water-levels estimated by tachometer; 14: flowing problems in pipelines; 15: flooded surface; 16: urbanised areas; 17: forests (similar in fig. 1).A : Potentiel de concentration des écoulements de surface. 1 : points de mesure ; 2 : valeurs élevées de l’IC ; 3 : valeur maximale de l’IC pour chaque bassin ; 4 : hauteur d’eau mesurée après une crue ; 5 : limite du bassin-versant ; 6 : problèmes d’écoulement. B : Carte des dommages réalisée à échelle fine après les crues rapides observées. 1 : courbes de niveau (équidistance : 10 m) ; 2 : principales courbes de niveau (équidistance : 50 m) ; 3 : altitude des courbes de niveau ; 4 : points côtés (en m) ; 5 : exutoire du bassin ; 6 : hauteur d’eau maximale atteinte ; 7 : largeur des zones inondées ; 8 : limite du bassin-versant ; 9 : dommages matériels recensés dans les maisons ; 10 : pertes en vie humaine ; 11 : incision remarquable sur les routes ; 12 : voitures emportées ; 13 : niveaux d’eau estimés à l’aide d’un tachéomètre ; 14 : problèmes d’évacuation recensés dans les canalisations ; 15 : zones inondées ; 16 : zones urbanisées ; 17 : zones boisées (identique sur la fig. 1).
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Johnny Douvinet, Daniel Delahaye et Patrice Langlois, « Measuring surface flow concentrations using a cellular automaton metric: a new way of detecting potential impacts of flash floods in sedimentary context », Géomorphologie : relief, processus, environnement, vol. 19 - n° 1 | 2013, 27-46.

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Johnny Douvinet, Daniel Delahaye et Patrice Langlois, « Measuring surface flow concentrations using a cellular automaton metric: a new way of detecting potential impacts of flash floods in sedimentary context », Géomorphologie : relief, processus, environnement [En ligne], vol. 19 - n° 1 | 2013, mis en ligne le 10 juin 2015, consulté le 23 mars 2017. URL : http://geomorphologie.revues.org/10112 ; DOI : 10.4000/geomorphologie.10112

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Auteurs

Johnny Douvinet

Université d’Avignon et des Pays du Vaucluse, Equipe d’Avignon – UMR ESPACE 7300 CNRS, Avignon – 74 rue Louis Pasteur – 84029 Avignon Cedex 1 – France (johnny.douvinet@univ-avignon.fr).

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Daniel Delahaye

Université de Caen Basse-Normandie - Laboratoire de géographie physique et environnement, GEOPHEN – UMR 6554 LETG CNRS - Esplanade de la Paix -14032 Caen Cedex - France (daniel.delahaye@unicaen.fr).

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Patrice Langlois

Laboratoire MTG, UMR IDEES 6266 CNRS - Université de Rouen - Rue Thomas Becket - 76130 Mont-Saint-Aignan - France (patrice.langlois@univ-rouen.fr).

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