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Joint spatial, topological and scaling analysis framework of river-network geomorphometry

Cadre d’analyse conjointe spatiale, topologique et scalante de la géomorphométrie des réseaux hydrographiques
Jallel Aouissi, Jean-Christophe Pouget, Houda Boudhraâ, Guillaume Storer et Christophe Cudennec
p. 7-16

Résumés

Les réseaux hydrographiques sont les ossatures structurelles et fonctionnelles des bassins versants. Ils présentent fréquemment des propriétés d’échelles à travers leur topologie de hiérarchie. De plus, leur description mathématique alimente une hydrologie à base géomorphologique, à travers des analyses et des modélisations peu exigeantes en calage. Cependant, les bassins versants présentent des structures géomorphométriques très variées, en lien avec le relief, la géologie, le climat et des contraintes anthropiques ainsi qu’une diversité de relations structure-fonction hydrologiques. Une approche robuste, flexible et systématique est par conséquent nécessaire pour faciliter des analyses conjointes spatiales, topologiques et scalantes et, ainsi, explorer la diversité hydro-géomorphologique. L’application logicielle HydroStruct est dédiée à de telles analyses, mais aussi à l’articulation des observations géomorphométriques avec des analyses et des modélisations hydrologiques telles que des approches basées sur des fonctions de transfert à base géomorphologique, la prise en compte de la variabilité de la pluie au sein de la modélisation pluie-débit et l’évaluation de l’impact de changements paysagers et hydrauliques. HydroStruct a été développé au sein du cadre générique OdefiX, qui fournit des composants logiciels en Java, dans l’optique de faciliter le co-développement et l’interfaçage de modèles orientés objet.

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Notes de la rédaction

Article soumis le 9 mars 2011, accepté le 16 novembre 2011.

Texte intégral

Introduction

1The river network is the basic geomorphological structure of a river basin, in both topological and geometric terms (Rodriguez-Iturbe and Rinaldo, 1997). It has furthermore a fundamental hydrological implication, being the pattern governing upstream-downstream transfers from hillslopes through channelised paths towards the outlet (Rinaldo et al., 1991; Woods and Sivapalan, 1999). Moreover, the river network’s branching organisation presents widely observed strong scaling properties. Finally, it determines inter-dependencies between locations in the basin territory, and consequently between associated socio-anthropogenic requirements as regards water resources and hazards. The HydroStruct software application is firstly dedicated to combined spatial, topological and scaling analysis of morphometry of river networks, with major perspectives of easily linking geomorphometric observations with hydrological analysis and modelling approaches. HydroStruct was developed within the generic OdefiX framework, which provides Java software components to allow co-development and interfacing of object-oriented models.

The studied hydro-geomorphometric objects, variables and functions

Hierarchy-based and whole-basin points of view

2In a basin, the river network is made up of particular points: the unique outlet, upstream extremities and junctions, generally binary. The part contained between two such successive particular points is a link. The A.N. Strahler (1952) ordering scheme permits the description of a link position in a river network (fig. 1A). According to this ordering method, the stream is defined as the set of successive links of the same order (fig. 1B). The spectrum of orders represented in the network can be seen as a cascade, in the frame of which evidence of scaling has been identified. Branching laws were then embraced within the application of fractal geometry to river networks, which led to the identification of numerous generic self-affine and self-similar properties (Rodriguez-Iturbe and Rinaldo, 1997; Dodds and Rothman, 1999, 2000). From their synthesis of the topic, I. Rodriguez-Iturbe and A. Rinaldo (1997) reached the conclusion that “the search for invariance properties across scales as a basic hidden order in hydrologic phenomena is one of the main themes of hydrologic science”. Parallel to these hierarchy-based approaches, and with a systemic hydrological point of view, one can focus on a function describing the basin organisation in terms of flow paths through the network down to the outlet. In this context, some functions have been introduced such as the area function and the width function. These are the probability density functions (pdfs) respectively of the basin contributing area and of the number of links in the network, with respect to flow distance to the outlet. Any eventual regular pattern observable for these functions would be a useful network-level geomorphometric gauge, eventually linked with basin-level hydrological processes and features. But one can notice that, even if the width function itself proves to have scaling characteristics (Rodriguez-Iturbe and Rinaldo, 1997), the relationship between the river network self-similarity and the shape – particularly the systematic skewness – of the area and width functions is not fully understood and assessed yet.

Combined approach and presumption of an underlying structural pattern

3Within the path followed by a water drop to reach the outlet, C. Cudennec et al. (2004a) considered separately the hillslope path and the channelised path through the river network. The hydraulic length L of the channelised path was considered. Furthermore, within the channelised path, the ‘ith order component’ was defined as the part run through successive links of the same order i (fig. 1C). By definition, for any geographic point of the basin, the hydraulic length is the sum L = Σi=1,n li where n is the basin Strahler order and li the length of the ith order component. The network scaling may apply to the components: besides Horton’s stream length ratio RL (Horton, 1945; Schumm, 1956) the component length ratio

was defined, where

is the mean length of the ith order components. pdf(L) and pdf(li) are structural functions, at the levels respectively of the whole network and of the Strahler levels. Moreover, in order to study subsets of the whole Strahler cascade, truncated hydraulic lengths L’ = Σi=1,m< n li were also introduced for various values of m, as well as the corresponding functions pdf(L’). Evidence of regularity has been shown first through: (i) the observed stability of scaling ratios (Horton ones – Horton, 1945; Schumm, 1956 – and the newly defined rl) and (ii) the identification of an underlying pattern at infra- and supra-basin levels of network organisation, for actual networks which respect a strong self-similarity (Cudennec et al., 2004a; Cudennec and Fouad 2006). A similar kind of regularity seems to exist for basins with heterogeneous constraints, such as lithologic ones, which all the more stresses the issue of variability in space and through scales (Cudennec et al., 2006). Theoretical rationales have furthermore been developed (Cudennec et al., 2004a, 2005a; Fleurant and Boulestreau, 2005), leading to models of pdf(li), pdf(L) and pdf(L’) which remain to be improved (i) from a wide corpus of observed data, and (ii) from systematic comparison with alternate models of the width and the area functions (Karlinger and Troutman, 1985; Rinaldo et al., 1995; Hung and Wang, 2005; Moussa, 2008).

Scale, space and upstream-downstream hydrological significance

4Geomorphology-based rainfall-runoff transfer functions were proposed, either from hierarchy-based considerations or from whole-basin functions (Rodriguez-Iturbe and Rinaldo, 1997; Cudennec, 2007). The explicit observable geomorphometric foundation of such approaches is of major interest for hydrological modelling in data-scarce contexts where extensive calibration cannot be implemented. Moreover, the conceptualisation of water transfers can be adjusted according to available data and knowledge related to flow (Rinaldo et al., 1991; Snell and Sivapalan, 1994; Woods and Sivapalan, 1999; Cudennec, 2007), allowing proposal of methods for assessing design floods (Duchesne et al., 1997; Veitzer and Gupta, 2001; Nasri et al., 2004; Rodriguez et al., 2005; Fleurant et al., 2006; Rigon et al., 2011) or for transposing discharges between outlets (Boudhraâ et al., 2009). Furthermore, the river network is inscribed in the basin territory, both (i) as the result of spatial processes and constraints, and (ii) as the integrating structure of spatially-distributed hydrological process and impacts of territorial properties. Geomorphology-based rainfall-runoff transfer functions may display a strong spatial correspondence, which may thus allow to account for spatial variability of rainfall input (Giannoni et al., 2003; Cudennec et al., 2005b; Cudennec, 2007; Hung and Wang, 2007; Moussa, 2008), and/or to account for the hydrological impact of spatially distributed hillslopes and streams infrastructures (Sumarjo Gatot et al., 2001; Cudennec et al., 2004b). Finally, impacts, hazards and management aspects are related and dependent through the network structure. The hydro-geomorphological connection of scales, space and upstream-downstream interdependencies can thus allow new analysis approaches in related disciplines and eventually coupling of models.

Fig. 1 – Schematic river network of order n=3.
Fig. 1 – Réseau hydrographique schématique d’ordre n=3.

Fig. 1 – Schematic river network of order n=3.Fig. 1 – Réseau hydrographique schématique d’ordre n=3.

A: Links and Strahler ordering. B: Streams. C: Example of a path run by a water drop from a point to the outlet. lh is the length of the path through the hillslope. l1, l2 and l3 are respectively the lengths of 1, 2 and 3 orders components. D: Sampling grid for spatial analysis.
A : Biefs et indexation de Strahler. B : Tronçons. C : Exemple d’un chemin parcouru par une goutte d’eau d’un point quelconque jusqu’à l’exutoire. lh est la longueur du chemin parcouru à travers le versant. l1, l2 et l3 sont respectivement les longueurs des composantes d’ordres 1, 2 et 3. D : Grille d’échantillonnage pour l’analyse spatiale.

HydroStruct: a dedicated analysis software application

5The HydroStruct software application was developed in order to (i) explore the eventual ubiquity and variability of the identified underlying structural pattern through a great diversity of contexts and constraints (climate, lithology, elevation…) and of scales, together with more classical evidence of scaling and branching, (ii) explore the eventual self-organisation of networks towards organisation rules through their genesis and maturation, (iii) observe artifacts and likelihood of network models (see Rodriguez-Iturbe and Rinaldo, 1997), (iv) feed a rainfall-runoff modelling downward approach to be adjusted according to hydrological contexts, degrees of knowledge, scales and queries, and (v) prepare coupling with related models, such as for water resources allocation or territorial analysis of water demand.

Inscription within the OdefiX Java framework

6HydroStruct was developed with the OdefiX software components, which result from the Java code generalisation of the HyD2002 modelling environment for water resources allocation (Pouget et al., 2006). The object-oriented design of the common OdefiX modelling framework aims at: (i) facilitating the development of software platforms for water resources management decision support; and then support, leading to (ii) easy-to-use and comprehensive tools, thanks to a user-friendly graphically-oriented interface (map representations, charts...), in order to support discussions between specialists and stakeholders. An overall longer-term aim is: (iii) allowing the co-construction of dedicated environments where several models (hydrological, bio-physical, socio-economic, etc.) can be combined to address river basin management issues (Pouget et al., 2006; Poussin et al., 2010). Using OdefiX generic components, the development of an application, such as HydroStruct, can be focused on model structures and functionalities and not on graphical user interfaces or data exchange problems. The graphical interface indeed permits definition of the models as structured objects facilitate navigation between them, and permits their visualisation under various facets (description, definition, validity, results) through tables, charts or maps. Particularly, OdefiX allows the user to deal with both spatial and temporal objects and data: time series can be represented through tables or temporal charts, and exchanged with spreadsheets; while a map representation of geographical areas, networks and objects is provided, with navigation facilities between information layers and scales. The use of GIS functionalities, and their integration with traditional water-resource models, constitute an obvious strategy for the development of basin management systems (Fedra and Jamieson, 1996). Moreover an interactive and adaptative map functionality is relevant to facilitate dialogue with stakeholders and between thematic specialists themselves. HydroStruct uses OdefiX vectorial 2D data in order to handle and visualise the networks and associated information. Conversely, development of HydroStruct made it possible to generalise the raster data management within OdefiX.

Rationale for data structure and analysis

7The input data are georeferenced vector layers of the basin river network and boundaries, which can be obtained from various kinds of data sources and through diverse human-based and/or automatic procedures. This is illustrated in fig. 2 for the central-Tunisian semi-arid basin of Skhira (the outlet being considered at the Skhira gauging station, 35°44’15”N/9°23’05”E UTM system or 39G71N/7G75E Tunisian Carthage 47 system, 192 km2; Cudennec et al., 2005b, 2006), part of the major central-Tunisian Merguellil basin. Then a topological analysis of the relationships between the vectors allows to build a branched-out tree. The interpretation of this tree leads to identification of the links and their Strahler orders, the streams, and to estimation of statistics of these constituents (fig. 1 A and B). In addition, a square grid is used as a set of points to sample the basin territory, and for each of these points the water path is identified across the hillslope and the network, i.e. also through the Strahler ordering cascade for hierarchical analyses (fig. 1). Then geomorphological variables, including the hillslope and the channelised paths lengths, lh and L, are assessed for each point, and georeferenced raster or vector images of the obtained values are built (fig. 2 B and C). The multi-layer raster mapping of geomorphometric variables allows one to use image processing as well as matrix-based statistical softwares to both analyse their spatial distribution and extract their statistics (fig. 2 D and E). Traditional and innovative scaling analyses are further allowed, in particular: (i) through the consideration of the channelised path splitting through the Strahler ordering cascade (Cudennec et al., 2004a; Cudennec and Fouad, 2006; Cudennec et al., 2006); (ii) through nested studies based on sub-settings of the whole-basin tree and territory, as proposed by C. Cudennec et al. (2006) for the Skhira basin; and (iii) through considering hydro-geomorphological entities comprising several basins through the spatial and statistical merging of results from neighbouring basins (Cudennec and Fouad, 2006).

Dedicated development for tree, grid and nesting analysis

8The HydroStruct modelling environment consists of the definition of: (i) a space environment, with the reference to the current studied cartographic document and the list of results map references; (ii) studies classified by categories such of an independent basin, a sub-basin and a population of basins; (iii) open documents, corresponding to result documents of various natures. Graphically, an explorer interface allows the user to navigate between objects (fig. 2A). In all study cases, the source cartographic document must be initially defined, made of at least two vector layers (the basin river network and limits). These layers can be made up from the import of vectorial files (Mif/Mid format). References on layer objects can be defined either directly by choice from lists, or by selection and copy from the map and joining in the corresponding reference. Then, studies of various types are created starting from the explorer. The study of an independent basin requires to define: (i) the outlet reference; (ii) the basin limit reference; (iii) the type of treatment, binary network or not; and (iv) the value of considered proximity. The validity view of the basin definition gives the list of possible problems (outlet orientation error, connections problems, etc.). Concerning the tree structure of the river network, we chose the R-TREE structure, used in geographical database management systems and suggested in the JTS library. The R-TREE is an object hierarchy, which is applicable to arbitrary spatial objects formed by aggregating their minimum bounding boxes and storing the aggregates in a tree structure. The aggregation is, partly, based on the proximity of objects or bounding boxes. The open-source library JTS Topology Suite (www.vividsolutions.com/jts/jtshome.htm) provides a complete and consistent implementation of fundamental 2D spatial algorithms. The result view gives access to various generated files: (i) a cartographic document (fig. 2A) of the network layer, eventually displaying hierarchical information according to the R-TREE structure; (ii) a matrix of links data (L, i, li, etc.); (iii) a table of statistics on streams; (iv) a table of global statistics. For each study of independent basin, several grids can be created. A grid is defined by the x, y steps, the limits being automatically defined based on the basin limits. The major grid calculation consists in determining the nearest link for each grid point, using search algorithms based on the R-TREE structure. Then grid points inherit hydro-geomorphometric attributes from the graph. The result view gives access to various documents, particularly to matrixes of values for each grid cell (nearest link, lh, li l≤i≤n, L, L’, etc.; fig. 1C and D), which allow mapping and statistical synthesis (fig. 2B and C). The other study types are carried out according to the same principle, the corresponding tasks being simplified through various filtering and merging functionalities. For instance, when studying a population of basins, a list of possible outlets is automatically provided from the crossing of network links and area limit.

Fig. 2 – HydroStruct facilities and outputs illustrated with the Tunisian Skhira basin, sub-basin of the Merguellil basin.
Fig. 2 – Fonctionnalités et sorties d’HydroStruct illustrées avec le basin-versant tunisien de Skhira, sous-bassin du bassin-versant de Merguellil.

Fig. 2 – HydroStruct facilities and outputs illustrated with the Tunisian Skhira basin, sub-basin of the Merguellil basin.Fig. 2 – Fonctionnalités et sorties d’HydroStruct illustrées avec le basin-versant tunisien de Skhira, sous-bassin du bassin-versant de Merguellil.

A: Viewing and management interface. B: Raster mapping of a geomorphometric variable resulting from the grid analysis – example of L. C: Iso-value vector contour mapping of a geomorphometric variable – example of L. D: Probability density functions of li, pdf(li), 1 ≤ i ≤, rescaled according to the scaling ratio rl. E: Probability density function of L, pdf(L).
A : Interface de visualisation et de gestion. B : Cartographie raster d’une variable géomorphométrique fournie par l’analyse par grille – exemple de L. C : Cartographie vectorielle en courbes d’iso-valeurs d’une variabble géomorphométrique – exemple de L. D : Fonctions densité de probabilité de li, pdf(li), 1 ≤ i ≤, normalisées selon le facteur d’échelle rl. E : Fonction densité de probabilité de L, pdf(L).

Sensitivity analysis of the grid parameterisation

9Given a river network input, the tree analysis is fully objective. But the grid analysis remains dependent on the grid parameterisation. The dependence of the assessment of metric variables on the grid spacing is presented for the central-Tunisian Merguellil basin closed by the big strategic El Haouareb Dam (1175 km², n=7; Cudennec et al., 2007; Kingumbi et al., 2007; Leduc et al., 2007; Lacombe et al., 2008) and for two sub-basins: respectively the gauged Skhira basin described above, on the Western upstream side of the Merguellil basin (192 km², n=6), and a much smaller Eastern sub-basin (6.3 km², n=4; fig. 3).

Fig. 3 – River network of the Tunisian wadi Merguellil river basin (the outlet being the El Haouareb dam) and location of the two studied sub-basins.
Fig. 3 – Réseau hydrographique du bassin-versant tunisien de l’oued Merguellil (l’exutoire étant le barrage El Haouareb) et localisation des deux sous-bassins versants étudiés.

Fig. 3 – River network of the Tunisian wadi Merguellil river basin (the outlet being the El Haouareb dam) and location of the two studied sub-basins.Fig. 3 – Réseau hydrographique du bassin-versant tunisien de l’oued Merguellil (l’exutoire étant le barrage El Haouareb) et localisation des deux sous-bassins versants étudiés.

Tunisian Carthage 47 geodetic system.
Système géodésique tunisien Carthage 47.

10The Merguellil basin was chosen as a pilot basin by Tunisian authorities for hydrological and geographic monitoring and assessments (Cudennec et al., 2007; Kingumbi et al., 2007) because of its emblematic situation: the basin is located in the semiarid area of the Tunisian South-Mediterranean climatic gradient from sub-humid to Saharan conditions (Slimani et al., 2007); its upstream mountainous part lies on a Trias-Quaternary geological ground (Kingumbi et al., 2007); geophysical and anthropogenic dynamics are much contrasted between the upstream mountain and the downstream plain, the El Haouareb Dam being located at the place where the wadi flows out of the mountain range into a large sedimentary plain. The river network is highly variable in space in terms of drainage density, bifurcation shapes and angles, and thus in terms of the considered metrics. It thus displays a relevant study case to test the sensitivity of the HydroStruct outputs as regards the grid spacing. The three basins have been studied with height spacing ranging from 25 m to 1500 m. Calculations could not succeed with the 25 m grid spacing for the whole Merguellil basin because the number of grid points was too great. Conversely however, spacing higher than 500 m are too large to be applied to the 6.3 km² sub-basin since they provide too few sampling points. In order to visualise the stabilisation of metrics when screening the grid spacing, results were reduced and centred on the 100 m-grid values, and then graphically displayed with centres shifted to 2-18 in fig. 4.

Fig. 4 – Charting view of shifted reduced centred results according to the grid spacing.
Fig. 4 – Visualisation graphique des résultats centrés réduits échelonnés selon le pas de la grille.

Fig. 4 – Charting view of shifted reduced centred results according to the grid spacing. Fig. 4 – Visualisation graphique des résultats centrés réduits échelonnés selon le pas de la grille.

A: Merguellil basin. B: Skhira sub-basin. C: Eastern sub-basin.
A : Bassin de Merguellil. B : Sous-bassin de Skhira. C : Sous-bassin oriental.

11It appears that all the metrics, for each of the three basins, are stable for grid spacing below 100 m. Our interpretation of this result, enhanced by other results from diverse river networks, is that stabilisation occurs when the grid spacing is inferior to twice the mean hillslope length (respectively 129.1 m, 107.4 m and 84.7 m for the Merguellil, Skhira and Eastern basins), i.e. the mean interfluve spacing (between two stream courses or vector elements of the river network).

Conclusions

12The dedicated HydroStruct application was developed within the generic OdefiX framework, which provides Java software components to allow co-developing and interfacing object-oriented models. Particularly, HydroStruct uses the OdefiX vectorial 2D data in order to handle and visualise the networks and associated information. Conversely, the HydroStruct development made it possible to generalise the raster data management within OdefiX. Vector data of river networks and basin boundaries are analysed through both tree formalisation and spatial sampling. Results are extracted as global, classified and scaled statistics; and in terms of spatial distribution through geographic images. Raster images of scaled geometric variables can be combined to assess and explore further structural evidences, and be linked with territorial maps of hydrological parameters and/or socio-anthropogenic properties. Sub-basins and populations of basins can be easily analysed, by interrelating, filtering and merging vector, raster and tree data. Finally, a major perspective is opened of interrelating hydro-geomorphometric results with spatial-temporal variables of different kinds, either for analysis or for interfacing with other models.

We thank the three anonymous reviewers for their constructive comments.

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Annexe

Version abrégée en français

Le réseau hydrographique est la structure géomorphologique de base d’un basin-versant, en termes topologique et géométrique. Il a de plus un rôle hydrologique fondamental, étant l’objet qui gouverne les transferts d’eau et d’éléments associés d’amont en aval, depuis les versants d’une part et à travers les « chemins chenalisés » vers l’exutoire d’autre part. En outre, le réseau hydrographique s’organise en une arborescence qui présente fréquemment des propriétés d’invariance d’échelle. Enfin, il est déterminant dans les interdépendances entre lieux du bassin-versant, et donc entre enjeux sociétaux territorialisés liés aux ressources et aux risques hydrologiques. Au sein d’un bassin-versant, le réseau hydrographique est constitué de points particuliers (i.e., l’exutoire unique, les sources et les confluences). L’objet linéaire compris entre deux points particuliers successifs est un bief, qui peut être caractérisé par une valeur selon la règle d’ordination d’A.N. Strahler (1952 ; fig. 1). Tout ensemble de biefs de même ordre (selon Strahler), successifs dans le sens de l’eau, est un nouvel objet appelé tronçon. La gamme des ordres identifiée au sein d’un réseau hydrographique peut être vue comme une cascade au sein de laquelle des propriétés d’invariance d’échelle ont été identifiées et mises en perspective à travers l’application de la géométrie fractale (Rodriguez-Iturbe et Rinaldo, 1997 ; Dodds et Rothman, 1999, 2000). Parallèlement, des fonctions globales présentent un intérêt au niveau de l’hydrogéomorphologie du bassin-versant dans son ensemble. Toute éventuelle règle d’organisation de telles fonctions globales aurait l’intérêt de fournir une jauge géomorphométrique en lien avec le fonctionnement hydrologique du bassin-versant. Dans cette optique, au-delà des fonctions « aire » et « largeur » traditionnelles, C. Cudennec et al. (2004a) considèrent le « chemin de l’eau » comme étant le chemin à travers le versant (de longueur lh) puis le chemin à travers le réseau hydrographique (de longueur L), et analysent ce dernier comme étant la succession de composantes à travers la cascade de Strahler (la composante d’ordre i ayant une longueur li, de telle sorte que L = Σi=1,n li). Ces auteurs proposent en outre d’étudier le rapport d’échelle des longueurs de composantes

parallèle au rapport de Horton classique pour les longueurs de tronçons (Horton, 1945 ; Schumm, 1956); ainsi que les troncatures L’ = Σi=1,m< n li correspondant aux longueurs des chemins de l’eau à travers un sous-ensemble de la cascade de Strahler. Des résultats encourageants ont été obtenus pour des bassins versants particuliers en termes de stabilité du nouveau rapport d’échelle, de régularité sous-jacente aux niveaux infra- et supra-bassin, en situations topographique et géologique homogènes et hétérogènes (Cudennec et al., 2004a ; Cudennec et Fouad 2006 ; Cudennec et al., 2006). Des premières formalisations théoriques ont été proposées (Cudennec et al., 2004, 2005a ; Fleurant et Boulestreau, 2005), qu’il reste à améliorer d’après l’observation systématique d’un grand nombre de bassins versants d’une part et d’après la confrontation avec des modèles théoriques connexes (Karlinger et Troutman, 1985 ; Rinaldo et al., 1995 ; Hung et Wang, 2005 ; Moussa, 2008) d’autre part. Par ailleurs, des approches de modélisation pluie-débit valorisent l’information géomorphométrique, qu’elle soit liée à l’invariance d’échelle ou à l’organisation globale (Rodriguez-Iturbe et Rinaldo, 1997 ; Cudennec, 2007). Ces approches sont adaptables aux données disponibles (Rinaldo et al., 1991 ; Snell et Sivapalan, 1994 ; Woods et Sivapalan, 1999 ; Cudennec, 2007), y compris en situation de données rares, et ouvrent donc de nombreuses perspectives en hydrologie.

L’application logicielle HydroStruct a été développée afin de : 1) explorer systématiquement la variabilité et l’éventuelle généricité des règles d’organisation du réseau hydrographique à travers une grande diversité de contextes, de contraintes (climatiques, topographiques, géologiques, anthropiques) et d’échelles ; 2) explorer l’éventuelle auto-organisation des réseaux hydrographiques au fil de leur genèse et de leur maturation ; 3) étudier les propriétés et la vraisemblance de modèles de réseaux ; 4) alimenter la modélisation hydrologique à base géomorphologique ; 5) tendre vers un couplage avec des modélisations de la gestion des ressources et des risques hydrologiques. HydroStruct a été développé au sein de la plateforme Java orientée objet OdefiX (Pouget et al., 2006 ; fig. 2). Pour l’étude d’un bassin-versant donné, les données d’entrée sont les couches vectorielles du réseau hydrographique et du contour. Une analyse topologique permet de construire un graphe informatique correspondant à l’arborescence des éléments constitutifs du réseau hydrographique puis d’en tirer les informations statistiques. L’application d’une grille et la manipulation d’informations matricielles permettent ensuite d’échantillonner le territoire du bassin-versant et d’analyser les grandeurs morphométriques liées aux chemins de l’eau, en termes de statistiques, d’organisation spatiale et de propriétés d’échelles. Ces fonctionnalités et la sensibilité au paramétrage de la grille, dans un souci de systématisation de la mise en œuvre, sont illustrées pour le bassin-versant tunisien de l’oued Merguellil et deux sous-bassins versants (fig. 3, fig. 4 et tab. 1).

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Table des illustrations

URL http://geomorphologie.revues.org/docannexe/image/10082/img-1.png
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Titre Fig. 1 – Schematic river network of order n=3.Fig. 1 – Réseau hydrographique schématique d’ordre n=3.
Légende A: Links and Strahler ordering. B: Streams. C: Example of a path run by a water drop from a point to the outlet. lh is the length of the path through the hillslope. l1, l2 and l3 are respectively the lengths of 1, 2 and 3 orders components. D: Sampling grid for spatial analysis.A : Biefs et indexation de Strahler. B : Tronçons. C : Exemple d’un chemin parcouru par une goutte d’eau d’un point quelconque jusqu’à l’exutoire. lh est la longueur du chemin parcouru à travers le versant. l1, l2 et l3 sont respectivement les longueurs des composantes d’ordres 1, 2 et 3. D : Grille d’échantillonnage pour l’analyse spatiale.
URL http://geomorphologie.revues.org/docannexe/image/10082/img-3.png
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Titre Fig. 2 – HydroStruct facilities and outputs illustrated with the Tunisian Skhira basin, sub-basin of the Merguellil basin.Fig. 2 – Fonctionnalités et sorties d’HydroStruct illustrées avec le basin-versant tunisien de Skhira, sous-bassin du bassin-versant de Merguellil.
Légende A: Viewing and management interface. B: Raster mapping of a geomorphometric variable resulting from the grid analysis – example of L. C: Iso-value vector contour mapping of a geomorphometric variable – example of L. D: Probability density functions of li, pdf(li), 1 ≤ i ≤, rescaled according to the scaling ratio rl. E: Probability density function of L, pdf(L). A : Interface de visualisation et de gestion. B : Cartographie raster d’une variable géomorphométrique fournie par l’analyse par grille – exemple de L. C : Cartographie vectorielle en courbes d’iso-valeurs d’une variabble géomorphométrique – exemple de L. D : Fonctions densité de probabilité de li, pdf(li), 1 ≤ i ≤, normalisées selon le facteur d’échelle rl. E : Fonction densité de probabilité de L, pdf(L).
URL http://geomorphologie.revues.org/docannexe/image/10082/img-4.png
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Titre Fig. 3 – River network of the Tunisian wadi Merguellil river basin (the outlet being the El Haouareb dam) and location of the two studied sub-basins.Fig. 3 – Réseau hydrographique du bassin-versant tunisien de l’oued Merguellil (l’exutoire étant le barrage El Haouareb) et localisation des deux sous-bassins versants étudiés.
Légende Tunisian Carthage 47 geodetic system.Système géodésique tunisien Carthage 47.
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Titre Fig. 4 – Charting view of shifted reduced centred results according to the grid spacing. Fig. 4 – Visualisation graphique des résultats centrés réduits échelonnés selon le pas de la grille.
Légende A: Merguellil basin. B: Skhira sub-basin. C: Eastern sub-basin. A : Bassin de Merguellil. B : Sous-bassin de Skhira. C : Sous-bassin oriental.
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Référence papier

Jallel Aouissi, Jean-Christophe Pouget, Houda Boudhraâ, Guillaume Storer et Christophe Cudennec, « Joint spatial, topological and scaling analysis framework of river-network geomorphometry », Géomorphologie : relief, processus, environnement, vol. 19 - n° 1 | 2013, 7-16.

Référence électronique

Jallel Aouissi, Jean-Christophe Pouget, Houda Boudhraâ, Guillaume Storer et Christophe Cudennec, « Joint spatial, topological and scaling analysis framework of river-network geomorphometry », 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/10082 ; DOI : 10.4000/geomorphologie.10082

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Auteurs

Jallel Aouissi

Institut National Agronomique de Tunisie - Génie rural - 1082 Tunis-Mahrajène - Tunisia (jalelaouissi@yahoo.fr)

Jean-Christophe Pouget

IRD - UMR G-EAU - 34394 Montpellier Cedex 5 - France (jean-christophe.pouget@ird.fr)

Houda Boudhraâ

ESIER - Medjez el Bab - Tunisia (Boudhraa_hda@yahoo.fr)

Guillaume Storer

AGROCAMPUS OUEST - INRA - UMR 1069 Sol Agro et hydrosystème, Spatialisation - 65, rue de Saint-Brieuc - CS 84215 - 35042 Rennes Cedex - France (storer@agrocampus-ouest.fr ; cudennec@agrocampus-ouest.fr)

Christophe Cudennec

AGROCAMPUS OUEST - INRA - UMR 1069 Sol Agro et hydrosystème, Spatialisation - 65, rue de Saint-Brieuc - CS 84215 - 35042 Rennes Cedex - France (storer@agrocampus-ouest.fr ; cudennec@agrocampus-ouest.fr)

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