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NUMERO 3-2007:Maquette Geomorpho Géomorphologie : relief, processus, environnement, 2007, n° 3, p. 247-258 Tri-dimensional parameterisation: an automated treatment to study the evolution of volcanic cones Apport de la paramétrisation tridimensionnelle à l’étude de l’évolution des cônes volcaniques Jean-François Parrot* Abstract An automated volcanic parameterisation has been developed in order to measure the evolution of a volcanic cone resulting from ero- sion, catastrophic events or human activity. In a first step, various parameters have been defined and retained: volume and 3D surface of the volcanic cone, volcanic base line radius and eventually its elongation, total height of the cone from the base line to the summit, crater radius when existing, crater depth, mean slope angle outside the crater, mean slope angle inside the crater. All these parameters are derived from a Digital Elevation Model. They can be used to characterize a volcanic cone and to compare all the cones of diverse studied regions in order to define different families based on their shape characteristics. On the other hand, the algorithm developed reconstitutes the original volcanic feature. Then, a comparison between the reconstituted cone and the presently observed shape allows assess to the erosion rate, to define precisely the eroded zones, and to measure either the degree of evolution or the volume mobilized during massive erosion processes. The algorithm developed in C++ is based on a calculation that requires only the altitude of the vol- canic base line and the coordinates of a point considered as the volcanic center; this requirement is important, especially when the edifice was subjected to high erosion rates or when it is deeply eroded. Combined with a tomomorphometric approach, this algorithm represents a new tool to study volcanic landforms. Three applications illustrate and validate the results. Key words: volcanic cone, parameterisation, denudation volume, DEM simulation, Jocotitlán volcano, Mexico. Résumé Une paramétrisation automatisée a été développée en vue de mesurer l’évolution d’un cône volcanique résultant de l’érosion, d’évé- nements catastrophiques ou de l’activité anthropique. Différents paramètres ont été testés et retenus : volume et surface tridimension- nelle du cône volcanique, rayon de la base de l’édifice, hauteur totale, rayon du cratère quand il existe, profondeur de ce dernier, pente moyenne des flancs et à l’intérieur du cratère. Tous ces paramètres sont obtenus à partir du traitement d’un Modèle Numérique de Ter- rain et peuvent être utilisés pour définir les caractéristiques morphologique d’un cône volcanique. L’algorithme développé en C++ de- mande uniquement à l’utilisateur d’indiquer quelle est l’altitude de la ligne de base et les coordonnées d’un point considéré comme étant le centre du cratère. Cette dernière précision est importante, surtout lorsque l’édifice étudié est fortement disséqué. L’algorithme engendre une forme susceptible de correspondre à celle que présentait le volcan avant l’érosion, ce qui permet entre autres de mesu- rer le volume de matériaux érodé. Des applications portant sur le volcan Jocotitlán (Mexique), qui a subi un important glissement de terrain, ainsi que sur deux volcans de la région de Chichinautzin illustrent et valident les résultats. Mots clés : paramétrisation, cône volcanique, volume érodé, MNT, volcan Jocotitlán, Mexique. Version française abrégée l’activité humaine. Différents auteurs (Porter, 1972 ; Bloomfield, 1975, Wood, 1980a, 1980b) ont par exemple L’étude de l’évolution morphologique des cônes volca- défini et quantifié les rapports existant entre la hauteur du niques formés par des fragments pyroclastiques repose, cône et le diamètre de sa ligne de base, entre ce diamètre et entre autres, sur une paramétrisation de ces édifices. Il est celui du cratère. Le premier rapport est compris entre 0,20 ainsi possible de caractériser à l’aide de paramètres quan- et 0,10 et diminue avec le temps ; le second entre 0,40 et titatifs les cônes volcaniques, de mesurer les effets produits 0,80 augmente au contraire avec le temps, cette évolution par l’érosion, par des événements catastrophiques ou par étant essentiellement due à l’érosion. Par ailleurs, la pente *Instituto de Geografía, UNAM, Apto. Postal 20-850, 01000 México D.F. México. E-mail:[email protected] Jean-François Parrot extérieure du cône serait également une caractéristique liée crater located in the summit (Macdonald, 1972). The first à la nature du matériel volcanique. geomorphological studies have shown that morphologic En fait, de telles mesures nécessitent d’étudier des édifices changes occur with time and are able to provide information volcaniques relativement bien conservés, se réfèrent en about the age of the edifice (Colton, 1967; Scott and Trask, général à des observations de terrain et résultent d’une esti- 1971). Porter (1972) was the first to define quantitative mation globale dépendant de l’équation employée. Les ratios between different parameters in order to characterize modèles numériques de terrain (MNT), en raison des possi- the volcanic shape: i.e., the ratio height of the cone versus bilités actuelles de stockage et des progrès technologiques, the base diameter would be equal to 0.18 and the ratio bet- se révèlent un moyen efficace d’étudier les cônes volca- ween the crater diameter and the base diameter would niques. L’analyse numérique des MNT (Wilson et Gallant, remain at 0.40. Bloomfield (1975), using radiometric age 2000) permet de définir des attributs primaires, comme la determinations, observed that the first ratio decreases from pente, l’aspect, la courbure, la convexité, etc, produisant 0.21 until 0.10 with time, meanwhile the second one ainsi de nombreux paramètres morphologiques. increases from 0.40 to 0.83. On the other hand, according to L’algorithme mis au point et présenté dans cet article a Settle (1979), the shape characteristics of the volcanic cones trait à la paramétrisation des édifices volcaniques à partir are related to the nature of the material involved in the effu- des MNT. Il est ainsi possible de calculer le volume et la sive process, and to the nature and duration of the erosion hauteur du cône (fig. 1), le rayon de la ligne de base, celui activity. Wood (1980a, 1980b) confirms and formalizes the du cratère et sa profondeur, la pente moyenne sur les flancs morphometric parameters proposed by Porter (1972). Until du volcan et à l’intérieur du cratère, la surface du cône now, numerous geomorphological studies concerning the (fig. 2). À la différence des estimations antérieures, toutes geomorphic definition of the volcanic characteristics or the ces mesures prennent en compte les valeurs altimétriques de effect of the erosion processes, are based on these parame- tous les pixels constituant l’édifice ; c’est par exemple le ters and ratio (Dohrenwed et al., 1986; McFadden et al., cas pour le calcul de la pente moyenne résultant de l’en- 1986; Hasenaka, 1994; Noyola-Medrano et al., 1994; Hoo- semble des valeurs de pente rencontrées en chaque point. per, 1995; Luhr et al., 1995; Hooper and Sheridan, 1998; Qui plus est, l’algorithme reconstitue si nécessaire le cône Rech et al., 2001; Aranda-Gomez et al., 2003; Nemeth et volcanique en se fondant sur les coordonnées du centre du al., 2005), even if their use remains problematic when the cratère et l’altitude de la ligne de base. On peut ainsi, non studied cone does not present a crater (Hasenaka and Car- seulement étudier des ensembles volcaniques fortement dis- michael, 1985a). séqués par l’érosion et dont le cratère se résume parfois à The possibility to obtain more detailed geomorphic infor- un unique sommet, mais encore quantifier le volume de mation has been explored by Garcia-Zuniga and Parrot matériel déplacé au cours du temps sous l’effet de l’érosion (1998) who proposed using a Digital Elevation Model (DEM) ou des événements mentionnés plus haut. and to define pattern recognition parameters applied to hyp- L’application de la méthode au volcan Jocotitlán, précé- sometric slices describing the volcanic cone, from its base demment étudié par Siebe et al. (1992), illustre les résultats line to its summit. This approach described as tomomorpho- obtenus (fig. 4, 5a, 5b, 6a, 6b, 7 ; tab. 1). Les estimations re- metric analysis registers the morphologic changes taking into latives à l’effondrement qui a affecté cet édifice volcanique account parameters such as the convexity index, direction of valident la méthode qui apporte par ailleurs de nombreuses the principal axis, etc. This recent approach has been used to informations complémentaires. Par exemple, la valeur study the lithospheric motion of the Somalian and Arabian moyenne de la pente confirme la nature dacitique des coulées plates (Collet et al., 2000), the Anatolian volcanic massif volcaniques et indique localement la hauteur du matériel ar- (Ozlem et al., 2003) and the Chichinautzin volcanic cinder raché à l’appareil (fig. 7). À titre d’illustration supplémentai- cone field, Mexico (Noyola and Parrot, 2005). re, deux volcans de la région orientale du Chichinautzin ont Square-grid digital elevation models (DEMs) represent été étudiés (fig. 8a et 8b). Le premier est un édifice scoriacé important and accurate tools to underline the different regio- ne présentant pas de cratère (El Tezoyo), l’autre un cône de nal geomorphic features and to simulate various scenarios, as cendres (Volcan del Aire) dont le cratère est parfaitement the possibility of storage and advances in computing techno- conservé, mais dont les flancs sont fortement ravinés. Les ré- logy increased strongly in recent years. The horizontal and sultats obtenus sont reportés dans le tableau 2. vertical resolutions are sufficient to accurately calculate dif- La méthode décrite dans cet article se révèle un nouvel ferent parameters extracted from the DEM surface. The outil capable de définir les caractéristiques morphologiques digital terrain analysis (Wilson and Gallant, 2000) allows des cônes volcaniques, de quantifier leur âge relatif et de defining primary and secondary attributes.
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