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 erosion, 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 volcanic 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 tridimensionnelle 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 mesurer 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. The secondary mesurer le degré de dégradation dû à l’érosion ou à divers attributes are devoted to estimate the role played by topogra- phénomènes érosifs. phy in the distribution of soil water or on the susceptibility of landscapes to erosion, for instance. Most of the primary attri- Introduction butes such as slope, aspect, plan and profile curvature are computed directly or by fitting an interpolation function to Volcanic cinder cones formed by cinder and pyroclastic the DEM in order to calculate them (Moore et al., 1993b; debris are generally considered as truncated cones with a Mitasova et al., 1996; Florinsky, 1998). These different attri-

248 Géomorphologie : relief, processus, environnement, 2007, n° 3, p. 247-258 An automated treatment to study the evolution of volcanic cones butes provide numerous geomorphological indicators (Tribe, the slope calculation in each DEM’s point. Complementary 1991). They are used to describe the morphometry, catch- information is provided: the percentage of downward angle ment position, stream channels, etc., and to compute located on the cone flank, as well as the percentage of the topographic attributes (Jenson and Domingue, 1988; Dikau, upward angle inside the crater, in order to measure irregula- 1989; Moore et al., 1993a; Dymond et al., 1995; Giles, 1998; rities that can emphasize for instance the presence of eroded Borrough et al., 2000). An exhaustive survey of the publica- zones (natural or artificial) or to control the degree of the tions concerning this topic can be found in the Pike’s report smoothness of the cone. The third generation of parameters (2002). Various softwares such as TAPES-G (Moore, 1992) concerns the calculation of the bi and tri-dimensional surfa- have been developed with such a goal. ce, as well as the volume of the edifice. This paper aims at defining and computing parameters of At the beginning of the procedure, the user has to define volcanic cones in order to enable the measurement of evo- the altitude of the base line and the coordinates of the vol- lution stages of these cones due to the erosion, catastrophic canic center CE. As the first step consists of researching on events or human activity. The first approach consisted of the DEM all the pixels whose altitude is equal or superior to defining some characteristic features that can be useful for the altitude of this base line, a labellization is required in this purpose. The algorithm presented in this paper has been order to choose among the different pixel components, the developed in C++. The automated parameterisation of vol- surface corresponding to the first altitude slice of the studied canic cones is based on seven parameters: the volume of the edifice. This surface is the base on which the different para- volcanic cone, the volcanic base line radius and eventually meters will be calculated. its elongation, the total height of the cone from the base line until its summit, the crater radius when existing, the depth of Radius and elongation of the base line this crater, the mean dipping angle outside the crater and the mean dipping angle inside the crater. This measurement needs to research the center of mass All these parameters and their relationships are not only CM of the base surface and the Principal Axis (PA) passing able to characterize a volcanic cone, but can be also used to through this point. PA is calculated as follows: α μ μ μ μ μ reconstitute the original volcanic landform. Moreover, the tg(2 ) = 2 xy/( yy - xx) if ( yy - xx) π 0 comparison between the reconstituted cone and the present- On the other hand, the center of mass CM (Xc, Yc) and the ly observed shape allows us to assess the erosion and moments of second order mxx , myy and mxy are respectively evolution stages. The developed algorithm is based on a cal- equal to: culation that only requires the altitude of the volcanic base line and the coordinates of a point considered as the center of the volcanic cone when it is present or to the summit if this feature is lacking. The algorithm is described in the following section. In the second section, the procedure that allows us to reconstitute the cone taking into account the formerly obtained parameters, is presented. Finally, the results are discussed in the third section. Nbp is the number of pixels of the object and Xi Yi the coordinates of the pixel i. Parametrisation procedure The greater distance between CM and the crossing point between the perimeter of the surface and PA corresponds to The main lines of the computation consists in defining and the value of the radius BRmax. The normal of PA passing extracting the parameters that characterize the studied vol- through CM is calculated in order to define the value of canic cone and, as a second step, in reconstructing the BRmin. The elongation is then calculated. original landform of the studied volcanic cone. The difference observed between these two cones also corresponds to Radius and elongation of the crater a parametrization of the erosion processes. The first calculated parameters are the volcanic height H The calculation of the crater radius CR takes into account of the cone, the base line radius BR which present two com- the estimated center of the edifice CE (coordinates defined ponents: the minimum base line radius BRmin and the by the user) and the highest altitude point. The normal of the maximum base line radius BRmax allowing calculation of the line linking these two points allows researching the perpen- elongation ratio ER of the volcanic base line, the depth of diular radius, taking into account the highest point located the crater HC as well as the crater radius CR and its two on the both sides of this normal. The second value is either components: the minimum crater radius CRmin and the maxi- greater or lower than the first one. CRmax and CRmin depend mum crater radius CRmax. on this comparison and then the elongation of the crater is The second group of parameters concerns the mean dip- computed. One can notice that a difference between the ping angle a outside the crater and the mean dipping angle coordinates of CE and CM previously defined represents b inside the crater. One can notice that contrary to the pro- another morphometric parameter, i.e. the existing tectonic cedure proposed by Wood (op. cit.), these values result from constraints during the volcano formation.

Géomorphologie : relief, processus, environnement, 2007, n° 3, p. 247-258 249 Jean-François Parrot

Crater depth, height and volume of the At this stage, for each resulting triangle issued from the 8 volcanic cone rectangular triangles that form the pixel surface, we know the values of each triangular side. The Heron’s formula The crater depth corresponds to the hypsometric difference allows calculating the surface of each triangle. In this case: between the altitude of the point CE and the highest altitude of the volcano. The height of the cone is the difference between this latter point and the altitude of the base line. where The procedure used to calculate the volume consists of computing the volume of each altitude slice (in meters or Then, the 3D surface S3D of the pixel corresponds to the decimeters according to the hypsometric resolution of the sum of the 8 resulting triangles: DEM). Each slice corresponds to the pixels whose altitude A’ is equal or greater than the former slice of altitude A that plays the role of the floor. The difference (A’-A) corresponds to the hypsometric resolution of the DEM. When the calcu- The total surface S3 corresponds to the sum of all the S3D. lation is done on a slice, the roof of this slice plays the role Actually, in the case of the pixel Pp located at the periphery of the floor for the following upper slice. We have to notice some of the 8 rectangular triangles are not taken into that the volumetric excess corresponding to the upper half account according to the local configuration (fig. 3). part of a slice is actually balanced by the loss registered in The ratio S3D/S2 is another indication concerning the the lower half part, blurring the staircase effect inherent in smoothing degree of the studied cone. It becomes lower this procedure. when the cinder cone is recent and does not present gullies, as well as when reconstituing the former shape (see table 1). Surface of the volcanic cone Slope Two types of surface can be defined, as well as the difference they present. The first calculated surface is the The mean slope calculation is as follows. Following each topographic surface directly calculated on the surface defi- line issued from CE (coordinates defined by the user) and ned by the base line. In a first approximation (Pratt, 1978), linking a pixel belonging to the perimeter describing the base this surface S2 is equal to: line, the algorithm compares the altitude of the successive points located on this line in order to know if the calculated angle corresponds to an ascending (b) or descending (a) where Ps and Pp are respectively the pixels describing slope. A clockwise linking is done in order to scan the whole the surface and the pixels belonging to the perimeter edifice and the local result is plotted if a previous one does (fig. 1). This measure corresponds only to the surface not exist. On the other hand, the presence of local ascending occupied on the map, but it is also possible to measure the slopes in the volcanic flank, as well as the presence of local tri-dimensional surface S3. In order to calculate the 3D sur- descending slopes inside the crater are researched in order to face, a new algorithm has been developed; each pixel is control the regularity of the conic shape. divided in eight rectangular triangles that converge in the pixel center. Figure 2 illustrates the computation process Volcanic cone reconstitution taking into account the altitude value of the studied pixel and the altitude values of the eight surrounding pixels. The In addition, the developed algorithm that can be provided altitude value of the pixel corners and the altitude of the by the author, reconstitutes the original volcanic cone using center of each pixel side result from a linear interpolation the following considerations. As formerly described a vol- between the altitude value of the pixel center and the alti- canic cinder cone corresponds to a truncated cone with a tude of the neighboring pixels. crater. The flank of the edifice is quite regular and smooth. A is the difference of altitude between the center of the Taking into account the value of the crater radius (CR) and pixel and the end of the different segment. It allows the cal- the altitude of the highest point (HP), a circle is drawn culation of the length of base and bside following the whose altitude is equal to HP. If the coordinates of the cen- formula: ter defined by the user are correct, this circle has to recover all the remnants of the crater wall. The calculated crater circle corresponds to the spatial reference on which the computation is based. Inside the cra- where hps corresponds to half part of the length of pixel side ter, circular curve lines are drawn, the altitude of which are (in meters) and hd to comprised between the altitude HP and the altitude value of a is the difference of altitude between two A. This value the crater bottom; similarly on the flank of the volcano, cir- allows measuring the length of aside that is equal to: cular curve lines are defined between the crater circle and the base line. The resulting DEM generation is obtained by using a curve dilation procedure (Taud et al., 1999).

250 Géomorphologie : relief, processus, environnement, 2007, n° 3, p. 247-258 An automated treatment to study the evolution of volcanic cones

Jocotitlán Reconstructed Parameters Computed elements Original shape cone Lower radius 3277.50 m 3277.50 m Base Line Greater radius 5964.93 m 5964.93 m Lower radius * 695.18 m 695.18 m Crater Greater radius * 695.18 m 695.18 m Base line 2800 m 2800 m Maximum altitude 3953 m 3953 m Edifice Height 1153 m 1153 m Crater depth 220 m 220 m Mean angle 17.47 ° 17.83 ° Flank Descending surfaces 88.76% 95.42% Mean angle 18.52 ° 17.08 ° Crater Ascending surfaces 94.27% 96.38% 2D surface 62.466 734 km2 62.466 734 km2 Surface Fig. 1 – Perimeter and surface pixels of an hypsome- 3D surface 65.370 608 km2 65.664 176 km2 tric slice. Total 17.338 396 km3 19.314 505 km3 Fig. 1 – Pixels du périmètre et de la surface dans une Volume 3 tranche altimétrique. Difference 1.976 109 km

Table 1 – Parametric values of the Jocotitlán volcano (original form and reconstituted edifice). * indicates that the involved algorithm encountered only Fig. 2 – Computation of the ‘3D surface’ inside a one summit; for this reason, the two radius of the crater are similar. pixel. Tableau 1 – Valeur des paramètres du volcan Jocotitlán (forme actuelle et Fig. 2 – Calcul de la « surface tridimensionelle » à édifice reconstitué). * indique que la séquence algorithmique n’a rencontré qu’un l’intérieur d’un pixel. seul sommet ; pour cette raison, les deux rayons du cratère ont la même valeur.

generation of a reconstituted edifice allows the quantification of the differences registered by the volcanic cone due to erosion processes, collapses or human activity. The parameters, formerly described in the case of the original shape of the volcanic cone, are calculated in the same way in the case of the reconstituted cone. Their comparison is a key to underline the features resulting form erosion processes, collapses or human utilization. Application and results

This paper was focused on two volcanic regions in Mexico. The first one comprises the Jocotitlan volcano, and the second is formed by two volcanoes from the Chichinautzin range. The Jocotitlán volcano (3950 meters) is a typical stratovolcano and dome complex, mostly composed by dacite lava flows. It is located in the central part of the Trans Mexican Volcanic Belt (TMVB), 60 km north of Mexico City. A huge collapse affected the NE sector of this edifice in pre-historic times. The associated avalanche covered an area of When the original altitude in some places is higher than 80 km2 with a maximal runout distance of 12 km and an the interpolated value, the original hypsometric value is pre- estimated volume of 2.8 km3 (Siebe et al., 1992). The preserved in order not to blur these features that can correspond sence of a major normal fault interesting the volcano sug- to adventive effusive centers or local tectonic events. The gests an extensional tectonic stress regime that could be res-

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Fig. 3 – The 22 first templates, their corresponding bi-dimensional surface values inside the central pixel, and the corresponding triangular zones inside the central pixel that will be used in order to calculate the surface of an hypsometric slice. Fig. 3 – Les 22 premiers patrons permettant de définir la portion d’un pixel du périmètre entrant dans le calcul de la surface d’une tranche d’altitude.

252 Géomorphologie : relief, processus, environnement, 2007, n° 3, p. 247-258 An automated treatment to study the evolution of volcanic cones

Fig. 4 – Contour lines of the Jocotitlán volcano used to pro- duce the DEM. Fig. 4 – Courbes de niveau du volcan Jocotitlán utilisées pour créer le MNT. ponsible for triggering such a slope failure. The objective of this investigation was not di- rected towards studying the relationships between the volcano and the regional tectonic pattern, but to present and dis- cuss the parameters calculation procedure (table 1), as well as the information obtained in terms of volume of the displaced material, and other measurements associated with the shape of the edifice. A 11- m resolution DEM produced taking into account a multidi- rectional interpolation (Parrot and Ochoa-Tejeda, 2004) method of curve lines was used as a base (fig. 4). By applying the proposed calculation procedure, it was possible to precisely characterize the volcanic original shape. They are compatible with the former pa- The calculation of the ratio Wcr/Wco (Crater diameter ver- rameters proposed by Porter (1972) and Wood (1980a, b). sus Base line diameter) depends on the position of the base For instance, the ratio Hco/Wco (Height versus Diameter) is line. In this case, the lower value obtained for this ratio equal to 0.17, and the main dipping angles (17.47 for the (0.21) suggests that the lower limit chosen for the volcanic flank and 18.52 for the crater) are comprised within the complex is located below the original base line in order to range defined by these authors for such a type of volcano. calculate the volume mobilized by the collapse event. The

Fig. 5 – Shadowed DEM of the Jocotitlán volcano. A: original shape; B: reconstituted volcano. Fig. 5 – MNT avec estompage du volcan Jocotitlán. A : forme actuelle ; B : forme reconstituée.

Géomorphologie : relief, processus, environnement, 2007, n° 3, p. 247-258 253 Jean-François Parrot

Fig. 6 – 3D diagram of the Jocotitlán volcano. A: original shape; B: reconstituted volcano. Fig. 6 – Bloc diagramme du volcan Jocotitlán. A : forme actuelle ; B : forme reconstituée.

relation 3D surface versus the global volume is an indicator of the regularity of the edifice. Considering the original form, this ratio is equal to 3.77, whereas the value decreased to 3.40 after the volcano reconstitution (fig. 5 and fig. 6). Moreover, such parameters used to describe the volcanic edifice can be also utilized to calculate the volume of the displaced material at the time of the collapse. The volume of the displaced material was calculated as 1.976 km3, that means a smaller volume than the assessment proposed by Siebe et al. (1992). The later took into account the volume of the scattered debris-avalanche deposits expressed by a hummocky topography (see fig. 5). In addition to the analysis of the changes of the original shape and the reconstituted volcanic edifice, this procedure also can be used to define different zones affected by erosion and further calculate the local dissection depth (fig. 7). On the other hand, two volcanoes of the Chichinautzin range were also studied. They are located 40 km south of Mexico City. The first one, El Tezoyo, a volcanic dome, is mainly composed by scorias and it lacks of a crater. The second one, Volcan del Aire, is

a cinder cone with a well preserved circular crater. Same calculation procedure was applied for the two volcanoes by using a 10-m resolution DEM (table 2). In order to enhance visual effects, resulting treatments of both were included within the same image (fig. 8a and fig. 8b). The analysis was performed on the upper part of the two volcanoes, taking into account the lower closed contour line as the base line. The treatment was done in order to illustrate the peculiarity of features. For instance (table 1), the lower and greater radius of the crater remain the same. Consequently,

Fig. 7 – Dissection depth provided by the alti- metric difference between the original form and the reconstituted edifice. 1: 1-47 m; 2: 48- 94 m; 3: 95-141 m; 4: 142-188 m; 5: 189-235 m. Fig. 7 – Profondeur de dissection calculée en fonction de la différence hypsométrique entre la forme actuelle et la forme reconsti- tuée. 1 : 1-47 m ; 2 : 48-94 m ; 3 : 95-141 m ; 4 : 142-188 m ; 5 : 189-235 m.

254 Géomorphologie : relief, processus, environnement, 2007, n° 3, p. 247-258 An automated treatment to study the evolution of volcanic cones

Parameters Computed elements Original shape Reconstructed cone Table 2 – Parametric values of El Tezoyo Volcan del Aire and Volcan del Aire volcanoes (original form and reconstituted edifice). Lower radius 391.15 m 391.15 m Base Line Greater radius 795.11 m 795.11 m Tableau 2 – Valeur des paramètres du Lower radius 197.23 m 197.23 m volcan El Tezoyo et du volcan del Aire Crater (forme actuelle et édifice reconstitué). Greater radius 219.32 m 219.32 m Base line 2 350 m 2 350 m Maximum altitude 2 435 m 2 435 m Edifice such result means that the involved Height 85 m 85 m algorithm encountered only one Crater depth 14 m 14 m summit, as it is the case for the Flank Mean angle 14.52 ° 16.55 ° Jocotitlán volcano. On the contrary, Crater Mean angle 7.53 ° 5.69 ° when the crater is almost complete 2D surface 0.801 600 km2 0.801600 km2 Surface (Volcan del Aire), these values are 3D surface 0.828699 km2 0.836409 km2 different (see table 2). Moreover, Total 0.031003 km3 0.035033 km3 Volume the value of the flanks mean slope 3 Difference 0.004031 km can be regarded as an indicator of El Tezoyo the volcanic morphology (14° for Lower radius 482.60 m 482.60 m Base Line the cinder cone, 10° for a dome Greater radius 3 422.66 m 3 422.66 m structure and 17° for a stratovolca- Lower radius 0 m 0 m Crater no complex). Greater radius 0 m 0 m Base line 2495 m 2495 m Conclusion Maximum altitude 2606 m 2606 m Edifice Height 111 m 111 m The procedure presented in this Crater depth 0 m 0 m paper calculates directly from a Flank Mean angle 9.76 ° 9.72 ° DEM, different parameters in order 2D surface 5.564 500 km2 5.564 500 km2 Surface to characterize a volcano. This fast 3D surface 5.623 234 km2 5.623 580 km2 computation procedure (1) can be Total 0.164 705 km3 0.178 806 km3 Volume applied on a volcanic cone indepen- Difference 0.014101 km3 dently of the presence or the absence of a crater, (2) it does not only concern regular cinder cones, and (3) it can be used to study a composite volcano. The first selected test zone, the Jocotitlán volcano, corresponds to a volcanic structure of about 1200 meters in height co- vering a surface of 62.5 km2. An important collapse of the northern flank occurred in pre-historic times. The values obtained by applying such proce- dures are useful to make calculations of parameters such those proposed by Wood (1980). However, the method also can be succesfully applied to perform measurements and analysis such as 3D surface or edifice volume. The reconstitution of the former volcanic landforms offers the possibility to accurately compute the ‘erosion’ and the volume of the displaced material. The whole measurement set can be considered as a new tool, able to discriminate different volcanic cones located in a volcanic field, to quan- tify their relative ages and emphasize the degree of degradation due to erosive processes.

Fig. 8 – 3D diagram of El Tezoyo and Volcan del Aire volcanoes. A: original shape; B: reconstituted volcanoes. Fig. 8 – Bloc diagramme des volcans El Tezoyo et Volcan del Aire. A : forme actuelle ; B : forme recons- tituée.

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