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The morphometric slope index (MSI) as an indicator of landscape evolution: a multi-scale analysis

L’indice morphométrique de pente comme indicateur de l’évolution d’un paysage : une approche multi-échelle
Laura Coco et Marcello Buccolini
p. 177-186

Résumés

L’un des principaux sujets d’étude des modèles d’évolution du paysage porte sur la relation versant-rivière, étudiée par des moyens expérimentaux en laboratoire, des modèles physiques ou numériques et des études de terrain. Dans cet article, nous discutons des études portant sur l’indice morphométrique de pente (MSI) avec deux objectifs principaux : le valider comme unique indice caractérisant la morphométrie d’une pente et proposer un modèle unique d’évolution du paysage appliqué à plusieurs bassins hydrographiques italiens d’échelle différente. En partant de la reconstruction d’une pente pré-érosion pour 3 sites d’étude à différentes échelles, nous avons réalisé une méta-analyse des données publiées via des analyses statistiques bivariées (corrélation et régression) pour évaluer l’influence de l’indice MSI pré-érosion sur les caractéristiques des réseaux de drainage. Nous avons également introduit un nouveau paramètre pour la caractérisation des réseaux de drainage.

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Notes de la rédaction

Soumis le 24 juillet 2015, accepté le 28 avril 2016.

Texte intégral

The Authors would like to thank Dr Armelle Decaulne, Dr Pierre-Gil Salvador and two anonymous Referees whose suggestions greatly improved the quality of this paper. Moreover, the Authors are very grateful to Prof Ian S. Evans (University of Durham) for the English check of the manuscript and for his precious suggestions about data analysis and validation.

1. Introduction

1Numerous studies demonstrated that the development and setting of drainage systems are strongly influenced by slope topography. This is a classical topic in Geomorphology and Physical Geography studies since the work of Horton (1945), but it is also an up-to-date topic dealt by a large numbers of recent papers. We can find laboratory experiments, numerical or physical modelling and field studies all focused on the river-hillslope relation (Parker, 1977; Schumm et al., 1987; Montgomery and Dietrich, 1989; Oguchi, 1997; Tucker and Bras, 1998; Talling and Sowter, 1999; Pelletier, 2003; Lin and Oguchi, 2004; de Vente et al., 2007). They demonstrated that the final arrangement of the river networks is changed considerably not only by varying the slope gradient, but also their form and the area available for expansion. Moreover, it depends on the dominant erosion process in the watersheds. In particular, the relation between drainage density and slope gradient can be positive or negative (Montgomery and Dietrich, 1989; Oguchi, 1997; Tucker and Bras, 1998; Talling and Sowter, 1999; Lin and Oguchi, 2004; Di Biase et al., 2012). It is negative in steep, mountainous landscapes because they are landslide-dominated: landslides erode the channel banks into gentler ones and fill them, resulting in low drainage density. The relation is positive on gentle landscapes where the erosion is the result of overland flow that allows the incision of stable channels, increasing drainage density.

2Undoubtedly, drainage density (D) is one of the most used parameters for the analysis of drainage networks. Its formulation was made from Horton (1945) as the ratio of the total length of streams in a watershed and its contributing area. Another often used parameter is the drainage frequency (F; Horton, 1945) obtained as the ratio between the number of streams in a watershed and its contributing area. These two indexes describe the basin’s evolutionary stage: a basin with high D and F is well organized therefore is at an advanced evolutionary stage in which the drainage network is fully developed, and vice versa. Their values and spatial distribution are mainly influenced by underlying geology and lithology, climate, vegetation and slope topography.

3Among the most recent studies, Castelltort et al. (2009) quantified the slope-control on drainage basins through mathematical equations that relate the early drainage basin geometry to the initial slope gradient, studying some river basins derived from SRTM topography and confirming some results from Schorghofer and Rothman (2001, 2002). Perron and Fagherazzi (2012) pointed out the importance of the initial topographical surface of hillslopes in landscape evolution: their numerical experiments demonstrated that simple topographies could evolve into complex landscapes with a wide variability and heterogeneity of the final landforms. Hurst et al. (2013) explored the influence of hillslope morphology on the degree of landscape dissection in two sample areas with different lithologies.

4Among the newest techniques, Cellular Automata is used for modelling landscape evolution and fluvial dynamics in spatial and the temporal scales starting from different basic equations for each of the processes involved (such as water flux, transport, fluvial processes, deposition, and different types of geomorphological instabilities). Also these methods demonstrated the influence of the initial slope on the final arrangement of the drainage networks (Davy and Crave, 2000; Crave and Davy, 2001; Dobnikar et al., 2002; Ting et al., 2009; Cirbus and Podhoranyi, 2013). On the other hand, the interaction between river networks and hillslopes is one of the main issues of the landscape evolution models. The papers of Temme et al. (2013) and Tucker (2015) described in detail the main studies on this topic.

5Our previous studies (Buccolini et al., 2012; Buccolini and Coco, 2013; Cappadonia et al., 2015; Coco et al., 2015) combined the main morphometric features of hillslopes in a unique index named Morphometric Slope Index (MSI). Moreover, we developed a methodology for reconstructing the topography prior to stream incision, starting from the actual topography of the basin. We demonstrated that MSI of the pre-erosion hillslope drives the evolution not only of drainage networks but also of erosion landforms in general within river basins. The main outcome was the inverse relation between MSI and D that highlighted the dependence of the drainage network parameters on the pre-erosion slope parameters, aligning these results with the other studies previously described. Furthermore, our studies also demonstrated that the MSI value of the pre-erosion topography drives the type of erosion landforms (slope landforms or fluvial incision).

6In this paper, we introduce an overview of the studies on MSI and validate the procedure considering all the case studies conducted so far. In addition, we conducted a meta-analysis of the data yet published by means of bivariate statistics (regression analysis), introducing a new parameter for the drainage networks. The main goal is to unify the studies about the influence of the pre-erosion MSI on the drainage network parameters at different scales, obtaining a unique law that links MSI to the drainage network parameters.

2. Materials and methods

2.1. Case studies at different scales

7The studies were conducted considering three spatial scales: large, medium and small scale. As a large and medium scale case study, we considered the Italian badlands (named calanchi) that are very dense drainage systems carved into steep clayey slopes, characterised by a close alternation of sharp crests and narrow streams (Alexander, 1980; Moretti and Rodolfi, 2000, Buccolini and Coco, 2010). Ridge heights can vary between a few meters and several tens of metres. The badlands were chosen as sample landforms for developing and testing the methodology of pre-erosion slope reconstruction because they can fully be considered as miniature drainage systems, carved into quite small slopes with rapid evolution (Howard, 1994). Thus, the morphometric features of the pre-erosion slopes can be derived from the surrounding areas, as they are often not yet involved in the erosion. They can be considered as ‘field laboratories’ for the study of landscape evolution, in which hillslope-river coupling is directly observed (Howard, 1994; Yair et al., 2013; Faulkner, 2008). Moreover, the great homogeneity of their geo-lithological and climate features throughout Italy allowed us to isolate relevant morphometric factors. In fact, they affect mainly clayey or sandy-clayey slopes, often with a caprock of conglomerates, in areas with typical Mediterranean climate.

8Italian badlands show two main drainage patterns (Buccolini and Coco, 2010): dendritic and parallel (fig. 1). The former has one main furrow that is tributary to the external drainage network and is similar to a miniature hydrological basin in its evolution (Howard, 1994), while the latter has several parallel furrows and generally evolves through parallel slope retreat (Della Seta et al., 2007). In the case of parallel badlands (Buccolini et al., 2012), the study area was located in northern Sicily in Southern Italy (Catalfimo and Ottosalme) and consisted in two calanchi fronts (fig. 2A). These fronts were subdivided into 65 small basins (called Hydrographic Units in Buccolini et al., 2012) each of which corresponded to a single gully tributary and its surrounding contributing area, and is directly connected to the external drainage network. These basins were analysed using a laser-scanner derived DTM with 2 m resolution provided by the Sicilian Regional Office for Territory and Environment, and represented our large scale study.

Fig. 1Example of parallel and dendritic badlands in the case studies.
Fig. 1Exemple de badlands parallèles et dendritiques dans les études de cas.

Fig. 1 – Example of parallel and dendritic badlands in the case studies.  Fig. 1 – Exemple de badlands parallèles et dendritiques dans les études de cas.

A. The parallel badland of Catalfimo (Sicily); B. One of the badlands in the Atri area (Abruzzo). Modified after Buccolini et al. (2012) and Buccolini and Coco (2013).
A. Badland parallèle de Catalfimo (Sicile); B. L’un des badlands de la région d’Atri (Abruzzes). Modifié d’après Boccolini et al. (2012) et Buccolini et Coco (2013).

Fig. 2Location of the sample areas, delimitation of the basins, and some example of drainage networks tracing.
Fig. 2Localisation des zones d’étude, délimitation des bassins et quelques exemples de réseaux de drainage.

Fig. 2 – Location of the sample areas, delimitation of the basins, and some example of drainage networks tracing.  Fig. 2 – Localisation des zones d’étude, délimitation des bassins et quelques exemples de réseaux de drainage.

A. Orthophotos of the parallel badlands in Sicily for the large scale case study and, in the inset, an example of Horton-Strahler ordering of one HU; B. Location of the dendritic badland basins for the medium scale case study with three enlargements for the DTMs in Tuscany (Orcia Valley area), Marche (Mount Ascensione area) and Abruzzo (Atri area); C. Location of basins for the small-scale case study in Marche and Abruzzo, listed from N to S, with an enlargement showing ordering for a sample basin on the TINITALY DEM.
A. Orthophotos des badlands parallèles en Sicile pour l’étude de cas à grande échelle et, dans l’encart, un exemple d’ordination d’une HU selon Horton-Strahler; B. Localisation des badlands dendritiques pour l’étude de cas à échelle moyenne, avec trois agrandissements des DTM en Toscane (Orcia zone Valley), Marche (Mont zone Ascensione) et Abruzzes (Région Atri); C. Localisation des bassins versants pour l’étude de cas à petite échelle dans les Marches et les Abruzzes, classés du Nord au Sud, avec un agrandissement montrant la production d’un bassin versant avec le MNT TINITALY.

9In the case of dendritic badlands (Buccolini et al., 2013), three sample areas were chosen in Central Italy (Atri in the Abruzzo region, Mount Ascensione in the Marche region, and Orcia Valley in the Tuscany region), in which 81 basins were selected (fig. 2B). They were analysed using a DTM with 10 m resolution derived by processing digital topographic maps at a scale of 1:5000 provided by Abruzzo, Tuscany and Marche Regions. They represent our medium scale study.

10As a small scale case study, we considered some small river basins in the Abruzzo and Marche Regions in Central Italy in order to extend the study to larger drainage systems (Coco et al., 2015). We selected 37 basins set on the Plio-Pleistocene foredeep succession composed by the alternation of clays and sandstones with conglomerates at the top, arranged in a homoclinal structure gently dipping to NE (Bigi et al., 1995; Crescenti et al., 2004). Low-order (cataclinal) symmetrical valleys cut this extensive coastal morphostructure and flow directly into the Adriatic Sea (Buccolini et al., 2007; Aringoli et al., 2015). These basins were chosen as samples (fig. 2C) for their great homogeneity in terms of geological and climatic features. We derived the morphometric data by processing the TINITALY DEM from the Italian National Institute of Geophysics and Volcanology (INGV) with 10 m resolution (Tarquini et al., 2007).

2.2. Characterization of the drainage networks

11The morphometric processing was conducted using ArcGIS 9.3©. For the parallel badland basins, the drainage networks and divides were traced manually based on the orthophotos of the Sicily Region and the parameters were obtained by processing the 2 m cell-size DTM. For the dendritic badlands the drainage networks were traced based on orthophotos provided by the Abruzzo, Tuscany and Marche Regions.

12In the case of the small-scale basins, the drainage features were derived through an automatic procedure by processing the TINITALY DEM. The processing tools were included in the TauDEM (Terrain Analysis Using Digital Elevation Models) toolbox (Tarboton, 1997) developed for ArcGIS. The Single Watershed Model tool was used that automatically delineated stream networks and watersheds starting from the DEM and outlet point shapefiles, and producing the hydrologically correct stream networks and divides shapefiles.

13For each case study, the parameters Drainage Density and Drainage Frequency were derived using the formulas, respectively:

14          D = Ʃ l / A2D  and  F = N / A2D                                    [1]

after measuring the basin areas (A2D) and the total length of the drainage network (l) and counting the number of streams (N) for each Horton-Strahler order. Moreover, we introduce the drainage parameter by computing the ratio between drainage frequency and density (F/D). This parameter was introduced in the study of Dramis and Gentili (1977) and represented a synthesis of D and F.

2.3. Reconstruction of the pre-erosion slopes

15As noted above, the initial slope topography, prior to streams incision, has a great impact on the final arrangement of a drainage system (Pelletier, 2003; Perron and Fagherazzi, 2012). For reconstructing this surface, we developed a methodology (Buccolini et al., 2012; Buccolini and Coco, 2013) that, starting from the current topography, fills the incised valleys.

16We marked the interpolation points between the divides and the current contour lines and considered them as Elevation-Points in the Topo-to-raster interpolation in ArcGIS 9.3© (fig 3). Thus, we obtained the pre-erosion DTM, with the same resolution of the initial DTM, in which the incision of the streams was filled and the surface smoothed. The derived contour lines resulted straight. Often in the case of small basins, a gentle small impluvium remained representing the early stage of the current drainage. One sample case of the pre-erosion slope reconstruction was reported in Figure 3 referring to a dendritic badland basin.

Fig. 3Example of current and pre-erosion DTMs, reconstructed through Topo-to-Raster tool, of a sample dendritic badland basin.
Fig. 3Exemple du DTM actuel et pré-érosion d’un bassin versant de badland dendritique, reconstruits avec l’outil Topo-to-Raster.

Fig. 3 – Example of current and pre-erosion DTMs, reconstructed through Topo-to-Raster tool, of a sample dendritic badland basin.  Fig. 3 – Exemple du DTM actuel et pré-érosion d’un bassin versant de badland dendritique, reconstruits avec l’outil Topo-to-Raster.

A. The image shows the current pre-erosion DTM with superimposed the contour lines (equidistance of 10 m) in light-grey and the interpolation points in white; the stream incision is well highlighted by the colour scale of the DTM in which dark-grey/black represent the most carved areas. B. The image shows the pre-erosion DTM (reconstructed via Topo-to-Raster interpolation) with superimposed the pre-erosion straight contour lines (equidistance of 10 m) in light-grey; the incision results filled and the surface is smooth, as we can see from the colour of the DTM that gradually became darker approaching the external drainage line.
A. L’image montre le DTM actuel avec les courbes de niveau (équidistance de 10 m) en gris-clair et les points d’interpolation en blanc; l’incision fluviale est bien mise en évidence par l’échelle de couleur du DTM sur lequel les plages gris foncé/noir représentent les zones les plus incisées. B. L’image montre le DTM pré-érosion (reconstruit via l’interpolation Topo-to-Raster) avec les courbes de niveau rectilignes pré-érosion (équidistance de 10 m) en gris clair; les vides liés à l’incision sont comblés et la surface lissée, comme nous pouvons le voir avec les plages de couleur du DTM devenues progressivement plus sombres à mesure qu’elles se rapprochent de l’exutoire.

2.4. MSI (Morphometric Slope Index)

17As said before, MSI was created for grouping in a single index the main morphometric features of a slope. It can be calculated using the formula:

          

                                     [2]

where A3D is the three-dimensional surface area of the slope, A2D is the plane surface area, L is the slope’s length and Rc is the circularity ratio. Therefore, MSI includes in a unique index the main linear and areal features of a slope: surface and plan size via A3D and A2D, shape via Rc, length via L, inclination that affect the ratio A3D/A2D, and width that affect the product L· Rc. By substituting the Rc Equation, Eq. (2) can be simplified as follows:

          

            [3]

where p is the slope perimeter. The graphical description of the parameters contained in the MSI formula is shown in Figure 4.

Fig. 4Scheme of the parameters contained in the formula of MSI referred to a sample a dendritic badland basin (the same of fig. 3).
Fig. 4Schéma des paramètres contenus dans la formule de l’indice MSI et appliqués à un bassin versant de badland dendritique (le même que celui de la fig. 3).

Fig. 4 – Scheme of the parameters contained in the formula of MSI referred to a sample a dendritic badland basin (the same of fig. 3).  Fig. 4 – Schéma des paramètres contenus dans la formule de l’indice MSI et appliqués à un bassin versant de badland dendritique (le même que celui de la fig. 3).

L = slope length, A2D = plane area, A3D = surface area, p = perimeter, Rc = circularity ratio.
L = longueur de la pente, A2D = plan surface, A3D = surface, p = périmètre, Rc = rapport de circularité.

18Each parameter was derived by processing the DTMs in ArcGIS 9.3©. The slope length was derived considering the longitudinal profiles of the pre-erosion basin connecting the lowest and the highest point of the divide. On this profile, we measured also the overall slope gradient (S) used for the validation of MSI.

19MSI was firstly tested on badlands and then on small basins considering as slope units the contributing areas delimited by the drainage divides and deriving its value from the pre-erosion surface. In this way, we could obtain the main morphometric features of the pre-erosion slope in a single index, and verify whether it influenced the characteristics of the subsequent drainage network. In the Results section, we describe (i) the validation of MSI via regression statistics and its effectiveness in representing the slope morphometry using all the data at the different scales, and (ii) regression analysis for detecting the influence of the MSI on the drainage network parameters.

3. Results

3.1. Validation of MSI

20The validation of MSI was aimed at verifying if it represents the single slope morphometric parameters. To this purpose, data from the published studies about MSI (Buccolini et al., 2012; Buccolini and Coco, 2013; Coco et al., 2015) were re-elaborated using regression statistics. We measured the regression coefficient between MSI and each of the parameters contained in its formula. Moreover, we performed the regression between MSI and the hillslope gradient (S) for verifying if MSI can represent also the mean slope.

21Figure 5 shows the plot charts and the relative interpolation curves with regression functions and goodness-of-fit measures (R²). The first outcome to point out from these plots was that every parameter considered fitted to MSI with non-linear functions, highlighting the complex relations between MSI and the other slope measures. In particular, a complex curvilinear relation related MSI and Rc with a polynomial function with R² = 0.304 (fig. 5A). The relation between MSI and L was fitted by a power function with positive exponent (R² = 0.955) showing the increasing of MSI with increasing L (fig. 5B). MSI and A3D/A2D were linked by a power-law with negative exponent (R² = 0.846) showing the decreasing of MSI with increasing A3D/A2D (fig. 5C). MSI was related to both A3D and A2D by power functions with positive exponents (R² = 0.986 and R² = 0.987, respectively) pointing out the increasing of MSI with increasing A3D and A2D (fig. 5D and fig. 5E).

22For verifying if also S influeces the value of MSI, we performed a regression also for this parameter, but only for the large and medium scale study cases (i.e. parallel and dendritic badlands basins, respectively). Only in these cases, the ratio could be considered as representative of inclination, giving also more information about the transversal shape of the slope without considering other parameters. Whereas, in the case of medium scale studies (i.e. small basins) we could not consider A3D/A2D as representative of S because it typified a single hillslope, not the complete basin that consisted of various hillslopes with various arrangements. The slope gradient of the entire watersheds (i.e. from the highest to the lowest point) would not be an actual measurement and would not give any information on the general inclination of the basins. Therefore, we performed a correlation analysis between S and A3D/A2D for the large and medium scale data, which revealed their direct correlation (R = 0.972, p < 0.01) that allowed us to considerate A3D/A2D as representative of S. Moreover, the regression analysis revealed that the relation between MSI and S was fitted by an exponential function with negative exponent (R² = 0.921), showing the decreasing of MSI by increasing S (fig. 5F). This result was similar to the relation between MSI and A3D/A2D.

23This validation procedure demonstrated the effectiveness of MSI in representing different slope parameters. In fact, it related not only to the parameters it contains (Rc, L, A3D, A2D, and A3D/A2D), as expected, but also to others not explicitly contained such as S. The regressions indicated that MSI generally increased when the slope was longer, larger, wider and steeper.

Fig. 5Non-linear regression between MSI and the single slope parameters showing data plots and interpolation curves with regression functions and goodness-of-fit measures (R²).
Fig. 5Régression non linéaire entre l’indice MSI et les paramètres de pente montrant les données et les courbes d’interpolation avec les fonctions de régression et les coefficients de détermination (R²).

Fig. 5 – Non-linear regression between MSI and the single slope parameters showing data plots and interpolation curves with regression functions and goodness-of-fit measures (R²).  Fig. 5 – Régression non linéaire entre l’indice MSI et les paramètres de pente montrant les données et les courbes d’interpolation avec les fonctions de régression et les coefficients de détermination (R²).

A. Curvilinear relation between MSI and Rc fitted by a polynomial function in a linear-log plot; B. Relation between MSI and L fitted by a power function in a log-log plot; C. Relation between MSI and A3D/A2D fitted by a power function in a linear-log plot; D. Relation between MSI and A3D fitted by a power function in a log-log plot; E. Relation between MSI and A2D fitted by a power function in a log-log plot; F. Relation between MSI and S fitted by an exponential function in a linear-log plot.
A. Relation curvilinéaire entre MSI et Rc établie par une fonction polynomiale avec une échelle linéaire-log; B. Relation entre MSI et L établie par une fonction de puissance avec une échelle log-log; C. Relation entre MSI et A3D/A2D établie par une fonction de puissance avec une échelle linéaire-log; D. Relation entre MSI et A3D établie par une fonction de puissance avec une échelle log-log; E. Relation entre MSI et A2D établie par une fonction de puissance avec une échelle log-log; F. Relation entre MSI et S établie par une fonction exponentielle avec une échelle linéaire-log.

3.2. Influence pre-erosion MSI on the drainage network

24A regression analysis was conducted for detecting the influence of the pre-erosion slope morphometry described by MSI on the parameters of the drainage network (D, F and F/D) considering the three reference scales of the study. This analysis was a meta-analysis of the published data re-elaborated to unify the results of the previous researches in a single landscape evolution model. We considered MSI as independent variable and D, F and F/D as dependent variables. The regression plots were reported in the Figure 6 and revealed the following main outcomes.

25The first outcome regarded the distribution of the data of D, F and F/D with respect to MSI. As we can see in the plot charts of Figure 6, the data can be clustered in three groups corresponding to the three case studies. The groups were separated by specific thresholds of the values of the parameter:
- parallel badlands (i.e. large scale case study) had D > 0.05 m-1, F > 0.0015 m-² and F/D > 0.03 m-1, and occurred on hillslopes with MSI < 200 m;
- dendritic badlands (i.e. medium scale case study) had 0.015 > D > 0.05 m-1, 0.0001 > F > 0.0015 m-² and 0.007 > F/D > 0.03 m-1, and occurred on hillslopes with MSI < 200 m;
- small basins (i.e. small scale case study) had D < 0.015 m-1, F < 0.0001 m and F/D < 0.007 m-1, and occurred on hillslopes with MSI  > 1,000 m.

26Thus, in general, we could say that the first group included the data of the parallel badland basins and it had low D and F and high MSI; the second group included the data of the dendritic badland basins with medium D and F and medium MSI; the third group included the data of the small basins with low D and F and high MSI.

27The second outcome is about the interpolation of the data points with the regression functions. All the data followed the same functions in which, increasing MSI both D and F decreases accordingly to power-law curves with negative exponents (fig. 6). This means that for small values of MSI (< 200), high decreases of D or F or F/D corresponded to small increases of MSI: this was the case of the large scale case study data (i.e. parallel badlands). On the other hand, for high values of MSI (< 1,000), low decreases of D or F or F/D corresponded to high increases of MSI, and this was the case of the small scale case study data (i.e. small basins). The medium scale case study (i.e. dendritic badlands) had an intermediate behaviour and its data were set around the inflection points of the curves. The overall goodness-of-fit measures given by R² indicated that 88 % of the data for D and F and 85 % for F/D followed the regression functions.

Fig. 6Regression plot charts of MSI with D, F and F/D.
Fig. 6 – Graphiques des droites de régression de MSI avec D, F et F/D.

Fig. 6 – Regression plot charts of MSI with D, F and F/D.  Fig. 6 – Graphiques des droites de régression de MSI avec D, F et F/D.

The data have different colours for the different case studies: grey for large scale (parallel badlands), white for medium scale (dendritic badlands) and black for small scale (small basins). The plot axes are both logarithmic, except for F/D.
Les données ont des couleurs différentes pour les différentes études de cas : gris à grande échelle (badlands parallèles), blanc à moyenne échelle (badlands dendritiques) et noir à petite échelle (petits bassins). Les axes du graphique sont logarithmiques, à l’exception de F/D.

4. Discussion

28The validation of MSI demonstrated its effectiveness in representing the single slope morphometric characteristics. Results of the regression analysis suggested that a single power law could describe the influence of pre-erosion hillslope morphometry on the characteristics of drainage basins, valid from the large to the small scale studies. In small basins with low MSI (like the Sicilian parallel badlands analysed), there are many short streams with many confluences that tend to occupy the entire alimentation area (high D and F); as the basin widens and MSI increased (like in the small Adriatic basins considered), the drainage network tends to stabilize with few streams but longer and few confluences (low D and F), in this case the stream incision deepens (Parker, 1977; Pelletier, 2003). In fact, our data demonstrated that the drainage basins with high MSI had low D and F; vice versa, drainage basins with low MSI had high D and F.

29If we considered basins having the same initial surface (A2D), MSI was high when L and Rc were higher and S lower; these values corresponded to low D and F values which, even if the drainage length and the number of streams are higher, the wide surface did not result in higher D or F. These characteristics were typical of gentle morphologies, which gave rise to organized drainage networks that had many long and stable streams in which valley incision prevailed over mass transport processes (Perron and Fagherazzi, 2012). This was the case of the small basins, which had incised streams and stable drainage networks. In fact, the basins considered were formed on an extensive initial paleo-surface that was gently dipping towards the Adriatic Sea formed during the uplift of the Apennine chain whose remnants currently occupy some of the highest portions of the water divides (Buccolini et al., 2010). These basins had stable, much incised drainage networks and, in many streams, the incision reached the substrate lithologies. Probably the deepening of the streams in this case was also controlled by relative base level lowering due to structural uplift.

30On the other hand, if we still considered basins having the same initial surface (A2D), MSI was low when L and Rc were lower and S higher; these values corresponded to high D and F values. These characteristics were typical of steep morphologies, which gave rise to drainage networks that had many short and often ephemeral streams, and in which mass transport often prevailed over valley incision (Perron and Fagherazzi, 2012). This was the case of Sicilian parallel badlands basins whose drainage networks had a great variability over time, with frequent modifications, even seasonal, of the low order streams. These basins were created on initial steep slopes and were affected by the interplay between slope erosion processes, such as landslides, and stream incision or even piping (Della Seta et al., 2007; Pulice et al., 2012; Cappadonia et al., 2015).

31The middle condition regarded the case of dendritic badlands of Central Italy in which both MSI and the drainage parameters had intermediate values. Actually, these basins were characterized by an intermediate condition between the other two: they have more stable drainage networks with a large number of short streams, and their basins were involved in frequent mass wasting (Moretti and Rodolfi, 2000). Also the initial morphometric conditions of their slopes were intermediate, with slope having an overall steepness between 9° and 30° as demonstrated by Buccolini and Coco (2010).

32The three study areas had quite similar geological, lithological and climatic features: in all of them, the main outcropping lithologies were clays or sand-clays, with the divides often on conglomerates, and the climate was Mediterranean, characterized by the alternation of wet and dry periods. Probably, these characteristics permitted a similar evolution of the three hydrographical situations that could be considered as different stages of drainage basin evolution depending on the initial hillslope morphology and on the external forces involved (Hasbargen and Paola, 2000).

5. Conclusions

33The present paper presented a meta-analysis of the published data about the influence of the pre-erosion slope morphometry described by MSI on the parameters of drainage network (Buccolini et al., 2012; Buccolini and Coco, 2013; Coco et al., 2015) in order to give a unique model of landscape evolution in some multi-scale drainage basins in Italy. We considered three study scales: large scale for the parallel badland basins, medium scale for the dendritic badland basins, and small scale for small basins. Firstly, the procedure for reconstructing the pre-erosion slope topography starting from the current height of the water divides was described. Subsequently, a validation of MSI as unique reference index for the slope morphometry was carried out using regression analysis. Finally, regression analysis was performed for detecting the influence of pre-erosion MSI on the characteristics of the drainage networks.

34The regression analysis between MSI and the parameters contained therein pointed out that it effectively represents and summarizes the main morphometric parameters of slopes (length, inclination, area, shape via L, S, A3D/A2D, A, Rc). The regression analysis between D or F and MSI highlighted the effectiveness of MSI in determining the arrangement of the drainage networks, giving a unique power law that links MSI to D, F and F/D. Moreover, the newly introduced parameter F/D was demonstrated to be useful for characterizing the drainage networks. The use of MSI as summary of the slope morphometric features and of F/D as summary for the drainage network ones could facilitate analysis of the river-hillslope relation in landscape evolution modelling, avoiding the need of multivariate analysis.

35The implementation of these researches could focus on geomorphological hazards considering MSI as a predictor of landscape evolution. The proposed methodology could be also used for predictive studies if we consider current slope topography, characterized by current MSI, as initial topography and, based on it, we could predict the future evolution of the landscape. Not only the future evolution of watersheds can be studied, but the same technique could be applied for studying the evolution of other erosion processes connected to drainage systems dynamic, such as landslides. Thus, current MSI could acquire a double significance: on the one hand, it depends on erosion processes that shaped slope in the past, and, on the other hand, it would be the driver condition for future evolution. Some preliminary studies are launched on this issue for reaching the goal to develop a model for landslide susceptibility.

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Annexe

Version française abrégée

De nombreuses études ont démontré que le développement des systèmes de drainage est fortement influencé par la topographie. Elles ont utilisé de nombreuses méthodes, comme l’expérimentation ou l’utilisation de modèles numériques ou physiques, associés aux études de terrain (Parker, 1977 ; Oguchi, 1997 ; Pelletier, 2003 ; Castelltort et al., 2009, Perron and Fagherazzi, 2012), mais aussi des modèles d’automates cellulaires (Davy and Crave, 2000 ; Cirbus and Podhoranyi, 2013), toutes ces méthodes étant centrées sur les relations versant-rivière.

L’index morphométrique de pente (Morphometric Slope Index : MSI) combine les principales caractéristiques des versants et peut être utilisé pour caractériser les pentes pré-érosion, reconstruites à partir de la topographie actuelle des bassins (Buccolini et al., 2012 ; Buccolini and Coco, 2013 ; Cappadonia et al., 2015 ; Coco et al., 2015). Il a été démontré que le MSI pré-érosion est lié à la densité de drainage (D) et sa valeur contrôle le type d’érosion affectant le paysage.

Cet article fait le point sur l’indice MSI et valide la procédure en considérant toutes les études de cas menées dans les travaux antérieurs. En outre, nous avons effectué une méta-analyse des données publiées au moyen de statistiques bivariées pour obtenir une loi unique qui relie MSI aux paramètres du réseau de drainage.

L’étude a été réalisée en considérant trois échelles spatiales : grande, moyenne et petite échelle. Aux grande et moyenne échelles, nous avons considéré successivement des réseaux de badlands italiens parallèles et dendritiques, qui sont assimilés à des systèmes de drainage miniatures. A petite échelle nous avons examiné quelques petits bassins hydrographiques en Italie centrale, afin d’étendre l’étude à de plus grands systèmes de drainage.

L’analyse morphométrique a été effectuée par traitement à différents niveaux de résolution de modèles numériques de terrain (MNT) avec ArcGIS 9.3. Pour chaque bassin sélectionné, les caractéristiques du drainage ont été tracées, manuellement pour les badlands et automatiquement pour les petits bassins versants. La Densité de Drainage et la Fréquence de Drainage ont été obtenues (D, F) et le paramètre F/D, représentant une synthèse des deux, a été calculé (Dramis et Gentili, 1977).

La topographie de la pente antérieure à l’érosion a été construite à partir de la hauteur actuelle des lignes de partage des eaux (Boccolini et al., 2012). Ces hauteurs ont été utilisés comme "Points-Elevation" (Altitude-Points) dans l’interpolation Topo-to-raster pour obtenir le modèle numérique de terrain (DTM) antérieur à l’érosion, avec la même résolution que le DTM initial, dans lequel l’incision des cours d’eau a été gommée et la surface lissée.

Pour chaque pente reconstruite, l’indice MSI a été calculé par la formule suivante :
          MSI = (A3D/A2D) . L . Rc
où A3D est la surface tridimensionnelle de la pente, A2D est la surface plane, L est la longueur de la pente et Rc est le rapport de circularité. L’indice MSI a d’abord été testé sur les badlands et ensuite sur les petits bassins, considérant comme unités de pente les secteurs contributifs délimités par les lignes de partage des eaux et dérivant leur valeur de la surface antérieure à l’érosion. Nous avons validé l’indice MSI en utilisant toutes les données à différentes échelles, par l’intermédiaire de statistiques de régression comme paramètre représentant efficacement la morphométrie de la pente, puis effectué une analyse de régression pour détecter l’influence de MSI sur les paramètres du réseau de drainage.

Pour la validation de l’indice MSI, nous avons procédé à une analyse de régression entre MSI et les paramètres de pente simples contenus dans sa formule et aussi avec l’inclinaison de la pente (S). Cette procédure a démontré l’efficacité de MSI dans la représentation de différents paramètres de pente, non seulement les paramètres qu’il contient (Rc, L, A3D, A2D et A3D/A2D), comme prévu, mais aussi d’autres paramètres qu’il n’inclut pas explicitement tels que S. Il apparait que l’indice MSI augmente généralement lorsque la pente est plus longue, plus large, plus évasée et plus raide.

Pour détecter l’influence de l’indice MSI sur les paramètres du réseau de drainage (D, F et F/D), nous avons réalisé une méta-analyse des données publiées afin d’unifier les résultats des recherches précédentes en un seul modèle d’évolution du paysage. Nous avons considéré MSI comme une variable indépendante et D, F et F/D comme des variables dépendantes. Deux résultats principaux ont été atteints. Le premier est dans la répartition des données de D, F et F/D par rapport à MSI : les données peuvent être rassemblées en trois groupes correspondant aux trois études de cas. Le premier groupe comprend les données des bassins versant de badlands parallèles, avec de faibles valeurs de D et F et haute MSI ; le second groupe comprenait des données des bassins versants de badlands dendritiques avec le milieu D et F et moyennes MSI ; le troisième groupe comprenait des données des petits bassins versants à faible D et F et un indice MSI élevé. Le second groupe comprend les données des bassins versants de badlands dendritiques, avec des valeurs moyennes de D et F et un indice MSI moyen ; le troisième groupe comprend les données des petits bassins versants, avec de faibles valeurs de D et F et un indice MSI élevé. Le second résultat concerne l’interpolation des données avec les fonctions de régression. Toutes les données ont suivi les mêmes fonctions pour lesquelles, en augmentant l’indice MSI, D et F diminuent selon les courbes de la loi de puissance avec des exposants négatifs. Cela signifie, pour les petites valeurs de MSI (< 200), qu’à une forte diminution de D, F ou F/D correspondent de faibles augmentations de MSI : ce fut le cas pour l’étude à grande échelle (à savoir les badlands parallèles). Par ailleurs, pour des valeurs élevées de MSI (< 1000), à une faible diminution de D, F ou F/D correspondent de plus fortes augmentations de MSI, et ce fut le cas des données de l’étude à petite échelle portant sur les petits bassins versants. L’étude de cas à moyenne échelle (à savoir celle portant sur les badlands dendritiques) a montré un comportement intermédiaire, les données étant positionnées autour des points d’inflexion des courbes. Ces résultats suggèrent qu’une loi de puissance unique pourrait décrire l’influence de la morphométrie du versant antérieur à l’érosion sur les caractéristiques des bassins versants, valables pour les études de la grande à la petite échelle.

Les trois zones d’étude ont des caractéristiques géologiques, lithologiques et climatiques assez similaires: dans chacune d’elle affleurent principalement des argiles ou des sables argileux, avec une ligne de partage des eaux dans des conglomérats, et le climat est méditerranéen, caractérisé par l’alternance de périodes sèches et humides. Il est probable que ces caractéristiques ont permis une évolution similaire des trois situations hydrographiques qui pourraient être considérés comme différentes étapes de l’évolution du bassin versant, fonction de la morphologie du versant initial et des forces externes impliquées.

La mise en œuvre de ces recherches pourrait se concentrer sur les risques géomorphologiques, en considérant l’indice MSI comme un indicateur prédictif de l’évolution du paysage, ou sur des études prédictives envisageant la topographie actuelle de la pente, caractérisée par un indice MSI actuel, comme la topographie initiale et, sur cette base, prévoir l’évolution future du paysage.

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Table des illustrations

Titre Fig. 1 – Example of parallel and dendritic badlands in the case studies. Fig. 1Exemple de badlands parallèles et dendritiques dans les études de cas.
Légende A. The parallel badland of Catalfimo (Sicily); B. One of the badlands in the Atri area (Abruzzo). Modified after Buccolini et al. (2012) and Buccolini and Coco (2013). A. Badland parallèle de Catalfimo (Sicile); B. L’un des badlands de la région d’Atri (Abruzzes). Modifié d’après Boccolini et al. (2012) et Buccolini et Coco (2013).
URL http://geomorphologie.revues.org/docannexe/image/11345/img-1.png
Fichier image/png, 7,0M
Titre Fig. 2 – Location of the sample areas, delimitation of the basins, and some example of drainage networks tracing. Fig. 2Localisation des zones d’étude, délimitation des bassins et quelques exemples de réseaux de drainage.
Légende A. Orthophotos of the parallel badlands in Sicily for the large scale case study and, in the inset, an example of Horton-Strahler ordering of one HU; B. Location of the dendritic badland basins for the medium scale case study with three enlargements for the DTMs in Tuscany (Orcia Valley area), Marche (Mount Ascensione area) and Abruzzo (Atri area); C. Location of basins for the small-scale case study in Marche and Abruzzo, listed from N to S, with an enlargement showing ordering for a sample basin on the TINITALY DEM. A. Orthophotos des badlands parallèles en Sicile pour l’étude de cas à grande échelle et, dans l’encart, un exemple d’ordination d’une HU selon Horton-Strahler; B. Localisation des badlands dendritiques pour l’étude de cas à échelle moyenne, avec trois agrandissements des DTM en Toscane (Orcia zone Valley), Marche (Mont zone Ascensione) et Abruzzes (Région Atri); C. Localisation des bassins versants pour l’étude de cas à petite échelle dans les Marches et les Abruzzes, classés du Nord au Sud, avec un agrandissement montrant la production d’un bassin versant avec le MNT TINITALY.
URL http://geomorphologie.revues.org/docannexe/image/11345/img-2.png
Fichier image/png, 8,3M
Titre Fig. 3 – Example of current and pre-erosion DTMs, reconstructed through Topo-to-Raster tool, of a sample dendritic badland basin. Fig. 3Exemple du DTM actuel et pré-érosion d’un bassin versant de badland dendritique, reconstruits avec l’outil Topo-to-Raster.
Légende A. The image shows the current pre-erosion DTM with superimposed the contour lines (equidistance of 10 m) in light-grey and the interpolation points in white; the stream incision is well highlighted by the colour scale of the DTM in which dark-grey/black represent the most carved areas. B. The image shows the pre-erosion DTM (reconstructed via Topo-to-Raster interpolation) with superimposed the pre-erosion straight contour lines (equidistance of 10 m) in light-grey; the incision results filled and the surface is smooth, as we can see from the colour of the DTM that gradually became darker approaching the external drainage line. A. L’image montre le DTM actuel avec les courbes de niveau (équidistance de 10 m) en gris-clair et les points d’interpolation en blanc; l’incision fluviale est bien mise en évidence par l’échelle de couleur du DTM sur lequel les plages gris foncé/noir représentent les zones les plus incisées. B. L’image montre le DTM pré-érosion (reconstruit via l’interpolation Topo-to-Raster) avec les courbes de niveau rectilignes pré-érosion (équidistance de 10 m) en gris clair; les vides liés à l’incision sont comblés et la surface lissée, comme nous pouvons le voir avec les plages de couleur du DTM devenues progressivement plus sombres à mesure qu’elles se rapprochent de l’exutoire.
URL http://geomorphologie.revues.org/docannexe/image/11345/img-3.png
Fichier image/png, 2,5M
URL http://geomorphologie.revues.org/docannexe/image/11345/img-4.png
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URL http://geomorphologie.revues.org/docannexe/image/11345/img-5.png
Fichier image/png, 2,1k
Titre Fig. 4 – Scheme of the parameters contained in the formula of MSI referred to a sample a dendritic badland basin (the same of fig. 3). Fig. 4Schéma des paramètres contenus dans la formule de l’indice MSI et appliqués à un bassin versant de badland dendritique (le même que celui de la fig. 3).
Légende L = slope length, A2D = plane area, A3D = surface area, p = perimeter, Rc = circularity ratio. L = longueur de la pente, A2D = plan surface, A3D = surface, p = périmètre, Rc = rapport de circularité.
URL http://geomorphologie.revues.org/docannexe/image/11345/img-6.png
Fichier image/png, 77k
Titre Fig. 5 – Non-linear regression between MSI and the single slope parameters showing data plots and interpolation curves with regression functions and goodness-of-fit measures (R²). Fig. 5Régression non linéaire entre l’indice MSI et les paramètres de pente montrant les données et les courbes d’interpolation avec les fonctions de régression et les coefficients de détermination (R²).
Légende A. Curvilinear relation between MSI and Rc fitted by a polynomial function in a linear-log plot; B. Relation between MSI and L fitted by a power function in a log-log plot; C. Relation between MSI and A3D/A2D fitted by a power function in a linear-log plot; D. Relation between MSI and A3D fitted by a power function in a log-log plot; E. Relation between MSI and A2D fitted by a power function in a log-log plot; F. Relation between MSI and S fitted by an exponential function in a linear-log plot. A. Relation curvilinéaire entre MSI et Rc établie par une fonction polynomiale avec une échelle linéaire-log; B. Relation entre MSI et L établie par une fonction de puissance avec une échelle log-log; C. Relation entre MSI et A3D/A2D établie par une fonction de puissance avec une échelle linéaire-log; D. Relation entre MSI et A3D établie par une fonction de puissance avec une échelle log-log; E. Relation entre MSI et A2D établie par une fonction de puissance avec une échelle log-log; F. Relation entre MSI et S établie par une fonction exponentielle avec une échelle linéaire-log.
URL http://geomorphologie.revues.org/docannexe/image/11345/img-7.png
Fichier image/png, 321k
Titre Fig. 6 – Regression plot charts of MSI with D, F and F/D. Fig. 6 – Graphiques des droites de régression de MSI avec D, F et F/D.
Légende The data have different colours for the different case studies: grey for large scale (parallel badlands), white for medium scale (dendritic badlands) and black for small scale (small basins). The plot axes are both logarithmic, except for F/D. Les données ont des couleurs différentes pour les différentes études de cas : gris à grande échelle (badlands parallèles), blanc à moyenne échelle (badlands dendritiques) et noir à petite échelle (petits bassins). Les axes du graphique sont logarithmiques, à l’exception de F/D.
URL http://geomorphologie.revues.org/docannexe/image/11345/img-8.png
Fichier image/png, 885k
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Référence papier

Laura Coco et Marcello Buccolini, « The morphometric slope index (MSI) as an indicator of landscape evolution: a multi-scale analysis », Géomorphologie : relief, processus, environnement, vol.22 - n° 2 | 2016, 177-186.

Référence électronique

Laura Coco et Marcello Buccolini, « The morphometric slope index (MSI) as an indicator of landscape evolution: a multi-scale analysis », Géomorphologie : relief, processus, environnement [En ligne], vol.22 - n° 2 | 2016, mis en ligne le 05 mai 2016, consulté le 20 octobre 2017. URL : http://geomorphologie.revues.org/11345 ; DOI : 10.4000/geomorphologie.11345

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Auteurs

Laura Coco

University “G. d’Annunzio” Chieti-Pescara – Department of Engineering and Geology – via dei Vestini 31 – 66100 Chieti – Italy (lauracoco@libero.it). Tél : +39 0871 3556425.

Marcello Buccolini

University “G. d’Annunzio” Chieti-Pescara – Department of Engineering and Geology – via dei Vestini 31 – 66100 Chieti – Italy (buccolini@unich.it).

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