FRACTAL GEOMORPHOLOGY OF THE SLOPES

Transcription

1 FRACTAL GEOMORPHOLOGY OF THE SLOPES ION MAC 1 Keywords: slopes, fractal geometry, functional and geomorphological units, direction of evolution (peneplain, pediments, glacisses). According to approximate calculations, hillslopes represent 35% of the topographic surface of the Earth. Hillslopes behave very much like open systems, having mass and energy inputs and outputs, being characterized by a cascade-like mechanism. These mechanisms draw in masses from the geological substrate and hydrosphere, in a continuous redistribution process from the high part of the terrain to the lower ones. Hillslope as a geomorphological term, refers to a bending surface, connecting drainage divides to talwegs. The latter represents base levels to which erosion and accumulation is related. In places where because of some tectonic, climatic or other causes, the talwegs are absent, hillslopes are related to other topographical levels (i.e. valley bottom, the base of endoreic basins). The study of slopes and their dynamics, the understanding of their specific mechanism of evolution, represents the most important path for the analyses and prediction of exogenetic relief. In the history of slope study, three main trends have been separated: - a traditional one, which stresses the analyses and cartographic representation in the study of the slope processes and slope deposition; - a morphological analyses with measurements and determinations of profiles; - a trend, which has in view the determination of the functional units of theoretical and practical interest. Geometrical analyses From the topographical point of view, a hillslope is characterized by three elements: height, being the vertical distance between the drainage divide or ridge and the lower parts (erosion levels); length, being the distance between the ridge and the insertion with the lower plane and dip angle, respectively the angle formed by the plane of the hillslope and the horizontal plane to which it is related to. (Fig. 1). From a morphological (physiographical) point of view, the hillslope is composed of three main parts: the edge, being the intersection of the upper plane (drainage divide, ridge) with the plane of the hillslope itself; the base (down slope - foot slope), being the intersection of the plane of the hillslope and a reference plane; the middle segment of the hillslope, representing the surface connecting the base with the edge. (Fig. 2) The above-mentioned components form the profile of the hillslope. According to Leopold, Wolman and Miller (1964) the profile of the hillslope depends on the lithology, erosion caused by water, landslides and base levels. According to Penck (1924) the profile of a hillslope is the morphological expression of the relation between tectonical forces that aim to distort the crust and exogenous forces that aim to level it. (Fig. 3) 1 University Babes-Bolyai Cluj-Napoca

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3 Fractal geomorphology of the slopes The term slope, as used in geomorphology, designates some small elements or areas of the land surface that is inclined and not horizontal. Thus, we speak of "mountain slopes", "hill slopes" or "valley-side slopes" with reference to the inclined (ground) surfaces extending from divides and summits down to valley bottoms. From a geometrical point of view, the profile of a hillslope may be formed by a large number of segments that can be: straight, concave, convex, concave-convex, convex- concave and complex. (Fig. 4) The surface of the hillslope or the plane of the hillslope has a variety of geometrical forms as well. It can be plane, truncated cone-convex, truncated cone-concave and reticular. (Fig. 5) The generalized model of the hillslopes reunites its profiles, drawn with relation to a vertical plane, the plane of the hillslopes and the one of the base level. In this way the three dimensional image of the hillslope is created, image that combines several straight, convex, concave segments separated by modulation points or morphological discontinuities.(fig. 6) 91

4 92 Ion Mac By combining the elements of a slope, we can get a model with different aspects. Profile recording is an important part of the investigation of the relationship of hillslope form with: processes, soil characteristics, bedrock features such as weathering grade and jointing slope stability, hydrology, vegetation cover and soils. Morphology and functions of slope profiles The development of slope profiles is one of the most difficult parts of the science of geomorphology. As a result, there is a vast literature concerning the morphological analyses of the slope. Synthesizing the opinions of diverse geomorphologists, we can come to the conclusion that there are diverse territorial situations according to which we can get a synoptic tableau of the types of slopes, each of them having a certain number of morphological units (Fig. 7). 1. The profile composed of only single unit means a straight and reticular front. It occurs on the very resistant rocks. The main processes are falling-in and landfall. 2. The profile composed of two units, the upper one, which is permanently affected by denudation processes, the lower one dominated by the accumulation of materials provided by the upper section. The evolution leads to the decrease of the upper part at the advantage of the lower section. Finally, the whole profile of the slope will only be composed of the accumulation talus, which has extended to the top of the slope. In this respect, there are some ideas that have been formulated by Fisher (1866), Lawson (1915), Lehmann (1933), Wood (1942), and, subsequently, by many other geomorphologists from the German and English school. 3. There is a general consensus of opinion though there have been those with different views, that slopes usually consist of an upper convex section, a middle straight one and a lower concave section. In areas of high relief and vigorous dissection, the straight slope may be very strongly developed and the low concavity reduced or absent (Strahller, 1950, Kirkby, 1969). 4. In a fully developed slope, according to Wood (1942) and King (1962), there are four elements: crest, scarp, debris slope and pediment (Fig. 8). Though locally one or more of the elements may fail to develop in a hillslope, such departure does not contradict the normality of full development. At this stage it may be useful to define the four elements of a hillside slope more closely. The crest (waxing slope) is the summit area of a hill or scarp, usually related to the zone of weathering and measuring from an infinitesimal portion to half the total length of hillslope. The scarp (free face) is the outcrop of bare bedrock exposed on the upper part of the hillslope. It is the most active element in backwearing of the slope as a whole. The debris slope consists of detritus slipped or fallen from the crest and scarp and resting as its angle of repose against the lower part of the scarp face. The pediment (waning slope) is a broad concave remp extending from the base of the other slope elements down to the bank or alluvial plain of an adjacent stream. 5. The nine units landsurface model (Dalrymple, Blong, Conacher, 1968), treats the hillslope system as a three dimensional complex extending from the drainage divide to the

5 Fractal geomorphology of the slopes center of the channel bed, and from the ground surface to the uppermost boundary of weathered rock. Each of the divided slope units is defined in terms of form and the dominant processes currently acting on it (Fig. 9). In reality it is unusual to find all nine units occurring on one slope profile; these do not necessarily occur in the order normally shown in Fig. 9, and the individual units may recur in a single profile. Concave-convex hillslopes are relatively common in many temperate environments, so the order of units may be 1, 2, 3, 6, 8, 9; on steep faces with several rock outcrops the order might be, for example, 1, 2, 3, 4, 5, 4, 5, 4, 5, 6, 8, 9. A cliff above a river might have only the 1, 2, 3 and 4 unit. The model thus provides a mean of describing and a mean of mapping slopes to show how they vary along the contours: it also relates processes to slope forms. Such relationships can be represented in drawings of profiles in blockdiagrams and maps. The nine units landsurface model is concerned with modern processes and their influence on hillslope. 93

6 Ion Mac The evolution of the slope A very important problem is the evolution of slope profiles. In this respect there are three major opinions: flattening, replacement and parallel retreat. This is a very difficult problem, which brings about very contradictory opinions: - Davis and successors have sustained the flattening mechanism of the slopes (Fig. 10). - Penck has formulated the opinion of the evolution of the slopes by fragmentation and erosion due to the exogenic processes. - Wood, King have considered that the most frequently way of analyses of the slopes is the parallel and constant retreat mechanism of the face of the slopes with their profile. 94

7 Fractal geomorphology of the slopes - We can also talk about the complex levelling mechanism (flattening, fragmentation and parallel retreat). Besides the evolution directions already mentioned we could take into consideration new approaching ways of the sub-units of the profile, their measurement, identification and interpretation (Saviger 1952, Young 1963, 1964) (Fig. 11). On the basis of those measurements, new units were brought so that the terminology of the study of the slope was multiplied lately. 95

8 Ion Mac BIBLIOGRAFIE Ahnert, F. (editor) (1976), Quantitative slope models. Zeitschrieft fur Geomorfologie, Supplementband, 25. Butzer, K. W. (1973), Pluralism in geomorphology. Association Of American Geographers, Proceedings, 5. Carson, M. A., Kirkby, M. J. (1972), Hillslope form and process. Cambridge Univ. Press, Cambridge. Dalrymple, Y. B., Blong, R. J., Conacher, A. J., (1968), An hypothetical nine unit land surface model, Zeitschrieft fur Geomorfologie, Supplementband, 12. Davis, W. M. (1924), Die erklarende Beschreibung der Landforms. Ed. Teubner, Leipzig. King, C. A. M. (1966), Techniques in geomorphology. Ed. Arnold, London. King, L. C. (1959), Canons of landscape evolution. Association Of American Geographers Bulletin, 64., 7. Mac, I. (1986), Elemente de geomorfologie dinamică. Ed. Academiei R. S. România, Bucureşti. Mac, I. (1986), Tipuri de versanţi din România. Terra, XVIII, 1. Mac, I. (1996), Geomorfosfera şi geomorfosistemele. Ed. Presa Universitară Clujeană, Cluj- Napoca. Mandelbrot, B. (1982), The Fractal Geometry of Nature. W. H. Freeman, San Francisco, USA. Mandelbrot, B. (1989), Les objects fractals. Flamarion, Paris. Panizza, M. (1978), Elementi di geomorphologia. Ed. Pitagora, Bologna. Penck, W. (1924), Die Morphologische Analyse. Ed. Engelhorn, Stuttgart. Scheidegger, A. E. (1970), Theoretical geomorphology. Ed. Springer, Berlin. Schumm, S. A., Mosley, P. M. (editor) (1973), Slope morphology. Ed. Downer, Hutchinson and Ross, Strondsburg. Strahler,A.N. (1950), Equilibrium theory of erosional slopes approached by frequency distribution analysis. American Journal of Science, 248. Young, A. (1964), Slope profile analysis. Zeitschrieft fur Geomorfologie, Supplementband, 5. Young, A. (1972), Slopes. Ed. Oliver and Boyd, Edinburgh. 96