The shape of the barchan dunes of Southern Morocco
Introduction
A wide variety of dune shapes is found in deserts and has been fitted into numerous classifications by geoscientists. The shapes depend mainly on the amount of available sand and on the change in the direction of the wind over the year Bagnold, 1941, Pye and Tsoar, 1990, Besler, 1992, Lancaster, 1995, Nickling, 1986, Brookfield and Ahlbrandt, 1983, Kocurek, 1996, the most famous being by Bagnold.
The simplest and best known type of dune is the barchan dune, shaped in a crescent, which occurs if the wind comes steadily from the same direction throughout the year and if there is not enough sand to cover the entire surface. Barchan dunes move proportionally to the wind velocity and inversely proportionally to their height. They are encountered for instance in Peru Finkel, 1959, Hastenrath, 1967, Hastenrath, 1987, Lettau and Lettau, 1969, Namibia (Slattery, 1990) and Morocco (Oulehri, 1992). On these dune fields, hundreds of barchans can be found, generally all of the same size. The dunes have heights between 1.5 and 10 m, while their bases are typically 40 to 150 m long and 30 to 100 m wide. The windward or stoss-side of the dune has typical slopes between 8° and 20° and is limited by a sharp edge, called the brink. The brink coincides in many cases with the crest of the dune and separates the slip face from the dune's windward side. Roughly speaking, its plan-shape is a parabola-like curve reaching from the tip of one horn to the point of maximum slip face height and back to the tip of the other horn Fig. 1, Fig. 2.
Despite the fact that for more than 50 years geologists and geographers have been measuring dunes in the field and have obtained data on height, width, length, volume and dune velocity, very little is yet known Hesp and Hastings, 1998, Wiggs et al., 1996 about the exact quantitative shape of barchans. From a mathematical point of view, the barchan dune is a symmetrical object in the wind direction, but in nature there are many factors, like non-steady winds or inclined ground surfaces leading to asymmetrical shapes. Numerical simulations to predict the evolution of barchan dunes and their exact shape have been performed by Wippermann and Gross (1986) and Howard and Morton (1978).
We performed exact measurements of the shape of several dunes instead of doing a large statistical survey in order to have precise surface data. Using these data the volumes of the dunes can be calculated without making any assumptions about their shape. A further objective was a detailed investigation of the scaling of barchan dunes using data from entire profiles instead of simple length, width and height relationships. Finally, we were interested in a simple geometric model in order to describe a barchan dune by only one parameter, which is the height.
Section snippets
The shape of a barchan dune
The crescent-like shape of the barchan is well known qualitatively. The first measurements concerning barchan dunes and their morphologic relationships were performed by Coursin (1964) in Mauritania and Finkel (1959) in the Pampa de La Joya in southern Peru. Hastenrath, 1967, Hastenrath, 1987 analysed barchans in the same area and revisited the site 20 years later. Additional investigations in the same field were undertaken by Lettau and Lettau (1969). Slattery (1990) measured barchan dunes in
The field area
We performed our field measurements in a dune field in the Sahara desert, located in southern Morocco (former Spanish Sahara) near the city of Laâyoune (Fig. 3).
The source of this dune field can be found approximately 100 km NNE of Laâyoune on the shore of the Atlantic ocean, near Tarfaya. The sediments are transported from the coast towards the SSW by the wind parallel to the coast. The entire dune field extends from Laâyoune 200 km to the SSW and 100 km to the NNE and has therefore 300 km in
Measurements
In our study we measured approximately 150 points per dune along certain characteristic lines, as shown in Fig. 5. The total station was placed at three different positions in order to access the entire surface. Some points have been measured twice in order to transform the three local coordinate systems to a common one. These points are located at the tips of the horns, at the toe of the windward side, and at the summit of the dune.
The measured points have been used to interpolate the entire
Morphologic relationships
In this section, we present the typical morphological relations and comparisons with measurements performed by Finkel (1959) in southern Peru. Of course, we cannot present good statistics from only eight measured dunes, but the general relations should still hold true and give us the possibility of comparing our data to previous data. A comparison between the data of Finkel (1959) and others can be found in Hesp and Hastings (1998). For this reason we restrict our discussion to the data of
A simple model for the shape of a barchan
Lettau and Lettau (1969) used a simple geometric shape consisting of parabolas, ellipses and straight lines to reconstruct a standard barchan dune from the measured height, horn width, and total length in order to calculate the volume of the dunes. In a similar way, we introduce here a simple model to describe the shape of a barchan dune, analyzing the precise shape using interpolated surfaces based on our measurements and taking the differences between small and large dunes into account. The
Discussion
The dunes measured in Morocco show typical relationships between height, length, width, and volume as reported from other deserts like the Pampa de La Joya in southern Peru. These simple relationships have led previously to the conclusion that the shape of a barchan is scale-invariant. However, our measurements have disproven this scaling invariance. We have shown an increasing ratio of the horn length to the length of the dune's windward side with height, which leads to different positions for
Acknowledgements
We thank A. Eichhorn and the IAGB of the University of Stuttgart for lending us the equipment, as well as J.-P. Delaporte, PDG of GeoAtlas and El. Moudden Hamid, Directeur Provincial des Travaux Publics Laâyoune, and his team for their support in Morocco. We also thank K. Kroy for many helpful discussions.
This work was partly supported by a scholarship from the DAAD (Deutsche Akademische Austausch Dienst).
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