Geomorphology 201 (2013) 52–59

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Geomorphology

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Erosion of a granite inselberg, Gross Spitzkoppe, Namib Desert

A. Matmon a,⁎, A. Mushkin b, Y. Enzel a, T. Grodek c, ASTER Teamd

a The Fredy and Nadine Herrmann Institute of Earth Sciences, The Hebrew University of Jerusalem, Edmond J. Safra Campus Givat Ram, Jerusalem 91904, Israelb Geological Survey of Israel, 30 Malkhe Israel St., Jerusalem 95501, Israelc Department of Geography, The Hebrew University of Jerusalem, Mt. Scopus, Jerusalem 91905, Israeld M. Arnold, G. Aumaître, D. Bourlès, K. Keddadouche, CEREGE, UMR 6635 CNRS-Aix-Marseille University, BP 80, 13 545 Aix en Provence Cedex 4, France

⁎ Corresponding author. Tel.: +972 265 86703; fax: +E-mail address: arimatmon@mail.huji.ac.il (A. Matm

0169-555X/$ – see front matter © 2013 Elsevier B.V. Alhttp://dx.doi.org/10.1016/j.geomorph.2013.06.005

a b s t r a c t

a r t i c l e i n f o

Article history:Received 2 February 2013Received in revised form 1 June 2013Accepted 10 June 2013Available online 3 July 2013

Keywords:Inselberg erosionCosmogenic isotopesSediment generationHyper arid environmentNamibiaSpitzkoppe

Namibia, with its passive margin setting, long-term tectonic stability, and long-lasting arid climate is a typicalgranitic landscape characterized by numerous dominating inselbergs. The Namib has been the focus of quan-titative studies on the overall rates of bedrock exhumation, escarpment retreat, and sediment generation,transport, and deposition. Results from these studies indicate steady bedrock erosion rates ranging between1 and 5 mm kyr−1 over the last 105–106 yr. This rate was determined from samples collected mostly fromsmall inselbergs with low relief. How fast the large and “classic” inselbergs, which dominate the NamibDesert landscape, erode, generate sediment, and contribute to the overall sediment supply has yet to be sys-tematically examined.We document erosion rates of the Gross Spitzkoppe (GS), one of the largest inselbergs in the Namib Desert,Namibia, based on measured concentrations of 10Be in samples collected from bedrock, boulders, and surfacegrus. The results suggest a slow lowering rate (1–2 mm kyr−1), while the overall slope processes deliver sed-iment to the base of the cliff with 5–6 × 105 atoms g−1 quartz. This concentration is equivalent to an averageerosion rate of ~8 mm kyr−1, 2–3 times faster than the bedrock lowering rate. Thus, the inselberg has beeneroding by cliff retreat. The concentration of cosmogenic isotopes in slope sediment is controlled by exposuretime on the slope, weathering of exposed bedrock, and weathering of subsurface bedrock.Sediment continues to accumulate cosmogenic isotopes while being transported on the flat pedimentssurrounding the inselberg. Within 1–2 km from the base of the GS, the concentration doubles to~10 × 105 atoms g−1 quartz. The increase is achieved by dosing due to exposure and mixing with highlydosed sediment eroded from near subsurface bedrock. From this area, grus is transported through a networkof low gradient channels to the Atlantic Ocean, ~100 km away. Cosmogenic isotope concentration in sedimentincreases to ~30 × 105 atoms of 10Be g−1 quartz, which is 3–4 times higher than that measured in the grusclose to the GS and is controlled by the erosion rate of stable bedrock throughout the entire drainage basin. Dos-ing due to exposure during transport obviously contributes to the overall measured concentration in the sedi-ment as it approaches the ocean.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

The occurrence of inselbergs is common in tropical/subtropical gra-nitic terrains (e.g., Römer, 2007) and also characterizes many semi-aridto arid environments. The dramatic appearance of inselbergs has longattracted human communities and some, such as Ayre Rock (alsoknown as Uluru) in central Australia, are considered holy places. Inarid and hyperarid landscapes the role of inselbergs extends beyondtheir unique appearance. Their topography and the runoff generatedon their exposed bedrock slopes support environments rich in life

972 256 62581.on).

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assemblages (e.g., Burke, 2003, 2005) and has enabled throughout theages, the flourishing of human groups in spite of the generally harshsurrounding conditions (e.g., Kinahan, 1990). The geomorphic under-standing of inselberg development and evolution concentrates aroundtwo end-member concepts: parallel retreat of hillslopes (e.g. King,1957, 1966; Selby, 1977; Thomas, 1978) and down wearing of sur-rounding rock (e.g. Oberlander, 1972; Twidale, 1978, 1993). In bothcases, inselbergs present an erosional remnant that can provide key in-sights into the geomorphic evolution of the terrains in which theyoccur.

Namibia,with its passivemargin setting, long-term tectonic stability,and long-lasting arid climate, has a typical granitic landscape character-ized by numerous inselbergs of various sizes. Consequently,many studieshave been conducted in Namibia regarding basic concepts and hypothe-ses of landscape evolution and geomorphic processes (King, 1953, 1957,1966; Partridge and Maud, 1987; Cockburn et al., 2000; Bierman and

53A. Matmon et al. / Geomorphology 201 (2013) 52–59

Caffee, 2001; Vermeesch et al., 2010; Codilean et al., 2012). In this context,southern Africa has also been the focus of quantitative studies on theoverall rates of bedrock exhumation, escarpment retreat, and sedimentgeneration, transport, and deposition (e.g. Cockburn et al., 2000;Bierman and Caffee, 2001). Results from these studies, which employedgeochronological methods such as fission track counting in apatite andzircons (Cockburn et al., 2000) and cosmogenic isotope exposure ages(Bierman and Caffee, 2001), indicated steady bedrock erosion ratesbetween 1–5 mm kyr−1 over the last 105–106 yr. Whereas sedimentsamples in these studies were collected from drainages of varioussizes, bedrock samples were typically collected from relativelysmall inselbergs or tors, although inselbergs of various sizes are com-mon in the region (Ollier, 1978). Thus, how fast the largest and “classic”inselbergs such as Erongo, Brandberg, and Spitzkoppe (Fig. 1), whichdominate the Namib Desert landscape, erode, generate sediment, andcontribute to the overall sediment supply has yet to be systematicallyexamined.

In this paper we document erosion rates of the Gross Spitzkoppe(GS), one of the largest inselbergs in the Namib Desert. Our study isbased on measured concentration of 10Be in samples collected frombedrock, boulders, and surface grus. We interpret the erosion patternof the GS in context with its surrounding low-relief terrain and in theframework of sediment contribution from the GS to the surroundingfluvial systems. Our results add to the general understanding of insel-berg erosion patterns and sediment supply and transport in low-reliefgranitic terrains in hyperarid environments.

2. Setting

The western Namibian landscape is dominated by: (A) an escarp-ment, parallel to the Atlantic Ocean, that originated during the breakupof Africa and South America ~135 million years ago (Partridge andMaud, 1987; Ward and Corbett, 1990; Brown et al., 2000); (B) theNamib Desert that extends across the coastal plain from the base ofthe Great Escarpment (approximately 1000 m a.s.l., Fig. 1) to the Atlan-tic Ocean; and (C) the highlands, 1500–2500 m above the escarpment(Fig. 1). The Namib Desert is generally a low relief surface where bed-rock is near the surface and is covered by a discontinuous mantle ofalluvium and colluvium (Selby, 1977). Exposed rock surfaces usually

Fig. 1. Study location. Inset: location of study area in the African continent. The locationof the Gross Spitzkoppe (GS) is marked with a red circle. Black lines represent isohyets(mm yr−1).

weather by continuous granular disintegration or the exfoliation ofcentimeter-scale sheets. Sediments resulting from mass wasting dooccur and rock piles are found at the base of large cliffs.

The Namib Desert is hyperarid. Subtropical easterly winds losetheir moisture as they cross the southern part of the African conti-nent, thus, delivering very little rain to its western side (Lancasteret al., 1984; Mendelsohn et al., 2002). Furthermore, the South Atlanticanticyclone, the cold Benguela current, and the resulting coastal up-welling offshore of Namibia, ensure that only little precipitationreaches the coast (Lancaster et al., 1984; Mendelsohn et al., 2002).Mean annual precipitation is b25 mm on the coast and 50 to200 mm at the base of the escarpment.

The GS (Fig. 2) is one of the largest inselbergs in Namibia. It is a land-mark rising ~600 m above its surrounding low-relief plain and peakingat 1728 m a.s.l. The granite comprising the GS belongs to the group ofthe magmatic complexes which dominated the geological events dur-ing the late Karoo ages (~150 Ma). The granitic bodies of the Karooare intruded into the Damara supergroup metamorphic rocks, whichunderlie the eroded plains surrounding the inselberg (Partridge andMaud, 1987). The lower part of the GS is mostly mantled by colluvialwedges composed of boulders, angular clasts and grus. The upper partof the inselberg presents vertical granitic cliffs (Figs. 2–4). Soil is absentfrom most of the inselberg and located only in small and protectedpockets. Vegetation occurs within these soil pockets, in the numerousgullies that drain from the mountain, and at the base of the inselberg.The GS is located in the Omaruru River drainage basin. This riverheads above the Great Escarpment in the EtjoMountains at an elevationof ~1450 m a.s.l. and drains an area of ~15,700 km2.

3. Methods

Samples for 10Be concentration measurements were collected alongobserved pathways of sediment generation and transport on the steepslopes of the GS (Fig. 3). Field observations at the study site indicatethat bedrock erodes through two primary mechanisms: 1) discreterock falls that produce a large number of boulders, which concentratein narrow gullies, and 2) grain-by-grain erosion of the surfaces of bothboulders and bedrock. We assume that the bedrock and boulder facesthat have been exposed for a long time will produce quartz grainsheavily dosed with cosmogenic isotopes. In contrast, grus producedfrom fresh bedrock scars, from previously shielded boulder faces andbedrock buried beneath amantle of boulders, will yield a lower concen-tration of cosmogenic isotopes. The downslopemovement of grus in the

Fig. 2. General view of the GS (Gross Spitzkoppe). The inselberg rises ~600 m abovethe flat lying surrounding plain and is composed of Cretaceous granite. Bedrock is ex-posed along most of the slope area. Grus accumulates and overlies bedrock only at thebottom parts of the slope and on the plain (see also Figs. 3 and 4).

Fig. 3. Sediment pathways sampled in this study. A) Trace of two pathways indicatedby black arrows. They converge at the base of the inselberg. B) The 1st pathway withsample locations indicated by white arrows. C) The 2nd pathway with sample locationsindicated by white arrows.

54 A. Matmon et al. / Geomorphology 201 (2013) 52–59

GS is episodic and is controlled by surface flow associatedwith rare rainstorms in this hyperarid environment. The steep gradients of the GSslopes promote downslope sediment transport that is also assisted bybioturbation.

Following a field survey, we collected a total of 17 samples. Amongeight bedrock samples, six are from the slopes of the GS, and two fromthe plain approximately 500 m north of the base of the GS (Fig. 3). Of

the six slope samples, two (SK11 and SK13) were collected from flatlying, varnished surfaces without an indication of recent and signifi-cant erosion (Fig. 4E). We consider them to be stable and continuous-ly slow-eroding surfaces. Three samples (SK1, SK2, and SK3) are froma base of one of the cliffs that lead up to the summit. Such cliffs areformed by repeated rock-fall events (Fig. 4D). Two of these threesamples (SK1 and SK3) were collected from the rock surface at thebase of the cliff. The third sample (SK2) was collected from the cliff it-self, about 2 m above its base. One sample (SK9) is from a bedrockoutcrop within a boulder-chocked gully (Fig. 4F). It may have beencovered by boulders and grus and only intermittently exposed. Thebedrock granite in this outcrop is weathered. Of the two bedrocksamples collected from the plain, one is from underneath 40 cm ofsoil and grus cover (SK14) and the other was from an exposed out-crop standing 20–30 cm above its surroundings (SK16).

Eight grus samples (SK4–8, SK12, SK15, and SK17) were collectedalong two pathways of grus transport initiating at the foot of bedrockexposures on the slopes and ending in the plain north of the GS. Sam-ple SK10 is an amalgamation of chipped-off rock pieces from 10 boul-ders scattered in a steep gully on the GS slope.

Although we mostly discuss the results in terms of isotope con-centrations, we also consider the concentrations in terms of equiva-lent erosion rates following Lal (1991) and assuming:

t ≫ 1= λþ μεð Þ ð1Þ

ε ¼ 1=μ P=N−λð Þ ð2Þ

where t is the time period; μ is the absorption coefficient (cm−1), whichis equal to ρ/Λwith ρ the target's density (g cm−3) and Λ the attenuationlength (g cm−2); ε is the erosion rate; and λ is the decay constant of themeasured nuclide; P is the production rate (atoms g−1 yr−1), and N isthe measured concentration (atoms g−1). P was scaled for latitude andaltitude following Stone (2000). The influence of topographic obstruc-tions and target geometry was calculated following Dunne et al.(1999). Samples were prepared at the Cosmogenic Laboratory, the He-brew University of Jerusalem, following the procedures of Bierman andCaffee (2001). 10Be/9Be ratios of samples SK3 and SK16 were measuredat theANTARESAcceleratorMass Spectrometry (AMS) facility at theAus-tralian Nuclear Science and Technology Organization (ANSTO) (Fink andSmith, 2007). All other samples were measured at the accelerator massspectrometry (AMS) facility (ASTER) at Cerege, Aix-en-Provence, France.All samples were normalized relative to the NIST SRM standard with a10Be/9Be ratio of 2.79 × 10−11 ± 0.03 × 10−11. This standardizationagrees with the 07KNSTD series of standards. A sea level high latitudespallation production rate of 4.43 ± 0.52 atoms g−1 SiO2 yr−1 (Balcoet al., 2008; updated at http://hess.ess.washington.edu/) was used forage and erosion rate calculations. Muon production values and attenua-tion lengths are from Granger and Muzikar (2001) and Granger andSmith (2000). A neutron attenuation length of 165 g cm−2, 10Be decayconstant of 4.99 × 10−7 yr−1, and absorption coefficient of 0.0138 ±0.001 cm−1were used for all calculations (Balco et al., 2008).We applieda rock density of 2.65 g cm−3.

4. Results

Measured 10Be concentrations (Table 1) range between 0.46 ±0.03 × 105 and 29.50 ± 0.81 × 105 atoms g−1 SiO2, with analytical un-certainties between 3% and 5%. Equivalent erosion rates range between1.2 ± 0.2 and 94.3 ± 12.7 mm kyr−1. 10Be concentrations measuredin samples fromflat-lying bedrock (SK11, SK13, SK14, and SK16) are uni-form and average 27 × 105 atoms g−1 SiO2. These concentrations areequivalent to an average erosion rate of ~1.5 mm kyr−1. The concentra-tions measured in bedrock samples SK1, SK2, and SK3 are 9.75 ±0.36 × 105, 4.00 ± 0.15 × 105, and 3.01 ± 0.10 × 105 atoms g−1 SiO2,respectively. These concentrations are equivalent to erosion rates of

Fig. 4. Photographs and images of the study area. A) Google Earth image of the northern slope of the GS and the plain extending northward from the inselberg. The base of thenorthern slope of the GS is apparent at the right side of the image. Dashed line indicates the location of channel initiation. Marked channels do not develop within a belt of1–2 km width around the inselberg. B) Photo of the northern plain extending from the base of the GS. The initiation of channels at a distance from the base of the inselberg is in-dicated by the appearance of vegetated stripes. C) Lower part of the GS slopes showing the transfer from bedrock cliffs to the lower colluvial aprons. D) Bedrock cliffs formed byboulder detachment. Samples SK1, SK2, and SK3 were collected from this kind of site. E) Flat-lying bedrock outcrop (right side of the photo). Samples Sk11 and SK13 were collectedfrom this kind of site. Grus accumulates at the foot of such outcrops (on the left of the photo). Samples SK4 and SK12 were collected from this kind of site. F) Weathered bedrockexposed at the base of the boulder-chocked gully.

55A. Matmon et al. / Geomorphology 201 (2013) 52–59

4.7 ± 0.6, 11.4 ± 1.5, and 17.0 ± 2.2 mm kyr−1 or to exposuretimes of 127 ± 14, 54 ± 6, and 36 ± 4 kyr, respectively. The bedrocksample collected from the base of a boulder-chocked gully (SK9)yielded the lowest concentration among all samples (0.46 ± 0.03 ×105 atoms g−1 SiO2).

Grus samples yielded 10Be concentrations between 2.34 ±0.09 × 105 and 10.55 ± 0.39 × 105 atoms g−1 SiO2. These concentra-tions are equivalent to erosion rates between 19.2 ± 2.5 and 4.3 ±0.6 mm kyr−1. Sample SK10, which is an amalgamation of rock frag-ments collected from 10 boulders, yielded a 10Be concentration of5.57 ± 0.25 × 105 atoms g−1 SiO2. This concentration is equivalent toan erosion rate of 8.7 ± 1.2 mm kyr−1, similar to those of the severalgrus samples. Based on the 10Be concentration in all samples, the calcu-lated steady state erosion rates could be valid over a period range of ~10to 600 kyr. However, most of the samples yielded erosion ratesb10 mm kyr−1, which are valid over periods N105 yr.

5. Discussion

5.1. Bedrock samples and long-term inselberg erosion

Bedrock samples can be categorized into three groups: 1) stable,continuously eroding, flat lying, horizontal bedrock outcrops (samplesSK11, SK13, SK14, and SK16), 2) bedrock outcrops positioned at thebase or on steep cliffs formed by the detachment of boulders (samplesSK1, SK2, and SK3), and 3) eroded bedrock exposures cropping out be-tween boulder piles at the base of a steep gully (sample SK9).

All samples from the first group yielded high 10Be concentrations(Table 1) indicating low erosion rates of ~1.5 mm kyr−1, regardless oftheir elevation and their position on, or near, the inselberg. These ero-sion rates are similar to bedrock erosion rates calculated in otherareas in Namibia (e.g. Cockburn et al., 1999; Bierman and Caffee,2001). Surprisingly, sample SK14 (Table 1), collected from beneath a

Table 1Cosmogenic isotope samples from Gross Spitzkoppe, Namibia.

Name Latitudea Longitudea Elevation(m a.s.l.)

Sample type Shieldingfactorb

Quartz(gr)

Be carrier(mg)

10Be/9Be(10−13)

Error 10Be (105 atoms g−1

quartz)Error Erosion rate

(mm kyr−1)Error

SK1 21°S 49.236 15°E 10.197 1275 Bedrock 0.898 24.299 0.287 12.336 0.382 9.747 0.359 4.7 0.6SK2 21°S 49.233 15°E 10.206 1283 Bedrock 0.852 24.602 0.276 5.345 0.169 4.003 0.150 11.4 1.5SK3 21°S 49.231 15°E 10.217 1266 Bedrock 0.814 22.779 0.212 4.840 0.120 3.010 0.100 17.0 2.2SK4 21°S 49.231 15°E 10.217 1266 Grus 1 24.619 0.268 3.886 0.126 2.827 0.108 16.8 2.2SK5 21°S 49.197 15°E 10.244 1230 Grus 1 24.324 0.291 3.699 0.138 2.959 0.125 15.5 2.0SK6 21°S 49.153 15°E 10.240 1178 Grus 1 24.066 0.303 5.399 0.183 4.538 0.178 9.6 1.3SK7 21°S 49.103 15°E 10.247 1140 Grus 1 24.441 0.308 6.223 0.196 5.233 0.195 8.0 1.1SK8 21°S 49.174 15°E 10.286 1140 Grus 1 24.385 0.274 2.982 0.100 2.238 0.087 19.2 2.5SK9 21°S 49.144 15°E 10.292 1154 Bedrock 0.868 25.060 0.290 0.595 0.030 0.460 0.025 94.3 12.7SK10c Between SK9 and SK11 1154–1224 Boulder amalgamation 1 22.009 0.299 6.132 0.242 5.565 0.246 8.7 1.2SK11 21°S 49.164 15°E 10.359 1224 Bedrock 0.945 22.007 0.301 27.835 0.850 25.424 0.928 1.7 0.3SK12 21°S 49.164 15°E 10.359 1224 Grus 1 22.012 0.294 6.126 0.196 5.469 0.206 9.3 1.2SK13 21°S 49.343 15°E 10.329 1302 Bedrock 0.922 22.015 0.302 28.734 0.990 26.320 1.049 1.6 0.3SK14 21°S 48.609 15°E 10.082 1106 Bedrock 1 22.004 0.296 30.468 0.690 27.387 0.827 1.4 0.2SK15 21°S 48.628 15°E 10.100 1108 Grus 1 22.015 0.297 9.367 0.322 8.443 0.336 5.4 0.7SK16 21°S 48.543 15°E 09.997 1100 Bedrock 1 17.448 0.213 36.120 0.580 29.500 0.810 1.2 0.2SK17 21°S 48.483 15°E 09.999 1100 Grus 1 22.002 0.275 12.636 0.397 10.545 0.393 4.3 0.6

Note: All bedrock samples are granite. Shielding factors calculated following Dunne et al., 1999.a WGS84.b Production rates used in erosion rate calculations consider these shielding factors.c Amalgamation of chips from top and bottom of 10 boulders.

56 A. Matmon et al. / Geomorphology 201 (2013) 52–59

40 cm cover of soil and grus, yielded a similar concentration as the ex-posed stable bedrock samples. The similarity in erosion rates, regardlessof position and elevation, suggests that the landscape is being loweredvery slowly and uniformly. 10Be concentrations from group 2 arelower than those of group 1 and indicate more active bedrock surfaces.The lower concentrations can be explained by rock faces exposed fol-lowing the detachment of boulders and therefore, a shorter exposuretime than that of the stable surfaces. For category 2 samples the total ac-cumulation of isotopes depends primarily on the timing of the last boul-der detachment: a bedrock face that was exposed by a more recentboulder detachment will yield a lower 10Be concentration and by infer-ence, a higher equivalent erosion rate than a bedrock face exposed by anearlier event. Erosion rates on the bedrock slopes and cliff faces are 2–3times higher than those of the flat and stable surfaces. This differentialerosion supports a long-term characteristic steep relief for theGS. In ad-dition, these results support King's (1966) suggestion that, over time,this inselberg has been eroding mostly through cliff retreat with verylittle change in relief.

10Be concentration from bedrock sample SK9 is low (0.46 ±0.03 × 105 atoms g−1 SiO2) relative to all other bedrock samplesanalyzed in this study. This low concentration can be explained bydifferent causes but most probably is the result of its unique geomor-phic setting in the boulder-choked gully where it was episodicallyshielded by overriding boulders and/or sediment. For example, if con-tinuously covered by 80 cm of grus, the measured concentrationwould be achieved in 10 to 15 kyr. In any case, the contribution ofsediment from weathering of such low-dosed bedrock to the overallsedimentary budget must be low because most of the landscape isnot covered by such large boulder piles that shield the rock from cos-mic radiation.

Overall, the calculated bedrock erosion rates on the GS fit wellwith the global trend of erosion in diverse climatic zones and theyare comparable to rates calculated in other arid regions of the world(Bierman and Caffee, 2001, 2002; Haviv et al., 2006; Matmon et al.,2009; Boroda et al., 2011). Furthermore, Portenga and Bierman(2011) found that igneous rocks erode under various climatic andtectonic conditions at rates between b1 and ~100 mm kyr−1. How-ever, the majority of their compiled data suggests that erosion ratesof igneous rocks range between 1 and 10 mm kyr−1, with an averageof 8.7 ± 1.0 mm kyr−1 (n = 230). Excluding the unique sample SK9,our bedrock samples yielded erosion rates within this restrictedrange.

5.2. Grus samples

10Be concentrations from grus samples range between 2.24 ±0.09 × 105 and 10.55 ± 0.39 × 105 atoms g−1 SiO2 and they tend toincrease downslope (Fig. 5). This increase can be attributed to: 1) iso-tope accumulation due to increasing residence time of the grus as ittravels downslope, and 2) additional contribution of highly-dosed sed-iment from the erosion of stable bedrock surfaces along the grus path-way. The contribution of low-dosed sediment derived from the erosionof subsurface bedrock, will negate this overall increase to some extent.

Two pathways of sediment generation and transport, each ap-proximately 1.5 km long, were identified in the field (Fig. 3). Thefirst initiates at the location of grus sample SK4, immediately belowwhere bedrock samples SK1–3 were collected. Downslope, the loca-tions of grus samples SK5–7 define the pathway. Grus samples SK15and SK17 were collected from the continuation of this pathway onthe plain. Bedrock sample SK14 collected from the bedrock buried be-neath a mantle of grus on the plain and bedrock sample SK16 collect-ed from exposed rock on the plain may represent the source foradditional sediment generated on the plain itself. The second path-way initiates at the location of grus sample SK12 and its associatedbedrock source (samples SK11 and SK13). The locations of grus sam-ples SK7–9 define the downslope pathway. Samples from the plain(SK14–17) are identical to those of the first pathway.

In the first pathway (Fig. 3), bedrock samples (SK1–3), which repre-sent the sediment source, yielded 10Be concentrations of 3.01 ±0.10 × 105, 4.00 ± 0.15 × 105, and 9.75 ± 0.36 × 105 atoms g−1

SiO2, respectively. However, the grus sample (SK4) collected immedi-ately below the cliff of these bedrock samples yielded a slightly lowerconcentration of 2.83 ± 0.11 × 105 atoms g−1 SiO2. If the cliff werethe only source for the grus at its base, we would expect the grus toyield a concentration as high as that of the cliff, or slightly higher dueto residence time of the grus at the surface. However, since the grusconcentration is lower, there must be another source for grus withlow 10Be concentration that would mix with the grus eroding fromthe cliff. Themost likely source is the erosion of subsurface granite bed-rock. Therefore, on the slopes of the GS, our results indicate low-dosedsubsurface contribution of grus to the overall sedimentary inventory.Grus derived from subsurface granite could contain a low 10Be concen-tration since it may erode faster and is dosed by a lower production ratethan exposed bedrock. A similar conclusion has been reached in previ-ous studies on other granitic terrains in arid and hyperarid regions

A

B

C

Fig. 5. 10Be concentrations in grus samples. A) 1st sediment transport pathway, with alinear fit including all samples and indicating a dosing rate of 470 atoms m−1. B) 1stsediment transport pathway, with a linear fit including only samples on the slopeand indicating a dosing rate of 904 atoms m−1. C) 2nd sediment transport pathway.Linear fit includes all samples and indicates a dosing rate of 430 atoms m−1.

57A. Matmon et al. / Geomorphology 201 (2013) 52–59

such as the southern Negev Desert, Israel (Clapp et al., 2000) and theSW USA (Clapp et al., 2001, 2002).

A linear fit that includes grus samples collected on the slope of theGS (SK4–7) indicates a steady increase in 10Be concentration at a rateof 904 atoms m−1 (Fig. 5B). This rapid increase rate is somewhatmisleading as the actual increase is only from 2.83 ± 0.11 × 105 to5.23 ± 0.20 × 105 atoms g−1 SiO2. However, it occurs over a shortdistance (200–300 m). Since the increase in concentration is the re-sult of production due to exposure and addition from both surfaceand subsurface bedrock erosion, the variables that control the rateof increase are residence time of grus on the slope, production rate,and rock weathering rate. Furthermore, bedrock may erode in alarge range of rates thus providing a mix of low dosed grus fromfast weathering subsurface bedrock and highly dosed grus fromslow weathering exposed bedrock. Therefore, a simple sedimenttransport rate cannot be calculated from the increase in cosmogenicisotope concentration. Nevertheless, if the increase in concentrationis all ascribed to exposure time on the slope, a transport rate of~1 cm yr−1 is calculated.

For all grus samples from thefirst pathway (SK4–7, SK15, and SK17),a linear fit indicates an average dosing rate of 470 atoms m−1 (Fig. 5A).The dosing rate on the flat part of the pathway, between the locationsof samples SK7 and SK17, is 416 atoms m−1, equivalent to a grus

transport rate of 2 cm yr−1. The relatively slow dosing on the flat partis the result of the greater distance overwhich it is calculated. The actualincrease is from 5.23 ± 0.20 × 105 to 10.55 ± 0.39 × 105 atoms g−1

SiO2, greater than that on the slopes.In the second pathway (Fig. 3), bedrock samples (SK11 and SK13),

which represent the sediment source, yielded 10Be concentrations of25.42 × 105 ± 0.93 × 105 and 26.32 × 105 ± 1.49 × 105 atoms g−1

SiO2. However, the grus sample (SK12) collected immediately belowthe cliff of sample SK11 yielded a lower concentration of 5.47 ×105 ± 0.21 × 105 atoms g−1 SiO2. Similarly to the first pathway, ifthe cliff were the only source for the grus at its base, we would expectthe grus to yield a concentration equal to or higher than that of thecliff. Since the grus concentration is lower, theremust be another sourcefor grus with low 10Be concentration that would mix with the gruseroded from the cliff. Again, this is most likely due to the erosion of sub-surface bedrock. Along this pathway the trend of increased 10Be concen-tration is not as clear as in the first one. On the slope of the GS, samplesSK12, SK8, and SK7 define the pathway. 10Be concentrations on samplesSK12 and SK7 are similar, showing no increase downslope. Sample SK8is an outlier with a decrease. This behavior may occur because sampleSK8 was collected from the bottom of a boulder-chocked gully. Never-theless, when all samples in this route are considered (SK12, SK8, SK7,SK15, and SK17)we see a steady increase in 10Be concentration. A linearfit to all samples indicates a dosing rate of 430 atoms m−1, very similarto that of the first route (Fig. 5). Both sediment pathways suggest simi-lar characteristics for the generation of grus and its downslope trans-port, including the contribution of low-dosed material derived fromthe erosion of subsurface granite, and the downslope increase in 10Beconcentrations due to the residence time of the grus on the slope.

Although our data do not allow us to quantify the relative contribu-tion of each variable (exposure time on the slope, weathering of ex-posed bedrock, and weathering of subsurface bedrock) to the totalconcentration of 10Be in the grus, the final concentrations at the baseof the slope, given by samples SK7 and SK10, are 5.23 ± 0.20 × 105

and 5.56 ± 0.25 × 105 atoms g−1 SiO2, respectively. These concentra-tions correlate to erosion rates of 8.7 ± 1.2 and 8.0 ± 1.0 mm kyr−1,respectively. Concentrations of 10Be in the grus increase to 8.44 ±0.34 × 105 and 10.55 ± 0.39 × 105 atoms g−1 SiO2 (samples SK15and SK17, respectively) on the flats or aprons within ~1 km from theinselberg's base (Fig. 4A,B) by dosing and/or mixing with highly dosedbedrock, as measured in samples SK14 and SK16. The increase inconcentration on the flats indicates dosing rates between 290 and530 atoms m−1. From a distance of 1–2 km from its source all theway to the Atlantic Ocean (~100 kmaway), grus is transported througha network of low gradient channels during rare floods (e.g., Morin et al.,2009). Bierman and Caffee (2001) measured a 10Be concentration of2.95 × 106 atoms g−1 in sediment at the outlet of the Omaruru River.Within 1σ, this concentration is similar to concentrations measured inour study on stable bedrock surfaces, but 3–4 times higher than thatmeasured for grus samples SK15 and SK17. The increase in concentra-tion along the route to the ocean could be achieved in three ways:(i) dosing due to exposure during transport, (ii) contribution of sedi-ment from subsurface rock, and/or (iii) mixing with sediment derivedfrom other highly-dosed bedrock surfaces. A transport rate of36 cm yr−1 is calculated for the grus on the assumption that the in-crease in 10Be concentration is entirely due to production during expo-sure at a production rate of 7.6 atoms g−1. However, the massivecontribution of highly dosed sediment from bedrock, as discussedbelow, implies a much faster transport rate.

The general trend inferred from the increase of 10Be concentrationin sediment from the GS to the ocean is that stable bedrock, whetherexposed or buried under a mantle of transported grus, controls thecosmogenic isotope inventory in sediment in this part of Namibia. Sta-ble bedrock erodes at 1–2 mm kyr−1, and supplies sediment with a10Be concentration of 2.5–3 × 106 atoms g−1. Therefore, sedimentgenerated on the GS slopes with a much lower concentration is

58 A. Matmon et al. / Geomorphology 201 (2013) 52–59

mixed and diluted with a greater amount of sediment derived fromstable bedrock. The increase in concentration is traced down the GSslope, across the 1–2 km apron surrounding the mountain, and inthe network of channels that deliver sediment to the ocean. Obviously,the increase in concentration stops when it reaches that of stable bed-rock. An implication of the above description is that most of the sedi-ment in central Namibia is generated from very stable bedrocksurfaces. Although the erosion rate of such bedrock is slow and theamount of sediment generated per unit area is small, the large areain which such sediment is generated compensates for the slow rateof sediment generation. On the other hand, large inselbergs, althougherode faster and may supply more sediment per unit area, providevery little sediment to the overall sediment budget of this region.

Although many studies in arid environments examined the concen-tration of cosmogenic isotopes in alluvium and colluvium to determineerosion rates, only a few studies determined the rate of sediment (orgrus) transport downslope and on gently tilted plains. Nichols et al.(2002, 2005, 2006) determined grus transport rates of 16–63 cm yr−1,depending on the complexity of themodel used, atGraniteMt., southernMojave Desert, California. At Iron Mt. they calculated rates between 65and 122 cm yr−1, which are of the same order of magnitude as thosemeasured in this study. Themean annual precipitation in both locationsis similar (~100 mm yr−1) as are the gradients of the pediment surfacesover which sediment is transported. Boroda et al. (2011) determinedsediment transport rates on low-gradient talus slopes in the Negev De-sert, Israel, which are three orders of magnitude slower than those cal-culated in Namibia. One reason for this is a more arid climate in theNegev. Another reason is lithological diversity. In theNamib andMojaveDeserts, grus results from the erosion of plutonic rocks. The size andshape of the grains in the grus is determined by those of crystals in theparent rock. Therefore, in these deserts most grains are spherical tosub-angular and b1 cm in diameter. In contrast, grus in the Negev isfrom chert and consists of flat and tabular grains 1–3 cm in size, andthe mobility of such grains tend to be lower.

The results of this study have implications for the major factors oferosion and the circular links between erosion and isostasy in passivemargin landscapes such as Namibia. This study has presented that theretreat rates of the inselberg's flanks are faster than the lowering rate

Fig. 6. Schematicmodel presenting the erosional pattern of the GS and its surrounding. Not to scthe base of the inselberg. Gray patch on slope indicates colluvial apron. Plain text—10Be concenresponds qualitatively to value. Numbers under “Inselberg slope”, “Proximal pediment”, and “Dunderlined. Bedrock erosion rates and 10Be concentration in samples from pediment are from

of the surrounding landscape. Nevertheless, the lowering of the land-scape poses a limiting boundary to the retreat rate as it determinesthe local base level for the inselberg (e.g. Whipple, 2001; Willettand Brandon, 2002). In turn, the general lowering rate of the land-scape is controlled by the rate at which channels incise into thelow-relief flat plains, and this incision expresses the response of thefluvial system to the isostatic uplift of this tectonically inactive pas-sive margin. On the other hand, the rate of isostatic uplift is dictatedby the overall rate of landscape erosion. The implication of such acycle is that, given that the climate remains arid to hyperarid andthat tectonic activity is not renewed, rates of erosion will slowly de-crease as the relief of the inselbergs diminishes. This will eventuallydecelerate isostatic uplift and will throw the Namibian landscapeinto a “fossil” state.

6. Conclusions

Our results suggest a slow lowering rate of the landscape in the GSarea. On the other hand, the rate of cliff retreat is 2–3 times faster(Fig. 6). Thus, the inselberg has been eroding by cliff retreat. The overallprocesses on the slopes deliver sediment to the base of the cliff with5–6 × 105 atoms g−1 quartz. This concentration is equivalent to anaverage erosion rate of ~8 mm kyr−1. This rate is somewhat fasterthan the average bedrock erosion rate of ~3 mm kyr−1 suggested byBierman and Caffee (2001) for the Namib Desert. This is not surprisingas the accepted rate was determined from samples collected fromsmall inselbergs with a significantly lower relief. The concentration ofcosmogenic isotopes in sediment on the slopes of the GS is controlledby exposure time on the slope, weathering of exposed bedrock, andweathering of subsurface bedrock.

Sediment continues to accumulate cosmogenic isotopes while beingtransported on the flat pediments surrounding the inselberg. Within1–2 km from the base of the GS, the concentration increases to10–11 × 105 atoms g−1 quartz, which is equivalent to an average ero-sion rate of ~4 mm kyr−1 (Fig. 6). The increase in concentration is dueto exposure and mixing with highly dosed sediment eroded from nearsubsurface bedrock. From this 1–2 kmwide zone surrounding the insel-berg, grus is transported through a network of low gradient channels

ale. Dashed line indicates streamprofiles. The streams initiate at a distance of 1–2 km fromtration in sediment. Bold italic text—bedrock erosion rate in mm ka−1. Arrow length cor-istal pediment” are 10Be concentrations in atoms g−1 quartz. Inferred concentrations areBierman and Caffee (2001).

59A. Matmon et al. / Geomorphology 201 (2013) 52–59

(Fig. 4) to the Atlantic Ocean, ~100 km away. Cosmogenic isotope con-centration in sediment increases to 2.95 × 106 atoms of 10Be in g−1

Quartz (Fig. 6; Bierman and Caffee, 2001). This concentration is 3–4times higher than that measured in the grus 1 km from the mountain.The increase in concentration is achieved by dosing due to exposure dur-ing transport, contribution of sediment from subsurface rock, andmixingwith sediment derived from other highly-dosed bedrock surfaces. Aminimum transport rate of 36 cm yr−1 is calculated assuming that theincrease in 10Be concentration is all due to production during exposure.However, the contribution of highly dosed sediment from bedrockseems to control the cosmogenic inventory in sediment, implying thatthe actual transport rate is higher.

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