Landscape Evolution and Glaciation of the Rwenzori Mountains, Uganda: Insights from Numerical Modeling

Geomorphology 138 (2012) 263–275

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Geomorphology

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Landscape evolution and glaciation of the Rwenzori Mountains, Uganda: Insights from numerical modeling

Georg Kaufmann ⁎, Douchko Romanov

Institute of Geological Sciences, Geophysics Section, Free University of Berlin, Malteserstr. 74-100, Haus D, 12249 Berlin, Germany article info abstract

Article history: The Rwenzori Mountains are a high alpine mountain chain, about 40×80 km in size, just north of the equator in the Received 1 October 2010 westernbranchoftheEastAfricanRiftSysteminAfrica.The central part of the mountain chain is located in Uganda, Received in revised form 5 September 2011 and the highest peak, the Margherita Peak with 5119 m, lies on the border to the Democratic Republic of Congo. Accepted 8 September 2011 Topography is very pronounced, with steeply incised valleys and clear glacial landforms in the upper part of the Available online 28 September 2011 mountain chain. The Rwenzori Mountains are an unusually high mountain chain located in the extensional setting of the East African Rift System, and the large elevation poses a challenging problem for geodynamists to explain. Keywords: ﬂ Rwenzori Mountains We have used the landscape evolution model ULTIMA THULE, which combines hillslope diffusion, uvial erosion, Landscape evolution and glacial abrasion and is driven by a climate driver, simulating the variations in temperature, precipitation, and Morphology relief over several glacial cycles. With a simulation time of 800 ka, we test the hypothesis of climate–tectonic in- Ice sheets climate modeling teractions on the uplift of the Rwenzori Mountains. Our results show that a moderate cooling of around 6° causes widespread glaciation of the high mountain regions as observed during the peak glacial phases, and that morphological processes degrading the landscape allow for a tectonic uplift rate of around 0.5 mm a−1. © 2011 Elsevier B.V. All rights reserved.

1. Introduction been glaciated several times throughout the Pleistocene ice-age cycles. We use the numerical landscape evolution model ULTIMA THULE,which The evolution of mountain landscapes is controlled by both climatic combines hillslope erosion, fluvial erosion, and glacial abrasion and is and tectonic forces (Molnar and England, 1990; Burbank et al., 2003; driven by climate boundary conditions (temperature, precipitation, Reiners et al., 2003). While numerical modeling of mountain landscapes and relief). The model is used to simulate the last 800 ka of evolution shaped by fluvial and hillslope erosion has been investigated intensely in the Rwenzori Mountains, covering several glacial phases. We in the past (Beaumont et al., 1992; Tucker and Slingerland, 1994; will answer three main questions: Whipple, 2001; Willet et al., 2001), the effect of glacial abrasion has been neglected in most numerical models. The importance of i. Which temperature drop is needed to reproduce the glacial glacial abrasion, however, in high-mountain regions is evident from extent at the Last Glacial Maximum observed in the Rwenzori the field. The mechanisms controlling glacial abrasion, such as material Mountains? removed by friction through warm-based ice sheets, the development ii. If glacial, fluvial, and hillslope processes are active, to what of glacial features such as U-shaped valleys, glacial cirques, overdee- degree is the shape of the Rwenzori Mountains reduced by pending of valley profile, to name a few, are still actively discussed in these morphological processes? the literature (Hallet, 1979; Harbor et al., 1988; MacGregor et al., iii. Can we infer a long-term average tectonic uplift component 2000; Anderson et al., 2006; MacGregor et al., 2009). However, studies needed to keep the Rwenzori Mountains high enough to become on the long-term evolution of mountain landscapes at larger scale over repeatedly glaciated? periods of several ice-age cycles are scarce (Tomkin, 2003; Herman and Braun, 2008). We test the hypothesis of climate–tectonic interactions on the uplift In this study, we aim to quantify the effect of landscape evolution in of the Rwenzori Mountains with several model runs. (i) Steady-state high-mountain areas, including glacial, fluvial, and hillslope processes, landscape, no morphological processes: In a first set of models, we esti- as well as tectonic uplift. As case example we choose the Rwenzori mate the temperature drop needed during glacial periods to reproduce Mountains in equatorial Africa, a high-mountain ridge, which has an ice cap of several 100 km2 in size on top of the Rwenzori Mountains. (ii) Steady-state landscape, morphological processes: In the second set of models, we allow the landscape to evolve through morphological pro- ⁎ Corresponding author. fl E-mail addresses: [email protected] (G. Kaufmann), cesses such as uvial erosion and glacial abrasion to estimate the lower- [email protected] (D. Romanov). ing capacity of the mountain chain through these processes.

(iii) Uplifting landscape, morphological processes: In the third set of Table 1 models, we compensate the morphological processes through a tectonic Variables and reference model parameters. uplift component to estimate the uplift rate needed to keep the Description Symbol Unit Value Rwenzori Mountains at 5 km height. Eastern coordinate x m Input parameter The remainder of the paper is organized as follows: In Section 2,we Northern coordinate y m Input parameter describe the morphological processes included in the landscape evolu- Time t s Input parameter − 2 tion model ULTIMA THULE.InSection 3, we introduce the regional setting Grav. acceleration g ms 9.81 of the Rwenzori Mountains and discuss shape and climate, and we pre- Relief sent topography and climate data used for the present study. In Section Relief height h m Calculated

4, we discuss the results of the three sets of model runs introduced Bedrock height hB m Calculated above. In Section 5, we discuss and summarize our results. Sediment thickness hS m Calculated Ice thickness hI m Calculated Slope s – Calculated 2. Model Ice sheet − 3 We describe the processes controlling landscape evolution and Density of ice ρI kg m 910 fi 6 − 1 − 3 − 16 their implementation into the numerical model ULTIMA THULE. All Ice-deformation coef cient AD m yr N 2.5×10 fi 7 − 1 − 3 − 10 model parameter values, and their respective standard values, are Ice-sliding coef cient AS m yr N 1.9×10 Ice exponent n – 3 listed in Table 1. 2 − 1 Abrasion parameter κI m s Eq. (3) The model is based on a regular grid, on which the relief h(x,y,t) [m] is described as a function of space and time, with x [m] and y Hillslope processes fi κ′ 2 − 1 − [m] the eastward and northward coordinates, and t [s] the time. The Diffusion coef cient (bedrock) D m yr 0 1.5 2 − 1 Diffusion coefficient (sediment) κ′D m yr 10×κ′D for bedrock relief h(x,y,t) [m] is the sum of bedrock topography hB(x,y,t) [m], 2 − 1 Diffusion coefficient (ice) κ′D m yr 0 sediment thickness h (x,y,t) [m], ice thickness h (x,y,t) [m], and ver- S I Critical slope scrit – 1 tical flexural–isostatic displacement hF(x,y,t) [m]. The change in relief is then given by Fluvial processes Precipitation N ms− 1 Input parameter ∘ dhðÞ x; y; t ∂hxðÞ; y; t Temperature T C Input parameter ¼ Evapo-transpiration ET ms− 1 Eq. (8) ∂ − dt t uplift Runoff q m3 s 1 Eq. (7) 3 − 1 ∂hxðÞ; y; t Sediment load Q m s Calculated þ 3 − 1 ∂ Carrying capacity Qe m s Eq. (12) t hillslope fi κ – − Erosion coef cient R 0 0.01 ∂hxðÞ; y; t Channel width w m Eq. (10) þ ð1Þ Channel coefficient w s0.5 m− 0.5 0.1 ∂ r t fluvial 3 Length scale (bedrock) L m 100×10 ∂ ðÞ; ; Length scale (sediment) L m10×103 þ hxy t ∂ t glacial Glacial processes fi κ 1−m m− 1 − ∂hxðÞ; y; t Abrasion coef cient G m s 0 0.01 þ – ∂ Abrasion exponent m 1 t flexure Valley constriction β – Eq. (14)

Constriction coefficient κC m 1000 The numerical model predicts changes in the relief according to Isostatic processes Eq. (1) as well as the movement of sediment, ice, and water through − 3 Density of crust ρC kg m 2500 the landscape. The different processes will be discussed next. − 3 Density of mantle ρM kg m 3000 − 3 Density of sediment ρS kg m 1500 3 2.1. Ice sheet Thickness of elastic plate hplate m30×10 Shear modulus μ Pa 6.7×1010 ν – Depending on the climatic conditions, ice might be present on Poisson ratio 0.25 parts of the landscape. We apply the shallow-ice approximation (SIA) (e.g. Hutter, 1983), which assumes that the horizontal derivatives of the ice stress and the ice velocity are small compared to the [N m− 2] the ice-overburden pressure, and P [N m− 2] the water pres- vertical derivatives. The resulting diffusion equation reads: sure. We do not explicitly account for water flow at the base of the ice ∂ ðÞ; ; cap, thus we follow (Knap et al., 1996)and(Braun et al., 1999)and hI x y t ¼ ∇ ðÞþ; ; ðÞ; ; ; ð Þ ·FI x y t Mxy t 2 use the simplification N−P=0.8ρ gh .Thefirst equation of Eq. (3) ac- ∂t I I counts for the internal deformation of ice, the second one for the sliding with M [m s− 1] the mass-balance, which depends on the local climate, over the bedrock, when melting occurs along the bottom of the ice. 2 − 1 and FI [m s ] the vertically integrated ice-flux, which is the product of After solving for a possible ice cover, the following morphological pro- − 1 ice thickness hI [m] and ice velocity uI [m s ], FI =hIuI =κI ∇h cesses are considered. [m2 s− 1], and can be rewritten in terms of the non-linear ice-diffusion 2 − 1 coefficient κI [m s ]: 2.2. Tectonic uplift 8 n > ðÞρ n−1 <> 2 Ig nþ2 A possible tectonic uplift or subsidence component is considered A h ∇h ; − 1 κ ¼ n þ 2 I I ð Þ through an external uplift velocity U(x,y,t)[ms ], which mimics the I > n 3 > 1ðÞρ g nþ1 n−1 rock uplift: : I A h ∇h ; N−P I I 6 − 1 − 3 7 − 1 − 3 ∂hxðÞ; y; t with n the ice-sliding exponent, AI [m a N ]andAI [m a N ] ¼ UxðÞ; y; t ; ð4Þ − 3 ∂t ice-flow and ice-sliding coefficients, ρI [kg m ] the density of ice, N uplift G. Kaufmann, D. Romanov / Geomorphology 138 (2012) 263–275 265

3 − 1 With this simplified scenario we can assign any uplift signal coming with Q e(x,y,t)[m s ] the carrying capacity described below, and either from field evidence or a numerical model. However, at this stage L [m] a length scale, which can be different for erosion of bedrock or of landscape evolution and tectonic uplift are decoupled and not modeled sediments. The river width w [m] is proportional to the square root of consistently. the runoff, pffiffiffi ¼ ; ð Þ 2.3. Hillslope processes w wr q 10

0.5 − 0.5 Small-scale processes such as weathering, rock and mud slides, with wr [s m ] a river-width constant. The change in relief for and soil creep are parameterized by a mass flux, which is oriented sedimentation is given as downwards and is proportional to the local slope (Beaumont et al., 1992; Kooi and Beaumont, 1994; Tucker and Slingerland, 1994; ∂hxðÞ; y; t QxðÞ; y; t −Q ðÞx; y; t ¼ e ; ð11Þ ∂ ðÞ; Braun and Sambridge, 1997). Then, the change in relief by hillslope t fluvial Axy processes can be described by a diffusion equation − with Q(x,y,t)[m3 s 1] the actual sediment load of the river, and A(x,y) ∂hxðÞ; y; t 2 ¼ ∇·F ðÞx; y; t ; ð5Þ [m ] the area of the river element. The carrying capacity describes the ∂ D t hillslope maximum sediment load the river can hold in suspension. It depends on the local slope s(x,y,t)[−], the runoff q(x,y,t)[m3 s− 1], and an ero- 2 − 1 fl with FD [m s ] the vertically integrated hillslope-diffusion ux. The sion coefficient κR [−] describing the resistivity of the eroded material: vertically integrated hillslope diffusion-flux FD is the product of sedi- − 1 ðÞ; ; ¼ κ ðÞ; ; ðÞ; ; : ð Þ ment thickness hS [m] and sediment velocity uS [m s ], FD =hSuS = Q e x y t Rsxy t qxy t 12 2 − 1 κD ∇h [m s ] and can be rewritten in terms of the non-linear fi κ 2 − 1 hillslope-diffusion coef cient D [m s ]. Thus the river model allows for a possible disequilibrium between We account for the increase in hillslope diffusion for steeper actual sediment load and carrying capacity. slopes as described in (Roering et al., 1999; Roering et al., 2001)by using the non-linear form of the hillslope-diffusion coefficient: 2.5. Glacial processes κV κ ¼ D ; ð6Þ Several processes of glacial erosion can change the relief of a land- D sxðÞ; y; t 2 1− scape, such as chemical weathering, subglacial stream erosion, abrasion scrit by transported debris, or plucking. We employ a simple relation describing abrasion, relating the abrasion to the basal velocity of the ice − κ′ 2 − 1 with s [ ] the slope and scrit a critical slope. Here, D [m s ]in stream (Hallet, 1979; Braun et al., 1999; Tomkin and Braun, 2002; Tom- κ′ − Eq. (6) for hard bedrock ( D)is0 1.5, that for softer sediment kin, 2010): cover is 10 times that for bedrock, and in glaciated areas the diffusion κ′ is zero ( D =0). ∂hxðÞ; y; t ¼ κ βu ðÞx; y; t m; ð13Þ ∂ G S t glacial 2.4. Fluvial processes 1−m m−1 With κG [m s ] the glacial coefficient describing the resistivity of On a larger scale, rivers and creeks are the most efficient way to re- − 1 the abraded bedrock, uS(x,y,t)[ms ] the sliding velocity of the over- move or deposit material. Here, we use a network of one-dimensional lying ice cap, and m apower–law exponent, set to m=1 in our model. rivers on the landscape, which collect the precipitation and channel As the SIA-method cannot correctly produce glacial landforms the water downstream. The parameterization of river incision is still de- such as U-shaped valleys, ice flow in narrow valleys has to be cor- bated in the literature (e.g. Kooi and Beaumont, 1994; van der Beek and rected. Here, we follow (Braun et al., 1999) and implement a valley Bishop, 2003). We have chosen the CASCADE algorithm to simulate the constriction factor β, which reduces the sliding velocity in steep river network (Braun and Sambridge, 1997), which allows for an explic- slopes. The formulation, originally from (Svennson, 1958), reads it calculation of the sediment load suspended in the water. 3 − 1 ! The runoff q(x,y,t)[m s ] is described as local recharge (precip- 2 −1 − − ∂ h itation N(x,y,t)[ms 1] minus evapo-transpiration ET(x,y,t)[ms 1]) β ¼ 1 þ κ B : ð14Þ C ∂n2 plus the water coming from the upstream catchment, qu(x,y,t) [m3 s− 1]:

Here, κC [m] is a parameter, and the second derivative is calculated ðÞ¼; ; ðÞðÞ; ; − ðÞ; ; ðÞþ; ðÞ; ; ; ð Þ qxy t Nxy t ET x y t Axy qu x y t 7 in the direction of ice ﬂow, indicated by the normal direction n.

2 with A(x,y)[m ] the area of the element. Evapo-transpiration ET(x,y, 2.6. Isostatic processes t)[ms− 1] is parameterized according to The reaction of the lithosphere and the asthenosphere to the NxðÞ; y; t ETðÞ x; y; t ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið8Þ changing relief is modeled by a thin elastic plate overlying a viscous NxðÞ; y; t 2 0:9 þ ; substratum (Turcotte and Schubert, 1982), according to 300 þ 25TxðÞþ; y; t 0:05TxðÞ; y; t 3 ∇4 ðÞþ; ; ðÞρ −ρ ðÞ; ; D hF x y t M C ghF x y t − ∘ ð Þ with N(x,y,t)[ms 1] precipitation, and T(x,y,t)[C] temperature. 15 ¼ ρ gh½þðÞþx; y; t h ðÞx; y; t ρ gh ðÞx; y; t ; The runoff then interacts with the substratum, either to remove or C B S I I to deposit material (Kooi and Beaumont, 1994; Braun and Sambridge, with D [N m] the elastic rigidity, defined as 1997). The change in relief for erosion is then given as

3 ∂hxðÞ; y; t Q ðÞx; y; t Ehplate ¼ − e ; ð9Þ D ¼ ÀÁ; ð16Þ ∂ −ν2 t fluvial wL 12 1 266 G. Kaufmann, D. Romanov / Geomorphology 138 (2012) 263–275 and E [Pa] die elastic Young modulus, defined as The glacial coverage fluctuated substantially during the Quaterna- ry (e.g. Osmaston and Harrison, 2005). The earliest phase was the E ¼ 2μðÞ1 þ ν : ð17Þ Katabarua Glaciation, whose moraines are older than 300 ka BP. From the locations of the moraines and tills associated to the Kata- − 3 2 In Eqs. (15)–(17), ρM, ρC, and ρI [kg m ] are the densities of the barua Glaciation, a large ice cap of around 500 km has been deduced, mantle, the crust and ice, respectively, g [m s− 2] the gravitational the largest glaciation of the Rwenzori Mountains. The subsequent acceleration, μ [Pa] the shear modulus, ν [−]isthePoissonnumber, Rwimi Glaciation occurred around 100 ka BP. The ice cap was slightly 2 and hplate [m] the thickness of the elastic plate. smaller, around 300 km in size, but the glaciers progressed to lower The term on the right-hand side is the load imposed onto the two- altitudes in the steep valleys. The Lake Mahoma Glaciation, coinciding dimensional elastic plate of uniform thickness. It is the sum of the with the Last Glacial Maximum (LGM) at around 21 ka BP, has well topography and the ice-sheet. Note that the inviscid mantle relaxes all preserved moraines, from which the character of the ice cap at the stresses, which is a valid assumption over geologic time scales (1 Ma), LGM can be deduced: A group of ice caps is covering the six main but not entirely correct on time scales of ice-age cycle (10–100 ka). peaks (around 260 km2), which were drained by deep glacial valleys Here, a viscoelastic mantle as modeled in glacial isostatic adjustment descending down to 2000–2400 m. The reconstruction of the equilib- (Kaufmann and Wu, 1998, 2002) would be more appropriate. This rium line altitude (ELA) results in a slightly tilted, elongated LGM ice time-dependent approach would, however, increase the computational cap following the general relief of the mountains and the predomi- cost significantly. nant wind direction (Osmaston and Harrison, 2005). Two later glaciations, the Omurubaho Glaciation (10 ka BP, 3. Rwenzori Mountains 70 km2) and the Lake Gris Glaciation (3 ka BP, 10 km2) mark later ad- vances of glaciers on the Rwenzori Mountains, which are probably re- 3.1. Tectonic framework lated to uplift events and subsequent changes in the local drainage system (Ring, 2008). The East African Rift System (EARS) dominates much of East Africa (Ebinger, 1989a, b; Ring, 1993). It consists of two parts, the Western 3.3. Model topography Branch and the Eastern Branch, separating the Nubian Plate to the west and the Somalian Plate to the East. In between the two branches, For the landscape evolution experiments in the Rwenzori Moun- the mechanically strong Tanzania Craton is located (Fig. 1). In both tains, a 90×90 km wide region from the Shuttle Radar Topography branches, rift basins of around 60–90 km length and 50 km width Mission (SRTM, Jarvis et al., 2008) is taken (Fig. 2), and discretized have evolved, which are half-graben structures bounded by faults. into surface elements 250×250 m in size. Thus, the experiments are The Moho is generally in about 30–35 km depth, and lithospheric based on the present-day relief of the Rwenzori Mountains. The thickness is around 125 km (Ritsema et al., 1999). The Eastern present-day equilibrium line is located in around 5000 m height, Branch stretches from the Afar Triangle in Ethiopia through Kenya but the equilibrium line at peak glacial times was in around 3900– and Tanzania, in the south it peters out in a network of small graben 4000 m, increasing the area of potential ice growth. structures. The Western Branch consists of the Albertine Rift with the From the topographical data, we have derived a hypsometric distri- lakes Albert, Edward, and George, then it continues through the Kivu, bution of elevations (Fig. 2). The distribution has a clear maximum in Tanganyika, Rukwa, and Malawi rifts. around 1000 m altitude, reflecting the local base level for the fluvial ero- The Albertine Rift is bounded by two major faults (Fig. 1). The sion of the Rwenzori Mountains. Between the present and the LGM Bunia Fault in the west has created a rift-flank topography of around snowlines, no clear second maximum is present. Following (Egholm 1300 m, compared to the low-lying Lake Albert in 620 m elevation. et al., 2009), this indicates no pronounced glacial influence, otherwise The Toro–Bunyoro Fault in the east is overlooked by a large escarpment. a local glacial base level should be present just below the present snow- Further south, the Bwamba Fault crosses the Albertine Rift from east to line. However, the steepness of the terrain in the Rwenzori Mountains west, following the western side of the Rwenzori Mountains. restricts the glaciated area substantially, thus a pronounced glacial ef- The divergent plate motion between the Nubian and the Somalian fect is not expected due to the limited area available for glacial abrasion. plates is around 2 mm yr− 1. This tectonic movement causes subsidence of the central parts of the East African Rift due to the extensive 3.4. Model climate movement, while the rift flanks have been uplifted by 1–2kmasaresult of isostatic adjustment. The Rwenzori Mountains, however, have been The Dome C Antarctic ice-core record (EPICA, 2004) describes the uplifted as a horst structure to heights up to 5 km (Fig. 1). This extreme hydrogen-isotope variation since 800 ka BP in Antarctica. We have cho- uplift in an extensional setting is exceptional, and only comparable to sen this record to describe the temporal variations in our model, as it re- the 4350 m high Transantarctic Mountains (Stern et al., 2005). It cannot sembles real climatic variations over a fairly long period. The record can be explained by rift-flank uplift through isostasy alone, thus other only provide a rough guide for the temporal evolution in the Rwenzori processes such as volcanism or glacial erosion must be considered Mountains, as the Dome-C location is too far away from the study area as likely candidates to provide the additional uplift needed. The and is located in a completely different setting. However, there is no de- enormous uplift of the Rwenzori Mountains has been episodic, tailed climatic record for the equatorial Africa area yet. with uplift phases around 8 and 3 Ma before present (BP) (Upcott We derive a glacial index function, GI(t), which is based on the et al., 1996; Karner et al., 2000; Ring, 2008). Dome-C hydrogen isotope record. The hydrogen isotope record is rescaled, with GI(t=0)=0 fixed to the present interglacial, and GI 3.2. Climate and glaciers (t=LGM)=1 fixed to the Last Glacial Maximum LGM (Fig. 3). Based on this glacial index, we vary temperatures, using an offset Annual rainfall in the Rwenzori Mountains is fairly high, up to temperature ΔT [∘C] between the present and the LGM. − 1 ∘ 2500 mm yr in 2000–3000 m height (Osmaston, 1989). The highest Present temperatures are assigned at sea level T0(x,y)[C], with peaks are permanently snow covered, and in 1906, glaciers covered cooling depending on altitude according to adiabatic lapse rate α of around 7.5 km2, at that time half of the total glacier area in Africa. −4°Ckm− 1. The total temperature function then reads: Modern glaciers, however, are fairly small, covering 1.7 km2 around 1990 (Kaser, 2001), and shrinking to 1.5 km2 by 1995 (Osmaston 2 ðÞ; ; ¼ ðÞ; þ α ðÞ; ; þ ðÞΔ : ð Þ and Harrison, 2005), and below 0.5 km at present. Txy t T0 x y hxy t GI t T 18 G. Kaufmann, D. Romanov / Geomorphology 138 (2012) 263–275 267

Fig. 1. Topography and tectonic structure of East Africa: Top: Overview of Africa, with the research area enclosed by red line. Bottom left: East African Rift System, with the Western and the Eastern Branch, the Nubian and Somalian Plates, and the Tanzania Craton in between. Major faults are shown as dashed lines, the rectangle marks the area shown on the right. Bottom right: Rwenzori Mountains, with major faults shown as dashed lines. The red line indicates the model area chosen for numerical simulations. LV: Lake Victoria, LT: Lake Tanganyika, LA: Lake Albert, LG: Lake George, LE: Lake Edward.

− 1 − 1 Present precipitation N0(x,y)[ms ]isﬁxed to 2500 mm yr , Parameterization of the ice-mass balance follows a simple temper- but local runoff R(x,y,t)[ms− 1] is variable due to variable evapo- ature relation (e.g. (Tomkin and Braun, 2002; Tomkin, 2003; Tomkin, transpiration ET(x,y,t)[ms− 1], which depends on temperature T(x, 2007)). For the present (Fig. 4), the above parameterization results in y,t), and thus on time: the following temperature, local runoff and mass-balance distribu- tions: Temperature varies between 2 and 20 °C, and local runoff be- ðÞ¼; ; ðÞ; − ðÞ; ; : ð Þ − 1 Rxy t N0 x y ET x y t 19 tween 1500 and 2000 mm yr , depending on altitude. The mass 268 G. Kaufmann, D. Romanov / Geomorphology 138 (2012) 263–275

Fig. 2. The 90×90 km model domain for the Rwenzori Mountains and its hypsometry. The thin blue line along the higher altitudes marks the extent of the Lake Mahoma Glaciation.

balance for an ice cap is negative over the entire region, thus no ice cap are able to separate the different mechanisms sculpturing the relief, develops. At the LGM (Fig. 4), temperatures are lower and reach values and their mutual interaction. below 0 °C along the mountain peaks, and local recharge is increased due to the lower temperatures, but falling as snow on the mountain 4.1. Setup 1: Ice sheet tops. Thus, the mass balance for an ice cap becomes positive along the peaks. In the first set of simulations, we use the present-day topography of the Rwenzori Mountains and simulate paleo-climate variations 4. Results through the introduced glacial index function. However, no morphological processes such as glacial abrasion, fluvial incision, or hillslope In this Section, three numerical experiments are described. All are diffusion are active. With this simple setup we can estimate the tem- based on the climate driver discussed above, thus the temperature perature drop ΔT between the present-day climate and the conditions and precipitation patterns are always the same. All parameter values at the last glacial maximum. controlling the evolution are kept fixed (Table 1). The experiments In Fig. 5, the ice extent for three simulations is shown. The temper- differ in the way, how landscape processes are active. In the first ature drops considered are 4.5 °C, 5.5 °C, and 6.5 °C, respectively. Also setup, only an ice cap is modeled, which grows and vanishes following shown are the estimated extensions of the ice cover from field evidence the variation in temperatures. In the second setup, the ice cap is for the three glacial phases, the Katubarua Glaciation, the Rwimi Glaci- modeled, including morphological processes such as hillslope diffusion, ation, and the Lake Mahoma Glaciation. The error bars are just indica- fluvial erosion, and glacial abrasion. In the third setup, an additional up- tive, as the times associated with the observations have large lift component is added to the system. By this choice of conditions we uncertainties. All simulations result in ice caps periodically covering

Fig. 3. Glacial index (GI) as a function of time before present (BP). The variation is derived from the hydrogen-isotope record of the Dome C Antarctic ice core record (Petit et al., 1999), which has been scaled to the present (GI=0) and the Last Glacial Maximum (GI=1). Corresponding Marine Isotope Stages (MIS) are shown on top. G. Kaufmann, D. Romanov / Geomorphology 138 (2012) 263–275 269

Fig. 4. Maps for surface temperature, local runoff, and mass balance for the present (top) and the LGM (bottom). the top of the Rwenzori Mountains, following the glacial index based on As an example, the modeled ice cover for the two epochs 650 ka BP the Dome C hydrogen-isotope variation. Ice cover is largest during the and 25 ka BP is shown in Fig. 6 for the temperature drop of ΔT=6.5 °C. glacial phases, covering between 100 and 400 km2, depending on the The areal extent of both the simulated and the Lake Mahoma Glaciation temperature drop. For the last glacial maximum, simulations with a are, to ﬁrst order, very similar. The ice covers all of the high alpine area temperature drop between 5.5−6.5 °C can be reconciled with the ob- of the Rwenzori Mountains, with several glacier tongues draining the servations for the Lake Mahoma Glaciation. The larger extent of the ice cap through steep ravines. The extent of the ice cap is similar for older glaciations, however, has not been reached by the simulations. all peak glacial phases, and it is entirely controlled by the glacial index This can be either attributed to the wrong climate driver, our glacial function used to modify the climate driver. index is based on Antarctic data and not on (unavailable) African data, From this Section, we progress with the model featuring a temper- or on the different paleo-topography during this older glaciations, ature drop of ΔT=6.5 °C, as this model can explain the extent of the which is not known, either. Rwenzori ice sheet at the last glacial maximum.

Fig. 5. Setup 1: Ice-covered area as a function of time BP. Colored areas represent runs for different temperature differences between LGM and present-day (see legend). Also shown are the observed moraine-covered areas for the three different glaciations Katabarua (K), Rwimi (R), and Lake Mahoma (LM). 270 G. Kaufmann, D. Romanov / Geomorphology 138 (2012) 263–275

4.2. Setup 2: Ice sheet, morphology As a last comparison we vary the strength of the glacial abrasion over two orders of magnitude. However, the effect of the ice cover In the second set of simulations, we add the three geomorphological is fairly small, which is a result of the small glaciated size, there is processes, hillslope diffusion, fluvial erosion, and glacial abrasion, to the simply not enough ice-covered area to significantly change to relief fluctuating climate conditions. While the precipitation is kept fixed, of the Rwenzori Mountains in terms of total height. local runoff varies due to the different amount of evapo-transpiration As a more general remark, a strong feedback is present between during glacial and interglacial phases. When temperatures drop below morphological processes and climate variability: The degradation of freezing at a location, rain is switched off and snow starts to accumulate the topography through hillslope diffusion, fluvial incision, and gla- to build an ice cap. With this setup we aim to quantify the change in to- cial abrasion is responsible for a decline in ice-covered area, even if pography through both fluvial and glacial processes, and the change in the climatic conditions for two peak glacial epochs are similar. ice coverage through several glacial periods. Next, we discuss the evolution of one model in more detail. We 2 − 1 We first aim to quantify the effect of hillslope diffusion, fluvial in- choose a setup with κD =1.5 m yr , κR =0.005, and κG =0.01. In cision, and glacial abrasion on the size of the periodically growing ice Fig. 8, two snapshots of the ice coverage are shown for this model, caps. We therefore vary hillslope diffusion between κD ∈[0.7,1.5] both being peak glacial phases. At 650 ka BP, the extent of the ice 2 − 1 m yr , the fluvial erosion coefficient between κR ∈[0.001,0.01]. cap is similar to the setup 1, because there was simply not enough and the glacial abrasion coefficient between κG ∈[0.0001,0.01]. We time for the morphological processes to reshape the landscape. At have chosen the parameter space for the three morphological pro- the last glacial maximum (25 ka BP), however, the size of the ice cesses in accordance with others (Herman and Braun, 2008, Tomkin, cap has decreased significantly, as the landscape surface has been 2010), but we admit that the scarcity of robust field evidence does lowered due to the removal of material by morphological processes. not allow us to properly limit the parameter values. Therefore, the We can quantify the strength of the morphological processes by choice does reflect more the numerical results generating a reason- discussing the removal rates for the different morphological process- able shape of the landscape, when compared to the real topography es. In Fig. 9, the removal rates are shown for hillslope diffusion, fluvial of the Rwenzori Mountains. incision, and glacial abrasion. For the chosen strength of the processes, In Fig. 7, the areal extent of the ice caps is shown as a function of both hillslope diffusion and fluvial incision have similar capacities to time for different strength of the three geomorphic processes. Focus- change the relief of the Rwenzori Mountains. The maximum removal ing on hillslope diffusion first, we observe a decrease in ice-covered rates close to 10 mm yr− 1 arearesultofthesteepnessoftherange. area through time, as material is removed from the surface and trans- Average removal rates are almost two orders of magnitude lower, ported downhill. Thus, with time less area above the equilibrium line thus more in accordance with global rates estimated for high tropical becomes available and the ice cover shrinks in size. The reduction in mountain ranges. Both the removal rate for hillsope diffusion and fluvial ice cover depends on the strength of the hillslope process, with stron- erosion show only moderate variations from the varying climate. The ger diffusion causing faster and more effective removal of material glacial removal rate, however, has a clear periodicity, resulting from and a more rapid reduction in topographic height. the climate variability. In peak glacial periods, its maximum removal If we consider the effect of fluvial incision, we observe an opposite rate is as strong as the two other processes. The same holds true for effect: The weaker the fluvial process is, the smaller the ice coverage the average removal rate for glacial abrasion, which, during cold spells, becomes. This seems counter intuitive at the first glance, but can be can be even higher than the hillslope diffusion and fluvial incision explained by the interaction of the morphological processes. A counter-parts. weaker fluvial incision transports less sediments, thus a thicker and In Fig. 10, we take a closer look at the spatial pattern of the three more widespread sediment cover remains for the hillslope diffusion. active morphological processes. Here, the cumulative rates are plot- As the effectivity of hillslope diffusion in our setup is coupled to the ted onto the landscape surface. Glacial abrasion is limited to the top material affected (bedrock, sediment, or ice), a weak fluvial incision of the Rwenzori Mountains, with a clear preference of removal on triggers stronger hillslope diffusion, and as a result a faster removal the steep slopes of the mountain tops. Thus the sliding ice is respon- of topography. sible for the oversteepening of slopes to form local cirques in that part

Fig. 6. Setup 1: Ice extent on top of the Rwenzori Mountains at 650 ka BP (left) and 25 ka BP (right). G. Kaufmann, D. Romanov / Geomorphology 138 (2012) 263–275 271

Fig. 7. Setup 2: Ice-covered area as a function of time BP. The solid blue area is the ΔT=6.5∘C run from setup 1. All other lines are runs from setup 2 with variations in either (top) hillslope diffusion, (middle) ﬂuvial incision or (bottom) glacial abrasion.

of the Rwenzori Mountains. The total removal by glacial abrasion pattern, with removal of material along the steep ridges, and deposi- since roughly 800 ka BP considered approaches 100 m. Fluvial inci- tion near the flatter valley bottoms. However, most of the material sion is by nature of this process more widespread in the model do- stored in the high-mountain valleys by hillslope diffusion is then re- main. Removal of material in most cases is focused on the steep moved downhill by fluvial transport. valleys, with incision of several hundred meters in the main valleys. We conclude this part by highlighting again the interaction of The material is then transported downstream and deposited in the climate-driven and morphologically-driven processes on the landscape foreland of the Rwenzori Mountains. On the eastern side, a large allu- evolution in the Rwenzori Mountains. In general, removing material by vial fan has been created in front of the Mobuku Valley, while on the hillslope diffusion, fluvial incision, and glacial abrasion reduces topogra- western Congolese side the sediments have drowned the rift valley. phy and thus decreases the height over the equilibrium line. Ice sheets Note that due to the limited extent of the model domain, the Semliki therefore become smaller with time due to the smaller accumulation River has no catchment and thus sediments are not correctly trans- area. With both climate-driven and morphologically-driven processes ported in the rift valley itself. Hillslope diffusion has a clear bimodal active in setup 2, we cannot reproduce the ice extent of the Lake 272 G. Kaufmann, D. Romanov / Geomorphology 138 (2012) 263–275

Fig. 8. Setup 2: Ice extent on top of the Rwenzori Mountains at 650 ka BP (left) and 25 ka BP (right).

Mahoma Glaciation at the last glacial maximum any more. We argue the surface elevation is lowering and thus less area is exposed that a third process, tectonic uplift, is needed to compensate the loss above the equilibrium line; and therefore less ice develops. The ice in elevation by the morphological processes. cover for setup 3 is almost identical to the setup 1 cover, as now the prescribed uplift function compensates for the loss in elevation 4.3. Setup 3: Ice sheet, morphology, uplift caused by the morphological processes. Again, we quantify the strength of the morphological processes by In this last Section, we simulate tectonic uplift by prescribing an discussing the removal rates for the different morphological process- uplift rate to the Rwenzori Mountains. We derive an uplift function es (Fig. 13). As during setup 2, both hillslope diffusion and ﬂuvial ero- from the present-day topography, which is smoothed by a low-pass sion has similar removal rates, both for the maximum amount ﬁlter to obtain a spatially varying uplift signal. Using the model dis- removed and the average rates. However, the removal rate for glacial cussed in detail in setup 2, we derive a maximum uplift rate from the abrasion has increased for the younger periods, which is a result of difference in peak height in the model between the start and the end the increased elevation available for ice coverage. Thus the tectonic of the model run. Thus, a peak uplift rate of 0.5 mm yr− 1 is deduced. uplift imposed has strengthened the glacial abrasion contribution, as The resulting uplift function is shown in Fig. 11, along with the ice now the area above the snowline becomes larger due to the uplift. cover at the last glacial maximum. The uplift function is responsible for uplift of the Rwenzori horst structure, and no uplift is present out- 5. Discussion side the mountain chain. The ice cover shown for the last glacial maximum is again as large as in setup 1, thus the additional tectonic uplift We have employed our numerical landscape evolution model component compensates the lowering in elevation through the mor- ULTIMA THULE to discuss the interaction between climate, morpholo- phological processes. gy, and uplift in the Rwenzori Mountains in Uganda. The model used This can also be shown with the temporal evolution of the ice- has been applied to the present-day topography of the Rwenzori Moun- covered area as shown in Fig. 12. Here, we compare model runs for tains to address three questions, which we now can answer: all three setups. The ice cover from setup 1, with a similar areal extent for all peak glacial phases is caused by the similarity of the amplitudes (i) Which temperature drop is needed to reproduce the glacial of the glacial index function. The ice cover resulting from setup 2 re- extent at the last glacial maximum observed in the Rwenzori duces in size due to the additional active morphological processes; Mountains? The average annual temperature needs to be

Fig. 9. Setup 2: Removal rates for different processes (see legend). Solid lines indicate maximum rates, dashed lines average rates. G. Kaufmann, D. Romanov / Geomorphology 138 (2012) 263–275 273

Fig. 10. Setup 2: Morphological processes at 25 ka BP. Shown are the contributions from ice cover (top left), glacial abrasion (top right), ﬂuvial erosion (bottom left), hillslope diffusion (bottom right).

Fig. 11. Setup 3: Left: Uplift rate. Right: Ice extent on top of the Rwenzori Mountains at 25 ka BP. 274 G. Kaufmann, D. Romanov / Geomorphology 138 (2012) 263–275

Fig. 12. Setup 3: Ice-covered area as a function of time BP. The solid blue area is the ΔT=6.5 °C run from setup 1. The solid black area is the standard run from setup 2. The red line is − 1 the ΔT=6.5 °C run from setup 3 with a maximum uplift rate of Umax =0.5 mm yr .

Fig. 13. Setup 3: Removal rates for different processes (see legend). Solid lines indicate maximum rates, dashed lines average rates.

between 5 and 6 °C colder than present to obtain a glacial cover- Acknowledgements age in agreement with the observations for the Lake Mahoma Glaciation of the last glacial maximum. The extent of the ice The authors acknowledge the support by the German Research Soci- cap does not change very much between the modeled glacial ety (DFG) under the research group RIFTLINK (FOR 703, Rift Dynamics, maxima. Uplift and Climate Change in Equatorial Africa: Interdisciplinary Re- (ii) If glacial, fluvial, and hillslope processes are active, to what de- search linking Asthenospere, Lithosphere, Biosphere and Atmosphere). gree is the shape of the Rwenzori Mountains reduced by these morphological processes? Morphological processes such as References weathering, slope-wash, and fluvial incision will reduce the height of the Rwenzori Mountains, thus the glaciated area be- Anderson, R., Molnar, P., Kessler, M., 2006. Features of glacial valley profiles simply comes smaller with time. A sensitivity test of the relevant mor- explained. J. Geophys. Res. 111, F01004. Beaumont, C., Fullsack, P., Hamilton, J., 1992. Erosional control of active compressional oro- phological parameter values has shown that the amount of gens. In: McClay, K.R. (Ed.), Thrust Tectonics. Chapman and Hall, New York, pp. 1–18. reduction in glaciated areas depends on the strength of the pro- Braun, J., Sambridge, M., 1997. Modelling landscape evolution on geological time cesses. But even for a moderate to weak strength of the hillslope scales: a new method based on irregular spatial discretisation. Basin Res. 9, 27–52. fl Braun, J., Zwartz, D., Tomkin, J.H., 1999. A new surface processes model combining gla- and uvial incision processes as suggested for the metamorphic cial and fluvial erosion. Ann. Glaciol. 28, 282–290. Rwenzori Mountains, the extent of the Lake Mahoma Glaciation Burbank, D.W., Blythe, A.E., Putkonen, J., Pratt-Sitaula, B., Gabet, E., Oskin, M., Barros4, will not be reached if these processes are taken into account. Gla- A., Ojha, T.P., 2003. Decoupling of erosion and precipitation in the Himalayas. Na- ture 426, 652–655. cial abrasion, though limited to the high-alpine area above Ebinger, C.J., 1989a. Geometric and kinematic development of border faults and accom- 3000 m, can locally reduce the relief by 100 m or more. modation zones, Kivi–Rusizi Rift, Africa. Tectonics 8, 117–133. (iii) Can we infer a long-term average tectonic uplift component Ebinger, C.J., 1989b. Tectonic development of the western branch of the East African – needed to keep the Rwenzori Mountains high enough to become Rift System. Geol. Soc. Am. Bull. 101, 885 903. Egholm, D., Nielsen, S.B., Pedersen, V.K., Lesemann, J.-E., 2009. Glacial effects limiting repeatedly glaciated? The reduction of topographic relief mountain height. Nature 460, 884–888. through the above mentioned morphological processes and the EPICA, 2004. Eight glacial cycles from an Antarctic ice core. Nature 429, 623–628. – subsequent reduction in glaciated areas during peak glacial Hallet, B., 1979. A theoretical model of glacial abrasion. J. Glaciol. 17, 209 222. Harbor, J.M., Halltet, B., Raymond, C.F., 1988. A numerical model for landform develop- phases can be compensated by uplifting of the Rwenzori Moun- ment by glacial erosion. Nature 333, 347–349. − tains. Here, a moderate long-term uplift of 0.5 mm yr 1 is Herman, F., Braun, J., 2008. Evolution of the glacial landscape of the Southern Alps of enough to reproduce the extent of the Lake Mahoma Glaciation. New Zealand: insights from a glacial erosion model. J. Geophys. Res. 113, F02009. Hutter, K., 1983. Theoretical Glaciology. Dortrecht, Riedel. 510 pp. We cannot, however, distinguish, if this uplift was continuous Jarvis, A., Reuter, H., Nelson, A., Guevara, E., 2008. Hole-filled seamless SRTM data V4. and slow, or episodic with faster intervals. International Centre for Tropical Agriculture (CIAT). http://srtm.csi.cgiar.org. G. Kaufmann, D. Romanov / Geomorphology 138 (2012) 263–275 275

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