Impact of hillslope-derived sediment supply on drainage basin development in small watersheds at the northern border of the central Alps of Switzerland

Geomorphology 46 (2002) 285 – 305 www.elsevier.com/locate/geomorph

Impact of hillslope-derived sediment supply on drainage basin development in small watersheds at the northern border of the central Alps of Switzerland Fritz Schlunegger * Geological Institute, ETH Zentrum, Sonneggstrasse 5, CH-8092 Zurich, Switzerland Received 20 August 2001; received in revised form 25 January 2002; accepted 27 January 2002

Abstract This paper explores the effects of hillslope mobility on the evolution of a 10-km2 drainage basin located at the northern border of the Swiss Alps. It uses geomorphologic maps and the results of numerical models that are based on the shear stress formulation for fluvial erosion and linear diffusion for hillslope processes. The geomorphic data suggest the presence of landscapes with specific cross-sectional geometries reflecting variations in the relationships between processes in channels and on hillslopes. In the headwaters, the landscape displays parabolic cross-sectional geometries indicating that mass delivered to channels by hillslope processes is efficiently removed. In the trunk stream portion, the landscape is (i) V-shaped if the downslope flux of mass is balanced by erosion in channels (i.e. if mass delivered to channels by hillslope processes is efficiently removed) and (ii) U-shaped if in-channel accumulation of hillslope-derived material occurs. This latter situation indicates a nonbalanced mass flux between processes in channels and on hillslopes. Information about the spatial pattern of the postglacial depth of erosion allows comparative estimates to be made about the erosional efficiency for the various landscapes that were mapped in the study area. The data suggest that the erosional potential and sediment discharge are reduced for the situation of a non-balanced mass flux between processes in channels and on hillslopes. These findings are also supported by the numerical model. Indeed, the model results show that high hillslope mobility tends to reduce the hillslope relief and to inhibit dissection and formation of channels. In contrast, stable hillslopes tend to promote fluvial incision, and the hillslope relief increases. The model results also show that very low erosional resistance of bedrock promotes backward erosion and steepening of channel profiles in headwaters. Beyond that, the model reveals that sediment discharge generally increases with decreasing erosional resistance of bedrock, but that this increase decays exponentially with increasing magnitudes of fluvial and hillslope mobilities. Very high hillslope diffusivities even tend to reduce the erosional potential of the whole watershed. It appears that besides rates of base-level lowering, factors limiting sediment discharge might be the nonlinear relationships between processes in channels and on hillslopes. D 2002 Elsevier Science B.V. All rights reserved Keywords: Geomorphology; Sediment flux; Surface process model; Hillslope mobility; Swiss Alps

1. Introduction *

Tel.: +41-1-632-3648; fax: +41-1-632-1030. E-mail address: [email protected] (F. Schlunegger).

It is generally accepted that except for glacial erosion, long-term ( > 1000 years) erosional processes consist of a fluvial and a hillslope component (e.g.

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Schumm, 1956; Slingerland et al., 1993; Ahnert, 1999). Fluvial erosion of bedrock occurs at and downslope of channel heads if a critical flow strength is exceeded (e.g. Hack, 1973; Montgomery and Dietrich, 1992; Montgomery et al., 1996). Processes controlling sediment mobilization on hillslopes comprise soil creep and related nonconcentrated hillslope processes (e.g. Gilbert, 1909; Schumm, 1956) that are often referred to as hillslope diffusion in modeling studies (e.g. Tucker and Slingerland, 1996), overland flow erosion (e.g. Lawson, 1932) and landsliding if critical values for slopes and/or pore pressures are exceeded (e.g. Montgomery and Dietrich, 1992; Anderson, 1994) (Fig. 1). Among the various erosional processes, fluvial erosion is frequently anticipated to exert the first-order control on landscape development and formation of relief. For instance, Playfair (1802) was one of the first scientists who interpreted that the rivers shape the valleys in which they form. This concept has also been used recently to interpret possible controls on the geomorphic development of the western escarpment of the Andes (Uhlig, 1999), or to predict height limits of mountain ranges in active tectonic settlings (e.g. Whipple and Tucker, 1999). The attraction for fluvial processes stems from the hypothesis that fluvial erosion sets the lower boundary conditions for geomorphic processes on the adjacent slopes (Fig. 1A). In this case, increasing (or decreasing) rates of fluvial erosion result in enhanced (or reduced) rates of erosion on the adjacent hillslopes. However, it has also been proposed that rates of hillslope erosion do not necessarily have to be controlled by erosion in channels. For instance, for the situation in badlands, Schumm (1956) thought that a shift towards more humid climatic conditions is likely to cause an increase in hillslope erosion rates to the extent that the resulting donwslope mass flux exceeds the erosional potential of rivers. As a result, sediment accumulates on the channel floor, and hillslope processes start to modify fluvial processes in channels and the geomorphologic development of drainage basins (Fig. 1B). In another study carried out in the Finisterre Mountains, Papua New Guinea, Hovius et al. (1998)

found that hillslope mass wasting at the channel heads governs the rates and the mode of drainage basin modification. Finally, based on a 30-year monitoring program of geomorphic change in the Carlingill valley, northwest England, Harvey (2001) showed that the width, depth and morphologies of channels and the meandering of flows are clearly influenced by adjacent hillslope processes. This paper concentrates on the role of hillslope processes in governing the erosional efficiency of watersheds from a long-term perspective (thousands of years). It presents an example from a small (ca. 10 km2) watershed in the central Alps of Switzerland (Fig. 2) that has experienced significant surface erosion under present-day humid climatic conditions. It uses the results of detailed geomorphic studies carried out by Schubert (2001) and Schlunegger et al. (2002) to propose that an unbalanced mass flux between processes on hillslopes and in channels (e.g. Fig. 1B) tends to decrease the erosional efficiency in the watershed. In a further step, the extent of controls of the relationships between hillslope and fluvial processes on the erosional efficiency of watersheds will be explored numerically. This will be done by application of a surface process model to the situation of the analyzed watershed. As will be shown later in this paper, the model combines fluvial erosion with hillslope processes in its simplest form in which fluvial erosion is treated as a non-linear (advective) process, and erosion on hillslopes as linear diffusion. As expected, the model calculations will show that the erosional efficiency in the model watershed and sediment discharge increase with decreasing resistance to fluvial and hillslope erosion. This increase, however, decays exponentially with decreasing erosional resistance. Surprisingly, discharge will start to decrease if critical magnitudes of hillslope mobilities are exceeded.

2. The case study The Fischenbach drainage basin that provides the case study for this paper is located in the northern

Fig. 1. Conceptual models showing the major components of landscape processes. Fluvial processes are considered as the advective component of landscape evolution, and hillslope diffusion is used as proxy for creep of soil, overland flow erosion and landsliding. This figure also shows that (A) relief increases if hillslope processes are closely coupled to erosion in channels and that (B) relief decreases if the coupling between both processes is limited. See text for further explanations.

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Fig. 2. (A) Drainage network of the Swiss Alps and (B) geomorphology of the study area. The digital elevation model (DEM) of (B) that is used here is taken from Hurni et al. (2000). It has a spatial resolution of 25 m. The DEM clearly illustrates the glacial topography that is characterized by a smooth surface. It is cut by fluvial dissection and associated hillslope mass failure. Atlas der Schweiz interactive n Bundesamt fu¨r Landestopographie (BA024221). Fig. 2A reprinted from Schlunegger, F., Detzner, K., Olsson, D., The evolution towards steady state erosion in a soil-mantled drainage basin: semi-quantitative data from a transient landscape in the Swiss Alps. Geomorphology 43, 55 – 76, n 2002. With permission from Elsevier Science.

foothills of the Swiss Alps (Fig. 2). It is ca. 10 km2 and comprises three perennial tributaries that drain the western, central and eastern parts of the drainage basin (Fig. 3A). All of these tributaries have similar sizes of ca. 3 –4 km2. Furthermore, they reveal a

dendritic drainage network in the headwaters that changes into a linear drainage geometry at ca. 2 km distance from the source. Fischenbach drainage basin displays perennial runoff with major discharge events occurring in summer after severe thunder-

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Fig. 3. (A) Topography and (B) geology of the Fischenbach drainage basin. The contour plot of (A) is based on the topographic map (sheet 1169, Schu¨pfheim, Swiss Federal Institute of Topography). The geological map is based on data from Schubert (1998) and Detzner (2000). Modified after Schlunegger et al. (2002). Fig. 3 reprinted from Schlunegger, F., Detzner, K., Olsson, D., The evolution towards steady state erosion in a soil-mantled drainage basin: semi-quantitative data from a transient landscape in the Swiss Alps. Geomorphology 43, 55 – 76, n 2002. With permission from Elsevier Science.

storms and in early spring as the snow melts. Presentday climatic conditions are humid with average precipitation rates of 1500 mm/year (Frei and Scha¨r, 1998). The bedrock of the Fischenbach drainage basin, the nature of erosional processes and the resulting landscape and particularly the causal relationships between erosion in channels and on hillslopes were studied in detail by Detzner (2000), Schubert (2001) and Schlunegger et al. (2002). The following paragraph presents a short summary of the geology and the geomorphic evolution of the study area. Based on this information, it then discusses possible controls on variations in erosional efficiencies for the various portions of the Fischenbach drainage basin.

2.1. Geology The source rocks of the Fischenbach watershed are made up of Tertiary siliciclastic rocks and glacial till (Fig. 3B). The Tertiary units strike perpendicular to the drainage direction of the Fischenbach River, and they dip steeply towards the southwest. In the lower portion of the drainage basin, the Tertiary strata are made up of Early Miocene fluvial sandstones and interbedded overbank mudstones. They are tectonically overlain by a >1000-m-thick succession of Late Oligocene offshore marls and continental alluvial fan conglomerates. This latter unit forms the highest ridges in the southwestern portion of the study area (Heuboden ridge, Fig. 3).

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In the western part of the study area as well as in the southern portion of the Fischenbach drainage basin east of Heuboden ridge, the Tertiary rocks are covered by Pleistocene ground moraines. The surfaces that are underlain by the glacial till are smooth with nearly constant curvatures. A landscape with the same geometric characteristics is also found in the eastern portion of the study area. There, the smooth surfaces are underlain by the Tertiary siliciclastic rocks. Schlunegger et al. (2002) thought that in this portion of the study area, the smooth geometries are presumably the result of permafrost creep of soil during the last glacial time interval. Specifically, these surfaces reveal the same base level as the side and ground moraines that were deposited during the last glaciation (Schubert, 2001). At present, the glacial topography is found as eroded remnants because erosion at present-day climatic conditions has continuously modified it. The activities of postglacial fluvial erosion and associated hillslope processes are clearly indicated by the presence of breaks-in-slope in the topography (Fig. 3A) that have formed as the smooth glacial surface has become progressively dissected (Fig. 2). 2.2. Surface erosion The postglacial landform elements that have formed under present-day humid climatic conditions are the result of the combined activity of fluvial processes in valleys and erosional processes on hillslopes. Based on a detailed analysis of landform geometries and the nature of erosion, Detzner (2000), Schubert (2001) and Schlunegger et al. (2002) identified landform elements with characteristic cross-sectional geometries (Fig. 4). They bear information about the relationships between erosion on hillslopes and in valleys. The paragraph below presents a summary of the main geomorphic characteristics of these landform elements and the inferred geomorphic processes. In addition, it interprets erosional efficiencies as a function of specific combinations of processes on hillslopes and in channels.

In the headwaters, the surfaces of the hillslopes are smooth, and the dip angles continuously increase in the downslope direction resulting in classical parabolic cross-sectional geometries (Fig. 4A). In the channels, exposure of bedrock is rare, and the channel floors are frequently covered by >1-m-thick aggregates of poorly sorted mud, mudstones, plant fragments and boulders derived from the bordering hillslopes and from the upper portions of the drainage basin. These deposits form lobate geometries with convex-downstream lower boundaries. In addition, they are often dissected by V-shaped structures (this is, however, not visible in Fig. 4A). Schlunegger et al. (2002) thought that the poor sorting and the lobate geometries of these deposits suggest the episodic occurrence of high concentration flows presumably during periods of enhanced precipitation in summer (e.g. thunderstorms) or in early spring when the snow melts. The down-channel movement of these flows is anticipated to exert a shear stress on the underlying bedrock that then becomes eroded if critical threshold conditions are exceeded. Secondary fluvial dissection is indicated by the presence of V-shaped scars on top of the flow deposits. On the hillslopes, the convex-up geometries with nearly constant curvatures suggest the occurrence of continuous (in terms of geologic time scales of thousands of years) creep of regolith that also results in erosion of the underlying material. The parabolic cross-sectional geometries suggest that the long-term downslope flux of mass that results from erosion on the hillslopes is balanced by erosional processes in channels. In the trunk stream portion, the hillslopes display sharp upper boundaries, resulting in the formation of classic breaks-in-slope in the topography. The surfaces are planar with angular lower contacts, and they dip at ca. 20 –25j. The resulting landscape is V-shaped, and the local relief measures between 50 and 150 m (Fig. 4B). In these locations, the bedrock is to a large extent exposed on the channel floor. Alternatively, the hillslopes display a down-dip decrease in the dip angle, which then causes the formation of concave-up cross-

Fig. 4. Landform elements mapped in the northern foothills of the Swiss Alps. (A) Landforms with parabolic cross-sectional geometries are preferentially found in headwaters. (B) V-shaped cross-sectional geometries establish where fluvial erosion of bedrock is observed. (C) Landform elements with U-shaped cross-sectional geometries are considered to experience similar hillslope processes as V-shaped but with much larger sediment flux on the hillslopes which then results in accumulation of sediment on channel floors. Modified after Schubert (1998), Detzner (2000) and Schlunegger et al. (2002).

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sectional geometries (U-shaped, Fig. 4C). In these locations, the channel floor is covered by several tens-of-meters-thick deposits derived from the adjacent hillslopes. In the V- and U-shaped landform elements, erosion in channels is considered to occur during high discharge events as the transported material hits the ground with a kinetic energy that exceeds the mechanical strength and/or the shear resistance of the channel floor. On the hillslopes, erosion is considered to occur by mass failure (e.g. landslides) as indicated by the upper sharp boundaries (e.g. Ahnert, 1999). It appears that the long-term downslope mass flux that results from erosion on hillslopes exceeds the erosional efficiency in channels for the situation where sediment accumulates on the channel floor (the situation with U-shaped cross-sectional geometries, Fig. 4C). Alternatively, mass derived from hillslopes is considered to be efficiently removed by processes in channels for the situation where the hillslopes display angular lower contacts and where the bedrock is, to a large extent, exposed on the channel floor (e.g. V-shaped landform element, Fig. 4B). Mapping reveals (Schubert, 1998; Detzner, 2000) that in locations with U-shaped cross-sectional geometries of landscapes, the bedrock is made up of the Tertiary marls and glacial till (Figs. 3B and 5A) These lithologies preferentially absorb water due to either the presence of abundant clay minerals (marls) or because of the relatively high porosity (glacial till). The resulting increase in pore pressure tends to reduce the mechanical strength of these lithologies (e.g. Heinimann et al., 1998), which, in turn, reduces the angle of failure. As discussed by Schlunegger et al. (2002), the differences in lithologies and the resulting variations in the downslope flux of mass clearly influence the nature of longitudinal stream profile development. For instance, the river that drains the northern part of the western tributary displays a classic graded profile with continuously decreasing channel gradients in the downstream direction (Fig. 5B). Interestingly, this portion of the Fischenbach drainage basin is underlain

by the Early Miocene alternation of fluvial sandstones and mudstones. It is also made up of landform elements that are considered to reflect a balanced mass flux between processes in channels and on hillslopes (see above and Fig. 5A). It appears that in this part of the study area, processes in channels exert the first-order controls on the long-term geomorphic development, which implies that the rates of landform development are limited by fluvial (linear) processes. In contrast, the longitudinal stream profiles of the southern part of the western tributary and of the central and eastern tributaries are divided into segments separated by several steps in the stream profile (Fig. 5B). These steps are found where the hillslopes display tangential lower contacts (U-shaped landform elements) and where the channel floors are covered by several tens-of-meters-thick accumulations of mud, boulders, gravel and sand derived from the adjacent hillslopes. These landform elements are mostly underlain by glacial till and Tertiary marls. It appears that the development of these portions of the Fischenbach drainage basin is significantly influenced by processes on hillslopes. It is even anticipated that enhanced mobility of hillslopes inhibits fluvial erosion (see below). In this case, rates of landform development are limited by processes on hillslopes. 2.3. Erosional efficiency Detzner (2000) and Schlunegger et al. (2002) determined the spatial pattern of the depth of erosion by calculation of the digital elevation model (DEM) representing the difference between the surfaces that formed during glacial time interval (Fig. 6A) and the modern one. The pattern of the cumulative depth of erosion since termination of the last glaciation at ca. 17 –15 ka (Fig. 6B) is used here as proxy for the longterm erosional efficiency. For the details about the methodological aspects of DEM calculation for the glacial surface, the reader is referred to the former authors. It is important to note here that an assignment of an age of ca. 17– 15 ka for the glacial surface is not constrained by any geochronological method. Never-

Fig. 5. Geomorphology of (A) the analyzed drainage basin and (B) longitudinal stream profiles. The white areas on the geomorphic maps represent eroded remnants of surfaces that presumably formed during the last glaciation. Modified after Schlunegger et al. (2002). Fig. 5 reprinted from Schlunegger, F., Detzner, K., Olsson, D., The evolution towards steady state erosion in a soil-mantled drainage basin: semiquantitative data from a transient landscape in the Swiss Alps. Geomorphology 43, 55 – 76, n 2002. With permission from Elsevier Science.

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theless, because the paper focuses on comparative erosional efficiencies and on the general aspects of how hillslope mobility alters the geomorphic characteristics of a landscape, it is not really relevant to know the absolute ages of surfaces. The DEM representing the cumulative amount of postglacial erosion (Fig. 6B) clearly illustrates that the northern part of the western tributary (I in Fig. 6B) displays the highest magnitude of the cumulative amount of erosion during the last 15 – 17 ka. Specifically, the depth of maximum incision has reached constant magnitudes of ca. 100 –150 m from the trunk stream portion to the headwaters. As outlined above, this part of Fischenbach drainage basin displays a balanced flux of mass between processes on hillslopes and in channels, i.e. rates of landform development are limited by processes in channels. In contrast, in the central (III) and eastern (IV) tributaries as well as in the southern part of the western tributary (II), the depth of incision decreases from >100 to < 20 m in the upstream direction (Fig. 6B). This observation implies that the erosional efficiency of this part of the Fischenbach drainage basin has been lower during the last 15 –17 ka than that of the northern part of the western system. Interestingly, the central and the eastern tributaries as well as the southern part of the western tributary are also considered to display a downslope mass flux that is in excess of the erosional potential of the processes in the channels (Fig. 5A), i.e. the rates of landform development in these systems are limited by processes on hillslopes. The observations outlined above imply that the long-term erosional efficiency possibly depends on the mobility of hillslopes. Furthermore, in case that the downslope mass flux is not compensated by Fig. 6. Contour plots representing (A) the surface of Fischenbach drainage basin at ca. 15 ka and (B) the cumulative amount of erosion since then. About 15 ka is the time when the climate changed from glacial to present-day humid conditions (e.g. Hinderer, 2001). The contour plot is based on a DEM with a resolution of 30 m. The DEM was calculated by interpolation of the digital information of the glacial surface that is still well preserved (Fig. 3A). For the methodology of DEM calculation and discussion of the quality of the data, the reader is referred to Schlunegger et al. (2002). Fig. 6 reprinted from Schlunegger, F., Detzner, K., Olsson, D., The evolution towards steady state erosion in a soil-mantled drainage basin: semi-quantitative data from a transient landscape in the Swiss Alps. Geomorphology 43, 55 – 76, n 2002. With permission from Elsevier Science.

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erosion in channels, hillslope processes modify the geometries of stream profiles. Specifically, the rivers will be subdivided into several segments that are separated by steps where hillslope mobility is enhanced. The next section is designed to test the extent of controls of hillslope mobility on the erosional efficiency and, hence, on sediment discharge. As a tool, a surface process model that combines fluvial erosion with hillslope processes will be applied to the situation of the Fischenbach drainage basin.

3. Modeling the topographic evolution 3.1. The surface process model Understanding the evolution of the topography z(x,y) as a function of time is a problem which has received considerable attention over the last 10 years leading to the development of several well-known ‘surface process’ models (e.g. Kooi and Beaumont, 1994; Tucker and Slingerland, 1994, 1996, 1997; Tucker and Bras, 1998). Such models have been reasonably successful in reproducing realistic topographies by incorporating a combination of short- and long-range processes. Short-range processes, which act on the hillslope (such as rain splash and soil creep), are typically modeled with a linear diffusion equation: Dz ¼ kj2 z, ð1Þ Dt where z(x,y,t) is the topographic height and k is the substrate diffusivity. The latter parameter basically calibrates the erosional resistance of hillslopes. Long-range processes tend to be fluvial in nature and have been modeled using a variety of formulations where the incision rate is proportional to the stream capacity (e.g. Kooi and Beaumont, 1994), stream power (e.g. Seidl and Dietrich, 1992), or shear stress (e.g. Howard and Kerby, 1983; Tucker and Slingerland, 1996). These different models produce similar results when implemented in a surface process code. As an example of a fluvial model, consider the hydrodynamically based ‘shear stress’ formulation that is simple and is able to explain observed stream profile geometries in tectonically active settings (e.g.

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Snyder et al., 2000). According to this model, the rate of change of surface elevation can be described by a combination of local slope (S), drainage area (A) (a surrogate for water discharge Q where precipitation is uniform over the drainage area), the fluvial substrate diffusivity (K) and rock uplift rate (U) (which is equivalent to surface uplift rate in the absence of erosion): Dz ¼ U  KQm S n Am , Dt

ð2Þ

which is a nonlinear advection-type equation. Formulation (2) allows for the localization of topography leading to the formation of river systems. Models incorporating more complexities such as bedrock weathering and landsliding have also been proposed, but the first-order effects can be reproduced without these additions (Kooi and Beaumont, 1994). For incision rates proportional to shear stress, various authors have shown that m f 1/3 and n f 2/3 under the following assumptions: flood flow can be treated as steady and uniform, channel width (W) scales with discharge as W– Q0.5 (e.g. Leopold and Maddock, 1953) and flood discharge scales approximately linearly with drainage area (cf. Slingerland et al., 1993). The erosion parameter K calibrates the fluvial erodibility of the substratum; it is inversely related to the resistance of the substratum to fluvial erosion. The model applied here is based on the shear stress equation formulation for fluvial erosion and the diffusion equation to simulate mass flux on hillslopes. Consequently, the model strategy of this paper is the simplest one as it considers the simplest scenarios of erosional processes. Certainly, fluvial erosion is much more complex than implied by the shear stress criterion (e.g. Hancock et al., 1998), and hillslope erosion, especially in mountainous landscapes such as the Swiss Alps, is clearly not diffusive and continuous (Heinimann et al., 1998). However, the model aims only at exploring, from a generic point of view, to what extent hillslope mobility influences the erosional potential in landscapes with the size and initial conditions of the selected area, i.e. it focuses on the effects of what Harvey (1994) considered uncoupled slope/stream process interactions. Accordingly, the reduction of the erosional processes to advective and diffusive terms in the simplest form appears justified.

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Finally, the shear stress approach is justified for this purpose because it is simple, it has a hydrological basis (e.g. Slingerland et al., 1993) and it reproduces the classical graded stream profiles for mountainous regions (e.g. Snyder et al., 2000). The model uses a discrete (cellular automation) algorithm for the calculation of the drainage area (water discharge). For details concerning the mathematical derivations for surface erosion and the finite difference technique (including boundary conditions), the reader is referred to the publications by the developers of the model (Slingerland et al., 1993; Tucker and Slingerland, 1994, 1996, 1997). 3.2. Initial conditions The model uses the restored glacial topography of the Fischenbach drainage basin of Schlunegger et al. (2002) as initial topography (Fig. 6A). For this surface, Schlunegger et al. (2002) calculated a digital elevation model (DEM) with a spatial resolution of 30 m and with a size of 128  94 cells (i.e. ca. 4  3 km). Data collection for DEM generation was accomplished by digitization of landform elements that were formed during the last glacial time interval. For identification of glacial landform elements as well as for a detailed description of the methodology of DEM calculation, the reader is referred to Schlunegger et al. (2002). Fluvial erosion is assumed to occur if the upstream size of the drainage basin exceeds a minimum area of ca. 14,000 m2 (0.014 km2) (threshold conditions for fluvial erosion). This magnitude of critical size is chosen because Detzner (2000) found that fluvial incision is initiated if the upstream size of the drainage basin exceeds that critical magnitude. Mass movements on hillslopes are modeled assuming linear diffusion (see justification above). Because Detzner (2000) mapped continuous transitions from regolith to bedrock in the study area, hillslope mobility is treated as non-weathering limited. A time interval of 15 ka is modeled that is anticipated to encompass the interpreted timespan between termination of the late glacial interval and the present (e.g. Hinderer, 2001). The total length of the model run was subdivided into 100-years-long time increments that will result in 150 calculation steps for each model run. For the Fischenbach system,

the depth of postglacial lowering of the base level was estimated to measure ca. 190 m (Detzner, 2000). It is implemented in the model by a simple surface uplift function, which is equivalent to lowering of the regional base level at the same rate. The lithologic architecture of the drainage basin is assumed to be uniform for simplicity. Certainly, the bedrock lithology and, hence, the pattern of erosional resistance are highly variable in the study area (see above). However, it is not the intent of the paper to reproduce the details of complexities in the watershed. As stated above, this analysis explores from a generic point of view the effects of different scenarios of erosional resistance on hillslopes and in channels. Accordingly, variations in bedrock lithologies are considered, performing various model runs with different contrasts between hillslope and fluvial diffusivities. Precipitation is considered to be uniform in space and time with rates of 1500 mm/year (Frei and Scha¨r, 1998). These magnitudes are based on present-day measurements (see above). This simplification is justified because any variations from these rates during the model runs will result in transient effects in the landscape (such as formation of terraces). These features are indeed present in the analyzed drainage basin, but they do not form predominant geomorphic elements (Schubert, 2001). For more sophisticated applications that paid special attention to the effects of temporal variations in precipitation rates and bedrock lithologies and differences in hillslope processes, the reader is referred to Tucker and Slingerland (1996, 1997) and to Tucker and Bras (1998). In summary, the simple approach of this paper is justified because it intends to document the basic effects of the ‘competition’ between fluvial and hillslope processes. Therefore, the hillslope (k) and the fluvial diffusivities (K) that scale the downslope sediment flux and the rates of fluvial incision, respectively, are iteratively modified. Very few studies have made efforts to quantify variations in fluvial diffusivities. In one of the few examples that is provided by a modeling study of the Central Zagros Mountain fold belt, Tucker and Slingerland (1996) used 10-fold contrasts between fluvial diffusivities of carbonate units and sandstone/mudstone alternations. Similarly, based on morphometric analyses carried out for the Swiss Alps, Ku¨hni and Pfiffner (2002a,b) suggested a 10-fold difference between the diffusivities of (meta)

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Fig. 7. Model results of numerical experiment for (A) stable hillslopes and low fluvial diffusivities, (B) moderate fluvial bedrock diffusivities and (C) very high fluvial bedrock diffusivity. The contour lines illustrate the calculated elevations in 50-m step intervals. The dimensions of the fluvial bedrock diffusivity (year  2/3) are chosen for the sake of the dimensional balance between erosion rates (m/year) and discharge (m3/year).

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Fig. 8. Stream profiles of the river of the central tributary of the modeled drainage basin. See Fig. 7 for location.

sedimentary units and crystalline lithologies. For this model exercise, magnitudes of erodibilities of between 250 and 1500 year  2/3 are assigned to the bedrock that spans the contrasts found in the literature, and that will result in reasonable longitudinal stream profiles (see below). Similarly, hillslope diffusivities of between 0.2 and 1.5 m2/year are assigned to hillslope processes that will encompass the range found in the literature (e.g. Saunders and Young, 1983; Reneau and Dietrich, 1991). Note, however, that it is not really important to know the absolute magnitudes of parameters for the modeling purposes of this study. Since the intent is to analyze the effects of the competition between hillslope and fluvial processes, it is more relevant to know the ratio between the hillslope and fluvial diffusivities.

4. Results Two situations are considered in this paper. The first one is designed to explore the outcome of increasing fluvial substrate diffusivities at moderate values for hillslope diffusivity (which is equivalent to hillslope mobility) (Fig. 7). As will be illustrated below, the surface becomes increasingly dissected at decreasing erosional resistance of bedrock (which is equivalent to an increase in the fluvial diffusivity) (Fig. 7), channel profiles develop towards graded geometries and fluvial erosion tends to become enhanced in the headwaters (Fig. 8). The second set of model runs (Fig. 9) attempts at exploring the controls of enhanced hillslope mobility on the geometric development of the model landscape and of the

Fig. 9. Model results of numerical experiment for (A) very high fluvial bedrock diffusivity and stable hillslopes (same as Fig. 7C) and low fluvial diffusivities, (B) high hillslope diffusivity and (C) very high hillslope diffusivites. The contour lines illustrate the calculated elevations in 50-m step intervals. The dimensions of the fluvial bedrock diffusivity (year  2/3) are chosen for the sake of the dimensional balance between erosion rates (m/year) and discharge (m3/year).

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stream profiles. This was done using the lowest erosional resistance of the first set of model runs (Fig. 7). The competitiveness of hillslope processes on the geometric evolution of the model topography (Fig. 9) was then explored by increasing the hillslope diffusivities. The results show that although the substrate displays low magnitudes of resistance to fluvial erosion, hilllslope processes start to dictate the evolution of the topography and the geometries of stream profiles if very high hillslope diffusivities are applied (Figs. 9 and 10). 4.1. Situation I: moderate hillslope diffusivity and increase in fluvial substrate diffusivity In the case where fluvial erosion exerts the firstorder controls on drainage basin development (as is generally believed), then fluvial bedrock diffusivity is a crucial parameter that scales rates of drainage basin development, formation of relief and lengths of response times. Experiments I, II and III (Fig. 7) illustrate the effect of such a scenario. In the case of

a very low fluvial bedrock diffusivity (experiment I, Fig. 7A), incision rates appear to be nearly equal to the rates of base-level lowering (or rates of surface uplift as implemented in the model, see above) as seen on the development of the stream profile of, e.g., the central system. This is illustrated in Fig. 8, where the difference between the initial and final situations is nearly constant for experiment I. Deviations from this pattern of constant magnitudes at x = 1000 m distance presumably occur in order to adjust to graded profile geometries. It appears, therefore, that for low fluvial substrate diffusivities, the evolution of the drainage basin is predominantly controlled by the rates of changes of the regional base level (or surface uplift). If the fluvial bedrock diffusivity is increased to the extent that fluvial erosion exceeds the rates of baselevel lowering (as seen at x = 2000 –3000 m distance for experiments II and III, Fig. 8), then the evolution of the drainage basin is slightly different to what is found in experiment I (Fig. 7B and C). The model results show that an increase in the fluvial bedrock diffusivity beyond the threshold of steady-state dis-

Fig. 10. Stream profiles of the river of the central tributary of the modeled drainage basin. See Fig. 9 for location.

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section (i.e. incision rates equal surface uplift rates) causes the rivers to erode backward especially in the headwaters. As a consequence, the gradients and the curvatures of the channels increase in the source areas (Fig. 8). However, despite contrasts of factors of 3 between magnitudes of bedrock erodibilities, the resulting geometries only differ by the establishment of steeper gradients in the headwaters (Figs. 7B,C and 8). These simple experiments illustrate that the evolution of drainage basins is simple for the case of stable hillslopes: enhanced fluvial substrate diffusivities tend to promote backward incision in the trunk stream portion and establishment of steep channel profiles especially in the headwaters (Fig. 7). As a result, the hillslope relief increases especially in the source areas. However, landscape evolution completely changes if the hillslopes become more mobile. This situation will be explored in the next section. 4.2. Situation II: changes in hillslope mobility An increase in hillslope diffusivities will result in enhanced flux of mass on the hillslopes. The effects of such scenarios are explored by the succeeding experiments III –V (Fig. 9). Note that the maximum fluvial diffusivities of experiment III are applied as a reference in order to better illustrate the potential of hillslope processes to drive, or at least to modify, the evolution of landscapes. The model results clearly show that an increase in the downslope flux of mass tends to decrease the hillslope relief as well as the density of channels. These reductions, however, occur only after a specific time interval. Specifically, the channel densities of all model experiments are higher after, e.g., 3 ka of model run than after 15 ka. The model results also show that enhanced downslope flux of mass affects the evolution of stream profiles. This is shown for the situation of the central tributary of the model topography (Fig. 10). Specifically, high flux of mass from hillslopes to channels tends to result in the accumulation of sediment in channels. As a result, the elevation of the channel floor increases, which, in turn, additionally contributes to the decrease in the hillslope relief. Rates of increase of the elevation of the channel floor, however, are enhanced in the headwaters of the drainage

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basin (Fig. 10). Interestingly, this is the location where relief would be formed at the highest rates for low hillslope diffusivity and high bedrock erodibility (Fig. 8). It appears, therefore, that if the hillslopes are very mobile, high bedrock diffusivities tend to have the opposite effects as actually anticipated: enhanced fluvial diffusivities tend to increase the formation of local relief especially in the headwaters (Fig. 8). As a result, the downslope flux of mass is enhanced in this portion of the drainage basin to the extent that the downslope flux of mass exceeds the erosional potential of the river, causing sediment to accumulate on the channel floor. Also, the stream profiles do not display the classic graded geometries that are found for the case of stable hillslopes. Indeed, the models suggest that enhanced downslope flux of mass results in the formation of various steps in the stream profile. It is interesting to observe that whereas the differences between model stream profiles are significant between experiments III and IV, they are negligible for model runs of experiment IV and V (Fig. 10).

5. Discussion The results of the models highlight the importance of hillslope mass flux on the evolution of drainage basins (see also Tucker and Bras, 1998). Nevertheless, it will be argued below that the initial topography exerts the primary controls on drainage basin establishment and that the first stages of landscape development are then controlled by fluvial erosion. Subsequent modifications, however, depend on contrasts between the hillslope and the fluvial bedrock diffusivities. Most important, however, is that evidence will be presented to propose that enhanced hillslope diffusivities tend to decrease sediment discharge. 5.1. Controls on drainage geometry The first-order characteristics of the drainage geometry of the Fischenbach drainage basin are successfully modeled despite the assumption of the simplest case of erosional parameters (Fig. 11). Specifically, for the whole range of fluvial and hillslope diffusivities, the modeled drainage basins reveal three tributaries that initially correspond in size, in locations

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Fig. 11. Comparison between the observed drainage network of the Fischenbach system and the modeled drainage geometry. It appears that the model predicts the main features of the observed geometric configuration of the fluvial network independent of the hillslope and fluvial diffusivities. Even in cases of very mobile hillslopes, the fluvial network will display the same first-order characteristics (i.e. three tributaries) as for the case of stable hillslopes. High flux of mass only tends to inhibit dissection and branching, thus resulting in modifications of the fluvial network.

where they join the trunk stream and in channel densities with the situation of the Fischenbach system (Fig. 11). Modifications of these first-order characteristics of the drainage pattern occur only during succeeding model steps as the downslope flux of mass on hillslopes increases. Specifically, high flux of mass from hillslopes to channels tends to reduce the channel density especially in the headwaters of the tributaries (e.g. Figs. 7 and 8). In contrast, variations in fluvial bedrock diffusivities do not affect the density of channels but influence the depth of incision and formation rates of hillslope relief. It appears, therefore, that the shear stress formulation for fluvial incision and the determination of threshold conditions for channel initiation as applied in this paper are adequate approaches to simulate the establishment of drainage systems in the Swiss Alps. The effects of other approaches, however, have to be tested by future studies (such as, e.g., erosion rates related to undercapacity and/or sediment discharge).

5.2. Controls on stream profile development The model results suggest that fluvial diffusivities and, hence, the erosional resistance of source rocks will not exert the primary controls on the establishment of the drainage geometry, but will control the depth of incision per unit time, formation of relief and the rates at which headward incision occurs. However, this is only the case for stable hillslopes, i.e. for situations with reduced downslope flux of mass (e.g. Fig. 8). In this case, an increase in the fluvial diffusivity (which is equivalent to a shift towards lithologies with lower erosional resistance) tends to promote the rates of headward incision (experiments II and III in Fig. 8). The resulting stream profile adapts a geometry that is characterized by an exponential downstream decrease in the concavity and by steep channel gradients in the headwaters. The model results show that these geometries establish for situations where rates of fluvial incision exceed rates of

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base-level lowering (or rates of surface uplift). In contrast, high erosional resistance of bedrock and, hence, low fluvial bedrock diffusivities result in lower or equal rates of fluvial erosion with respect to

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changes in the regional base level, which in turn results in rather linear longitudinal stream profiles (or graded stream profiles with low curvatures) (see also Anderson, 1994, and Fig. 8).

Fig. 12. Calculated sediment discharge for (A) increasing fluvial bedrock erodibilities (which is equivalent to fluvial diffusivities) at a moderate hillslope diffusivity and (B) increasing hillslope diffusivity at very high bedrock erodibility. Note that the measured sediment discharge is reproduced by input parameters of experiment I (Fig. 7A). Higher magnitudes of diffusivites are chosen to outline the potential effects of hillslope mobility.

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5.3. Fluvial and hillslope diffusivities and sediment discharge Additional experiments were performed to calculate the sediment discharge for various scenarios of fluvial and hillslope mobilites. The resulting pattern clearly shows that although fluvial erosion rates linearly relate to fluvial diffusivity (Eq. (2)), the increase in sediment discharge decays exponentially with increasing fluvial erodibilities (Fig. 12A). Similarly, sediment discharge increases if hillslope mobilities are enhanced, but this augmentation decays exponentially with increasing bedrock diffusivities. However, sediment discharge starts to decrease for hillslope mobilities >0.5 m2/year (Fig. 12B) despite the application of maximum fluvial erodibilities (Fig. 12A). As seen on the development of the model stream profiles (Fig. 10), high hillslope mobility tends to enhance the downslope flux of mass in excess of the erosional potential of the river. As a result, sediment starts to accumulate on the channel floor, which, in turn, causes the formation of steps in the longitudinal stream profiles and a reduction of the local relief. It appears, therefore, that enhanced hillslope mobility causes an augmentation of sediment yield within the drainage basin but a decrease in sediment discharge out of the system (see Fig. 12).

6. Conclusion The data collected from the Fischenbach drainage basin, a 10-km2 large watershed located in the northern foothills of the Swiss Alps, suggest that hillslope processes potentially modify, or even drive, the evolution of drainage basins under humid climatic conditions. Specifically, the stream profiles of the Fischenbach drainage basin reveal geometries that reflect the influence of landslides derived from the adjacent hillslopes (southern part of the western tributary, central and eastern tributaries, Fig. 5). In these areas, the rates of landform development were considered to be limited by hillslope processes. In contrast, if the rates of landscape development are limited by fluvial erosion (which was interpreted for the northern part of the western tributary), then the stream profiles are graded with nearly constantly decreasing stream gradients in the downstream direc-

tion. The geomorphic data and information about the cumulative amount of postglacial erosion also indicate that fluvially dominated systems tend to be more efficient in modifying topographies by erosion than landscapes whose development rates are limited by hillslope processes. These findings are reproduced by the numerical model. Beyond that, the model predicts limits on controls of erosion such as that sediment discharge does not linearly increase with fluvial bedrock and hillslope diffusivities. Indeed, the increase decays exponentially with increasing magnitudes of fluvial and hillslope mobilities. Very high hilllslope diffusivities even tend to reduce the erosional potential of the whole watershed. This latter aspect of controls on sediment discharge should be analyzed more carefully in future studies. Acknowledgements This research was supported by the Federal Office for Water and Geology of Switzerland, the Deutsche German Science Foundation (DFG, project no. SCHL 518/1-1) and by the Swiss National Science Foundation (NSF, project no. 620-57863). The technical support of O. Anspach (Univ. Jena) is kindly acknowledged. This paper benefited from the scientific exchange with J. Melzer (University of Jena) who also helped me during DEM generation and during the installation of the software. Also, very supportive discussions with G. Simpson (ETH Zurich) are kindly acknowledged. I thank Greg Tucker for making his software available and for scientific exchange. The constructive reviews of an anonymous referee and of a second referee, ‘Martin Stokes’, are kindly acknowledged. References Ahnert, F., 1999. Einfu¨hrung in die Geomorphologie. Eugen Ulmer, Stuttgart, 440 pp. Anderson, R.S., 1994. Evolution of the Santa Cruz Mountains, California, through tectonic growth and geomorphic decay. Journal of Geophysical Research 99, 20161 – 20179. Detzner, K., 2000. Beziehung zwischen Fluvialerosion und denudativen Hangprozessen-Geomorphologische Analyse und GIS-unterstu¨tzte Modellierung eines nordalpinen Einzugsgebietes, Zentrralschweiz. Unpublished report to master thesis project, University of Jena, Jena, 72 pp.

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