Drainage Rearrangement: a Modelling Approach

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Drainage rearrangement: a modelling approach

Maricke van Leeuwen

June, 2013

Drainage rearrangement: a modelling approach

MSc thesis (SGL-80436)

Maricke van Leeuwen 901027509070

MSc Earth and Environment, specialization Soil Geography and Landscape Wageningen University

Wageningen, June 2013

Supervisors dr. ir. A.J.A.M. Temme Soil Geography and Landscape Group Wageningen University drs. W. van Gorp Soil Geography and Landscape Group Wageningen University dr. ir. J.E.M. Baartman Soil Physics and Land Management Wageningen University

iii Abstract Drainage rearrangement can be defined as the rerouting of a (sub)stream, through capture, migration, diversion or beheading. Drainage rearrangements play an important role in landscape evolution, by changing fluvial morphology and geomorphology. Although many studies have described these phenomena, quantitative descriptions and comparative studies are lacking. This study aimed to quantitatively explore the dynamics and consequences of drainage rearrangement. This was done for a set of rearrangement mechanisms using landscape evolution model LAPSUS (LandscApe ProcesS modelling at mUlti-dimensions and Scales). Five scenarios were designed using idealized DEMs: equal (i) and unequal tectonic uplift (ii), strike-slip faulting (iii), river damming by a lava flow (iv) and glacial activity (v). Also the effect of climate on river sensitivity to forcing was assessed. For the scenarios strike-slip faulting, equal and unequal tectonic uplift, the majority of rearrangements in a wet climate were river captures, whereas in a dry climate mainly channel migrations were taking place. The number of rearrangements was decreasing in time, indicating that landscapes were going to reach a topological steady-state. Climate played an important role in the reactivity of the landscape to forcing. For the scenarios river damming by a lava flow and glacial activity, rivers were directly diverted due to forcing. For all scenarios geomorphological signatures of rearrangement included the change of drainage pattern. Some rearrangement types resulted in the presence of knickpoints along the river course. The effect of drainage rearrangements on erosion, and the efficiency of sediment transport by rivers, was debatable.

Keywords: landscape modelling; drainage rearrangement; capture; channel migration; diversion

iv Preface During the study ‘Soil Geography and Landscape’, my interest was more and more going out to geomorphology. One year ago, I read for the first time about stream capture and that it can cause large-scale redistribution of watersheds and rivers. I wanted to study this topic, because during courses there was never paid attention to this subject. Also I wanted to obtain modelling skills. These two aspects were perfectly combined in the topic of my thesis: ‘drainage rearrangement: a modelling approach’.

I want to thank Arnaud Temme for his critical view, for motivating me, his patience and for his always-critical voice in my head when I am writing a text.

I want to thank Wouter van Gorp and Jantiene Baartman for helping me with LAPSUS and giving feedback on my work.

And I want to thank all my friends, family and corridor mates, who gave mental support and who surprised me with breakfasts and lunches.

v Table of Contents 1. Introduction ...... 8 1.1 Definition of terms ...... 10 1.2 Problem description ...... 10 1.3 Objective and research questions ...... 11 2. Methods ...... 12 2.1 LAPSUS ...... 12 2.2 Scenario description ...... 13 2.2.1 Input data ...... 13 2.2.2 Equal tectonic uplift ...... 15 2.2.3 Unequal tectonic uplift...... 15 2.2.4 Strike-slip faulting ...... 15 2.2.5 Sudden disruption: river damming by a lava flow ...... 15 2.2.6 Gradual disruption: glacial activity ...... 15 2.3 Analysis ...... 16 2.3.1 Response of rivers to forcing ...... 16 2.3.2 Geomorphological signatures ...... 17 3. Results ...... 18 3.1 Equal tectonic uplift...... 18 3.2 Unequal tectonic uplift ...... 21 3.3 Strike-slip faulting ...... 23 3.4 Sudden disruption: river damming by a lava flow ...... 25 3.5 Gradual disruption: glacial activity ...... 27 4. Discussion ...... 29 4.1 Model limitations ...... 29 4.2 Occurrence of drainage rearrangements over time ...... 29 4.3 Rearrangement types ...... 29 4.4 Rearrangement mechanisms ...... 30 4.5 Geomorphological signatures ...... 31 4.5.1 Morphological changes ...... 31 4.5.2 Sediment supply ...... 31 5. Conclusions ...... 33 References ...... 34 Appendix ...... 37 Collapse component ...... 37 Equal tectonic uplift ...... 37 Unequal tectonic uplift ...... 37 Strike-slip faulting ...... 38 River damming by a lava flow ...... 38 Glacial activity ...... 38

vi Table of Figures Figure 1. Overview of drainage rearrangement types displaying main drainage lines and watershed divides (dashed lines). A: Stream capture due to headward erosion. B: A diversion is displayed where the diverted river is redirected into an existing flow path. When the rate of migration is low, the rearrangement is classified as migration. C: Beheading due to exchange of catchment area. (Source: modified from Bishop, 1995)...... 9 Figure 2. Overview of geomorphological signatures. A. Boathook bends can be found when the captive had a strong deviating flow direction than the captor. Barbed tributaries are the result of subsequent captures and formation of boathook bends...... 10 Figure 3. Virtual input DEMs and their characteristics. Contours are displayed on the location where forcing is imposed. A: Equal and unequal tectonic uplift; B: strike-slip faulting; C: river damming by a lava flow; D: glacial activity...... 14 Figure 4. An example output from the glacial activity scenario, shortly after the first part of the glacier was moved in. The white arrows indicate river junctions where the sub-catchments were considered as one watershed. The characters A to J refer to the nested sub-catchments...... 17 Figure 5. Knickpoint formed due to river capture...... 18 Figure 6. Number and type of rearrangement events over time, for the equal tectonic uplift scenario. The vertical black lines show the moment that forcing started, at t = 2000...... 18 Figure 7. Elevation change during 500 simulation years. Light grey colours indicate increased elevation, the contours of the rising structure are visible. Black colours indicate decreased elevation, mainly due to incised channels. The upper arrow points at an increased elevation upstream of the rising structure, where rivers are blocked. Water is diverted to the left or right. In this example tributaries of the channel on the left hand side are capturing the diverted water. The lower arrow points at dark colours in the river course, which gradually turn to lighter colours upstream, indicating a knickpoint...... 19 Figure 8. Drainage pattern of the study area at t = 15000 where equal tectonic uplift was imposed...... 19 Figure 9. Example of river profiles of a captor and a captive, crossing the lower boundary of the rising structure at t = 7500. There is not a knickpoint formed at the location of capture, but knickpoints were formed due to incision of the lower margin of the rising structure. The location of capture is taken as reference for the measured distance along the river profiles, but the relative location of the lower margin of the rising structure is indicated as well, represented by the vertical lines. The captor has a longer flow path over the rising structure than the abandoned channel...... 20 Figure 10. Annual time series of the total erosion and SDR for the equal uplift scenario. Note that the graphs of the total erosion wet, total erosion dry, SDR wet and SDR dry are considered for half of the study area...... 21 Figure 11. Annual time series of the displaced sediment due to collapses, for the equal tectonic uplift scenario. Per collapse around 25 x 400 m3 is displaced, so there was mainly one collapse per year, with a maximum of four collapses per year...... 21 Figure 12. Number and type of rearrangement events over time, for the unequal tectonic uplift scenario...... 22 Figure 13. DEM of the unequal tectonic uplift study area at t = 15000...... 22 Figure 14. Annual time series of total erosion and SDR for the strike-slip faulting scenario. Note that the total erosion wet, total erosion dry, SDR wet and SDR dry are considered for half of the study area...... 23 Figure 15. Number and type of rearrangement events over time, for the strike-slip faulting scenario...... 24 Figure 16. DEM of strike-slip scenario study area at t = 15000. The lower 5 km of the study area was shifted to the right hand side, with a total length of 340 m in 13000 y...... 24 Figure 17. Example of knickpoints in river profiles due to diversion (at t = 9500, left) and due to capture (at t = 10500, right). In the case of diversion directly due to strike-slip faulting (left), a new channel was formed due to blocking. Note the higher elevation of the abandoned channel a few meters above the fault and the change of the river profile as result of deposition upstream of this point. In case of capture (right) streams below the fault were shifted and able to capture channels which were nearby above the fault...... 25 Figure 18. Annual time series of the total erosion and SDR for the strike-slip faulting scenario. Note that the total erosion wet, total erosion dry, SDR wet and SDR dry are considered for half of the study area...... 25 Figure 19. DEM of the study area at t = 5000 for the scenario river damming by a lava dam...... 26 Figure 20. River incision along the narrow margin of the lava dam. The rivers flow along the narrow margin of the dam. At a distance of 0 m, rivers were halfway of the narrow side of the dam. Going upstream, river were flowing along the narrow margin of the dam until 220 m, further upstream rivers are not following the dam...... 26 Figure 21. Annual time series of the total erosion and SDR for the scenario river damming by a lava flow...... 27 Figure 22. Sub-catchment distribution within a time span of 1000 years. Note that in 2050 catchment E was added at the expense of catchment B and that a new division was made at t = 2400...... 27 Figure 23. DEM of the study area at t = 3000...... 28 Figure 24. Annual time series of the total erosion and the SDR for the glacier activity scenario...... 28

Table of Tables Table 1. Scenario settings of the erodibility factor precipitation...... 15 Table 2. Number and types of drainage rearrangements per scenario...... 30 Table 3. Geomorphological signatures per scenario. An ‘x’ means that the drainage rearrangement mechanism is not found under the scenario settings...... 31

vii 1. Introduction Sediment budget studies are becoming more and more of interest for landscape evolution, soil formation and erosion (Walling, 1983; Bishop, 1995; Foster et al., 1977; Baartman et al., 2012, Lee et al., 2012). The effectiveness of sediment transport is largely determined by the rate of geomorphic connectivity and coupling. Methods are developed to assess the systems connectivity. Heckmann and Schwanghart (2013) were able to simulate sediment pathways using graph theory and Brierley et al. (2006) chose the sediment delivery ratio (SDR) as a measure for sediment connectivity on catchment scale. The SDR is calculated as the annual amount of sediment that leaves a catchment, relative to the total annual amount of erosion within a catchment (Glymph, 1954). A high SDR means that there is a high sediment connectivity in the fluvial system, due to an effective transport of sediment.

Sediment transport can be affected by drainage rearrangements. Drainage rearrangement is the notion that (part of) a river flows in a new direction. Although many studies describe this phenomenon (Calvache and Viseras, 1997; Mather, 2000; Stokes et al., 2002; Brocard et al., 2012; Castelltort et al., 2012), some inconsistency persists about rearrangement terminology. E.g. Mather (2000) explained that river capture can involve beheading and diversion; Douglass and Schmeeckle (2007) considered diversion as part of capture; and Brocard et al. (2011) defined diversion as ‘any type of change in river patterns resulting from the interaction of two rivers’, which is not a strict classification of rearrangement types. In this study rearrangement terminology is based on work of Bishop (1995). He mentions that there are three types of drainage rearrangement: stream piracy (1), drainage diversion (2) and beheading (3), which will be clarified below. The type ‘channel migration’ (4) is added, in order to have more distinction in diversion mechanisms.

1. Stream piracy or capture. A river can be captured by an adjacent river that is eroding and extending. The captor is always increasing drainage area in the expense of the captive (Stokes et al., 2002). Since the captor is actively involved in this process, stream capture is known as a bottom-up process. According to Bishop (1995) capture is the most common mechanism of river rearrangement found in literature. It is often promoted by an extreme base level lowering, which causes the headwaters to incise faster (Stokes et al., 2002; Douglass and Schmeeckle, 2007) (Figure 1A). 2. Drainage diversion. A river can be redirected into an adjacent river or create a new flow path as result of top-down processes, i.e. a river is pushed to rearrange as result of external factors. It can be the result of tectonic activity, aggradation (Brocard et al., 2011), river damming (Maddy et al., 2012), river breaching (Brocard et al., 2012) and extreme flooding (Bishop, 1995) (Figure 1B). 3. River beheading. River beheading is the transfer of catchment area from one river to another via groundwater (Bishop, 1995;Brocard et al., 2011). Beheading can be caused by escarpment retreat, where the escarpment is also the drainage divide. This leads to extension of the most active river at the expense of another. Rivers never cross aboveground (in contrast to other rearrangement mechanisms), because the suppressed river is beheaded before it can be reached aboveground (Figure 1C). 4. Channel migration. Channel migration is based on the same processes that cause stream diversion, but migration occurs more gradually and rivers are not directed into an existing flow path. Therefore the extent of rearrangement is much smaller than diversions (Figure 1B).

A. B. C.

Time

Figure 1. Overview of drainage rearrangement types, displaying main drainage lines and watershed divides (dashed lines). A: Stream capture due to headward erosion. B: A diversion is displayed where the diverted river is redirected into an existing flow path. When the rate of migration is low, the rearrangement is classified as migration. C: Beheading due to exchange of catchment area (Source: modified from Bishop, 1995).

The mechanisms that cause drainage rearrangement can be subsequently divided into top-down and bottom-up processes. Top-down processes force a river to flow into another direction (the rearranging river is not actively involved), whereas bottom-up processes are caused by a river itself (the rearranging river is actively involved). Top-down processes are related to drainage diversion and migration, whereas stream piracy by drainage head retreat is a typical bottom-up process (Bishop, 1995). Beheading can either be a top-down or a bottom-up process, depending on the cause of the drainage divide retreat. River sensitivity to forcing is influenced by lithology (intrinsic control), anthropogenic influences (extrinsic control) and climate (extrinsic control) (Mather, 2000). Climate fluctuates through time and alternates between glacials and interglacials, influencing the precipitation amount and base level. Rivers respond to this and alternate between aggradation respectively incision. The erosive power of rivers is therefore alternating as well due to a fluctuating sediment supply (Mather, 2000; Whitfield and Harvey, 2012; Wernicke, 2011).

Drainage rearrangements leave signatures in the landscape which can be typical for a type of rearrangement. The knowledge of these geomorphological signatures can provide more insight in landscape evolution. A necessary geomorphological signature of rearrangement is a changed drainage pattern, either by the presence of boathook bends (sharp bend in the river course) and barbed tributaries. Often knickpoints and wind gaps are found (Figure 2) (Calvache and Viseras, 1997; Humphrey and Konrad, 2000; Mather, 2000; Stokes et al., 2002; Brocard et al., 2012; Whitfield and Harvey, 2012; Goren et al., in press). Boathook bends can be found when the rearranged river had a strong deviating flow direction than the new connected river channels. Barbed tributaries are the result of subsequent captures and formation of boathook bends (Figure 2A). In case of capture, the abandoned river segment between the captive and the captor is called a wind gap. A knickpoint is formed due to a base level difference between a rearranged river and the new connected river channels (Figure 2B).

A. B.

Elevation Channel profile

Figure 2. Overview of geomorphological signatures. A. Plan view showing the locations of wind gaps, boathook bends and barbed tributaries. B. River profile showing a knickpoint. 1.1 Definition of terms The following definitions regarding drainage rearrangement will be used in this study: Driving factor or forcing: The initial cause that forces a river to change its flow direction. Control: Influences the sensitivity of a river to forcing. Intrinsic controls originate from the catchment itself, whereas extrinsic controls originate from outside the catchment. Process: The manner in which a driving factor forces a river to rearrange, or the manner in which a control can influence a river sensitivity to forcing. Mechanism: The manner in which drainage rearrangements take place as result of driving factors, controls and processes.

Two different mechanisms behind drainage rearrangement will illustrate the definitions: 1. Tectonic uplift (driving factor) promotes a river to incise due to an increased slope (process). How fast a river incises depends amongst others on lithology (intrinsic control) and land use (extrinsic control). A quickly eroding river is able to capture a slow eroding river. 2. Extreme rain fall (driving factor) can result in river breaching, where a river spills over (process) to another course. In a reactive system extreme rainfall often results in high peak discharges. This depends amongst others on the infiltration capacity of the soil, which is dependent on its parent material (intrinsic control) and current management (extrinsic control).

1.2 Problem description Many studies described rearrangements in a qualitative manner. Examples are the descriptions of captures and the assessment of consequences in the Sorbas Basin in Spain (Mather, 2000); the relation between faulting and captures in the Cahabón region in Guatemala (Brocard et al., 2012); the relation between an entering ice sheet, river diversion and sedimentary characteristics (Busschers et al., 2008) and the relation between uplift and the presence of wind gaps due to capture on a stream table (Douglass and Schmeeckle, 2007). Some studies attempted to study drainage rearrangements in a quantitative manner, e.g. Stokes et al. (2002) studied valley shapes and related erosion and deposition patterns to capture events and Goren et al. (in press) studied topological steady-state of systems and related erosion patterns to rearrangement events using landscape evolution model (LEM) DAC.

However, it is not known how the intensity and type of forcing are related to the occurrence and types of drainage rearrangements. Although many consequences of drainage rearrangements have been described in literature, clear relations between drainage rearrangement types and its specific consequences are lacking.

10 1.3 Objective and research questions The aim of this study is to quantitatively explore the dynamics and consequences of drainage rearrangement for a set of common rearrangement mechanisms using the LAPSUS landscape evolution model. The effect of precipitation amount on rearrangement mechanisms will be assessed.

To reach this objective the following main question and sub-questions will be answered:

When and where does drainage rearrangement occur and what are its consequences for landscape evolution?

1. Does a river respond to forcing of the driving factors and does drainage rearrangement happen? a. How sensitive is a river system to forcing of driving factors? b. How long does it take for drainage rearrangement to occur? c. What is the effect of precipitation amount on drainage rearrangement? 2. What are the geomorphological signatures of drainage rearrangement? a. Which geomorphological signatures are known from literature? b. What are typical geomorphological signature for the types of rearrangement? c. Are there necessary geomorphological signatures of drainage rearrangement?

11 2. Methods A description of the landscape evolution model (LEM) LAPSUS is given, followed by a scenario description and analysis.

2.1 LAPSUS LAPSUS (LAndscape ProcesS modelling at mUlti dimensions and Scales) simulates landscape development by calculating water erosion and deposition balances on an annual basis, using the kinematic wave approach (Schoorl et al., 2002). Water erosion and deposition were assumed the main processes in this study, although later versions of LAPSUS also include tillage erosion (Schoorl et al., 2004), land sliding (Claessens et al., 2007), soil creep, solifluction, weathering and tectonics (Temme and Veldkamp, 2009). Water is routed according to a simplified continuity equation, consisting of a gravity term. Water is always following topography, which implies that all the water is directed to the lowest neighbouring cell. However to mimic the diffusive behaviour of overland flow, LAPSUS uses a multiple flow algorithm that spreads the flow proportionally over lower neighbouring cells (Holmgren, 1994; Tucker and Hancock, 2010):

[1] ∑

where fraction of the amount of flow out of a cell in direction , is equal to the slope gradient (tangent) in direction powered by the multiple flow factor , divided by the summation of for all (maximum eight) downslope neighbours powered by factor . Typical values of are larger than 1 (Schoorl et al., 2002; Temme and Veldkamp, 2009). Higher values result in a more narrow and converging flow, than for low values for .

For every grid cell the transport capacity C (m3 y-1) is calculated:

[2] where is the discharge (m3 y-1), is the slope gradient (tangent), m is the exponent for overland flow and n is the exponent of slope. By comparing the transport capacity with incoming flow, it is determined whether sediment is transported or deposited. Erosion occurs when the calculated 3 -1 transport capacity exceeds the incoming sediment in transport ( , in m y ) and deposition when the incoming sediment in transport ( , in m3 y-1) exceeds the transport capacity:

[3] with dx the cell size (m). The term h (m) is equal to the transport capacity divided by the detachment capacity D (m2 y-1) in case of erosion (equation 4), or settlement capacity T (m2 y-1) in case of deposition (equation 5).

[4] and

[5]

-1 -1 where Kes is the lumped erodibility factor (m ) and Pes is the lumped sedimentability factor (m ).

12 In this study an extra component was added to LAPSUS to make very steep walls collapse when they exceed a predefined threshold (Appendix). When the surface gradient to a lower cell is higher than

5 m m-1, the current cell decreases half of the elevation difference m) while the lower cell increases half of the elevation difference, where = 2.5 m. The inequality of and is to avoid that the model will be stuck in a loop. These calculations are repeated until all the gradients in the grid are less steep than 5 m m-1 (500%).

LAPSUS is a kinematic wave landscape evolution model, which means that a river can only change its flow direction when the channel is filled up with sediment and when the lowest neighbour cell becomes higher than another lower neighbour cell. Regarding the simulation of drainage rearrangement mechanisms, it is therefore not possible to simulate mechanisms based on lateral erosion such as river breaching and channel bed erosion. However it is possible to simulate rearrangements based on headward erosion and subsequently river capture, and channel migration or diversion based on aggradation of the channel. The rearrangement mechanisms found and described in this study were based on these latter characteristics. Although Bishop (1995) considered beheading as a rearrangement mechanism as well, it was not possible to simulate it with LAPSUS because there is no groundwater component. Moreover, groundwater plays an important role in river capture. Brocard et al (2011 and 2012) and Pederson (2001) argue that groundwater sapping promotes headward erosion, by weathering of soil and rock below the surface. This means that the absence of groundwater introduced an underestimation in the occurrence of captures.

2.2 Scenario description Five different scenarios were defined to quantitatively explore the dynamics and consequences of drainage rearrangement for as many as possible drainage rearrangement mechanisms. The scenarios included equal tectonic uplift, unequal tectonic uplift, strike-slip faulting, river damming by a lava flow and glacial forcing.

2.2.1 Input data For each scenario idealized DEMs were created in order to relate river behaviour directly to the type of forcing (Figure 3). Surface randomness was added to the initial surface. Firstly random values were generated between -10 m and +10 m for every 50th cell, which were interpolated in ArcGIS using the natural neighbour method, secondly random noise between 0 m and 0.1 m was added to every grid cell.

13 A. Equal and unequal tectonic uplift B. Strike-slip faulting

Precipitation: Precipitation: Precipitation: Precipitation: 550 mm y-1 850 mm y-1 550 mm y-1 850 mm y-1

DEM extent: 10.0 x 17.4 km with DEM extent: 11.0 x 17.4 km with a cell size of 20 m (500 rows a cell size of 20 m (550 rows and and 870 columns). The DEM has 870 columns). The DEM has a a convex profile curvature with convex profile curvature with a a maximum slope of 5°. maximum slope of 5°.

C. River damming by a lava flow D. Glacial activity

DEM extent: 10.0 x 8.7 DEM extent: 10.0 x 4.36 km with a cell km with a cell size of 20 size of 20 m (500 rows and 218 m (500 rows and 435 columns). The DEM has Precipitation: columns). The DEM has a concave Precipitation: -1 profile curvature with a maximal slope -1 a concave profile 700 mm y 700 mm y of 5°. curvature with a maximal slope of 5°.

Figure 3. Virtual input DEMs and their characteristics. Contours are displayed on the location where forcing is imposed. A: Equal and unequal tectonic uplift; B: strike-slip faulting; C: river damming by a lava flow; D: glacial activity.

For each scenario the first 2000 simulation years did not include forcing, so rivers could attain an equilibrium before scenario-specific forcing started. The scenarios equal tectonic uplift, unequal tectonic uplift and strike-slip faulting were run for 15000 years and the scenarios river damming by a lava flow and glacial activity were run for 5000 years (Table 1). For each scenario default values and uniform spatial distributions were used for the m-exponent (1.65), n-exponent (1.65), sedimentability factor (0.0003 m-1), soil depth (100 m), land use (no classes), infiltration rate (150 mm y-1) and evaporation rate (350 mm y-1). The erodibility factor was set to 3.0•10-6 for the scenarios equal tectonic uplift, unequal tectonic uplift and strike-slip faulting. For the scenarios river damming by a lava flow and glacial activity the erodibility factor was set to 3.0•10-5. The multiple flow factor was set to 1.5 (Table 1). Sinks and flats were removed while running. Also the effect of precipitation amount was assessed for the scenarios equal uplift, unequal uplift and strike-slip faulting. The study areas were divided in two halves. On the right hand side a precipitation amount of 550 mm y-1 and on the left hand side a precipitation amount of 850 mm y-1 was imposed (Figure 3 and Table 1).

Model outputs were altitude and altitude change, for every 500 simulation years. In case of the glacial activity scenario, model outputs were given every 50 years. Also annual time series of the total erosion and the SDR were recorded, separated for the dry and wet part of the area.

14 Table 1. Scenario settings of the erodibility factor, multiple flow factor, total precipitation and total run time.

Equal tectonic Unequal Strike-slip River Glacial uplift tectonic uplift faulting damming by activity a lava flow K (m-1) 3.0•10-6 3.0•10-6 3.0•10-6 3.0•10-5 3.0•10-5 p 1.5 1.5 1.5 1.5 1.5 Total precipitation Left hand side: Left hand side: Left hand side: 700 700 (mm y-1) 550 550 550 Right hand side: Right hand side: Right hand side: 850 850 850 Total run time (y) 15000 15000 15000 5000 5000

2.2.2 Equal tectonic uplift In order to mimic rearrangements related to tectonic uplift, a block with a width of 1000 m was equally uplifted with a rate of 1.2 mm y-1 (Figure 3A). Although Mather (2000) and Stokes et al. (2002) found an uplift rate of 0.12 mm y-1, a higher uplift rate was imposed to simulate more rearrangement mechanisms. It was expected that aggradation would occur on top of the rising structure, causing rerouting of rivers. On the bottom of the rising structure it was expected that river captures were promoted due to an increased slope gradient.

2.2.3 Unequal tectonic uplift This scenario was a repetition of the equal uplift scenario, except that the block was tilted. It was expected that stream migration and diversion would be promoted (relative to the equal tectonic uplift scenario) due to an increased lateral surface gradient (Bishop, 1995). Unequal tectonic uplift was induced with an uplift rate of 1.2 mm y-1 on the left hand side while the right hand side was not uplifted. The same study area and parameters of the equal tectonic uplift scenario area were used (Figure 3A).

2.2.4 Strike-slip faulting Strike-slip faulting was closely mimicked by shifting the lower 5 km of the study area to the right (Figure 3B). Ideally the strike-slip rate would be 27 mm y-1 (Norris and Cooper, 2001). However with a cell size of 20 m, only a shift of 20 m every 740 y was feasible. It was expected that rearrangements would occur at the location of faulting, where rivers could not adapt to the strike-slip rate.

2.2.5 Sudden disruption: river damming by a lava flow A virtual lava flow was created that instantaneously blocked several rivers (Figure 3C). It was moved in from the right hand side of the study area, as if there was a volcanic active mountain range. The extent of the lava flow was 1000 x 500 m, with a thickness ranging from 5 m upstream, to 30 m downstream. The dam had the same erodibility as the landscape. Dam collapse or overflow was not considered in this study.

2.2.6 Gradual disruption: glacial activity A virtual glacier tongue was created that gradually disrupted several rivers. This scenario was loosely based on the ice sheet that entered Europe during the Saalien, in the sense that it caused stream diversion of many rivers. In this scenario, a glacier moved in from the left hand side of the study area (Figure 3D). The glacier tongue was uplifted with 3 m every 5 years and horizontally extended with 20 m every 5 year, until a maximum extent was reached of 825 m. Dam collapsing and extreme

15 flooding were not considered in this study. The glacier was growing from 2000 to 2850 years, after which it remained in the landscape. As long as the glacier was growing, it was unerodible.

2.3 Analysis

2.3.1 Response of rivers to forcing For the scenarios with equal tectonic uplift, unequal tectonic uplift and strike-slip faulting the occurrence of river rearrangement as response to forcing by the driving factors was assessed.

A channel map was created from a flow accumulation map, displaying drainage lines using a threshold of 3000 draining cells. Subsequently two flow path maps with 500 y difference were compared. When more than 5 grid cells of the flow path were rerouted, it was considered as a drainage rearrangement event. For all selected events, the type of rearrangement was classified manually. The number and type of rearrangements were subsequently plotted over time.

Below a classification is given of different rearrangement types. Green: new river channel; red: abandoned channel; black: no change.

- Channel migration A river follows a new flow path within 3 grid cells from the old flow path, representing a gradual migration. The new river has the same headwaters and it follows the same downstream flow path as the abandoned river segment.

- Diversion There is a minimum width of 3 grid cells in between the old and the new flow path and the river headwaters are not necessarily equal. The outlets may be different.

- Capture or piracy Flow accumulation maps are necessary to classify captures, because the maps show whether there are tributaries which are accumulating water (blue arrow, A) and able to capture another river branch (B). When such a tributary is absent, the drainage rearrangement event is classified as migrations or diversion.

A. B. For the scenario river damming by a lava flow it was expected that the types and locations of rearrangement were all similar within the scenario, therefore only a visual description was given.

For the glacial activity scenario it was expected that mainly drainage diversion would occur around the glacier margin. In order to have a clear overview of the interaction between the glacier and surrounding catchments, sub-catchments were constructed with their outlets at selected junctions (white arrows, Figure 4).

16 A

B C

I J

Figure 4. An example output from the glacial activity scenario, shortly after the first part of the glacier was moved in. The white arrows indicate river junctions where the sub-catchments were considered as one watershed. The characters A to J refer to the nested sub-catchments.

2.3.2 Geomorphological signatures For every type of rearrangement the geomorphological signatures were assessed in terms of change in drainage pattern and changes along a river profile. For the scenarios river damming by a lava flow and glacial activity, the surface area of catchments was recorded and plotted over time. For all scenarios, time series of erosion and deposition were analysed to assess the effect of drainage rearrangements on sediment transport.

17 3. Results In each scenario rearrangements were taking place which were not related to forcing. These rearrangements were not located on or adjacent to the location of forcing. These rearrangements resulted in more curved flow paths when the rivers had a low rate of sinuosity, but diversions often resulted in a higher rate of sinuosity than migrations or captures. Captures caused knickpoints in river profiles between the captive and captor due to base level differences. An example of a knickpoint is displayed in Figure 5, but also smaller knickpoints were found with only a few meters difference between the captor and the captive.

3550

3510 Captive

Captor 3470 Abandoned channel 3430 -300 -200 -100 0 100 200 Distance from location of capture (m)

Figure 5. Knickpoint formed due to river capture. 3.1 Equal tectonic uplift A distinction was made between the climatic regions to assess the effect of a varying precipitation amount on the sensitivity of the river system. The first rearrangements occurred in the wet part of the study area already before forcing initiated (Figure 6). In the dry part of the area rearrangements occurred 2500 years later compared to the wet part of the area. In the wet part of the area more rearrangements occurred (94 events) compared to the dry part (47 events). In the wet part they consisted mainly of captures, whereas in the dry part of the area the rearrangements were mainly channel migrations. Summed over the area, mainly migrations took place followed by captures and diversions. The number of rearrangements decreased to zero over time for both climatic regions.

Dry area Wet area 5 10 Diversion

Migration 4 8 Capture 3 6

2 4 Numberof

rearrangements 1 2 0 0 0 2500 5000 7500 10000 12500 0 2500 5000 7500 10000 12500 Time (y) Time (y)

Figure 6. Number and type of rearrangement events over time, for the equal tectonic uplift scenario. The vertical black lines show the moment that forcing started, at t = 2000.

The initial stage of fluvial development was characterized by diversion of water due to sediment trapping upstream of the rising structure. This was often not recorded because the flows were mainly

18 below the threshold of 3000 draining cells. Characteristic rearrangements were the combination of diversion and capture. Uplift resulted in aggradation and blocking of water, tributaries were formed along the upper margin of the rising structure. When rivers could not balance the uplift by incision, they were disconnected (upper arrow, Figure 7). Strong streams that were crossing the rising structure were able to capture this water. Furthermore, migrating streams that were crossing the rising structure, were migrated with the upper margin of the rising structure as starting point or end point. It was found that river incision along the lower margin of the rising structure was promoted due to an increased gradient (Figure 7 and Figure 9), but this did not lead to capture.

Figure 7. Elevation change during 500 simulation years. Light grey colours indicate increased elevation, the contours of the rising structure are visible. Black colours indicate decreased elevation, mainly due to incised channels. The upper arrow points at an increased elevation upstream of the rising structure, where rivers are blocked. Water is diverted to the left or right. In this example a tributary of the channel on the left hand side is capturing the diverted water. The lower arrow points at dark colours in the river course, which gradually turn to lighter colours upstream, indicating a knickpoint.

A geomorphological signatures was a changed drainage pattern. Especially tributaries were following the upper margin of the rising structure due to uplift and aggradation (Figure 8Error! Reference source not found.). The drainage density in the dry area was much lower than in the wet area.

Main drainage lines Elevation (m) 3843

3126

Figure 8. Drainage pattern of the study area at t = 15000 where equal tectonic uplift was imposed.

Most of the rearrangements were not leaving observable knickpoints, but when a river was crossing the lower boundary of the rising structure, a knickpoint was formed due to the elevation difference (Figure 9). It is debatable whether captures were promoted due to uplift, because the knickpoint of the captor was relatively far downstream from the location of capture. However, it was always found that the knickpoint of a captor was faster migrating upstream than the knickpoint of an abandoned channel, due to a larger draining area of the captor.

3565

3545 Captive

Captor

Lower margin uplifting 3525 structure captor Elevation Elevation (m) Abandoned channel

Lower margin uplifting structure abandoned channel 3505 -400 -200 0 200 Distance from capture (m)

Figure 9. Example of river profiles of a captor and a captive, crossing the lower boundary of the rising structure at t = 7500. There is no knickpoint formed at the location of capture, but knickpoints were formed due to incision of the lower margin of the rising structure. The location of capture is taken as reference for the measured distance along the river profiles, but the relative location of the lower margin of the rising structure is represented by the vertical lines.

The annual time series of total erosion and SDR are plotted in Figure 10. The total erosion in the dry part is lower than the total erosion in the wet part of the area. The total erosion in the wet part increases during the first 3500 y, whereas the total erosion in the dry part is decreasing. The total erosion in the dry part of the area was stable from 3300 y until 9100 y. After 4000 simulation years, most rivers were diverted due to aggradation upstream the rising structure. These diversions caused a higher connectivity in the study area, because the SDR was increased. Also, during this period 70% of the rearrangements in the dry area were taking place. In the wet part the total erosion decreased slightly after 3500 y. Around 4400 years, the graph of the total erosion in the wet part of the area shows more noise, which coincides with the occurrence of collapses (Figure 11). In the dry part of the area the SDR was slightly increasing after 4000 years, with some lows in between. Striking is the lower SDR after 4000, 6700, 9500 and 13000 years. The SDR in the wet part of the area was slightly increasing, but decreasing after 3000 years. After 10000 years the SDR in the wet area was more or less stable. From the SDR it is not clear whether rearrangements are visible (Figure 10).

120

100

60 Total erosion wet Total erosion dry 40

20 Totalerosion (x400 m^3)

0 0 2000 4000 6000 8000 10000 12000 14000

0.95

]

- 0.85

SDR [ 0.75 SDR wet SDR dry 0.65 0 2000 4000 6000 8000 10000 12000 14000 Time (y) Figure 10. Annual time series of the total erosion and SDR for the equal uplift scenario.

Collapses were observed after 4400 years (Figure 11). The total displaced sediment was equal to 3.3% of the total volume eroded sediment. A maximum number of four collapses was achieved per time step. Collapses resulted in an instantaneous pile of sediment in the river course. This caused aggradation upstream of the pile of sediment and the formation of a knickpoint which was migrating upstream in time.

100

(x400 (x400 m^3)

duetocollapse Displaced Displaced sediment 0 0 5000 Time (y) 10000 15000 Figure 11. Annual time series of the displaced sediment due to collapses, for the equal tectonic uplift scenario. Per collapse around 25 x 400 m3 is displaced, so there was mainly one collapse per year, with a maximum of four collapses per year. 3.2 Unequal tectonic uplift The first rearrangements occurred in the wet part of the area. With a delay of 2500 y, also rearrangements were observed in the dry area (Figure 12). More rearrangements occurred in the wet part of the area (100 events) than in the dry part of the area (52 events). In the dry part of the area the rearrangements mainly consisted of migrations and in the wet part mainly of captures. Summed

21 over the entire study area, a few more migrations took place than captures. In the dry part of the area, in case of migration most new channels were rearranged to a lower position on the rising structure than the abandoned channels, whereas in the wet part of the area there was no significant effect observable of the increased lateral gradient on the rising structure. The number of rearrangement events was declining in time, but for the wet area to a higher extent than for the dry area. The same drainage rearrangement mechanisms were found as in the equal tectonic uplift scenario.

5 10 Dry area Wet area Diversion 4 8 Migration Capture 3 6

2 4

1 2

Numverofrearrangements 0 0 0 2500 5000 7500 10000 12500 0 2500 5000 7500 10000 12500 Time (y) Time (y)

Figure 12. Number and type of rearrangement events over time, for the unequal tectonic uplift scenario.

As result of unequal uplift and rearrangements, the drainage pattern in the dry area was changed. In the wet part of the area there was hardly any effect of the unequal uplift observable (Figure 13). As the case of the equal uplift scenario, there were almost no knickpoints visible as result of rearrangements. However there were knickpoints formed when rivers were crossing the lower margin of the rising structure, due to an elevation difference.

Main drainage lines Elevation (m) 3843

3126

Figure 13. DEM of the unequal tectonic uplift study area at t = 15000.

The annual time series of total erosion and SDR are visualized in Figure 14. Compared to the equal tectonic uplift scenario, the graphs show less noise. Some features are comparable with the equal tectonic uplift scenario, such as the increase of the total erosion in the wet part of the area; the decrease of the total erosion in the dry part of the area; and the start of scatter which coincides with

22 the start of collapses. However, the total erosion wet is slightly higher and the total erosion in the dry part is lower than in the equal tectonic uplift scenario. The total erosion in the wet part shows an abrupt decrease around 7300 y and the total erosion in the dry part decreases fast until 3400 y. It increases again around 5000 y and is stable and slightly decreasing until the end of the simulation.

The SDR from the dry part shows less noise than in the equal tectonic uplift scenario. Based on this output it is not clear when rearrangements occur. The abrupt decrease of the total erosion is not recognizable in the SDR output, meaning that the deposition was also decreased.

120 100 80 60 Total erosion wet 40 Total erosion dry 20

Totalerosion (x m^3) 400 0 0 2000 4000 6000 8000 10000 12000 14000 1

0.95

]

- 0.9

SDR SDR [ 0.85 SDR wet 0.8 SDR dry 0.75 0 2000 4000 6000 8000 10000 12000 14000 Time (y)

Figure 14. Annual time series of total erosion and SDR for the strike-slip faulting scenario.. 3.3 Strike-slip faulting All channels that were crossing the fault were clearly disrupted by strike-slip faulting. The first rearrangements occurred in the wet part of the area, after 1000 simulation years (1000 years before forcing started). 2000 years later also rearrangements were observed in the dry part of the area. In the wet part of the area there were 100 rearrangements recorded during the time span of 15000 years, of which river captures (41) took mainly place. In the dry area 41 rearrangements were recorded, which were mainly channel migrations (32) (Figure 15). After 8000 years, the number of rearrangements was declining in the wet part of the area, but not in the dry part of the area.

23 Wet area 5 Dry area 10 Diversion 4 8 Migration Capture 3 6

2 4

1 2

Numberofrearrangements 0 0 0 2500 5000 7500 10000 12500 0 2500 5000 7500 10000 12500 15000 Time (y) Time (y)

Figure 15. Number and type of rearrangement events over time, for the strike-slip faulting scenario.

Compared to the uplift scenarios, much more diversions were taking place. Diversions were directly caused by strike-slip faulting, because rivers downstream the fault were disconnected from their headwaters.

While strike-slip faulting was induced, river segments that were crossing the fault were elongating along the fault. A typical drainage pattern developed (Figure 16). However, elongated river segments were sometimes erased due to rearrangements, when the strike-slip offset was as long as the spacing between two rivers.

Figure 16. DEM of the strike-slip scenario study area at t = 15000. The lower 5 km of the study area was shifted to the right hand side, with a total length of 340 m in 13000 y.

Knickpoints were present at locations where diversions and captures took place as direct result of strike-slip faulting (Figure 17). When diversion caused by strike-slip faulting was due to blocking by the valley walls of downstream shifted river segments. This mechanism was always recognizable by an abrupt elevation change along the river profile, due to sedimentation upstream the blockade (left hand side Figure 17). Captures were occurring when rivers downstream the fault shifted closer to river above the fault and when there was enough stream-power. Knickpoints were always formed.

3600 3600

3590 Diverted 3560 Captive headwater New channel Captor

3580 3520 Elevation Elevation (m) Abandoned Abandoned channel channel 3570 3480 -200 -100 0 100 200 -300 -200 -100 0 100 200 300 Distance from fault (m) Distance from fault (m)

Figure 17. Example of knickpoints in river profiles due to diversion (at t = 9500, left) and due to capture (at t = 10500, right). In the case of diversion directly due to strike-slip faulting (left), a new channel was formed due to blocking. Note the higher elevation of the abandoned channel a few meters above the fault and the change of the river profile as result of deposition upstream of this point. In case of capture (right) streams below the fault were shifted and able to capture channels which were nearby above the fault.

It is not clear whether the sediment budget changed as result of rearrangements (Figure 18). The total erosion of the dry part was decreasing until 8200 y, after which it became stable. The SDR in the dry part of the area shows irregularities with an interval of 740 years, reflecting the area shifts at the same intervals. The SDR wet shows many irregularities and abrupt changes over time (Figure 18), but the trend is decreasing.

100

60 Total erosion dry Total erosion wet 40

20 Totalerosion (x m^3) 400 0 0 2000 4000 6000 8000 10000 12000 14000 1

0.95

] - 0.9

SDR SDR [ 0.85 SDR wet 0.8 SDR dry 0.75 0 2000 4000 6000 8000 10000 12000 14000 Time (y) Figure 18. Annual time series of the total erosion and SDR for the strike-slip faulting scenario. 3.4 Sudden disruption: river damming by a lava flow The presence of a lava dam immediately disrupted the drainage network. An instantaneous diversion occurred of water that was rerouted to flow around the dam. Some small channel migrations occurred

25 along the upper margin of the dam. Downstream of the dam, some additional minor diversions and migrations took place.

Geomorphological signatures included an obvious change of the drainage pattern (Figure 19), due to river diversion around the dam.

Main drainage lines Elevation (m) 3843

3126

Figure 19. DEM of the study area at t = 5000 for the scenario river damming by a lava flow.

Moreover, a knickpoint developed along the narrow side of the dam. The lava dam caused aggradation of sediment upstream and it decreased local river profile gradients. A base level difference was developed and downstream rivers were incising upwards through this depositions, following the same margin of the dam. A knickpoints was formed which was retreating in time (Figure 20).

3050

3045 3040 t = 2000 3035 t = 2500

Elevation Elevation (m) 3030 t = 3000 t = 3500 3025 0 100 200 300 400 500 Distance (m) Figure 20. River incision along the narrow margin of the lava flow. A river main trunk flows along the narrow margin of the dam. At a distance of 0 m, the river was halfway of the narrow side of the dam. Going upstream, the river was flowing along the narrow margin of the dam until 220 m, further upstream the river was not following the dam.

A reduction in total erosion of 0.5 m3 per year was recorded at the moment that the lava dam moved in (Figure 21). The SDR was decreased at the same moment. The general trend in SDR was slightly increasing when the dam was appeared, with some lows during the first 1000 years. Around 4000 years there was a period of 500 y with a higher SDR.

30.2

29.7 Totalerosion (m^3) 29.2 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 1

0.9

] - 0.8

SDR SDR [ 0.7 0.6 0.5 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Time (year)

Figure 21. Annual time series of the total erosion and SDR for the scenario river damming by a lava flow.

3.5 Gradual disruption: glacial activity As soon as the glacier moved in, it disrupted the drainage system around the glacier. Rivers along the glacier margin were diverted laterally due to pushing. As long as the glacier was extending, it reached new catchments where rivers were subsequently diverted. This resulted in the disappearance of catchments (catchment D at t = 2400, D and E t = 2550), while other catchments could expand (catchments B, F and G at respectively t = 2600, t = 2650 and t = 2750) (Figure 22). Catchments that were not directly adjacent to the glacier, remained more or less equal in size, indicating that almost all the activity in the disturbed catchments was due to the glacial disturbance.

140

120

100 J I H 80 G F 60 E D 40 C B

(x 1000 1000 (x ofnr cells) grid 20

Catchementsurface area A

0 2000 2100 2200 2300 2400 2450 2550 2650 2750 2850 2950 Glacier growth from 2000 until 2850 y Time (year) Figure 22. Sub-catchment distribution within a time span of 1000 years. Note that in 2050 catchment E was added at the expense of catchment B and that a new division was made at t = 2400.

27 A clear geomorphological signature was the changing drainage pattern as result of gradual river redirection around the glacier margin (Figure 23). Rivers that flowed along the lower edge of the glacier margin, were shifted laterally due to glacier forcing. Shifting river channels were not deeply incising. After every shift rivers had to incise again to find a new equilibrium.

Main drainage lines Elevation (m) 3843

3126

Figure 23. DEM of the study area at t = 3000.

Total erosion increased with more than 30 m3 as result of the growing glacier (Figure 24). As soon as the glacier stopped growing, total erosion was stable and slightly decreased. The SDR was increasing with a maximum of 0.1 in 3000 y from the moment that the glacier moved in until the end of the simulation, while it was decreasing before the glacier moved in. The period between 2500 and 2550 y was characterized by a stable increase. Fluctuation in the SDDR was caused by a fluctuating

deposition.

Totalerosion (m^3) 60 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 0.9

0.8

] -

0.7 SDR SDR [ 0.6

0.5 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Time (year)

Figure 24. Annual time series of the total erosion and the SDR for the glacier activity scenario. The vertical black lines represent the time span in which the glacier was growing.

28 4. Discussion

4.1 Model limitations It was found that the collapse component resulted in a more scattered signal in the time series of total erosion in the wet parts. Lower values of the total erosion coincided with the occurrence of collapses. Collapses resulted in an instantaneous pile of sediment, which was trapping sediment upstream of this pile. It could be the case that collapses were disturbing local fluvial behaviour, but since the total amount of displaced sediment was equal to 3.3% of the total eroded amount of sediment, regional fluvial behaviour was not disrupted.

4.2 Occurrence of drainage rearrangements over time Topological steady-state can be reached when no additional rearrangement events occur (Goren et al., in press). Although the scenarios of strike-slip faulting, equal and unequal tectonic uplift showed a short time range, especially for the equal tectonic uplift scenario it was visible that there was a clear peak of rearrangements for both the dry and wet area. For the wet area of the equal tectonic uplift scenario, topological steady-state was reached because the number of rearrangement events was decreased to zero. In the other cases a topological steady-state was going to be reached when the run time was longer, because the number of rearrangement events was slightly decreasing in time. This is in accordance with Goren et al. (in press), who observed that the number of rearrangement events was tailing out over a very long time scale and that events in the last stage of running were mainly small events on catchment boundaries, while forcing continued.

Before forcing started, rearrangements were observed due to unforced drainage network development. Climate was clearly influencing the system reactivity to forcing. A wet climate was reacting faster than a dry climate and a wet climate was characterized by a higher total number of rearrangement events than a dry climate. Both observations can be explained by the available stream- power. A high precipitation surplus results in a high stream-power and therefore a higher incision capacity. This results in a higher reactivity of the system than a dry climate, accompanied with drainage rearrangements.

The scenarios lava damming and glacial forcing caused abrupt changes in drainage network morphology. It can be concluded that for all scenarios the type and rate of forcing directly affected the occurrence of rearrangements. Topography, climate and the extent of forcing played an important role in fluvial behaviour and the occurrence of rearrangements, corresponding to earlier field-based conclusions by Whipple and Tucker (1999) and Tucker and Hancock (2010).

4.3 Rearrangement types In the dry climatic areas of the scenarios equal tectonic uplift, unequal tectonic uplift and strike-slip faulting, rivers were incising less deeply than in wet climatic areas, due to a lower precipitation amount and a lower stream-power. This resulted in straight channels in dry areas, whereas rivers in wet areas showed a higher sinuosity. In a dry climate more time was needed for a drainage network to find an equilibrium. Rivers were not deeply incised and due to variable erosion patterns, relative increase of elevation could result in migrations. A wet climate however, was characterized by deeply incised rivers, which are considered as stable in the landscape (Brocard, 2011). Therefore less migrations were found and mainly captures were taking place due to a high stream-power (Table 2).

29 Table 2. Number and types of drainage rearrangements per scenario.

Equal tectonic Unequal tectonic Strike-slip River damming Glacial activity uplift uplift faulting by a lava flow Dry Wet Dry Wet Dry Wet Number of Diversion: only Diversion: rearrangements 47 94 52 100 41 100 when the dam continuously appeared in the during glacier landscape growth Capture 9 48 10 61 3 41 Migration 34 37 41 32 32 26 Diversion 4 9 1 7 6 33

4.4 Rearrangement mechanisms For each type of forcing a typical rearrangement mechanism was found.

Equal tectonic uplift. Typical rearrangement mechanisms included the combination of capture and diversion, upstream of the rising structure. Water was blocked due to uplift and therefore tributaries were developing along the upper margin of the rising structure. River captures occurred along the upper margin of the rising structure, resulting in straight headwater elongation of tributaries. The rising structure was often the start or end point of channel migrations, due to local increased elevation. There was no evidence that captures on the rising structure were governed by an increased slope at the lower margin of the rising structure, because the distance between the location of capture and the knickpoints was relatively large and elevation differences near the location of capture were small. However it was found that river incision was promoted due to an increased gradient along the lower margin of the rising structure, corresponding to earlier field-based conclusions by Stokes et al. (2002). Knickpoints were formed that migrated upstream, but this did not lead to capture because rivers were mainly flowing parallel to each other.

Unequal tectonic uplift. The same mechanisms were found as for the equal tectonic uplift scenario, but the majority of the rearrangements was caused by uplift rather than an increased lateral gradient. Only in the dry part of the area most migrated channels were located lower on the rising structure than former channels. In the wet part there was no significant effect of unequal uplift, because the local uplift rate was too low and rivers could easily adapt to forcing, due to a high stream-power.

Strike-slip faulting. There were two main mechanisms acting. When a channel below the fault was not able to compensate shifting by increasing its erosion or by extending the river segment flowing along the fault, the channel above the fault became disconnected and drained water to another downstream channel nearby (classified as diversion) as recognized by Walker and Allen (2012). However, when a channel below the fault shifted to the vicinity of an adjacent upstream channel, it could capture it by headward erosion.

River damming by a lava flow and glacial activity. Rivers were rerouted around the dam or glacier margin. The lava flow could dam a river because it appeared instantaneously, changing the drainage system abruptly. However, the glacier was not able to dam rivers because rivers could adapt their flow path before the glacier could dam it. Drainage systems were continuously shifted laterally. This caused an increased surface area for some catchments, in the expense of neighbouring catchments.

30 4.5 Geomorphological signatures

4.5.1 Morphological changes For all scenarios drainage patterns were changed as reaction to forcing (Table 3). All types of rearrangements resulted in more sinuous flow paths (as recognized by Mather, 2000) but diversions often with a higher rate of curvature than migrations or captures. Although many studies showed that rearrangements result in boathook bends (Mather, 2000; Stokes et al., 2002; Brocard et al., 2012; Whitfield and Harvey, 2012), in this study they were not found because rivers were mainly flowing parallel to each other in the start situation. Bends were found with lower angles than 90 degrees and therefore not classified as boathook bends.

The rearrangements caused by uplift were not leaving observable knickpoints in the landscape, due to a surplus of trapped sediment upstream the rising structure. Diversions and captures due to strike- slip faulting were always leaving knickpoints in the landscape. In case of diversion, local river blocking caused sediment trapping and a higher base level difference. In case of capture, headward erosion caused a base level difference and the formation of a knickpoint. A knickpoint was therefore formed, as recognized by Goren et al. (in press). River damming by a lava flow created a knickpoint due to sediment trapping upstream the dam (as recognized by Van Gorp, submitted).

In the scenarios equal tectonic uplift, unequal tectonic uplift and strike-slip faulting, there were also rearrangements taking place unrelated to forcing, from which captures were leaving knickpoints. Diversions and migrations never caused observable knickpoints, because the elevation differences were to small (Bishop, 1995).

Table 3. Geomorphological signatures per scenario. An ‘x’ means that the drainage rearrangement mechanism is not found under the scenario settings.

Equal Unequal Strike-slip River Glacial Unrelated tectonic uplift tectonic uplift faulting damming by activity to forcing Dry Wet Dry Wet Dry Wet a lava flow Changed drainage Yes Yes Yes Yes Yes Yes Yes Yes Yes pattern Knickpoints Capture x x x x Yes Yes x x Yes Migration No No No No x x x x No Diversion No No No No Yes Yes Yes No No Total erosion Capture No No No No No No x x x Migration No No No No No No x x x Diversion No No No No No No Yes Yes x SDR Capture No No No No No No x x x Migration No No No No No No x x x Diversion No No No No No No Yes Yes x

4.5.2 Sediment supply For most scenarios the total erosion and the SDR were changed due to forcing. It was expected that the total erosion and the SDR were good measures to see whether drainage rearrangements were taking place, although it is known that a non-linearity exists between forcing and sediment transport (Coulthard and Van de Wiel, 2007; Baartman et al., 2013). However, for the scenarios equal uplift, unequal uplift and strike-slip forcing, it was not possible to link the occurrence and type of rearrangements to a change of total erosion or SDR (as recognized by Van Gorp et al., submitted). The

31 time interval between model outputs was 500 years, which made it difficult to relate occurrence of rearrangements to total erosion or SDR. The study areas were large and contained many catchments. This caused masking of local erosion and deposition signals by regional variation (Baartman et al., 2013). However, the dry climatic areas had less complex drainage networks, lower sediment export and larger catchments than wet areas, so more variation in total erosion and SDR could be explained. General trends were explained by forcing, whereas abrupt changes in the trends were assumed to be the result of rearrangements.

For example, in the dry part of the equal uplift area the SDR was decreased during a period of large rearrangements. There were mainly six main channels draining the area. Large rearrangement decreased the number of main channels, resulting in a lower SDR due to a less effective sediment transport along the upper margin of the uplifting structure. However, the SDR could increase again due to stabilization of the channels.

For the scenarios river damming by a lava flow and glacial activity, total erosion and SDR outputs were useful, because fluvial morphology was abruptly changed by forcing. For both scenarios, the SDR was decreasing in the first stage of river development as result of sink filling, because both study areas have a concave profile curvature. The total erosion was changed as result of the lava dam and the glacier moving in. The lava dam was trapping sediment which decreased the slope of river channels upstream the dam, resulting in a decreased total erosion in the study area (as recognized by Ely et al., 2012; Van Gorp et al., submitted). However, the growing glacier resulted in an increased total erosion. As soon as the glacier stopped growing, the total erosion was stable and slightly decreasing. This indicates that the erosion was not coming from the glacier body, but from the diverted rivers that continuously had to find a new equilibrium in the landscape, by incising it. The SDR was also increased, indicating that the sediment connectivity was increased as result of a more efficient transport of river sediment.

32 5. Conclusions Five different rearrangement mechanisms were studied using a modelling approach: equal tectonic uplift; unequal tectonic uplift; strike-slip faulting; river damming by a lava flow and glacial activity. For each type of forcing specific rearrangement mechanisms were found.

Equal tectonic uplift resulted in blocking and diversion of water. Captures occurred along the upper margin of the rising structure but were not leaving knickpoints, due to a surplus of sediment. Unequal tectonic uplift caused the same mechanisms, but to a lesser extent due to local lower uplift rates. It was expected that rivers were rearranging due to tilting, but this was only observed for channel migrations in a dry climate. Strike-slip faulting resulted in diversions when rivers were blocked, or in captures when rivers below the fault shifted to the vicinity of an upstream river. The instantaneous appearance of a lava flow resulted in sediment trapping upstream the dam and subsequent a base level difference. A knickpoint formed and retreated upstream. Glacial activity resulted in a continuous shift of rivers along the lower margin of the glacier. Some catchments disappeared while others could expand. Besides also rearrangements were taking place which were not related to forcing.

Climate played an important role in the reactivity of the landscape to forcing. A wet climate was reacting faster considering drainage development, adaptation to forcing and in reaching a topological steady-state. This is due to the available stream-power in a wet climate. A wet climate was characterized by a higher number of rearrangements than in a dry climate, whereas in a dry climate less rearrangements were observed. In dry climates most rearrangement types were migrations due to a low stream-power, whereas in a wet climate mainly captures occurred due to a high stream- power.

Each combination of rearrangement type and type of forcing resulted in specific rearrangement mechanisms. The most important were the presence of knickpoints due to diversions and captures in a strike-slip faulting setting and due to river damming by a lava flow. Time series of total erosion and deposition summed over a study area, could reflect forcing and rearrangements as long as the number of catchments within the area was low. It showed a decreased total erosion in case of river damming by a lava flow and an increased total erosion in case of glacial activity. Every type of rearrangement resulted in a changed drainage pattern. Changes were an increased sinuosity of flow paths after rearrangements and tributaries which were following structures in the landscape due to forcing. There were also rearrangements observed which were not related to forcing. These rearrangements resulted in knickpoints after capture and also resulted in flow paths with a higher sinuosity.

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36 Appendix

Collapse component private void calculate_collapse() { double slope; total_collapse = 0; bool last_time_activity = true; while (last_time_activity == true) last_time_activity = false; for (row = 0; row < nr; row++) { //visit all cells in the DEM and ... for (col = 0; col < nc; col++) { for (i = (-1); i <= 1; i++) { // maakt een rondje om de cel for (j = (-1); j <= 1; j++) { if (((row + i) >= 0) && ((row + i) < nr) && ((col + j) >= 0) && ((col + j) < nc) && !((i == 0) && (j == 0))) { dh = dtm[row, col] - dtm[row + i, col + j] // Calculates elevation difference if ((row != row + i) && (col != col + j)) { d_x = dx * Math.Sqrt(2); } else { d_x = dx; } // Calculates distance between cell centres for (straight and diagonal) neighbouring cells slope = dh / d_x; // slope gradient between cell and neighbour cell. dh_tol = d_x * 2.5; // The factor is lower than the acceptable slope, in order to avoid that dh and dh_tol become equal (otherwise it keeps running...). if (slope > 5) // The acceptable slope is 5 m/m or lower. { dtm[row, col] -= (dh - dh_tol) / 2; // The current cell decreases elevation => collapse dtm[row + i, col + j] += (dh - dh_tol) / 2; // The lower neighbour cell receives the sediment total_collapse += ((dh - dh_tol) / 2) * 400; // calculates collapse balance in m^3 (400: cell size of 20*20 m) last_time_activity = true; } } // end height difference } // end for-loop j neighbour } // end for-loop i neighbour } // end col visit } // end row visit } // end while loop } // end void collapse ()

Equal tectonic uplift private void uplift() { if (t >= 2000) //Start scenario after 2000 y running { for (row = 250; row < 300; row++) { for (col = 0; col < nc; col++) { dtm[row, col] += 0.0012; // Uplift rate is 12 mm/y } } } }

Unequal tectonic uplift private void unequal_uplift() { if (t >= 2000) //Start scenario after 2000 y running { for (row = 250; row < 300; row++) {

37 for (col = 0; col < nc; col++) { dtm[row, col] += (0.0012 / nc) * (nc - col); // 0.0012 max uplift rate on the left hand side. } } } }

Strike-slip faulting if (t >= 2000) //start scenario after 2000 years running { if (fault_time == 740) //strike-slip: shifting 1 cell every 740 year { fault_time = 0; } if (fault_time == 0) { for (row = 0; row < 249; row++) { for (col = nc-1; col > 0; col--) // On the left hand side there is the low precipitation amount. Therefore the upper part of the DEM moves to the right. { dtm[row, col] = dtm[row, col - 1]; // strike-slip faulting. } } } fault_time += dt; } // end strike-slip

River damming by a lava flow private void lava() { if (t == 2000) //start scenario after 2000 years running { for (row = 275; row < 300; row++) // Extent of the dam. Width: 25 cells = 500 m. { for (col = 128; col < nc; col++) // Extent of the dam. Length: 90 cells = 180 m. { dtm[row, col] = 3055; // Elevation of the dam. } } } }

Glacial activity private void glacier() { if (t >= 2000) //Start scenario after 2000 y running { glacier_growth += dt;

if (glacier_growth == 5) // 1 cell growth every 5 years { glacier_growth = 0; extent += dt; // The extent grows 1 cell every 5 years (until a maximum extent of 175 cells). grow_rate += 3; // every 5 years the glacier increases elevation with 3 meters. } if (glacier_growth == 0 && extent <= 175) // max extent of 175 years { for (row = 200; row < 300; row++) // Location of glacier { for (col = 0; col < extent; col++) { if (col == 0) { dtm[row, 0] = 3050 + grow_rate; } // The elevation is determined in the first col. 3050 is the elevation of the DEM at t = 0 else { dtm[row, col] = dtm[row, col - 1] - (dtm[row, 0] - 3050)/ extent; } // The elevation in the other cols is based on the elevation in the first col. }

38 } } } }