Bedload Transport in Mountain Streams Model Development, Numeric Simulation and Time Series Analysis

Research Collection

Doctoral Thesis

Bedload transport in mountain streams Model development, numeric simulation and time series analysis

Author(s): Heimann, Florian U.M.

Publication Date: 2015

Permanent Link: https://doi.org/10.3929/ethz-a-010406973

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ETH Library DISS. ETH NO. 22530

Bedload transport in mountain streams: Model development, numeric simulation and time series analysis

A thesis submitted to attain the degree of

DOCTOR OF SCIENCES of ETH ZURICH

(Dr. sc. ETH Zurich)

presented by

FLORIAN ULRICH MAXIMILIAN HEIMANN

M.Sc., Ludwig-Maximilians-Universität München and Technische Universität München

born on 09.01.1985

citizen of Germany

accepted on the recommendation of

Prof. Dr. James W. Kirchner Dr. Dieter Rickenmann Dr. Jens M. Turowski Prof. Dr. Stuart N. Lane

2015 Contents

Abstract ...... 6 Kurzfassung ...... 8

1 Introduction 10 1.1 Motivation ...... 10 1.2 Research gaps ...... 11 1.3 Objectives and structure of the thesis ...... 13 Study 1 ...... 13 Study 2 ...... 13 Study 3 ...... 14 Study 4 ...... 15

2 sedFlow – a tool for simulating fractional bedload transport and longitudinal proﬁle evolution in mountain streams 19 2.1 Introduction ...... 20 2.2 Implementation of the sedFlow model ...... 24 2.2.1 Hydraulic calculation ...... 24 Flow routing ...... 24 Flow resistance ...... 26 2.2.2 Bedload transport calculation ...... 27 Bedload transport rate ...... 27 Evolution of channel bed elevation and slope ...... 30 2.2.3 Grain-size distribution changes ...... 32 2.3 Discussion ...... 34 2.3.1 Comparison of sedFlow implementations with similar models ...... 34 Fractional transport and grain-size distributions . . . . . 34 Adverse channel slopes ...... 36 Simulation speed ...... 37 Flexibility ...... 37 2.3.2 Advantages and limits of the sedFlow modelling approach ...... 38 2.4 Conclusions ...... 39

2 CONTENTS 3

Appendix of chapter 2 43 2.A1 Supplementary methods ...... 43 2.A1.1 Explicit hydraulics ...... 43 2.A1.2 Bedload capacity estimation according to Wilcock and Crowe (2003) ...... 43 2.A1.3 Bedload capacity estimation according to Recking (2010) 44 2.A1.4 Bedload capacity estimation according to Rickenmann (2001) based on θ ...... 44 2.A1.5 Bedload capacity estimation according to Rickenmann (2001) based on q ...... 44 2.A1.6 Fractional bedload capacity estimation according to Rick- enmann (2001) based on θ ...... 45

3 Calculation of bedload transport in Swiss mountain rivers using the model sedFlow: proof of concept 59 3.1 Introduction ...... 60 3.2 Material and methods ...... 62 3.2.1 General catchment characteristics ...... 63 3.2.2 Hydrology ...... 66 3.2.3 Channel morphology and bedload observations ...... 66 Rectangular channels ...... 66 Reference data ...... 67 Accumulated bedload transport ...... 69 3.2.4 The model sedFlow ...... 71 3.2.5 Model calibration and sensitivity calculations ...... 74 3.3 Results ...... 77 3.3.1 Simulations for the calibration period ...... 77 3.3.2 Sensitivity analyses ...... 78 3.4 Discussion ...... 79 3.4.1 Simulations for the calibration period ...... 79 3.4.2 Sensitivity analyses ...... 82 3.5 Conclusions ...... 83

Appendix of chapter 3 92

4 Assessing the impact of climate change on brown trout (Salmo trutta fario) recruitment 100 4.1 Introduction ...... 101 4.2 Materials and methods ...... 103 4.2.1 Study area ...... 103 4.2.2 Catchment scale: Impact of future climate change scenarios on discharge ...... 103 4.2.3 Reach scale: Climate change impacts on bedload transport and channel morphodynamics ...... 105 CONTENTS 4

4.2.4 Local scale: Climate change impacts on habitat stability and distribution ...... 107 Terrestrial survey / DTM generation ...... 107 Hydrodynamic-numerical modelling ...... 108 Classification and stability testing of spawning ground and mesohabitats ...... 109 Sensitivity testing and distribution of mesohabitats under differing discharges ...... 110 Mesohabitat suitability for different brown trout age classes110 4.3 Results ...... 111 4.3.1 Catchment scale ...... 111 4.3.2 Reach scale ...... 112 Bedload transport and morphodynamics ...... 112 4.3.3 Local scale ...... 114 Stability of spawning ground ...... 114 Sensitivity testing of flow variation ...... 115 Mesohabitat distribution under summer low flow conditions in the near and far future ...... 116 Ecological relevance of mesohabitat modelling ...... 118 4.4 Discussion ...... 118 4.4.1 Bedload transport and morphodynamics ...... 118 4.4.2 Spawning and incubation phase ...... 120 4.4.3 Parr phase ...... 121 4.5 Conclusions and possible mitigation measures ...... 122

Appendix of chapter 4 128

5 Spectral characteristics of bedload transport 140 5.1 Introduction ...... 140 5.2 Material and methods ...... 144 5.2.1 Study site ...... 144 5.2.2 Bedload transport measurements ...... 145 5.2.3 Time series analysis ...... 146 5.3 Results ...... 148 5.3.1 Power spectral density ...... 148 Observations ...... 148 Reshuﬄed impulse counts benchmark test ...... 149 5.3.2 Coherence and phase shift of discharge and bedload . . . 149 5.4 Discussion ...... 150 5.4.1 The inter-event scale range ...... 151 5.4.2 The event scale range ...... 151 5.4.3 The phaseshift at the transition from the inter-event to the event scale range ...... 152 CONTENTS 5

5.4.4 The phaseshift at the transition from the event to the intra-event scale range ...... 153 5.4.5 Spectral slopes at the transition from the event to the intra-event scale range ...... 154 5.4.6 The intra-event scale range ...... 154 General characteristics of the intra-event scale range . . 154 The systematic intra-event scale range ...... 155 The random intra-event scale range ...... 155 5.4.7 The periods of 20 to 40 minutes ...... 155 5.5 Conclusions ...... 156

Appendix of chapter 5 164 5.A1 Block randomisation ...... 165 5.A2 Distance to a sediment source based on phaseshift at the transition from the event to the intra-event scale range ...... 166 5.A3 Artiﬁcial time series ...... 168 5.A3.1 Methods ...... 168 5.A3.2 Results ...... 169 Const.Size-NoMod...... 169 Var.Size-NoMod...... 169 Var.Size-Const.Mod...... 170 Var.Size-Var.Mod...... 170 Const.Size-Var.Mod...... 170 5.A3.3 Discussion ...... 171

6 Synthesis and outlook 190 6.1 Synthesis ...... 190 6.2 Outlook ...... 193

Danksagung 195 Abstract

Bedload transport has a wide range of implications for research studies and for civil engineering practice in mountain regions. Considering these implications, the thesis aims to improve the estimation and prediction of bedload transport. These improvements include the provision, assessment, and example application of the new modelling tool sedFlow and a more profound understanding of the temporal dynamics of natural bedload transport systems, which define the scale range of applicability for a deterministic model like the one presented in this thesis. The new one-dimensional model sedFlow is designed to realistically reproduce the total transport volumes and overall morphodynamic changes resulting from sediment transport events such as major floods, and complements the range of existing tools for the simulation of bedload transport in steep mountain streams. It is intended for temporal scales from the individual event (several hours to a few days) up to longer-term evolution of stream channels (several years). The envisaged spatial scale covers complete catchments at a spatial discretisation of several tens of metres to a few hundreds of metres. sedFlow offers different options for bedload transport equations, flow-resistance relationships and other elements which can be selected to fit the current application in a particular catchment. The presented model is an appropriate tool if (I) grain size distributions need to be dynamically adjusted in the course of a simulation, if (II) the effects of ponding, e.g. due to massive sediment inputs through debris flows, might play a role in the study catchment or if (III) one simply needs a fast simulation of bedload transport in a mountain stream with quick and easy pre- and post-processing. We use the model sedFlow to calculate bedload transport observations in two Swiss mountain rivers. Observations from bedload transport events are successfully reproduced with plausible parameter settings, meaning that calibration parameters are only varied within ranges of uncertainty that have been pre- determined either by previous research or by field observations in the simulated study reaches. The influence of different parameters on simulation results is semi-quantitatively evaluated in a simple sensitivity study. Besides some other study results that help to interpret the model behaviour, the presented proof-of- concept study demonstrates the usefulness of sedFlow for a range of practical applications in alpine mountain streams. Using sedFlow in an example application, we simulate the effect of climate change in terms of bed erosion during the incubation time of fish eggs i.e. during the winter months. Due to the simulated trends of increasing magnitudes and durations of winter scour, it is likely that the stable brown trout spawning habitat areas might decrease in the future, and erosion depths will more frequently exceed the average egg burial depth thus exerting stress on the trout population. Complementing the simulation studies, we analyse a unique high resolution time series of bedload transport data from a steep alpine mountain stream by

6 ABSTRACT 7 means of spectral analysis. Four scale ranges of different temporal dynamics are distinguished and described. In the presented pilot study, for the first time, the discharge-independent autoregressive dependency of bedload transport has been attributed to a clearly defined band of frequencies in field data. Furthermore we make suggestions for an optimised measurement strategy, based on the structure of the analysed data set. Altogether, the four studies of the present thesis contribute to an improved prediction of bedload transport in mountain catchments. With sedFlow an open- source modelling tool is provided that combines state of the art approaches for the calculation of fractional bedload transport in steep channels with fast simulations and with easy and straightforward pre- and postprocessing of simulation data. The behaviour of the new simulation tool is assessed in a best practice example for the recalculation of spatially distributed field observations related to bedload transport, as well as in a simple sensitivity study. The capabilities of the model are demonstrated in an example application studying the possible climate-change induced trends in winter erosion, which have considerable ecological implications. Finally the simulation studies are complemented with a spectral analysis of the temporal dynamics of bedload transport, which have been observed in the field and which cannot be reproduced at small time scales with a deterministic model like sedFlow. Kurzfassung

Geschiebetransport spielt in Gebirgsregionen in vielerlei Hinsicht eine grosse Rolle. Dies gilt sowohl für wissenschaftliche als auch praktische Fragestellungen. Vor diesem Hintergrund zielt die vorliegende Arbeit darauf ab die Abschätzung und Vorhersage des Geschiebetransportes zu verbessern. Diese Verbesserun- gen umfassen die Entwicklung, Untersuchung und bespielhafte Anwendung des neuen Modellierungswerkzeuges sedFlow sowie ein vertieftes Verständnis der zeitlichen Dynamik und Variabilität von natürlichem Geschiebetransport, die den zeitlichen Skalenbereich für die Anwendbarkeit eines deterministischen Modelles wie sedFlow festlegen. Das neue eindimensionale Modell ist darauf ausgelegt, die totalen Trans- portvolumina und resultierenden morphodynamischen Veränderungen von Sedi- menttransportereignissen wie etwa grösserer Hochwasser realistisch abzubilden, und ergänzt die Bandbreite vorhandener Werkzeuge für die Simulation von Ge- schiebetransport in steilen Gebirgsgewässern. Es ist für zeitliche Skalen vom Einzelereignis (mehrere Stunden bis wenige Tage) bis zu längerfristigen Gerin- neentwicklungen (mehrere Jahre) vorgesehen. Die räumliche Anwendungsskala deckt ganze Einzugsgebiete bei einer räumlichen Auflösung von mehreren Zehn- ermeter bis zu wenigen hundert Metern ab. sedFlow bietet für die Geschiebe- transportgleichungen, für die Fliesswiderstandsbeziehungen und für weitere Ele- mente verschiedene Optionen, die entsprechend der zu beantwortenden Fra- gestellung und dem jeweiligen Einzugsgebiet ausgewählt werden können. Das vorgestellte Modell ist ein geeignetes Werkzeug, wenn (I) die Kornverteilun- gen im Laufe einer Simulation dynamisch angepasst werden sollen, wenn (II) Aufstaueffekte beispielsweise durch massive Geschiebeeinträge aus Murgängen im Untersuchungsgebiet eine Rolle spielen könnten, oder auch wenn (III) man für die Modellierung von Geschiebetransport in Gebirgsgewässern eine hohe Simula- tionsgeschwindigkeit zusammen mit einer schnellen und einfachen Aufbereitung und Auswertung der Simulationsdaten benötigt. Wir verwenden das Modell sedFlow um Beobachtungen zum Geschiebe- transport aus zwei Gebirgsflüssen in der Schweiz nachzurechnen. Die vor- handenen Beobachtungen von Transportereignissen können dabei mit plausi- blen Parametereinstellungen erfolgreich reproduziert werden, wobei in diesem Zusammenhang “plausibel” bedeutet, dass die Kalibrationsparameter nur inner- halb jenes Unsicherheitsbereiches variiert werden, der durch frühere Forschung sowie durch Feldbeobachtungen aus den Untersuchungsstrecken vorgegeben ist. Der Einfluss verschiedener Parameter auf die Simulationsergebnisse wird in einer einfachen Sensitivitätsstudie halbquantitativ abgeschätzt. Neben wei- teren Untersuchungsergebnissen, die bei der Interpretation des Modellverhaltens helfen, demonstriert die vorgestellte Machbarkeitsstudie den Nutzen des Modells sedFlow für eine Bandbreite praktischer Anwendungen in verschiedenen Gebirgs- gewässern der Alpen. In einer bespielhaften Anwendung simulieren wir mit sedFlow die möglichen

8 KURZFASSUNG 9

Auswirkungen des Klimawandels auf die Betterosion während der Inkubations- zeit, das heisst während der Wintermonate. Durch die simulierten Trends einer stärkeren und länger andauernden Wintererosion ist es wahrscheinlich, dass die Flächen der erosionsgeschützten Laichhabitate der Bachforelle in Zukunft ab- nehmen werden und dass die Erosionstiefen immer häufiger die durchschnitt- lichen Eingrabungstiefen der Eier überschreiten und so Stress auf die Forellen- population ausüben werden. Ergänzend zu den Simulationsstudien analysieren wir eine bis dato einzigar- tige, hoch aufgelöste Geschiebetransport-Zeitreihe aus einem alpinen Wildbach mit den Mitteln der Spektralanalyse. Dabei werden vier Skalenbereiche mit unterschiedlicher Dynamik ausgeschieden und beschrieben. In der vorliegenden Pilotstudie kann erstmalig ein vom Abfluss unabhängiges, autoregressives Verhalten des Geschiebetransportes in Felddaten einem klar begrenzten Fre- quenzband zugewiesen werden. Zusätzlich ergeben sich aus der Struktur des untersuchten Datensatzes Vorschläge für eine optimierte Mess-Strategie. In ihrer Kombination leisten die vier Untersuchungen der vorliegenden Ar- beit einen Beitrag zu einer verbesserten Vorhersage von Geschiebetransport in Gebirgseinzugsgebieten. Mit sedFlow wird ein quelloffenes Modellwerkzeug zur Verfügung gestellt, das aktuelle Methoden zur fraktionierten Berechnung von Geschiebetransport in steilen Gerinnen sowohl mit hohen Simulationsgeschwin- digkeiten als auch mit einfacher und schneller Aufbereitung und Auswertung von Simulationsdaten kombiniert. Das Verhalten des neuen Simulationswerkzeuges wird in einer Muster-Anwendung zur Nachrechnung von räumlich verteilten Ge- schiebetransportbeobachtungen aus dem Gelände sowie in einer einfachen Sen- sitivitätsstudie untersucht. Die Möglichkeiten, die das Modell bietet, werden in einer beispielhaften Anwendung aufgezeigt, in der durch den Klimawandel möglicherweise zu erwartende Trends der winterlichen Betterosion mit nennens- werten ökologischen Auswirkungen untersucht werden. Schliesslich werden die simulationsbasierten Untersuchungen ergänzt durch eine Spektralanalyse der zeitlichen Dynamik von Geschiebetransport, wie sie im Feld beobachtet wurde und wie sie mit einem deterministischen Modell wie etwa sedFlow für kurzzeitige Änderungen nicht abgebildet werden kann. Chapter 1

Introduction

1.1 Motivation

The rolling, sliding or saltating transport of sediment grains along river beds, which is summarised as bedload transport, represents one of the main morphodynamic processes in steep mountain streams. Such steep channels make up the major part of total stream length in mountain regions. For example, 74% of total stream length in Switzerland are steeper than 3% (Nitsche, 2012). In these steep channels, the system of bedload transport interactions is notably complex (e.g. Rickenmann, 2012) and many of its details are not completely understood yet. At the same time, especially in steep channels, bedload transport has various implications for the scientific and civil engineering practice. The bedload dynamics determine the long term sustainability of many civil river engineering projects. Sediment inflow may reduce the efficiency of reservoirs used for hydro-electric power production and create additional maintenance costs for the operating company (Schleiss and Oehy, 2002; Jenzer et al., 2005; Jenzer Althaus and de Cesare, 2006). Bedload transport has the potential to amplify the impact of severe flood events and there are numerous examples documented in which the deposition (e.g. Bezzola et al., 1994; White et al., 1997; Arnaud- Fassetta et al., 2005; Bezzola and Hegg, 2007; Totschnig et al., 2011) or erosion (e.g. Waananen et al., 1971; Balog, 1978; Walther et al., 2004; Hunzinger and Krähenbühl, 2008; Krapesch et al., 2011) of sediment caused serious financial damage. Badoux et al. (2014) quantified that in Switzerland within 40 years since 1972 a sum of CHF 4.3 to 5.1 billion of damage costs can be attributed to bedload transport processes. This value corresponds to more than 30% of the total financial losses due to natural hazards excluding snow avalanches and windstorms. Further on, bedload transport processes have considerable eco- logic influence as they reorganise the channel bed and thus affect potential spawning grounds (e.g. Kondolf and Wolman, 1993; Elliott et al., 1998; Unfer et al., 2011). Therefore, the restoration of the stream sediment budgets is im- plicitly requested by the Water Framework Directive (Directive 2000/60/EC of

10 CHAPTER 1. INTRODUCTION 11 the European Parliament and of the Council of 23 October 2000 establishing a framework for Community action in the field of water policy), which aims for good ecological status for all ground and surface waters. It is also explicitly requested by the revised Swiss Federal Act on the Protection of Waters (Gewässerschutzgesetz, GSchG). This implies the estimation and comparison of sediment transport under current conditions as well as without anthropogenic influences. This means the various implications of bedload transport in general and the Water Framework Directive as well as the revised Swiss Waters Protection Act in specific make improvements in the estimation and prediction of bedload transport in mountain streams essential. Such improvements include numeric modelling tools, best practice examples for their application as well as enhanced knowledge about the interactions and temporal dynamics of the involved processes that define the scale range for the applicability of a deterministic model.

1.2 Research gaps

In recent years many numeric models have been developed for the simulation of sediment transport in rivers. Summarising overviews have been given by Habersack et al. (2011) and Coulthard and van de Wiel (2012). However, most of these models are intended for and only applicable to lowland rivers with gentle channel slopes. In mountain streams the effects of macro-roughness and shear stress partitioning have to be considered. Otherwise, the sediment transport rates may be overestimated by several orders of magnitude (Yager et al., 2007; Rickenmann and Recking, 2011; Nitsche et al., 2011, 2012). The number of sediment transport models specifically designed for mountain streams is limited. The comprehensive overview given in Chapter 2 shows that none of the available modelling tools fulfils all of the following requirements: 1. provision of a sediment transport model together with a comprehensive manual and its complete source code, open-source and free of charge, 2. implementation of recently proposed and tested approaches for calculating bedload transport in steep channels accounting for macro-roughness effects, 3. individual calculations for several grain diameter fractions (fractional transport), 4. consideration of ponding effects of adverse slopes (uphill slopes in the downstream direction), e.g., due to sudden sediment deposition by debris flows from steep lateral tributaries, 5. fast calculations for modelling entire catchments over long periods, and for automated calculation of multiple scenarios exploring a range of parameter space, CHAPTER 1. INTRODUCTION 12

6. an object-oriented code design that facilitates flexibility in model development, 7. flexibility in model application featuring different options for, e.g., the bedload transport equations, which can be selected to fit the current application, as well as straightforward pre- and postprocessing of simulation data. For any bedload transport simulation tool, the model behaviour needs to be evaluated and documented to allow for a reliable interpretation of simulation results. First, simulation results should be compared to field observations to assess the quality of the model representation. As simulation results are commonly calculated for each cell in the simulated system, the comparison to field data should be spatially distributed as well. However, there are only few examples of such spatially distributed comparisons in the literature (e.g. Chiari and Rickenmann, 2011; Mouri et al., 2011; Lopez and Falcon, 1999). Second, simulation results produced with different model set-ups should be compared to each other in order to assess the influence of the set-ups on the model output. Third, a sensitivity study needs to be performed in order to assess the effects of uncertainty and changes in the input parameters. Finally, the description of a best-practice calibration procedure is desirable for any modelling tool. Due to the above listed limitations of available models, it has not been feasible so far to apply sediment transport models for studying the potential impact of climate change on bedload transport in a mountain river. In this context, the expectable trends of erosion activity during the winter months are of special interest. This erosion activity and more precisely its magnitude and timing is crucial for the reproduction success of e.g. the brown trout (Unfer et al., 2011). Therefore, the climate induced changes in winter erosion will have an important, yet up to now unknown effect on the fish populations in Swiss mountain rivers. Besides (a) the description of a model’s properties, (b) a proof-of-concept assessment, and (c) an example application, it is important to consider (d) the scale ranges, at which a model can be applied. In general, bedload transport is mainly driven by channel gradient and discharge. This dependency has been described in numerous transport equations, which in turn can be used in deterministic numerical models for simulating this process. However, considerable differences can be observed in the temporal dynamics of discharge and bedload transport. These differences can be subdivided into two groups: (I) Under conditions of constant discharge, bedload transport shows fluctuation, even though water and sediment are fed to the system at a constant rate such as in flume studies (e.g. Iseya and Ikeda, 1987). (II) Under conditions of temporally changing discharge, bedload transport shows hysteresis, i.e. the bedload transport rates at the rising limb of a hydrograph differ systematically from the transport rates at the falling limb (e.g. Mao, 2012). The previous research on these differences in the behaviour of bedload transport and discharge is comprehensively CHAPTER 1. INTRODUCTION 13 summarised in the introduction of chapter 5. It shows that the large majority of previous studies were either based on flume investigations (often using a constant discharge) or focussed on the analysis of individual transport events. Up to now, there is no field based and quantitative description of scale ranges of comparable or differing bedload transport and discharge behaviour. In other words, the temporal scales at which a deterministic discharge-based model can be used to predict bedload transport have not been determined quantitatively so far.

1.3 Objectives and structure of the thesis

The thesis consists of six chapters. The topic is introduced and a motivation is provided in Chapter 1. Based on the described research gaps, the objectives of this thesis were tackled within four distinct studies, the results of which are presented in Chapters 2 to 5. The outcome of this work is summarised and concluded in Chapter 6.

Study 1 The objectives of the ﬁrst study were:

• Select and describe the equations and algorithms, which are necessary for an eﬃcient simulation of bedload transport dynamics in mountain streams.

• Provide the complete source code for the numeric modelling tool sedFlow together with a comprehensive manual.

• Assess the eﬀects of the simpliﬁcation of a rectangular channel on the resulting bedload transport volumes.

This study is presented in Chapter 2 and has been published as a research article: Heimann, F. U. M., Rickenmann, D., Turowski, J. M., and Kirchner, J. W.: sedFlow – a tool for simulating fractional bedload transport and longitudinal proﬁle evolution in mountain streams, Earth Surf. Dynam., 3, 15–34, doi: 10.5194/esurf-3-15-2015, 2015.

Study 2 The objectives of the second study were:

• Calibrate and apply the sedFlow modelling tool in a best practice example to recalculate spatially distributed observations related to bedload transport in two Swiss mountain streams. CHAPTER 1. INTRODUCTION 14

• Discuss the experiences with the modelling tool with respect to properties of the underlying equations, such as the problems of traditional ﬂow resistance estimation methods to consider the inﬂuence of large blocks.

• Assess the inﬂuence of various input parameter uncertainties on the simulation results in a simple sensitivity study.

• Check the adequacy of the simpliﬁed hydraulic routing schemes, which are used in sedFlow to reproduce bedload transport observations.

This study is presented in Chapter 3 and has been published as a research article: Heimann, F. U. M., Rickenmann, D., Böckli, M., Badoux, A., Turowski, J. M., and Kirchner, J. W.: Calculation of bedload transport in Swiss mountain rivers using the model sedFlow: proof of concept, Earth Surf. Dynam., 3, 35–54, doi: 10.5194/esurf-3-35-2015, 2015.

Study 3 The objectives of the third study were:

• Simulate and discuss expectable trends in winter erosion due to climate change in a Swiss mountain stream in terms of

– magnitude, – timing, – and spatial distribution over reaches with diﬀerent channel gradients.

This study is presented in Chapter 4 and has been published as a research article: Junker, J., Heimann, F. U. M., Hauer, C., Turowski, J. M., Rickenmann, D., Zappa, M., and Peter, A.: Assessing the impact of climate change on brown trout (Salmo trutta fario) recruitment, Hydrobiologia, doi: 10.1007/s10750-014-2073-4, 2014. The author of the presented dissertation is the second author of this article. His contribution primarily comprises the simulation and discussion of the expectable trends in winter erosion. This mainly includes the section “Reach scale: climate change impacts on bedload transport and channel morphodynamics” in the “Materials and methods”, the section “Reach scale – Bedload transport and morphodynamics” in the “Results”, and the section “Bedload transport and morphodynamics” in the “Discussion”. CHAPTER 1. INTRODUCTION 15

Study 4 The objectives of the fourth study were:

• Assess and compare the temporal dynamics of discharge and bedload transport time series from an alpine mountain stream by means of spectral analysis.

• Distinguish scale ranges of diﬀerent temporal dynamics and interpret them with respect to the typical duration of bedload transport events.

• Interpret observed spectral behaviour in terms of bedload transport process interactions.

This study is presented in Chapter 5.

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Yager, E. M., Kirchner, J. W., and Dietrich, W. E.: Calculating bed load transport in steep boulder bed channels, Water Resour. Res., 43, W07 418, doi: 10.1029/2006WR005432, 2007. Chapter 2 sedFlow – a tool for simulating fractional bedload transport and longitudinal proﬁle evolution in mountain streams

Heimann, F. U. M., Rickenmann, D., Turowski, J. M., and Kirchner, J. W.: sedFlow – a tool for simulating fractional bedload transport and longitudinal proﬁle evolution in mountain streams, Earth Surf. Dynam., 3, 15–34, doi: 10.5194/esurf-3-15-2015, 2015. Published under the Creative Commons Attribution 3.0 License

Abstract

Especially in mountainous environments, the prediction of sediment dynamics is important for managing natural hazards, assessing in-stream habitats and understanding geomorphic evolution. We present the new modelling tool sed- Flow for simulating fractional bedload transport dynamics in mountain streams. sedFlow is a one-dimensional model that aims to realistically reproduce the total transport volumes and overall morphodynamic changes resulting from sediment transport events such as major floods. The model is intended for temporal scales from the individual event (several hours to few days) up to longer-term evolution of stream channels (several years). The envisaged spatial scale covers complete catchments at a spatial discretisation of several tens of metres to a few hundreds of metres. sedFlow can deal with the effects of streambeds that slope uphill in a downstream direction and uses recently proposed and tested approaches for quantifying macro-roughness effects in steep channels. sedFlow offers different options for bedload transport equations, flow-resistance relationships and other elements which can be selected to fit the current application in a particular catchment. Local grain-size distributions are dynamically ad-

19 CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 20 justed according to the transport dynamics of each grain-size fraction. sedFlow features fast calculations and straightforward pre- and postprocessing of simulation data. The high simulation speed allows for simulations of several years, which can be used, e.g., to assess the long-term impact of river engineering works or climate change effects. In combination with the straightforward pre- and postprocessing, the fast calculations facilitate efficient workflows for the simulation of individual flood events, because the modeller gets the immediate results as direct feedback to the selected parameter inputs. The model is provided together with its complete source code free of charge under the terms of the GNU General Public License (GPL) (www.wsl.ch/sedFlow). Examples of the application of sedFlow are given in a companion article by Heimann et al. (2015).

2.1 Introduction

Environmental models typically seek to predict the future state of a system, based on information about its current state and the mechanisms that regulate its evolution through time. In the case of sediment transport by flowing water in open channels, the temporal evolution of these variables is determined by a complex interaction of multiple processes including hydraulic water routing, sediment entrainment, erosion and deposition. In recent years many numerical models have been developed for simulating sediment transport in rivers. How- ever, most of these models are intended for, and only applicable in, lowland rivers with gentle slopes. In mountain streams the effects of macro-roughness and shear stress partitioning have to be considered. Otherwise, sediment transport rates may be overestimated by several orders of magnitude (Rickenmann and Recking, 2011; Nitsche et al., 2011, 2012). Based on these observations and contrasting the dominantly gradient-based definition used by, e.g., Wohl (2000), we define mountain streams as streams which are located within a mountainous region and in which the effects of macro-roughness and shear stress partitioning play an important role in the sediment transport system. Few sediment transport models have been specifically designed for mountain streams. Cui et al. (2006) developed the two Dam Removal Express Assessment Models (DREAM-1&2), based on the previous models of Cui and Parker (2005) and Cui and Wilcox (2008), to focus specifically on dam removal scenarios. The DREAM models therefore feature the simulation of (a) bank erosion during the downcutting of reservoir deposits, (b) transcritical flow conditions, (c) combined bedload and suspended load transport, (d) the details of gravel abrasion and (e) staged dam removal and partial dredging as options in the dam removal scenarios. Due to their specific focus, the wider applicability of the DREAM models is limited. Both the model of García-Martinez et al. (2006) and the model MIKE21C (DHI, 1999, with its modifications by Li and Millar, 2007) focus on a two-dimensional representation of hydraulic and sediment transport CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 21 processes. Therefore, these models require more extensive input data and longer calculation times compared to one-dimensional model representations. As another example, the model of Papanicolaou et al. (2004) is intended for studying sediment transport under transcritical flow conditions by solving the unsteady form of the Saint-Venant equations, which results in long calculation times. Other sediment transport models have been described by Mouri et al. (2011), Lopez and Falcon (1999) and Hoey and Ferguson (1994), all of which feature the one-dimensional simulation of fractional bedload transport using a simplified representation of the hydraulic processes. The model of Mouri et al. (2011) can represent a combination of debris flow, bedload and suspension load processes. In contrast, SEDROUT (Hoey and Ferguson, 1994) is designed to study the spatial and temporal evolution of local grain-size distributions. Therefore, it determines the composition of the sediment surface layer by a numeric iteration within each time step. In its latest version, SEDROUT has been also extended to deal with islands and other features of river bifurcation (Verhaar et al., 2008). However, neither the source code, the executable model binary nor a detailed description of the model implementation is available for any of the three models mentioned in this paragraph. The model TomSed (formerly known as SEdiment TRansport model in Alpine Catchments (SETRAC)) was developed to study the influence of different shapes of channel cross sections on bedload transport in steep streams (Chiari et al., 2010; Chiari and Rickenmann, 2011). Therefore, the user can define cross sections with laterally varying bed elevations. The shape of a particular cross section stays the same during the complete simulation. Most published model applications used bedload transport calculations for a single grain size. In such a situation, all grain sizes and their spatial distribution are constant for the complete simulation. In this set-up, TomSed is slightly faster than real time in a typical application. A fractional transport approach with dynamic grain-size distributions is implemented in TomSed as well. However, it is rarely used due to the long calculation times. The TOPographic Kinematic wave APproximation and Integration (Top- kapi) model was originally developed as a rainfall–runoff model providing fast hydrologic simulations (Ciarapica and Todini, 2002). Later a sediment transport module was added, and this model version is called Topkapi ETH (Konz et al., 2011). The code is intended for the study of reach-scale sediment transport in the context of large-scale hydrologic processes. Due to this scope that integrates different processes and scales, the model features a spatial as well as temporal sub-gridding approach. The hydrologic processes are simulated on a coarse two-dimensional grid with time steps that are an integer multiple of the time steps for the hydraulic and sediment transport processes. The latter two processes are simulated in a one-dimensional channel at a finer spatial resolution. This channel receives water from the hydrologic two-dimensional grid, but the morphodynamic changes due to bedload transport have no influence on the topography used for the hydrologic calculations. The channel cross section is CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 22

hydrauliccondition bedloadtransport fluxofwater fluxofsediment localtributary influence

upstreamreach localreach downstreamreach

hydrauliccondition hydrauliccondition hydrauliccondition

bedloadtransport bedloadtransport bedloadtransport

activelayer activelayer activelayer

subsurfacealluvium subsurfacealluvium subsurfacealluvium

Figure 2.1: Simplified overview over the main process interactions within the sedFlow model. represented by a rectangle and bedload transport is based on a single grain-size approach, in which local grain-size distributions do not change over time. In typical applications, a flood event of several days can be simulated within a few minutes of calculation time. Currently, no model is available that combines short calculation times with easy use and up-to-date sediment transport equations for mountain catchments. The new model sedFlow (Figs. 2.1, 2.A1, 2.A2, 2.A3) presented in this contribution has been developed to provide an efficient tool for the simulation of bedload transport in mountain streams. By efficient tool we mean a model that combines straightforward pre- and postprocessing of simulation data with fast calculation speeds. sedFlow is intended for temporal scales from the individual event (several hours to a few days) to longer-term channel evolution (several years). The envisaged spatial scale covers complete catchments at a spatial discretisation of several tens to a few hundreds of metres. The following elements were important for the development of sedFlow:

1. a sediment transport model provided together with its complete source code, open source and free of charge;

2. implementation of recently proposed and tested approaches for calculating bedload transport in steep channels accounting for macro-roughness eﬀects;

3. individual calculations for several grain diameter fractions (fractional transport) resulting in more robust simulations as compared to single-grain approaches;

4. consideration of ponding eﬀects of adverse slopes (uphill slopes in the downstream direction), e.g. due to sudden sediment deposition by debris ﬂow inputs; CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 23

Table 2.1: Comparison of bedload transport models for steep mountain streams. Estimated calculation speeds refer to the simulation of a 20 km long study reach of a regular mountain river.

Topkapi ETH TomSed SEDROUT sedFlow Main aims integral simulation of dif- simulation of the effect detailed simulation of the fractional transport, ferent processes at differ- of the shape of chan- spatial and temporal evo- consideration of uphill ent scales featuring spa- nel cross sections on bed- lution of local grain-size slopes, fast simulations tial and temporal sub- load transport featuring distributions; river bifur- and straightforward pre- gridding a user-defined, detailed cations and postprocessing of channel geometry simulation data Speed simulation of several days slightly faster than real simulation of several within few minutes of time years within few hours of computation time computation time Input format partially MATLAB XML files mainly regular preprocessing required spreadsheets Intended applications mainly scientific engineering and scientific mainly scientific mainly engineering and operational References Konz et al. (2011); Chiari et al. (2010); Hoey and Ferguson Junker et al. (2014); Carpentier et al. (2012) Chiari and Rickenmann (1994); Ferguson et al. Heimann et al. (2015) (2011); Kaitna et al. (2001); Talbot and (2011) Lapointe (2002); Hoey et al. (2003); Verhaar et al. (2008); Boyer et al. (2010)

5. fast calculations for modelling entire catchments, and for automated calculation of multiple scenarios exploring a range of parameter space;

6. an object-oriented code design that facilitates ﬂexibility in model development;

7. flexibility in model application featuring different options (Figs. 2.A1, 2.A2), e.g. for the bedload transport equations, which can be selected to fit the current application, as well as straightforward pre- and postprocessing of simulation data.

The model sedFlow thus ﬁlls a gap in the range of existing sediment transport models for mountain streams (Table 2.1) and the goals outlined above have led to the implementation described in the following sections. This implementation represents the current state of the model, and may be easily extended and adjusted in the future. Examples of sedFlow application are given in a companion article by Heimann et al. (2015). CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 24

2.2 Implementation of the sedFlow model

2.2.1 Hydraulic calculation Hydraulic equations describe the temporal evolution of the three-dimensional flow field of the water continuum. A formalised description of the dynamics has been provided by Navier and Stokes (given in the form for incompressible flow).

∂(~v) ρ + ~v · ∇~v = −∇p + µ∇2~v + f,~ (2.1) ∂t where ρ is fluid density, ~v is flow velocity, t is time, p is pressure and µ is dynamic viscosity. f~ summarises other influencing body forces. If large-scale backwater effects are not present, as is often the case in steep channels of mountain streams, the energy slope can be approximated by the bed slope (i.e. assumption of kinematic wave propagation) and the complete Navier–Stokes equation can be reduced to the following simplified, cross-sectional averaged conservation of volume (e.g. Chow et al., 1988).

∂Q ∂A + = Q , (2.2) ∂x ∂t lat where Q is discharge, x is distance in ﬂow direction, A is wetted cross-sectional area and Qlat is lateral water inﬂux.

Flow routing Within sedFlow a channel network joined by confluences can be simulated. At the upstream ends of the main channel and each of the user-defined tributaries, a discharge time series is input and has to be routed through the channel system. For the following discussion of hydraulic routing schemes we will differentiate between three cases: first, in ponding – i.e. water collecting behind sediment obstructions – the friction slope Sf is approximately zero (Sf ≈ 0). Second, in situations with parallel slopes, the friction slope approximately equals the channel bed slope Sb (Sf ≈ Sb), which is commonly true for steep Sb. Third, the situations of moderate backwater effects cover all cases between the extremes of ponding on the one hand and situations with parallel slopes on the other. Especially in models not focussing on the details of the hydraulic routing, the kinematic wave approach (assuming the situation of parallel slopes) can be implemented using a temporally explicit Eulerian forward approach (van de Wiel et al., 2007; Chiari et al., 2010). Such an approach can be used in sedFlow as well (see Sect. 2.A1.1). However, Eulerian forward approaches must assume that all parameters within one time step can be sufficiently approximated by their values at the beginning of the time step. To ensure this approximation, Eulerian forward approaches require very small time steps, especially for fast processes. This can be problematic when a relatively fast process, such as the CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 25 routing of water, is combined with a relatively slow process, such as bedload transport including bed level adjustments. The water routing requires small time steps and thus calculation times that may be orders of magnitude too long and slow from the perspective of bedload dynamics. Therefore, as an alternative, an implicit discharge routing is implemented in sedFlow. The implicit routing is unconditionally stable, and thus has no requirements concerning the length of time steps. In sedFlow the approach of Liu and Todini (2002) is used, which omits time-consuming iterations and finds the solution for the kinematic wave analytically via a Taylor series approximation. However, the approach depends on a power-law representation of discharge as a function of water volume in a reach. This means that it can only be applied to the specific cross-sectional shapes of infinitely deep rectangular or V-shaped channels in combination with a power-law flow-resistance equation. The kinematic wave assumption of parallel slopes is usually valid for steep channel gradients, which are typical of mountain catchments. Nevertheless, the kinematic wave assumption can be problematic, especially in mountain streams, when tributaries deliver large amounts of sediment to the main channel within a relatively short time, e.g. during debris flow events. This may result in adverse channel slopes (uphill slopes in the downstream direction) and backwaters in the main channel, violating the assumptions of a kinematic wave. If configured for kinematic wave routing, sedFlow will abort simulations whenever adverse channel slopes occur. When it is necessary to deal with adverse channel slopes, one has to drop the kinematic wave approximation and use a backwater calculation instead. Unfor- tunately, the backwater calculation is numerically intensive. Therefore, within sedFlow, a pragmatic approach can be selected to deal with adverse channel slopes: discharge is assumed to be uniform and thus equal along the entire channel for a given time step only increasing at confluences. This assumption of uniform discharge is reasonable because the temporal scale for water routing is orders of magnitude smaller than the temporal scale for morphodynamic adjustments. In the case of positive slopes, flow depth and velocity are commonly calculated using the bed slope as proxy for the friction slope (thus assuming the bed slope and water surface are parallel). However, the flow resistance may be adjusted such that a maximum Froude number is not exceeded. In cases of adverse channel slopes, the formation of ponding is simulated. That is, flow depth and velocity are selected to ensure a minimum gradient of hydraulic head, which is positive but close to zero, and thus ensures numeric stability, and approximately corresponds to the hydraulic gradient of ponding water. For bedload transport calculations the gradient of the hydraulic head is used, which by definition can only have positive slopes. Thus, the energy slope for bedload transport estimation is not the result of a backwater calculation, but it is the gradient between individual hydraulic head values, which under non-ponding conditions have been calculated independently from each other using the local bed slope as a proxy for friction slope. This approach is based on the assumption that the CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 26 simulated system only consists of the two extreme cases of ponding on the one hand and parallel slopes on the other. At a spatial discretisation of several tens of metres, the assumption of the two extreme cases is valid for many mountain streams and it allows efficient simulation of ponding, by omitting numerically intensive backwater calculations. However, it has to be noted that this approach will produce large errors when intermediate cases of moderate backwater effects are part of the simulated system. In such systems, the first approach, which uses bed slope both as friction slope for the hydraulic calculations and as energy slope for the sediment transport calculations, will produce better estimates of the transported sediment volumes, but it cannot accommodate adverse channel gradients. Heimann et al. (2015) have demonstrated that, despite their simplicity, the implemented hydraulic concepts (Fig. 2.2) appear to be sufficient for a realistic integrated representation of bedload transport processes. In that study, for the different hydraulic routing schemes, results have been obtained, which are close to the observed morphodynamic changes and very similar among each other.

Flow resistance The interaction of flowing water with the river bed and banks determines the relation between the average downstream velocity and the wetted cross section. This interaction is summarised as flow resistance, which can be described by the following physically based relation: s 8 v = √ , (2.3) f g · rh · Sf where f is the Darcy–Weisbach friction factor, v is cross-sectional mean flow velocity, g is gravitational acceleration and rh is hydraulic radius. The flow routing method of Liu and Todini (2002) requires a power-law relation between discharge and water volume within a reach. Therefore, the following flow- resistance law can be used in sedFlow. s l 8 rh = j1 · (2.4a) f k · Dx s 1 8 r 6 = 6.5 · h (2.4b) f D84

Here j1, k and l are empirical constants and Dx is the xth percentile diameter of the local grain-size distribution. Unless otherwise stated, all grain sizes refer to 1 the surface layer. By selecting l = 6 , this formula represents a classic grain-size dependent Gauckler–Manning–Strickler relation. For the other variables, the values j1 = 6.5, k = 1 and x = 84 (Eq. 2.4b) have been found to reproduce observational data well for deeper flows with rh larger than about 7–10 (Rick- D84 enmann and Recking, 2011). If another flow routing is used, one can select the CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 27 variable power-equation flow-resistance approach provided by Ferguson (2007) with the parameter values proposed by Rickenmann and Recking (2011), which was recommended also for applications in steep channels, including shallow flows with small relative flow depths rh : D84

s j · j · rh 8 1 2 D84 = r , f 5 j2 + j2 · rh 3 1 2 D84

where j1 = 6.5 and j2 = 2.5. (2.5)

In general, flow resistance describes the effects of drag forces exerted on the bed and its structures. A part of this drag, namely skin drag, is responsible for the transport of sediment grains (e.g. Morvan et al., 2008). The drag created by larger-scale surface geometries, such as bed forms and channel shape features (e.g. bends and irregular channel width), may be summarised as macro- roughness, which reduces the energy available for the transport of sediment. If macro-roughness is not accounted for in steep channels, bedload transport capacity may be greatly overestimated (Rickenmann, 2001, 2012; Yager et al., 2007; Badoux and Rickenmann, 2008; Chiari and Rickenmann, 2011; Nitsche et al., 2011, 2012; Yager et al., 2012). To correct for macro-roughness, Nitsche et al. (2011) suggested the use of a reduced energy slope, which represents a fraction of the real gradient, and which is based on a flow-resistance partitioning approach of Rickenmann and Recking (2011) and Nitsche et al. (2011).

e  5  0.5·e rh 6 f 2.5 · D S = S · 0 = S ·  84  (2.6) red r 5  ftot   6.52 + 2.52 · rh 3 D84

Here Sred is the reduced slope that accounts for macro-roughness effects, S is channel or hydraulic energy slope, f0 is base-level flow resistance according to Eq. (2.4b), ftot is total flow resistance according to Eq. (2.5) and e is an exponent ranging from 1 to 2, with a typical value of e = 1.5. Within sedFlow, one can select to use Sred based on Eq. (2.6) to account for macro-roughness.

2.2.2 Bedload transport calculation Bedload transport rate Several methods for the calculation of bedload transport capacity are implemented in sedFlow: Sects. 2.A1.2–2.A1.5 describe the method of Wilcock and Crowe (2003) based on flume data, the method of Recking (2010) based on field observations and the method of Rickenmann (2001) based on flume data together with a simplified version of the Rickenmann method and another version based on discharge instead of shear stress. The method of Rickenmann (2001) CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 28 was tested together with Eq. (2.6), by comparison with bedload transport observations in steep mountain streams (Nitsche et al., 2011). The equations of Wilcock and Crowe (2003) were derived from fractional bedload transport data. The equation of Recking (2010) was developed for the estimation of total bedload transport rates. In the same way as the equations of Meyer-Peter and Müller (1948), Fer- nandez Luque and van Beek (1976) and Soulsby and Damgaard (2005), the equation of Rickenmann (2001) (Sect. 2.A1.4; especially its simplified version in Eq. 2.A20) is a good example of the following generic type of bedload estimation methods: b d Φb = a · θ · (θ − θc) , (2.7)

qb τ where Φb = √ is dimensionless bedload flux, θ = is dimen- (s−1)gD3 (s−1)ρgD sionless bed shear stress, θc is the dimensionless bed shear stress threshold for the initiation of motion, qb is bedload flux per unit flow width, D is grain diameter, a, b and d are empirical constants, τ = (ρ · g · rh · S) is bed shear ρs stress and s = ρ is the density ratio of solids ρs and fluids ρ. To account for macro-roughness, S can be replaced by Sred in the calculation of the bed shear stress τ. In the case of the Rickenmann (2001) equation, a is the product of an empirical constant and the Froude number F r. In equations like Eq. (2.7), bedload transport is mainly a power law of the dimensionless bed shear stress that exceeds some threshold for the initiation of bedload motion. This threshold is known as the Shields criterion (Shields, 1936) with typical values ranging from 0.03 to 0.05. In natural channels, geometric complexity and thus energy losses increase at steep bed slopes Sb. Therefore, Lamb et al. (2008) suggested the following empirical relation to account for increasing θc values with increasing Sb: 0.25 θc = 0.15 · Sb . (2.8) The main objective of Lamb et al. (2008) is a theoretical explanation for the observed increase of θc with increasing bed slopes Sb. However, for very small values of Sb, the power law of Eq. (2.8) predicts values of θc that are approaching zero. This contrasts with the results of other studies (e.g. Recking, 2009) that observed roughly constant values of θc larger than zero for small slopes. sedFlow can be configured to use either a constant threshold or a slope- dependent threshold according to Eq. (2.8) combined with a minimum value θcMin. The estimated bedload flux can be corrected for gravel abrasion according to the classic equation of Sternberg (1875), in which qbabr is bedload flux per unit flow width corrected for abrasion, λ is an empirical abrasion coefficient and ∆X is the travel distance of the grains. Here the material loss due to abrasion is regarded as suspension throughput load:

qbabr = qb · exp (−λ · ∆X) . (2.9) CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 29

If grain-size fractions are treated individually, the calculated bedload capacity Φb needs to be normalised with Fi, the relative volumetric portion of bed surface material of a grain-size fraction i, compared to the total surface material with D > 2 mm (e.g. Parker, 1990). Here Fi can be interpreted as the availability of a certain grain-size fraction in the bed; for an example, see Eq. (2.A23) in Sect. 2.A1.6 compared to Eq. (2.A20) in Sect. 2.A1.4. Further details also have to be accounted for, such as the varying exposure of diﬀerent grain-size fractions, grain-size-dependent grain–grain interactions, etc. This is commonly done using some sort of hiding function. Hiding functions not only focus mainly on grain exposure but also integrate all kinds of grain-size-dependent eﬀects which are not covered by the capacity estimation methods. Within sedFlow a relatively simple power-law hiding function can be used (Parker, 2008): m Di θci = θc · , (2.10) Dx as well as the hiding function of Wilcock and Crowe (2003):

mwc Di θci = θc · , Dm 0.67 where mwc = − 1. (2.11) 1 + exp 1.5 − Di Dm

Here θci is the θc for the ith grain-size fraction, Di is the mean grain diameter for ith grain-size fraction, m is an empirical hiding exponent, Dm is the geometric mean diameter of the local grain-size distribution and mwc is the hiding exponent according to Wilcock and Crowe (2003). The empirical exponent m ranges from 0 to −1, where m = −1 corresponds to the so-called “equal mobility” case in which all grains start moving at the same bed shear stress τ, and m = 0 corresponds to no inﬂuence by hiding at all. For x = 50, the values for m, which have been derived from various ﬁeld observations, typically vary within a range from −0.60 to −1.00 (Recking, 2009), and unfortunately there are only few data points for Di > D50 (Bathurst, 2013; Bunte et al., 2013). For consistency, the following θci,r is used in bedload transport calculations.

θci,r = θci · γ (2.12)

Within sedFlow two alternatives are implemented for the calculation of the correction factor γ: S γ = red (2.13a) S and S γ = c . (2.13b) S CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 30

In Eq. (2.13a), θci,r varies with discharge, as it depends on Sred, which in turn is a function of the hydraulic radius rh. In Eq. (2.13b), suggested by Nitsche et al. (2011), θci,r is independent of discharge. The value of Sc is calculated using Eq. (2.6), with the value of rh replaced by the critical hydraulic radius rh, c: ρ 1 r = θ · s − 1 · D · . (2.14) h, c c ρ 50 S Good arguments can be found for both approaches (Eqs. 2.13a and 2.13b). Due to the lack of suitable data, it is unclear which approach is more plausible.

Evolution of channel bed elevation and slope The temporal evolution of the longitudinal profile is simulated in sedFlow based on a finite-difference version of the general Exner equation (e.g. Parker, 2008). ∂z ∂q (1 − η ) · = q − b (2.15) pore ∂t blat ∂x

Here ηpore is pore volume fraction, z is elevation of the channel bed and qblat is lateral bedload influx per unit flow width. Eq. (2.15) allows for the calculation ∆z of the new channel slope ∆x after each time step. Heretofore, infinitely deep rectangles are used within sedFlow as the shape of the cross-sectional profiles, with the complete width defined as active width (i.e. sediment transport takes place over the complete width). All three elements (the cross-sectional channel geometry, its alteration due to morphodynamics and the determination of the active width) are implemented as abstract classes. Thus, the presented realisations just represent the current state of the code and any programmer can easily extend the code to deal with more complex cross-sectional geometries. However, the implicit flow routing by Liu and Todini (2002), with its advantages in terms of simulation efficiency, requires infinitely deep rectangular or V-shaped channels (together with a simple power-equation flow-resistance law such as Eq. 2.4a). Additionally, Stephan (2012) has studied the impact of the rectangular- shaped approximation and found that, at least during major flood events, it is negligible compared to the other uncertainties. Stephan (2012) recalculated bedload transport for the August 2005 transport event in the catchments of the Chiene, Chirel and Schwarze Lütschine. For details on the catchments and event characteristics see Chiari and Rickenmann (2011). For the simulations, Stephan (2012) used the one-dimensional model TomSed (Chiari et al., 2010), which allows for the definition of cross sections with laterally varying bed elevations. The simulations were repeated with a detailed channel geometry as presented in Chiari and Rickenmann (2011) and with two different rectangular substitute channels. The widths of the rectangular substitute channels w were determined based on a discharge Qrep that is representative of the simulation period. The CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 31

Table 2.2: Relative root mean square deviations (rRMSDs) determined according to Eq. (2.16) for the simulations and observations displayed in Fig. 2.3: obs denotes the reference data derived from observations, orig denotes the simulation results using the detailed channel geometry, and rect(Q) and rect(w) denote simulation results using a rectangular substitute channel based on averaged representative discharges (Q) and widths (w), respectively. The numerical values in the table are the rRMSDs between the two data sets determined by the row and column. The labels for the rows and columns (bold type face) are given in the diagonal of each panel. For example, at the Chirel the simulations using a detailed channel geometry and using a substitute rectangle based on averaged widths diﬀer from each other by a rRMSD value of 0.28.

obs 0.65 0.60 0.71 orig 0.13 0.18 rect(Q) 0.22 (a) Chiene rect(w) obs 0.90 0.94 0.89 orig 0.24 0.28 rect(Q) 0.12 (b) Chirel rect(w) obs 0.69 0.50 0.46 orig 0.30 0.40 rect(Q) 0.20 (c) Schwarze Lütschine rect(w)

channel width was selected to produce the same wetted cross-sectional area and hydraulic radius for the representative discharge as was simulated for the detailed channel geometry. In one approach the threshold discharge for the initiation of bedload motion Qc, as well as the maximum discharge of the simulation period Qmax, were averaged to find Qrep, for which the representative channel width was determined. In the second approach, one width w was determined for both Qc and Qmax and then the two widths were averaged to find the representative channel width. The detailed channel geometry produced results that were broadly similar to the rectangular substitutes when compared with the field observations on bedload transport (Fig. 2.3). To quantify the deviations between the different simulations and between the simulations and the observations, Table 2.2 summarises the relative root mean square deviations (rRMSD) CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 32 which have been calculated according to the following equation: r Pn (χ −ψ )2 i=1 i i n rRMSD = . (2.16) χ+ψ 2

Here χ and ψ are two arbitrary data sets of length n, with χ and ψ being their average values, and i is a running index. As can be seen from Table 2.2, the simulations on average differ from each other by a rRMSD value of only 0.23, while the simulations differ from the observations on average by a rRMSD value of 0.70. However, it has to be noted that these results are for a flood event with high discharge values. For low discharges close to the initiation of bedload motion, a detailed representation of channel geometry may play a more important role than the one suggested by Fig. 2.3 and Table 2.2. For further details see Stephan (2012). Finally, the introduction of more complex cross-sectional shapes raises the question of how these shapes are influenced and altered through morphodynamics. As far as we know, no generally accepted concepts are available for this problem.

2.2.3 Grain-size distribution changes In sedFlow the alluvial substrate of the river is represented by a stack of horizontal layers with homogeneous grain-size characteristics. The topmost layer of the bed interacts with the flow and is typically called the active surface layer. The grain-size distribution of the active surface layer is used for the determination of the flow resistance, hiding processes and bedload transport capacity (Fig. 2.1). All deposited material is added to this layer; all eroded material is taken from it. The thickness of this layer determines the inertia of its evolving grain-size distribution. Therefore, the active surface layer and especially its thickness play an important role in the numeric representation of bedload transport systems (e.g. Belleudy and Sogreah, 2000). When the alluvium thickness is smaller than the expected usual active layer thickness, sedFlow makes use of the shape properties of bedrock to determine flow resistance and hiding. The thickness of the active surface layer may be set constant or dynamic as a multiple of some grain-size percentile. Three different approaches are available within sedFlow for the interaction between the active surface layer and the underlying subsurface alluvium. The first method (Fig. 2.A4) has been adapted from the one described by van de Wiel et al. (2007). Lower and upper thresholds are defined for the thickness of the active surface layer. Whenever these thresholds are exceeded, sediment increments are incorporated from, or released to, the subsurface alluvium underneath until the active surface layer thickness again takes a value within the given thresholds. The sediment increments are stored as bed strata CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 33 underneath the active surface layer. In this way the simulated river bed is able to remember its history. In contrast to the procedure of van de Wiel et al. (2007) the thickness of the sediment increments can be defined independently of the thickness of the active surface layer. Trivially, the thickness of the increments defines the minimum distance between the thresholds for the active surface layer thickness.1 The smaller this distance between the thresholds is, the more intense the interaction is between the active surface layer and the underlying subsurface alluvium. The second approach (Fig. 2.A5), which has been applied in various models (e.g. Hunziker, 1995), can be described as an extreme case of the first one, in which the two thresholds collapse to a single target thickness for the active surface layer. In this case, any addition or removal of material to or from the active surface layer is instantaneously balanced against the underlying subsurface alluvium. In this case of maximum interaction between active surface layer and subsurface alluvium, the subsurface alluvium is represented by one homogenised volume without any internal structure. The target thickness is usually determined at the start of a simulation and then kept constant. Alternatively, it can be dynamically adjusted based on a Eulerian forward approach, in which the thickness is updated at the end of each time step. The third approach (Fig. 2.A6) is a variation of the second one. When sediment is eroded, only the volume of the active surface layer is instantaneously replaced from the subsurface, while the grain-size distribution stays the same. The sediment volume that is transported from the subsurface alluvium to the active surface layer shares the grain-size distribution of the subsurface alluvium

1 Here hs is the active surface layer thickness, within a time step, after erosion or deposition but before the interaction between the active surface layer and the subsurface alluvium; accordingly, hs,post is the active surface layer thickness after the layer interaction, ∆hs is the thickness of sediment increments, |y| is the number of sediment increments that are incorporated from or released to the subsurface alluvium, threshhs,low and threshhs,high are the thresholds for the thickness of the active surface layer with threshhs,low < threshhs,high and threshhs,prox is an alias for the threshold that is closer to hs. It is the objective of the layer interaction to reach a state in which hs,post is as close as possible to the middle between the thresholds and

threshhs,low ≤ hs,post ≤ threshhs,high

with hs,post = hs + (y · ∆hs) and y ∈ Z. (F1) However, the state of Eq. (F1) cannot be reached if

|hs − threshhs,prox| mod < ∆hs ∆hs

− (threshhs,high − threshhs,low) . (F2)

This might cause instability. In simple terms, if ∆hs was larger than the distance between the thresholds, situations might occur in which the addition or subtraction of another ∆hs will cause hs,post to jump over both thresholds, such that it can never reach a value between the thresholds. Therefore, ∆hs is deﬁned as the minimum distance between the thresholds. With this minimum distance, the right-hand side of Eq. (F2) cannot become larger than zero, while the left-hand side of Eq. (F2) cannot become smaller than zero anyway. CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 34 only if a condition for the break-up of an armouring layer is fulﬁlled:

θ50 ≥ θc,s. (2.17)

Here θ50 is a representative dimensionless shear stress θ for the median diameter D50 of the active surface layer and θc,s is a representative θc for the active surface layer. To avoid artefacts due to a hard threshold, some fraction isub of the sediment transported from the subsurface alluvium to the active surface layer has the grain-size distribution of the subsurface alluvium already before the break-up condition is fulﬁlled. The rest (1 − isub) has the grain-size distribution of the active surface layer:

θ50 − θc,sub isub = with 0 ≤ isub ≤ 1 θc,s − θc,sub

and 0 < θc,sub < θc,s. (2.18)

Here isub is the relative grain-size inﬂuence from the subsurface alluvium and θc,sub is a representative θc for the subsurface alluvium. The value of θc,sub can be estimated, e.g. according to Eq. (2.8), while the value of θc,s can be estimated using the following relation of Jäggi (1992):

2 ! 3 DmAriths θc,s = θc,sub · . (2.19) DmArithsub

Here DmAriths and DmArithsub are the arithmetic mean diameters of the grain-size distribution of the active surface layer (s) and of the subsurface alluvium (sub). For non-fractional studies, the active surface layer concept can be turned oﬀ. In that case, the complete alluvium is represented by a single homogeneous layer, which directly interacts with the ﬂow.

2.3 Discussion

2.3.1 Comparison of sedFlow implementations with similar models In the following subsections, various details of the implementation of sedFlow are discussed and compared to implementations in similar models. Diﬀerences between the individual models are explained in the context of their diﬀering objectives.

Fractional transport and grain-size distributions In streams, local grain-size distributions and bedload transport inﬂuence each other in various ways. For example, ﬂow resistance is often determined as a function of a characteristic bed surface grain diameter such as in Eqs. (2.4b) and CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 35

(2.5) that use D84. Therefore, local grain-size distributions have a high influence on the local hydraulic radius rh, which in turn determines bed shear stress and thus bedload transport capacity. In addition, the shear stress partitioning in Eq. (2.6) is based on D84 as well. Finally, the stream can only mobilise and transport the grains which are available in the bed and, as transport capacity is inversely related to the transported grain diameter, fine-grained bed material will yield high transport rates. These mechanisms let the bed surface grain-size distribution influence the transport capacity, which in turn alters the local grain- size distributions. At high transport capacity, the stream will erode and deplete particles with transportable diameters and will leave only coarse grains in the bed. At low transport capacity, the stream cannot transport and will, thus, even deposit grains with small diameters. This will accumulate fine-grained material in the bed. Therefore, the spatial pattern of bed surface grain-size distributions at the end of a simulation can be interpreted as a function of bed slope (coarse grains in steep sections), channel width (coarse grains in narrow sections) and channel network effects (coarse grains at confluences with steep tributaries). In order to study dynamically evolving grain-size distributions and their effects on hydraulics and bedload transport, together with the effects of an evolving channel slope, sedFlow is optimised for the simulation of fractional bedload transport. In this context, different concepts are provided for the interaction between the active surface layer and the underlying alluvium. As grain-size distributions dynamically adjust to be consistent with the local circumstances (channel width, slope, etc.), this numeric concept might partially compensate the uncertainty in local grain-size distribution data. For a more detailed discussion of this topic see Heimann et al. (2015). To the authors’ knowledge there are no in-depth studies assessing the influence of different representations of active surface layer dynamics on simulated bedload volumes. As sedFlow contains three different formulations of active surface layer dynamics in the same modelling tool, it provides the base for a future study on the effects of different active surface layer algorithms. Within Topkapi ETH (Konz et al., 2011) fractional transport is not implemented, and within TomSed (Chiari et al., 2010) it is rarely used due to long calculation times. These models have a different application objective, for which dynamic grain-size distributions are of lesser relevance. The threshold-based layer interaction (Fig. 2.A4) implemented in sedFlow is similar to the approach of Lopez and Falcon (1999) for the evolution of the local grain-size distribution. However, Lopez and Falcon (1999) only introduced a lower threshold for the thickness of the active surface layer. This means that the subsurface alluvium remains constant even in cases of massive aggradation and that the active surface layer may reach unrealistically high thickness values, especially in cases of intense aggradation. In SEDROUT (Hoey and Ferguson, 1994), the surface layer grain-size distribution is determined as a function of the spatial derivative of fractional transport rates and the thickness of the surface layer, which in turn is a function of the CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 36 surface layer grain-size distribution. This set of equations is solved by numeric iteration within each time step. In sedFlow, this numerically extensive procedure is replaced by a constant surface layer thickness or an Eulerian forward approach, in which the layer thickness is updated at the end of each time step. These more pragmatic approaches have been selected because fast simulations are one of the main aims of sedFlow.

Adverse channel slopes Within sedFlow adverse channel slopes (uphill slopes in the downstream direction) and their effects in terms of ponding can be considered using uniform discharge hydraulics. This approach is based on the assumption that the simulated system only consists of two extreme cases: ponding on the one hand, and parallel slopes on the other. This assumption is valid in many mountain streams and it allows for fast simulations, which have been another main objective for the development of sedFlow. However, in the intermediate case of moderate backwater effects, it may produce large errors. The implemented approach corresponds to the situation of a confined channel, in which the sudden deposition of large volumes of sediment, e.g. by debris flow inputs, may produce ponding. Within Topkapi ETH any large volumes of deposited material, which would produce adverse channel slopes, are instantaneously distributed to downstream river reaches until all slopes are positive. This algorithm would correspond to instantaneous landslides within the channel or to debris flows with short travel distances, but such phenomena are typically not observed in mountain streams. However, instantaneous lateral sediment input is not the main focus of the Topkapi ETH model. In the context of its intended applications, the described algorithm of Topkapi ETH is an appropriate pragmatic approach to conserve mass and ensure positive bed slopes, which are used as energy slopes in the implemented kinematic wave approach. Within TomSed any deposited material that would produce adverse channel slopes is fed to a virtual sediment storage, which does not contribute to elevation changes in the main channel. As long as there is sediment in this virtual storage, any erosion or deposition is applied to this storage keeping the main channel untouched. That means that the elevation of the main channel is frozen as long as there is material in the virtual storage. In some way this algorithm corresponds to a lateral displacement of the river channel due to large volumes of deposited material that are stored next to the new channel. However, in mountain rivers the amount of material that is fed from the deposits to the main channel depends on the stability of the deposit slopes. Therefore, the new channel may well lower its elevation due to erosion, even if there is still some material in storage next to the channel. However, the situation of lateral channel displacement is close to the limits of a one-dimensional simulation and the described algorithm of TomSed ensures positive bed slopes (used as proxy for the energy slopes) in a way which corresponds to some extent to a natural CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 37 process, even though it violates conservation of mass within the main channel.

Simulation speed sedFlow has been designed for optimal computation speeds. Besides the selection of the coding language C++, for which there are powerful compilers available, we have implemented a spatially uniform discharge (within each seg- ment of the channel network), as well as an implicit kinematic wave flow routing approach, both aimed at providing a modelling tool for fast simulations. Both hydraulic approaches allow for coarse temporal discretisations and the implemented algorithm of Liu and Todini (2002) omits computationally demanding iterations. The ideal temporal discretisation (as fine as necessary and as coarse as possible) can be obtained from the Courant–Friedrichs–Lewy (CFL) criterion based on the speed of bedload multiplied by a user-defined safety factor. As a result, several years of bedload transport and resulting slope and grain-size distribution adjustment can be simulated with sedFlow within only few hours of calculation time on a regular 2.8 GHz central processing unit (CPU) core. In Topkapi ETH the implicit kinematic wave flow routing is also implemented using the algorithms of Liu and Todini (2002). However, the length of the time steps used for the bedload transport simulations may differ from the ideal length, as it is defined as an integer multiple of the time steps used for the hydrologic simulations. This implementation is due to Topkapi ETH’s aim to simulate different processes at different scales. Within TomSed, explicit kinematic wave flow routing is implemented. Thus, time steps need to be determined using the CFL criterion based on water flow velocity. Therefore, time steps are shorter than in sedFlow or Topkapi ETH and slow down the simulations considerably. The choice of the explicit water flow routing is due to TomSed’s aim to simulate the effects of the shape of channel cross sections. The implicit flow routing based on the algorithms of Liu and Todini (2002) requires simple rectangular or V-shaped channels and would therefore prevent any detailed study of channel geometry.

Flexibility To ensure flexibility of application, we selected regular spreadsheets as the file format for the data input to sedFlow. Thus, preprocessing can be done with common software applications, which are familiar to most users, so that data from any study catchment can be quickly and easily prepared for a sedFlow simulation. This contrasts with TomSed, which uses the extensible markup language (XML) file format for data input, as well as with Topkapi ETH, which partially requires MATLAB preprocessing. In sedFlow different equation sets can be selected and combined by the user for the main process representations (flow routing, flow resistance, initiation of bedload motion, transport capacity, etc.). The number, content and format of the output files can be defined by the CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 38 user as well, in order to get the best solution for the respective study objectives. To ensure flexibility of model development we selected an object-oriented design for the internal structure of the sedFlow code. In such a code, succeeding programmers just create new realisations for predefined code interfaces without revising the model core. It is not necessary to know (virtually) anything about the model itself. The only piece of code that the programmer will have to read is the specification of the relevant code interface, which is typically not longer than two printout pages.

2.3.2 Advantages and limits of the sedFlow modelling approach The limits of the sedFlow modelling approach are defined by the implemented process representations. Hydraulics are considered in a cross-sectionally averaged way. The effects of turbulence and eddies, such as the formation of dunes and pool-riffle sequences, are not considered explicitly. Therefore, sed- Flow should not be applied at spatial discretisations small enough for these processes to become relevant. Within sedFlow, discharge is assumed to be generally subcritical. It should not be applied in systems where Froude numbers larger than one occur at the scale of spatial discretisation. As sedFlow generally assumes kinematic wave propagation, bed slopes Sb should be steep enough for friction slopes Sf to approximately equal bed slopes (Sf ≈ Sb). Slight violations of this assumption will not cause major errors. However, if one uses the flow routing approach that allows for adverse channel slopes (uphill slopes in the downstream direction), any occurrence of moderate backwater effects (Sf 6≈ 0 ∧ Sf 6≈ Sb) will produce large errors (cf. Sect. 2.2.1). sedFlow considers sediment transport only in terms of bedload. Therefore, it should not be applied if suspension load and wash load play a major role in the studied system. However, if the limits of applicability are respected, sedFlow provides several benefits for the user interested in the simulation of bedload transport in steep mountain streams. The model is optimised for the calculation of fractional bedload transport resulting in more robust simulations as compared to single-grain approaches. Based on an assumption that is valid for many mountain streams, sedFlow provides for the efficient simulation of adverse slopes and ponding. The selected coding language and two implemented hydraulics representations are all aimed at providing a modelling tool for fast simulations. Finally, with the user- defined structure of the model outputs, with the straightforward preprocessing of the inputs, and with the provision of different selectable options, e.g., for the flow resistance and bedload transport equations, sedFlow offers the flexibility to be easily adjusted to fit a specific application in a particular catchment. CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 39

2.4 Conclusions

The new model sedFlow complements the range of existing tools for the simulation of bedload transport in steep mountain streams. It is an appropriate tool if (i) grain-size distributions need to be dynamically adjusted in the course of a simulation, (ii) the eﬀects of ponding, e.g., due to debris ﬂow inputs might play a role in the study catchment or (iii) one simply needs a fast simulation of bedload transport in a mountain stream with quick and easy pre- and postprocessing. Examples of the application of sedFlow are presented in a companion article by Heimann et al. (2015). The current version of the sedFlow code and model can be downloaded under the terms of the GNU General Public License (GPL) at the following web page: www.wsl.ch/sedFlow. CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 40

uniformdischarge kinematicwave QQ

t t QQ

x x

z z

x x

z z

x x

Figure 2.2: Qualitative comparison of uniform discharge (left) and kinematic wave (right) flow routing approaches. The top row shows a hypothetical discharge time series at the upstream boundary, which can be used in both approaches. The point in time for the following rows is indicated by the dashed vertical line. In the uniform discharge approach, the current discharge value of the time series defines the discharge for all reaches of the simulated system at the current point in time (second row left). In contrast, for the kinematic wave approach, the temporal variability of discharge is reflected in a spatial variability as well (second row right). Therefore, in the uniform discharge approach, the spatial variation of flow depth (third row), as well as water surface (blue curve), is mainly a function of roughness and slope, which is determined by the river bed (black curve). For the kinematic wave approach, flow depth may also vary due to the spatial variation of discharge (third row right). In cases of uphill channel slopes in the downstream direction, the uniform discharge approach will reproduce the effects of ponding (fourth row left), while the kinematic wave approach cannot deal with such situations (fourth row right). CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 41 ]

50000 (a) Chiene 3 [m b Q Σ 40000 30000 20000 10000 Accumulated bedload transportAccumulated 0

8 6 4 2 0

(b) Chirel ] 3 80000 [m b observation Q

Σ detailed geometry rectangle (averaged Q)

60000 rectangle (averaged w) 40000 20000 Accumulated bedload transportAccumulated 0

8 6 4 2 0 ]

3 (c) Schwarze Lütschine [m b 100000 Q Σ 60000 20000 Accumulated bedload transportAccumulated 0

10 8 6 4 2 0

Distance to outlet [km]

Figure 2.3: Comparison of the eﬀects of diﬀerent channel representations on accumulated bedload transport estimates simulated with the TomSed model in three Swiss mountain rivers. See Table 2.2, text, and Stephan (2012) for details. CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 42

Acknowledgements

We are especially grateful to Christa Stephan (project thesis ETH/WSL), Lynn Burkhard (MSc thesis ETH/WSL) and Martin Böckli (WSL) for their contributions to the development of sedFlow, and to Alexandre Badoux (WSL) for his support. We thank the Swiss National Science Foundation for funding this work in the framework of the NRP 61 project “Sedriver” (SNF grant no. 4061- 125975/1/2). Jeﬀ Warburton and two anonymous referees provided thoughtful and constructive suggestions to improve this manuscript. Appendix for chapter 2

2.A1 Supplementary methods

2.A1.1 Explicit hydraulics

∂V = Qu − Q (2.A1) ∂t T −1 T −1 ∂V V = V + · ∆t (2.A2) T T −1 ∂t

rhT = geom(VT ) (2.A3)

QT = fr (rhT ) (2.A4)

2.A1.2 Bedload capacity estimation according to Wilcock and Crowe (2003)

rτ v∗ = (2.A5) ρ 0.67 mwc = − 1 (2.A6) 1 + exp 1.5 − Di Dm τ D mwc+1 r = i (2.A7) τrm Dm ∗ τrm = 0.021 + [0.015 · exp (−20Fs)] (2.A8) ρ τ = τ ∗ · ρ · g · D · s − 1 (2.A9) rm rm m ρ τ 7.5 τ W ∗ = 0.002 · for < 1.35 (2.A10) τr τr  4.5 ∗ 0.894 τ W = 14 · 1 − q  for ≥ 1.35 (2.A11) τ τr τr W ∗ · v∗3 qb = Fi · (2.A12) ρs ρ − 1 · g

43 CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 44

2.A1.3 Bedload capacity estimation according to Recking (2010)

−0.93 D84 θc84 = (1.32 · S + 0.037) · (2.A13) D50 √ 4.445 S D84 1.605 L = 12.53 · · θc84 (2.A14) D50 τ θ84 = (2.A15) (ρs − ρ) · g · D84 √ −18 S 6.5 D84 θ84 Φb = 0.0005 · · for θ84 < L; (2.A16) D50 θc84 2.45 Φb = 14 · θ84 for θ84 ≥ L (2.A17) s ρ q = Φ · s − 1 · g · D3 (2.A18) b b ρ 84

2.A1.4 Bedload capacity estimation according to Rickenmann (2001) based on θ

D 0.2 √ 1 Φ = 3.1 · 90 · θ · (θ − θ ) · F r · (2.A19) b c q ρ D30 s ρ − 1

In this equation, Φb and θ are based on D50. Equation (2.A19) may be 0.2 simpliﬁed using the mean experimental value of D90 = 1.05 and a common D30 ρs value of ρ = 2.65: √ Φb = 2.5 · θ · (θ − θc) · F r (2.A20)

2.A1.5 Bedload capacity estimation according to Rickenmann (2001) based on q

−1.5 0.2 ρs D90 1.5 qb = 3.1 · − 1 · · (q − qc) · S (2.A21) ρ D30 ρ 1.67 √ q = 0.065 · s − 1 · g · D1.5 · S−1.12 (2.A22) c ρ 50 CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 45

2.A1.6 Fractional bedload capacity estimation according to Rick- enmann (2001) based on θ

p Φbi = 2.5 · θi,r · (θi,r − θci,r) · F r (2.A23) qbi with Φbi = and qb = Σqbi. q ρs 3 Fi ( ρ − 1)gDi

In the simulations of the companion manuscript of Heimann et al. (2015), a fractional version of Eq. (2.A19) was used instead of Eq. (2.A23). CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 46

Table 2.A1: Notation.

The following symbols are used in this article. ∇ vector differential operator β an empirical constant γ correction factor for θci ∆hs thickness of sediment increments for the interaction between the active surface layer and the subsurface alluvium ∆t temporal discretisation (time step) ∆x spatial discretisation (reach length) ∆X travel distance of grains ηpore pore volume fraction θ dimensionless bed shear stress θ50 representative θ for D50 θc dimensionless bed shear stress threshold for initiation of bedload motion θcMin minimum value for θc θci θc for ith grain size fraction θci,r θci corrected for macro-roughness θc,s representative θc for the active surface layer θc,sub representative θc for the subsurface alluvium θc84 θc for D84 θi θ for ith grain-size fraction θi,r θi corrected for macro-roughness λ empirical abrasion coefficient µ dynamic viscosity ρ fluid density ρs sediment density τ bed shear stress τr reference bed shear stress τrm reference bed shear stress of mean bed surface grain size ∗ τrm reference dimensionless Shields stress for mean bed surface grain size Φb Einstein parameter of dimensionless bedload transport rate Φbi Φb for ith grain size fraction χ, ψ two arbitrary data sets χ, ψ the average values of χ and ψ CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 47

Table 2.A1: Continued.

A wetted cross-sectional area a,b,d empirical constants D grain diameter Di mean grain diameter for ith grain-size fraction Dm geometric mean for grain diameters DmArith arithmetic mean for grain diameters

DmAriths DmArith for the active surface layer

DmArithsub DmArith for the subsurface alluvium Dx xth percentile for grain diameters D50 median grain diameter e empirical constant ranging from 1 to 2 exp exponential function f~ body forces f Darcy–Weisbach friction factor Fi volumetric proportion of ith grain-size fraction fr flow resistance F r Froude number g gravitational acceleration geom channel geometry hs active surface layer thickness after erosion or deposition but before the interaction between the active surface layer and the subsurface alluvium hs,post active surface layer thickness after the interaction between the active surface layer and the subsurface alluvium i a running index isub grain-size influence from the subsurface alluvium j1,j2,k,l empirical constants L process break point m empirical hiding exponent mwc hiding exponent according to Wilcock and Crowe (2003) mod modulo function n the length of χ and ψ p pressure q discharge per unit flow width qb bedload flux per unit flow width

qbabr qb corrected for gravel abrasion

qblat lateral bedload inﬂux per unit ﬂow width qc threshold q for initiation of bedload motion CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 48

Table 2.A1: Continued.

Q discharge Qc threshold Q for initiation of bedload motion Qmax maximum Q for the simulation period Qrep representative Q for the simulation period Qlat lateral water influx rh hydraulic radius rh, c rh for [θ50 = θc] rRMSD relative root mean square deviation s density ratio of solids and fluids S slope Sb channel bed slope Sc virtual slope for the correction of θci based on rh, c Sf friction slope Sred slope reduced for macro-roughness t time T of current time step T −1 of previous time step threshhs,low, threshhs,high thresholds for the thickness of the active surface layer with [threshhs,low < threshhs,high] threshhs,prox an alias for the threshold (either threshhs,low or threshhs,high) that is closer to hs u of upstream river reach ~v flow velocity vector v flow velocity scalar v∗ shear velocity V water volume in reach w channel width W ∗ dimensionless bedload transport rate according to Parker et al. (1982) x distance in flow direction |y| number of sediment increments that are incorporated from or released to the subsurface alluvium z elevation of channel bed CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 49

Transportequation Initiationofmotion θc

Fixed θc Rickenmann2001 θ Eqs.(A19A20; - A23) Lambetal.2008

Eq. (8)with θcMin

τ* Rickenmann2001q Initiationofmotion rm Eqs.(A21- A22) Basedon

uniform const.sandfraction

Recking2010 Activelayerdynamics Eqs.(A13- A18) Threshold-based Fig. A4

Continuous Fig. A5 Rickenmann2001 θ Eqs.(A19A20; - A23) Shear-stress-based Fig. A6

Rickenmann2001q Hidingfunction Eqs.(A21- A22) Powerlaw fractional Eq.(10)

Wilcock&Crowe2003 Wilcock&Crowe2003 Eqs.(A5- A12) Eq.(11)

Figure 2.A1: Simpliﬁed summary diagram of the bedload transport part of sed- Flow, showing a selection of the most important general types of functions (bold type face) and their selectable realisations (regular type face). For the transport equations of Rickenmann (2001), versions for both fractional and uniform grain sizes are implemented in sedFlow. Among the implemented equations, only the θ-based ones of Rickenmann (2001) use θc to determine the initiation of bedload motion. The selection of a hiding function and active surface layer dynamics is only necessary if a fractional transport equation is used. The transport equation of Wilcock and Crowe (2003) is always combined with their proposed ∗ hiding function and uses τrm to determine the initiation of bedload motion. CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 50

Hydraulicflowrouting Flowresistance

Simplifiedhydraulics foradverseslopes Variablepowerlaw Eq. (5) Explicitrouting Eqs.(A1- A4)

Implicitrouting Fixedpowerlaw Liu& Todini2002 Eq. (4a-4b)

Figure 2.A2: Simplified summary diagram of the hydraulic part of sedFlow, showing a selection of the most important general types of functions (bold type face) and their selectable realisations (regular type face). The implicit flow routing of Liu and Todini (2002) is always combined with a fixed power law flow resistance.

1 Adjustboundaryconditions • Waterdischargeinputs • Sedimentinputs 9WriteOutputs 2Calculaterates • Localdischarges 8Updateproperties • Localtransportcapacities • Updatelocalslopes • Updatelocalshearstresses • ... • Updatesimulationtime 3Handdownrates • Changerateofwatervolumesbasedon differencebetweenlocalandupstreamdischarge • Erosionordepositionratebasedondifference 7 Applychanges betweenlocalandupstreamtransportcapacity • Exchangewater • Erodeordepositsediment

4Determinestabletimesteplength 6Optionalmethods’ Basedoncalculatedratesandratedifferences actions

5Calculateandhanddownchanges • Volumeofwaterexchangeincurrenttimestep • Erosionordepositionvolumeincurrenttimestep consideringfractionalavailabilityinbed

Figure 2.A3: Simpliﬁed summary diagram of a time step in sedFlow. The timing of the optional methods’ actions has been selected in a way that all changes, such as, e.g., erosion or deposition volumes, are readily calculated and available for possible modiﬁcations before the changes, such as, e.g., erosion or deposition, are then actually applied. CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 51

aggradation

erosion

(a) (b)

aggradation

erosion

Figure 2.A4: Qualitative sketch of threshold-based interaction between the active surface layer and subsurface alluvium. The water level is displayed in blue, the active surface layer with its variable thickness is light grey and bedrock is black. The subsurface alluvium consists of several strata layers with user-deﬁned constant thickness displayed in reddish colours and one base layer with variable thickness displayed in dark grey. The horizontal dashed lines indicate the thresholds for the thickness of the active surface layer. In case of aggradation (a and c), the material input from upstream, which is displayed in green, is added to the active surface layer, which is instantaneously homogenised. Any homogenisation process is displayed by diagonal stripes. If the thickness of the active surface layer does not exceed its thresholds after aggradation or erosion (a and b), the thresholds of the active surface layer and the layers of the subsurface alluvium remain constant. If the active surface layer thickness exceeds its upper threshold after aggradation (c), the complete system of layers and thresholds is shifted upwards so that the upper boundary of the active surface layer is in the middle between its thresholds. The upper strata layers are populated with material from the homogenised active surface layer, while the material of the lower strata layers is added to the base layer, which is instantaneously homogenised. If the active surface layer thickness exceeds its lower threshold after erosion (d), the complete system of layers and thresholds is shifted downwards so that the upper boundary of the active surface layer is in the middle between its thresholds. The lower strata layers are populated with material from the base layer, while the material of the upper strata layers is added to the active surface layer, which is instantaneously homogenised. CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 52

aggradation

erosion

(a) (b)

Figure 2.A5: Qualitative sketch of continuous interaction between the active surface layer and subsurface alluvium. The water level is displayed in blue, the active surface layer with its constant thickness is light grey, the subsurface alluvium consisting of one layer with variable thickness is dark grey and bedrock is black. The dashed bracket indicates the position of the active surface layer after aggradation or erosion. In case of aggradation (a), the material input from upstream, which is displayed in green, is added to the active surface layer, which is instantaneously homogenised. Any material of the homogenised active surface layer, which exceeds the constant thickness, is transferred to the subsurface alluvium, which is instantaneously homogenised as well. Any homogenisation process is displayed by diagonal stripes. In case of erosion (b), the sediment deﬁcit of the active surface layer is replaced by material from the subsurface alluvium and the active surface layer is instantaneously homogenised. CHAPTER 2. THE BEDLOAD TRANSPORT MODEL SEDFLOW 53

erosion ≤ ≥ θ50θ c,sub θc,sub< θ50 < θ c,s θ50θ c,s

(a) (b) (c)

Figure 2.A6: Qualitative sketch of shear-stress-based interaction between the active surface layer and subsurface alluvium. For an explanation of the symbols see the caption of Fig. 2.A5. In this approach, the aggradation case is treated identically to the continuous update approach displayed in Fig. 2.A5a. For erosion, three cases are differentiated, with the representative dimensionless shear stress θ50 increasing from case (a) to case (c). If θ50 equals or exceeds the threshold for the active surface layer θc,s (c), the layers interact in the same way as in the continuous update approach displayed in Fig. 2.A5b. If θ50 does not exceed the threshold for the subsurface alluvium θc,sub (a), the volume deficit of the active surface layer is replaced by material from the subsurface alluvium, but the grain-size distribution of the active surface layer remains constant. For the intermediate case with θ50 greater than θc,sub and smaller than θc,s (b), the influence of the grain-size distribution of the subsurface alluvium on the grain-size distribution of the active surface layer is interpolated linearly between cases (a) and (c). REFERENCES 54

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Calculation of bedload transport in Swiss mountain rivers using the model sedFlow: proof of concept

Heimann, F. U. M., Rickenmann, D., Böckli, M., Badoux, A., Turowski, J. M., and Kirchner, J. W.: Calculation of bedload transport in Swiss mountain rivers using the model sedFlow: proof of concept, Earth Surf. Dynam., 3, 35–54, doi: 10.5194/esurf-3-35-2015, 2015. Published under the Creative Commons Attribution 3.0 License

Abstract

Fully validated numerical models specifically designed for simulating bedload transport dynamics in mountain streams are rare. In this study, the recently developed modelling tool sedFlow has been applied to simulate bedload transport in the Swiss mountain rivers Kleine Emme and Brenno. It is shown that sedFlow can be used to successfully reproduce observations from historic bedload transport events with plausible parameter set-ups, meaning that calibration parameters are only varied within ranges of uncertainty that have been pre- determined either by previous research or by field observations in the simulated study reaches. In the Brenno river, the spatial distribution of total transport volumes has been reproduced with a Nash–Sutcliffe goodness of fit of 0.733; this relatively low value is partially due to anthropogenic extraction of sediment that was not considered. In the Kleine Emme river, the spatial distribution of total transport volumes has been reproduced with a goodness of fit of 0.949. The simulation results shed light on the difficulties that arise with traditional flow-resistance estimation methods when macro-roughness is present. In addition, our results demonstrate that greatly simplified hydraulic routing schemes,

59 CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 60 such as kinematic wave or uniform discharge approaches, are probably sufficient for a good representation of bedload transport processes in reach-scale simulations of steep mountain streams. The influence of different parameters on simulation results is semi-quantitatively evaluated in a simple sensitivity study. This proof-of-concept study demonstrates the usefulness of sedFlow for a range of practical applications in alpine mountain streams.

3.1 Introduction

The rolling, sliding or saltating transport of sediment grains along river beds, which is summarised as bedload transport, represents one of the main morphodynamic processes in mountain streams. Bedload transport has implications which go beyond mere morphodynamics. It exerts considerable ecological influence by reorganising the bed and thus potential spawning grounds (e.g. Unfer et al., 2011). In mixed alluvial–bedrock channels, the bedload flux is one of the dominant controls on bedrock erosion (e.g. Turowski, 2012). Frequently, bedload fluxes are also responsible for damage to engineering structures (e.g. Jaeggi, 2008; Totschnig et al., 2011). Because bedload transport can amplify the impact of severe floods, it is also important in natural hazard management (e.g. Badoux et al., 2014). This wide range of implications is reflected in numerous applied engineering projects which evaluate potential bedload transport using one- or two-dimensional simulation models. A summary of the applied aspects of bedload transport assessment has been given by Habersack et al. (2011). The available models for simulating sediment transport may be divided into two groups. The first group of models does not focus on process details. It rather sees fluvial sediment transport as a part of a network of interacting processes within the landscape. Therefore, such models use simplified representations of river hydraulics and are often combined with hydrologic or soil erosion model components. Large-scale spatial resolutions and fast calculations are common in this group of models. The SHE-TRANsport model SHETRAN with SHE standing for Système Hydrologique Européen (Lukey et al., 2000; Bathurst et al., 2010), the Distributed Hydrology-Soil-Vegetation Model (DHSVM) (Doten et al., 2006) and others (e.g. Mouri et al., 2011) fall in this group. The SHE SEDiment component SHESED (Wicks and Bathurst, 1996) for the Système Hydrologique Européen also combines sediment transport routines with hydrologic and soil erosion routines, but without the strong simplifications (and associated efficiency gains) of the models mentioned above. The second group of models concentrates on hydraulic processes as the main driving factor of sediment transport. Therefore, such models commonly solve the full Saint-Venant equations, but neglect any processes outside the channel. Small-scale spatial resolutions and slow calculations are common in this group of models. The Steep Stream Sediment Transport 1-D model (3ST1D) (Papan- CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 61 icolaou et al., 2004), the Hydrologic Engineering Center model no. 6 (HEC-6) (Bhowmik et al., 2008), the model SEDROUT (Ferguson et al., 2001), the Generalized Stream Tube Alluvial River Simulation model (GSTARS) (Hall and Cratchley, 2006), the FLUvial Modelling ENgine (FLUMEN) (Beffa, 2005), the BASic EnvironMENT for simulation of environmental flow and natural hazard simulation (BASEMENT) (Faeh et al., 2011) and others (e.g. Lopez and Falcon, 1999; García-Martinez et al., 2006; Li et al., 2008) fall in this group. Similar to TomSed (formerly known as SEdiment TRansport model in Alpine Catchments (SETRAC)) (Chiari et al., 2010), the model sedFlow (Heimann et al., 2015) is intended to bridge the gap between these two groups of models by providing good representation of fluvial bedload transport processes at intermediate spatial scales and high calculation speeds. Here the focus of modelling is not on the details of the temporal evolution of sediment transport, but rather on a realistic reproduction of the total transport volumes and overall morphodynamic changes resulting from sediment transport events such as major floods. In spite of the considerable need for modelling tools in scientific and engineering applications and in spite of the interest in the relevant physical processes, bedload transport in mountain streams is not entirely understood. This is partly due to the complex measurement conditions in gravel-bed rivers (Bunte et al., 2008; Gray et al., 2010). Because of these difficulties, there are relatively few data sets available for deriving conceptual models or for validating and testing numeric models. Based on the available field observations, it has become clear that river bed morphology and thus hydraulic processes become increasingly complex as channel gradients become steeper. The range of observed grain diameters becomes larger, which entails more complex grain–grain and grain–flow interactions as well. Summarising available field data on flow velocity, Rickenmann and Recking (2011) showed that a considerable part of the river’s shear stress is consumed by turbulence due to complex bed morphology, summarised as macro-roughness. They also suggested an approach to quantify the impact of macro-roughness based on the relative flow depth compared to a characteristic grain diameter. Lamb et al. (2008) and Bunte et al. (2013) have noted that in steep channels higher energies are needed for the initiation of bedload motion, compared to channels with gentle slopes. Turowski et al. (2011) have shown that the conditions for the initiation of bedload motion vary in time and are strongly linked to the conditions at the end of the last bedload transport event. Parker (2008) and Wilcock and Crowe (2003) have discussed and proposed approaches for quantifying grain–grain interactions in so-called hiding functions. Finally, several methods have been suggested for predicting bedload transport in mountain streams. Some of these methods are based on flume experiments, such as those of Rickenmann (2001) and Wilcock and Crowe (2003), and some are based on field observations, such as those of Recking (2010; 2013a). For recent applications and discussions of the conceptual models and methods mentioned CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 62 in this paragraph see Chiari and Rickenmann (2011), Nitsche et al. (2011) and Rickenmann (2012). A selection of such methods related to the estimation of bedload transport in steep channels has been implemented in the modelling tool sedFlow. For the bedload transport equation, the flow-resistance relation and several other elements, sedFlow offers different options which can be selected to fit the current application in a particular catchment. The model architecture and implementation are described in detail in a companion article (Heimann et al., 2015), and are only briefly reviewed here. The program is intended for quantitatively simulating bedload transport processes in mountain streams at temporal scales from the individual event (several hours to few days) to longer- term evolution of stream channels (several years). It is designed for spatial scales covering complete catchments at a spatial discretisation of several tens of metres to a few hundred metres. sedFlow has been developed to provide a tool which combines recently proposed and tested process representations with fast computational algorithms and user-friendly file formats for easy pre- and postprocessing of simulation data. In this article, we show that sedFlow can reproduce observations from his- torical bedload transport events, using plausible parameter set-ups. Here by plausible parameter set-ups we mean that calibration parameters are only varied within ranges of uncertainty that have been pre-determined either by previous research or by field observations in the simulated study reaches. The main aim of this proof-of-concept study is defined by the objective of the sedFlow model, namely the realistic simulation of total transport volumes and overall morphodynamic effects of sediment transport events such as major floods. The results of this study may help to interpret simulation results produced with sedFlow in applied engineering projects. Experiences with the simulation tool are discussed with respect to the problems of quantifying the influence of macro-roughness within traditional flow-resistance equations. In addition, the uncertainties introduced by common graphical representations of bedload transport reconstructions are highlighted based on the results of a simple sensitivity study.

3.2 Material and methods

For our study we selected two Swiss rivers, the Kleine Emme and the Brenno (Figs. 3.1 and 3.2). The Kleine Emme was chosen because extensive data are available to validate and test the sedFlow model in this catchment. The Brenno river was selected as a complementary case study to cover a wider range of channel gradients and streambed morphology. In this article we differentiate between net and gross channel gradients in the context of sills. Net channel gradients are defined as gross channel gradients corrected for the elevation differences attributable to sills or other drop-down structures. CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 63

Figure 3.1: The Kleine Emme catchment in central Switzerland. The study reach from Doppleschwand to the conﬂuence with the Renggbach is indicated by the bold blue line.

3.2.1 General catchment characteristics The Kleine Emme is a mountain river in central Switzerland (Fig. 3.1). It drains an area of 477 km2 and flows into the Reuss at Reussegg. The Kleine Emme’s net channel gradient averages 0.8 % with a maximum of 3.5 %. Near Doppleschwand the in situ bedrock is close to the surface, limiting the alluvium that can potentially be eroded. Further downstream the river was channelised in the late 19th and early 20th century. To mitigate the subsequent erosion, the bed was stabilised in the early 20th centuries with numerous bottom sills (documented by Geoportal Kanton Luzern, 2013). The Kleine Emme is an alpine mountain river catchment with gentle slopes, without glaciers or debris flow inputs and with only very moderate influence from hydropower installations, but with intensive modifications by fluvial engineering. The Brenno is situated in southern Switzerland (Fig. 3.2) and drains into the river Ticino. Its drainage area is 397 km2 and its channel gradient averages 2.6 %, with a maximum of 17 %. There are no sills in the Brenno, so the CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 64

Figure 3.2: The Brenno catchment in southern Switzerland. The study reach from Olivone to Biasca is indicated by the bold blue line. net and gross gradients are the same. About 1 % of the catchment area is glaciated. Especially in the northern and eastern part of the catchment, its hydrology is substantially influenced by hydropower (Fig. 3.2). The water used for hydropower production is returned to the Ticino river downstream of Biasca. The tributaries Riale Riascio and Ri di Soi are currently the most important sediment sources to the Brenno river (Table 3.1). The sediment input from the Riale Riascio is dominated by debris flows, while the larger subcatchment Ri di Soi delivers sediment both as debris flows and as fluvial bedload transport. Downstream of the confluences with these tributaries, the bed of the Brenno is stabilised by large blocks and the main channel shows pronounced knickpoints at these positions. Other tributaries on the western side of the Brenno catchment were very active in the decades from 1970 to 1990, but their sediment delivery to the Brenno is much reduced at the time of writing due to intense torrent control works and sediment retention basins. The course of the Brenno is partially channelised and partially near natural. The Brenno represents a moderately steep mountain river influenced by glaciation, hydropower production and debris CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 65

Table 3.1: Estimated sediment input yields from tributaries to the Brenno (based on Flussbau AG, 2003, 2005; Stricker, 2010) (Process types: DF = debris ﬂow, FT = ﬂuvial bedload transport).

Tributary Type Per year [m3 a−1] Calibration period [m3] Min. Mean Max. Min. Mean Max. Brenno della Greina FT 2500 7500 25 000 75 000 Brenno del Lucomagno/Ri di Piera FT 1500 5000 15 000 50 000 Riale Riascio DF 4000 10 000 22 000 40 000 100 000 220 000 Ri di Soi DF + FT 10 000 20 000 30 000 100 000 200 000 300 000 Lesgiüna FT 1000 2000 5000 10 000 20 000 50 000 Crenone (Vallone) DF 1000 1500 4000 10 000 15 000 40 000

flow inputs. The two catchments are impacted and show a range of engineering interventions typical of many mountain catchments. The Kleine Emme is marked by river training works, including numerous bottom sills as well as riprap and groynes in some locations. The Brenno is strongly influenced by controls on water and sediment delivery to the channel. The Brenno’s hydrology is substantially influenced by hydropower production and lateral sediment input is limited by torrent control works and sediment retention basins in the tributaries. Along a few kilometres of the Brenno river gravel extraction occurred during the calibration period. The two catchments contrast with each other not only by their different management histories. Even though the two catchment areas are of similar size, channel gradients are steeper in the Brenno river than in the Kleine Emme river. While in the Kleine Emme channel bank erosion played a dominant role in feeding sediment to the transport system, in the Brenno lateral sediment input due to debris flows from tributaries was important during the calibration period. In summary, the two study catchments differ substantially and present a range of characteristics common to many mountain catchments. Several channel cross sections are periodically surveyed for both rivers. In the case of the Kleine Emme, they are measured by the Swiss Federal Office for the Environment (FOEN) and in the case of the Brenno, they are measured by the authorities of the canton of Ticino. Cross-sectional profiles are recorded at 200 m intervals in the Kleine Emme and at about 150 m intervals in the Brenno. For the Kleine Emme we used measurements from September 2000 to November 2005. For the Brenno we used measurements from April 1999 to June/July 2009. We selected our study reaches to overlap with these surveyed cross sections. Doppleschwand, about 25 km upstream from the Kleine Emme mouth, represents the upper boundary of our simulation reach. A large, long-duration flood event occurred in August 2005, with a return period of around 50 years for the peak discharge. During this event, widespread flooding occurred along CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 66 the lowermost 5 km of the river in the area of Littau. Therefore, the lower boundary of our one-dimensional model simulations is the confluence of the Kleine Emme and the Renggbach (Fig. 3.1). At the Brenno, our study reach extends from Olivone at the upper end to Biasca at the confluence with the Ticino river (Fig. 3.2).

3.2.2 Hydrology The discharge of the Kleine Emme has been measured at Werthenstein since 1985 and at Littau–Emmen since 1978 (Fig. 3.1). Peak discharge at Littau– Emmen during the August 2005 flood was 650 m3 s−1. To account for the reduced catchment area of the Kleine Emme upstream of the Renggbach at the simulation outlet, the discharge at Littau–Emmen is reduced by 5 % as suggested by VAW (1997). The discharge of the Rümlig tributary is estimated by the difference between the values of Werthenstein and the simulation outlet. The discharge of the Fontanne is simulated using the fully-distributed version of the Precipitation-Runoff-EVApotranspiration HRU model PREVAH (Viviroli et al., 2009; Schattan et al., 2013) in which HRU stands for hydrological response units. The discharge of the headwater is estimated by the difference between the measured discharge at Werthenstein and the simulated Fontanne discharge. Discharge of the Brenno has been measured at Loderio ever since the es- tablishment of the hydropower reservoirs in the catchment in 1962. A peak discharge of 515 m3 s−1 was recorded during the July 1987 flood, corresponding to a return period of about 150 years. For the simulations, the discharge at Loderio has been distributed among the subcatchments according to rainfall– runoff simulations using the PREVAH model. The discharge is assumed to be zero at dams and reduced by the intake capacity at water intakes. In this reduction, we accounted for the regulations that specify the minimum residual discharge in the river channel downstream of a water intake. The values of this minimum residual discharge were defined based on ecological aspects and vary with intake location and time of the year.

3.2.3 Channel morphology and bedload observations Rectangular channels For use in the sedFlow model, the cross-sectional profiles were transformed into the equivalent width of a simple rectangular substitute channel. For this transformation a representative discharge was defined as the mean of the peak discharge of the simulation period and the discharge at the initiation of bedload motion, as these two values define the range of discharges relevant for bedload transport. The variable power equation flow-resistance relation was used to translate discharge into flow depth based on the same grain-size distributions (GSDs) that were used in the simulations. Then, a rectangular channel was found which has the same cross-sectional flow area and hydraulic radius CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 67

b schematic ABT

ΣQ tributaries sills

140000 inputs from bank erosion

100000 stabilisedbed bypassingofsediment

60000

20000 25 20 15 10 5

Accumulatedbedloadtransport [m ]

Distancetooutlet[km]

Figure 3.3: Schematic representation of accumulated bedload transport (ABT) in the Kleine Emme with locations of tributaries and sills (tributaries from up- to downstream: Fontanne, Rümlig). as the original cross-sectional profile at this flow depth. The channel of the Kleine Emme has been regulated in the past and its geometry is well defined by a trapezoidal profile with steep banks. In contrast, the Brenno study reach is in a natural condition over most parts, including both more incised reaches with a well-defined width and depositional reaches in flatter areas with riparian forest. The latter reaches are characterised by river banks with gentle slopes. In such channels, a slight change of the representative discharge may result in a substantial change in the width of the rectangular substitute channel. There- fore, in the depositional reaches of the Brenno, the uncertainty in representative discharge entails a considerable uncertainty in substitute channel widths, which contrasts with the better-constrained substitute channel widths in the incised Brenno reaches and Kleine Emme reaches, due to their steeper banks.

Reference data To test the sedFlow model, a reference is needed, to which the simulation results can be compared. Therefore, the bedload transport during the calibration period, which was not observed by itself, needs to be reconstructed from available observations. To volumetrically quantify the reconstructed bedload transport, the change in average bed level between each pair of cross-sectional surveys is multiplied with the mean of the substitute channel width of both profile measurements and with the distance to the next profile. These bed volume changes give an integrated value of the minimum bed material transported over the observation period. However, to obtain a complete sediment budget, data on bank erosion, lateral sediment input from tributaries and the material that leaves the catchment at the outflow have to be considered. At the Kleine CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 68

3 schematic ABT b morphodynamicswithout tributaries

ΣQ nettoerosionordeposition

150000 ABT reducedto transportcapacity; bypassingofsediment

100000

excavation

RidiSoi

RialeRiascio

50000 increasedwidth

20 15 10 5 0

Accumulatedbedloadtransport [m ]

Distancetooutlet[km]

Figure 3.4: Schematic representation of accumulated bedload transport (ABT) in the Brenno, with labels indicating major sediment sources and sinks (tributaries from up- to downstream: Riale Riascio, Ri di Soi, Lesgiüna).

Emme, bank erosion volumes were estimated from the difference between the FOEN cross-sectional profiles in 2000 and 2005 and from field assessments of the erosion scars (Flussbau AG, 2009; Hunzinger and Krähenbühl, 2008), and the sediment outflow was quantified based on data of regular gravel extraction at the confluence of the Kleine Emme with the Reuss (Hunzinger and Krähen- bühl, 2008; Hunziker, Zarn and Partner AG, 2009). For the Brenno the lateral inputs by debris flows or fluvial bedload transport were estimated based on data from a number of previous studies (Flussbau AG, 2003, 2005; Stricker, 2010), as listed in Table 3.1. The spatial pattern of changes in sediment transport, as well as the absolute value of sediment transport, is greatly influenced by sediment input from the tributaries. Thus, the uncertainty in the estimates of tributary sediment inputs largely determines the overall uncertainty in sediment transport in the Brenno. The sediment outflow at the mouth of the Brenno and thus the volume of the throughput load of the complete system is unknown. Therefore, we used the result of the sedFlow simulations as a best guess for this parameter, since no other proxies are available. Of course, this approach for the determination of sediment outflow at the mouth of the Brenno partially compro- mises the independence of the evaluation of model performance, regarding the overall transport rate. However, this approach still allows for an independent evaluation of the along-channel changes in transport rates as well as any other variables such as erosion and deposition rates or characteristic bed surface grain diameters. CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 69

Accumulated bedload transport All volumetric data related to the sediment budget are summarised in accumulated bedload transport (ABT) diagrams, e.g. Figs. 3.3 and 3.4. ABT represents the net bedload amount which has been transported through a given stream section during the period of interest (Chiari et al., 2010). It is a temporal integral of the transport rates and it is a spatial integral of the volumetric changes including bed net erosion and deposition, lateral inputs and sediment outﬂow. In this article, all ABT values include an assumed pore volume fraction of 30 %. The ABT can be derived from the morphodynamic relation, which has been described by Exner in its continuous form (e.g. Parker, 2008):

∂z ∂q (1 − η ) · = q − b . (3.1) pore ∂t blat ∂x

Here ηpore is the pore volume fraction, z is elevation of channel bed, t is time, qb is sediment flux per unit flow width, x is distance in flow direction and qblat is lateral sediment influx per unit flow width. Equation (3.1) represents a balance of input and output volumes and it can be rewritten in a discretised form for a finite reach and period of time as

Vin − Vout − VEroDepo = 0, (3.2)

Vin = VinUp + VinLat, (3.3)

Vout = Vcap. (3.4)

Here Vin designates the volume of sediment that enters a reach, subdivided into the volume VinUp coming from upstream and the volume VinLat introduced laterally, e.g. by tributaries or bank erosion. VEroDepo is the volume eroded or deposited in the reach, with positive values indicating deposition. Vout is the volume that exits the reach, which in the case of unlimited (or at least sufficient) supply of material (Eq. 3.4) equals the volume Vcap corresponding to the transport capacity within the reach, multiplied by the considered time interval. Equation (3.2) constitutes the difference between inputs and outputs is counterbalanced by erosion or deposition (Fig. 3.5). For erosion, the local Vin will always be smaller than Vcap and will result in ABT increasing downstream. In the same way, deposition will result in a decreasing ABT, while a roughly constant ABT reflects throughflow of sediment without net erosion or deposition. GSDs have been estimated for different reaches, based on transect pebble counts using the method of Fehr (1986, 1987). To determine the subsurface GSD, the pebble count was transformed into a full GSD by assuming an average proportion of 25 % fine material with D < 10 mm according to Fehr (1987). To determine the surface GSD, the pebble count was transformed into a full GSD by assuming an average proportion of 10 % fine material with D < 10 mm according to observations reported in Recking (2013b) and Anastasi (1984). In CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 70

VinLat

VinUp Reach Vcap

VEroDepo

Figure 3.5: Schematic visualisation of Eqs. (3.2) to (3.4). some cases at the Brenno, coarser sediment portions were added to the recorded GSDs, because coarse blocks have been underrepresented in the transect counts and thus the original transect GSDs partially led to unrealistic model behaviour. The measured GSDs were assumed to be representative for entire reaches, which are separated from each other by features such as confluences or considerable changes in channel gradient. This spatial extrapolation entails some uncertainty. The current GSD measurements, which were obtained after the end of the calibration period, are used as proxy estimates for the initial GSDs at the beginning of the calibration period. This time shift introduces additional uncertainty. The bedload transport system of the Kleine Emme can be subdivided into two regimes (Fig. 3.3). In the upper part from 25 to ∼ 15 km, the bed is stabilised by in situ bedrock and numerous sills. Therefore, the system is dominated by throughflow of sediment without considerable trends or jumps in the along-channel evolution of the ABT. In the lower part from ∼ 15 to 5 km, the bedload transport system is mainly influenced by sediment inputs from bank erosion during the 2005 flood event, which increase the downstream ABT in a step-like way. The Brenno bedload transport system is mainly influenced by local elements (Fig. 3.4). The Riale Riascio at 20.8 km introduced a considerable amount of sediment to the system, resulting in a step-like downstream increase in the ABT. Large amounts of the material delivered by the Ri di Soi at 18.1 km have been deposited at the confluence. These deposits reduced upstream channel gradients and thus transport capacity. The lack of material coming from upstream is overcompensated by the input from the Ri di Soi. However, the excess material has been deposited shortly after the confluence. All processes around the confluence with the Ri di Soi are reflected in a pronounced negative peak and small positive peak in the along-channel evolution of the ABT. The following stretch down to 10 km exhibits erosion and deposition corresponding to the interaction CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 71 of GSD, channel gradient and width, but without any overall erosion or deposition trend. At 10 km sediment has been anthropogenically extracted from the riverbed by excavation, which results in a step-like downstream decrease of ABT. Because the excavation reduces the amount of transported material down to the transport capacity of the river, sediment bypasses the following reaches. At 4.5 km, the deposits at the confluence with the Lesgiüna decrease the upstream slope and thus cause a drop in transport capacity. In the stretch from 4.5 to 3 km, an increased channel width keeps the ABT at low values.

3.2.4 The model sedFlow The bedload transport modelling tool sedFlow has been designed especially for application to mountain rivers. Consistent with this objective, it exhibits the following main features: (i) it uses recently proposed and tested approaches for calculating bedload transport in steep channels accounting for macro-roughness, (ii) it calculates several grain diameter fractions individually, i.e. fractional transport, (iii) it uses fast algorithms and thus can be used for modelling complete catchments and for scenario studies with automated calculations over many variations in the input data or parameter set-up. Here we give a short overview of the essential components of sedFlow. For a detailed account of the model structure and implementation see Heimann et al. (2015). The current version of the sedFlow code and model can be downloaded at the following web page: www.wsl.ch/sedFlow. Flow resistance is either calculated with the variable power equation of Fer- guson (2007) according to Eq. (3.5) or with a grain-size-dependent Manning– Strickler equation (Eq. 3.6): a a rh vm 1 2 D84 = r , (3.5) v∗ 5 a2 + a2 rh 3 1 2 D84 1 vm rh 6 ∗ = a1 . (3.6) v D84

∗ √ Here vm is the average flow velocity, v = grhS is the shear velocity, rh is the hydraulic radius, S is the gradient of hydraulic head, which may be approximated by the gradient of the water surface or channel bed, D84 is the characteristic grain diameter of the surface material, for which 84 % of the material is finer, and g is gravitational acceleration. Equation (3.5) has been tested by Ricken- mann and Recking (2011) based on nearly 3000 field data points. With the coefficients a1 = 6.5 and a2 = 2.5, it shows very good agreement with the average trend of observations, especially including small relative flow depths that are characterised by high flow resistance. Rickenmann and Recking (2011) also rewrote Eq. (3.5) in an alternative version, in which flow velocity is written as a direct function of q, the discharge per unit flow width. CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 72

sedFlow allows three methods for the calculation of channel hydraulics: an explicit kinematic wave routing, an implicit kinematic wave routing and a uniform discharge approach. The explicit flow routing corresponds to a Eulerian forward approach. In such an approach, all relevant variables are assumed constant for the duration of one time step. For numeric stability, time steps have to be short enough for this approximation to be valid. For morphodynamic simulations this may be impractical. The fast process of running water defines the short time step lengths, even though it is not the process of interest and the relatively slower morphodynamic changes would allow for much longer time steps and thus faster calculations. Apart from this disadvantage, the explicit flow routing provides a routing of discharge without any restrictions concerning other concepts or parameters. To overcome the short time steps, sedFlow also provides capabilities for implicit flow routing. Because they are unconditionally stable, implicit methods impose no requirements concerning the length of time steps. However, in implicit methods the unknown variables usually have to be found via computationally demanding iterations. In sedFlow, the algorithm of Liu and Todini (2002) is implemented for solving the implicit flow routing. It avoids time-consuming iterations by analytically finding the solution using Taylor series approximations. However, this algorithm requires a power-law representation of discharge as a function of water volume in a reach. That means it can only be applied to infinitely deep rectangular or V-shaped channels in combination with a power- law flow resistance such as Eq. (3.6). Except for this restriction, the implicit flow-routing algorithm provides a routing of discharge with fast computational performance. The explicit and implicit flow routings use the bed slope as proxy for energy slope for all hydraulic and bedload transport computations. This approximation, which corresponds to the assumption of a kinematic wave, is acceptable for most mountain channels, as river bed gradients are commonly steep there. However, problems arise when tributaries deposit debris flow material in the main channel, producing adverse slopes (uphill slopes in the downstream direction). A pragmatic solution to deal with adverse slopes is the uniform discharge approach. Discharge is assumed to be equal along the entire channel, only increasing at confluences for a given time step. This procedure can be justified keeping in mind that the temporal scale of hydraulic processes is very small compared to the temporal scale of morphodynamic processes. Hydraulic calculations are performed using the bed slope proxy for the hydraulic gradient. In cases of adverse slopes, ponding is simulated. That is, flow depth and velocity are selected to ensure a minimum gradient of hydraulic head, which is positive and close to zero. For bedload transport calculations the gradient of the hydraulic head is used, which by definition can only exhibit positive slopes. Thus, the energy slope for bedload transport estimation is not the result of a backwater calculation, but it is the gradient between individual hydraulic head values, which CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 73 under normal conditions have been calculated independently from each other using the local bed slope as a proxy for friction slope. It has to be noted that this approach will produce large errors if moderate backwater effects are part of the simulated system. In such systems, the other approach, which uses bed slope both as the friction slope for the hydraulic calculations and as the energy slope for the sediment transport calculations, will produce better estimates of the transported sediment volumes, but it cannot accommodate adverse channel gradients. Partially due to the simple and efficient hydraulic schemes, several years of bedload transport and resulting slope and GSD adjustment can be simulated with sedFlow within only few hours of calculation time on a regular 2.8 GHz central processing unit (CPU) core. For optimising calculation speed, amongst others the time steps should be as long as possible. However, there are stability concerns that limit the potential time step lengths. Within sedFlow, the time step length used for the current time step is obtained from three different methods of calculation. When explicit or implicit kinematic-wave flow routing is used, the first method ensures that local slope changes do not exceed a user-defined fraction. When explicit kinematic- wave flow routing is used, the first method further calculates another time step length based on the Courant–Friedrichs–Lewy (CFL) criterion (Courant et al., 1928) for the water flow velocity multiplied by a user-defined safety factor1. The second method is based on the CFL criterion for the estimated bedload grain velocity multiplied by a user-defined safety factor. The third method ensures that erosion of the active layer is always less than a user-defined maximum fraction. The actual time step length is the minimum of the values obtained for each simulated reach from the three methods described in this paragraph, provided that this minimum is smaller than a user-defined maximum time step length. Different formulas can be used for the estimation of bedload transport capacity. The approaches of Rickenmann (2001), Wilcock and Crowe (2003) and Recking (2010) are implemented in sedFlow. The formula of Rickenmann (2001) modified for fractional transport was used here:

0.2 D90 q 1 Φbi = 3.1 · · θi,r · (θi,r − θci,r) · F r · √ , D30 s − 1

with qb = Σqbi. (3.7)

√ qbi Here Φbi = 3 is the dimensionless bedload transport rate per Fi (s−1)gDi grain-size fraction, Fi is the relative portion compared to the total surface material with D > 2 mm of a grain-size fraction i with Di as its mean diameter,

1When explicit kinematic-wave flow routing is used, the model does not check whether the calculated time step length is smaller than a user-defined maximum length, because the CFL criterion for the water flow velocity usually produces time step lengths which are considerably smaller than commonly used maxima. CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 74

qbi is the volumetric bedload transport per grain-size fraction and unit channel ρs width, s = ρ is the density ratio of solids ρs and the fluid ρ, F r is the Froude rhSred number, θi,r = is the dimensionless bed shear stress and S is the re- (s−1)Di red duced energy slope according to Rickenmann and Recking (2011) and Nitsche et al. (2011). Here D90 and D30 are characteristic grain diameters, for which 90 or 30 % of the local GSD is finer, and qb is the volumetric bedload transport rate per unit channel width. The critical dimensionless bed shear stress at the initiation of transport θci is modified by the so-called hiding function either in the form of a relatively simple power-law relation (Parker, 2008): m Di θci = θc50 (3.8) D50 or in the form proposed by Wilcock and Crowe (2003):

mwc Di θci = θc50 · Dm 0.67 with mwc = − 1 . (3.9) 1 + exp 1.5 − Di Dm

Here D50 and Dm are the median and geometric mean grain diameter of surface material, m is an empirical hiding exponent and mwc is the hiding exponent according to Wilcock and Crowe (2003). The empirical exponent m ranges from 0 to −1, where m = −1 corresponds to the so-called “equal mobility” case in which all grains start moving at the same dimensionful bed shear stress τ, and m = 0 corresponds to no inﬂuence by hiding at all. The critical dimensionless bed shear stress at initiation of transport θc50 is estimated based on the bed slope Sb with the empirical relation of Lamb et al. (2008) according to Eq. (3.10):

0.25 θc50 = 0.15 · Sb . (3.10)

Within sedFlow a minimum value θc50,Min can be deﬁned for θc50, as Eq. (3.10) results in unrealistically low θc50 values for small channel gradients. For consis- Sred tency of calculations, θci,r = θci S is used in Eq. (3.7).

3.2.5 Model calibration and sensitivity calculations Using the data on channel geometry, GSD, and hydrology from the Brenno and Kleine Emme catchments, we ran the model sedFlow aiming to reproduce the observed bedload transport. The following criteria were applied to assess the agreement between simulation results and observations, which are stated in order of decreasing importance: (i) the input values, such as the local GSDs, should generally remain within the uncertainty range of observations. (ii) The input parameters, such as the threshold bed shear stress at the beginning of bedload CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 75

Table 3.2: Summary of calibration period simulations with diﬀerent equation sets.

Figure River Flow resistance Bedload Threshold for ABT- ABT- transport transport RMSE Nash–Sutcliﬀe 3.6 Kleine Emme Manning– Rickenmann (Eq. 3.7) Lamb et al. (2008) 7.83 × 103 m3 0.949 ∗ Strickler-type W and C hiding θc50,Min = 0.06 3.7 Brenno Variable Rickenmann (Eq. 3.7) Lamb et al. (2008) 18.0 × 103 m3 0.733 power-law no hiding θc50,Min = 0.1 ∗ Wilcock and Crowe (2003) hiding (Eq. 3.9).

motion, should vary within a plausible range. (iii) The simulated erosion and deposition should be as close as possible to the observed pattern. (iv) The simulated ABT should be as close as possible to the one reconstructed from field observations. (v) The GSDs at the end of the simulation should vary within a plausible range. In the calibration of this study, we examined these criteria (i–v) by visual inspection. The calibration process consists of five steps. First, a hydraulic routing scheme is selected. Second, a bedload transport relation is selected. Third, the threshold for the initiation of motion is adjusted. Fourth, if the simple power-law hiding function of Eq. (3.8) is used, the exponent m is adjusted as well. Fifth, some fine-tuning is made via local reach-scale adjustments. In general, the calibration parameters for bedload transport can be divided into three groups. The selection of the transport equation and the threshold for the initiation of motion θc50 (or θc50,Min in combination with the relation of Lamb et al., 2008) are global calibration parameters, which determine the overall level of transport rate. The local GSDs and representative channel widths are local calibration parameters, which can be used to locally modify the transport rates and thus the along-channel distribution pattern of transport rates. Finally, the selection of the hiding function and the hiding exponent m, the method for the interaction between the active surface layer and the subsurface alluvium, and the thickness of the active surface layers form the remaining calibration parameters. To the authors’ knowledge, there are no in-depth studies assessing the effects of these remaining parameters, which are hard to predict for a natural river system without a systematic sensitivity study. In the first step of the calibration process of the presented study, the implicit kinematic wave hydraulic routing scheme was selected for the Kleine Emme, because the gentle slopes preclude the uniform discharge approach and the long simulated time period requires fast simulations. For the Brenno, the uniform discharge approach was selected, because the intense sediment inputs from the tributaries require the consideration of adverse slopes. In the fifth step of the calibration process, reach-scale adjustments have been made to the GSD in the Kleine Emme and to the representative channel width in the Brenno river. For the Kleine Emme, the representative channel width was well constrained, while measured GSD’s were relatively poorly constrained because the riverbed CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 76 is accessible only at a limited number of gravel bars. For the Brenno, the uncertainty about the effective channel width is relatively large along the depositional reaches in flatter areas, and for the calibration of the sedFlow simulations the mean channel width was adjusted primarily in these reaches. The corresponding simulation set-ups are summarised in Table 3.2. For the sediment exchange mechanism between the active surface layer and the subsurface alluvium, in the Brenno, we used a threshold-based interaction approach with 20 and 70 cm as thresholds for the active surface layer thickness. In the Kleine Emme, we used a shear-stress-based interaction approach in which the constant active surface layer thickness equals twice the local surface D84 at the beginning of the simulation. For the Brenno, the simulation of the calibration period was repeated using all three different hydraulic schemes and two flow-resistance relations, which are implemented in sedFlow. Comparing these simulation results allows us to study the influence of the hydraulic algorithm on the simulated bedload transport. To explicitly study the influence of different time step lengths, we used a set- up in which the actual time step generally equals the user-defined maximum time step value2. We compared the simulation results for different maximum time steps ranging from 1 min to 1 h. For any other simulation outside this time step comparison, we used a maximum time step of 15 min for the Kleine Emme and a maximum time step of 1 h for the Brenno. These two values have been selected in order to achieve reasonably short calculation times. After the calibration exercise, the best-fit parameter set was used as a base for two sensitivity studies. For the first study, in each simulation, all parameters but one are set to their original best-fit values and the remaining parameter is increased and decreased by a certain fraction. In the following we will call this procedure a one-at-a-time range sensitivity study. We varied the parameters discharge, minimum threshold for the initiation of bedload motion θc50,Min, grain size and channel width by either plus or minus 10, 20 and 30 %. The maximum variation of 30 % fits the order of magnitude of the different uncertainties typically involved in bedload transport simulations. For example, discharge values are affected by the uncertainties of the rainfall–runoff simulations. The GSD of river reaches is measured at individual and accessible points and therefore cannot sufficiently capture the spatial variability of this parameter. The value of the minimal threshold for the initiation of bedload motion θc50,Min may vary along the river length (we assumed a constant value for the best-case simulation) and, as described before, the effective channel width exhibits considerable uncertainty in depositional reaches. However, considering the more detailed knowledge of the system of the Kleine Emme, a reduced uncertainty of only plus or minus 20 % is more appropriate than an uncertainty of 30 % for discharge and channel width in this catchment. 2However, it cannot be excluded that in a few time steps another of the conditions for temporal discretisation (listed in Sect. 3.2.4) caused a different time step length. CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 77

For the second sensitivity study, all possible combinations of maximum decreased (−30 %), best-ﬁt and maximum increased (+30 %) values for all treated parameters were simulated3. In the following we will call this a complete range sensitivity study. In this complete range sensitivity analysis, the sediment input volumes from the tributaries to the Brenno were varied as well by plus or minus 30 %. Some model parameters described in the companion paper by Heimann et al. (2015) have not been included in the sensitivity analyses for the following reasons:

• For the exponent e of the ﬂow-resistance partitioning approach of Rick- enmann and Recking (2011) and Nitsche et al. (2011), previous studies have shown that for various cases and conditions the value of 1.5 performed well in reproducing available observations (Nitsche et al., 2011). Therefore, we have not included e in our sensitivity study and instead recommended the use of a default value of 1.5.

• The abrasion coeﬃcient λ of the equation of Sternberg (1875) is commonly only used in simulations of test reaches longer than 30 km, as this is the minimum distance for λ to have considerable inﬂuence.

• The hiding exponents mwc and m (Eqs. 3.8 and 3.9) do not fit in the concept of the presented sensitivity analysis, which is the variation of a best-fit value by a certain percentage. In addition, there are almost no field data providing guidance for suitable values of the hiding function for the coarser part of the GSD.

3.3 Results

3.3.1 Simulations for the calibration period At the Kleine Emme, the simulated ABT shows agreement with the observed sediment budget (Fig. 3.6). Locally, however, simulations and observations of erosion and deposition can diﬀer considerably. In the uppermost part down to ∼ 17 km, peaks of very coarse GSDs are simulated. The gaps in the simulated GSD represent reaches in which the alluvial cover is washed out completely and the river runs over bedrock. Downstream of ∼ 17 km, simulated ﬁnal GSDs are close to the initial values. At the Brenno, the simulation depicts well the interactions and qualitative transport behaviour in the vicinity of the tributaries Riale Riascio and Ri di Soi

3 In three simulations at the Kleine Emme with high θc50,Min, low discharge, coarse GSD and narrow, mean or wide channel widths, the river could not transport the bank erosion sediment inputs near 12 km. This resulted in the creation of adverse slopes. Therefore, these three simulations have been excluded from the complete range sensitivity study. CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 78

(Fig. 3.7). Downstream of the anthropogenic excavation at 10 km, which is not considered in the simulation, the model exhibits an overall depositional trend. The low sediment transport from 4.5 to 3 km due to a locally increased channel width is well reflected in the simulations. Except for the depositional trend from ∼ 8 to ∼ 4.5 km (which did not occur in reality because substantial sediment volume was anthropogenically excavated from this reach) the simulated erosion and deposition show good agreement with the observations. In reaches with larger channel gradients the model produces a coarsening of GSDs. Apart from these reaches, simulated final GSDs are close to their initial values. In both rivers, the model tends to smoothen spatially varying channel gradients (Figs. 3.6 and 3.7). Furthermore, in both rivers, the GSDs evolve over the course of a model run such that the final GSDs can be interpreted as a function of bed slope (coarse grains in steep sections), channel width (coarse grains in narrow sections) and channel network (coarse grains at confluences with steep tributaries). The channel width is not modified during the simulations. The simulations of the Brenno suggest an intense backward migrating erosion of the knickpoints at the confluences with debris flow tributaries, but this is not observed in the field. This erosion can be prevented in the simulations either by limiting the alluvium thickness and thus potential erosion depth, or by adding coarse blocks to the local GSD, which have not been captured in the transect pebble count, or by introducing a maximum Froude number limit in the flow resistance and drag-force partitioning calculations. In both rivers, early in the course of a simulation the model tends to adjust surface GSDs, which stay roughly the same for the rest of the simulation and which therefore seem to be stable under the local conditions (i.e. local slope, channel width, subsurface GSD and discharge pattern). In the Kleine Emme, the variation of maximum time step length caused differences in the modelled erosion and deposition only at a few locations. This results in small differences in modelled ABT along the complete river length (Fig. 3.10). In the Brenno, long maximum time step lengths caused an underestimation of the depositional trend from 6 to 5 km. Downstream of this position, the underestimation of deposition resulted in an overestimation of simulated ABT (Fig. 3.11).

3.3.2 Sensitivity analyses The local sensitivity analysis (Fig. 3.8) shows that variations in input discharge and GSDs have a large influence on the resulting ABT in both rivers. The impact of variations of the minimum value for the threshold dimensionless shear stress at the initiation of bedload motion (θc50,Min) ranges from low in the Brenno to high in the Kleine Emme. In general, relative output variations are larger in the Kleine Emme than in the Brenno. However, this statement is only true when uncertainties of 30 % are assumed for both rivers. The difference in trend is less pronounced when the smaller uncertainties of 20 % for discharge and channel CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 79 width at the Kleine Emme are taken into account. Comparing the three implemented hydraulic schemes, the explicit and implicit hydraulic flow routing produce practically identical results and the differences to using an uniform discharge approach are small in the Brenno catchment (Fig. 3.9). In contrast, there is a considerable difference in ABT between the simulations based on the two different flow-resistance relations (Fig. 3.9). As a main result of the complete range sensitivity study, the variation of input values caused considerable variation in the simulated ABT, but caused very little variability in the simulated erosion and deposition (Figs. 3.12 and 3.13).

3.4 Discussion

3.4.1 Simulations for the calibration period Bedload transport and morphodynamic observation of both rivers can be reproduced with plausible parameter set-ups (Table 3.2 and Figs. 3.6 and 3.7). At the Kleine Emme the simulated absolute values of net erosion and net deposition at the end of the calibration period are small and thus close to the noise of the measurements. Therefore, the differences between observed and simulated morphodynamics may be partly explained as noise. The simulated peaks of very coarse GSD in the upper part of the Kleine Emme are due to the small alluvium thickness, which is in some places washed out completely (or nearly so). If only a few coarse grains are left in a reach, they will produce extremely coarse grain-size percentiles. At the Brenno, the deposition from ∼ 8 to ∼ 4.5 km (Fig. 3.7), which substitutes for the unconsidered excavation, appears as a plausible behaviour of the river without any anthropogenic interventions. Coarsening at reaches with increased channel gradient is plausible as well. At the Brenno, the minimum threshold dimensionless shear stress θc50,Min for the initiation of bedload motion has been calibrated to a value of 0.1 (Table 3.2). This corresponds to the findings of Lamb et al. (2008) and Bunte et al. (2013), who showed that in mountain rivers θc may well assume values in this order of magnitude. The good agreement of bedload transport simulations and observations may be surprising, given that the natural system is complex and the model representation is relatively simple, with only a few parameters for calibration. The selected transport equation and threshold for the initiation of motion determine the average level of transport volumes. The selected hiding function locally modulates the calculated volumes and in particular influences the evolution of the GSD. Despite its simplicity, the described modelling framework appears to be adequate for a quantitative description of bedload transport processes, as suggested by the reasonable agreement of simulation and observation. The better agreement of simulated and reference ABT at the Kleine Emme compared to the Brenno is not surprising. At the Kleine Emme, there are no debris flow inputs, the influence of tributaries is limited and the sediment outflow CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 80 is known. The Kleine Emme is a well-defined system with low uncertainties and thus is ideal for simulation. In addition, spatially distributed calibration was applied more extensively to the Kleine Emme than to the Brenno. For the Brenno, spatially distributed calibration was performed by adjusting the width of the channel. This was done only at depositional reaches, which entail considerable uncertainty in the representative substitute channel width and which correspond to only ca. 30 % of the total study-reach length. In contrast, at the Kleine Emme, spatially distributed calibration was performed by adjusting local GSDs along the complete study reach. This more extensive, spatially distributed calibration at the Kleine Emme partly also explains the better agreement of simulated and reference ABT at the Kleine Emme compared to the Brenno. Few studies (Lopez and Falcon, 1999; Chiari and Rickenmann, 2011; Mouri et al., 2011) have performed a spatially distributed comparison of simulations and field observations, similar to what is presented in this article. However, these studies focused on shorter river lengths than the Brenno and the Kleine Emme. Lopez and Falcon (1999) performed a lumped calibration by simply multiplying calculated transport rates by four. In all aforementioned studies, the models have been calibrated but not independently validated (similarly to the present investigation). This contrasts with approaches used in other research fields such as hydrology (Beven and Young, 2013), where it is common practice to perform a calibration and a validation separately. The lack of independent validation is mainly due to the marked scarcity of available field data on bedload transport. Other studies compared simulation results against point data derived from field observations (Hall and Cratchley, 2006; Li et al., 2008), against analytic considerations (García-Martinez et al., 2006) or against a combination of field data and analytical results along with additional flume experiment data and results from other models (Papanicolaou et al., 2004). Many studies discuss model behaviour without any explicit comparison between that behaviour and observational data (Lopez and Falcon, 1999; Papanicolaou et al., 2004; Hall and Cratchley, 2006; Li et al., 2008; García-Martinez et al., 2006; Radice et al., 2012). The simulated GSDs might be seen as a proxy for GSDs which are consistent with the local slope, channel geometry and discharge pattern. This idea is rather attractive, as the model would use variables with a low uncertainty to estimate the local GSD, which is associated with a relatively large uncertainty. Unfortunately, the simulated surface GSD also depends on the subsurface GSD, and on the algorithm regulating the exchange between the surface and subsurface layers (for details see Heimann et al., 2015). In any case, the simulated surface GSD is consistent with local conditions. However, the simulated surface GSD is influenced either by an unrealistically small interaction between surface and subsurface, or by a highly uncertain and possibly incorrect subsurface GSD. Nevertheless, these simulated GSDs will be internally consistent with the other assumptions in the model and thus may have the potential to serve as input for calibration exercises and follow-up studies. A detailed investigation of this topic CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 81 is beyond the scope of this article. The simulated erosion of knickpoints in the Brenno was not observed in the field and is thus unrealistic. This suggests that large blocks, which are present in these reaches, but which have not been captured by the transect pebble counts, are important to stabilise the bed. The influence of large blocks also explains why the GSD at these positions had to be coarsened to achieve realistic model behaviour. In addition, the simulated GSDs coarsened even further. Both the unrealistic erosion and the need for coarsened GSDs point to the limitations of a volumetric percentile grain diameter to serve as a proxy for channel roughness. Flow-resistance estimation depends on the representative grain diameter D84 in both the Manning–Strickler and variable power equation formulations (Ferguson, 2007). However, even a few large blocks, possibly at percentiles higher than 84, can heavily influence the properties of the flow. The problems of a single representative grain-size percentile used as a proxy for bed roughness become more severe in the case of a discontinuous GSD, for example if the coarse blocks originate from rock fall and thus from a different source than the alluvial gravel. In such cases, any percentile diameter will considerably over- or underestimate the roughness, if its value falls in the gap of the discontinuous GSD. Coarse blocks are also a problem for the general concept of a volumetric percentile. Only a small fraction of the volume of a large block belongs to the surface layer of the river bed, which is assumed to define its roughness. Large parts of such blocks protrude into the deeper alluvium or into the water flow not belonging to the surface layer (or even into the air above the flow). Therefore, the volumetric contribution of such blocks to the surface layer is hard to determine. These issues are reflected in conceptual models for flow resistance, such as the ones of Yager et al. (2007) or Nitsche et al. (2012), which consider large blocks explicitly, e.g., in terms of a surface block density. In a recent study, Ghilardi (2013) suggested that the protrusion height of large blocks into the flow could be used as a potential proxy for flow resistance. Based on this approach, the visual appearance of the Brenno river bed (Fig. 3.14) suggests a roughness of about 1–2 m. This value is of the same order of magnitude as the D84 of the coarsened GSDs (Fig. 3.7), which we used as a roughness proxy in our simulations. It is further supported by additional area block counts in the Brenno, which showed that grains with a diameter smaller than 1 m only make up 90 % of the surface layer’s sediment volume or even only 75 % at the confluence with the Riale Riascio (Fig. 3.14). These blocks observed in the field dominate the macro-roughness. Since D84 is selected to represent macro-roughness, the block counts support the D84 values which are used in the simulations, and which are of the same order of magnitude as the observed block diameters. To assess the influence of time step length, the user-defined maximum time step length was varied between 1 min and 1 h. In the Kleine Emme, the influence of time step length is negligible compared to the overall uncertainty of bedload transport simulations (Fig. 3.10). In the Brenno, the effect of large maximum CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 82 time step lengths is spatially limited and well defined (Fig. 3.11) and thus can be easily considered in the interpretation of the simulation results.

3.4.2 Sensitivity analyses The limitations of simple one-at-a-time sensitivity studies for the analysis of non- linear processes are well known (Saltelli et al., 2006). However, an adequate global sensitivity analysis, in which the complete parameter space is covered, would go beyond the scope of this article. As shown in Fig. 3.8 the model reacts differently to input changes, depending on which parameter is modified. The model’s reaction to input changes also depends on the current river setting. For example, the relative variability and thus uncertainty of model outputs is generally larger in the Kleine Emme as compared to the Brenno. This may be partially due to the fact that the volumes of transported sediment are generally smaller in the Kleine Emme as compared to the Brenno. However, the output uncertainty can be partially compensated by better-supported knowledge and thus higher confidence in the inputs (reduced uncertainty of only plus or minus 20 % for discharge and channel width at the Kleine Emme). Interestingly, even the order of parameter sensitivities may change depending on the current river setting. For example, the reaction to changes in the minimum threshold for the initiation of bedload transport θc50,Min differs considerably for the two rivers. In the Kleine Emme, the uncertainty of this parameter seems to be responsible for a large part of the model output uncertainty. In contrast, in the Brenno θc50,Min plays a rather subordinate role. In the complete range sensitivity study (Figs. 3.12 and 3.13) all input variations have been applied to the complete length of the river. This may explain why the simulated erosion and deposition show only limited variation compared to the simulated ABT. Erosion and deposition are a function of changes of channel properties (gradient, width, GSD, inputs) along the river. Applying the input variation to the complete length of the river keeps the relative changes of channel properties the same. Even though bedload transport is not a linear system, the input variation on the complete length of the river did not cause considerable variation of simulated erosion and deposition. Nevertheless, the sensitivity study with its highly variable ABT and almost constant morphodynamics stresses the uncertainty of ABT estimates that are only derived from morphologic changes. These simulation results support previous studies that have discussed this issue (Kondolf and Matthews, 1991; Reid and Dunne, 2003; Erwin et al., 2012). This is especially important because ABT plots are very common for the description of bedload transport in applied engineering practice and are even recommended by authorities (e.g. Schälchli and Kirchhofer, 2012). As is illustrated in Fig. 3.9 for the Brenno river, the two different flow- resistance relations produce considerably different values of simulated ABT. This further stresses the limitations of Manning–Strickler-type flow-resistance relations in steep mountain streams, as discussed in Rickenmann and Recking CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 83

(2011). In contrast, the three different flow-routing schemes predict similar transported bedload volumes in the Brenno river (Fig. 3.9). Differences can be neglected when compared to the overall uncertainties of bedload transport simulations. Therefore, the influence on the model outputs does not constitute a preference for any of the hydraulic schemes and any scheme can be selected based on its characteristics. If adverse slopes occur or if the variable power equation flow resistance, which is more suitable for shallow flow in steeper channels, is to be used without slowing down the calculations, one may select the uniform discharge approach. If one needs neither the ability to deal with adverse slopes nor the use of the variable power equation flow resistance, one may select the implicit kinematic wave routing, as it provides a routing of discharge. If a variable power equation approach is to be combined with a routing of discharge, one may select the explicit kinematic wave routing, even though this option is not recommended due to its long calculation times.

3.5 Conclusions

In this article, we used the model sedFlow to calculate bedload transport in two Swiss mountain rivers. sedFlow is a tool designed for the simulation of bedload dynamics in mountain streams. Observations of bedload transport in these two rivers have been successfully reproduced with plausible parameter settings. The results of the one-at-a-time range sensitivity analysis have shown that a defined change of an input parameter produces larger relative changes of output sediment transport rates in the Kleine Emme as compared to the Brenno, which may be due to the generally smaller transport rates at the Kleine Emme. Simulation results highlighted the problems that can arise because traditional flow-resistance estimation methods fail to account for the influence of large blocks. As an important result of our study, we conclude that a very detailed and sophisticated representation of hydraulic processes is apparently not necessary for a good representation of bedload transport processes in steep mountain streams. Both uniform flow routing and kinematic wave routing performed well in simulating field observations related to bedload transport. Moreover, it has been shown that bedload transport events with widely differing accumulated bedload transport (ABT) may produce identical patterns of erosion and deposition. This highlights the uncertainty in ABT estimates that are derived only from morphologic changes. This proof-of-concept study demonstrates the usefulness of sedFlow for a range of practical applications in alpine mountain streams. CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 84 ]

3 reference or initial values simulation [m b tributaries Q

Σ | sills Accumulated bedload transportAccumulated 20000 60000 100000 140000 180000 erosion / deposition [m]

| | | | |||||| | ||| | | | | | | | ||| ||| | | | −1.0 −0.5 0.0 0.5 1.0 1.5 channel gradient [%] channel gradient 0 1 2 3 4 [m] 50 D 0.0 0.1 0.2 0.3 0.4 0.5 [m] 84 D 0.0 0.1 0.2 0.3 0.4 0.5 0.6 channel width [m] 20 30 40 50 60 70 80

25 20 15 10 5

Distance to outlet [km]

Figure 3.6: Comparison of predictions and observations related to bedload transport in the Kleine Emme for the period 2000–2005 (tributaries from up- to downstream: Fontanne, Rümlig). CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 85

] reference or initial values 3 simulation [m

b tributaries Q Σ 0 50000 100000 150000 200000 Accumulated bedload transportAccumulated erosion / deposition [m] −2 0 2 4 6 channel gradient [%] channel gradient 0 5 10 15 20 [m] 50 D 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 [m] 84 D 0.0 0.5 1.0 1.5 2.0 channel width [m] 0 20 40 60 80 100 120

25 20 15 10 5 0

Distance to outlet [km]

Figure 3.7: Comparison of predictions and observations related to bedload transport in the Brenno for the period 1999–2009 (tributaries from up- to downstream: Riale Riascio, Ri di Soi, Lesgiüna). CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 86 ] 3 − Brenno Kleine Emme 2 + − − + − 80000 − 180000 − 60000 1 120000 + + 40000 + + + 80000 30000 − 0.5 + 60000 Median ABT per unit median reference ABT [−] Median ABT per unit median reference −

θ [m bedload transportMedian accumulated value (ABT) abs. cMin discharge grain size channel width Brenno Kleine Emme

Figure 3.8: Simulation sensitivity with respect to simulated accumulated bedload transport (ABT) for diﬀerent input parameters. The horizontal line represents the reference best-ﬁt simulations of Figs. 3.6 and 3.7. The tick marks at the vertical bars display the simulation results for input parameter variations of either plus or minus 10, 20, and 30 %. Plus or minus signs at the end of the bars indicate whether the input parameter was increased (plus) or decreased (minus). CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 87

VP−expl ] 3 VP−unif [m

b MS−expl Q

Σ MS−impl MS−unif tributaries 50000 100000 150000 Accumulated bedload transportAccumulated

20 15 10 5 0

Distance to outlet [km]

Figure 3.9: Comparison of simulated accumulated bedload transport in the Brenno for different combinations of flow-routing schemes and flow-resistance relations. Two flow-resistance relations are shown: the variable power relation given in Eq. (3.5) (denoted VP) and the grain-size-dependent Manning–Strickler relation given in Eq. (3.6) (denoted MS). Three flow-routing schemes are shown: explicit kinematic wave (denoted expl), implicit kinematic wave (denoted impl) and uniform discharge (denoted unif). The VP-unif curve (green dot-dashed line) is the same as the red line in the top panel of Fig. 3.7 and displays the reference best-fit simulation. CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 88 ] 3 [m b 1 min 40 min Q Σ 140000 5 min 45 min 10 min 50 min 15 min 55 min 20 min 60 min 100000 25 min tributaries 30 min | sills 35 min 60000 1.5 1.0 20000 Accumulated bedload transportAccumulated 0.5 0.0 erosion / deposition [m] −0.5 | | | | |||||| | ||| | | | | | | | ||| ||| | | |

25 20 15 10 5 −1.0

Distance to outlet [km]

Figure 3.10: Comparison of simulated accumulated bedload transport and erosion and deposition in the Kleine Emme for diﬀerent maximum time step lengths denoted in the plot legend. The maximum time step length value, which has been used for any other simulation in the Kleine Emme (e.g. Fig. 3.6), is displayed in red. CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 89 ] 3 [m b Q Σ 140000 80000 1 min 35 min 5 min 40 min

40000 10 min 45 min 15 min 50 min 6

20 min 55 min 5 0

Accumulated bedload transportAccumulated 25 min 60 min 30 min tributaries 4 3 2 1 0 erosion / deposition [m] −2 20 15 10 5 0

Distance to outlet [km]

Figure 3.11: Comparison of simulated accumulated bedload transport and erosion and deposition in the Brenno for diﬀerent maximum time step lengths denoted in the plot legend. The maximum time step length value, which has been used for any other simulation in the Brenno (e.g. Fig. 3.7), is displayed in red. ] 3 [m b median Q

Σ interquartile range 2.5 or 97.5 percentile tributaries | sills 0e+00 2e+05 4e+05 6e+05 Accumulated bedload transportAccumulated erosion / deposition [m]

| | | | | || ||| | || | | | | | | | | ||| || | | | | −2 −1 0 1 2

25 20 15 10 5

Distance to outlet [km]

Figure 3.12: Output variability within the sensitivity study for the Kleine Emme. CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 90 ] 3 [m b Q

Σ median interquartile range 2.5 or 97.5 percentile tributaries Accumulated bedload transportAccumulated 0e+00 2e+05 4e+05 erosion / deposition [m]

20 15 10 5 0 −10 −5 0 5 10 15 Distance to outlet [km]

Figure 3.13: Output variability within the sensitivity study for the Brenno.

Figure 3.14: River bed of the Brenno at the conﬂuence with the Riale Riascio (at 20.8 km, Fig. 3.7) exhibiting blocks with diameters of up to 2 m. CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 91

Acknowledgements

We are grateful to Christa Stephan (project thesis ETH/WSL), Lynn Burkhard (MSc thesis ETH/WSL), Anna Pöhlmann (WSL), Claudia Bieler (MSc thesis ETH/WSL) and Christian Greber (MSc thesis ETH/WSL) for their contributions to the development and application of sedFlow. Special thanks to Massim- iliano Zappa for his PREVAH support and the hydrologic input data. We thank the Swiss National Science Foundation for funding this work in the framework of the NRP 61 project “Sedriver” (SNF grant no. 4061-125975/1/2). The simulations in the Brenno river were also supported by the BAFU (GHO) project “Fest- stofftransport in Gebirgs-Einzugsgebieten” (contract no. 11.0026.PJ/K154-7241) of the Swiss Federal Office for the Environment. Jeff Warburton and an anonymous referee provided thoughtful and constructive suggestions to improve this manuscript. Appendix for chapter 3

92 CHAPTER 3. CALC. OF BEDLOAD TRANSP. USING SEDFLOW 93

Table 3.A1: Notation.

The following symbols are used in this article. ηpore pore volume fraction θi dimensionless bed shear stress for ith grain-size fraction θi,r θi using Sred to account for macro-roughness θc dimensionless bed shear stress at initiation of bedload motion θci θc for ith grain-size fraction θc50 θc for the median grain diameter θc50,Min minimum value for θc50 θci,r θci accounting for macro-roughness λ abrasion coefficient of the equation of Sternberg (1875) ρ fluid density ρs sediment density τ dimensionful bed shear stress Φbi dimensionless bedload flux for ith grain-size fraction a1,a2 empirical constants Di mean grain diameter for ith grain-size fraction Dm geometric mean for grain diameters Dx xth percentile for grain diameters D50 median grain diameter e exponent of the flow-resistance partitioning approach of Rickenmann and Recking (2011) and Nitsche et al. (2011) Fi proportion of ith grain-size fraction F r Froude number g gravitational acceleration m empirical hiding exponent ranging from 0 to −1 mwc hiding exponent according to Wilcock and Crowe (2003) q discharge per unit flow width Qb bedload flux qb bedload flux per unit flow width qbi qb for ith grain-size fraction

qblat lateral bedload influx per unit flow width qc threshold q for initiation of bedload motion rh hydraulic radius s density ratio of solids and the fluid S slope of hydraulic head Sb slope of river bed Sred slope reduced for macro-roughness t time vm average flow velocity v∗ shear velocity Vcap volume of sediment corresponding to the transport capacity in a reach VEroDepo volume of sediment that is eroded or deposited in a reach Vin volume of sediment that enters a reach VinUp volume of sediment that enters a reach from upstream VinLat volume of sediment that is introduced laterally to a reach Vout volume of sediment that exits a reach x distance in flow direction z elevation of channel bed REFERENCES 94

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Assessing the impact of climate change on brown trout (Salmo trutta fario) recruitment

Junker, J., Heimann, F. U. M., Hauer, C., Turowski, J. M., Rickenmann, D., Zappa, M., and Peter, A.: Assessing the impact of climate change on brown trout (Salmo trutta fario) recruitment, Hydrobiologia, doi: 10.1007/s10750-014-2073-4, 2014. c Springer International Publishing Switzerland 2014 With kind permission of Springer Science+Business Media Junker, J., Heimann, F. U. M., Hauer, C., Turowski, J. M., Rickenmann, D., Zappa, M., and Peter, A.: Erratum to: Assessing the impact of climate change on brown trout (Salmo trutta fario) recruitment, Hydrobiologia, doi: 10.1007/s10750-015-2223-3, 2015. c Springer International Publishing Switzerland 2015 With kind permission of Springer Science+Business Media

Abstract

Climate change influences air temperature and precipitation, and as a direct consequence the annual discharge pattern in rivers will change as climate warming continues. This has an impact on bedload transport and consequently on aquatic life, because coarse sediments in streams provide important habitat for many species. Salmonids, for example, spawn in gravel, and during their early life stages live in or on top of the substrate. We used a multiple model approach to assess how predicted discharge changes affect bedload transport and the vulnerable early life stages of brown trout (Salmo trutta fario) in a pre-alpine catchment in Switzerland. In the study area, future discharge scenarios predict an increased frequency of flood occurrence in winter, and long-lasting low-flow periods in summer. As a result, bed erosion will become more frequent during winter, leading to less stable spawning grounds and deeper scouring, but during

100 CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT101 summer an improvement in habitat diversity can be expected, which is advan- tageous for young-of-the-year ﬁsh. To face the future challenges of climate change we recommend widening of riverbeds and improvements in longitudinal connectivity.

4.1 Introduction

It is now generally accepted that the atmosphere is warming, to a large part due to anthropogenic influences. The changing climate is altering precipitation patterns. The last two centuries have seen an increase in precipitation during winter and spring months in the northern regions of the alps (Brunetti et al., 2006), a trend that is likely to continue in future. In addition, a larger fraction of winter precipitation will fall in the form of rain rather than snow, snowmelt will have an earlier onset, and the snow line will shift upwards to higher altitudes (Birsan et al., 2005; Parry et al., 2007; Scheurer et al., 2009). In high mountain regions, glaciers are receding and the amount of water stored as ice is declining. As a result, the seasonal discharge regime in rivers will continue to change (Parry et al., 2007). Especially for the European Alps, a substantial temporal shift in runoff is expected (Horton et al., 2006). For streams at altitudes between 500- 1500 m.a.s.l. several studies predict increased winter runoff, 0.5 to 2 month earlier but reduced snowmelt-induced peak flows and reduced summer runoff (Jasper et al., 2004; Zierl and Bugmann, 2005; Horton et al., 2006; FOEN, 2012). It thus seems likely that climate change will affect flooding and therefore bedload transport in Swiss mountain catchments over the coming 40 to 100 years (OcCC and ProClim, 2007). For many aquatic species coarse sediment in streams provides an important habitat, particularly for reproduction and for early life stages. For salmonid populations, the area and distribution of suitable spawning gravel in rivers determines breeding success (Kondolf and Wolman, 1993). Hence, large flood events transporting sediment can severely affect a population. Already Jager et al. (1999) stated that anticipated hydrological changes for mountain streams due to climate change have clear consequences for salmonid survival. We selected brown trout (Salmo trutta fario) as the target species. The early life cycle of brown trout is strongly associated with the river sediment and slow flowing habitats. It initiates in autumn with the spawning time, followed by a phase called incubation. During the incubation brown trout remain, first as eggs and afterwards as alevins, in the gravel bed. A study on seven alpine and prealpine rivers in Switzerland (Riedl and Peter, 2013) found that spawning lasted from the end of October until the beginning of January. The spawning season was closely connected to water temperature and altitude. Riedl and Peter (2013) also measured redd features like hydraulic parameters and channel bed properties. The observations were comparable to current literature results (e.g. Grost et al., 1990; Zimmer and Power, 2006; Pulg et al., 2013). However, a discrep- CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT102 ancy was found for egg burial depth, which was measured in two different ways. Taken from the level of the accumulated overlaying gravel, burial depth ranged from 1-16 cm (mean 5.8, SD = ± 2.6 cm). Measured from the original bed level the depth is between -9-13 cm (3.8 cm, SD ± 3.2). These values, recorded by Riedl and Peter (2013), are lower than most mean literature values, which are between 4 cm and 20 cm (Elliott, 1984; Crisp, 1989; Grost et al., 1990). In spring young brown trout, then called parr, emerge from the gravel into the water column (e.g. Elliott, 1994; Jonsson and Jonsson, 2011). The habitats of salmonid individuals are structured according to age and size, with juvenile fish using shallow, slow-flowing areas of the river, and moving into faster, deeper areas as they grow (Morantz et al., 1987; Keeley and Grant, 1995). A way to describe this lateral and longitudinal mosaic of different river areas based on their physical condition, like water depth and flow velocity, is the use of hydro-morphological units (HMU), also called mesohabitats (Bisson et al., 1981; Frissell et al., 1986). However, so far there are only a limited number of studies investigating the effect of climate change on bedload transport in alpine catchments (e.g. Bathurst et al., 2004; Coulthard et al., 2012; Diodato et al., 2013; Elliott et al., 2012; Layzell et al., 2012) and an integration of interdisciplinary research linking climate change models to hydro-morphology and impacts on fish populations are lacking. We evaluate here the possible future impacts of climate change using brown trout as indicator species within this interdisciplinary framework. We assess in detail how predicted climatic changes affect discharge and bedload transport, and thus the vulnerable early life stages of brown trout in a Swiss prealpine river (Kleine Emme), including time of spawning, incubation and the early phase as parr. To address these issues, we used a multi-scale modelling approach including the following elements:

(i) Simulation of future discharge conditions using input from general circu- lation models and regional climate models to a rainfall-runoﬀ model at the catchment scale.

(ii) Simulation of bed erosion and scour depths, during spawning and incubation time of brown trout, using a one-dimensional bedload transport model at the reach scale.

(iii) Field investigations and hydrodynamic modeling of spawning ground stability and mesohabitats at the local scale.

These investigations are based on observed discharges for a control period (1980-2009) (hereafter abbreviated by CTRL) and on predicted discharges for the near (2021-2050) and far (2070-2099) future obtained from the rainfall- runoﬀ model. CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT103

4.2 Materials and methods

4.2.1 Study area The river Kleine Emme is located in the prealpine area of central Switzer- land (Fig. 4.1a). It rises from the Brienzer Rothorn Mountains (46◦ 48’ 5” N, 8◦ 4’ 0” E, 1460 m.a.s.l) and flows into the river Reuss (47◦ 4’ 2” N, 8◦ 17’ 16” E, 434 m.a.s.l), which belongs to the Rhine drainage. The river is 58 km long, and its total catchment is 477 km2. The main geological units in the catchment are flysch, molasse conglomerate, and sandstone. The channel bed slope varies between 0.4 and 4%. The Kleine Emme runoff regime is characterized by maximum yearly discharge in spring or early summer and the minimum discharge in the winter months. However, this pattern is more pronounced in the head reaches (Weingartner, 1992; FOEN, 2005). For the reach scale analysis, a total length of 20 km of the Kleine Emme was simulated, starting downstream of Entlebuch and continuing until Littau, which is situated 5 km upstream of the confluence with the Reuss (Fig. 4.1b). For the local scale analysis, three reaches in the river were chosen which are representative for the variability of the hydrogeological features of the Kleine Emme. Reach 1 has a total length of 205m (upstream end at 47◦ 2’ 9.30” N, 8◦ 4’ 5.92” E). It represents the de- graded lower parts of the Kleine Emme. The channel is straightened and the left bank is enforced by a concrete wall and three groins. In addition, an artificial bed drop has been introduced to decrease channel bed slope. The substrate consists mainly of gravel, pebble, cobble and boulders (Fig. 4.1c). The banks of Reach 2 (47◦ 1’ 38.14” N, 8◦ 3’ 59.89” E, with a length of 170m) are natural. In this reach the bed consists partly of exposed bedrock. The alluvial cover is thin and patchy, and consists of sand, gravel, pebble, cobble and boulders (Fig. 4.1d). The most diverse and near natural reach is Reach 3 (47◦ 0’ 0.03” N, 8◦ 3’ 39.49” E, 210m). The substrate is dominated by cobbles, pebbles and boulders with a minor fraction of sand and gravel (Fig. 4.1e).

4.2.2 Catchment scale: Impact of future climate change scenarios on discharge The data for the hydrologic scenarios have been obtained from results of the CCHydro project (Bernhard and Zappa, 2012; Kobierska et al., 2013), in which hydrologic simulations have been performed using the rainfall-runoff model PRE- VAH (Viviroli et al., 2009). PREVAH is a well-established fully-distributed rainfall-runoff model specifically designed for alpine catchments. Hydrologi- cal computations for the near (2021-2050) and far future (2070-2099) used climate impact scenarios prepared by Bosshard et al. (2011), which have been obtained by the application of an advanced delta-change methodology (Gleick, 1986; Graham et al., 2007). A total of 10 scenarios for each future period could be considered here, stemming from the ENSEMBLES project (van der Linden CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT104

Figure 4.1: a Map of Switzerland, showing the investigated catchment of the river Kleine Emme (shaded). b Kleine Emme and its main tributaries. The three test reaches are represented by square symbols. The two gauging stations are indicated by triangles. Digital terrain data used for mesohabitat modelling of possible future climate change impacts on brown trout reproduction and juvenile habitats: c Reach 1, d Reach 2, e Reach 3 (see section 4.4.3) and Mitchell, 2009) and relating to the A1B emission scenario. The simulation within the CCHydro experiment has been validated at 70 gauging stations maintained by the Swiss Hydrological Service (Zappa et al., 2012). One of the verification points coincides with the main gauging station of the Kleine Emme (Table 4.1). Hydrological models need careful calibration within a pre-defined control (CTRL) period. Following the procedure used by Kobierska et al. (2013) we modelled a 30 year period with PREVAH (1980–2009) as CTRL. The meteoro- logical input forcing had a temporal resolution of one day, and was obtained by interpolating data of the Swiss Federal Office for Meteorology and Climatology, MeteoSwiss (Begert et al., 2005). As presented by Schattan et al. (2013) and Kobierska et al. (2013), we adopted the fully-distributed version of PREVAH for the hydrological impact study. This version allows for the assimilation of land-use change scenarios and for improved coupling with further impact models such as the bedload transport model presented below. We quantified model performance of the PREVAH simulations for the calibration and verification periods by computing the Nash criterion (NSE, Nash and Sutcliffe, 1970) and by CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT105

Table 4.1: Hydrological characteristics of the Kleine Emme River (FOEN, 2013)

Gaugingstation Werthenstein Littau h m3 i NM30Q s – 1.16 h m3 i MQ s 11.0 15.6 h m3 i HQ2 s 196 313 h m3 i HQ30 s 417 595 h m3 i HQ100 s 544 712 NM30Q = minimal daily mean flow over 30 days, MQ = mean flow, HQx = high flow (x = recurrence interval)

assessing water volume error DV, which indicates the value in percent of the bias between simulated and observed discharge (Table 4.2). Further details on the setup used herein were presented by Schattan et al. (2013), Kobierska et al. (2013) and Köplin et al. (2010).

4.2.3 Reach scale: Climate change impacts on bedload transport and channel morphodynamics For the bedload transport and channel morphodynamic simulations we used the model sedFlow (Heimann et al., 2014b). This model performs a one-dimensional hydraulic routing of the runoff using a kinematic wave approach for a rectangular cross-section. The boundaries of the simulated system have constant elevation and grain size distributions. Sediment input at the upstream boundaries is determined corresponding to the current discharge without limitations in sediment availability. The model has been developed for the simulation of bedload transport per grain size fraction in mountain streams. The modeling concept is similar to the one-dimensional bedload transport model for steep slopes presented by Chiari et al. (2010). To calculate bedload transport as a function of shear stress, an equation proposed by Rickenmann (2001) is used in combination with a reduced energy slope to account for macro-roughness effects (Rickenmann and Recking, 2011). The use of a reduced energy slope significantly improves the prediction of bedload transport in steep mountain streams (Chiari et al., 2010; Nitsche et al., 2011; Rickenmann, 2012). The critical dimensionless shear stress for initiation of transport was determined using the empirical approach of Lamb et al. (2008). For slopes approaching zero the equation of Lamb et al. CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT106

Table 4.2: Basic information on hydrological veriﬁcation for the target area (gauging station Littau)

h i Catchment km2 Elevation [m.a.s.l.] Performance Period NSE [−] DV [%] Min: 431 Cal 0.823 1.9 477 Avg: 1050 VER 0.831 5.8 Max: 2300 TOT 0.828 4.0 We indicate the performance (NSE and DV) of hydrological model PREVAH during calibration (CAL, 1984–1996), veriﬁcation (VER, excl. 1984–1996) and for the whole control period (TOT, 1980–2009).

1.0 sublayer armour layer suitable for spawning 0.8 0.6 0.4 0.2 Cumulative relative abundance [−] abundance relative Cumulative 0.0

0.1 1.0 10.0 100.0

Grain diameter [cm]

Figure 4.2: Grain size distribution derived from 22 line-by-number samples recorded at the Kleine Emme. Solid lines represent the median. Shaded areas are conﬁned by the quartiles.

(2008) predicts a threshold value near zero, which is unrealistic. Therefore, a minimal critical dimensionless shear stress of 0.06 was used whenever the equation predicted lower values. This value of 0.06 performed best for the numeric reproduction of observed bed level changes and is close to 0.047 as proposed by Meyer-Peter and Müller (1948). Grain size distributions were measured using the transect-by-number sampling method (Fehr, 1987) at 19 locations along the river profile. Following the Wentworth scale (Wentworth, 1922), gravel and cobble grain sizes are most dominant in the channel (Fig. 4.2). The bedload transport model sedFlow was calibrated for the Kleine Emme for the period 2000-2005 for which independent measurements of sediment input and changes in bed elevation were available. For the simulation the investigated 20 km river length of the Kleine Emme was subdivided into legs ranging CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT107 in length from about 50m to 200m. For each leg, two cross-sectional profile measurements are available from September 2000 and November 2005, which served as a basis for the calibration of sedFlow. The agreement of modelled with observed cross-sectional changes was evaluated by comparing the simulated accumulated bedload transport with the one derived from observed bed level changes (Heimann et al., 2014a), resulting in a Nash-Sutcliffe goodness- of-fit measure of 0.949 (Nash and Sutcliffe, 1970). The parameter set from the model calibration runs was used for the simulations of both the CTRL and future periods (Badoux et al., 2014). The same initial conditions were used for all model runs and only the hydrologic input was varied. Each run was started on April 16th and finished on April 15th of the following year. The summer months were used as priming for the spatial pattern of grain size distributions. Simulation state variables were recorded every three hours during low and intermediate flow and every 15 minutes when discharge exceeded its upper 90th percentile. The analysis focused on the maximum erosion depth during incubation and the timing of lowest bed elevation during winter. These simulated variables are recorded for each leg along the river, during a single winter, for all different years within the study period (30 years in each of CTRL, near future, and far future), and for each available hydrologic/climatic scenario. To obtain the maximum erosion depth during incubation, the minimum bed elevation during the period from December 20th to April 15th was subtracted from the bed elevation on December 20th. The timing of the lowest bed elevation was assessed for the period between October 15th and April 15th of each simulated year. To charac- terize the effect of climate change on erosion depth and timing of the lowest bed level, spatial as well as temporal quantiles of the CTRL period were compared to the intervariability of the different hydrologic/climatic scenarios for both the near and far future. To specify the spatial distribution of changes, we studied how simulated grain sizes and bed stability depend on the channel gradient. For this, we defined the bed to be stable when the maximum erosion depth did not exceed a threshold value of 5 cm. This threshold is higher than the average egg burial depth of 3.8 cm as measured from the original bed level (Riedl and Peter, 2013), but also slightly lower than the 5.2 cm as measured from the overlaying gravel at the redd.

4.2.4 Local scale: Climate change impacts on habitat stability and distribution Terrestrial survey / DTM generation The bathymetric shape (main channel) of the three investigated sites at the local scale of the Kleine Emme has been measured by terrestrial survey (17.7.2012 – 18.7.2012). A total station (Leica TC805) was used to survey all relevant mor- CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT108 phological features for meso-habitat classiﬁcation (e.g. gravel bars, Riﬄe-Pool features) based on cross-sectional measurements (Reach 1: 23 cross sections, Reach 2: 14 cross sections, Reach 3: 20 cross sections). Additional points were surveyed between those transects if important hydraulic (habitat) characteristics were observed (e.g. groins and the related backwaters) to determine basics for high quality Digital Terrain Models (DTMs). The terrestrial sampling points (Reach 1: 525 points, reach 2: 261 points, Reach 3: 453 points) were placed onto a regular grid in a second step before modelling. For the present study, the Surface Water Modelling System (SMS) was selected. SMS combines various algorithms for the generation of modelling meshes with boundaries of arbitrary shape and the interpolation of topographic data (French, 2003). More- over, basic tools for presenting map, terrain and feature data are provided as a series of geographical information (using GIS polygons) (French, 2003). For DTM generation of the investigated sites at the Kleine Emme a patch-based algorithm was used which automatically determines elongated quadrilaterals or triangular elements. In total, 11712 elements (Reach 1), 5902 elements (Reach 2) and 12838 (Reach 3) were used to provide bathymetric information for hydrodynamic-numerical modelling (Fig. 4.1c, d and e).

Hydrodynamic-numerical modelling For hydrodynamic-numerical modelling a two-dimensional depth-averaged model was used to achieve the required abiotic resolution (e.g. flow velocity) for instream habitat studies on the meso- and microunit scale. The applied software Hydro_as-2d (Nujic, 1998) calculates the hydraulic conditions (water depth, depth-averaged flow velocity, bottom shear stress) on a linear grid by a finite volume approach. Time was discretised using an explicit second-order Runge- Kutta method and the convective flow was calculated based on the Upwind scheme (Pironneau, 1989). The bed shear stress τ, which was used as a parameter for determining spawning habitat stability during the period of reproduction (November – January) or incubation (February – April), was calculated for each node of the grid based on following formulas (Nujic, 2004):

τ = ρ · g · h · Sf , (4.1)

v2 Sf = , (4.2) 2 4 kstr · h 3 kg where ρ is the density of water (1000 m3 ), g the acceleration due to grav- m ity (9.81 s2 ), h the water depth at each node [m], Sf the friction slope [−], m v the depth-averaged flow velocity at each node s , and kstr is the roughness coefficient by Strickler (which is equal to the inverse of Manning’s roughness coefficient). CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT109

To ensure steady state flow conditions (input discharge = output discharge) for the investigated reaches, 30600 seconds (8.5 hours) were required as total modelling time for each of the 242 modelling runs (sum of all climate change scenarios and low flow sensitivity testings). Moreover, discrete time steps of 900 seconds have been applied as computational and/or detailed output interval (e.g. flow velocity).

Classification and stability testing of spawning ground and mesohabitats For the impact analysis of climate change on brown trout habitats at the Kleine Emme the Mesohabitat Evaluation Model (MEM) was used (Hauer et al., 2009). The MEM model enables the determination and quantitative calculation of six significant different hydro-morphological units (mesohabitats). Based on depth- averaged flow velocity, water depth and bottom shear stress the mesohabitats riffles and fast runs (as high energetic habitats), runs and pools (as moderate energetic habitats) shallow waters and backwaters (as low energetic habitats) can be numerically distinguished (Hauer et al., 2009). Furthermore, by knowing the hydrological characteristics (depth and flow velocity) of spawning grounds of a certain fish species, it is possible to identify suitable areas for reproduction within selected stretches. For engineering practice, the MEM-concept was implemented into a Java software application, which can be used for the postprocessing of modelling results of three different two-dimensional (CCHE2D, River2D, Hydro_as-2d) and two different three-dimensional models (RSIM-3D, SSIIM) (Tritthart et al., 2008). MEM-modelling results are presented in visual forms (plots) and/or quantified by area m2 and in relation to the total wetted area [%]. The stability of the bed is assessed using a simple threshold criterion on the shear stress (Eq. 4.1). When the critical shear stress τcr is exceeded locally for the discharge of interest, the bed is said to be unstable. Following the suggestion of Meyer-Peter and Müller (1948), the value of τcr is set to:

τcr = 0.047 · (ρs − ρ) · g · dm (4.3) kg Here ρs is the density of the sediment (=2665 m3 ), and dm is the characteristic grain size [m]. Similar to mesohabitat evaluation the bed stability for each of the hydro-morphological units is quantified by area m2 and in relation to the total planimetric extent [%] of a specific habitat type (e.g. riffles). Note that the definition of bed stability in the MEM differs from the definition used in the reach-scale modelling approach (see section 4.4.1). We used the MEM to find suitable spawning grounds for reproduction in the three test reaches of the Kleine Emme. Our data for the suitable depth and flow velocity of spawning grounds are based on records during the years 2010 and 2011 by Riedl and Peter (2013) in seven pre-alpine and alpine Swiss streams that are comparable to the Kleine Emme. These data were supple- mented with additional spawning observations during this study in the Kleine CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT110

Emme catchment in 2012, adding up to a total sample size of 124 redds for the present study. At three points on each redd (pit, middle and tail), depth, flow velocity at a depth of 60% of the water column and substrate were measured. By calculating the average of the three measured points we produced the usability range of a maximal depth use, which was between 0.15 and 0.2m, m with a flow velocity of 0.45 s . Using the MEM we searched, within the three river reaches, for all areas with the mentioned suitable abiotic characteristics under autumn low flow conditions, and aligned them with our own observations in the test reaches of suitable spawning gravel (average size 3.1 cm). If a patch showed the right depth, velocity, and substrate, we considered it as a designated spawning ground. These patches were tested for their stability under different m3 discharges (4-26 s ) using two representative grain diameters (dm=20 mm and 50 mm). Here we considered a patch as 100% stable if no movement of the bed surface was found.

Sensitivity testing and distribution of mesohabitats under differing discharges Mesohabitat distribution was modeled in the three test reaches to investigate the m3 sensitivity of available (suitable) habitat area for variable discharges of 4-12 s . This range coincides with the lowest flow magnitude during the summer period (June, July, August) of each of the 10 climate scenarios. To determine and quantify the shifts in habitat availability during summer months (June, July, August) in the near and far future the specific discharge of each of the 10 climate scenarios was modelled in a second analysis.

Mesohabitat suitability for different brown trout age classes During October 2012 electrofishing surveys were conducted in the three test reaches. Fishing was done within hydromorphological units, according to the MEM and to pre-modeled mesohabitat distribution maps for the specific discharge during the fieldwork. Every mesohabitat type was sampled separately and fish were kept in different tanks after. The fish were grouped into different age classes based on their lengths (according to our own observations these are: young of the year (YOY); 61-130 mm, subadult; 161-210 mm, and adult >221 mm). We calculated the relative frequency of fish density for each age class in a certain mesohabitat type, dividing number of fish caught by sampled mesohabitat area. By normalizing these values (the highest relative frequency of fish density of a mesohabitat type is given a value of one and the rest of the results are set in relation to it) we obtained an index of habitat suitability. CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT111

Figure 4.3: Water balance scenarios for the “Kleine Emme” for the reference period (black line in both panels) and ten realizations for both future periods (coloured lines. Left panel a: 2021-2050, Right panel b: 2070-2099. The labels on the x-axis deﬁne the average water balance elements expressed in mm per year: precipitation (P-kor), actual evapotranspiration (EREA), total discharge (RGES), glacier melt (GLAC) and snowmelt (P-SME)

4.3 Results

4.3.1 Catchment scale The yearly water balance of the catchment for the CTRL period 1980-2009 (Zappa et al., 2012) resulted in 1505 mm precipitation, 980 mm discharge, 504 mm evapotranspiration and 20 mm storage change (Fig. 4.3). Storage change is due to different snow accumulation and groundwater storage between the beginning and the end of the simulation with PREVAH. The model predicts that under current conditions 11.5% of runoff is generated from snowmelt. The average discharge hydrograph of the CTRL period clearly indicates that the snowmelt governs the high-flow season between mid-March and mid-June (Fig. 4.3a). The results obtained for the near future (Fig. 4.4a) already hint at a distinct increase of average discharge in the winter half-year. This is because of both the expected precipitation increase in winter (Bosshard et al., 2011), and the reduction of snow accumulation as a consequence of increased average temperature (i.e., a larger fraction of the winter precipitation falls as rain rather than as snow). The predicted average discharge in January to March is below the average value of present-day conditions in only one scenario. The average seasonal discharge maximum in spring is predicted to decrease in magnitude. In the near future the discharge regime is predicted to be less seasonal. Most of the scenarios predict lower runoff in the summer season in comparison to the CTRL. Averaged over all ten realizations, the models predict no relevant change in the average annual water balance. Only the average contribution of snowmelt might be reduced from 11.5% to 8%. Note that the individual scenarios result in predictions of runoff changes ranging between -8% and +8% (Fig. 4.3a). CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT112

h m3 i Figure 4.4: Scenarios of mean discharge s for the “Kleine Emme” for the reference period (black line in both panels) and ten realizations for both future periods (colour lines: a 2021-2050, b 2070-2099). A centred 30-day averaging ﬁlter was applied.

The further increase in temperature expected for the latter portion of the 21st century (Bosshard et al., 2011) is cause of the further decrease in the predicted summer low flow periods in the far future (Fig. 4.4b). The reduction of snow accumulation and strong increase in liquid precipitation in the winter will change the discharge regime in the Kleine Emme, resulting in a distinct runoff maximum in winter and long-lasting low-flow periods in the summer- time. Again, the ten realizations show no clear change in the yearly water balance components, but the relative differences in the predictions for the ten scenarios increase. Specific scenarios result in predictions of runoff changes ranging between -14% and +18%.

4.3.2 Reach scale Bedload transport and morphodynamics Here, we use spatial and temporal percentiles to illustrate the model outputs. To obtain the spatial percentiles, the maximum erosion rate for each leg in the model was determined for a given simulated year. Out of these values, the desired spatial percentile was then calculated for each individual year (30 years for each of the near and far future). Temporal percentiles were calculated from the results for different years in the studied periods for a given spatial percentile. Only a slight increase of erosion depths is predicted for the near future, when the 75th spatial percentile is used (Fig. 4.5). The increase is more distinct for the far future, where it exceeds the range in predicted values obtained for the different hydrologic/climatic scenarios. Different temporal percentiles exhibit a qualitatively similar behavior (Fig. 4.5). For other spatial percentiles the picture is similar as well (see appendix). Thus, the increase of winter erosion depths appear to be consistent across all years and reaches. During the sensitive phases of spawning and incubation of brown trout, the CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT113

● control period

0.12 near future far future 0.10

● ● 0.08 0.06 0.04 0.02

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Perc2.5 Perc25 Perc50 Perc75 Perc97.5

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Figure 4.5: Spatial 75th percentile of maximum scour depth during incubation. Temporal percentiles refer to years within the study period. The boxplots re- flect the variability over the available hydrologic/climatic scenarios. The 75th percentile value separates those 25% reaches with larger erosion depths from those 75% reaches with smaller erosion depths. The abscissa represents the temporal percentiles of erosion depth. Years on the left part of the figure have little winter erosion, years on the right part have more intense winter erosion. lowest bed elevation tends to occur at a later time than in the CTRL period (Fig. 4.6). In general this means that the period in which erosion takes place continues for a longer time. The trend is clearer for the far future than for the near future. The fraction of stable legs (i.e., the maximum erosion depth is less than 5 cm) decreases in the future (Fig. 4.7). In general, legs with smaller slopes are more stable than legs with higher slopes. In addition, the number of unstable legs declines more steeply with increasing bed slope in the near future than in CTRL, and in the far future than in the near future. Generally, the median grain size of the surface layer D50 at the beginning of incubation period (to be taken the 18th to 22nd December) increases with increasing channel bed slope S (Fig. 4.8). Below a threshold bed slope of about 0.9% the vast majority of simulated D50’s are finer than 12 cm. Above this threshold simulated D50’s range from about 10 cm to more than 40 cm. The CTRL period as well as the near and the far future exhibit a similar behavior. CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT114

● control period

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Perc2.5 Perc25 Perc50 Perc75 Perc97.5

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Figure 4.6: Moment of minimum bed level occurrence in winter. Temporal percentiles refer to years within the study period. The boxplots reﬂect the variability over the available hydrologic/climatic scenarios. Spatial and temporal percentiles are used as described for Figure 4.5. Instead of the spatial 75th percentile the spatial median is used and the abscissa represents diﬀerent years grouped according to early or late occurrence of maximum erosion.

4.3.3 Local scale Stability of spawning ground

m3 The selected spawning site in Reach 1 is stable for discharges between 4 s and m3 5 s and the grain size dm of 20 mm and 50 mm (Table 4.3). But the stability m3 starts to decrease at discharges higher than 5 s and is totally unstable with a m3 discharge of 11 s for the grain size of 20 mm diameter. Under this discharge the same patch with a grain size dm of 50 mm remains stable. The erosion starts m3 at a discharge higher than 12 s and reaches 100% instability with more than m3 20 s water. The designated spawning site in Reach 2 is already partly unstable m3 m3 for the smaller grain size at a discharge of 4 s , and 8 s is enough to reach 100% instability. The site is also unstable for the dm = 50 mm substrate with a m3 m3 discharge of 4 s , but 100% instability requires discharges of more than 24 s . m3 The site in Reach 3 is the most unstable. At a discharge of 4 s just 2.65% of the bed area is stable with dm = 20 mm, and 100% instability is reached m3 at discharges smaller than 5 s . Also with dm = 50 mm just 32.92% is stable CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT115 100 95 90 85 Percentage of stable bed [%] of stable Percentage

80 threshold 5 cm control period near future far future

0.0 0.5 1.0 1.5

Bedslope [%]

Figure 4.7: Moving average of relative abundance of stable profiles compared to bedslope. The spatial distribution of erosion is shown as a function of channel slope S with a moving window width of ∆S = 0.5%. That means for a given slope S all reaches with slopes in a range of S ± 0.25% are analysed. Among these reaches, the relative abundance of profiles is counted, for which the maximum erosion during incubation (Dec 20th to April 15th) does not exceed a threshold of 5 cm. This relative abundance of stable profiles is given in the ordinate, while the abscissa shows the center of the moving bed slope window. with the smallest calculated discharge and the 100% instability is reached for m3 discharges under 11 s (Table 4.3).

Sensitivity testing of ﬂow variation In addition to the availability and the stability of spawning habitats, possible changes of the quantitative habitat distribution due to predicted climate change are of special interest, ostensibly for the early life stages of the selected salmonid species. The relative mesohabitat distribution clearly changes over the discharge m3 m3 range of 4-12 s (Fig. 4.9). At low ﬂows (4 s ) the three mesohabitat types shallow water (24%), fast run (28%) and run (38%) dominate. Run reaches its m3 maximum expansion at a discharge of 5 s . With further increasing discharge, the area covered by this habitat type starts to decrease to a minimum extent m3 of 18% at 12 s . Shallow water mesohabitats have their maximum extension m3 at 4 s . With increasing discharge the total area of the shallow water meso- CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT116

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Figure 4.8: Median grain diameter at individual simulation legs compared to bedslope. The displayed diameter and slope values represent medians of the values calculated for five days at the beginning of the incubation period (18th to 22nd December) across all years and hydrologic/climatic scenarios. habitat becomes smaller. However, the decrease is especially strong between m3 4 and 8 s , when the area shrinks to about half of its size at low flow. Between m3 9 and 12 s the area remains nearly the same, mostly due to the increase of total wetted area. As more parts in the riverbed overflow, larger areas with low water depth and nearly stagnant water can be found. Fast run mesohabitats m3 m3 increase in areal extent if discharge increases. From 4 s to 12 s the area of fast run mesohabitats more than doubles. Pool mesohabitats consist of deep m3 water with low flow velocity. Pools are largest at a discharge of 4 s and almost m3 disappear at the discharges of 11 s . Backwaters and riffles peak both under m3 m3 low flow conditions and are smallest at discharge of 9 s and 8 s respectively (Fig. 4.9).

Mesohabitat distribution under summer low flow conditions in the near and far future Only the climate scenario DMI_ECHAM_HIRHAM leads to predictions of increasing summer flow levels for the future, while the other nine scenarios result in decreasing flow levels (Table 4.4). Thus, we can expect decreasing summer flow levels in future, and we will base our discussion on this notion. CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT117

Figure 4.9: Distribution of mesohabitat types in relation to the total wetted m3 area of the three reaches calculated for a discharge range of 4–12 s

Within the CTRL period the total wetted area in Reach 1 is under summer low flow, on average 4734 m2; the surface area of the same stretch would decrease to 4427 m2 (±158 m2) in the near future, and 4220 m2 (±180 m2) in the far future. The mesohabitat distribution changes accordingly. The biggest change is predicted for fast runs and runs. While the relative area of fast runs is decreasing (CTRL period 77%, near future mean 53%, far future mean 36%), the area of runs is increasing (CTRL period 13%, near future mean 31%, far future mean 44%). The fraction of shallow water increases with the decreasing discharge (CTRL period 6.5%, near future mean 8.3%, far future mean 12%), and so does the area of riffles (CTRL period 0.56%, near future mean 4.44%, far future mean 4.9%). Slight changes appear for pools (CTRL period 0.79%, near future mean 0.09%, far future mean 0.03%) and backwaters (CTRL period 2.0%, near future mean 3.4%, far future mean 3.6%). In Reach 2 the total wetted area during the CTRL period is 3351 m2, calculated with the average discharge of the hydrologic/climatic scenarios it would be reduced to 3222 m2±163 m2 in the near future, and to 3015 m2±196 m2 in the far future (Table 4.4). However, the relative changes in mesohabitat composition are relatively small. Fast runs remain the most dominant habitat type (CTRL period 78%, near future mean 73%, far future mean 63%), but the fractions of runs (CTRL period 13%, near future mean 17%, far future mean 24%) and shallow waters (CTRL period 7.0%, near future mean 8.0%, far future mean 10%) expand. The changes in riffle (CTRL period 1.7%, near future mean 1.9%, far future mean 2.4%) and backwaters (CTRL period 0.10%, near future mean 0.08%, far future mean 0.03%) are small. The pool appears in the future scenarios (CTRL period 0.00%, near future mean 0.16%, far future mean 0.58%). The total wetted area of Reach 3 decreases from 7249 m2 to a mean of 7045 m2 ± 327 m2 in the near future, and to a mean of 6612 m2 ± 480 m2 CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT118 in the far future (Table 4.4). The change of the mesohabitat distribution is comparable to Reach 1. The fast runs decrease drastically (CTRL period 70%, near future mean 61%, far future mean 45%), runs (CTRL period 18%, near future mean 25%, far future mean 31%) and shallow water (CTRL period 10%, near future mean 12%, far future mean 18%) become more dominant. The less dominant habitats increase and the most expansion is found in the pool (CTRL period 0.02%, near future mean 0.51%, far future mean 2.0%) compared to riffle (CTRL period 0.99%, near future mean 1.2%, far future mean 1.4%) and backwaters (CTRL period 0.47%, near future mean 0.73%, far future mean 1.7%).

Ecological relevance of mesohabitat modelling The electrofishing survey across different types of mesohabitats showed a clear pattern of usability for the different age classes (Fig. 4.10). The YOY clearly preferred shallow water mesohabitats. Within these habitats the density was more than twice as high as it was in the next most frequently used backwater mesohabitats. In runs and riffles YOY could still be found whereas fast runs and pools were unused (Fig. 4.10a). A different pattern can be seen in subadult and adult classes. Both were found in all of the six habitat types, showing the highest density in backwaters and riffles. Whereas the subadult class was also found in runs, fast runs and shallow water, they were least frequent in pools, and adults used fast runs, pools, and runs but rarely shallow water (Fig. 4.10b and c). Combining the results of future summer low flow scenarios and habitat suitability we find a habitat area increase for YOY. This age class was mostly found in shallow water mesohabitats, which increases with a decreasing water discharge. The shallow water area in the three test reaches during the CTRL period is 1276 m2. The near future shows an average increase up to 1485 m2 and for the far future the shallow water surface is 1992 m2. This means an increase of the most used habitat type of the YOY of 36%.

4.4 Discussion

We used an interdisciplinary approach to investigate the influence of climate change on the early life stages of brown trout. Our results show different outcomes for different stages of the reproductive cycle, and at different times into the future, with especially pronounced impacts in the far future scenarios.

4.4.1 Bedload transport and morphodynamics Bedload transport predictions are often associated with a large uncertainty (Gomez and Church, 1989; Rickenmann, 2001; Barry et al., 2004; Nitsche et al., 2011). Therefore, we focused our analysis on relative comparisons of the results CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT119

Figure 4.10: Mesohabitat suitability for a YOY, b subadult and c adult. Usability index was calculated with the relative frequency of density, normalized by taking the highest value as one. of different simulation runs between the CTRL period and the future situation. We did not interpret the simulation results in terms of absolute values, but rather in terms of relative changes compared to other simulation results to derive general trends. However, it is important to consider that all predictions by the bedload routing model sedFlow are averaged for each simulation leg of the stream, with leg length varying between 50m and 200m. Variation within each leg cannot be resolved, and locally much higher or lower values can be expected. Bedload transport simulations were performed for a total river length of 20 km including about 150 legs. These legs represent a considerable range of channel slopes, grain size distributions and shear stresses, and all these parameters evolve over time during the simulation runs. On the local scale, spatially and temporally variable bed morphologies and grain sizes may induce variations in local bed slopes and shear stress covering a similar range to that of the reach- scale simulations. We may therefore speculate that the general trends identified from the bedload transport simulations at the reach scale may, at least in part, also be representative of possible changes expected to occur at local scales. Along the same lines, the minimum Shields value of 0.06 used in the sedFlow simulations at the reach scale is not consistent with the critical Shields value of 0.047 of Eq. (4.3) used for the local scale analysis with the MEM model. However, it should be noted that the sedFlow simulations were performed in CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT120 one dimension and included a calibration with bedload transport observations, while the MEM model uses a two dimensional approach on a local scale. In reality, one may expect Shields values to vary both in space (Kirchner et al., 1990) and in time (Turowski et al., 2011), and thus the use of different critical Shields values appears to be acceptable. The rainfall-runoff simulations of the CCHydro (Bernhard and Zappa, 2012) project predict an increase in winter discharges (Fig. 4.4). This prediction is the main driving factor for the simulated trends of increasing magnitudes and durations of winter scour. Across virtually all years and profiles in which scouring occurs, we observed an increase in erosion depth. The highest erosion depths tend to occur later in winter. This means that erosion occurs over longer time periods. This is not surprising, as the increased discharges will stay above the threshold for bedload transport and thus erode for a longer time in the future than in the CTRL period. Further challenges to the fish fauna for finding suitable spawning grounds may be presented by the sharper transition between stable and unstable regions predicted for the future, which implies sharper boundaries of potential spawning grounds. Most previous studies of the impact of climate change on sediment transport either focused on lowland rivers (Verhaar et al., 2010, 2011) or did not report erosion and deposition resolved for different seasons (Gomez et al., 2009). These studies are therefore of limited value for our purposes. Coulthard et al. (2012) predicted a future increase in sediment transport, especially during the winter months, for the Swale River (United Kingdom). This is in qualitative agreement with our prediction of an increase in winter erosion depths for the river Kleine Emme. Goode et al. (2013) assessed the potential future impacts of changing sediment transport on salmonid habitat on the catchment scale in the Middle Fork Salmon River (USA). They predict climate change to increase scour magnitude, which will lead to a smaller breeding success, especially for smaller-bodied fall spawners. Thus, the results of their large-scale study are in line with our detailed assessment of the Kleine Emme.

4.4.2 Spawning and incubation phase In a study of the alpine river Ybbs, a tributary of the Danube, Unfer et al. (2011) found high survival of YOY if the discharge during incubation time was lower m3 than 30 s , which compares to an annual mean high flow at the study site of m3 57 s . Higher water flow led to substantial sediment transport, resulting in egg and fry damage due to scouring. As a result, only a small proportion of YOY in the population was found the following autumn. On the other hand Unfer et al. (2011) found a positive correlation between reproductive success and high flow events, if the flow events happened during spawning time. This can be explained by a rearrangement of suitable spawning ground (Unfer et al., 2011) and a washout of deleterious fine sediment (Zeh and Dönni, 1994) before the incubation actually starts. For the Kleine Emme, the discharge during spawning CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT121

m3 and incubation time might increase by about 2 s in the near future and by m3 about 3 s in the far future (Fig. 4.4). As a direct consequence, the lowest bed elevation will occur later in the year and scouring depths will increase. In our simulations, the entire spawning ground is 100% unstable at discharges smaller m3 than 26 s (Table 4.3). Peak ﬂows of this magnitude presently occur on average about six times during the incubation time (FOEN, 2013), but will most likely occur more often in the future. In our scenario it is therefore likely that the stable spawning habitat areas might decrease in the future and erosion depths will more frequently exceed the average egg burial depth.

4.4.3 Parr phase Another critical period in the life cycle of salmonids occurs when juvenile fish emerge from the gravel and establish their feeding territories. Considering the average water temperature during incubation time of about 5◦C in the Kleine Emme, this happens in the study reach during April and May. Feeding habitats are usually in the direct surroundings of the redd, and after settling the fish do not typically disperse till autumn (Egglishaw and Shackley, 1980; Rimmer et al., 1983, 1984; Armstrong et al., 1994). Habitat quality near spawning grounds is therefore crucial for the development of juveniles. Typically, the flow velocity m near the snouts of brown trout parr smaller than 7 cm is between 0 and 0.1 s and they can rarely be found in parts of the stream with flow velocities exceeding m 0.5 s (Heggenes et al., 1999). The preferred depth of parr is between 0.05m and 0.3m and both, preferred depth and flow velocity, increase with fish size (Greenberg, 1994; Maki-Petäys et al., 1997; Riley et al., 2009). Our fishing survey at the Kleine Emme River based on modeled mesohabitats confirmed these values from the literature. We found a clear age class distribution. The m YOY were most abundant in shallow waters (flow velocity < 0.2 s , flow depth < 0.4m). Subadult and adult fish showed a more diverse distribution, with increased use of high energy habitats like riffles and fast runs. Both of these two age classes were mostly found in backwaters, which are by definition low energetic habitats. However, an exclusive focus on depth and flow velocity does not do justice to the whole complexity of a habitat. Other major parameters like substrate, vegetation cover, competition or predation can strongly influence the distribution of fish in a stream. On the other hand, the importance of shallow, slow flowing water for recruitment, and the movement into deeper parts of a river with increasing growth has been shown in many other studies (e.g. Bardonnet and Heland, 1994; Crisp, 1996; Heggenes, 1996), and these findings are consistent with our results. We furthermore predict more pronounced summer low flows, which can lead to higher habitat diversity, especially due to an increase in shallow water habitats (see Hauer et al., 2012). Such an increase in suitable habitat area could lead to a higher carrying capacity of the habitat of brown trout parr during early summer, and reduce self-thinning effects for early free living life stages (Elliott, 1994; Milner et al., 2003). CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT122

4.5 Conclusions and possible mitigation measures

Predictions of how salmonids will adapt to a changing environment driven by climate change are difficult to make due to the complex interplay of many factors. For example, changing temperature may influence the onset of spawning (Wedekind and Küng, 2010), sex determination (Craig et al., 1996; Baroiller and D’Cotta, 2009), fry development (Elliott, 1994), prey availability (Crozier et al., 2008) or diseases (Wedekind et al., 2010). Seasonal variation in discharge also relates to the initiation of migration (Banks, 1969; Jonsson, 1991) and spawning (Lobón-Cerviá, 2004). We have focused on the effect of climate change on discharge and bedload transport during the incubation time, and the availability of physical habitat later in the year. From this point of view, the results indicate two different and important outcomes for different life stages. Whereas future conditions during incubation time may become less favorable for brown trout survival due to higher and more frequent floods in the winter season, it is possible that conditions later in the year become more favorable. As was suggested by Goode et al. (2013) and Hauer et al. (2012), predicted outcomes on early brown trout development depend strongly on river morphology and the flow regime. In general, a natural riverbed has the ability to buffer the power of a flood, and maintain habitat diversity. This, on the other hand, is not true for embanked and artificially channelized parts of a river. There, water level increases with increasing discharge up to bankfull stage and beyond. The corresponding increases in stream power can lead to high erosion and hence a predominance of high-energy habitats. Depending on timing of the flooding, this will lead to egg scour and/or displacement of juvenile fish. Our results indicate that in the future small tributaries may become more important for spawning, due to their lower discharge and flood power compared to the main river stem. The fact that many smaller tributaries in Switzerland and elsewhere are blocked by barriers (e.g. Zeh Weissmann et al., 2009; Yamamoto et al., 2004; Raeymaekers et al., 2009) that will have to be removed if fish are to be able access these areas. We conclude that the restoration of lateral and longitudinal connectivity through the removal of artificial embankments and tributary weirs should be a high priority of rehabilitation works in these systems to maintain essential spawning habitat under future climates. CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT123 ] % [ 50 mm m 2 d m and two different 3 s m ] % [ 20 mm m 2 d m ] % [ 50 mm m 2 d m ] % [ 20 mm m 2 d m ] = 50 mm) % [ m d 50 mm m 2 d m = 20 mm or Reach 1 Reach 2 Reach 3 m ] d % [ 20 mm m 2 d m i 3 grain size diameters ( Total stable area in square meters and stable area in percentage calculated with discharges between 4 and 26 s m dischargeh Stable Stable45 Stable6 Stable7 67.70 Stable8 Stable 67.709 100 63.6710 100 Stable 49.74 94.0511 Stable 67.70 30.08 73.4712 67.70 13.19 44.43 67.70 10014 Stable 3.16 19.48 67.70 100 Stable16 100 67.7018 0 4.67 100 Stable 32 67.7020 0 23.05 100 Stable 7.0622 0 67.70 100 40.88 56.74 0 3.6324 0 12.50 0 100 1.4626 0 6.44 56.39 56.39 0 0 56.39 67.70 0 2.59 0 100 100 0 67.70 0 56.39 100 0 100 0 64.20 0 52.78 100 0 0 100 60.83 0.54 94.83 0 93.60 0 11.88 0 89.85 0 0 0 2.65 17.55 1.03 0 49.99 0 0 0 0 0 88.65 0 1.52 47.62 0 0 0 6.7 0 0 84.45 0 0 0 0 0 32.92 2.69 0 0 0 0 39.23 2.69 0 0 0 3.97 26.58 69.57 0 2.14 18.1 3.97 0 1.6 47.14 15.12 0 32.10 0 3.16 0 26.81 11.6 2.36 0 0 0 20.57 1.07 0 9.27 0 0 0 0.54 0 1.58 0 16.44 0 0 0 0.80 0 6.6 0 0.54 2.87 0 11.70 0 0 0.80 0 5.09 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Table 4.3: Stability analysis of possible suitable spawning areas of brown trout using variable grain sizes CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT124 2 m Shallow Water Back-water Pool Run Fast Run Riffle Total wetted area i 3 s m h FF; 4.45FF; 5.08 20.64FF; 4.96 15.51FF; 7.05 4.03 18.58FF; 11.77 3.84 9.45FF; 7.39 0.02 7.59 3.92 52.71FF; 9.09 15.56 0.01 9.56 54.64 3.55FF; 9.02 19.67 7.03 0.01 3.3 8.96 53.43 3979.58 FF; 7.68 17.22 6.32 0.02 8.92 4020.79 3.57FF; 50.17 9.61 6.84 32.76 0.1 9.73 3999.11 3.43 25.98 4.05 0.02 58.53 8.57 3.45 47.79 4156.97 35.47 0.03 4.51 3.52 36.64 4502.52 46.66 3.59 0.02 3.38 37.19 4213.92 46.24 4.27 0.02 45.95 4353.51 37.07 4.18 0.05 34.27 4347.41 49.52 3.71 4243.19 4.21 4384.86 control period 13.09 6.54 2.04 0.79 13.42 76.64 0.56 4733.86 Climate model Discharge SMHI_BCM_RCA NF; 13.57 6.99 3.14 0.17 21.51 64.19 4 4567.84 SMHI_ECHAM_RCA NF; 11.61 7.69 3.34 0.09 26.54 57.88 4.46 4497.06 MPI_ECHAM_REMO NF; 11.06 7.26 3.38 0.08 28.57 56.07 4.64 4443.29 ICTP_ECHAM_REGCM NF; 11.97 7.48 3.28 0.11 25.44 59.32 4.37 4507.63 DMI_ECHAM_HIRHAM NF; 11.07 7.37 3.35 0.07 28.4 55.93 4.88 4440.99 SMHI_HadCM3Q3_RCA NF; 12.87 7.34 3.27 0.13 23.27 62.1 3.91 4544.86 KNMI_ECHAM_RACMO NF; 13.0 7.2 3.28 0.16 22.8 62.59 3.96 4546.87 ETHZ_HadCM3Q0_CLM NF; 8.51 9.03 3.44 0.02 40.75 42.8 3.96 4312.34

CNRM_ARPEGE_ALADIN NF; 9.29 8.72 3.41 0.02 35.9 47.7 4.24 4367.31

HC_HadCM3Q0_HadRM3Q0 NF; 5.32 14.16 3.76 0.01 54.93 21.16 5.98 4041.56 ec 1 Reach Table 4.4: Mesohabitat distributionof in the the different three modeled climate models river reaches under summer low flow conditions for the control period and the predictions CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT125 2 m Shallow Water Back-water Pool Run Fast Run Riffle Total wetted area i 3 s m h FF; 4.1FF; 4.65 13.71FF; 4.38 12.38FF; 6.51 13.29 0FF; 10.6 0 10.6FF; 6.81 0 7.22FF; 1.34 8.27 32.33 8.95 1.3 0 48.74FF; 8.13 31.01 8.72 1.28 0.1 51.67FF; 3.88 7.06 31.53 2726.75 8.79 50 0FF; 3.64 0.78 8.76 24.15 2816.73 0 9.8 0.04 62.59 3.89 14.47 8.35 2777.74 0.04 1.87 0.56 76.41 23.73 0.04 3026.81 65 19.47 0.01 1.8 70.13 0.03 0.04 3282.97 19.76 69.74 1.6 1.76 0.44 3005.89 22.67 3138.09 1.64 0.02 65.35 18.75 3126.06 71.17 1.72 3057.14 1.68 3178.58 control period 11.87 6.96 0.1 0 12.85 78.39 1.71 3351.33 Climate model Discharge SMHI_BCM_RCA NF; 12.14 6.98 0.1 0 12.62 78.68 1.61 3365.63 SMHI_ECHAM_RCA NF; 10.63 6.83 0.1 0 14.54 76.74 1.78 3272.86 MPI_ECHAM_REMO NF; 10.13 7.49 0.1 0 15.21 75.56 1.64 3255.26 ICTP_ECHAM_REGCM NF; 10.92 7.3 0.12 0 14.21 76.58 1.79 3307.77 DMI_ECHAM_HIRHAM NF; 10.18 7.51 0.1 0 15.12 75.6 1.67 3258.89 SMHI_HadCM3Q3_RCA NF; 11.71 6.89 0.1 0 13.15 78.12 1.74 3342.34 KNMI_ECHAM_RACMO NF; 11.84 6.95 0.1 0 12.9 78.39 1.66 3350.4 ETHZ_HadCM3Q0_CLM NF; 7.8 8.93 0.04 0.09 21.11 68.14 1.69 3106.77

CNRM_ARPEGE_ALADIN NF; 8.44 8.48 0.04 0.04 19.36 70.34 1.76 3149.8

HC_HadCM3Q0_HadRM3Q0 NF; 4.95 11.72 0 1.31 29.91 53.8 3.26 2858.65 ec 2 Reach Table 4.4: Continued. CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT126 2 m output; for the near future 2021-2050 (NF) and the far future 2070-2099 (FF), 2 Shallow Water Back-water Pool Run Fast Run Riﬄe Total wetted area i 3 s m h FF; 3.98FF; 4.51 2.03FF; 4.28 1.82FF; 6.33 1.91 29.44FF; 10.24 1.28 33.6FF; 6.62 31.93 1.07 3.83 31.84FF; 8.01 4.49 32.57 1.4 44.36 3.48FF; 7.85 32.95 3.53 28.28 64.42 1.16 3.56FF; 5856.37 6.86 31.86 3.92 1.18 2.63 25.01FF; 45.52 8.49 23.34 6057.92 1 0.06 25.82 1.34 52.4 5968.23 0.49 31.8 1.23 51.74 18.88 2.39 10.62 31.58 6606.17 0.86 7154.12 46.17 0.73 31.73 0.65 0.95 54.6 18.03 31.43 0.67 6688.09 2.05 13.47 6984.8 0.83 30.49 13.73 0.36 6963.22 0.61 18.17 6814.23 12.71 7030.83 control period 11.47 10.12 0.47 0.02 18.09 70.3 0.99 7249.26 Climate model Discharge SMHI_BCM_RCA NF; 11.71 1.08 71.38 17.05 0.02 0.48 9.99 7263 SMHI_ECHAM_RCA NF; 10.31 1.09 64.79 23.02 0.05 0.49 10.56 7158.37 MPI_ECHAM_REMO NF; 9.82 1.06 61.94 25.34 0.08 0.51 11.07 7128.88 ICTP_ECHAM_REGCM NF; 10.58 1.09 66.62 21.35 0.04 0.48 10.42 7183.98 DMI_ECHAM_HIRHAM NF; 9.87 1.07 62.22 25.14 0.07 0.51 11 7133.69 SMHI_HadCM3Q3_RCA NF; 11.34 1.1 69.81 18.41 0.02 0.47 10.19 7241.09 KNMI_ECHAM_RACMO NF; 11.46 0.99 70.28 18.17 0.02 0.47 10.07 7248.45 ETHZ_HadCM3Q0_CLM NF; 7.56 1.26 49.84 32.13 1.19 0.72 14.86 6931.62 CNRM_ARPEGE_ALADIN NF; 8.18 1.15 53.24 31.41 0.54 0.64 13.03 6998.06 HC_HadCM3Q0_HadRM3Q0 NF; 4.83 1.79 35.45 34.04 3.13 2.57 23.01 6164.32

Control period 1980-2009 andmesohabitat climate distribution models in with percentage a of AB1 total CO wetted area and total wetted area in square meters of each river reach ec 3 Reach Table 4.4: Continued. CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT127

Acknowledgements

The investigations related to the fish habitat and the bedload transport modeling were supported by a grant of the Swiss National Science Foundation (NRP 61 project SEDRIVER contract no. 406140-125975/1) to DR, AP, and JMT. The hydrological impact study has been supported by a grant from the Swiss Federal Office for Environment (CCHydro). We are indebted to the EU FP6 Project ENSEMBLES (Contract 505539) and MeteoSwiss for providing us access to all necessary data. Many thanks go to Reto Haas for support on GIS and in the field. We are also grateful for field support to Salome Mwaiko, Cristina Hertz and Brigitte German. Furthermore we thank Catherine E. Wagner for reviewing the manuscript. Appendix for chapter 4

● control period near future far future 0.030

0.020 ● ● 0.010

● ●

● ● ● ● ● ● Maximum erosion depth duringMaximum incubation [m] 0.000 Perc2.5 Perc25 Perc50 Perc75 Perc97.5

Temporal percentiles

Figure 4.A1: Spatial 50th percentile of maximum scour depth during incubation. Temporal percentiles refer to years within the study period. The boxplots reﬂect the variability over the available hydrologic/climatic scenarios. The 50th percentile value separates those 50% reaches with larger erosion depths from those 50% reaches with smaller erosion depths. The abscissa represents the temporal percentiles of erosion depth. Years on the left part of the ﬁgure have little winter erosion, years on the right part have more intense winter erosion.

128 CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT129

● 0.20 ● control period near future far future 0.15

● ● 0.10 0.05

● ●

● ● ● ● ● ● Maximum erosion depth duringMaximum incubation [m] 0.00

Perc2.5 Perc25 Perc50 Perc75 Perc97.5

Temporal percentiles

Figure 4.A2: Spatial 84th percentile of maximum scour depth during incubation. Temporal percentiles refer to years within the study period. The boxplots reﬂect the variability over the available hydrologic/climatic scenarios. The 84th percentile value separates those 16% reaches with larger erosion depths from those 84% reaches with smaller erosion depths. The abscissa represents the temporal percentiles of erosion depth. Years on the left part of the ﬁgure have little winter erosion, years on the right part have more intense winter erosion. CHAPTER 4. CLIMATE CHANGE IMPACT ON TROUT RECRUITMENT130

● control period near future far future

0.3 ● ● 0.2 0.1

● ●

● ● ● ● ● ● ● Maximum erosion depth duringMaximum incubation [m] 0.0

Perc2.5 Perc25 Perc50 Perc75 Perc97.5

Temporal percentiles

Figure 4.A3: Spatial 97.5th percentile of maximum scour depth during incubation. Temporal percentiles refer to years within the study period. The boxplots reﬂect the variability over the available hydrologic/climatic scenarios. The 97.5th percentile value separates those 2.5% reaches with larger erosion depths from those 97.5% reaches with smaller erosion depths. The abscissa represents the temporal percentiles of erosion depth. Years on the left part of the ﬁgure have little winter erosion, years on the right part have more intense winter erosion. REFERENCES 131

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Spectral characteristics of bedload transport

Abstract

Fluvial bedload transport is one of the main processes in the morphodynamics of mountain catchments with various implications for the scientific and civil engineering practice in terms of e.g. bedrock erosion, reorganisation of spawning grounds or flood hazard management. However, only little is known about the temporal dynamics of this natural process, which may differ considerably from the dynamics of its driving factor discharge. Previous studies have either focussed on individual events and isolated temporal scales or were based on experimental flume data, which often lack the complexity and interactions of a natural system. In this contribution, we study high resolution time series of bedload transport data from an alpine mountain stream by means of spectral analysis. Four scale ranges of different temporal dynamics are distinguished and described. That means in this pilot study we have exemplarily applied a method for structurising the analysis results of bedload transport time series. Any future study of similar bedload time series data can make use of the presented method and concentrate right away on the peculiarities of the specific data set, as the overall behaviour which can be expected in general has been presented and discussed in this study. In the presented study, for the first time, discharge- independent autoregressive dependency of bedload transport has been attributed to a clearly defined band of frequencies in field data. Furthermore we make suggestions for an optimised measurement strategy, based on the structure of the analysed data set.

5.1 Introduction

The rolling, sliding or saltating transport of sediment grains along river beds is summarised as bedload transport. In mountain streams it is one of the dominant

140 CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 141 1200 0.0 /s] 3 1.0 2.0 1000 2.0 800 precipitation [m 1.5 /s] 3.0 Erlenbach 3 | precipitation 600 discharge geophone impulses 1.0 discharge [m 400 geophone Impulses [−] 0.5 200 0 0.0

Fri 00:00 Sat 00:00 Sun 00:00 Mon 00:00

2013 May 31 to Jun 02

Figure 5.1: Overview over four examples of bedload transport events in the Erlenbach at the transition from May to June 2013. 1200 0.0 /s] 3 1.0 2.0 1000 2.0 800 precipitation [m 1.5 /s] 3.0 Erlenbach 3 | precipitation 600 discharge geophone impulses 1.0 discharge [m 400 geophone Impulses [−] 0.5 200 0 0.0

Fri 22:00 Sat 00:00 Sat 02:00 Sat 04:00 Sat 06:00 Sat 08:00

2013 May 31 to Jun 01

Figure 5.2: Detailed view of an example bedload transport event in the Erlenbach at the transition from May to June 2013. geomorphological processes and has various implications in the fields of e.g. river ecology (e.g., Unfer et al., 2011), bedrock erosion (e.g., Turowski, 2012) and natural hazard management (e.g., Badoux et al., 2014). However, the bedload transport process is still mainly described by averaged transport equations (e.g., Rickenmann, 2001; Wilcock and Crowe, 2003; Recking, 2010). These transport equations are not capable to capture the temporal variability and dynamics, which are characteristic of the process (e.g. Fig. 5.1 and 5.2). This deficiency of the commonly used transport equations demonstrates how little is known about the temporal dynamics of bedload transport. In the following we will give a short summary of previous studies on this topic. Water discharge is the main driving factor for fluvial bedload transport. Nev- ertheless, considerable differences can be observed in the temporal dynamics of discharge and bedload transport. These differences can be subdivided into two groups: (I) Under conditions of constant discharge, bedload transport shows CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 142

fluctuation, even though water and sediment are fed to the system at a constant rate such as in flume studies (e.g. Iseya and Ikeda, 1987). (II) Under conditions of temporally changing discharge, bedload transport shows hysteresis, i.e. the bedload transport rates during the rising limb of a hydrograph differ systematically from the transport rates during the falling limb (e.g. Mao, 2012). The fluctuations of bedload transport under constant feeding conditions (I) have been documented in numerous flume studies (e.g. Iseya and Ikeda, 1987; Kuhnle and Southard, 1988; Frey et al., 2003; Recking et al., 2009; Ghilardi et al., 2014a). In these studies, the bedload transport rate has been described as part of a fluctuating system of interacting local state variables, which include the bed morphology, the grain size distribution of the bed and the channel gradient. Temporal maxima of total bedload transport rate were associated with high transport rates of fine grained sediment, with gentle slopes and with smooth bed surfaces containing only few coarse grains. Temporal minima of total bedload transport rates were associated with low transport rates of fine grained sediments, with steep slopes and with rough, congested bed surfaces consisting almost only of coarse grains. Some authors have sugggested the presence of a wide grain size distribution to be a prerequisite for bedload transport fluctuations, as experiments with uniform grain size distribution exhibit negligible fluctuations of bedload transport (Recking et al., 2008, 2009). Vertical and longitudinal sorting of grain sizes (Iseya and Ikeda, 1987) has been suggested together with the mobility increase of coarse particles in the presence of transported fine particles (Frey et al., 2003; Recking et al., 2009) or together with the dynamics of bedforms (Kuhnle and Southard, 1988; Ghilardi et al., 2014a) as potential causes for bedload transport fluctuations. The amplitudes (Iseya and Ikeda, 1987; Kuhnle and Southard, 1988; Recking et al., 2009; Ghilardi et al., 2014a,b) as well as the period (Ghilardi et al., 2014a,b) of the fluctuations decrease with increasing stream power. In addition, Ghilardi et al. (2014a,b) showed that an increase in the spatial density of immobile boulders also causes decreasing amplitude and period of bedload transport fluctuations. The bedload transport fluctuations exhibit a skewed distribution of transport rates, i.e. the abundance of occurences of high and low transport rates are different (Bunte and Abt, 2005; Singh et al., 2009; Turowski, 2010, 2011). Based on field observations, Bunte and Abt (2005) demonstrated the practical consequence of this skewed distribution, that short sampling times (few minutes instead of several tens of minutes) may considerably distort the estimation of actual transport rates. For high discharges the short sampling time caused an underprediction of the actual transport rates, while at flows near the incipient motion of gravel particles the short sampling time caused an overestimation of actual transport rates. These observations have been confirmed in the flume study of Singh et al. (2009), who derived an expression for the dependence of estimated transport rates on sampling time. Furthermore, the authors applied the multifractal formalism to quantify the qualitative observation that time series of bedload transport rate tend to be burstier (i.e. more dominated by rare but CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 143 extreme variations) for low discharge conditions as compared to high discharge conditions. In his literature review, Hoey (1992) distinguished the governing factors for different spatial and temporal scales of bedload fluctuations. Further on, he discussed different conceptual models for the reproduction of observed fluctuations. In a recent contribution, Heyman et al. (2013) showed from the statistics of a Markov process of individual grains that the fluctuations of bedload transport may be reproduced without considering any grain size-dependent effects, if the entrainment of grains by grain-grain interaction is considerably more efficient than the entrainment of grains by the flowing water. Their model is capable to reproduce the reduced fluctuation intensity for high discharges. Bedload hystereses (II), i.e. systematically differing bedload transport rates during the rising and falling limb of a hydrograph, have often been observed in the field (e.g. Kuhnle, 1992; Moog and Whiting, 1998; Habersack et al., 2001; Turowski et al., 2009; Swingle et al., 2012; Mao et al., 2014) and in the flume (e.g. Lee et al., 2004; Humphries et al., 2012; Mao, 2012). In these studies, a wide variety of processes has been suggested as potential causes for the observed hystereses. The first systematic study of potential causes of bedload transport hysteresis under conditions of unlimited sediment supply was provided by Mao (2012). In this set of experiments, the bedload transport rate as well as the relative fraction of active grains did exhibit a clockwise hysteresis, i.e. more bedload was transported during the rising limb of the hydrographs than during the falling limb. Just like in the previously mentioned studies of bedload transport fluctuations, the higher transport rates are accompanied by smaller diameters of transported material. Therefore, the transported grain diameters showed a counter-clockwise hysteresis. Such a counter-clockwise hysteresis is also observed for the reference shear stresses. That means during the rising limb grains are entrained already at smaller shear stresses than during the falling limb. This effect seems to be caused by a restructuring of the channel bed. Even though the grain size distribution of the bed surface stayed the same during both limbs of the hydrograph, the standard deviation of bed elevations as a measure of bed roughness increased from the rising to the falling limb and thus showed a counter-clockwise hysteresis. Clockwise bedload transport hysteresis is often attributed to the depletion of transportable material, but the study of Mao (2012) demonstrated how a clockwise hysteresis can occur even under conditions of unlimited sediment supply. For their field data, Swingle et al. (2012) showed the existence of hysteresis on an intra-seasonal as well as on an event scale. However, the authors focussed only on isolated temporal scales, neglecting any other temporal dynamics of the system. Lane et al. (1996) and Mao et al. (2014) analysed the bedload transport dynamics in glacier fed mountain streams. They showed that the patterns of the bedload transport hystereses in the daily melt water pulses depend on the position in the stream relatively to the glacier snout (Lane et al., 1996) and that the direction of the hystereses changed from a predominantly clockwise pattern during the early melting period (i.e. snowmelt period) to a predominantly CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 144 counter-clockwise pattern during the late melting period (i.e. late glaciermelt period) (Mao et al., 2014). In summary, all previous studies on the temporal dynamics of bedload transport were either based on flume investigations (often using a constant discharge) or focussed on the analysis of individual transport events. In this study we present the spectral analysis of an up to now unique dataset including a time series of several years of field measurements of bedload transport at a resolution of one minute. For the first time the temporal dynamics of bedload transport are analysed and compared to the dynamics of discharge based on field data that go beyond the individual event. In this pilot study, we distinguish and characterise four different scale ranges of bedload dynamics. By the description and exemplary application of this method for structurising the analysis results of bedload transport time series, we provide the base for future studies of similar datasets, which can be expected to play an important role in upcoming bedload transport research. Furthermore, we make suggestions for an optimised measurement strategy, based on the structure of the analysed data set.

5.2 Material and methods

5.2.1 Study site The Erlenbach is a steep stream in central Switzerland (Tab. 5.1). Its channel is characterised by dominant step-pool morphology (Molnar et al., 2010) and sediment is continuously fed to the stream by creeping and sliding hillslopes (Schuerch et al., 2006). On average in the Erlenbach, there are about 20 bedload transport events per year (Rickenmann and McArdell, 2007; Turowski et al., 2009; Rickenmann et al., 2012). The most intensive events are triggered by summer thunderstorms (Turowski et al., 2009). Debris flows have never been observed in the Erlenbach as its channel gradient is not steep enough. Bedload transport and discharge characteristics are measured in the Erlenbach for more than 25 years (Hegg et al., 2006; Rickenmann et al., 2012). Since July 2009 continuous time series of bedload transport intensity are recorded at 1-minute resolution using a Swiss plate geophone system (Rickenmann et al., 2014). Since 1981 continuous time series of flow depth (which can be used to estimate discharge) and precipitation are recorded at 10-minute resolution. Since July 2011 the continuous time series of flow depth is available at 1-minute resolution. The 10-minute resolution data display the current sensor values at the time of recording. For the 1-minute resolution data, the raw time series of sensor values with its resolution of 1 second is temporarily stored in a measurement computer. Afterwards an algorithm is applied to aggregate this raw time series to the final 1-minute resolution time series of bedload transport intensity and average flow depth. In this study, we use the data from July 2009 to December 2013 for any analysis only considering bedload transport and we use the data from July 2011 to December 2013 for any analysis considering bedload transport and discharge. CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 145

Table 5.1: Catchment characteristics of the Erlenbach

Catchment parameter Value h i Catchment area km2 0.7 Maximum elevation [m] 1655 Minimum elevation [m] 1110 Average channel gradient [%] 18 Average annual precipitation [m] 2.3 Average annual discharge volume 106 m3 1.24 h m3 i Average annual discharge s 0.04 h m3 i Average annual peak discharge s 2.00 Average annual sediment transport m3 480

The Erlenbach may be seen as prototype for a thunderstorm driven steep headwater stream with intense channel-slope interactions and dominant step-pool morphology. Details on the catchment characteristics, ﬁeld instrumentation, measurement techniques and measurement accuracies are given elsewhere (Hegg et al., 2006; Turowski et al., 2009; Molnar et al., 2010; Rickenmann et al., 2012; Badoux et al., 2012; Turowski et al., 2013; Beer et al., 2014) and the reader is referred to these publications for further information.

5.2.2 Bedload transport measurements For bedload transport measurements, steel plates of deﬁned dimensions (length: 0.36 m; width: 0.50 m; thickness: 0.015 m) are installed in the streambed covering a complete transect of the channel (Rickenmann et al., 2012). In the centre underneath each plate, a sensor is mounted, which transforms the vibration of the plate caused by the impacts of transported sediment grains into an electric potential. The voltage peaks exceeding a predeﬁned threshold, are counted as impulses. For such a measurement system Rickenmann et al. (2014) have introduced the term “Swiss plate geophone system”. Previous studies (Etter, 1996; Rickenmann, 1997; Rickenmann and McArdell, 2007, 2008; Rickenmann et al., 2012) have shown that the number of impulses is proportional to the amount of sediment transported across the sensor plate. Therefore, we will treat bedload impulses as proxy for bedload transport rate and use the terms “bedload impulses”, “bedload impulse counts” and “bedload transport” as synonyms in the following. For this study we use the sum of the impulses of all sensor plates of a complete transect. CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 146

5.2.3 Time series analysis Here, we give only a short summary of the classic tools of spectral analysis, which we use in our study including spectral density, coherence and phase functions. For more detailed descriptions including the mathematical expressions, the reader is referred to the corresponding literature (e.g. Shumway and Stoffer, 2011). The application of the Fourier transformation from time domain to frequency domain yields the power spectral density function. This function illustrates how the variance of the signal is distributed over different frequencies. Similarly, the coherence function shows the distribution of linearity between two signals over different frequencies. Linearity means that a change in one signal is accompanied by a proportional change in the other signal, with high coherence values indicating a strong dependence between the two signals. If one signal is a linear function of the other signal, the coherence equals 1 for alle frequencies. In contrast, the coherence equals 0, if there is no dependence between the two signals. Among the most important causes for coherence values different from 1 are (a) non-linear behaviour of the system, (b) uncorrelated noise influencing either one or both signals, and (c) one of the signals being influenced by another signal that has not been considered. The information given by the coherence is complemented by the phase function, which represents the average delay between two signals at different frequencies. In the phaseshift context, we will use the terms “lead” and “lag”. If some variable a leads in front of some other variable b that means that a shows some behaviour in time domain (e.g. reaching a peak value) usually before b will show some comparable behaviour. If a lags behind b that means that a shows some time-domain-behaviour usually after b has already shown some comparable behaviour. We performed our analysis using the R statistics software package (R Core Team, 2014). As a first step we visually checked plausibility of the discharge and bedload transport time series. We used data from the 10-minute-resolution discharge dataset to replace missing or implausible values in the 1-minute- resolution discharge time series. In this replacement we interpolated linearly between the 10 minutes values and paid attention to have a smooth transition between the original and replaced parts of the new time series. In the bedload transport time series, we replaced missing or implausible values with zero impulse counts. Finally we standardised i.e. we divided each variable by its standard deviation, in order to roughly equalise the overall level of all spectral density functions and thus concentrate on their shape instead of level. In addition, we calculated a binary transport variable, which is 1, whenever the observed impulse count is larger than zero, and which is 0 otherwise. For each variable (i.e. precipitation, discharge, geophone impulse counts and binary transport) we calculated the spectral density function. For discharge and observed impulse counts, we additionally calculated the coherence and phase functions. In all these calculations, the mean and linear trend of the signal was CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 147 subtracted from the series; a split cosine bell taper was applied to 10 % of the time series at its beginning and end; and two smoothers were applied to smooth the output functions. The first smoother, a modified Daniell smoother (i.e. a box shaped smoother with the first and last filter weight equalling half the value of any other filter weight) with a width of 50 datapoints, was used to smooth the low frequency part of the spectrum and has a constant width in linear frequencies. The second smoother, a cosine window, was used to smooth the high frequency parts of the spectrum and has a constant width in logarithmised frequencies of [0.2 log10(ω)], in which ω denotes frequency. We did our calculations for the complete study period as well as for the individual years and months. In this, each temporal subsample (complete study period, year, month) is standardised i.e. it is divided by its own standard deviation before any spectral analysis is applied. The results of the different years are displayed as individual lines, while for the months the interquartile range of the calculation results is shown. The analysis of the individual years can be seen as a data-splitting benchmark test. The comparison of the individual subsamples (complete period with the individual years and individual years with each other) reveals whether any observed feature is a persistent characteristic that is observed in all subsamples or just a random artefact that occurs only in one specific subsample. Furthermore, the comparison of the long subsamples with the interquartile range of the individual months helps to distinguish the behaviour for different event magnitudes. Any spectral or cross-spectral calculation of an individual year or the complete study period is an average measure i.e. value based statistics of the studied time series. In contrast, the interquartile range of the corresponding individual months is a robust measure i.e. rank based statistics of the studied time series. This implies that the interquartile range of the months’ results exhibits the behaviour of the common and small events while the results of the complete years or study period exhibit the behaviour of the rare and large events. To quantify the decrease in variability for increasing signal frequencies we fitted power law functions to the spectral density of the complete study period for different variables and reported the spectral slopes of the individual fits. For the binary transport we fitted the slope to the data at frequencies corresponding to periods ranging from 3 hours to 1 hour. For all other variables we used the periods ranging from 3 hours to 20 minutes. The mentioned period ranges have been selected visually as those period ranges in that the spectral density functions can be approximated by a simple power law. To check the significance of observed spectral behaviour, we compared the spectral density functions of bedload impulses with stochastic realisations of white noise, which still captures the dependency between discharge and bedload transport as well as parts of the autoregressive dependency of discharge. For this, we first selected those time steps with bedload impulse counts larger than zero. Then we defined 100 discharge bins, with each bin containing 1 % of the discharge values of the selected time steps. Within each discharge bin, CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 148

Table 5.2: Names and periods of the four scale ranges discussed in this manuscript

Scale range name period range inter-event longer 15 h event 15 h – 1 h systematic intra-event 1 h – 5 min random intra-event shorter 5 min

all pairs of discharge and (non-zero) bedload transport rates were reshuffled. This reshuffling algorithm preserves the following properties of the original time series: (i) the occurence or absence of bedload transport at a given time, (ii) the rough magnitude of discharge at a given time, and (iii) each combination of discharge and bedload transport. For 500 reshuffle realisations, the spectral density functions were calculated and representative percentiles were compared to the observed spectral density function of discharge and bedload impulses. In addition, we compared the spectral density functions of bedload impulses with block randomisation realisations in which the order of the bedload transport events as well as the inter-event durations have been reshuffled (cf. appendix 5.A1); and for a more reliable interpretation of the observed spectra, we analysed the spectral behaviour of artificial time series with defined properties (cf. appendix 5.A3).

5.3 Results

5.3.1 Power spectral density Observations In the spectrum of the Erlenbach data (Figs. 5.3 and 5.4), at least four scale ranges of different temporal dynamics may be distinguished. The names and periods (i.e. wavelengths) of these four scale ranges are given in table 5.2. Even though the names of table 5.2 anticipate parts of the discussion, we will use them in the manuscript as they contribute to the clarity of the text. The inter-event scale range covers the low frequencies of periods longer than about 15 hours. In this range the spectral density of bedload impulses and binary transport is roughly the same for all frequencies resulting in a spectral slope of zero. The event scale range extends from about 15 hours to about 1 hour. In this range the discharge, the bedload impulses and the binary transport exhibit comparable spectral behaviour. However, the individual spectral slopes differ considerably. The spectral slope of discharge SQ is by a difference of 2 steeper than the spectral slope of precipitation SPr: CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 149

SQ = SPr − 2. (5.1)

The spectral slope of bedload transport is by far more gentle than SQ. For the intra-event scale range i.e. at any period shorter than about 1 hour, the spectral density of the binary transport is on average the same resulting in a spectral slope of zero. The intra-event scale range can be subdivided further in a systematic and a random section. The systematic intra-event scale range extends from about 1 hour to about 5 minutes. In this range the bedload impulses deviate considerably from the spectral behaviour of the discharge. Discharge exhibits a spectral density that is a smooth function of frequency. In contrast, the bedload impulses show various spectral wiggles (i.e. regions that exhibit a higher spectral density than its direct vicinity) at diﬀerent periods. The random intra-event scale range covers the periods shorter than about 5 minutes. In this range the spectral density of the bedload impulses is on average equal for all frequencies resulting in a spectral slope of zero (Figs. 5.3 and 5.4).

Reshuffled impulse counts benchmark test In the inter-event and event scale ranges, the reshuffled discharge and bedload transport time series show a similar spectral behaviour as the observed time series (Fig. 5.5). In the high frequency part of the intra-event scale ranges, the reshuffled discharge and bedload transport time series exhibit white noise behaviour (expressed by a spectral slope of zero). The reshuffled realisations of discharge are similar compared to each other, which can be seen from the small difference between spectral densities of the 2.5 and 97.5 percentiles. In contrast, for periods shorter than roughly five hours, the individual bedload transport realisations differ considerably from each other, which is expressed by the notable difference between spectral densities of the 2.5 and 97.5 percentiles (Fig. 5.5). Most interesting is the behaviour at frequencies corresponding to periods of 20 to 40 minutes. At these frequencies, the bedload transport exhibits white noise behaviour, while the discharge still shows a considerable spectral slope of autoregressive dependency. (An autoregressive dependency describes the fact that any value in a time series (at least partially) depends on its preceeding values.) Furthermore, at these frequencies, the bedload transport realisations show the largest relative differences among each other, visible by the difference between spectral densities of the 2.5 and 97.5 percentiles.

5.3.2 Coherence and phase shift of discharge and bedload In the cross-spectral analysis of discharge and bedload impulses, scale ranges can be identiﬁed that are comparable to those described in section 5.3.1. CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 150

The squared coherence (Fig. 5.6) exhibits two distinct average levels. The low frequencies covering the inter-event and event scale ranges exhibit a squared coherence of roughly 0.4. The high frequencies covering the high frequency part of the intra-event scale range exhibit a lower squared coherence of roughly 0.15. These two coherence levels are separated from each other by a scale range of very low squared coherencies of roughly 0.04. These very low coherencies cover the frequencies that correspond to periods of 20 to 40 minutes. At a first glance (Fig. 5.7) the phase function of discharge and bedload transport reveals that for any period shorter than one hour the behaviours of the individual years and months differ from each other to a large extent and no common pattern can be identified. This is an expression of the very low coherence at this scale range and simply means that the phase function should not be interpreted at these frequencies. The more detailed view shows that the complete period as well as the individual years and months exhibit a similar qualitative behaviour of phaseshifts between discharge and bedload transport for periods shorter than about a week and longer than 1 hour. In the following we will describe this behaviour starting at periods longer than one week and proceeding with our description of Fig. 5.7 from left to right up to periods shorter than 1 hour. Coming from long periods, the phase function deviates from zero and bends down. These negative phase shift values indicate that bedload transport leads in front of discharge. The months exhibit only one local minimum. The individual years and complete study period exhibit two local minima that are separated from each other by phaseshifts close to zero at a period of roughly one day. Proceeding further to shorter periods, the phase function rises across zero up to roughly 50 degrees which approximately equals 15 % of 2π. These positive values indicate that bedload transport lags several minutes behind discharge. At periods shorter than 1 hour, the phase functions of the individual years and months deviate from each other as described before.

5.4 Discussion

In the bedload time series of the Erlenbach, four scale ranges of different temporal dynamics have been identified. In the two ranges of either very long or very short periods the bedload signal exhibits behaviour close to white noise. In the range from about 15 hours to about 1 hour, bedload follows the driving factor discharge i.e. it exhibits temporal dynamics that are determined by discharge. In the range from about 1 hour to about 5 minutes, bedload transport exhibits dynamics, which differ from noise- or discharge-like behaviour and therefore re- flect internal processes of bedload transport. This is especially true for periods of 20 to 40 minutes. The interpretation of the behaviour of the spectral density at the different scale ranges can be supported by the analysis of artificial time series data sets with increasing complexity. By gradually adding elements of time-domain complexity CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 151 similar to those observed in the geophone data set, the frequency-domain effects of these individual complexity elements can be analysed and distinguished from each other (cf. appendix 5.A3 for further details). In this we did not try to reproduce the absolute values of the observed spectral slopes. Instead the scope of the artificial time series study is to help interpreting the general shape features of the spectral density functions such as the succession of horizontal and inclined regions, sharp and smooth transitions between these regions, and so on. In the next sections we will in turn discuss the four different scale ranges and their implications.

5.4.1 The inter-event scale range The first scale range of periods longer than about 15 hours, can be interpreted as the inter-event scale. At this scale, the time series can be approximated by constantly absent bedload transport activity with bedload transport events represented by randomly scattered delta peaks. Therefore bedload transport data has the spectral signature of white noise at this scale (Figs. 5.3 and 5.4). Naturally, bedload transport events coincide with high-flow events. Therefore, discharge and bedload transport are roughly in phase at the low frequency part of this scale (Fig. 5.7). The coincidence of bedload transport with major high-flow events also entails the high coherence between discharge and bedload transport at this scale (Fig. 5.6). The interpretation of the inter-event scale range is limited by the short duration of the studied time series of only 2.5 years (bedload transport and discharge) or 4.5 years (only bedload). For example, Rickenmann (1997) has shown for the Erlenbach that event-based transport efficiency is tendentially higher during summer than during winter. Here, event-based transport efficiency is the ratio Vs , in which V is the event-based sediment volume, and V is the effective Ve s e runoff volume, which in turn is the integral of the discharge for the times when discharge exceeds the critical value for the beginning of bedload transport. Such seasonal tendencies might be visible in the spectral representation, if longer study time series are available. In the current study of only 2.5 years (bedload transport and discharge) or 4.5 years (only bedload), they are hidden by noise effects.

5.4.2 The event scale range The second scale range can be interpreted as the event scale. As is obvious from time domain plots of example events (Figs. 5.1 and 5.2), the bedload transport activity roughly follows the rising and falling limb of the event discharge hydrograph. Thus, the bedload transport inherits its variability from the driving factor discharge at this scale and the binary transport and the bedload show a similar spectral behaviour. The coherence spectrum shows the expected high CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 152 agreement between discharge and bedload transport (Fig. 5.6). The high coherence at this scale range is consistent with the observation that event-based effective runoff volume Ve is a reasonable predictor for event-based impulse counts Is (Fig. 5.8). Here an event is regarded as any sequence of non-zero impulse count values that may be interrupted by any number of breaks as long as each break does not exceed 3 hours. The event-based impulse counts Is is the sum of all impulse counts recorded in an individual event. The event-based effective runoff volume Ve is the integral of the discharge Q for the times when (Q > Qc), in which Qc is the critical discharge for the beginning of bedload m3 transport. For consistency with appendix 5.A2, we used Qc = 0.4 s . The results of Fig. 5.8 correspond to the observations of e.g. Rickenmann (2001) and Rickenmann and McArdell (2007), who demonstrated a similar relation using a different definition of an event and using the event-based sediment volume Vs instead of Is.

5.4.3 The phaseshift at the transition from the inter-event to the event scale range The lead of bedload transport in front of discharge, which is observed at the high frequency part of the inter-event scale range and at the event scale range for the individual months, the individual years, and the complete study period, can be interpreted in terms of a clockwise hysteresis of bedload transport. For the inter-event scale range that means that in a sequence of high-flow events bedload transport rates are higher during the first events than during the last events. For the event scale range that means that transport rates are higher during the rising limb of a high-flow event than during the falling limb. This interpretation is consistent with the observations of previous field studies such as the ones of Kuhnle (1992) or Swingle et al. (2012), which have documented such clockwise hysteresis of bedload transport for the event scale in other mountain streams. For the Erlenbach, Turowski et al. (2009) have shown that the bedload transport exhibits counterclockwise hysteresis during exceptional high- flow events. As the morphodynamic effect of a high-flow event in the Erlenbach changes from dominant erosion during exceptional high-flow events to dominant deposition during regular and small high-flow events (Turowski et al., 2013), it is not surprising that the direction of bedload transport hysteresis changes from counterclockwise during exceptional high-flow events (Turowski et al., 2009) to clockwise during regular and small high-flow events (Fig. 5.7). As potential causes for the clockwise hysteresis at the Erlenbach may serve either the depletion of transportable material or as described by Mao (2012) the reorganisation of the channel bed morphology. At periods longer than one week, no consistent phaseshift and thus hysteresis is observed, as at that scale the channel bed reorganisation caused by the bedload transport events will be over- printed by the effects of the creeping and sliding hillslopes (as already suggested by Turowski et al., 2011), which feed substantial amounts of material to the CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 153

Erlenbach (Schuerch et al., 2006). In any case, the observed hysteresis represents a systematic bias of the discharge–bedload relation. This bias cannot be reproduced by common empirical bedload transport equations (such as Rickenmann, 2001; Wilcock and Crowe, 2003; Recking, 2010), because these equations only consider the current hydraulic forces and neglect the preceding temporal evolution of the hydraulic forces and bedload transport rates. In that, the observed hysteresis reflects one of the limitations of common empirical bedload transport relations. The fact that the years and complete study period show two regions of negative phaseshifts separated from each other by frequencies with phaseshifts close to zero corresponding to periods of roughly one day (Fig. 5.7) can be interpreted in terms of duration and interarrival times of high-flow events. As stated before, the most intensive bedload transport events at the Erlenbach are triggered by temperature driven convective summer thunderstorms. Thus the events are linked to the diurnal cyclicity of air temperature expressed by the fact that bedload transport is not evenly distributed but clustered at certain times of the day (Fig. 5.9). That means that the duration of a high-flow events will be considerably shorter than one day, while the shortest interarrival time between two major high-flow peaks will roughly equal one day. Therefore, the period of one day is too long to display the phaseshift due to differences in transport efficiency in the rising and falling limb of a single event and it is too short to capture the phaseshift due to differences in transport efficiency in two consecutive events. As a result the frequencies corresponding to the period of roughly one day exhibit phaseshifts close to zero and separate the two regions of negative phaseshifts at lower and higher frequencies.

5.4.4 The phaseshift at the transition from the event to the intra- event scale range At the transition from periods longer than about 1 hour to shorter periods, the phase shift rises up to few minutes lead of discharge, before the phase functions of the individual months and years start to deviate from each other (Fig. 5.7). This may be interpreted as follows: At some position upstream of the geophone, a discharge pulse triggers a bedload pulse. Both pulses travel downstream, but the bedload pulse is much slower than the discharge. Therefore the bedload pulse reaches the geophone with a certain delay after the discharge. Based on this delay and some further assumptions the distance to the sediment source, where the sediment pulse was triggered, can be estimated to few tens of metres (cf. appendix 5.A2). The interpretation based on appendix 5.A2 is highly speculative and the estimate of the distance to a potential sediment source is associated with large and unquantified uncertainties. Nevertheless, the estimated distance to some sort of sediment source falls into the same order of magnitude that one would expect for e.g. the distance to the position of a regularly filled and flushed sediment reservoir in the step-pool-system of the CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 154

Erlenbach. Therefore, appendix 5.A2 has served its purpose of demonstrating a potential interpretation for the observed phase shifts that is consistent with other observations from the catchment.

5.4.5 Spectral slopes at the transition from the event to the intra-event scale range The difference of 2 between the spectral slopes of precipitation and discharge (Fig. 5.3 and Eq. 5.1) equals the value that can be expected assuming that (a) discharge can be approximated by a linear function of the volume of water stored in the catchment and that (b) at the relevant frequencies (corresponding to periods ranging from 3 hours to 20 minutes) the fluctuations of evapotranspiration are negligible compared to the fluctuations of precipitation (Thompson and Katul, 2012). Both approximations (a and b) are plausible in the case of the Erlenbach. The spectral slope of bedload transport which is by far more gentle than the spectral slope of discharge (Fig. 5.3) shows that the ratio between the variability in bedload transport and the variability in discharge increases for decreasing signal period. At the inter-event scale range, the roughly constant ratio of variabilities reflects the clear correlation between storm event magnitude and sediment transport during each event. However at the intra-event scale range, this ratio increases, meaning that internal dynamics in the bedload transport process generate fluctuations and thus variability in the bedload transport signal beyond a simple correlation with changes in discharge. A potential process that can cause the observed addition of variability is the positive feedback between high rates of bedload transport triggering the mobilisation of further grains and thus even higher bedload transport e.g. by dislodging sediment from the bed or disrupting pocket geometries.

5.4.6 The intra-event scale range General characteristics of the intra-event scale range The definition of the binary transport values cancels any intra-event variability, as they constantly equal 1 within an event. Therefore at this scale, the spectral density of the binary transport is dominated by edge effects of the boundaries of the individual events and thus exhibit white noise (Fig. 5.3). In turn, the third and fourth scale ranges can be interpreted as the intra-event scale, as they cover the high frequency white noise of the binary transport. As can be clearly seen from time domain plots of example events (Figs. 5.1 and 5.2), the within-event dynamics of bedload transport is greatly independent of discharge and at small temporal scales the two variables discharge and bedload transport may differ strongly in their temporal dynamics and thus spectral behaviour. The interpretation that at the intra-event scale bedload transport exhibits temporal dynamics which are largely independent of discharge is further supported by the fact that the coherence between discharge and bedload transport drops to a CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 155 considerably lower level at the intra-event scale range as compared to the event- and inter-event-scale (Fig. 5.6).

The systematic intra-event scale range The third scale range can be interpreted as a systematic intra-event-scale. At that scale various interactions related to the reorganisation of the bed are reflected in the temporal dynamics of bedload transport (Fig. 5.4). As outlined in section 5.4.5, the system receives additional variability from the interaction with the bed. As the effect of such an interaction, the spectral wiggles at the systematic intra-event-scale point to periodicities and cyclic behaviour in bedload transport. Different processes may lead to such cyclic behaviour. An example of such a process, which is probable in the Erlenbach, is the sedimentary filling and flushing of the pools in a step-pool system, as described in a flume study by Saletti et al. (2014) and similar to what has been suggested as cause of debris flow fluctuations by Kean et al. (2013) in form of their sediment capacitor model.

The random intra-event scale range The white noise ﬂoor of the random intra-event scale range (Figs. 5.6 and 5.7) could potentially be attributed to (i) varying transport rates i.e. process noise or to (ii) varying impulse counts at a constant transport rate i.e. measurement noise (e.g. documented by Turowski and Rickenmann, 2009) or to (iii) a combination of both. It cannot be attributed to spectral aliasing as the discretised transport values represent averages over the discretisation length, which in turn tends to suppress aliasing of high-frequency components of a signal (Kirchner, 2005). Unfortunately, the contributions of process and measurement noise are hard to quantify. If the temporal dynamics of the random intra-event scale range was dominantly due to process noise, it could be interpreted to be caused by a complex network of interactions between the channel bed and the transported material. However, this interpretation is very speculative due to the unquantiﬁed contributions of the two potential noise sources.

5.4.7 The periods of 20 to 40 minutes The frequencies corresponding to periods of 20 to 40 minutes exhibit interesting behaviour. In the results of the reshuffling exercise (Fig. 5.5), at these frequencies, the bedload transport exhibits white noise behaviour, while the discharge still shows a considerable spectral slope of autoregressive dependency. In other words, the same reshuffling algorithm that preserves the autoregressive dependencies in discharge is capable to destroy the autoregressive dependencies in bedload transport. Such a selective signal destruction requires that at these frequencies the autoregressive dependency of bedload transport is independent and thus not inherited from discharge. This is consistent with the observation CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 156 that at frequencies corresponding to periods of 20 to 40 minutes the squared coherence between discharge and bedload transport is extremely low as compared to values at other frequencies (Fig. 5.6). This observation is true for the complete study period as well as for all three individual years. The fact that it is not true for the majority of the individual months may indicate that the physical processes that cause the described observations are associated with large events. In contrast to the clear pattern of the squared coherence, no distinct or consistent pattern can be recognised within these frequencies in the spectral densities of (Fig. 5.3) or in the phaseshift between (Fig. 5.7) discharge and bedload transport. This emphasises the power of squared coherence as a tool for identifying scale ranges of differing discharge and bedload transport behaviour. The observations of the reshuffling exercise and the coherence function correspond to the results of numerous studies, in which it has been shown that parts of the discharge input signal can be completely obscured by the sediment transport system and thus not be visible in the output bedload transport rate (Coulthard and van de Wiel, 2007; van de Wiel and Coulthard, 2010; Jerolmack and Paola, 2010; Coulthard and van de Wiel, 2012, 2013). Coulthard and van de Wiel (2012) attribute this signal obscuration to geomorphic units in that deposition as well as erosion occur. Such units are present in the Erlenbach in terms of pools of a step-pool-sequence that can be filled and flushed. In contrast to Jerolmack and Paola (2010), who suggested a simple threshold frequency sep- arating the preserved low frequencies from the obscured high frequencies, we observed a scale range of signal obscuration with a clearly defined upper and lower limit in terms of frequency.

5.5 Conclusions

The discussed results of this study allow for conclusions in the fields of (I) the analysis of bedload transport time series, (II) measurement strategies for recording bedload transport, (III) optimised sampling rates for bedload transport measurement systems, and (IV) preservation and obscuration of discharge input signals by the sediment transport system. (I) In this contribution we have demonstrated the suitability of spectral analysis for studying time series of bedload transport measurements. Especially squared coherence proofed to be a powerful tool for identifying scale ranges of differing discharge and bedload transport behaviour. (II) The pronounced clustering of bedload transport at certain times of the day (Fig. 5.9) gives a strong argument for automated systems for both scientific measurements as well as hazard warning (as described for debris flows by e.g. Praschnig et al., 2008, and Badoux et al., 2009). During the time at which people are available for facilitating measurements or for deciding whether or not a hazard warning should be released the bedload transport activity is close to zero. In contrast, the times of highest activity fall into the late evening or the CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 157 night outside common working hours. (III) For such an automated bedload transport measurement system intended for studying the intra-event variability, the ideal sampling frequency can be determined based on the observation that the bedload transport spectra exhibit white noise behaviour for periods shorter than roughly 5 minutes. Considering that the sampling frequency should be at least twice the frequency of the signal of interest (Shannon, 1949) which in our case is the non-noise behaviour, the ideal sampling frequency for bedload transport measurements roughly equals 1 1 0.4 min to 0.5 min . Considerably lower sampling frequencies would miss parts of the bedload transport dynamics that are to be studied. Considerably higher sampling frequencies would waste measurement and analysis efforts by mainly recording random noise behaviour. (IV) In addition to this high frequency white noise, the periods of 20 to 40 minutes show a bedload transport behaviour that is clearly not inherited from discharge. This behaviour is caused by varying transport rates and can therefore be attributed to physical processes and interactions in the stream channel upstream of the measurement site. This observation confirms that parts of the input signal of discharge will be obscured by the bedload transport system. Fur- thermore, it adds that this signal obscuration is limited to a certain temporal scale range with clearly defined upper and lower boundaries. In other words, whether or not a discharge behaviour can be reconstructed from a sedimentary record highly depends on the studied temporal scales. CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 158

inter−event syst.−intra event rand.−intra discharge

precipitation 1e−03 slope: −1.1

slope: −3.1 1e−06 geophones spectral density [arbitraryspectral scale] slope: −1.6 transport yes/no 1e−09

Erlenbach standardised variables slope: −2.4 Jul2011 − Dec2013 individual years interquartile range for individual months 1e−12 1e−06 1e−04 1e−02

1 year 1 month 1 week 1 day 5 hours 1 hour 15 mins 5 mins

frequency [1/min] and period

Figure 5.3: Smoothed power spectral density functions for different variables measured at the Erlenbach from July 2011 to December 2013, covering the complete period of continuous bedload transport and discharge measurements both at 1 minute resolution. The bars at the top of the figure indicate scale ranges of different temporal dynamics. See text for details. CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 159

inter−event syst.−intra event rand.−intra

interquartile range for individual months

2009 1e−01

2010

2011

2012 1e−04

2013 spectral density [arbitraryspectral scale]

Jul2009 − Dec2013 1e−07

Erlenbach standardised geophones

1e−06 1e−04 1e−02 1e−10

1 year 1 month 1 week 1 day 5 hours 1 hour 15 mins 5 mins

frequency [1/min] and period

Figure 5.4: Smoothed power spectral density functions for bedload transport intensity measured at the Erlenbach from July 2009 to December 2013, covering the complete period of continuous bedload transport measurements at 1 minute resolution. The bars at the top of the ﬁgure indicate scale ranges of diﬀerent temporal dynamics. See text for details. CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 160

inter−event syst.−intra event rand.−intra

discharge 1e−02

Erlenbach

1e−05 Jul2011−Dec2013 100 discharge bins

original reshuffled within each discharge bin − median reshuffled within each discharge bin − quartiles reshuffled within each discharge bin − 2.5 and 97.5 percentiles spectral density [arbitraryspectral scale] geophones 1e−08

1e−06 1e−04 1e−02 1e−11 1 year 1 month 1 week 1 day 5 hours 1 hour 15 mins 5 mins

frequency [1/min] and period

Figure 5.5: Smoothed power spectral density function for bedload impulse counts observed at the Erlenbach from July 2011 to December 2013, covering the complete period of continuous bedload transport and discharge measurements both at 1 minute resolution. The black curves display quantiles of 500 realisations of reshuffling the non-zero impulse count and discharge values within each of 100 discharge bins. The two vertical lines are located at periods of 20 and 40 minutes. The bars at the top of the figure indicate scale ranges of different temporal dynamics. See text for details. CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 161

inter−event syst.−intra event rand.−intra

Erlenbach 0.8 discharge vs. bedload impulses standardised variables 0.6 0.4 squared coherence 0.2 Jul2011 − Dec2013 individual years interquartile range for individual months 1e−06 1e−04 1e−02 0.0

1 year 1 month 1 week 1 day 5 hours 1 hour 15 mins 5 mins

frequency [1/min] and period

Figure 5.6: Smoothed squared coherence function for discharge and bedload impulses measured at the Erlenbach from July 2011 to December 2013, covering the complete period of continuous bedload transport and discharge measurements both at 1 minute resolution. The two vertical lines are located at periods of 20 and 40 minutes. The bars at the top of the ﬁgure indicate scale ranges of diﬀerent temporal dynamics. See text for details. CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 162

inter−event syst.−intra event rand.−intra

Erlenbach 100 discharge vs. bedload impulses standardised variables

Jul2011 − Dec2013

50 individual years interquartile range for individual months 0

phase shift [degree] positive phase−shift values indicate leading discharge −50 negative phase−shift values indicate leading bedload impulses −100 1e−06 1e−04 1e−02

1 year 1 month 1 week 1 day 5 hours 1 hour 15 mins 5 mins

frequency [1/min] and period

Figure 5.7: Smoothed phase function for discharge and bedload impulses measured at the Erlenbach from July 2011 to December 2013, covering the complete period of continuous bedload transport and discharge measurements both at 1 minute resolution. Positive values indicate leading discharge, while negative values indicate leading bedload impulses. The bars at the top of the ﬁgure indicate scale ranges of diﬀerent temporal dynamics. See text for details.

1.18 ● Is = 0.11 Ve ● R2 = 0.65 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 10000 ●● ●● ● ● [−] ● ●

s ● ● ●

● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 100 ●

● Event based impulse sums I Event

●

● 1

20 50 100 200 500 1000 2000 5000 10000 20000 50000

3 Effective runoff volume Ve [m ]

Figure 5.8: Event-based relation of discharge and bedload transport. See text for details. The given coeﬃcient of determination has been derived for the linear regression of the logarithmised variables. CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 163

● 6e+05

● ● ● 4e+05 ●

● ● ● ● ● 2e+05

● ● ● ● ●

Geophone impulse sums Jul2009 − Dec2013 [−] Geophone impulse sums Jul2009 ● ● ● ● ● ● ● ● ● ● ● ● ● 0e+00 0 5 10 15 20

Hours of the day [−]

Figure 5.9: Diurnal clustering of bedload transport from July 2009 to December 2013. The ordinate shows the sums of geophone impulse counts that were recorded during the same hour of the day regardless on which date they occured. The ﬁrst and last point of the plot are the same and display the impulse count sums from 11pm to 12pm. Appendix for chapter 5

Table 5.A1: Notation.

The following symbols are used in this article. ∆t delay between the arrival of a discharge and bedload pulse ∆x distance from the geophone to a sediment source π the ratio of a circle’s circumference to its diameter ω frequency a, b example variables Is the event-based geophone impulse count sums log10 logarithm to base 10 Q discharge Qc critical discharge for the beginning of bedload motion rmi relative modulation intensity SPr spectral slope of precipitation SQ spectral slope of discharge tb travel time of a bedload pulse tw travel time of a discharge pulse vb bedload velocity vw water velocity Ve the event-based eﬀective runoﬀ volume Vs the event-based sediment volume

164 CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 165

inter−event syst.−intra event rand.−intra 1e+06

Erlenbach 1e+05 Jul2009−Dec2013

500 block randomisation realisations

1e+04 bedload impulses block randomisations median spectral density spectral block randomisations quartiles block randomisations 2.5 and 97.5 percentiles 1e+03

1e+02 1e−06 1e−04 1e−02

1 year 1 month 1 week 1 day 5 hours 1 hour 15 mins 5 mins

frequency [1/min] and period

Figure 5.A1: Smoothed power spectral density function for bedload impulse counts observed at the Erlenbach from July 2009 to December 2013, covering the complete period of continuous bedload transport measurements at 1 minute resolution. The black curves display quantiles of 500 realisations of block randomisation. The bars at the top of the ﬁgure indicate scale ranges of diﬀerent temporal dynamics. See text for details.

5.A1 Block randomisation

Here an event is regarded as any sequence of non-zero impulse count values that may be interrupted by any number of breaks as long as each break does not exceed 3 hours. Complementarily, the inter-event durations are the times from the end of one event to the start of the next event as well as the non- event times at the start and end of the complete time series. For the block randomisation, we independently reshuffled the order of the events and the order of the inter-event durations. For 500 reshuffle realisations, we calculated the spectral density functions and compared representative percentiles to the observed spectral density function of bedload impulses. As can be expected, the reshuffling destroys any structure at the inter-event scale range. This is expressed by the white noise behaviour and the considerable difference between the spectral densities of the individual percentiles at this scale. In contrast, at the event and especially at the intra-event scale ranges, the block randomisation preserves the shape of the spectral density function also including the observed wiggles. This suggests that these wiggles are an expression of what happens within individual events and are not just the result of the distance between two large events accidentially matching some multiple of the period of one of these wiggles. CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 166

5.A2 Distance to a sediment source based on phaseshift at the transition from the event to the intra-event scale range

The distance from the geophone to a source position, where a sediment pulse has been triggered (cf. section 5.4.4), can be estimated based on the converted deﬁnitions of travel velocities:

∆x tb = (5.A1a) vb ∆x tw = (5.A1b) vw Subtracting equation (5.A1a) from equation (5.A1b) yields after some simple conversion:

∆t · v ∆x = w ; (5.A2) vw − 1 vb

Here, ∆x is the distance from the geophone to the source position, ∆t = tb −tw is the delay between the arrival of the discharge and bedload pulse, tw and tb are the travel times of the water and bedload pulses, and vw and vb are the water and bedload velocities. In the following we will derive estimates of vb and vw, which are necessary to estimate ∆x based on ∆t. The bedload velocity vb can be estimated by the particle travel distance divided by the time of particle motion. Schneider et al. (2014) measured bedload particle travel distances for one or several discharge events (see Table 3 of Schneider et al., 2014). As the measurements of Schneider et al. (2014) do not fall completely into the time of continuous bedload transport measurements, we used a discharge threshold to estimate the transport times. m3 At the Erlenbach a discharge of 0.4 s represents the flow conditions near the beginning of bedload transport (Rickenmann et al., 2012). Therefore, any time m3 steps between the survey dates with discharges larger than 0.4 s are regarded as transport times. As the transport times include times during that the particles rest on the ground, the transport times are not equivalent to the times of particle motion. Based on the field observations of Habersack (2001), the time of actual particle motion roughly equals the transport time divided by 40. The mean bedload velocity vb was calculated by dividing the observed transport distances by the duration of the corresponding times of particle motion. The mean water flow velocity vw was determined by the mean of the square root of discharges during the transport times, as flow velocity approximately scales with the square root of discharge in the Erlenbach (see Fig. 5a of Nitsche et al., 2012). As a result ∆x can be estimated to few tens of metres (Fig. 5.A2). CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 167

● ● ● ● ●● ● ● ● 500 circles display 9 observations of velocity ratios based on Schneider et al. (2014)

200 with their interquartile range indicated by the grey background x [m]

∆ and their median indicated by vertical dotted line 100 water flow velocity mean: 0.8 m/s

50 water flow standard deviation: 0.2 m/s 20 10 5

Distance to sediment source water flow velocity 0.6 m/s water flow velocity 0.8 m/s 2 water flow velocity 1 m/s with time lag 10 min 1

0.5 1.0 2.0 5.0 10.0 20.0

Bedload velocity as fraction of water velocity vb/vw [%]

Figure 5.A2: Estimation of the distances to a sediment source based on the time lags between the arrival of discharge and bedload transport peaks (see text for details). CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 168

Table 5.A2: Names and characteristics of the ﬁve degrees of complexity of the aritiﬁcial time series

Name Event size Internal Modulation Const.Size-NoMod. Constant None Var.Size-NoMod. Varying None Var.Size-Const.Mod. Varying Constant Var.Size-Var.Mod. Varying Varying Const.Size-Var.Mod. Constant Varying

5.A3 Artiﬁcial time series

5.A3.1 Methods To check the response of spectral analysis to time series consisting of individual events, we created artificial time series with known properties. As raw signal of an artificial event we used a sine function between two minima ranging from 0 to 1. This raw event signal is multiplied with a modulation signal, which is another sine function at a different period and ranges from (1 − rmi) to 1, with rmi being the relative modulation intensity. For the resulting modulated event signal the total amplitude, the event period, the modulation period and the modulation intensity can be selected individually. The concept for the creation of an artificial, modulated event signal is summarised in Fig. 5.A3. The artificial events are added to a time series, which initially just consists of zeroes. The interarrival times are measured from the peak of one event to the peak of the next event. Therefore the individual events may partially or fully overlap. We analysed increasing degrees of complexity, which are displayed exemplarily in Fig. 5.A4 and which are listed in table 5.A2. For each degree of complexity, we created four different time series with 1, 10, 100 or 1000 events respectively. The interarrival times and event amplitudes were drawn separately from a lognormal distribution. Event periods were defined as a linear function of event amplitude. Relative modulation intensity was set to 0.75 for all events and modulation periods were drawn from a uniform distribution ranging between a defined minimum and maximum period. For all artificial time series, the spectral density function was determined. In the creation of the artificial time series’, we did not try to reproduce the absolute values of the observed spectral slopes. Instead the scope of the artificial time series study is to help interpreting the general shape features of the spectral density functions such as the succession of horizontal and inclined regions, sharp and smooth transitions between these regions, and so on. CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 169 1.0 1.0 1.0 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4

( 1 − ModulationIntensity ) 0.2 0.2 0.2 0.0 0.0 0.0

ModulatedEventSignal = RawEventSignal ModulationSignal RawEventSignal * ModulationSignal

Figure 5.A3: Concept for the creation of a modulated event signal intended for building artiﬁcial time series with known properties.

5.A3.2 Results Const.Size-NoMod. The spectra (Fig. 5.A6) of the artificial time series (Fig. 5.A5) of Const.Size- NoMod. (i.e. scattered events with constant amplitude and duration and no internal modulation) are separated into two scale ranges. The high frequencies exhibit a constant spectral slope with slight and regular variation of spectral density. This variation can be attributed to boundary effects as the individual events have a defined start and end. The low frequencies exhibit a spectral slope of zero and an irregular variation of spectral density, which is pronounced for the time series with few events and which decreases for the time series with many events. The white noise slope of zero is due to the random distribution of events over time. The irregular variation can be interpreted as the spectral peaks and their harmonics produced by the distance between two individual events. For an increasing number of events, these peaks tend to cancel out each other resulting in a vanishing variation of spectral density. The scale ranges of low and high frequencies are separated from each other by a sharp edge roughly located at the inverse of the duration of the individual events (Fig. 5.A6).

Var.Size-NoMod. In Var.Size-NoMod. the event amplitudes exhibit a lognormal distribution and the event durations are a linear function of the amplitude, but the individual events still do not exhibit any internal modulation (Fig. 5.A7). In the spectra CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 170

(Fig. 5.A8) of this complexity, the variation of spectral density at the high frequencies disappears, because the event durations now vary and thus smear the boundary eﬀects over diﬀerent frequencies, which cancel out each other. The irregular variation of spectral density at the low frequencies (for Const.Size- NoMod. only visible in series with few events) now persists also for the time series with many events. This can be explained as the variation represents the peaks produced by the distance between individual pairs of the relatively largest events, which are few for any total number of events. The edge between the low and high frequency ranges is now smooth as the duration of the individual events now varies and thus smears it over a range of frequencies.

Var.Size-Const.Mod. In Var.Size-Const.Mod. the events of varying sizes (duration and peak) are modulated by a sine wave, the frequency of which is the same for all events (Fig. 5.A9). The spectra (Fig. 5.A10) of this degree of complexity are similar to those of the previous complexity but exhibit an additional pronounced spectral peak at the frequency of the internal modulation. This peak tends to be like a wiggle (i.e. smooth and wide) for the time series with few events and narrow and sharp for the time series with many events.

Var.Size-Var.Mod. In Var.Size-Var.Mod., the highest degree of complexity, the events of varying sizes are modulated by sine waves with frequencies changing from event to event (Fig. 5.A11). The spectra (Fig. 5.A12) of this degree of complexity are similar to the spectra of time series with unmodulated events of varying sizes. However, the spectra of this highest degree of complexity exhibit a band, in which the spectral density is increased compared to the surrounding spectrum and which covers the range of modulation frequencies. In this band, the spectral density exhibits irregular variation in terms of smooth and wide spectral wiggles for the time series with few events and this variation vanishes for time series with many events. The spectral wiggles may be attributed to the modulation frequencies of the few largest events, which are cancelled out if too many events and thus too many diﬀerent modulation frequencies are included in the time series.

Const.Size-Var.Mod. Finally, the intermediate degree of complexity Const.Size-Var.Mod. (roughly located between the first and second degree) shall be considered. At this complexity, temporally scattered events of constant amplitude and duration are modified by sine waves with frequencies changing from event to event (Fig. 5.A13). The spectra (Fig. 5.A14) of this intermediate complexity may be described as the spectra of the lowest complexity including the band of increased spectral density taken from the highest complexity spectra. However, the spectral wiggles CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 171 in this band are only visible for time series with very few events and vanish rapidly, if more events are included. In this setting any spectral wiggle of a modulation frequency will be cancelled out if only few events with a slightly different modulation frequency exist. This contrasts the situation of the highest complexity, where the spectral wiggle of the modulation frequency of a major event persists, even if there are other events with slightly different modulation frequencies, as the signal of the other events is less dominant than the signal of the major event.

5.A3.3 Discussion Among the spectra of the artiﬁcial time series, the spectrum of Var.Size- Var.Mod. i.e. the highest degree of complexity (Fig. 5.A12) with ten events is most similar to the annual spectra of bedload transport at the Erlenbach (Fig. 5.4), since they both share the following characteristics:

• White noise behaviour at low frequencies • Irregular variation of spectral density at low frequencies (In the very low frequencies of the bedload transport spectra, this variation is cancelled by the applied Daniell-smoother.) • Smooth transition between low and high frequency scale ranges • Generally constant spectral slope at high frequencies without regular variation of spectral density • Band of increased spectral density within the high frequency scale range • Within the mentioned band, irregular variation of spectral density in terms of wide and smooth spectral wiggles.

Based on the results of the artificial time series study the common characteristics may be interpreted as follows. The white noise behaviour is the result of the random distribution of the individual bedload transport events over time. The irregular variation of spectral density at low frequencies are spectral peaks and their harmonics that are both produced by the distance of individual pairs of major transport events. The transition between the low frequency inter-event behaviour and the high frequency intra-event behaviour is smooth, as the duration of the individual events varies and thus smears the transition over a range of frequencies. The same smearing effect of varying event durations cancels out any regular variation of spectral density at high frequencies, which otherwise would have been produced by margin effects due to the defined start and end of individual events. The band of increased spectral density is produced by intra- event fluctuations of bedload transport at varying frequencies. The wide and smooth spectral wiggles within this band presumably represent the fluctuation signals of major events. CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 172

The described similarities suggest that the model of a lognormal distribution for the event amplitudes and interarrival times, of a linear relation between event amplitude and duration, and of a uniform distribution of modulation frequencies might be close to the natural situation in the Erlenbach. In this context it is worth noting that the artiﬁcial spectrum, which is most similar to the observed annual bedload transport spectra, contains ten events. This number falls into the same order of magnitude as the average of anually observed events in the Erlenbach (approximately twenty). CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 173

1.0 Const.Size−NoMod. 0.8 0.6 0.4 0.2 0.0

2.5 Var.Size−NoMod. 2.0 1.5 1.0 0.5 0.0

2.5 Var.Size−Const.Mod. 2.0 1.5 1.0 0.5 0.0

2.5 Var.Size−Var.Mod. 2.0 1.5 1.0 0.5 0.0

1.0 Const.Size−Var.Mod. 0.8 0.6 0.4 0.2 0.0

Figure 5.A4: Concept of the degrees of complexity for building artiﬁcial time series with known properties. CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 174

1 event

1.0 Const.Size−NoMod. 0.8 0.6 0.4 0.2 0.0

10 events

1.0 Const.Size−NoMod. 0.8 0.6 0.4 0.2 0.0

100 events

1.0 Const.Size−NoMod. 0.8 0.6 0.4 0.2 0.0

1000 events

Const.Size−NoMod. 3.0 2.0 1.0 0.0

Figure 5.A5: Artiﬁcial time series with 1, 10, 100, and 1000 events. The lag times between the peaks of consecutive events are lognormally distributed. The event amplitudes and durations are the same for all events. No internal modulation is applied to the individual events. CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 175

1 event

Const.Size−NoMod. 1e−02 1e−10 spectral density spectral 1e−18 1e−05 1e−04 1e−03 1e−02 1e−01

frequency

10 events

Const.Size−NoMod. 1e+00

reciprocal median event duration 1e−08 spectral density spectral 1e−16 1e−05 1e−04 1e−03 1e−02 1e−01

frequency

100 events

Const.Size−NoMod. 1e−01 1e−09 spectral density spectral 1e−17 1e−05 1e−04 1e−03 1e−02 1e−01

frequency

1000 events

Const.Size−NoMod. 1e+02 1e−06 spectral density spectral 1e−14 1e−05 1e−04 1e−03 1e−02 1e−01

frequency

Figure 5.A6: Power spectral density functions of the artiﬁcial time series displayed in Fig. 5.A5. The reciprocal median event duration is indicated in the plots by a vertical line. CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 176

1 event

0.4 Var.Size−NoMod. 0.3 0.2 0.1 0.0

10 events

Var.Size−NoMod. 6 4 2 0

100 events

12 Var.Size−NoMod. 10 8 6 4 2 0

1000 events

30 Var.Size−NoMod. 25 20 15 10 5 0

Figure 5.A7: Artiﬁcial time series with 1, 10, 100, and 1000 events. The lag times between the peaks of consecutive events are lognormally distributed. The event amplitudes are lognormally distributed as well. The event durations are a linear function of the event amplitudes. No internal modulation is applied to the individual events. CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 177

1 event

Var.Size−NoMod. 1e−03 1e−11 spectral density spectral 1e−19 1e−05 1e−04 1e−03 1e−02 1e−01

frequency

10 events

Var.Size−NoMod. 1e+02

reciprocal median event duration 1e−06 spectral density spectral 1e−14 1e−05 1e−04 1e−03 1e−02 1e−01

frequency

100 events

Var.Size−NoMod. 1e+03 1e−05 spectral density spectral 1e−13 1e−05 1e−04 1e−03 1e−02 1e−01

frequency

1000 events

Var.Size−NoMod. 1e+05 1e−03 spectral density spectral 1e−11 1e−05 1e−04 1e−03 1e−02 1e−01

frequency

Figure 5.A8: Power spectral density functions of the artiﬁcial time series displayed in Fig. 5.A7. The reciprocal median event duration is given in the plots. CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 178

1 event

Var.Size−Const.Mod. 0.30 0.20 0.10 0.00

10 events

7 Var.Size−Const.Mod. 6 5 4 3 2 1 0

100 events

8 Var.Size−Const.Mod. 6 4 2 0

1000 events

Var.Size−Const.Mod. 20 15 10 5 0

Figure 5.A9: Artiﬁcial time series with 1, 10, 100, and 1000 events. The lag times between the peaks of consecutive events are lognormally distributed. The event amplitudes are lognormally distributed as well. The event durations are a linear function of the event amplitudes. The modulation frequency is the same for all events. CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 179

1 event

Var.Size−Const.Mod. 1e−03 1e−11 spectral density spectral 1e−19 1e−05 1e−04 1e−03 1e−02 1e−01

frequency

10 events

Var.Size−Const.Mod. 1e+01

reciprocal median event duration constant modulation frequency 1e−07 spectral density spectral 1e−15 1e−05 1e−04 1e−03 1e−02 1e−01

frequency

100 events

Var.Size−Const.Mod. 1e+01 1e−07 spectral density spectral 1e−15 1e−05 1e−04 1e−03 1e−02 1e−01

frequency

1000 events

Var.Size−Const.Mod. 1e+03 1e−05 spectral density spectral 1e−13 1e−05 1e−04 1e−03 1e−02 1e−01

frequency

Figure 5.A10: Power spectral density functions of the artiﬁcial time series displayed in Fig. 5.A9. The reciprocal median event duration and the constant modulation frequency are given in the plots as vertical lines. CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 180

1 event

Var.Size−Var.Mod. 0.30 0.20 0.10 0.00

10 events

7 Var.Size−Var.Mod. 6 5 4 3 2 1 0

100 events

Var.Size−Var.Mod. 8 6 4 2 0

1000 events

25 Var.Size−Var.Mod. 20 15 10 5 0

Figure 5.A11: Artiﬁcial time series with 1, 10, 100, and 1000 events. The lag times between the peaks of consecutive events are lognormally distributed. The event amplitudes are lognormally distributed as well. The event durations are a linear function of the event amplitudes. The modulation frequencies are uniformly distributed between a deﬁned minimum and maximum. CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 181

1 event

Var.Size−Var.Mod. 1e−05 1e−13 spectral density spectral

1e−21 1e−05 1e−04 1e−03 1e−02 1e−01

frequency

10 events

Var.Size−Var.Mod. 1e+01

reciprocal median event duration margins of uniformly distributed modulation frequencies 1e−07 spectral density spectral 1e−15 1e−05 1e−04 1e−03 1e−02 1e−01

frequency

100 events

Var.Size−Var.Mod. 1e+01 1e−07 spectral density spectral 1e−15 1e−05 1e−04 1e−03 1e−02 1e−01

frequency

1000 events

Var.Size−Var.Mod. 1e+04 1e−04 spectral density spectral 1e−12 1e−05 1e−04 1e−03 1e−02 1e−01

frequency

Figure 5.A12: Power spectral density functions of the artiﬁcial time series displayed in Fig. 5.A11. The reciprocal median event duration and the margins of the uniformly distributed modulation frequencies are given in the plots. CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 182

1 event

0.8 Const.Size−Var.Mod. 0.6 0.4 0.2 0.0

10 events

1.0 Const.Size−Var.Mod. 0.8 0.6 0.4 0.2 0.0

100 events

1.0 Const.Size−Var.Mod. 0.8 0.6 0.4 0.2 0.0

1000 events

Const.Size−Var.Mod. 3.0 2.0 1.0 0.0

Figure 5.A13: Artiﬁcial time series with 1, 10, 100, and 1000 events. The lag times between the peaks of consecutive events are lognormally distributed. The event amplitudes and durations are the same for all events. The modulation frequencies are uniformly distributed between a deﬁned minimum and maximum. CHAPTER 5. SPECTRAL CHAR. OF BEDLOAD TRANSPORT 183

1 event

Const.Size−Var.Mod. 1e−04 1e−12 spectral density spectral 1e−20 1e−05 1e−04 1e−03 1e−02 1e−01

frequency

10 events

Const.Size−Var.Mod. 1e−01

reciprocal median event duration margins of uniformly distributed modulation frequencies 1e−09 spectral density spectral 1e−17 1e−05 1e−04 1e−03 1e−02 1e−01

frequency

100 events

Const.Size−Var.Mod. 1e+00 1e−08 spectral density spectral 1e−16 1e−05 1e−04 1e−03 1e−02 1e−01

frequency

1000 events

Const.Size−Var.Mod. 1e+01 1e−07 spectral density spectral 1e−15 1e−05 1e−04 1e−03 1e−02 1e−01

frequency

Figure 5.A14: Power spectral density functions of the artiﬁcial time series displayed in Fig. 5.A13. The reciprocal median event duration and the margins of the uniformly distributed modulation frequencies are given in the plots. REFERENCES 184

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Synthesis and outlook

6.1 Synthesis

Bedload transport has a wide range of various implications for research studies and for the civil engineering practice in mountain regions. Considering these implications, the thesis aimed to improve the estimation and prediction of bedload transport. These improvements include the provision of the modelling tool sedFlow (Chapter 2), the assessment of the model behaviour (Chapter 3), an example application demonstrating the capabilities of sedFlow (Chapter 4), and a more profound understanding of the temporal dynamics of natural bedload transport systems, which define the scale range of applicability for a deterministic model like sedFlow (Chapter 5). The new model sedFlow (Chapter 2) complements the range of existing tools for the simulation of bedload transport in steep mountain streams. It is an appropriate tool if (I) grain size distributions need to be dynamically adjusted in the course of a simulation, if (II) the effects of ponding, e.g. due to massive sediment inputs through debris flows, might play a role in the study catchment or if (III) one simply needs a fast simulation of bedload transport in a mountain stream with quick and easy pre- and post-processing. In chapter 3, we used the model sedFlow to simulate bedload transport in two Swiss mountain rivers. Observations from bedload transport events have been successfully reproduced with plausible parameter settings meaning that calibration parameters are only varied within ranges of uncertainty that have been pre-determined either by previous research or by field observations in the study reaches. It is important to note that the good agreement between simulated and observed accumulated bedload transport is the result of the calibration of the model. It is improbable that such good agreement could be achieved without calibration. Furthermore, it has to be stated that the accumulated bedload transport as a spatial integral of morphodynamic changes is of limited use in evaluating the results of a spatially distributed simulation. The accumulated bedload transport curve generated by the model may look similar to

190 CHAPTER 6. SYNTHESIS AND OUTLOOK 191 the observed accumulated bedload transport curve, even if the spatial patterns of erosion and deposition differ substantially between the model and the observations. Nevertheless, the discussion of chapter 3 (and of comparable studies such as Chiari and Rickenmann (2011)) is focussed on accumulated bedload transport, because only this variable combines information on the along channel changes of bedload transport with information on the overall level of transport rates. The erosion and deposition displays the along channel changes of bedload transport in a more pronounced way, but lacks information on the transmission volumes of sediment which largely determine the overall level transport rates. In turn, this overall level of transport rates has considerable implications and is therefore of interest both in a scientific and in an applied engineering context. This is also reflected by the fact that accumulated bedload transport plots are commonly used in the Swiss applied engineering community to characterise spatially distributed bedload transport and their use is even recommended by authorities (e.g. Schälchli and Kirchhofer, 2012). Simulation results highlighted the problems that can arise because traditional flow resistance estimation methods fail to account for the influence of large blocks. As an important result of our study, we conclude that a very detailed and sophisticated representation of hydraulic processes is apparently not necessary for a good representation of bedload transport processes in steep mountain streams, given that there are still considerable uncertainties regarding the “true” bedload transport conditions. Moreover, it has been shown that bedload transport events with widely differing accumulated bedload transport volumes may produce very similar patterns of erosion and deposition. This highlights the uncertainty in accumulated bedload transport estimates that are derived only from morphologic changes represent- ing the net erosion or deposition volumes along river reaches, without knowing the in- or output of sediments. The proof-of-concept study of chapter 3 demonstrates the usefulness of sedFlow for a range of practical applications in alpine mountain streams. In chapter 4, we have focused on the effect of climate change on discharge and bedload transport in a mountain river during the incubation time of brown trout i.e. during the winter months. Future conditions during that time may become less favorable for brown trout survival due to higher and more frequent floods in the winter season resulting in simulated trends of increasing magnitudes and durations of winter scour. The trend of increasing erosion depths is crucial as Riedl and Peter (2013) documented that the egg burial depths of brown trout in alpine rivers are considerably lower than most literature values. It is likely that the stable spawning habitat areas might decrease in the future, and erosion depths will more frequently exceed the average egg burial depth thus exerting stress on the trout population. The results of chapter 5 allow for conclusions in the fields of (I) the analysis of bedload transport time series, (II) measurement strategies for recording bedload transport, and (III) preservation and obscuration of discharge input signals by the sediment transport system: (I) In this contribution we have demonstrated CHAPTER 6. SYNTHESIS AND OUTLOOK 192 the suitability of spectral analysis for studying time series of bedload transport measurements. Especially squared coherency proofed to be a powerful tool for identifying scale ranges of differing discharge and bedload transport behaviour. (II) The observation that the bedload transport spectra exhibit white noise behaviour for periods shorter than roughly 5 minutes can be used to determine the ideal sampling frequency for an automated bedload transport measurement system. Considering that the sampling frequency should be at least twice the frequency of the signal of interest (Shannon, 1949), the ideal sampling frequency for bedload transport measurements (at least at the Erlenbach) roughly equals 1 1 0.4 min to 0.5 min . Considerably lower sampling frequencies will miss parts of the bedload transport dynamics that are to be studied. Considerably higher sampling frequencies will waste measurement and analysis efforts by simply displaying random noise behaviour. (III) In addition to this high frequency white noise, the periods of 20 to 40 minutes show a bedload transport behaviour that is clearly not inherited from discharge. This behaviour is caused by varying transport rates and can therefore be attributed to physical processes and interactions in the stream channel upstream of the measurement site. This observation confirms that parts of the input signal of discharge will be obscured by the bedload transport system. Furthermore, it adds that this signal obscuration is limited to a certain temporal scale range with clearly defined upper and lower boundaries. In other words, whether or not a discharge behaviour can be reconstructed from a sedimentary record highly depends on the studied temporal scales. Transferred to the context of modelling, that means that at the described scale range it is not possible to predict bedload transport rates with a deterministic model based on discharge such as sedFlow. The straightforward pre- and postprocessing of sedFlow simulation data and its high calculation speed, have demonstrated that realistic simulations of bedload transport in steep mountain streams can be made easy and efficient. The efficiency makes large scale projects possible such as the one of chapter 4 or such as assessing the long-term effects of river engineering measures. Furthermore, the easy and efficient workflow allows for an adequate consideration of the difficulties in predicting bedload transport. Fluvial bedload transport is a highly non-linear process; the input parameters are usually associated with high uncertainties; and the individual conditions may change completely from one river to another. Therefore, a one-simulation-one-result approach is commonly not sufficient for a realistic prediction of bedload transport behaviour. Rather it is important to perform an adequate sensitivity analysis for each river or project. Such an analysis covers the range of plausible values for the different input parameters and yields a range of plausible outcomes instead of a single result. With its easy use and efficient simulations, sedFlow supports the described approach. CHAPTER 6. SYNTHESIS AND OUTLOOK 193

6.2 Outlook

As described before, sedFlow supports performing sensitivity studies in bedload transport simulation projects. The logical next step would be to study the properties of these uncertainty assessments and to suggest a standardised structure for these assessments. Finally, this should lead to a modified version of the sedFlow model that will automatically perform such assessments and return confidence bands instead of single results. For any numerical model it is desirable that its concepts and algorithms are derived based on physical considerations. It is further desirable that the effects of simplifications and empiric approximations are known qualitatively or in the best case quantitatively. For fractional bedload transport models, a widely used example of such a simplified approximation is the concept of the active layer. This approximation is well known to differ considerably from the situation in natural streams, and Parker et al. (2000) already suggested an alternative concept. Nevertheless, the active layer is still used in many simulation tools for practical reasons. Unfortunately, only little is known on the effects of the active layer concept and on how these effects vary for different realisations of this concept. Within sedFlow, different versions of an active layer are implemented in the same simulation framework. Therefore, the model might serve as a platform for a sensitivity study exploring the effects of this commonly used approximation. In chapter 5 a method for structuring the analysis of bedload transport time series is described and exemplarily applied. That provides the base for future studies of similar datasets, which can be expected to play an important role in upcoming bedload transport research. For example Rickenmann et al. (2014) list thirteen study sites with calibrated, indirect measurement systems for recording bedload transport time series. A comparison of the spectral behaviour of different streams may reveal further insights into bedload dynamics and probably site-specific prevailing dominant processes. As another potential application, the work of Wyss et al. (2014) has shown that geophone datasets can be used to extract time series of bedload transport for individual grain size fractions. The comparison of the bedload transport spectra for different grain size classes may shed new light on the grain-grain interactions and grain exposure and hiding processes. For both the assessment of other streams or of fractional data, the time series study of the present thesis has prepared the base for straightforward analyses on the way to a more profound understanding of bedload transport dynamics. REFERENCES 194

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Parker, G., Paola, C., and Leclair, S.: Probabilistic Exner Sediment Continuity Equation for Mixtures with No Active Layer, J. Hydr. Eng., 126, 818–826, doi: 10.1061/(ASCE)0733-9429(2000)126:11(818), 2000.

Rickenmann, D., Turowski, J. M., Fritschi, B., Wyss, C., Laronne, J., Barzilai, R., Reid, I., Kreisler, A., Aigner, J., Seitz, H., and Habersack, H.: Bedload transport measurements with impact plate geophones: comparison of sensor calibration in diﬀerent gravel-bed streams, Earth Surf. Process. Landforms, 39, 928–942, doi: 10.1002/esp.3499, 2014.

Riedl, C. and Peter, A.: Timing of brown trout spawning in Alpine rivers with special consideration of egg burial depth, Ecol. Freshw. Fish, 22, 384–397, doi: 10.1111/eﬀ.12033, 2013.

Shannon, C. E.: Communication in the Presence of Noise, Proceedings of the IRE, 37, 10–21, doi: 10.1109/JRPROC.1949.232969, 1949.

Wyss, C. R., Rickenmann, D., Fritschi, B., Turowski, J. M., Weitbrecht, V., and Boes, R. M.: Bedload grain size estimation from the indirect monitoring of bedload transport with Swiss plate geophones at the Erlenbach stream, in: River Flow 2014, edited by Schleiss, A. J., Cesare, G. D., Franca, M. J., and Pﬁster, M., pp. 1907–1912, Taylor & Francis, London, 2014. Danksagung

Ich möchte mich bei allen bedanken, die mich während der letzten Jahre unter- stützt haben und mehr als einmal für mich da waren. Ich möchte mich bedanken für all die Zeit, die Ihr Euch für mich genommen habt, und für all die schöne Zeit, die ich mit Euch verbringen durfte. I would like to thank James Kirchner for our amazing discussions and all the things that I learned from you and your great experience. Bei Dieter Rickenmann möchte ich mich dafür bedanken, dass Deine Türe für meine Fragen immer offen stand. Bei Jens Turowski für die Klarheit Deiner Ideen und Gedanken mit der wir selbst die schwierigsten Fragen lösen konnten. Thank you Stuart Lane for revising my thesis and having agreed to be my external examiner. Dem SNF und der ETH Zürich danke ich für die Finanzierung dieser Arbeit im Rahmen des NFP-61 Projektes Sedriver und darüber hinaus. Bei Alexandre Badoux möchte ich mich für Deinen Humor und Deine Un- terstützung über das rein Wissenschaftliche hinaus bedanken. Bei Manfred Stähli für die guten Rahmenbedingungen an der WSL. Bei der gesamten For- schungseinheit Gebirgshydrologie und Massenbewegungen für die mehr als nur angenehme Arbeitsatmosphäre. Bei Massimiliano Zappa für die hydrologisch- en Simulationen mit PREVAH. Bei Martin Böckli für Deine unermüdlichen Beiträge und für unseren gemeinsamen Ritt durch die Welt der Geschiebetrans- portsimulation. Bei Christa Stephan, Lynn Burkhard, Anna Pöhlmann, Claudia Bieler, Christian Greber, Thomas Weninger, Nicolas Zogg, Christian Schaer und Alexander Stahel für Eure Anregungen und Auswertungen und dafür, dass Ihr Euch auf das Wagnis einer Arbeit mit einem sich noch in Entwicklung befin- denden Modell eingelassen habt. Bei Armin Peter, Julian Junker, Christina Riedl und Christoph Hauer für die gute Zusammenarbeit. Bei der Sedriver Begleitgruppe, bei Stefan Braito, Andreas Rimböck, Karl Mayer, Georg Kokai und Max Weiß für die Anregungen aus der Sicht der angewandten Praxis. Bei Simon Etter für die Erstellung des sedFlow Tutorial Beispiels und für das Hand- buch zum Postprocessing Werkzeug sedFlowPlotGUI. Bei Jesse Lieberman und Patrick Stierli für das Korrekturlesen des sedFlow Handbuchs. Bei Mina Ossiaa, Thomas Wüst und Luzi Bernhard für Eure Unterstützung in Programmierfra- gen. Bei Alexander Beer und Martin Böckli dafür, dass Ihr über mehrere Jahre hinweg meinen Dauerohrwurm des Ring of fire ertragen habt. Es ist klasse mit Euch das Büro zu teilen. Bei Käthi Liechti und Stefanie Jörg-Hess dafür, dass

195 DANKSAGUNG 196 ich immer mit meinen “diesmal-aber-wirklich-ganz-einfachen”-Fragen bei Euch vorbei kommen konnte. Bei Brian McArdell, Fabian Walter, Konrad Bogner und Albrecht von Boetticher für die anregenden Diskussionen. Bei Axel Volkwein für Deine Aufmunterungen und Dein Mut-Machen im Programmieralltag vor dem Hintergrund Deiner eigenen Erfahrung. Bei Johannes Schneider für unseren gemeinsamen Endspurt. Und bei Alexander Beer und Carlos Wyss für unsere geniale “Klassenfahrt” nach Potsdam. Bei Wolfgang Müller, Sophie und Christopher Krüger, Melanie Lehmann, Jens Wilken und Tina Sellmeier möchte ich mich dafür bedanken, dass Ihr Euer Versprechen mich in Zürich besuchen zu kommen wirklich wahr gemacht habt. Bei Arthur Dubowicz für die Einladungen nach Lugano, die Eisdielen und unsere Unterhaltungen über das Doktorandenleben nördlich und südlich der Alpen. Bei meinen Eltern für alles. Und bei Kathrin für Deine Geduld, Deine Liebe und noch so vieles mehr. Danke!