Continental Margin Sedimentation: From Sediment

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SPECIAL PUBLICATION NUMBER 37 OF THE INTERNATIONAL ASSOCIATION OF SEDIMENTOLOGISTS

Continental Margin Sedimentation: From Sediment Transport to Sequence Stratigraphy EDITED BY

Charles A. Nittrouer, James A. Austin, Michael E. Field, Joseph H. Kravitz, James P.M. Syvitski and Patricia L. Wiberg SERIES EDITOR

Ian Jarvis School of Earth Sciences & Geography Centre for Earth & Environmental Science Research Kingston University Penrhyn Road Kingston upon Thames KT1 2EE UK

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© 2007 International Association of Sedimentologists and published for them by Blackwell Publishing Ltd BLACKWELL PUBLISHING 350 Main Street, Malden, MA 02148-5020, USA 9600 Garsington Road, Oxford OX4 2DQ, UK 550 Swanston Street, Carlton, Victoria 3053, Australia The right of C.A. Nittrouer, J.A. Austin, M.E. Field, J.H. Kravitz, J.P.M. Syvitski and P.L. Wiberg to be identified as the Authors of the Editorial Material in this Work has been asserted in accordance with the UK Copyright, Designs, and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs, and Patents Act 1988, without the prior permission of the publisher. First published 2007 by Blackwell Publishing Ltd 1

2007

Library of Congress Cataloging-in-Publication Data Continental margin sedimentation : from sediment transport to sequence stratigraphy / edited by C.A. Nittrouer . . . [et al.]. p. cm. – (Special publication number 37 of the International Association of Sedimentologists) Includes bibliographical references and index. ISBN 978-1-4051-6934-9 (hardback : alk. paper) 1. Sedimentation and deposition. 2. Sedimentology. 3. Sequence stratigraphy. 4. Sediment transport. 5. Continental margins. I. Nittrouer, Charles A. QE571.C57 2007 551.3′53 – dc22 2007007166 A catalogue record for this title is available from the British Library. Set in 10.5/12.5pt Palatino by Graphicraft Limited, Hong Kong Printed and bound in Singapore by Markono Print Media Pte Ltd The publisher’s policy is to use permanent paper from mills that operate a sustainable forestry policy, and which has been manufactured from pulp processed using acid-free and elementary chlorine-free practices. Furthermore, the publisher ensures that the text paper and cover board used have met acceptable environmental accreditation standards. For further information on Blackwell Publishing, visit our website: www.blackwellpublishing.com

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Contents Preface, ix Writing a Rosetta stone: insights into continental-margin sedimentary processes and strata, 1 Charles A. Nittrouer, James A. Austin Jr, Michael E. Field, Joseph H. Kravitz, James P.M. Syvitski and Patricia L. Wiberg Introduction, 1 The boundary conditions, 2 The common threads, 3 Eel River (California) continental margin, 3 New Jersey continental margin, 6 Sediment delivery, 7 General considerations, 7 Delivery of Eel margin sediment, 9 Sediment alteration, 11 General considerations, 11 Alteration of Eel margin sediment, 13 Sediment dispersal system, 15 General considerations, 15 Eel margin sediment dispersal system, 17 Seabed failure, 19 General considerations, 19 Eel margin failure, 21 Gravity flows, 23 General considerations, 23 Eel margin gravity flows, 26 Margin morphology, 26 General considerations, 26 New Jersey margin morphology, 29 Eel margin morphology, 31 Margin stratigraphy, 31 General considerations, 31 New Jersey margin stratigraphy, 33 Eel margin stratigraphy, 35 Conclusions, 37 Acknowledgements, 38 References, 38 Sediment delivery to the seabed on continental margins, 49 Paul S. Hill, Jason M. Fox, John S. Crockett, Kristian J. Curran, Carl T. Friedrichs, W. Rockwell Geyer, Timothy G. Milligan, Andrea S. Ogston, Pere Puig, Malcolm E. Scully, Peter A. Traykovski and Robert A. Wheatcroft

Introduction, 49 Review of previous work, 52 Early conceptual models, 52 Sediment loss from discharge plumes, 54 Advective transport in river plumes, 56 Bottom-boundary-layer transport of flood sediment, 59 Summary of past research, 60 Sediment delivery to the Eel margin, 61 Site description, 61 Observational programme, 61 Results, 63 Fate of missing sediment, 86 Summary and conclusion, 92 Summary of strataform sediment delivery, 92 Questions for future research, 92 Acknowledgements, 94 Nomenclature, 94 References, 94 Post-depositional alteration and preservation of sedimentary strata, 101 Robert A. Wheatcroft, Patricia L. Wiberg, Clark R. Alexander, Samuel J. Bentley, David E. Drake, Courtney K. Harris and Andrea S. Ogston Introduction and scope, 101 Consolidation, 104 Theoretical framework, 106 Observations, 108 Physical alteration, 111 Fluid forcing, 111 Bed properties, 116 Deposition, 124 Biological alteration, 125 Alteration of key dynamical bed properties, 125 Bioturbation, 129 Biogenic sedimentary structures, 136 Preservation, 137 Controlling parameters, 138 Dissipation times, 141 The key role of episodic sedimentation, 142 Summary, 144 Acknowledgements, 147 Nomenclature, 147 References, 148

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Oceanic dispersal and accumulation of river sediment, 157 Christopher K. Sommerfield, Andrea S. Ogston, Beth L. Mullenbach, David E. Drake, Clark R. Alexander, Charles A. Nittrouer, Jeffry C. Borgeld, Robert A. Wheatcroft, and Elana L. Leithold Introduction, 157 Margin sediment dispersal systems: a Holocene perspective, 158 Research background, 161 Quantifying sedimentary processes, 162 Suspended-sediment transport, 162 Sediment deposition and accumulation, 164 The northern California margin, 167 Previous work and insight, 167 Sediment production and coastal delivery, 169 Tectonics and sediment yield, 169 Hydroclimatology and recorded streamflow, 171 Floods, land use and sediment delivery, 173 Coastal ocean circulation, 175 Sediment transort and accumulation, 176 Mechanisms of sediment transport, 178 Dynamic trapping mechanisms, 183 Static trapping mechanisms, 183 Sedimentation patterns and rates, 186 Sedimentary event deposition, 186 Centennial to millennial accumulation, 190 Latest Holocene sedimentary record, 194 Accumulation rates and stratigraphic completeness, 197 Sediment budgets of dispersal systems, 199 Development of sediment budgets, 199 Eel margin sediment budget, 201 Conclusions, 203 Acknowledgements, 204 Nomenclature, 204 References, 205 Submarine mass movements on continental margins, 213 Homa J. Lee, Jacques Locat, Priscilla Desgagnés, Jeffrey D. Parsons, Brian G. McAdoo, Daniel L. Orange, Pere Puig, Florence L. Wong, Peter Dartnell and Eric Boulanger Introduction, 213 Historic development of understanding, 214

Contents

Classification, 215 Environments, 216 Fjords, 216 Active river deltas on the continental shelf, 217 Submarine canyon-fan systems, 218 The open continental slope, 219 Statistics of submarine landslides, 219 Mechanics of slope failure, 221 Driving stress, 221 Resisting stress (strength), 221 Slope stability analysis, 224 Pore-water pressure, 224 Sediment mobilization and strength loss, 226 Triggers, 228 Sediment accumulation, 228 Erosion, 228 Earthquakes, 228 Volcanoes, 231 Waves, 233 Gas and gas hydrates, 233 Groundwater seepage, 234 Diapirism, 234 Human activity, 234 Contributions to submarine landslide research from the strataform program, 235 ‘Humboldt Slide’ controversy, 236 Liquefaction failures in Eel Canyon, 247 Gas charging and pore pressures, 248 Development of shear strength and rheology in marine sediment, 249 Submarine landslide geomorphology, 256 Regional mapping of landslide susceptibility, 259 Summary, 261 Overall occurrence and triggers, 261 Controversies, 264 Importance of the liquidity index, 265 Pore pressures and the development of anomalously weak sediment, 265 Development of anomalously high strength, 265 Slope stability analysis and regional assessment of landslide susceptibility, 265 An important contribution, 265 Acknowledgements, 265 Nomenclature, 265 References, 267

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The mechanics of marine sediment gravity flows, 275 Jeffrey D. Parsons, Carl T. Friedrichs, Peter A. Traykovski, David Mohrig, Jasim Imran, James P.M. Syvitski, Gary Parker, Pere Puig, James L. Buttles and Marcello H. García Introduction, 275 Turbidity currents, 278 Basic mechanics, 279 Frontal dynamics, 283 Turbidity-current fans, 285 Channelization and channel processes, 289 Observations of turbidity currents, 294 Debris flows, 295 Basic mechanics, 296 Hydroplaning, 299 Advances in analytical and numerical solutions, 302 Observations of submarine debris flows, 303 Wave-supported sediment gravity flows, 305 Wave-boundary-layer mechanics, 305 Wave-supported sediment gravity flows and the role of buoyancy, 306 Vertical distribution of momentum and sediment concentration, 309 Observations of wave-supported sediment gravity flows, 315 Origin and transformation of sediment gravity flows, 320 Failure-induced formation, 320 Wave/tide-induced formation, 322 Direct formation from river loading, 323 Linkages between phenomena, 325 Conclusions, 327 Acknowledgements, 328 List of nomenclature, 328 References, 330 Seascape evolution on clastic continental shelves and slopes, 339 Lincoln F. Pratson, Charles A. Nittrouer, Patricia L. Wiberg, Michael S. Steckler, John B. Swenson, David A. Cacchione, Jeffery A. Karson, A. Bradley Murray, Matthew A. Wolinsky, Thomas P. Gerber, Beth L. Mullenbach, Glenn A. Spinelli, Craig S. Fulthorpe, Damian B. O’Grady, Gary Parker, Neal W. Driscoll, Robert L. Burger, Christopher Paola, Daniel L. Orange, Michael E. Field, Carl T. Friedrichs and Juan J. Fedele

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Introduction, 340 From bathymetry to seascape evolution, 340 Scope of paper, 341 Background, 341 Physiographic definitions, 341 Historical interest in and importance of the continental shelf and slope, 341 Processes governing shelf width and slope relief, 342 Plate tectonics and the stair-step shape of continental margins, 342 First-order effects of thermal subsidence and tectonic uplift, 344 Second-order effects of isostasy, compaction and faulting, 345 Added effects of faulting, 347 Processes that form the shelf profile, 348 Rivers, deltas and growth of the coastal plain, 348 Bedload deposition, sediment plumes and clinoforms, 351 The impacts of waves and currents on the shelf and shoreface profile, 353 Subaqueous deltas and wave-supported sediment gravity flows, 356 Independent movements of the shoreline and shelf break, 357 Shelf evolution during sea-level change, 359 Processes that act to limit the slope of the continental slope, 362 Seafloor failure and submarine groundwater flow, 362 Bottom shear from internal waves, 364 Turbidity-current erosion and deposition, 365 Processes that create submarine canyons and slope gullies, 366 Turbidity currents versus seafloor failure in forming submarine canyons, 366 Turbidity currents versus seafloor failure in forming slope gullies, 370 Future research, 372 Acknowledgments, 373 References, 373

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The long-term stratigraphic record on continental margins, 381 Gregory S. Mountain, Robert L. Burger, Heike Delius, Craig S. Fulthorpe, James A. Austin, David S. Goldberg, Michael S. Steckler, Cecilia M. McHugh, Kenneth G. Miller, Donald H. Monteverde, Daniel L. Orange and Lincoln F. Pratson Introduction, 381 Distinguishing time-scales, 382 The importance of the long-term record, 382 Long-term geochronology: dating continental-margin records, 383 Analysing the long-term record, 383 Basin-wide surfaces and long-term processes, 383 Tools for accessing the long-term record, 387 The Eel River Basin, 390 Tectonism – a major control of sediment distribution and preservation, 390 Offshore stratigraphy – local variations of governing processes, 398 Stratigraphic modelling, 412 The New Jersey margin, 415 Cenozoic sedimentation on a passive margin, 415 Pleistocene sequences, 425 The last eustatic cycle and its preserved record, 432 New Jersey submarine canyons, 436 Stratigraphic modelling, 439 Summary, 444 The long-term record: its challenges and rewards, 444 The Eel River Basin: difficulties in recognizing eustatic control, 445

The New Jersey margin: eustatic imprint, with complications, 446 The long-term record – where next?, 448 Acknowledgements, 448 References, 449 Prediction of margin stratigraphy, 459 James P.M. Syvitski, Lincoln F. Pratson, Patricia L. Wiberg, Michael S. Steckler, Marcelo H. Garcia, W. Rockwell Geyer, Courtney K. Harris, Eric W.H. Hutton, Jasim Imran, Homa J. Lee, Mark D. Morehead and Gary Parker Introduction, 459 Component sed-strat modules, 462 River flux, 462 Surface plumes from rivers, 467 Hyperpycnal flow from rivers, 471 Shelf boundary-layer sediment transport, 475 Slope stability analysis, 481 Subaqueous debris flows and turbidity currents, 484 Compaction, 490 Integrated models, 493 sedflux approach, 493 Stratigraphic sequences, 501 Seismic models, 510 Physical properties, 510 Acoustic properties, 512 Seismic modelling, 514 The way forward, 515 Acknowledgements, 516 Nomenclature, 516 References, 519 Index, 531

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Prediction of margin stratigraphy JAMES P.M. SYVITSKI*, LINCOLN F. PRATSON†, PATRICIA L. WIBERG‡, MICHAEL S. STECKLER§, MARCELO H. GARCÍA¶, W. ROCKWELL GEYER**, COURTNEY K. HARRIS††, ERIC W.H. HUTTON*, JASIM IMRAN‡‡, HOMA J. LEE§§, MARK D. MOREHEAD¶¶ and GARY PARKER*** *Environmental Computation and Imaging Facility, INSTAAR, University of Colorado, Boulder, CO 80309-0450, USA (Email: [email protected]) †Earth and Ocean Sciences, Duke University, Box 90230, Durham, NC 27708, USA ‡Department of Environmental Sciences, University of Virginia, Charlottesville, VA 22904, USA §Lamont-Doherty Earth Observatory of Columbia University, Palisades, NY 10964, USA ¶Ven Te Chow Hydrosystems Laboratory, University of Illinois, Urbana, IL 61801, USA **Department of Applied Ocean Physics and Engineering, WHOI, Woods Hole, MA 02543, USA ††Department of Physical Sciences, Virginia Institute of Marine Sciences, Gloucester Point, VA 23062, USA ‡‡Department of Civil and Environmental Engineering, University of South Carolina, Columbia, SC 29208, USA §§US Geological Survey, Menlo Park, CA 94025, USA ¶¶Department of Civil Engineering, University of Idaho, Boise, ID 83702, USA ***Department of Civil and Environmental Engineering, University of Illinois, Urbana, IL 61801, USA

ABSTRACT

A new generation of predictive, process–response models provides insight about how sedimenttransport processes work to form and destroy strata, and to influence the developing architecture along continental margins. The spectrum of models considered in this paper includes short-term sedimentary processes (river discharge, surface plumes, hyperpycnal plumes, wave-current interactions, subaqueous debris flows, turbidity currents), the filling of geological basins where tectonics and subsidence are important controls on sediment dispersal (slope stability, compaction, tectonics, sea-level fluctuations, subsidence), and acoustic models for comparison to seismic images. Recent efforts have coordinated individual modelling studies and catalysed Earth-surface research by: 1 empowering scientists with computing tools and knowledge from interlinked fields; 2 streamlining the process of hypothesis testing through linked surface dynamics models; 3 creating models tailored to specific settings, scientific problems and time-scales.

The extreme ranges of space- and time-scales that define Earth history demand an array of approaches, including model nesting, rather than a single monolithic modelling structure. Numerical models that simulate the development of landscapes and sedimentary architecture are the repositories of our understanding about basic physics and thermodynamics underlying the field of sedimentology. Keywords Numerical modelling, compaction, acoustic properties, river discharge, gravity flows, clinoforms, river plumes, sequence stratigraphy.

INTRODUCTION

This paper highlights a new generation of predictive process–response models that have been developed by the STRATAFORM programme.

These simulators provide insights on how sedimenttransport processes work to form and destroy strata, and influence the developing architecture along the world’s continental margins. The paper provides an overview of these models, written for

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Response Model

Geometric model (observational)

Statistical model (regression analysis)

Conceptual model (inferential) Empirical model (predictive relationships)

Process Model Deterministic model (conservation inputs - outputs) Computer model (high resolution simulations)

Mathematical model (fluid dynamics) Probabilistic model (steady-state conditions in flux)

Statistical comparison (observations & predictions)

the non-expert and those not desiring a comprehensive mathematical treatment. The models cover the spectrum of both short time-scale sedimentary processes and those relating to the filling of geological basins where tectonics and subsidence are important controls on sediment dispersal. Students and researchers who are interested in pursuing this subject are encouraged to read the overviews of Slingerland et al. (1994), Watney et al. (1999), Paola (2000) and Tetzlaff & Priddy (2001). There are two main approaches to modelling the fill of basins (Fig. 1). The response model begins with: (i) observing the stratigraphic record to determine the temporal and spatial distribution of the properties of sedimentary deposits; followed by (ii) constructing a schema of how the sedimentary system works; (iii) developing statistical relationships from these or other observations; (iv) generating an empirical model from the observational statistics; and finally (v) applying the model to new

Fig. 1 Organization of the process–response modelling environment in the field of quantitative dynamic stratigraphy. (After Syvitski, 1989.)

geographical regions for validation and verification. Markov analysis of the transitions between sedimentary facies is an example where statistically defined relationships are used to develop conceptual models (Sonu & James, 1973). The applicability of response models is usually limited to environments with similar conditions (Fox, 1978). The process model relies on the rudiments of fluid–sediment interactions and the processes that govern those interactions. Key equations are considered to be mathematical approximations of reality, which are linked to describe the physical system. The equations describe the conservation of mass, momentum and sometimes energy. Equations describing the conservation of mass are called continuity equations, and, for water, describe the rate of change in water mass as a function of spatial gradients of water discharge. The continuity equation for sediment in transport is called the Exner equation and describes the rate of change in bed

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Prediction of margin stratigraphy

elevation as a function of spatial gradients in sediment flux. The conservation of momentum refers to the spatial balance of forces (change in momentum over time) on a fluid system (gravity and pressure balanced by friction), although secondary terms relating to acceleration may be included. Momentum equations evaluate the operating forces at a given location and provide information on the velocity and boundary shear stresses in sediment transport models. The conservation of energy tracks the conversion of turbulence to work done as a function of boundary friction and other actions, for example energy expended on particle suspension, fluid entrainment and bed erosion. Forces that are either steady or vary with time drive the conservation equations. In some models a stochastic element is introduced to simulate the seemingly random nature of Earth-surface processes (earthquakes, floods, storms, and so on). Computer models are the numerical schemes used to solve these mathematical constructs (Fig. 1). They may be designed using finite-element or finite-difference schemes, and solved on a variety of numerical grids according to the dynamics being simulated or the complexity of the domain boundaries. Solutions may involve the full domain (Eulerian view), or a subset of the domain through the tracking of individual fluid particles (Lagrangian view). Four classes of models are available to the earth scientist, depending on the objective of the investigation. These include: 1 models whose predictions are at the resolution of modern sampling rates that are used to hindcast and forecast real time and space events (transport or realistic-domain models); 2 models that predict the net product of a particular set of processes at a time or space resolution beyond normal sampling schemes (depositional models); 3 models that principally describe one class of processes and their geological response (single-process models); 4 models that describe the complete sedimentary environment (whole-margin models).

Combinations of these four classes of models are possible and common. Engineers, oceanographers and environmental scientists use transport models (Jewell et al., 1993; Mulder et al., 1997; Lou et al., 2000; Kassem &

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Imran, 2001) because they usually predict the consequences of sediment erosion or deposition on very short time-scales. For example, an engineer might want to predict the advent of the next turbidity current and whether it is capable of breaking communication cables or breaching a pipeline. By contrast, geologists who relate modern processes to the stratigraphic record often use depositional models that combine a steady-state condition with rare but important geological events (Mulder et al., 1998a). Such models provide simulations of geological environments encompassing thousands of years. The interest here is in the properties of a sedimentary deposit, not the physics of sediment transport, even though the laws of physics are employed to predict the properties of the final deposit. Single-process models simulate a single transport/deposition process for a particular sedimentary environment. For example, delta progradation can be modelled with sedimentation from river plumes as the dominant process (Bonham-Carter & Sutherland, 1967; Wang & Wei, 1986), or through bulk-transport processes (Kenyon & Turcotte, 1985). Both processes may duplicate how bathymetric profiles of a prograding delta can vary with time. This similarity of result (equifinality) occurs through the judicious use of empirical coefficients. In a wholemargin model, these two processes would be linked together with other processes to simulate multiple sediment transfer mechanisms (Syvitski et al., 1988). In 1988, there were few whole-margin models available (Syvitski, 1989), examples being twodimensional, dynamic models for the transport, deposition, erosion and compaction of clastic sediments (Bitzer & Harbaugh, 1987; Syvitski et al., 1988), and a diffusion-based model that moved sediment across key boundaries (Jervey, 1988). Many more whole-margin models have since become available in a variety of flavours: (i) geometric models for the study of sequence stratigraphy; (ii) analytical models; (iii) mechanistic models; (iv) hybrid models that combine these elements; and (v) inverse models. Geometric models build sequences using knowledge of the geometry and timing of deposits (Cant, 1991; Reynolds et al., 1991; Mackey & Bridge, 1995; Prather, 2000). Analytical models apply general equations that define the longterm nature of stratal evolution. The analytical equations take the form of diffusion, advection or

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advective-diffusion formulations (Kaufman et al., 1991; Niedoroda et al., 1995; Flemings & Grotzinger, 1996; Pirmez et al., 1998; Ganjeon & Joseph, 1999; Kendall & Sen, 1999; Swenson et al., 2000; Storms et al., 2002). Mechanistic models apply physical laws to model the important sedimentary processes (Tetzlaff & Harbaugh, 1989; Martinez & Harbaugh, 1993; Haupt & Stattegger, 1999; Syvitski & Hutton, 2001). Hybrid models combine a variety of approaches and acknowledge that some processes are known well and can employ physical laws while other processes do not yet have accepted physics (Loseth, 1999; Ritchie et al., 1999; Syvitski et al., 1999). Inverse models simultaneously solve for the values of multiple process parameters using bounded unique solutions constrained by field observations (Cross & Lessenger, 1999). Whole-margin models are useful for predicting the time-varying impact of sedimentary processes, and the distribution of lithostratigraphic properties away from points of control (Franseen et al., 1991). Whole-margin models also prove valuable to those working on modern environmental applications (Martinez & Harbaugh, 1993), global warming scenarios (Syvitski & Andrews, 1994; Schäfer-Neth & Stattegger, 1999), natural disaster mitigation efforts (Caruccio, 1989), reservoir characterization (Shelton & Cross, 1989; Pratson et al., 2000a), oil exploration (Tetzlaff & Harbaugh, 1989) and national security (Syvitski et al., 1999). This paper will first review individual process models that emphasize important margin environments, and sediment transport or seafloor dynamics. A source-to-sink modelling approach is used, first discussing how a river’s discharge of water and sediment may be simulated, followed by its dispersal across the shelf as surface (hypopycnal) plumes, or subsurface (hyperpycnal) plumes, and through wave-current interactions within the bottom boundary-layer. Next, the stability of seafloor deposits is discussed, as failures may remobilize material as either debris flows or turbidity currents. Compaction is discussed as a separate modifier of seafloor deposits. It is then considered how these separate modules can be united into whole-margin models, able to examine the role of sea-level fluctuations, subsidence, isostasy and tectonics on the evolving sedimentary deposits, and how whole-margin models can be coupled to acoustic models, for comparison with seismic

images. The paper concludes with a sense of the future, the development of a Community SurfaceDynamics Modelling System.

COMPONENT SED-STRAT MODULES River flux

Most sediment is delivered to the ocean by rivers, and this accounts for approximately 95% of the global flux from land to sea (Syvitski, 2003; Syvitski et al., 2003). Most of the flux is as suspended sediment load. Dissolved load and bedload are nearly an order-of-magnitude less than the suspended load. Thus the first step in modelling the evolution of a continental margin is to simulate a time series for the fluxes of water and sediment reaching the sedimentary basin. The temporal variations in a river’s discharge and sediment flux to the ocean can strongly influence the creation and preservation of stratigraphic layers (Steckler et al., 1996; Morehead et al., 2001). The temporal variability of river discharge and sediment flux to the ocean ranges from daily cycles due to diurnal snow melt events or diurnal rains, to seasonal moisture and temperature cycles, to annual weather patterns, up to long-term climatic shifts. Modelling of the spatial and temporal variability of river discharge and its associated sediment flux to the ocean is the focus of this section. The suspended-sediment concentration (cs) in a river is commonly related to the discharge (Q) of the river and can be approximated by a power law: cs = aQb

(1)

This is exemplified by work on the Mackenzie River in Canada. Within the cloud of data points depicted in Fig. 2A, well-defined patterns exist that relate to various events occurring in the river basin. For the Mackenzie River, the rising limb of the flood has lower sediment concentrations than the falling flood limb, producing what is known as a hysteresis loop (Fig. 2B). Depending on the river basin, its source of discharge variability and its sediment sources, hysteresis loops can proceed clockwise, counterclockwise, or have complex patterns. Hysteresis loops occur on many time-scales, from daily loops associated with snow or glacial melt

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Power Law Relationship

Hysteresis Loops

1

10

3

A

B

Fig. 2 The complex relationship between discharge (Q) and suspended-sediment concentration (Cs) on the Mackenzie River. (A) The relationship between Q and Cs can be approximated by a power law with the rating coefficient a and exponent b. (B) A counterclockwise hysteresis loop exists on the Mackenzie River, with high concentrations later in the season due to increasing glacial melt water (after Morehead et al., 2003). Hysteresis loops account for part of the suspended-sediment variability at a given discharge. (Data are from Environment Canada, Ottawa.)

0

Cs (kg m-3)

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2

-1

10

-2

10

(Richards, 1984), to flood-wave loops occurring over several days to weeks (Brown & Ritter, 1971), to annual patterns occurring on larger river systems (Kostaschuk et al., 1989; Morehead et al., 2003). Floods on rivers larger than creeks (> 25 m3 s−1 mean discharge) typically last for days to weeks. In order to adequately resolve this type of flood in a hydrological-basin model, it is necessary to simulate the basin processes on daily time-steps. With the present technology, it is feasible to model sedimentary and hydrological basin processes on a daily time-step for intervals from individual events up to tens of thousands of years (Syvitski & Morehead, 1999). Models designed for longer time-scales typically use bulk properties for the river flux that parameterize the character of the river without explicitly modelling individual events (Steckler, 1999). In order to simulate the temporal variability and magnitude of the discharge and sediment flux from a river into a sedimentary basin, the main processes controlling runoff must be accounted for in a model (Beschta, 1987). River discharge is controlled by many factors including: river-basin characteristics (soil properties, vegetation, relief and size); weather (precipitation rate, timing and type, temperature and lapse rate); glaciated extent; and the hydrogeology (groundwater effects) of the basin. Each of these factors contributes its own signal to the temporal variability of the discharge. A successful hydrological basin model will produce

1

Cs = 6.83e-013 Q2.77 4

10

Q (m3 s-1)

5

10

0 15

20

25

30

35

Q (103 m3 s-1)

time-variable output with realistic distribution and timing of events. In order to simulate past climates, the model must either have a weather simulator embedded in it or be able to accept weather generated by another model, such as an atmospheric global-circulation model (GCM). The first part of a hydrological basin model is the inclusion of meteorological information. Observations from meteorological stations can be fed directly into the model. However, direct observations are typically sparse and overrepresent lowland valleys, while underrepresenting higher mountains where much of the precipitation falls. A number of methods have been developed to distribute station data across a landscape to provide more realistic forcing fields. The prism climate maps are one example of an expert-weighted regression analysis that provides spatially distributed forcing fields for hydrological modelling (Daly et al., 1994). Other models such as isnobal, a distributed snow energy-balance model (Marks et al., 2001), use similar regression methods to distribute atmospheric forcing fields over a watershed. Both the prism and isnobal distribution routines were developed to produce forcing fields using measured data. hydrotrend is an example of a two-dimensional (elevation and upstream distance) water-balance model used for simulations at the dynamic level (daily) of discharge (Syvitski & Alcott, 1995b; Syvitski et al., 1998a). The model resides within

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a geographical information system (GIS) where climatic environmental data are fused with basin characteristics to create a synthetic river-discharge time series. hydrotrend accepts direct input from meteorological-station data, GCM output, or past global-change proxies of climate. The model can either use the forcing data directly or it can generate daily temperature and precipitation using Monte Carlo techniques (Syvitski & Morehead, 1999) based on input climate statistics. The observed or simulated meteorological data are distributed across the model basin using a geographically determined (by latitude) lapse rate and the basin morphology (area, maximum elevation, hypsometry, glacial equilibrium-line altitude). The hydrotrend climate simulator can generate weather scenarios for modern, past and changing climate.

A second component of any hydrological model is a tracking algorithm for the various water reservoirs and flow pathways (e.g. topmodel; Beven et al., 1995). hydrotrend also tracks the various water pools (surface water, groundwater, snow, glaciers and overland flow) and accounts for additions (precipitation, infiltration) and reductions (evapotranspiration, runoff, melt) from each pool. Simple energy-balance models are incorporated into hydrotrend to account for snow and glacial accumulation and melt. Each of these pools feeds into a simplified routing routine to simulate daily discharge (velocity, width, depth) at the river mouth. Once the velocity, width and depth at the river mouth are determined, hydrotrend utilizes predicted power-law rating equations (see Box 1) for the calculation of suspended load (Syvitski et al.,

Box 1 Stochastic modelling of a river’s sediment load Morehead et al. (2003) proposed a stochastic model for the simulation of the sediment discharge of ungauged rivers Qs/Qs = ψF(Q/M)C

(B1.1)

where Qs is daily sediment discharge, ψ is a lognormal random variable designed to capture measurement error and flood dynamics, F is a constant of mass flux,Qs is power-law average of the long-term average of Qs, Q is daily discharge at the river mouth, M is power-law average of the long-term average of Q, and C is a normal random variable, otherwise known as the rating coefficient. The following relationships define these terms E(ψ) = 1

(B1.2)

σ (ψ) = δ (10−φM)

(B1.3)

E(C) = a1 − a2{ + a3H + a4 ln(Qs)

(B1.4)

σ (C) = b + mM

(B1.5)

Q = Qr + Qice + Qn − Qevap ± Qg

(B1.6)

where E and σ represent mean and standard deviation of the stated variable, δ, φ, ai, b and m are empirical constants, Qg is ground-water discharge, Qr is discharge from rainfall as surface runoff, Qice is icemelt discharge, Qn is snowmelt (nival) discharge, and Qevap is discharge component lost via evaporation. Q is thus a function of precipitation, basin location, temperature, elevation and soil properties. Large rivers suppress small perturbations in time-varying sediment and water sources and have relatively small σ(ψ )(Syvitski et al., 2000). Small rivers are inherently noisy in terms of their discharge signal with larger values of σ(ψ). C varies annually, dependent on M. Smaller rivers have more invariant values of C. Rivers with large discharge have a greater range in annual C, depending on the importance of their various tributaries to the overall discharge within a given year. Qs is Qs = α1Hα Aα ek{ 2

3

(B1.7)

where H is river-basin relief, A is river-basin area, { is mean surface temperature of the drainage basin, and αi and k are dimensionless constants that vary with the global climate belts.

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Table 1 Comparison of hydrotrend modelled output with US Geological Survey observations for the Eel River (After Morehead et al., 2001) Parameter

Observation

Model

Total annual load (t yr−1) Mean discharge (m3 s−1) Mean concentration (g m−3) Rating coefficient, a (g m−3) Rating exponent, b

4 × 107 to 2 × 108 240 2170 0.35 1.14

2 × 107 to 1 × 108 230 2120 0.14 1.06

2000, 2003; Morehead et al., 2003), and Bagnold’s (1966) transport equation for the calculation of bedload. By predicting the daily discharge hydraulics at a river’s mouth, the model output allows for direct input to shelf circulation and sedimentation models. hydrotrend has simulated the relatively small icemelt-dominated Klinaklini River (Syvitski et al., 1998b) in British Columbia, the raindominated Eel River in northern California (Syvitski & Morehead, 1999), the snowmelt-dominated Liard River in northern Canada (Syvitski, 2002), cyclonedominated Lanyang, Taiwan (Syvitski et al., 2005a), and the reservoir-influenced Po, Italy (Syvitski et al., 2005b). Model validation of hydrotrend on the Eel River is based on (Morehead et al., 2001; Table 1): (i) daily discharge hydrographs including flood frequency based on US Geological Survey observations; and (ii) daily and annual sedimentload variability based on 16 yr of US Geological Survey observations. Hydrological, hydraulic and water quality models are classified as deterministic, stochastic, or some combination of these two types. Processes that are too complex or poorly understood to be modelled deterministically are represented by statistical characteristics, while many statistical models also employ simple process-type mechanisms. Below are some commonly used models (Syvitski et al., 2004): rorb rafts – rainfall-runoff and stream-flow routing model hec – surface runoff model suite idro – rainfall-runoff and storm-forecasting model iris – Interactive River System Simulation program wqrrs – Water Quality for River-Reservoir System topmodel – hillslope hydrology simulator

hydrotrend – climate-driven sediment discharge simulator wepp – Water Erosion Prediction Project model answers – Areal Non-point Source Watershed Environment Response Simulation fhantm – Field Hydrological And Nutrient Transport Model mike 11 – river flow simulation model with data assimilation watflood – integrated models to forecast watershed flows

Once a river model is shown capable of simulating an appropriately wide range of conditions in the modern environment, it can be used to represent past environmental conditions, assuming the input climatic and basin parameters can be estimated. The ability to simulate the full distribution of discharge events, including the rare, extremely large events likely to be preserved in deposits, is crucial for a hydrological model being used to supply sediment to a stratigraphic model. Over the Holocene period, sea-level fluctuations have greatly impacted the drainage areas of rivers (Mulder & Syvitski, 1996). Although basin area increases for all non-glacial rivers during glacial periods, around former ice sheets, isostatic depression would have caused a local rise in sea level and thus a decrease in a river’s drainage area. In most cases, the glacial to interglacial drainage areas of rivers vary by < 30%. Following the global lowering (~120 m) of sea level, small rivers fronted by a wide continental shelf may become tributaries of larger rivers, while large rivers may merge to form enormous rivers (Mulder & Syvitski, 1996).

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When modelling the hydrological changes between glacial conditions and Holocene temperate conditions, changes in climate can widely alter the discharge of water and sediment. Many modern temperate rivers may have been under polar conditions where snow or even icemelt would have dominated the discharge to the ocean (Morehead et al., 2001). It is illustrative to compare the modern Eel River to its glacial-stage counterpart. In today’s climate, the Eel River Basin is strongly affected by the southern excursion of the Jet Stream in the winter, which propagates storm fronts onto the coast from the Pacific Ocean, producing intense precipitation. The Eel River Basin receives as much as 80% of its annual precipitation in the winter. Sometimes a winter month may experience 20 to 30 days of nearly continuous rainfall, reaching inputs of 0.5 m in a month. As a result of the high discharges and the power-law relation of sediment load to discharge, the Eel River transports six orders-of-magnitude more sediment in the winter than during the drier summer. Most years have a winter month where the river transports between 106 and 107 t of sediment. The month of December

in 1964 is significant in that the sediment load exceeded 108 t. In the three peak days of this December flood, the river may have transported more sediment than during the previous 8 yr of river flow combined (Syvitski & Morehead, 1999). The Eel River Basin is comprised of the loosely consolidated Franciscan and Rio Dell Formations that are easy to erode and land slides are generated on a regular basis (Brown & Ritter, 1971). This makes the Eel River one of the dirtiest rivers in North America (Milliman & Syvitski, 1992). Climate proxies for the western USA (Hostetler et al., 1994; Benson et al., 1996, 1997a,b) were used to set the climate statistics in hydrotrend in order to simulate the last glacial period (about 18 kyr BP). These proxies indicate that the Eel River Basin was wetter and colder during the Last Glacial Maximum (LGM) than at present. Figure 3A depicts the climate (averaged weather) trends used as input to hydrotrend to simulate the transition from a glacial interval to the modern interglacial. Random annual, monthly and daily weather variations were imposed upon these climate trends to create the precipitation and temperature

Fig. 3 A hydrotrend simulation indicating profound changes in the total flux of sediment from the Eel River for an idealized climate-change scenario depicting a 300-yr transition from the last glacial (first 300 yr) to the modern climate (last 300 yr; after Morehead et al., 2001). (A) Modelled climatic values of temperature and precipitation for the Eel River Basin taken from climatic proxies. (B) Mean annual discharge under modern climate is about half that of the glacial scenario. (C) The largest floods in the two scenarios are of similar magnitude, but the average annual floods are smaller in the modern period. (D) The mean annual sediment flux of the glacial period was about twice the modern flux. The modelled modern flux of sediment is more temporally variable.

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Table 2 Characteristics of the Eel River, California, as simulated by hydrotrend (After Syvitski & Morehead, 1999)

Parameter

Glacial

Modern

Total annual load (Mt yr−1) Mean discharge (m3 s−1) Mean annual peak (m3 s−1)

15.6 380 6160

7.8 200 4240

time-series used to generate river discharge in hydrotrend. During the LGM, the Jet Stream may have been confined to the central California region causing increased storm frequency, colder temperatures and increased precipitation in the Eel River Basin (the first 300 yr of the simulation experiment; Morehead et al., 2001). As the North American continental glaciers retreated, the Jet Stream moved progressively northward during the summer months. The climate transition is thought to have occurred rapidly as the glaciers retreated (the second 300 yr of the simulation). During modern climate (the last 300 yr of the simulation), the Jet Stream is north of northern California during the summer and only moves over the region during the winter months. The increased precipitation and cooler climate of the glacial period yielded approximately double the annual discharge and sediment loads of the modern period (Fig. 3B & D; Table 2) according to hydrotrend (Syvitski & Morehead, 1999). The flow conditions were more constant during the glacial period, due to the basin being snowmelt dominated, consistent with modern river systems (Pitlick, 1994). The mean of the annual peak discharges for each of the periods shows a marked decrease during the modern period (Fig. 3C; Table 2). The largest floods, however, are of similar magnitudes during both periods. The largest modern floods are due to rain events on top of widespread low-elevation snow, which provides more water to the river for runoff than either a pure rain event or a pure snowmelt event. Presumably the largest floods during the last glacial period would have been caused by the same mechanism. Assuming the model is correct, the present-day Eel River has much more interannual variability than during the last glacial period. A change in the total flux of sediment out

467

of the river, along with a change in the variability of the flux, probably occurred between the two periods, and would have had marked effects on the type of sedimentary layers that are accumulated on the continental margin. Modelling river basins over longer time-scales has revealed a number of important characteristics that affect how rivers behave. A simulation on the Klinaklini River, British Columbia, Canada, demonstrated how a river can switch discharge states rather abruptly during a slow and continuous climate-change scenario (Morehead et al., 2001). During a brief period, as the river switched from a glacial-melt-dominated system to a mixed-glacialand-snow system, larger than expected fluctuations in discharge were simulated. During this portion of the simulation, certain summers were not warm enough to melt the entire snow pack, leading to lower than normal peak discharge for those years. On subsequent warmer years, accumulated snow would melt entirely, yielding higher than normal peak discharges for those years. In summary, climate change produces complex temporal changes in a river basin’s discharge and sediment load, and this may have profound effects on the resultant sedimentary deposits (Morehead et al., 2001; Syvitski, 2002; Syvitski et al., 2003). It is interesting to speculate that the dominant flux of sediment to temperate continental margins follows the location of the Jet Stream, as the climate system moves in and out of glacial periods. In contrast, tropical systems are less impacted by fluctuations in temperature and its inherent effects on sediment production and transport (permafrost soils, freeze– thaw intervals, snowmelt and icemelt), but are rather more impacted by the intensity and duration of rainfall. An abundance of proxy records show an enhanced monsoonal regime in the early Holocene (Overpeck, 1996), and the monsoondriven river systems strongly responded to this enhanced regime (Goodbred & Kuehl, 2000a,b). The Ganges–Brahmaputra system then carried over 2.5 times its present load. Surface plumes from rivers

Freshwater plumes provide the initial dispersal of terrestrially derived particulate matter in the coastal ocean. The lower density of freshwater compared with seawater generally produces buoyant plumes; however, in rare cases the concentration

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of suspended sediment may be so great that the density of the inflowing turbid water is greater than the ambient seawater, forming a hyperpycnal plume (Mulder & Syvitski, 1996). This section addresses the more common case of buoyant plumes. The behaviour of a buoyant plume depends on the freshwater flow, the geometry of the river mouth and receiving waters, and oceanographic conditions in the coastal ocean (Wright & Coleman, 1971; Garvine, 1974; Geyer et al., 2000, 2004). River plumes that enter shallow receiving waters may remain attached to the bottom for significant distances from the mouth (Wright et al., 1990; Geyer & Kineke, 1995). In contrast, rivers entering deep water or narrow continental margins separate from the bottom at locations close to the mouth (Eisma & Kalf, 1984; Geyer et al., 2004). These two types of plumes contain distinctly different sediment transport processes: bottom-attached plumes recycle sediment by resuspension in the bottom boundary layer, whereas detached plumes lose sediment to the underlying, ambient seawater due to isolation of the plume from the turbulent boundary layer. Surface plumes are particularly sensitive to wind forcing, due both to the direct forcing of wind stress on the plume and to the influence of the winds on the ambient coastal currents (Chao, 1988; Fong & Geyer, 2001). The Eel River enters a relatively steep and narrow continental shelf, resulting in a surface plume that detaches from the bottom just seaward of the surf zone (Geyer et al., 2000). As sediment enters the coastal ocean and moves away from the river mouth, it settles out of the surface plume at a rate dependent on its settling characteristics (Hill et al., 2000, this volume, pp. 49–99; Curran et al., 2002). Once removed from the surface plume, sediment is dispersed by oceanographic transport in the underlying water, which may include resuspension in the bottom boundary layer. Predicting the deposition of fluvially derived material in an environment such as the Eel shelf depends on the characterization of resuspension, particle settling velocities, and the structures of both plume and oceanographic waters. These evolve in time, due to changes in discharge and oceanographic forcing conditions. Sediment transport in the coastal ocean also responds to significant variability in the vertical, across-shelf and along-shelf dimensions. Full representation of the behaviour of freshwa-

ter plumes in the coastal ocean requires a threedimensional, time-dependent model. Some basic aspects of plume behaviour and initial deposition can still be captured by more parameterized representations (Scully et al., 2003). Two numerical models have been developed as part of the STRATAFORM Project in order to characterize plume dispersal on the Eel shelf, northern California (Morehead & Syvitski, 1999; Harris et al., 2000; Harris & Wiberg, 2002). Both incorporate sediment transport within the plume and settling of sediment into underlying waters, but the models differ in the level of detail included in the dynamics, and in the time-scales over which they can be applied. Morehead & Syvitski (1999) represented the freshwater plume as a turbulent-jet entering the coastal ocean (see Box 2), while Harris et al. (2000, 2005) used a primitive-equation ocean model (see Blumberg & Mellor, 1987) to predict the structure and velocities of the plume and underlying waters. The primitive-equation model used 45-s time-steps to resolve vertical sediment advection. This, and the challenge of specifying robust boundary forcing, have limited the length of their simulations to time-scales of a few weeks. The turbulent jet model used simplified physics of plume dynamics and sediment transport, and longer timesteps (~1 day). This avoided the need for detailed open-boundary conditions and allowed for simulations that are more suitable to making predictions over geological time-scales. The plume model predicts sediment delivery to the coastal ocean as a function of sediment load, along-shelf currents and, as the dominant factor, the initial momentum of the plume as it enters the ocean (Morehead & Syvitski, 1999). The plume is modelled as a turbulent jet that can be steered by underlying currents, and that interacts with seawater through diffusion of momentum and sediment. Moving away from the river mouth, plume width increases, and velocities and turbulence levels within the plume decrease. Turbulent diffusion of the plume’s momentum slows the flow, and enables sediment to settle out of the plume and into the underlying water column. The plume model handles transport of sediment below the brackish plume, by assuming that it settles directly to the bed or, alternatively, computes its transport by using a bottom-boundary-layer model (Syvitski & Bahr, 2001). This approach simplifies a number of

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469

Box 2 Non-conservative, advection-diffusion model for a steady, two-dimensional surface plume The sediment inventory of a surface plume from a river’s discharge into the ocean can be largely captured by three terms: (i) advection of sediment by the river-induced velocity field (term a); (ii) diffusion of the sediment by turbulence (term c); and (iii) settling of sediment out of the plume at a rate governed by a first-order removal-rate constant λ for each grain size (term b). The governing equation in this case is the two-dimensional advection–diffusion equation

∂vI ∂y

+ λI = b

∂ A ∂I D ∂ A ∂I D Ks + Ks ∂x C ∂x F ∂y C ∂y F

(B2.1)

1 4 4 4 2 4 4 4 3

∂x

+

{

∂uI

1 4 2 4 3

CMS_C09.qxd

a

c

where x is longitudinal or axial direction, y is lateral direction, u is longitudinal velocity, v is lateral velocity, I is sediment inventory or mass per unit area of the plume, λ is first-order removal-rate constant for a given grain size, and Ks is sediment diffusivity driven by turbulence. Syvitski et al. (1998a) defined the position of the centreline of a plume as: x b0

= 1.53 + 0.90

A u0 D A y D 0.37 Cv F Cb F 0 0

(B2.2)

where b0 is the river-mouth width. The suspended-sediment concentration, cs, around the centreline is cs (x,y) = C0 e

− λt

b0 π C1x

⋅e

⎛ y ⎞ −⎜ ⎟ ⎝ 2 C1x ⎠

2

(B2.3)

where C0 and C1 are empirical constants. The flow field of a plume is influenced by: (i) the Coriolis force (i.e. the latitudinal position determines the deflection of the angular acceleration); (ii) angle of the river mouth in relation to the coastline; (iii) a Kelvin wave effect (causing plumes to hug the coast when the plume flows in the direction of the Coriolis force); (iv) shore winds (Ekman effect) causing upwelling or downwelling along the coast; (v) the hydraulics of the river mouth (i.e. supercritical or subcritical nature of flow); and (vi) the general nature of the ambient coastal circulation.

potentially important processes, including bottom friction, wind stress and bottom-boundary-layer transport. As an example, simulation of a large Eel River flood in 1995 predicted sediment delivery from the plume to be highest near the river mouth, and to be confined shoreward of the 50-m isobath (Fig. 4). The primitive-equation model is able to compute the sediment transport and deposition from the Eel plume, based on sediment settling, advection by ocean currents and resuspension in the bottom boundary layer (Harris et al., 2000, 2005). The model predicts velocities and water-column structure under forcing by winds, momentum input from the Eel River discharge, buoyancy, tides and alongshelf currents. Sediment is treated as a settling tracer that is transported with ambient currents, and can be deposited and resuspended from the seafloor. Sediment delivered during floods is trans-

ported with the floodwater until it settles out of the surface plume with a specified settling velocity. Beneath the plume, sediment is transported with ambient water and continues to settle towards the bed. Wave-current interaction and bottom friction are incorporated to account for a bottom boundary layer (Grant & Madsen, 1979). Sediment is deposited on the bed when the supply exceeds the ability of the flow to carry the material in suspension, but can be resuspended should the flow capacity increase or supply decrease. Applied to a large flood of the Eel River ( January 1997), the depositional patterns depended most critically on the settling properties of the sediment and on wind forcing during peak discharge (Harris et al., 2000). Winds for this simulation were strong (15 m s−1) and northward during the first 3 days of the flood, and then relaxed to be weaker and southward. Peak sediment discharge (5 g L−1) at

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60

B

A 1 mm

50

40

50 m

10

100 m

30

50 m

1 mm 100 m

Along-shelf Distance (km)

CMS_C09.qxd

20 10

100

10

100

1000

0

10 15

Discharge = 8040 m3 s-1

Discharge = 3650 m3 s-1

Valongshore = 1.07 m s-1

Valongshore = 0.95 m s-1

10

5

0

15

10

5

0

Across-shelf Distance (km) Fig. 4 Snapshots of predicted plume deposition (mm) summed over four grain sizes for the January 1995 flood of the Eel River, CA. (A) The first and largest peak on 8 January. (B) The start of the falling flood limb on 14 January. (Modified from Morehead and Syvitski, 1999.)

the river mouth occurred 3 days into the flood event, and by day six of the simulation most sediment had been delivered to the coastal ocean. Wave energy was held constant, with significant wave heights of 3 m throughout the simulation. Based on field observations of particle aggregation (Hill et al., 2000), 60% of the sediment was flocculated (settling velocity ws = 0.1 cm s−1), and 40% unflocculated (ws = 0.01 cm s−1). Results showed the direction of the plume responds to Earth’s rotation, wind forcing and the angle of the river mouth.

These factors deflect the plume to the north, and confine it to the inner shelf during the early stages of the simulation (Fig. 5A). As winds relax and turn southward, the plume thins and spreads out over deeper waters (Fig. 5B). Dispersal patterns depend critically on settling characteristics. The unflocculated, fine-grained material remains, for the most part, within the surface plume, and its dispersal pattern depends on plume velocity and structure. During strong northward winds, the unflocculated portion of the sediment load is transported beyond Trinidad Head (50 km north of the river mouth), resulting in export of approximately 10–20% of the sediment load (see Fig. 5A). Under southward winds, the unflocculated sediment that remains in the plume is dispersed over a wide area. Cross-shelf currents carry some sediment to mid-shelf depths, where a muddy flood deposit is observed. While the location of this mid-shelf deposit matches that of the deposits observed soon after flood events, the thickness of deposition predicted by this mechanism is much smaller (< 1 cm) than the observed deposit (up to 10 cm; Wheatcroft et al., 1997). Flocculated material is predicted to settle out of the plume within a few kilometres north of the river mouth, and it accounts for the majority of the deposit (outlined in red in Fig. 5A & B). The mass of flocculated sediment delivered by the surface plume accounts for the amount observed in the mid-shelf flood deposit (Fig. 5C), but a cross-shelf transport mechanism is needed to reconcile the predicted inner-shelf delivery with observed mid-shelf deposition. One hypothesis is that resuspension by energetic waves prevents sediment deposition on the energetic inner shelf, and cross-shelf currents transport sediment to the less-energetic mid-shelf depths where deposition occurs (Hill et al., this volume, pp. 49 – 99). Model calculations indicate that the supply of sediment to the inner-shelf overwhelms resuspension processes there, however, and even simulations that included energetic waves predicted a thick innershelf deposit within the timeframe of observable mid-shelf deposition (Fig. 5B). Field observations suggest that a near-bed fluidmud layer with significant offshore velocities can develop on the Eel River shelf during times of ample sediment supply and energetic waves (Ogston et al., 2000; Traykovski et al., 2000). The buoyancy

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471

Observed Deposit

Total Sediment in Motion and Deposited 50

Thickness (cm)

Thickness (cm)

0.1

0.1

1

10

1

A

50

40

Trinidad Head

10

C

B 70

50

50

70 90 90


CMS_C09.qxd

30

70

\

90

150

150

150

20

10

0

10

Day 3 20

0

Day 9 10

0

20

10

0

10

20

Across-shelf Distance (km)

Fig. 5 Plume structure, ocean currents and sediment dispersal simulated for the January 1997 flood of the Eel river, compared with observed deposit (after Harris et al., 2000). Bathymetric contours shown as dashed lines. Snapshots shown at: (A) peak of flood and northward wind forcing; and (B) when discharge and winds are low. (A & B) Colour contours show total suspended and bed sediment for a simulation containing 40% unflocculated and 60% flocculated material. Red line indicates contour of > 1 cm deposited on the bed. Blue lines illustrate the isohaline for a salinity of 30. Arrows indicate depth-averaged velocities. (C) Location of observed deposit following the January 1997 flood. (From Wheatcroft et al., 1997.)

anomaly of the sediment-laden layer could create seaward velocities. This hypothesis has been tested by including a representation of the fluid-mud layer within the three-dimensional model (Harris et al., 2005). Inclusion of a thin near-bed fluidmud layer resulted in a mid-shelf deposit of appropriate thickness and mass within the timescale of observed deposition (Fig. 6). The role of gravity-driven fluid mud was parameterized by a two-dimensional (x − y) model (see Box 4) which assumes that plume sediment is deposited directly into the wave boundary layer on the inner shelf (Scully et al., 2003). This fluid-mud model predicted that 26% of the fine sediment discharge by the Eel River was deposited on the mid-shelf, with a distribution consistent with field observations.

These and other modelling studies indicate that plume dynamics and sediment settling rate determine the along-shelf position of deposition, and the fraction of sediment that remains on the proximal shelf. Even for a bottom-detached plume, such as the Eel River plume, the cross-shelf location of the deposit depends on transport that occurs in the bottom boundary layer after sediment settles from the surface plume. Hyperpycnal flow from rivers

Turbidity currents are sediment-laden underflows that occur in relatively quiescent bodies of water such as dammed reservoirs, natural lakes, fjords and oceans. The current obtains its driving force

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Dispersal with Gravity-driven Flow 50

Thickness (cm) 0.1

40

1

10

50 70 90

30


CMS_C09.qxd

150

20

10

0

10 Day 9 20

10

0

Across-shelf Distance (km) Fig. 6 Simulation of the January 1997 Eel River flood using a model that accounts for a thin fluid-mud layer at the seafloor. Bathymetric contours (m) shown as dashed lines. Simulation represents the end of the flood event, when discharge and winds are low. Colour contours show total suspended and bed sediment for a simulation containing 40% unflocculated, and 60% flocculated material. Red line indicates contour of > 1-cm seabed deposit. Blue lines illustrate the isohaline for a salinity of 30. Arrows indicate depth-averaged velocities. (After Harris et al., 2005.)

from a density difference with the ambient water. A turbidity current can be triggered by one or more of several processes such as wave action, subaqueous slumps induced by seismic or other loading, or plunging of river water as a hyperpycnal plume (see Parsons et al. (this volume, pp. 275–337) for further discussion). Among the various mechanisms, a hyperpycnal plume generated at a river mouth is most capable of maintaining a sustained turbidity current event. Even rivers with moderate to small loads of suspended sediment (e.g. < 1.0 kg m−3) can

create hyperpycnal plumes in freshwater lakes (Weirich, 1984). The Rhine plume flowing into Lake Constance, Switzerland, can produce bottom currents of > 100 cm s−1 (Lambert, 1982). Concentrations > 0.10 kg m−3 in river water are enough to produce underflows in the freshwater Katsurazawa Reservoir, Japan (Chikita, 1989). Initiation of a sustained turbidity current from the direct delivery of sediment into the ocean by a river is considered to be a rare event, as seawater with a specific gravity of ~1.026 poses a strong density barrier to plunging. The critical concentration of suspended sediment needed to create a hyperpycnal plume in seawater is considered to be 35–45 kg m−3. There are few rivers in the world that discharge into the ocean with such large sediment concentrations, even during flood events (Mulder & Syvitski, 1995). Alternatively, Parsons et al. (2001) found that fresh warm water with suspendedsediment concentration as small as 1 kg m−3 can produce a hyperpycnal flow in cold brine by means of double diffusive convection. Rare or not, marine hyperpycnal flows associated with large floods can significantly alter the seascape. A case in point is an 11-m-thick deposit in the Saguenay Fjord, eastern Canada, apparently formed from a historical hyperpycnal discharge event (Syvitski & Schafer, 1996; Skene et al., 1997). Turbidity currents generated at a river mouth consist of three distinct parts: the plunge region, the main body and the leading head. Each part of the current has distinct characteristics and plays an important role in the overall flow and transport processes (Kassem & Imran, 2001). The ambientwater entrainment during plunging affects the remainder of the current. Vertical structures of sediment concentration and velocity in the main body of the current are responsible for sustained scour of, and deposition on, the lake or ocean floor. The mixing at the leading head determines how far the current will travel before it loses its identity. The plunging phenomenon has been widely studied as a practical engineering problem associated with industrial effluent discharge, reservoir sedimentation and stratified flow ( Johnson et al., 1987). Various factors, such as the inflow Richardson number, inflow Reynolds number, bottom slope of the receiving water body and confluence divergence angle, influence the plunging process and such factors as plunge depth and location, and the sub-

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sequent evolution of the current. Once the current is established the hyperpycnal flow evolves with momentum balance set up between the pull of gravity and fluid pressure with frictional forces that dissipate energy (see Box 3). Studies on the plunging phenomenon have involved laboratory and field observations, and parameterization of different processes in empirical equations (Akiyama & Stefan, 1984; Johnson et al., 1987; Stefan & Johnson, 1987). Such empirical equations address the effect of just one or two variables at a time, and therefore lack universal applicability. A robust numerical model, in contrast, can incor-

473

porate many of the contributing factors simultaneously. Often empirical relationships are needed to determine upstream boundary conditions when using one-dimensional depth-averaged models of turbidity currents (Skene et al., 1997; Mulder et al., 1998b). Few attempts have been made to model the plunging process and subsequent generation of hyperpycnal plume (Akiyama & Stefan, 1984; Bournet et al., 1999; Kassem & Imran, 2001). Higher-dimensional numerical models can predict the development of the entire process from the free-surface-flow condition at the upstream end to the formation of the turbidity current, including the

Box 3 Layer-averaged hyperpycnal plume in Lagrangian form The layer-averaged hyperpycnal plume consists of four conservation equations: (i) continuity of water; (ii) continuity of sediment; (iii) conservation of momentum; and (iv) conservation of energy (after Parker et al., 1986; Pratson et al., 2000a). Continuity of fluid

∂Uh

+

∂x

= ewU

(B3.1)

b

1 4 2 4 3

∂t

{

∂h

a

where h is current thickness, t is time and x is distance along the flow path, U is layer-averaged flow velocity and ew is a dimensionless entrainment coefficient. Equation (B3.1) reflects the dependency of the height of the current (term a) on the entrainment rate of ambient water (term b). Continuity of sediment

∂UCh ∂x

= ws(Es − roC)

(B3.2)

b

1 4 2 4 3

∂t

+

1 4 2 4 3

∂ Ch

a

where C is the layer-averaged bulk sediment concentration, ws is the settling velocity of particles, Es is dimensionless erosion coefficient that determines the rate that sediment is entrained into the current by erosion, and ro is the ratio of sediment concentrated at the base of the flow. The mass of sediment in the flow (term a) depends on the rate that sediment is either added to the flow or settles out of the flow (term b). Conservation of momentum

∂x

a

= RgChα − –12 Rg

∂ Ch2 ∂x

b

− u2*

(B3.3)

{

∂U2h

1 4 2 43

∂t

+

1 2 3

∂Uh

1 4 2 4 3

CMS_C09.qxd

d

c

where R denotes the submerged specific gravity of the sediment, g is gravitational acceleration, α is seafloor slope, and u* is the shear velocity at the base of the current and reflects the loss of momentum to the current flowing across a rough sea floor. Equation (B3.3) describes the balance of momentum in a turbidity current (term a), with the current’s downslope acceleration due to gravity (term b), fluid pressure gradients within it (term c), and frictional slowing (term d).

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Conservation of energy

b

c

d

(B3.4)

1 4 4 2 4 4 3

1 4 2 4 3

= u2*U + –12 U3ew − ε0h − RgwsCh − –12 RgChUew − –12 Rghws(Es − roC)

{

∂x

1 2 3

∂UKh

+

1 4 2 4 3

∂t

1 4 2 4 3

∂Kh

e

f

a

where K is the layer-averaged turbulent kinetic energy, and ε0 is the layer-averaged dissipation rate. The distributed kinetic energy (term a) represents the balance between the rate at which the current produces turbulent kinetic energy (term b) and then consumes it through dissipation by the viscosity of the current (term c), energy consumption needed to keep the sediments in suspension (term d), turbulent kinetic energy converted to potential energy as the flow thickens through entrainment thus raising its centre of gravity (term e), and the expenditure of energy in eroding the bed (term f ). Note that if the current deposits sediment, then the current actually gains energy back. Mixing of freshwater and seawater Hyperpycnal flows in the marine environment involve freshwater and the sediment it carries mixing with salt water (Skene et al., 1997). River water enters the marine basin with a density of 1000 kg m−3, where it mixes with ocean water having a density typically of 1028 kg m−3. This mixing increases the fluid density of a hyperpycnal current, and alters the value of C and R (above), where

∂ρ ∂x

=

ew h

(ρsw − ρ),

C=

ρf − ρ ρs − ρ

,

R=

ρs − ρ ρ

, ρf = (1 − C)ρ + Cρs

(B3.5a, b, c, d)

where ρ is density of the fluid in the hyperpycnal current, ρsw is density of the ambient seawater, ρf is density of the hyperpycnal current (sediment and water), and ρs is grain density.

stabilization of the plunge point (Fig. 7: Kassem & Imran, 2001). As the sediment-laden water flows in with a dominant dynamic force, the reservoir water is pushed forward and a separation surface becomes pronounced (Fig. 7A). When the pressure

A

Time = 10 s

force at the bottom becomes significant, it accelerates the flow at the bottom at a rate higher than the movement at the top (Fig. 7B). As the pressure forces continue to grow, the flow plunges to the bottom and begins to move as an underflow (Fig. 7C). At this

B

Time = 20 s

D

Time = 120 s

Hyperpycnal Plume C Elevation (m)

CMS_C09.qxd

Time = 30 s

Fig. 7 A numerical simulation

0

5 s 10 s 15 s 20 s 25 s 30 s

-0.25

40 s 120 s

-0.50 4

5

6

7

8

Distance (m) E

Time Sequence

9

10

11

that depicts (A) an open channel flow, or river, transforming into a hyperpycnal flow (B through to D) beneath ambient marine water. This simulation is in the dimensions of a similar laboratory experiment where sediment-laden freshwater flowed in a saltwater basin (E) along an inclined plane. (After Kassem & Imran, 2001.)

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stage, the velocity at the top surface is still significant enough to move the plunging point forward. When equilibrium is reached, the velocity at the top disappears, a stable plunge point (plunge line in a three-dimensional flow) forms, and the current moves forward with a bulge-shaped head and an elongated body (Fig. 7D). The entire process is chronicled in Fig. 7E. Of the measured global rivers, only nine can produce hyperpycnal flow on an annual basis (Mulder & Syvitski, 1995). The Eel River in northern California is one of seven rivers located in the USA that can produce hyperpycnal flow during a 100-yr flood event. The Eel experienced large floods in 1995 and 1997. Estimated concentrations obtained using a rating curve (Mulder & Syvitski, 1995) indicated that the 1995 Eel River might have exceeded the critical concentration for plunging over a 2-day period (Imran & Syvitski, 2000). A survey conducted by investigators of the STRATAFORM programme immediately after the 1995 flood revealed that only ~25% of the flood sediment discharged by the Eel River remained on the shelf. While storm-induced waves and currents may play a role in resuspending and transporting the flood sediment, hyperpycnal discharge may be a dominant sediment transport mechanism during the peak flood flow. A hyperpycnal flow may have been directed towards the adjacent Eel Canyon and delivered sediment to the base of the continental slope through the canyon (Puig et al., 2003, 2004; Mullenbach et al., 2004). Hyperpycnal flows can also be strongly influenced by along-shelf currents. The impact of the 1995 Eel hyperpycnal flow was modelled using a two-dimensional depth-averaged formulation that incorporates alongshore currents (Imran et al., 1998; Imran & Syvitski, 2000). To provide the upstream boundary condition, river data were obtained from a nearby gauging station (Scotia, CA; Brown & Ritter, 1971), and the width of the river mouth was estimated to be 1.5 km during peak discharge. A current thickness of 4.4 m, velocity of 1.3 m s−1, sediment concentration of 0.019 by volume, and a reduced specific gravity of 1.58 were specified for the river-mouth boundary condition. Other input parameters were obtained using the empirical formulae developed by Akiyama & Stefan (1984). The bottom slopes were calculated from seafloor bathymetry. Based on wind data (NDBC Buoy

475

46022), the along-shelf current velocity ranged from 0 to 1.4 m s−1 during the flood period (Morehead & Syvitski, 1999). Model results revealed hyperpycnal plumes generated by the Eel River that could flow into the adjacent Eel Canyon, or move northward towards Trinidad Head depending on the strength of along-shelf currents (Imran & Syvitski, 2000). Velocity vectors and contours of plume thickness (Fig. 8A) indicate that, if along-shelf currents do not influence the hyperpycnal plume, it has a tendency to flow towards the canyon along a natural gradient. The presence of an along-shelf current of modest magnitude, directed to the northeast, will turn the the hyperpycnal flow away from the canyon (Fig. 8B). The above discussion shows the complex nature of hyperpycnal flow as a hydrological event, and its effectiveness in dispersal of sediment delivered by large floods in certain rivers (see global review by Mulder et al., 2003). Hyperpycnal flows form in the marine environment when river discharge enters the ocean with suspended concentrations in excess of 36 kg m−3 due to buoyancy considerations, or as little as 1–5 kg m−3 when convective instability is considered. They form at a river mouth during floods of small to medium size rivers including extreme events such as jökulhaups, dam breaking and draining, and lahar events. Associated with high suspended-sediment concentration, hyperpycnal flows can transport a considerable volume of sediment to the ocean. The typical deposits or hyperpycnites differ from turbidites because of their well-developed inversely graded facies and intrasequence erosional contacts (Mulder et al., 2003). Hyperpycnite stacking can locally generate high sediment accumulation rates, in the range of 10–20 cm kyr−1. Hyperpycnites are related to climate through flood frequency and magnitude, so their record should vary with sea level and climate change. Shelf boundary-layer sediment transport

Flows observed on the continental shelf are typically combinations of unidirectional currents and oscillatory motions due to wind-generated water waves. Currents, with variations on time-scales of hours or days, are principally tidal, wind-driven, or related to larger-scale patterns of ocean circulation. Wave-generated oscillatory flows, with

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200 300 400

500 00 600 7

1300

800 900

0

1000 1100

1300

120

B

200 300 400

0

500 00 600 7

120

800 900

A

1000 1100

41°15´


15 km

Trinity Canyon

Trinity Canyon

50

100

50

100

Trinidad Head

Trinidad Head

41°N

Sediment Wave Field

Sediment Wave Field

22 m 12 m

40°45´

12 m

2m

2m eell

n o CCa yonn

32 m EE

EE

CMS_C09.qxd

eell

n o CCa yonn Eel River

Eel River 100

100

40°45´ 124°45´

124°30´

124°15´ W

124°45´

124°30´

124°15´ W

Fig. 8 Simulated thickness of a hyperpycnal current originating from the Eel River, after 8 h of flow. Velocity vectors show the direction and relative magnitude of the current. Base map shows the bathymetry (m) of the margin. (A) Under a no-along-shelf-current scenario, the hyperpycnal flow heads towards the Eel canyon following the natural topography. (B) With an along-shelf current of 35 cm s−1, in a north-east direction, the hyperpycnal flow is directed towards the north-west and the sediment wave field, and away from the canyon.

periods in the order of seconds to tens of seconds, are produced by surface gravity waves, although lower frequency internal waves can also be present. When wave-generated oscillatory fluid motions extend to the seabed, they produce shear stresses on the bed and within the relatively thin (~0.1-mthick) wave boundary layer. The velocity of nearbed wave orbital motion depends on wave height, period and water depth. In general, the larger the waves and the shallower the water, the larger the near-bed wave orbital velocities and wavegenerated shear stresses that could exceed the threshold of grain motion. When both currents and waves contribute to near-bed flow, shear stresses in the wave and the current (bottom) boundary layer are enhanced. Sediment transport on the continental shelf is strongly affected by the combined presence of

waves and currents. Coastal currents in many locations are insufficient to mobilize sediment outside of the nearshore zone. In these regions, it is only when moderate to high wave conditions are present that bed shear stresses are sufficient to mobilize sediment at the seabed. Even at depths of 50–100 m, mean winter wave-generated shear velocities can be considerably larger than current shear velocity. Waves, however, are inefficient at transporting sediment owing to their oscillatory motion. Directions and rates of transport depend largely on the currents present during episodes of high wave-generated bed shear stress. The first and still the most widely used models of shelf sediment transport are one-dimensional models in which vertical profiles of velocity and suspended-sediment concentration are calculated from near-bed wave and current conditions (Smith,

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1977; Grant & Madsen, 1979). One-dimensional models assume that flow and sediment conditions are spatially uniform. This yields

∂ cs ∂ A ∂c D = wscs + Ks s ∂t ∂z C ∂z F

(2)

as the governing equation for suspended-sediment concentration, where cs is sediment concentration, ws is particle settling velocity and Ks is sediment diffusivity. Additionally, these models often neglect transient effects, instead assuming an instantaneous adjustment of shear stress and suspended-sediment concentration to changes in wave and current velocities. Despite these somewhat limiting assumptions, one-dimensional models of sediment transport on the shelf provide near-bed suspended-sediment concentrations in reasonable agreement with measured concentrations (Li et al., 1996; Cacchione et al., 1999; Wright et al., 1999; Wiberg et al., 2002). This suggests that local resuspension tends to dominate measured near-bed suspended-sediment concentrations. Often these models are applied with at least one adjustable parameter: the resuspension coefficient that scales the bottom boundary condition on suspendedsediment concentrations. Further development of shelf sediment-transport models has followed four directions. First, a number of efforts have been made to improve the representations of near-bed transport processes and model parameterizations. These studies address the parameterization of bottom roughness (Xu & Wright, 1995; Li & Amos, 1998), reference concentration (Li et al., 1996), effects of flocculation (Carr, 2002), near-bed stratification due to suspended sediment (Styles & Glenn, 2000), and bed armouring (Wiberg et al., 1994; Reed et al., 1999). Second, twodimensional, time-dependent models can resolve effects of advection as well as patterns of net erosion or deposition (Zhang et al., 1999; Harris & Wiberg, 2001). Third, shelf sediment-transport models have been embedded into, or coupled with, models of shelf circulation, allowing spatial patterns of transport, erosion and deposition to be determined (Keen & Slingerland, 1993; Harris et al., 2000). Finally, various approaches are used to represent shelf sediment-transport processes in models predicting the evolution of margin form and stratigraphy (Thorne et al., 1991; Niedoroda et al., 1995) in which time-steps of days to tens of years

477

are employed, much longer than the time-steps used in most shelf-transport models. Examples from STRATAFORM studies of the Eel River and New Jersey continental shelf are provided below. The Eel shelf has a very energetic wave environment and yet mud is able to accumulate on the shelf. The Eel River provides a large source of sediment to the shelf, with estimated finegrained (< 63 µm) sediment discharges averaging 15 Mt yr−1 (Sommerfield & Nittrouer, 1999). Analysis of modern and ancient shelf deposits indicates that very fine-grained mud (predominantly < 20 µm) layers are preserved in the bed (Leithold, 1989; Drake, 1999). Yet analysis of transport on the Eel shelf indicates that wave and current conditions are sufficient to remove at least the very fine-grained mud delivered to the shelf (Harris & Wiberg, 2002). The source of the apparent contradiction appears to lie in the properties of fine-grained deposits that are not adequately accounted for in the most commonly used shelf sediment-transport models, because they were developed for sediment that behaves like sand. Several processes are important in the transport of mud that generally can be neglected when modelling sand transport: compaction and cohesion, flocculation and near-bed stratification produced by sediment in suspension. Each of these tends to limit the suspended-sediment flux. Compaction and cohesion place a limit on entrainment rates, thereby reducing the volume of sediment in suspension (Wiberg, 2000, Sanford & Maa, 2001). Flocculation of suspended sediment on the Eel shelf increases the settling of sediment from a flood plume to the seabed (Harris et al., 2000; Hill et al., 2000) and is an important control on limiting nearbed suspended-sediment concentrations (Harris & Wiberg, 2001; Carr, 2002). Observation and modelling suggest that near-bed stratification associated with fine-grained suspensions strongly affects the distribution of sediment in the water column (Friedrichs et al., 2000). This is particularly true near the top of the wave-boundary-layer when current shear velocities are significantly smaller than wave shear velocities (Reed et al., 1999). Under these conditions, stratification can inhibit the upward diffusion of sediment out of the wave-boundarylayer, resulting in wave-boundary-layer concentrations that under some conditions reach fluid-mud concentrations (Ogston et al., 2000; Traykovski et al., 2000; Scully et al., 2002). The resulting fluid-mud

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suspensions can travel across the shelf as density currents (Parsons et al., this volume, pp. 275–337). Models of this cross-shelf gravity-driven transport process indicate that it is important in forming the flood deposits found on the Eel shelf (Traykovski et al., 2000; Scully et al., 2003; Harris et al., 2005). One-dimensional shelf sediment-transport models provide a good framework for investigating the detailed mechanics of transport, but they cannot account for spatial variations in flow and/or bed sediment properties that might lead to divergences in sediment flux. Calculating patterns of net erosion and deposition, as well as changes in bed texture on the shelf, requires two- or three-dimensional modelling. One approach is to extend the equation for conservation of sediment mass to yield a timedependent advection-diffusion equation in two dimensions (vertical and one horizontal dimension)

∂ cs ∂c ∂ A ∂ csD ∂c ∂ A ∂ csD + ws s + Ks = −u s + Ks C F ∂t ∂x ∂x ∂x ∂z ∂z C ∂z F

(3)

and to couple it with an equation for conservation of mass in the bed

∂η 1 A ∂ qsx ∂Vs D =− + ∂t F ∂t cbed C ∂ x

(4)

where u is the x-component of flow velocity, η is bed elevation, cbed is the sediment concentration of the bed surface (1-porosity), qsx is the x-component of sediment flux and Vs is the volume of sediment in suspension (Zhang et al., 1999; Harris & Wiberg, 2001, 2002). Applied to a cross-shelf transect, these models capture the effects of sediment advection, bed winnowing, and net erosion and deposition on sediment redistribution and the formation of fine-scale stratigraphy on the shelf. These models show that there is a general tendency for winnowing of fine-grained sediment from the inner shelf with subsequent deposition on the mid-shelf. Resulting depths of net erosion and deposition are in the order of several centimetres for typical storm events on the Eel shelf (Zhang et al., 1999; Harris & Wiberg, 2002). While useful for developing an understanding of the importance of various processes to crossshelf sediment redistribution, fully two-dimensional (x–z) advection-diffusion models of shelf sediment

transport have several drawbacks that limit their potential for general operational use or direct extension to three dimensions. First, they are computationally intensive because the equations must be solved on a two-dimensional grid at relatively small time-steps to assure numerical stability. Second, the models require input of near-bed wave and current conditions across the shelf. While wave conditions can in some cases be determined from deep-water measurements of surface wave spectra, as in the case of the Eel shelf, no comparable information is available on cross-shelf variations in currents. Currents are typically measured at one or several cross-shore locations, but never at the resolution of a model grid, and rarely for long periods of time. Furthermore, while along-shelf currents tend to be correlated over large distances, across-shelf currents tend to exhibit little or no correlation, even over relatively short distances. One solution is to use an ocean circulation model to characterize the currents. For example the cross-shelf model slice computes boundary-layer currents, sediment transport and bed modification (Reed et al., 1999). It embodies the dynamics of the two-dimensional models described above, while relying only on an imposed wind field and wave and tidal conditions as forcing terms. Spatial wind fields are available globally, which allows the slice model to be used in locations where no direct measurements of currents exist. While some shelf systems can be reasonably approximated as a two-dimensional system (e.g. no significant alongshelf variations), many cannot. In these cases, a full three-dimensional circulation model must be used to represent the currents on the shelf. Three-dimensional models, such as the Princeton Ocean Model (Blumberg & Mellor, 1987), not only include effects of waves, winds, tides and mean currents, but can also account for freshwater buoyancy, which is important in understanding the delivery of sediment to the shelf during river flood events (Geyer et al., 2000). Application of a threedimensional circulation model (ecom-sed) that includes suspended-sediment transport equations has revealed that the volume and location of deposition are critically sensitive to the settling properties of fine-grained flood sediment (Fig. 9; Harris et al., 2000, 2005). The sediment transport models described above are primarily used to investigate shelf sediment

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Unflocculated

0.1

50

1

Observed Deposit

Thickness (cm)

B

10

0.1

1

C

10

50

50

40

479

Flocculated

Thickness (cm)

A

50 70

70

70 90

90

90

30 150

150

150

km


CMS_C09.qxd

20

10

0

10

20

10

0

20

10

0

20

10

0

Across-shelf Distance (km) Fig. 9 Flood deposits on the Eel shelf following the January 1997 flood of the Eel River. (A) Calculated when sediment in the flood plume settled as individual grains. (B) Calculated when sediment in the flood plume settled as flocs. (C) The observed flood deposit. The calculations were made using a three-dimensional circulation model with suspended-sediment transport. Although the unflocculated calculations put the flood deposit in approximately the correct position, the thicknesses are too small. Other observations suggest that the calculated flocculated deposit (B) is located in the region of initial plume deposition, and that a cross-shelf gravity-driven fluid-mud flow transferred the sediment from the inner to the mid-shelf shortly after the flood (see Fig. 6). (After Harris et al., 2002.)

transport during storm or flood events for which the forcing conditions (waves and currents or winds) are known. When modelling the long-term evolution of margin morphology or stratigraphy, a different approach is needed. First, there are no direct measurements of forcing conditions over these long time-scales and, second, the small (several hours or less) time-steps used in the models are neither computationally practical nor necessary to capture long-term patterns of shelf sedimentation. There are several ways to represent shelf sediment-transport processes over long time periods. One approach is to force a simple one-dimensional shelf sedimenttransport model with conditions representative of a day or a year, rather than an hour or minutes.

In doing so, care must be taken to find statistics of the forcing conditions that, when used as input to the model, yield appropriate average sediment fluxes. For example, characterizing waves in terms of annual average conditions or currents in terms of daily or longer averages will underestimate sediment transport rates owing to the non-linear relationship between transport and wave height (or orbital velocity) and to the neglect of tidal currents, respectively. Another approach is to develop a time-averaged form of the conservation-of-mass equation for suspended-sediment concentration, to yield an equation for long-term average sediment fluxes on the continental shelf. Niedoroda et al. (1995),

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for example, proposed a two-dimensional, depthaveraged and time-generalized equation in which the sediment flux on the shelf was related to advection, wave-biased bedload transport, and largescale diffusion. The diffusive fluxes were specified such that an equilibrium shelf profile is maintained on average (Niedoroda et al., 1995). This model sequence has been used to represent shelf processes in a model of long-term margin stratigraphy (Steckler et al., 1996), which is described below. Alternatively, available measurements of wave and current conditions can be used to formulate shelf diffusion coefficients representative of specific shelf locations, which can be used in a diffusive model of shelf sediment fluxes (Wiberg, 2001). A third approach to incorporating shelf sedimenttransport processes in continental-margin models

is to develop simple analytical representations of the important processes. As an example, a recent analytical shelf-transport model based on the importance of wave-supported sediment gravity flows to cross-shelf transport on energetic shelves subject to high loads of fine sediment (Traykovski et al., 2000; Wright et al., 2001; Scully et al., 2002) has been implemented in sedflux. The model is based on two relationships, a linear momentum balance for sediment-laden gravity flows and a critical Richardson number which determines the maximum amount of sediment that can be suspended before stratification effects shut down turbulence production (Box 4). From these, gravity-flow sediment flux, sediment deposition rates and equilibrium shelf profiles can be calculated. Results suggest that margins with large sediment

Box 4 Gravity-driven sediment flows from wave resuspension on continental shelves The maximum sediment load carried in a shelf bottom boundary layer (BBL) is determined by the critical Richardson number, Rcr, defined as the ratio of the depth-integrated buoyancy anomaly B to bottom velocity shear U2max (Trowbridge & Kineke, 1994) Ricr =

B U 2max

= 1/4

(B4.1)

and Umax = U w2 + U c2 + U g2

(B4.2)

where Uw is near-bed velocity due to the action of waves, Uc is the near-bed velocity due to ambient currents, and Ug is the velocity of the bottom boundary layer (BBL) under the influence of gravity. Shear instabilities occur when Ri < Ricr and shear instabilities are suppressed for Ri > Ricr. If excess sediment enters the BBL, and Ri increases beyond Ricr, then turbulence is dampened. In that case, sediment settles out of the boundary layer, stratification in the boundary layer is reduced and Ri returns to Ricr. If excess sediment settles out of the BBL, or bottom stress increases and Ri decreases beyond Ricr, then turbulence intensifies. Sediment then will re-enter the base of the boundary layer, stratification will increase in the lower boundary layer and Ri returns to Ricr. At high suspended-sediment concentrations in the BBL, the momentum balance for shelf gravity-driven sediment flow is (Wright et al., 2001)

αB = CD〈4P4u〉 = CDUmaxUg

(B4.3)

where CD is the coefficient of drag, 〈4P4u〉 is the wave-averaged, cross-shelf component of the quadratic velocity and Umax is the total velocity. The sediment deposition rate D is given by D=

Ricr2 d 3 (αU max ) ⎛ ρsw ⎞ dx (1 − φ )CD g⎜ − 1⎟ ⎝ ρw ⎠

where φ is porosity, ρs is grain density and ρsw is the density of the ambient seawater.

(B4.4)

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481

A Total mid-shelf gravity-driven deposition (>50m) 0.4

1994-95 1995-96 1996-97

0.2

Fig. 10 Modelled along-shelf distribution of cumulative sediment deposition on the Eel shelf. (A) Midshelf gravity-driven deposition. (B) Inner-shelf deposition. (C) Off-shelf gravity-driven flux. Predictions based on a two-dimensional model of largescale gravity-flow deposition run for four flood seasons (1994–1998) on the shelf (Scully et al., 2003). The position of the maximum mid-shelf deposition, roughly 10–30 km north of the river mouth, is consistent with observations of the flood deposit (Fig. 9C). When the river delivers sufficient sediment to critically stratify the wave boundary layer, wave intensity and shelf bathymetry are the main factors controlling the pattern of deposition.

Sediment Flux (Mt km-1)

CMS_C09.qxd

1997-98

0 0.8

B Total inner-shelf gravity-driven deposition (