READING THE RECORDED HISTORY OF SOIL MANTLED HILLSLOPES By Simon Marius Mudd Dissertation Submitted to the Faculty of the Graduate School of Vanderbilt University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in Environmental Engineering May, 2006 Nashville, Tennessee Approved: Professor David J. Furbish Professor James H. Clarke Professor Kaye S. Savage Professor Florence Sanchez To my wife Robin, my mother Monika, and my father Brian ii ACKNOWLEDGMENTS This work was made possible through the financial support of the National Science Foundation, the Florida State University, and Vanderbilt University. I am grateful to my peers, colleagues, and mentors with whom I have had countless hours of discussion about geomorphology that have shaped my ideas about the physics of the Earth’s surface. I wish to give special thanks to the people with whom I have generally looked for beautiful landscapes to work in and understand. These people include (in semi-chronological order) Ian MacMillan, Manny Gabet, Mike Singer, Daniel Malmon, Tom Dunne, Steve Lancaster, Ryosuke Akahori, Jeroen Sonke, Jiun-Yee Yen, Sergio Fagherazzi, Andrea D’Alpaos, Mark Schmeekle, and Kyungsoo Yoo. Finally, and perhaps most significantly, I wish to acknowledge David Furbish, my advisor and mentor. It will be my pleasure to carry on David’s intellectual legacy, and will strive in my career to be his equal in ability and enthusiasm for both teaching and creating knowledge in the field of earth surface processes. iii TABLE OF CONTENTS Page DEDICATION ................................................................................................................ii ACKNOWLEDGMENTS ..............................................................................................iii LIST OF TABLES ...........................................................................................................vii LIST OF FIGURES ..........................................................................................................viii Chapter I. INTRODUCTION .................................................................................................1 1. Overview ...............................................................................................1 2. Components of the Thesis .....................................................................7 3. Summary .............................................................................................14 3. References ...........................................................................................16 II. THE INFLUENCE OF CHEMICAL DENUDATION ON HILLSLOPE MORPHOLOGY .................................................................................................19 Abstract ...................................................................................................19 1. Introduction .........................................................................................20 2. A Depth-Integrated Equation of Hillslope Mass Conservation Incorporating Chemical Denudation and Deposition ..............................25 2.1. Previous Work ......................................................................25 2.2. General Statement of Mass Conservation ............................26 2.3. Depth-Integration of the Statement of Mass Conservation ..28 2.4. Kinematic Conditions at the Soil Surface and the Soil-Bedrock Boundary ........................................................29 2.5. The Depth-Integrated Equation for Mass Conservation of Soil on a Hillslope ............................................................31 2.6. Simplifying Assumptions for Conservation of Mass Equation .......................................................................32 3. The Steady-State, Chemically Denuding Hillslope: 1-D Analysis .....33 3.1. Derivation of Governing Equations .....................................33 3.2. Denudation Rates .................................................................36 3.2.1. Mechanical Denudation Rate ................................36 3.2.2. Chemical Denudation Rate ...................................36 3.3. Curvature, Slope, and Profile of the 1-D Steady- State Hillslope ......................................................................39 iv 3.3.1. Features of the 1-D Steady-State Hillslope ...........40 3.4. Non-Dimensionalization .......................................................43 4. Discussion ............................................................................................46 4.1 Effect of Chemical Weathering on the Morphology of Steady-State Hillslopes .....................................................46 4.2. Conceptual Explanation of the Steady-State Convex-Concave Hillslope ...................................................47 4.3. Conditions for Steady-State Hillslopes with Convex-Concave Profiles .....................................................48 4.4. Transport Ratios for Steady-State Hillslopes With Convex-Concave Profiles ............................................50 4.5. Comparison of Theoretical Transport Ratios with Transport Ratios Calculated From Field Data ......................51 4.6. The Occurrence of Hillslopes with Denudation Ratios Greater Than 0.5 .......................................................54 5. Conclusions .........................................................................................55 Appendix 1 ..............................................................................................56 Appendix 2 ..............................................................................................57 Appendix 3 ..............................................................................................58 6. List of Symbols ...................................................................................60 7. References ...........................................................................................62 III. USING CHEMICAL TRACERS IN HILLSLOPE SOILS TO ESTIMATE THE IMPORTANCE OF CHEMICAL DENUDATION UNDER CONDITIONS OF DOWNSLOPE SEDIMENT TRANSPORT.........................................................68 Abstract ...................................................................................................68 1. Introduction .........................................................................................69 2. A Coupled Model of Hillslope Evolution ...........................................72 2.1. Conservation of Total Soil Mass .........................................72 2.2. Conservation of a Soil Phase ...............................................74 3. A 1-D, Two Phase Model of Hillslope Weathering and Transport ....77 3.1. Simplifying assumptions ......................................................78 3.2. Flux Laws .............................................................................79 3.3. Lagrangian Coordinate System ............................................80 3.4. The Governing Equations for a Hillslope Soil Composed of Two Phases .....................................................81 3.5. Non-Dimensionalization and Scaling ...................................84 4. On the Use of the Two Phase Hillslope System ..................................87 4.1. Steady State Solution of the Two Phase Hillslope Model ....90 4.2. Quantifying the Changes in the Concentration of the Immobile Phase Related to Transient Incision or Deposition .............................................................................99 5. Conclusions ........................................................................................105 Appendix A ............................................................................................107 6. List of Symbols ..................................................................................109 v 7. References ..........................................................................................111 IV. LATERAL MIGRATION OF HILLCRESTS IN RESPONSE TO CHANNEL INCISION IN SOIL MANTLED LANDSCAPES.............................................117 Abstract .................................................................................................117 1. Introduction ........................................................................................118 2. A 1-D Model of Hillcrest Migration ..................................................122 2.1. Governing Equations ...........................................................122 2.2. Scaling and Nondimensionalization of the Governing Equations ...........................................................126 2.3. Dimensionless Governing Equations ..................................128 3. Analytical Solutions of Hillcrest Migration .......................................129 3.1. Hillcrest Offset Due to Channel Elevation Differences at Topographic Steady State ................................................129 3.2. Migrating Hillcrest Due to Steady But Unequal Channel Incision Rates .......................................................135 4. Numerical Simulations of Transient Hillcrest Migration ..................142 4.1. The Effect of Delayed Knickpoint Migration .....................143 4.1.1. Linear Flux Law ..................................................144 4.1.2. Linear-Critical Flux Law .....................................151 4.1.3. Soil Storage and Thickness Effects .....................153 4.2. The Effect of Variations in Amplitude and Frequency of Incision Rates ..................................................................155 5. Conclusions