Incision of Steepland Valleys by Debris Flows

Jonathan David Stock

B.S. (University of California, Santa Cruz) 1992 M.S. (University of Washington) 1996

A dissertation submitted in partial satisfaction of the

requirements for the degree of

Doctor of Philosophy

Earth and Planetary Science

in the

GRADUATE DIVISION

of the

UNIVERSITY OF CALIFORNIA, BERKELEY

Committee in charge:

Professor William E. Dietrich, Chair Professor Roland Bürgmann Professor T. M. Narasimhan

Fall 2003

This dissertation of Jonathan David Stock is approved.

______Chair Date

______Date

University of California, Berkeley

Fall, 2003

Incision of Steepland Valleys by Debris Flows

Jonathan David Stock

ABSTRACT

Incision of Steepland Valleys by Debris Flows

Jonathan David Stock

Doctor of Philosophy in Earth and Planetary Science

University of California, Berkeley

Professor William E. Dietrich, Chair

Steepland valleys are prone to episodic debris flows, which are flowing mixtures of rock and water. Debate continues about whether debris flow valley incision is adequately represented by modified fluvial incision laws (e.g., stream power law) that predict power laws of drainage area against valley slope. Using a wide range of topography from debris flow-prone temperate steeplands in the U.S and around the world, I find that inverse fluvial power laws (straight lines on log-log plots) rarely extend to valley slopes greater than ~ 0.03 to 0.10, values below which debris flows rarely travel. Instead, with decreasing drainage area the rate of increase in slope declines, leading to a curved relationship on a log-log plot of slope against drainage area. This curved relation is found along recent debris flow runouts in the

U.S. with extensive evidence for bedrock lowering by the impact of large particles entrained in the debris flow, and along field-mapped runouts of older debris flows in the western U.S. and Taiwan. By contrast, downvalley from terminal debris flow

deposits, where strath terraces often begin, area-slope data follow fluvial power laws.

Valleys cut by debris flows have long-profiles different from those cut by rivers.

To measure bedrock lowering rates in both places, I installed hundreds of erosion pins in the rock floors of steep valleys recently eroded by debris flows in

Oregon, and in bedrock rivers in Washington, Oregon, California and Taiwan. I monitored these sites for 1 - 7 years. Pins in valleys scoured by debris flows have been buried by colluvium, indicating a lack of fluvial incision. By contrast, pins in riverbeds (with power law area-slope plots) have lowered at rates up to cm’s per year, at values that are proportional to the square of bedrock tensile strength. Cultural artifacts in the fluvial deposits of adjoining strath terraces in Washington and Taiwan rivers indicate at least several decades of lowering at these extreme rates following historic exposure of bedrock. Observed lowering rates at most sites far exceed estimated long-term rock uplift rates, so the observed reaches of these rivers cannot be adjusted to either bedrock hardness or rock uplift rate in the manner predicted by the stream power law. Although power law plots of area versus slope may be consistent with regions of fluvial incision, they need not reflect the stream power bedrock river incision law.

To explore why area-slope data is curved for valleys cut by debris flows, and to construct a debris flow incision law, I visited recent debris flow sites around the western U.S. I found that rock damage by impacts accounted for the majority of lowering. Field measurements of debris flow valley slope and bedrock weathering at these sites show a tendency for both to increase abruptly above tributaries that

contribute throughgoing debris flows. Indirect measurements indicate that debris flow length and long-term frequency increase downvalley as individual flows gain material, and as tributaries with more debris flow sources join the mainstem. From these field observations, I propose that long-term debris flow incision rate is proportional to the integral of solid inertial normal stresses from particle impacts along the length of a flow of unit width, and the number of upvalley debris flow sources. I construct a model which predicts that downvalley increases in flow length and frequency are balanced by reductions in inertial normal stress from reduced slopes and less weathered bedrock, leading towards equilibrium lowering. I hypothesize that reductions in valley slope compensates for gains in debris flow frequency and length and leads to observed non-power law plots of slope against drainage area.

On the basis of this fieldwork and modeling, I propose that steepland valleys above 3-10% slope are predominately cut by debris flows, whose topographic signature is an area-slope plot that curves in log-log space. These valleys are both extensive by length (>80% of large steepland basins) and comprise large fractions of mainstem valley relief (25-100%), so valleys carved by debris flows, not rivers, bound most hillslopes in unglaciated steeplands. Debris flow scour of these valleys appears to limit the height of some mountains to substantially lower elevations than river incision laws would predict, an effect absent in current landscape evolution models. Forward modeling indicates that stream power laws poorly capture steepland

valley long-profiles, and that an incision law particular to debris flows is required to evolve most unglaciated steeplands.

ACKNOWLEDGEMENTS

I would like to thank those who labored in the field with me, in alphabetical order: Simon Cardinale, Mauro Cassidei, Tegan Churcher, Alex Geddes-Osborne,

Meng-Long Hsieh, the Kapor family, Taylor Perron, N. P. Peterson, Cliff Riebe, Josh

Roering, Joel Rowland, Kevin Schmidt, Leonard Sklar, Adam Varat, and Elowyn

Yager. Others labored in the lab, including Douglas Allen and Dino Bellugi who taught me what GIS skills I have, Charlie Paffenberger our systems administrator, and

Chad Pedriolli, who did a substantial portion of the map area-slope analysis. Their generosity and patience resulted in much of the data presented hereafter. Many have contributed intellectual ideas through reviews or offhand comments. These include

Michael Singer, Greg Tucker and Stephen Lancaster who improved Chapter 1 considerably, and Jim Kirchner who helped with the analysis of curved vs. linear area-slope data. Others have contributed data, including Stephen Lancaster who shared 10-m DEM's of the Elliot State Forest and Tracy Allen who provided stage records for the Eel River. I thank Leonard Sklar for rock tensile data in Chapter 2. I thank the following grant for funding: NASA grant NAG 59629.

Those who educated me can take credit for any lasting contributions from this work. I would not have begun my studies without the wise and gentle encouragement of Robert Garrison and Leo Laporte of U. C. Santa Cruz Earth Sciences. They taught me to think of myself as a young professional, and I am still trying to live up to their high ethical ideals. To Robert Anderson of U.C. Santa Cruz I owe much of my initial love of geomorphology, for he taught me both the breadth and depth of landform

analysis. I thank the Earth Science department at Santa Cruz for an education rich in

technical and humanistic ideas. Other faculties could benefit greatly from their example. During my M.S. work at the Department of Geology, University of

Washington, I benefited greatly from the wise guidance of David Montgomery and

Tom Dunne, two extraordinary teachers and scientists. They have had a profound effect on my professional life as examples of people who were both great researchers and mentors, alive to the possibilities of students and new ideas. Their mentoring has stood me in good stead during many rough times, and I cannot imagine being a geomorphologist without their guidance.

In my time at Berkeley I have found great comfort from my colleagues starting with Douglas Allen, Dino Bellugi, Josh Roering and Ray “FBI” Torres, and continuing with Elowyn Yager. I would like to thank Michael Singer for many joyful hours in the field, and for reawakening much of my enjoyment of geomorphology. I owe a debt to Professors Narasimhan and Bürgmann for their cheerful support on my committee. My advisor William Dietrich has truly shaped me as a professional, for it is his voice that I hear whenever I am confronted with the unknown in the field. I have tried to adopt his extraordinary analytical skills, and his ability to simplify problems to a set of measurements to be made and analyzed. Throughout many trying times, he has consistently supported this debris flow research, sometimes from his own pocket I think. Thank you Bill.

The last and greatest debt I owe to my immediate family and to Ana Kapor.

From my family came the love of learning, from the times I spent on Mom’s lap

reading, to digging for dinosaur fossils with Dad in the desert. They never flagged in their support, both spiritual and material. At last I can start returning the material support! To Ana I owe the energy and confidence to make it through the final lap.

You stood by me and gave me strength, thank you.

iii

“It exceeds my powers but not my zeal”

J. J. Rousseau (from the private papers of James Boswell)

Jonathan David Stock-Vitae Personal Born March 16, 1970 in San Francisco

Education: Jesuit High School, Carmichael, CA B.S., 1992, University of California, Santa Cruz M.S., 1996, University of Washington

Present Position: Ph. D. candidate, Earth & Planetary Sciences, U.C. Berkeley

Experience: 1989-1991 Field and soils lab technician, Environmental Impact Report writer, Raney Geotechnical 1990 X-Ray Fluorescence Lab technician, U.C. Santa Cruz. 1991 Summer Student Fellow, Woods Hole Oceanographic Institute. 1992-1996 Research and Teaching Assistant, University of Washington. Expert consultant on debris flows for Johnson, Clifton, Larson & Corson, attorneys-at-law (975 Oak St. #1050, Eugene, OR). 1999 Expert consultant on debris flow hazard mapping, City of Fremont 1996- Research and Teaching Assistant, U.C. Berkeley

Professional Societies: American Geophysical Union, Geological Society of America

Professional Responsibilities: Organizer, International Geomorphology meeting (Gilbert Club) 1999-2001

Honors: Outstanding student paper, Hydrology, Fall 1998 American Geophysical Union

Volunteer work: 1996-, Marine Mammal Center (care & rehabilitation of pinnipeds)

Publications: Stock, J. D., and Dietrich, W. E., Valley incision by debris flows: evidence of a topographic signature, Water Res. Res., 37(12):3371-3381, 2003. Stock, J. D., Coil, J., and Kirch, P. V., Paleohydrology of arid southeastern Maui, Hawaiian Islands: Implications for prehistoric human settlement, Quarternary. Res., 59, 12-24, 2003. Roering, J. J., Schmidt, K. M., Stock, J. D., Dietrich, W. E., and Montgomery, D. R., Shallow landsliding, root reinforcement, and the spatial distribution of trees in the Oregon Coast Ranges, Canadian Geotechnical J., in press.

Schmidt, K. M., Roering, J. J., Stock, J. D., Dietrich, W. E., Montgomery, D. R., and Schaub, T., The variability of root cohesion as an influence on shallow landslide susceptibility in the Oregon Coast Range, Canadian Geotechnical J., 38:995-1024, 2001. Stock, J. D., and Montgomery, D. M., Geologic constraints on bedrock river incision using the stream power law, Journal of Geophysical Research, 104:4983- 4993, 1999. Montgomery, D. R., Abbe, T. B., Buffington, J. B., Peterson, N. P., Schmidt, K. M., and Stock, J. D., Distribution of bedrock and alluvial channels in forested mountain drainage basins, Nature, 381:587-589, 1996. Stock, J.D. and Montgomery, D.M., Estimating paleorelief from detrital mineral age ranges, Basin Research, 8:317-327, 1996. Stock, J.D. Neotectonics, drainage persistence and constraints on the long-term offset rate along the McKinley strand of the Denali Fault, Central Alaska Range, GSA Abstracts with Programs, V. 26, A-303, 1994. Behl, R.J., and Stock, J.D., The interplay of diagenesis and deformation in Monterey Formation cherts, GSA Abstracts with Programs, V. 26, A-468, 1994.

TABLE OF CONTENTS

INTRODUCTION ...... 1 CHAPTER 1. VALLEY INCISION BY DEBRIS FLOWS: EVIDENCE OF A TOPOGRAPHIC SIGNATURE ...... 6 ABSTRACT...... 6 INTRODUCTION...... 7 SITE SELECTION ...... 13 SITE DESCRIPTION ...... 16 METHODS...... 20 Techniques for hand extraction of area-slope data ...... 22 Techniques to extract power law portion of data...... 23 RESULTS ...... 26 Curvature of area-slope data ...... 26 Scaling break at ~0.10 slope...... 28 Extension to other steeplands...... 30 DISCUSSION...... 33 Implication of scaling transition ...... 36 Interpretation of curvature...... 38 Implications for stream power law exponents...... 41 CONCLUSION ...... 42 REFERENCES...... 44

CHAPTER 2. INCISION RATES FOLLOWING BEDROCK EXPOSURE: THEIR IMPLICATIONS FOR PROCESS CONTROLS ON THE LONG-PROFILES OF VALLEYS CUT BY RIVERS AND DEBRIS FLOWS ...... 74 ABSTRACT...... 74 INTRODUCTION...... 75 RAPID BEDROCK WEATHERING ...... 78 FIELD SITES ...... 80 Olympic Mountains, Washington ...... 81 Washington Cascades ...... 83 Oregon Cascades ...... 85 Oregon Coast Range ...... 86 California Coast Range...... 87 Western Foothills, Taiwan ...... 88 METHODS...... 91 RESULTS ...... 95 Erosion pins...... 95

vii

Folia ...... 98 Strath terraces...... 99 Rock strength...... 100 Area-slope analysis ...... 102 DISCUSSION...... 103 CONCLUSION ...... 106 REFERENCES...... 109

CHAPTER 3. INCISION OF STEEPLAND VALLEYS FROM DEBRIS FLOWS: FIELD EVIDENCE AND A HYPOTHESIS FOR A DEBRIS FLOW INCISION LAW...... 133 ABSTRACT...... 133 INTRODUCTION...... 134 CONCEPTUAL FRAMEWORK ...... 137 A view of debris flow valley networks...... 137 A view of debris flow stresses relevant to bedrock lowering ...... 141 Limitations to calculating stresses ...... 145 METHODS...... 148 Field surveying...... 148 Rock weathering...... 150 Digital data ...... 151 Cosmogenic radionuclide analysis...... 151 FIELD SITES...... 152 Southern California: Yucaipa, Bear, Redbox...... 152 California Coast Ranges: Highway 9, Pescadero, Scotia ...... 154 Utah: Joe’s Canyon...... 154 Oregon Coast Range: Sullivan, Scottsburg, Marlow, Silver, Elk ...... 155 Olympics: FR 23...... 157 RESULTS ...... 157 Bedrock erosion by debris flows and attendant bulk stresses...... 157 A systematic slope pattern with trigger hollows ...... 161 A systematic weathering pattern with trigger hollows...... 162 Long-term equilibrium lowering ...... 163 HYPOTHESIS FOR A DEBRIS FLOW EROSION LAW...... 163 Event expression...... 168 Parameterization of event law...... 171 Geomorphic transport law ...... 175 Long-profile evolution modeling...... 176 DISCUSSION...... 179 CONCLUSION ...... 182 LIST OF SYMBOLS...... 184 REFERENCES...... 187

viii

APPENDIX 1, SITE LOCATION MAPS ...... 222

LIST OF FIGURES

Figure 1.1 Hypothetical topographic signatures for hillslope and valley processes as

shown by a plot of drinage area versus slope...... 54

Figure 1.2 Debris flow valley network outlined by 1996 failures in the Oregon Coast

Range...... 55

Figure 1.3 Valley scoured by 1996 debris flow, Sullivan 1, Oregon Coast Range ... 56

Figure 1.4 Evidence for bedrock lowering by debris flows along Sullivan 1...... 57

Figure 1.5 Shaded relief images of Coos Bay and Scottsburg debris flow sites,

Oregon Coast Range...... 58

Figure 1.6 Valley networks extracted from digital topography of Coos Bay and

Scottsburg...... 59

Figure 1.7 Comparison of area-slope data from 30-m DEM and from hand extraction

for contour map, King Range, California...... 60

Figure 1.8 Plot of three methods to extract power law segments of area-slope data. 61

Figure 1.9 Area-slope data from valleys with bedrock lowering by recent debris

flows...... 62

Figure 1.10 Debris flow activity mapped onto area-slope data ...... 63

Figure 1.11 Plots illustrating curvature of area-slope data from Deer Creek,

California...... 64

Figure 1.12 Area-slope data from steeplands of the U.S. and around the world

illustrating the curved signature of debris flow incision...... 65

Figure 1.13 Extensive debris flow network of the Millicoma Basin, Oregon Coast

Range...... 66

Figure 1.14 Long-profile relief within debris flow region and overprediction of relief

if fluvial power laws are extrapolated into debris flow reaches...... 67

Figure 1.15 Hypothethical response of valleys to changes in rock uplift rate...... 68

Figure 1.16 Apparent effects of rock uplift rate on valley slope ...... 69

Figure 1.17 Apparent effects of lithology on valley slope...... 70

Figure 2.1 Area-slope plot illustrating power law and curved data for fluvial and

debris flow regions, respectively...... 115

Figure 2.2 Pervasive bedrock weathering above baseflow, Satsop River, Washington.

...... 116

Figure 2.3 Bedrock weathering resulting in folia, Oregon ...... 117

Figure 2.4 Cross-sections of four erosion pin monitoring sites in Washington, Oregon

and California...... 118

Figure 2.5 Shaded relief image of Coos Bay site, Oregon Coast Range ...... 119

Figure 2.6 Partial discharge record for Eel River erosion pin site...... 120

Figure 2.7 Photos of bedrock lowered around erosion pins at selected Washington,

Oregon and California sites...... 121

Figure 2.8 Comparison of bedrock lowering rates from erosion pins to long-term

estimates...... 122

Figure 2.9 Images of Kate Creek debris flow runout, illustrating burial of erosion

pins in debris flow reaches...... 123

Figure 2.10 Yearly bedrock lowering rates for selected erosion pin monitoring sites,

graphed onto channel cross-sections...... 124

Figure 2.11 Yearly bedrock lowering rates for remaining sites, graphed onto channel

cross-sections ...... 125

Figure 2.12 Summary of evidence for recent bedrock lowering at two Taiwanese

rivers...... 126

Figure 2.13 Thickness ditributions for weathering folia...... 127

Figure 2.14 Plot of rock tensile strength versus cross-section averaged erosion pin

lowering rates ...... 128

Figure 2.15 Area-slope plots for selected sites with rapid lowering rates ...... 129

Figure 2.16 Area-slope plots for remaining sites with rapid lowering rates...... 130

Figure 3.1 Debris flow valley network in an Oregon Coast Range clearcut ...... 198

Figure 3.2 Recent bouldery debris flow deposit in the San Bernardino Mountains 199

Figure 3.3 Field data showing debris flow velocity versus slope, Japan and Oregon

...... 200

Figure 3.4 Theoretical frequency-magnitude plot for inertial normal stresses

associated with a ditribution of impacting spheres ...... 201

Figure 3.5 Shaded relief images of Coos bay and Scottsburg debris flow sites ...... 202

Figure 3.6 Comparison of laser altimetry to 1-m hand-level long-profile...... 203

Figure 3.7 Curved area-slope data for valleys scoured by debris flows ...... 204

Figure 3.8 Photographs of bedrock lowering from debris flows ...... 205

Figure 3.9 Graph of debris flow depth against runout length ...... 206

xii

Figure 3.10 Plot of the number of upvalley trigger hollows against mainstem

drainage area ...... 207

Figure 3.11 Plots of reach slope versus trigger link magnitude from field surveys 208

Figure 3.12 Plots of reach slope versus area at Scottsburg sites, illustrating the

influence of link magnitude on valley slope ...... 209

Figure 3.13 Distribution of Schmidt hammer rebound values (R) with trigger link

magnitude for Kate Creek, Oregon Coast Range...... 210

Figure 3.14 Summary of field evidence for systematic increases in bedrock

weathering with decreasing trigger link magnitude, approaching landslide

headscarps ...... 211

Figure 3.15 Schmidt hammer R-values from Kate Creek plotted in relation to area-

slope data...... 212

Figure 3.16 Theoretical plot of maxiumum impact pressure against sphere size for

elastic collisions ...... 213

Figure 3.17 Illustration of a model for the lowering of fractured rock by particle

impact, and some supporting data from rock excavation studies...... 214

Figure 3.18 Steady-state long-profiles from the application of a debris flow incision

law (19) to Sul3 valley ...... 215

Figure 3.19 Combinations of bulking and velocity exponents from (19) which

yielded steady-state model long-profiles that closely match existing valley long-

profiles...... 216

xiii

Figure 3.20 Comparison of selected long-profiles from laser altimetry and contour

maps to steady-state fluvial and debris flow incsion models...... 217

xiv

LIST OF TABLES

Table 1.1 Sampling of slopes at debris flow deposition ...... 71

Table 1.2 Data for valleys with recent and recorded debris flows...... 72

Table 1.3 Data for valleys used in area-slope analysis from contour maps...... 73

Table 2.1 Field data for sites with erosion pins...... 131

Table 2.2 Erosion rate data for sites with erosion pins ...... 132

Table 3.1 Observations and claculated values from debris flow field sites ...... 219

Table 3.2 Dimensions of all grooves found along Kate creek debris flow runout... 220

Table 3.3 Site parameters for long-profile evolution with 3.19...... 221

INTRODUCTION

In steeplands, landslides at the tip of the valley network may mobilize as mixtures of rock water that flow downvalley as debris flows. These events move catastrophically down the landscape, from landslide sources near ridgetops to valley slopes of 3-10%, below which they are rarely observed to occur. Because debris flows can initiate near the highest points of the landscape and travel down to valley slopes where rivers predominate, they transport sediment (and possibly erode bedrock) across most of the landscape relief (i.e. 25-100%). Although parts of the debris flow may deform internally and flow like a fluid, solid forces including friction at the surge head resist motion. This combination of solid and fluid forces has thus far resisted any simple description of motion, and we lack the idealized equations of motion and stresses that can be used to characterize transport and erosion by fluvial and landslide processes. An additional impediment is the infrequency and short duration of debris flows that make them difficult to study in real time. Unlike fluvial processes, few people have seen active debris flows, which may occur once in a century or a millennium within a given basin. So, few have asked what role debris flows could play in carving the steeplands of the world, despite the recognition that they are both widespread and extraordinarily destructive when they occur.

During the El Nino storms of 1996/1997, debris flows occurred over an unusually large portion of the Oregon Coast Range as a result of numerous and widespread shallow landslides. Together with colleagues from U.C. Berkeley, I walked many of these runouts, from landslide source to terminal deposit, and

measured the 100’s to 1000’s of cubic meters of sediment they had transported. I

mapped debris flow bedrock erosion between the landslide headscarps near ridgetops,

and their debris flow terminal levees deposited at valley slopes where river-formed

features like banks and bedforms first appeared. On the basis of these field

observations, I hypothesized that most of the steepland valley network, both by relief

and length, might be carved by infrequent but catastrophic debris flows, rather than rivers.

This view is a radical departure from the prevailing view that unglaciated valleys are carved by running water, for which the stream power law is the most widely used expression. This expression predicts that bedrock river incision rates are proportional to power functions of water discharge, channel bed width and slope. The expression can be arranged so that it predicts a power law plot of valley slope against drainage area, which is widely observed along large rivers. As implemented in most landscape evolution models, the stream power law is used to erode all non-glacial valleys, no matter how steep. In the following chapters we present evidence that debris flows, not fluvial processes, cut and maintain steepland valleys. We explore the role that debris flows play in carving steepland valleys by making systematic observations and measurements along debris flow runouts that occurred between

1996 and 1999. We integrate these field observations with theory to produce a hypothesis for a debris flow incision law that accurately replicates high-resolution debris flow valley long-profiles. Although there is much basic work yet to be done before a geomorphic transport law for debris flows can be validated, such a law will

likely fundamentally change the way we idealize topographic growth and decay because of the prominent role that debris flows play in eroding mountainous landscapes.

In Chapter 1, I make a case that valleys carved by debris flows have a topographic signature that is distinct from those carved by rivers. By field mapping of debris flow bedrock erosion, and older debris flow deposits, I illustrate that the log- log linear area-slope plots that characterize valleys cut by rivers do not extend into reaches where debris flows occur. Instead, reaches transited by debris flows have a curved plot of area versus slope, so that the rate at which slope increases with decreasing drainage area declines. This leads to long-profiles that are shaped not unlike ski-jump ramps, with straighter upper reaches, and curved lower reaches approaching the downstream-most debris flow deposits. I show that this signature can be found in steeplands where debris flows are known to occur, around the U.S. and the world. Because this signature extends to valley slopes as low as 3-10%, debris flows likely carve most of the steepland relief. A full understanding of how mountains grow and decay and why they have the relief they do requires some understanding of how debris flows cut valleys.

In Chapter 2, I explore the proposed topographic signatures of debris flow

(curved area-slope relations) and fluvial incision (power law area-slope relations) using a network of erosion pins installed in the western U.S. and Taiwan and monitored over 1994-2001. I used hundreds of erosion pins emplaced into bedrock along steep valleys soon after erosive debris flows to explore whether post-event

fluvial processes also lowered bedrock. After 6 years of monitoring, none of the bedrock had lowered around the pins, and most were buried by hillslope sediment.

These results demonstrate that debris flows are the dominant process carving these valleys and producing the observed curved area-slope signature. I also installed erosion pins into bedrock rivers with log-log linear area-slope plots and found that for rocks of lower tensile strength (<3-5 MPa), short-term erosion rates far exceed long- term rates. Although these rivers have power law plots of drainage area versus slope, these plots cannot be interpreted in terms of a bedrock river incision law (e.g., stream power law) because river slopes are set by conditions to retain cover over the rapidly eroding bedrock, rather than rock strength. These results indicate that great caution must be used interpreting area-slope power law plots for rivers, because they may reflect sediment transport and bed stability rather than the form of bedrock incision laws, even for rivers that are currently bedrock dominated.

In Chapter 3 I return to a detailed investigation of recent debris flow runouts with the intent of hypothesizing a debris flow incision law that is faithful to field observations. I find evidence that is consistent with the view that lowering along runouts is dominated by removal of fracture-bounded bedrock during the energetic impact of large particles in the flow. Using what little is known about how to calculate stresses in debris flows, I crudely estimate the bulk stresses associated with observed lowering, and propose that excursions from bulk values are required to break strong rock observed along many runouts. I find that bedrock valley floor weathering and link slope (i.e. slope between valley tributary junctions) may vary

systematically with the number of upvalley mobile debris flow sources (trigger link

magnitude). The fewer the number of sources, the more weathered the bedrock, and

the steeper the slope. Slope between tributary junctions has a tendency to be constant,

so that debris flow valley long-profiles have a tendency to look like straight-line segments connected at tributary junctions. I use these field observations to hypothesize an incision expression for a single debris flow that is proportional to the integral of inertial solid stresses (i.e. stress from impacting particles) along the

granular flow front, and inversely proportional to rock weathering as characterized by

tensile strength and a measure of fracture spacing. I express this event law over

geomorphic time scales by parameterizing its variables in terms of runout length and

valley slope, so that debris flow incision rate is proportional to the length of the

granular flow front, the solid inertial normal stresses and the long-term frequency of

events. Although this parameterization is excessively crude because we lack much

necessary data about the velocity and bulking rate of debris flows, the resulting

expression offers an explanation for many of the observed features of debris flow

valleys, including curved area-slope data. Unlike stream power laws, it has the ability

to capture the shape of debris flow valley long-profiles, and it may help explain the

long lifespan of steepland topography after rock uplift has ceased. We are far from a

validated debris flow incision law, but this work illustrates the necessity of such an

expression to understand much of the evolution of steep topography around the

world.

CHAPTER 1. VALLEY INCISION BY DEBRIS FLOWS: EVIDENCE

OF A TOPOGRAPHIC SIGNATURE

(Portions of this chapter were published in Water Resources Research, 37(12):3371-3381,

2003)

Abstract

The sculpture of valleys by flowing water is widely recognized and simplified models of incision by this process (e.g., the stream power law) are the basis for most recent landscape evolution models. Under steady state conditions, a stream power law predicts that channel slope varies as an inverse power law of drainage area. Using both contour maps and laser altimetry, I find that this inverse power law rarely extends to slopes greater than ~ 0.03 to 0.10, values below which debris flows rarely travel. Instead, with decreasing drainage area the rate of increase in slope declines, leading to a curved relationship on a log-log plot of slope against drainage area.

Fieldwork in the western U.S. and Taiwan indicates that debris flow incision of bedrock valley floor tends to terminate upstream of where strath terraces begin and where area-slope data follow fluvial power laws. These observations lead us to propose that the steeper portions of unglaciated valley networks of landscapes steep enough to produce mass failures are predominately cut by debris flows, whose topographic signature is an area-slope plot that curves in log-log space. This matters greatly as valleys with curved area-slope plots are both extensive by length (>80% of large steepland basins) and comprise large fractions of mainstem valley relief (25-

100%). As a consequence, valleys carved by debris flows, not rivers, bound most

hillslopes in unglaciated steeplands. Debris flow scour of these valleys appears to

limit the height of some mountains to substantially lower elevations than river

incision laws would predict, an effect absent in current landscape evolution models. I

anticipate that an understanding of debris flow incision, for which I currently lack

even an empirical expression, would substantially change model results and inferences drawn about linkages between landscape morphology and tectonics, climate, and geology.

Introduction

The sculpture of earth's unglaciated valleys by water has long been explored to understand both the processes and rates that create and maintain valleys [e.g.,

Playfair, 1802; Gilbert, 1877; Davis, 1902; Horton, 1945]. These early workers recognized that strath terraces bordering rivers and the adjustment of tributaries to mainstems are evidence that rivers incise valleys. These visible signs of lowering, and the fascination with river longitudinal profile shape led to early speculation by

19th century workers [e.g., Gilbert, 1877] that rivers cut through earth's crust at rates

determined by water discharge and channel slope (S) for a given substrate (K). The

recognition that valley incision may transmit the effects of climate change and

tectonism throughout the landscape has led to a renewed interest in the problem of bedrock river incision and its erosion laws. The first and simplest approach was to assume that fluvial processes cut most unglaciated valleys, and that lowering rate was

either a function of boundary shear stress or stream power (ω). For instance, Howard

and Kerby [1983] proposed that bedrock incision rate ∂z/∂t was a power function of shear stress applied to the bed by a moving fluid so that:

b b -∂z/∂t = K1τ = K1 (ρwgRS) (1.1),

where z is elevation (positive upward), K1 was a measure of bed erodibility, τ is shear

stress, b is unknown, ρw is fluid density, R is hydraulic radius and S is slope. In the spirit of Bagnold [1966], Seidl and Dietrich [1992] proposed that bedrock lowering rate was proportional to work/unit time done on the river bed (i.e. power) so that

n n -∂z/∂t = ω = (ρwgQS) (1.2)

where n is an unknown exponent and Q is discharge. As reviewed by many others

[e.g., Sklar and Dietrich, 1998; Whipple and Tucker, 1999], expressions (1.1) and

(1.2) can be parameterized in terms of drainage area and slope using hydraulic

relations, so that they take the form

∂z/∂t = U - K Am Sn (1.3)

where U is rock uplift rate, S is slope, and m and n are exponents whose values are

debated but may be calibrated by direct measurement of erosion rates [e.g., Howard

and Kerby, 1983; Seidl et al., 1994; Whipple et al., 2000] or longitudinal profile

fitting [e.g., Seidl and Dietrich, 1992; Rosenbloom and Anderson, 1994; Stock and

Montgomery, 1999; Snyder et al., 2000; Kirby and Whipple, 2001]. When rock uplift rate and lowering rate are balanced so that the valley long-profile is at steady state, the expression leads to the expectation that

1/n -m/n S = [U/K] A (1.4a) or,

log S = log (U/K)1/n - m/n log A (1.4b)

Availability of topography as DEM's (digital elevation models) and the desire

to invert landforms quantitatively for erosion rate invites much use of equation (1.3).

The expression has been used to infer parameters in the stream power law from area-

slope data (see above) and the response of river profiles to tectonism [Snyder et al.,

2000; Lague et al., 2000; Kirby and Whipple, 2001] or climate change [Tucker and

Slingerland, 1997; Whipple et al., 1999]. Most recent landscape evolution models

use some form of equation (1.3) to model valley incision, either by including the

possibility of alluvial channels which require the calculation of the divergence of

sediment transport [e.g., Willgoose et al., 1991; Howard, 1994; Tucker and

Slingerland, 1994; Kooi and Beaumont, 1996; Howard, 1997; Tucker and Bras, 1998; van der Beek and Braun, 1999] or by assuming that bedrock river incision is the dominant process shaping channel long-profiles [e.g., Anderson, 1994; Whipple and

Tucker, 1999; Whipple et al., 1999; Davy and Crague, 2000; Willett et al., 2001].

This long (yet incomplete) reference list is a measure of the reliance placed upon

area-slope formulations like equation (1.3) to answer questions of widespread interest, like the response of landforms to climate change or rock uplift.

Yet, little attention is paid to the extent of the valley network in which the stream power law is valid. For instance, in the steeplands of the Western U.S. I have not observed field evidence for long-term bedrock river incision (like a strath terrace) above valley slopes of 0.05 - 0.10, a region below which debris flows rarely travel, and where well-developed fluvial bedforms like step-pools occur [e.g., Montgomery and Buffington, 1997]. Nor is it obvious that the power law trend observed in area- slope plots of many rivers [e.g., Flint, 1974] can be projected upstream of the steepest reaches where strath terraces are commonly observed (e.g., Fig. 1.1b). Upstream lies a steep valley network whose properties are largely unexplored, where other processes such as debris flows are capable of carving valleys (e.g., Fig. 1.2). Here topography is convergent in planform, but valleys lack banks or other fluvial features that define channels (e.g., Fig. 1.3). Hillslopes deposit coarse, unsorted material in these valleys, leading some to call them colluvial valleys [Montgomery and

Buffington, 1997]. The coarsest sediment size is often meters in dimension, many times the common water flow depth. In steeplands capable of generating landslides, the bulk of downvalley sediment transport is by debris flows [e.g., Dietrich and

Dunne, 1978; Benda, 1990]. Case studies in the Oregon Coast Range and other steeplands document that debris flows are rarely mobile below valley slopes of 0.02 -

0.05 (Table 1.1) although confinement, grain-size, fluid pressure, volume and junction angle also play a role [e.g., Hungr et al., 1984; Benda and Cundy, 1990;

Iverson, 1997]. The apparent lower limit of 0.02-0.05 in Table 1.1 corresponds to

slopes reported for step-pool bedforms in Montgomery and Buffington [1997], while

higher terminal slope values above 0.10 are typical of open slopes or fans in glaciated

areas like British Columbia, Switzerland and Scandinavia. These observations lead to

the expectation that valley network incision above slopes of 0.02-0.05 is influenced

(at least in part) by debris flows.

Perhaps because of the poor resolution of most DEM’s, these valleys are often

written about as if they were part of hillslopes. For instance, some have found a

change in power law slope (or a scaling break) in area-slope data from DEM’s such

that valley slope ceases to change below a certain drainage area. This has been

inferred to represent a transition to hillslope processes [Fig. 1a; e.g., Ijjasz-Vasquez

and Bras, 1995; Moglen and Bras, 1995; Lague et al., 2000]. But this scaling break

is inferred to occur at 0.1-1 km2, drainage areas at which valleys may occur. By contrast, others interpret the appearance of a scaling break as the topographic signature for debris flow valley incision [Seidl and Dietrich, 1992; Montgomery and

Foufoula-Geourgiu, 1993; Sklar and Dietrich, 1998]. With the exception of Howard

[1998], there are no proposals for a debris flow incision law or rule. When I started this investigation, little field evidence had been used to test either hypothesis.

Examples of each are shown graphically in Figure 1.1a, from which two focused questions arise: what is the location of the scaling break (if any) and what is the form of the area-slope data above it? Since the form of area-slope data in steeplands could indicate a non-fluvial incision law, the location of the scaling break could define the

extent of fluvial incision in steeplands. Given the widespread use of some form of

stream power law, answers to these two questions have substantial implications for

both landscape evolution models and geomorphic theory.

In this paper I investigate the notion that debris flow valley incision in

unglaciated steeplands has an area-slope topographic signature distinct from that of

bedrock river incision (Fig. 1.1b). To do so, I avoid collection of data from

hillslopes, and focus exclusively on valleys, which reflect concentrative erosional

processes. I report results from visits to sites of recent debris flows where I observed

evidence for bedrock lowering along their runout. Using both high- and low-

resolution topography, I examine area-slope plots to see if they have a common form

along the debris flow runout path. I also measure mainstem area and slope for larger, unglaciated steepland valleys where the form of area-slope data follow fluvial power laws at large drainage areas, but may have a different form in the valley headwaters where I have mapped older debris flow deposits. I ask if the downvalley disappearance of debris flow deposits and appearance of strath terraces (where present) has a consistent signature, such as a scaling break, that might separate fluvial from debris flow valley incision. Finally, I plot mainstem valley slope and area from

U.S. 1:24,000 and global 1:50,000 maps to investigate the generality of such signatures, and by inference the generality of debris flow valley incision in unglaciated mountain ranges.

Site Selection

To investigate if debris flows imprint a topographic signature on valley

longitudinal profiles, I visited sites of recent (< 1 year-old) and historically recorded

debris flows in the western U.S. (Table 1.2). Although these sites were selected

opportunistically, they span a wide range of climates and erosion rates from soil-

mantled sandstone terrain lowering at 0.1 mm/a (Oregon Coast Range), to semi-arid,

bedrock-dominated gneissic terrain eroding at ~ 1 mm/a (San Bernardino Mountains).

In these valleys (numbers 1-16 in Table 1.2) I measured area and slope from laser

altimetry (Sullivan, Scottsburg and Roseburg) or 1:24,000 USGS topography, and

walked the runout of debris flows looking for evidence of bedrock erosion. In Table

1.2 I report deposition slopes measured in the field over the last 10 m of runout, or

from high-resolution topography. These slopes tend to be higher than values from

1:24,000 maps for the same reach. Deposition slopes for historic debris flows in the

Wasatch Range are from fan slopes on 1:24,000 maps.

With the goal of distinguishing river-cut valleys from those cut by debris

flows, I selected river basins from steeplands with a range of rock uplift rate and

climate including the San Gabriel Mountains, California Coast Range, King Range,

Oregon Coast Range and Taiwan (valleys with a superscript a in Table 1.3). In these basins, I mapped the down-valley extent of existing debris flow deposits, and strath terraces to contrast fluvial with debris flow valley profiles. At all of the above sites, I compared the extent of the debris flows as judged from field mapping or historical accounts to area-slope plots of the same valley to look for a common topographic

signature in the overlap. I also selected basins from unglaciated mountain ranges with reported debris flows in the U.S., and from unglaciated steeplands around the world (Table 1.3). I constructed area-slope plots for these latter basins to explore the commonality of a potential topographic signature for debris flows.

For sites of recent or historic debris flows, I measured area and slope from topographic maps along the runout path and mapped the spatial extent and style of bedrock erosion where present. I identified the downstream-most debris flow deposits along the valley mainstem and compared area-slope data above and below this point to contrast the area-slope signature of debris flow basins with the proposed stream power law of fluvial basins. Although debris flows can stop on steeper slopes,

I focused on the lowest gradients at which debris flows are commonly mobile because these reaches define the maximum potential influence of debris flow incision by larger events. I defined the mainstem as the valley with the larger drainage area at each tributary junction. I selected valleys of relatively uniform geology that contained both lower gradient rivers, and steeplands known to have debris flows. I chose mainstem profiles without systematic changes in slope that might reflect deep- seated landsliding, faulting or lithologic changes. Exceptions are Marlow and

Sullivan Creek, which have significant knickpoints on them that are not related to lithology. I included these basins because they have high-resolution DEM’s and many recent debris flows in their catchments. The choice of mainstem rather than tributary allows us to show the maximum possible extent of fluvial influence. I then mapped the extent of debris flow deposits and strath terraces onto 1:24,000

topography by walking the valley mainstem. I used a conservative definition for debris flow deposits that required the following three observations:

• matrix-support of large clasts in diamictons

• boulder berms

• deposits located away from tributary junction fans

The intent was to avoid identifying coarse-grained fluvial deposits as debris flow deposits, and not to mistake small tributary fan deposits for along-valley debris flows.

This means that I will underestimate long-term debris flow run-out because I do not include older, eroded debris flow deposits or matrix-poor debris flow deposits.

To survey the commonality of a potential topographic signature for debris flows, I selected basins from around the world by: 1) identifying a steepland region of relatively uniform valley density, 2) locating an area of uniform lithology within that region, and 3) selecting a basin within the region of uniform lithology with a concave up profile that included lower gradient sections beyond the occurrence of debris flows

(e.g., slopes < 0.02). I measured area and slope along mainstems, bounded at the lower end by lakes, oceans, changes in geology or reaches with slopes below 0.001 where gravel-sand transitions may lead to longitudinal profile changes [e.g., Yatsu,

1955]. In the U.S. I use 1:24,000 topography. I chose 1:50,000 scale maps for the rest of the world because they are the largest scale topographic maps available for many countries. I selected an average of five basins per continent from Europe,

Africa, Asia, and South America. From North America, I selected steepland basins

from the Appalachians, Oauchitas and the western U.S. All of the basins I sampled

are reported, including those with large amounts of local scatter in river slope. The

quality of geologic and topographic data outside the U.S. varies greatly, so I use the

global data primarily to explore the generality of a scaling break, rather than the form

of the area-slope data above it. In one case (Anghou River, Taiwan), I can evaluate

the accuracy of 1:50,000 data because I have 1:5,000 data for the same basin from the

Taiwan Department of Forestry. Also included in Table 1.3 are estimates of mean annual rainfall, geology and erosion rate for each of the basins considered. The quality of these estimates varies and most should be regarded as illustrative. The last column of Table 1.3 lists sources for erosion rate data, many of which are from reservoir sedimentation studies or fission-track data, each of which has limitations.

The term “other” encompasses techniques like dating of strath terraces or sediment dating by cosmogenic radionuclides.

Site Description

We report field and topographic evidence for bedrock incision by recent

debris flows from 13 sites (Table 1.2) in the Western U.S. At three other sites, older

debris flow deposits lie directly on the valley bedrock floor, indicating the possibility of a similar erosion process (last 3 sites, Table 1.2). In addition, I mapped the locations of the upstream-most strath terrace and the downstream-most debris flow deposits at eight basins in the Western U.S. and Taiwan (super-scripted basins in

Table 1.3), and compared this approximate process boundary to the pattern of area- slope data. Below, I report site descriptions for these localities in the order in which they are shown in Tables 1.2 and 1.3.

In Oregon, intense rainfall of the 1996/1997 El Niño storms triggered landslides across the Coast Range, including Elliot State Forest near Coos Bay.

Here, many landslides mobilized as debris flows (Fig. 2), sweeping sediment from valley floors to expose sandstones and siltstones of the Eocene Tyee Formation (Fig.

3-4). Erosion rates in the central Oregon Coast Range are thought to be between 0.1 and 0.2 mm/a on the basis of strath terrace ages [Personious, 1995], sediment yield

[Reneau and Dietrich, 1991] and cosmogenic radionuclides from the Coos Bay site in

Figure 1.5a [Heimsath et al., 2001]. I used ground reconnaissance and maps of debris flows provided by Oregon Department of Forestry to locate debris flow sites in or near to Elliot State Forest (numbers 1-8 in Table 1.2). High-resolution topography from laser altimetry covers two sites with recent debris flows (Fig. 1.5a, b) near the northern (Scottsburg) and southern (Sullivan) extremities of Elliot State Forest.

Figure 1.5a shows a shaded relief image of Sullivan Creek in which average data spacing was 2.5 m with ~0.3 m vertical resolution; Figure 1.5b shows a similar image for Scottsburg in which average data spacing was 4 m with ~0.3 m vertical resolution.

During the winter of 1996/1997, many of the prominent tributary valleys in Figure

1.5a experienced debris flows (dotted lines) that scoured bedrock to the mainstem confluence with Sullivan Creek. I walked debris flow runouts shown in Fig. 1.5a and mapped the occurrence and style of bedrock lowering. Although difficult to quantify

systematically, I found that bedrock had been removed as 1) grooves and lineations at the scale of the component rock grains and as 2) fracture-bounded blocks one to several cm’s thick (Fig. 1.3-1.4). I did not observe fluvial potholes, sorted sediment or strath terraces along debris flow runout paths. The remaining basins have not been scoured in the last several years, except for Sullivan 4 (just west of Fig. 1.6a), which was largely scoured to bedrock, but was too steep to access. Figure 1.5b is a shaded relief image from high resolution laser altimetry showing steeplands at the northern edge of Elliot with a 1996/1997 debris flow (dotted line) that scoured bedrock along its runout path. I also used high-resolution laser altimetry (average data spacing was

2.5 m with ~0.3 m vertical resolution) from 1997 debris flow sites in the Tyee

Formation near Roseburg (numbers 9-11 in Table 1.2), which I do not show for space reasons.

In Utah I visited valleys scoured by debris flows along the Wasatch front, whose long-term erosion rates in the vicinity of the Salt Lake City segment are of order 1-2 mm/a on the basis of fission-track and U/Th-He data [Armstrong et al.,

1999]. Just north of Salt Lake City in Paleozoic gneiss of the Farmington canyon complex, I walked the lower reaches of two valleys (Steed and Rick’s Ford, numbers

14-15 in Table 1.2) scoured to their fans by debris flows in the early part of the century [Wooley, 1946]. These have largely been refilled with bouldery debris, and bedrock is exposed only at a few waterfalls. Adjoining basins that were scoured to bedrock during 1982 debris flows [Williams and Lowe, 1990] also have only rare exposures of bedrock. Further south, I walked the runout of a 1997 debris flow (Joe’s

Canyon, number 13 in Table 1.2) that scoured the Mesozoic Oquirrh Formation, a

quartzite in the foothills of the Wasatch near Spanish Forks. There I observed

decimeter-sized blocks missing from the jointed quartzite bedrock of the valley bed,

which also had ubiquitous abrasion marks like those in the Tyee Fm. (Fig. 1.4).

When I walked the channel it was dry, and lacked exposures of sorted sediment, well

defined channel banks and fluvial features like potholes or plunge-pools.

In the San Bernardino Mountains a 1999 debris flow scoured schists of the

Yucaipa Ridge (number 12 in Table 1.2), before depositing in Valley of the Falls.

Here, long-term erosion rates are estimated to be around 1 mm/a from U/Th-He data

[Spotila et al., 1999]. Along the runout, I observed abrasion and block-plucking of the bedrock valley floor caused by the debris flow, which also removed a pre-existing talus cover at valley slopes mostly above 0.10.

We visited a basalt basin (Aa, number 16 in Table 1.2) in East Maui and mapped debris flow deposits to its confluence with the mainstem Iao Valley.

Bedrock near the junction was largely buried with diamicton, and only exposed in a roadcut.

Bear River in the San Gabriels cuts Mesozoic granodiorites at long-term erosion rates of ~ 1 mm/a [Blythe et al., 2000]. Its headwater valley is filled with coarse talus, and several debris flows occurred in its tributaries the day before I visited, running out to slopes of 0.11 (Table 1.1). Below these recent debris flow

deposits, boulder fields fill the valley for several hundred meters until the first

widespread bedrock exposure occurs with potholes and runnels.

In the Santa Cruz Mountains, Deer Creek (Table 1.3) cuts Neogene arkoses at

rates that range from 0.2-0.3 mm/a, as estimated from sediment yield [Brown, 1973]

and cosmogenic radionuclide analysis of sediment [Perg et al., 2000]. The

headwaters of this valley are filled with coarse colluvium with rare exposures of

sandstone cliffs. At around 0.10 valley slope I found a field of boulder berms

containing auto tires from historic debris flows. Downstream of these recent deposits

I found cascades of boulders and isolated patches of older diamicton. Strath terraces

begin downstream in pool-riffle reaches.

Honeydew, Elder and Noyo rivers in the northern California Coast Range cut

Mesozoic greywackes of the Franciscan Formation and strath terraces are common up

to slopes of ~ 0.05. Projection of marine terrace rock uplift rates from Merrits and

Vincent [1989] inland to these basins yields approximate rock uplift rates of 4.0, 0.7, and 0.4 mm/a, respectively. Headwater reaches in these valleys share the features of

Deer Creek, although deep-seated failures occur in the Noyo basin.

Finally, Anghou River drains the Eastern side of Taiwan, cutting sand- and siltstones

of the Miocene Lushan Formation at rates estimated to be 1-2 mm/a by fission-track analysis [Liu et al., 2001]. Its downstream braided reaches transition to step-pool bedforms near the end of recent debris flow boulder berms.

Methods

The handwork involved in collecting area and slope from paper contour maps

is labor intensive and slow. I tested the possibility that I could extract similar data

quickly from 30-m USGS DEM’s by comparing them to hand-collected data from

their source 1:24,000 maps, and to laser altimetry in Figure 1.5b. I used a common

threshold drainage area of 4500 m2 (five 30-m grid cells) to extract a valley network from DEM’s, and looked for mismatches in the network position, and resulting area- slope graphs.

Figure 6 reveals substantial errors in both the position and extent of the network as estimated from the USGS 30-m DEM in green, compared to laser altimetry in red. The upper branches of the 30-m network are largely artifacts [e.g., feathering; see Montgomery and Foufoula-Georgiou, 1993], and include portions of hillslopes rather than just valley floors (which are commonly between 3 and 6 m in these valleys). In some places, the 30-m valleys are entirely artifacts, like the valley in the center left panel of Figure 1.6b that cuts through a ridge (marked as X). In addition, 30-m DEM's poorly resolve small valleys compared to the original 1:24,000 contour maps. For instance, Figure 1.7 compares hand-measured area-slope data with

30-m DEM data for a steep basin in the King Range, California. I removed sinks from the source 30-m data by increasing the elevation of such cells in 0.1 m increments. I extracted the valley network with a threshold drainage area of 5 or more cells, and removed cells that were influenced by sinks. Although the derivative

30-m data are similar to the contour data in some respects (m/n values are almost within one standard error), the scatter of the 30-m data obscures the region in which the data change trend. It is this region that defines the extent of fluvial power law relations, and therefore 30-m data are not adequate to resolve this issue. Although

averaging by log-binning smoothes noise, it does not recreate the original data pattern.

Techniques for hand extraction of area-slope data We conclude that network extraction from 30-m DEM’s in steeplands where valley bottoms are substantially less than 30 m wide introduces noise to the source data. Therefore, except for the laser altimetry, I measured mainstem valley area and slope by hand from contoured 1:24,000 or 1:50,000 scale topographic maps. To make area-slope plots for valleys in the laser altimetry coverage, I extracted the valley network using a simple threshold drainage area of 1000 m2, which approximates the valley network that I observe in the field here. I used a maximum fall algorithm for slope with a forward difference of two grid cells, extracted the profile data, and binned and averaged values over 10-m increments to smooth slope variations from thick-bedded sandstone cliffs. For all other sites I measured slope and drainage area at a point equidistant between elevation contours for every contour crossing of the valley. I enlarged steep areas with closely spaced contours 200% on a photocopier.

Where contours are closely spaced, I sampled area at every other contour interval, measuring slope between adjacent contours. I calculated slope as the contour interval divided by the valley blue-line distance, or if these are absent, the shortest distance along valley between adjacent contours. I stopped collecting data near the drainage divide at the valley head, which I defined as the last segment where the contour direction angle from one side of the valley to the opposite changes by ~150° or less, measured from linear tangents on either side of the valley axis. This is a crude

approximation for the actual hollow location, but I found it to be a rough measure of

valley head location based on comparison of 1:24,000 maps to field observations of

hollows in Figure 1.5. I used a polar planimeter to measure drainage area, resulting in

a precision of +/- 0.001 square inches (e.g., 3.7 x 10-4 km2 for 1:24,000 maps). Using a ruler to measure horizontal distance between contours results in a precision of +/-

0.25 mm (6 m for 1:24,000 maps, 3 m for the 200% enlargement). Corresponding point uncertainties in slope range from small fractions of a percent in the lowlands to

50% in the steepest parts of the profile, although practical uncertainties appear less than 20% on the basis of field and laser altimetry comparison to contour maps.

Techniques to extract power-law portion of data We used three methods to identify potential fluvial power law segments of mainstem area-slope plots. All three assumed that valleys carved by fluvial processes have area-slope data fit best by a power law, although I recognize that systematic variations in lithology, rock uplift rate [Kirby and Whipple, 2001], sediment supply

[Sklar and Dietrich, 1998; Sklar and Dietrich, 2001], orography [Roe et al., 2002] or grain size can influence this pattern. Although I assume that power laws approximate the lower portions of valley profiles, I am not able to demonstrate this over more than

2-3 log cycles because the gravel-bedded rivers that I examine are commonly bounded by dams, oceans or the gravel-sand transition at 0.001 slope. Many of the data that I present have substantial scatter when compared to area-slope plots often presented in the literature because I do not smooth data by averaging it.

Our first two methods used successive pruning of data starting at the top of the

profile and proceeding downvalley until a specific criteria for linearity was met. For

instance, in the first method I fit a power law to all of the data and recorded its slope.

I then pruned the smallest drainage area data point and refit the power law to get a

new slope. When this process is repeated, regression slopes tend to increase as

successively larger drainage areas are removed, indicating that the data do not follow

a single power law. I found that regression slopes stopped increasing systematically

where the remaining data included only low valley slopes and large drainage areas,

consistent with a power law in the fluvial region. A complementary method used the

same pruning procedure but fit log-log quadratic curves to data until the t-statistic of

the quadratic term was judged to be negligible and remaining data were well

represented by a single power law.

A third approach is to fit a function to the data which approaches valley head

slopes (s0) at small drainage area, and curves towards a linear power law scaling

a2 (a1A ) at large drainage area:

s S = 0 (1.5) a2 (1+ a1 A )

Equation (1.5) provides an empirical fit to the curved debris flow valley data with a

minimum number of parameters. In it, s0 represents the slope at the valley head, a1 is

2 a2 inversely proportional to curvature [and has units 1/(length ) ], and a2 tends towards

a power law slope at large drainage areas. The second derivative of (1.5) can be

written:

2 2()a a Aa2 −1 − a a ()a −1 Aa2 −2 (1+ a Aa2 ) ′′ [ 1 2 1 2 2 1 ] f (A) = s0 3 (1.6) a2 ()1+ a1 A

which has units of 1/length4. I infer that data follow a power law in the region of the plot where this second derivative has a marginally small value (marginal curvature technique) for parameter values from the fit to the full data set.

The first two methods have the disadvantage that endpoints (particularly those that are downstream) exert a tremendous leverage on both m/n values in equation

(1.4) and quadratic curvature. Even small deviations from linearity on a single downstream end point can lead to transition slope values well downstream of debris flow runouts (e.g., < 0.02). Therefore, these methods can only be applied to data that follow a power law exceedingly well. The third method has the advantage of being very robust to scatter in data, but requires a judgment of the threshold curvature at which the function is well approximated by a line. Therefore, I use a combination of these three techniques. I used m/n and t-statistics on data sets with well-defined linear portions as judged by R2 values greater than 0.9 (bold m/n values in Table 1.3).

Where m/n stopped increasing monotonically and the t-statistic indicated that there

was little significance to a quadratic fit parameter (|t | <1), I inferred a single power

law. I then used these results to choose a curvature value at which equation (1.5)'s

second derivative was judged to be vanishingly small, so that the remaining data

approximate a power law. I call the upstream-most data point on the power law the

river valley head.

For instance, Figure 1.8 shows all three methods applied to Deer Creek, for

data spanning its headwaters to near the mouth of the mainstem San Lorenzo at the

Pacific Ocean (Figure 1.1b). The m/n value stops increasing systematically where

the t-statistic approaches -1 at a drainage area of ~ 4 km2. The third line indicates curvature derived from a Levenberg-Marquardt non-linear fit to the data using equation (1.5) with inverse slope weighting. Curvature values of ~10-3 correspond to the transition to linearity as judged by the previous two techniques. I fit (1.5) to each full data set, and where its second derivative reaches 10-3 I infer the beginning of a single power law. To characterize the curvature of the data above the power law, I refit (1.5) to data above the threshold curvature value. For both fits, I weight each data point by the inverse of its slope, which is equivalent to weighting each data point by the valley length over which its slope is evaluated. Thus the more frequent data from steeper portions of the profile have proportionally less weight and do not bias

the fit. This is comparable to weighting each DEM pixel equally along a profile, and

reduces the influence of knickpoints or other short-length scale features on the fit.

Results

Curvature of area-slope data

In steepland valleys of the western U.S. I have observed sediment removal

and bedrock lowering along the entire runout of 13 recent debris flows in Oregon,

California and Utah (Table 1.2, Fig. 1.2-1.4). The lithologies, long-term erosion rates

and climatic histories of these field sites are diverse (Table 1.2), yet all share evidence

for bedrock lowering by block-plucking and grain-scale scour during the debris flow.

These features are illustrated for Oregon field sites in Figures 1.3-1.4, and I have

observed them where debris flows cross quartzites in Utah (number 13 in Table 1.2)

and schists in southern California (number 12 in Table 1.2). Area-slope data from

along all of these scoured runout paths appear non-linear in log-log space (Fig. 1.9)

and cannot be fit with a single power law without non-random residuals. Area-slope

data from basins with historic or pre-historic debris flows to their terminuses in Utah

and Maui are also curved, although in these basins bedrock exposure along the old

runout path is rare. This is consistent with rapid mantling of the bedrock surface by

coarse colluvium following exposure by the debris flow. Valleys in Figure 1.5a that

were scoured to bedrock in 1997 by debris flows were largely infilled with colluvium

or vegetation when I revisited them in 2001. Although each data set in Figure 1.9

could be decomposed into an arbitrary number of linear segments, these would not

correspond to any process transition that I observed while walking these profiles.

Laser data sets in Figure 1.9 have substantially denser data spacing than

1:24,000 contour data, and show greater scatter, despite averaging to 10-m

increments. Although the coarser 1:24,000 data capture area-slope curvature seen in

laser altimetry, they do not replicate its exact form. For instance, basin number 1 has

higher curvature in the laser altimetry than the 1:24,000 data, leading to higher a1 and a2 values in Table 1.2. Basin number 5, by contrast, has similar curvature values, but a higher valley head slope in the 1:24,000 data. Some of the basins have curves that are largely indistinguishable from each other (e.g., Scottsburg numbers 5, 6 and 7).

Amongst the rest there is substantial variation in the shape of the curvature, sometimes between adjacent basins (e.g., Sullivan and Roseburg). Variations in lithology, catchment size and transient conditions are all possible sources for different curve shapes. For instance, curvature sometimes decreases as catchment size increases (e.g., number 4 vs. number 3; number 9 vs. number 10) and sandstone cliffs are more frequent in some catchments (e.g., number 1).

Scaling break at ~0.10 slope

Along eight valleys in the western U.S. and Taiwan I walked from the valley headwaters past the downstream-most debris flow deposits into fluvial reaches. I found that the lowermost mainstem debris flow deposits terminate at 0.04 – 0.12 slope, and strath terraces (if they occurred) began several hundred meters downvalley from these deposits (Fig. 1.10). Area-slope data upvalley from these mapped terminal debris flow deposits (open symbols) are curved in the same manner as data from basins where I recorded bedrock scour from debris flows (e.g., Fig. 1.9). For instance, Figure 1.11b shows residuals from two power law fits to Deer Creek shown in Figure 1.11a, the entire data set and a subset of slopes greater than 0.10 (location of recent debris flow deposits). For both fits, positive residuals occupy the middle of the plot, negative residuals the ends. Neither the whole plot, nor the steep portion where

I have mapped modern debris flows can be fit with a single power law.

Valley slopes downstream of the first strath terrace approximate a linear power law (infilled symbols) as judged by a marginal curvature technique. For

instance, strath terraces in Deer, Noyo, Honeydew and Elder Creeks map downstream

of the beginning of the power law. In Bear, straths are absent, but the beginning of

the power law region corresponds to the appearance of large potholes and runnels in

the granite-floored channel. The extension of power law scaling above this transition

region substantially over-predicts valley slope at low drainage areas (Fig. 1.10) and is therefore a poor approximation for steeper valley slopes. Marlow and Sullivan Creek basins are smaller than our other examples and may not have enough data to define a power law, particularly with knickpoints that obscure potential trends. Curvature for these basins is lower than higher-resolution laser altimetry indicates for adjoining basins, but still present in 1:24,000 data.

Above the end of the power law and the upstream-most strath terraces of the valleys in Figure 1.10, I observed evidence that reaches transition from fluvial to debris flow activity over several hundred meters or more. In them, I observed fluvial bedforms (commonly step-pools) and fill terraces, but also occasional debris flow deposits. In Anghou, Deer, Honeydew, Elder and Bear, step-pools and rare debris flow deposits of the transition reaches gave way upstream to boulder cascades that filled the valley. In some basins, the slopes of these transition reaches are smaller than those found further downstream (e.g., Noyo, Deer, and Honeydew basins) but increase rapidly upstream once debris flow deposits become common. Valleys upstream of the transition region are straight or broadly curved in planform, but lack the repetitive meandering seen in rivers. If present, fill terraces were commonly

bouldery debris flow deposits that had been partially incised. Bedrock exposures along the valley floor were restricted to a few waterfalls.

Extension to other steeplands

The scaling break that I observe in Figure 1.10 also occurs in steepland basins in the U.S. (Fig. 1.12a) and around the unglaciated world (Fig. 1.12b). At larger drainage areas, the slopes of many of these basins approximate a power law (e.g.,

Djemaa, Vistula, Golema, Deer, Noyo, Bear, Indian and Honeydew basins).

Although there is significant scatter in some of the basins (e.g., Nam Se, Trapachillo,

Simbolar), projection of power laws to small drainage areas would over-predict valley head slopes substantially in most cases (e.g., Fig. 1.10). The sole exception is a mudstone basin from Italy (Marecchia) that may have badlands dominated by overland flow in its headwaters (Mauro Casedei, UCB Earth & Planetary Science,

2002, per. comm.).

We extracted the power law portion of the data for most of the basins in

Figure 1.12 (except Marecchia, Marlow and Sullivan) using marginal curvature techniques with equation (1.5) and then fit non-linear data upvalley (usually including transition reaches discussed above) with equation (1.5). Table 1.3 summarizes parameters from fluvial power law fits including the slope (m/n) and intercept {[(-∂z/∂t)/K]1/n}, as well as parameters from the fit of equation (1.5) to data above the power law region. Also shown are the approximate slopes and drainage areas at the transition, elevations of valley and river valley heads on the source

contour map, and the fraction of valley relief within the debris flow region. This

fraction is defined as elevation difference between valley head and scaling transition

point (river head) divided by the elevation of drainage divide. I used the last drainage area in the debris flow region, and the first in the power law region to bracket the drainage area of the scaling transition. I estimated the slope values at the transition by using the lowest debris flow slopes and the highest river slopes around the transition. Where rivers have locally steep slopes (e.g., Simbolar, Jellamayo) or debris flows have locally low slopes (e.g., Knawls, Indian), these values are included, leading to substantial ranges.

We found that valley slopes begin to fall systematically below the fluvial power law prediction as they approach values from 0.03-0.10 (see scaling transitions column in Table 1.3), similar to results from Figure 1.10. Just above the river head, there is commonly a short region where slope increases more rapidly than anywhere else on the plot (e.g., Honeydew, Deer, Djemaa, Nam Se, St. Germain, Ter, and

Simbolar). This occurs where the curved data do not join the power law fluvial trend

asymptotically. Above this high curvature region, there is commonly a more gentle

curvature as the valley head is approached. The magnitude of curvature

(approximated by a1 in Table 1.3) varies widely among basins. Grouping the basins

by map scale, and by lithology and erosion rate can reduce the variation. For

instance, for the last 12 U.S. basins dominated by sedimentary rocks in Table 1.3, a

2 plot of erosion rate against a1 in log-log space shows a rough correlation (R =0.77) with curvature increasing with erosion rate. Global data in basins of sedimentary

rock (excluding the Marecchia and basins with combinations of clastics and

metamorphic rocks) show a similar relation, although they are more scattered

(R2=0.70). Basins with crystalline rocks on the other hand tend to have lower

curvature for similar erosion rates. For instance, at erosion rates between 0.1-0.3

mm/a, Djemaa and Toplodolska basins cut in sedimentary rocks have lower a1 values

(thus, higher curvature) than Simbolar, Chasong-gang and Jellamayo basins, which are cut in granites and gneisses. Because a1 trends with erosion rate and lithology are

weak enough to be challenged, and the erosion rates for many of the basins have large

but unquantifiable uncertainties, a more focused effort is required to evaluate these

correlations with lithology and erosion rate.

Figure 1.12 and s0's value in Table 1.3 illustrate that these valleys heads

approach slopes of 0.3-1, and more commonly slopes of 0.4-0.5, over a wide range of

lithology and erosion rates. Comparison of 1:50,000 to 1:5,000 data for the same

basin (upper-left panel in Fig. 1.12b) indicate that coarser topography captures a

smoothed version of finer resolution data, so curvature from 1:50,000 scale maps is

not an artifact of coarse scale.

Below the scaling break, the exponents of the power law regression vary

substantially, from near zero values to 1.4 (Table 1.3). Basins with power law fits

whose R2 is greater than 0.9 are shown in bold, and those with R2 less than 0.7 are

italicized. The former have m/n values from ~ 0.7 to 1.0 for sedimentary and

metamorphic lithologies. Basins with intermediate R2 values have a greater range of

m/n, from ~ 0.5-1.4. Many low R2 values result from local, steep downvalley reaches

that disrupt a power law trend (e.g., Big Creek, Sandymush and Toplodolska) or pervasive scatter so that linear trends are less obvious (e.g., Nam Se, Simbolar,

Jellamayo, and Trapachillo). Power laws fits to the latter basins have low slopes whose upstream projections intersect data above the river valley head, but do so in regions where data actually curve.

Discussion

Four categories of observations indicate that debris flows carve the bedrock of some steepland valleys, producing a distinctive area-slope topographic signature:

• field observations of bedrock lowering caused by debris flows

• area-slope curvature in valleys with observed debris flow bedrock lowering

• scaling break near terminal debris flow deposits, upvalley from straths (if they

occur)

• scaling break in U.S. and global data near typical debris flow runout slopes of

~ 0.03 – 0.10

First, field observation along recent debris flow runouts indicates that where bedrock is exposed, there is evidence for lowering caused by the debris flow. The lowering is of sufficient magnitude to be geomorphically relevant (e.g., Fig. 1.4), although its style varies with lithology. Debris flows appear to be the dominant process exposing bedrock in steepland valleys whose floors are often mantled with

very coarse particles. Headwater valleys that have not had recent debris flows (e.g.,

those in Fig. 1.10) lack or have only rare exposures of bedrock above step-pool

reaches in slope ranges where debris flows occur. The rapid mantling of valleys in

Oregon that were scoured to bedrock in 1997 also indicates that debris flows here

may be the only process capable of transporting away coarse material that

accumulates rapidly in valley bottoms from hillslope processes. Although sediment

in valleys in Figures 1.2 and 1.3 may eventually acquire a thin veneer of fluvially-

sorted sediment, it is usually colluvium below the surface [see also Benda, 1990;

Benda and Dunne, 1997]. Transport of colluvium by concentrated flow following debris flows is also reported [Larsson, 1982], but I know of no evidence for bedrock lowering by concentrated flow following debris flows. Although fluvial incision may be possible in this kind of circumstance, debris flows appear to be required just to expose most of the valley floor bedrock.

Second, valleys where I have mapped scour (e.g., Fig. 1.5a, b) have area-slope plots that curve in log-log space (Fig. 1.9) throughout the overlapping regions of observed bedrock lowering and debris flow runout. Although there is much local scatter in high-resolution Oregon slope data due to alternation between sandstone and siltstone beds, linear power laws will not fit the high-resolution topography of these valleys. This curvature is also apparent on coarser resolution data (e.g., 1:24,000 data in Fig. 1.9), although I suspect that its exact parameterization requires higher resolution data because Marlow and Sullivan Creek plots (Fig. 1.9) show different curvature. I propose that although the valley networks shown in Figures 1.2 and 1.5

closely resemble fluvial networks in planform, they are predominately carved by the entirely different process of debris flow incision, whose signature is curvature in log

A-log S space.

Third, I find that a scaling break in the 1:24,000 area-slope data occurs approximately where identifiable debris flow deposits end and strath terraces begin

(e.g., Fig. 1.10). This transition in process is mirrored in the topography as a scaling break in valley area-slope data when plotted in log-log space. I interpret the region between frequent debris flow deposits and the beginning of strath terraces as a transition between fluvial bedrock incision and debris flow incision. Although these reaches are likely a combination of processes, I include their few data points in the debris flow region because their upvalley extent is difficult to estimate.

Fourth, analysis of many unglaciated steepland valleys in the U.S. and around the world indicates a scaling break from data that could be modeled with a single power law to data that are non-linear in log-log space (Table 1.3) near where field observations (e.g., Tables 1.1, 1.2) indicate that debris flows deposit (slopes > 0.03).

Since many rivers lack strath terraces (e.g., Bear River), there are substantial uncertainties in the long-term boundary between fluvial and debris flow valley incision. Therefore, the transition boundaries listed in Table 1.3 for valleys that I have not walked should be regarded as illustrative rather than definitive.

Transient changes in valley long profile or systematic variations in rock uplift rate [Kirby and Whipple, 2001] or lithology may also have their own signature on area-slope plots. I have tried to minimize these effects by careful site selection, but I

cannot demonstrate that all of our sites have topography at steady state. Some are likely to be out of equilibrium at some time or space scale. For instance, basins whose data are poorly fit with power laws in fluvial regions (e.g., Nam Se, Simbolar,

Jellamayo, and Trapachillo) may have transient knickpoints that lower m/n values.

Although fluvial power laws do not overestimate some slopes above river valley heads in these basins, they also do not capture curvature above the river valley head.

What I find convincing is that across a wide range of rock uplift rates and lithologies, the scaling break takes place at around 0.03 – 0.10, the lowest slopes that many field studies indicate that larger debris flows can reach (e.g., Table 1.1).

While the evidence that I have acquired points towards the dominant role that debris flows play cutting steepland valleys, it does not mean that all valleys greater than 0.03-0.10 slope are cut solely by debris flows. In landscapes without mass failures (e.g., some badlands), overland flow may still predominate. Nor have I established that fluvial processes play no role in steepland valley incision. Rather, I find that the tendency for rapid burial of valley floors after debris flows precludes the widespread occurrence of fluvial incision along debris flow runouts. In field areas where sediment cover is absent and flow occurs, fluvial incision at steep slopes might give rise to a different signature (e.g., Marecchia).

Implication of scaling transition

Large fractions of valley relief (25-75%) lie above the scaling break at the river valley head for basins that I investigated in Table 1.3, in reaches steep enough to transport debris flows. Although increasing basin size and distance from base-level

(hence average slope) reduce this fraction, it is still substantial even for large basins

far away from coasts (e.g., Toplodolska, Vistula, St. Germain). In steep ranges near

the coast (e.g., Honeydew, Franklin, Anghou), debris flow valleys are the dominant

portions of valley relief (>70%). The location of the transition near the end of debris

flow runouts is consistent with a threshold slope beyond which debris flows are not

mobile and cannot incise valleys (e.g., Tables 1.1, 1.2). Using 0.10 valley slope as a

conservative estimate for this limit, I find that in steeplands like the Oregon Coast

Range, most of the valley network by length, and large fractions of it by relief (Table

1.3) are cut by debris flows, not rivers. Figure 1.13 illustrates this in the 100-km2

Millicoma basin (from a 10-m DEM kindly provided by Stephen Lancaster, Oregon

State University, Corvallis, OR), cut in the Tyee Formation of the Oregon Coast

Range. In blue are 10-m valley segments of less than 0.10 slope, a maximum estimate for the extent of fluvial incision. Nonetheless, the red valley network of

>0.10 slopes occupies nearly 90% of the channel network length, including much of the local relief. The image indicates that most of the hillslopes in this basin have boundary lowering rates that are set predominately by debris flow incision, not fluvial lowering, and that much of the landscape relief resides in valleys cut by debris flows.

Figure 1.14 shows profiles for three basins where I have identified process transitions in the field and scaling breaks on area-slope plots. The scaling break in the area-slope plots for each basin occurs at the intersection of the dashed lines with the existing long-profile (solid line). Above the intersection, the valley has a curved area-slope plot that I infer represents debris flows incision by. For these basins,

debris flow portions of the mainstem valley occupy 40-80% of the mainstem relief.

The dashed lines represent what the profile would look like if the fluvial power law

scaling of the lower part of the plots (Fig. 1.10) extended to the valley head defined

by contour direction angle. They indicate the role that debris flows have in

controlling existing valley relief, although other processes like deep-seated

landsliding would probably occur before valleys reached these extreme slopes.

Figure 1.14 and the fraction of valley relief above river valley heads (Table

1.3) illustrate that a debris flow incision law, as yet unknown, determines much of the

mainstem relief and most of the tributary relief for unglaciated steeplands. This

means that there is much yet to be learned about the evolution of steep escarpments,

river valley walls, and the persistence of topography in orogens, all of which are

commonly characterized by valleys with slopes greater than 0.10. Likewise, the influence of climate and erosion rate on relief will require some assessment of the role of debris flows. The transition zone between fluvial and debris flow valley incision, where debris flow material accumulates in the short term, also remains a problematic region about which we know very little.

Interpretation of curvature

Fits of equation (1.5) to U.S. and global debris flow valley profiles have substantial variability, as shown by the range of parameters in Tables 1.2 and 1.3.

Some of the variation is likely a size effect, with smaller catchments having higher curvature as their longitudinal profiles curve rapidly to join mainstems. This size

effect in itself indicates that equation (1.5) does not adequately capture all of the

relevant effects controlling curvature.

Other variations in area-slope curvature may reflect response to boundary

lowering rates. For instance, catchments on either side of the knickpoint in Sullivan

Creek have different curvature (e.g., number 1 vs. number 2 in Table 1.2) that may

reflect a transient response. Steady-state responses to rock uplift rates and lithology

may also influence curvature.

For instance, Figure 1.15 summarizes hypotheses about valley response to

variations in rock uplift rate and lithology, based on inverse correlation between a1 and erosion rate that I observe for some basins of similar lithology in Table 1.3.

Valleys cut by debris flows are shown as dashed lines and solid lines show river-cut valleys. While river valleys follow a power law that translates upward with rock uplift rate, debris flow valley slopes in Figure 1.15a converge to an upper limit within the range of slopes commonly reported for hollows in soil-mantled landscapes. By

visual analogy to the string of a bow, Figure 1.15 shows the debris flow curve pulled

upwards and towards greater drainage areas as erosion rates increase, but pinned

below slopes at which landslides initiate. This is consistent with the observation that

in most of the basins in Figure 1.12, valley heads reach a limiting slope at vanishingly

small drainage areas that is seemingly insensitive to rock uplift rate. This value is

near the friction angle for many soils, and is likely set by landslide initiation at

hollows, 20-100 m below the ridgeline in our examples. I cannot say whether the

upper threshold slope is set by material properties, or the maintenance of slopes above

which debris flow incision is extraordinarily rapid. At the other end of the profile, the

bowstring is pinned by the lowermost slope values at which debris flows tend to

deposit in confined valleys, often slopes of 0.03 - 0.10. Here there is occasionally an

abrupt increase in slope at the upstream end of the linear fluvial trend (see for

instance Deer, Cook, Djemaa) leading to a profile steepening at the river valley head.

As rock uplift rates increase, I hypothesize that there is a tendency for lower

threshold slopes to migrate to successively larger drainage areas (e.g., Yucaipa,

Honeydew). Similar tendencies have been predicted for fluvial systems by the

models of Howard [1997] and Tucker and Bras [1998]. For debris flow cut valleys,

this would focus both long-profile and area-slope curvature in the remaining region

above the river valley head, resulting in nearly linear upper long-profiles that curve

rapidly concave upwards approaching the river valley head. This region of response

to rock uplift rates is consistent with the finding by Merrits and Vincent [1989] that

first order channels respond most sensitively to rock uplift rates, because their blue-

line first order channels occur at drainage areas of ~0.1 to 1 km2, within the highly curved lower section of debris flow area-slope data where small changes in curvature lead to large changes in slope. For the purposes of illustrating this hypothesis, I compare area-slope data from predominately sandstone basins with erosion rates ranging from ~0.01 to 4 mm/a (Fig. 1.16a). For these basins, area-slope data are more curved at high erosion rates (e.g., Honeydew Creek) compared to low erosion rates (e.g., Knawls Creek, West Virginia). Hypothetical differences between tectonically active areas and passive ones can also be illustrated by comparing granite

basins with little active tectonism (Korea) to those with high erosion rates (San

Gabriels) in Figure 1.16b. Here again there is higher curvature in the debris flow region where erosion rates are higher.

We hypothesize that there is also an influence of lithology on valley profile.

Figure 1.17 illustrates that for roughly equivalent erosion rates, valleys in crystalline rocks like gneisses and granites may be steeper for a given drainage area than those cut in sandstones. Valleys in crystalline rocks or indurated rocks like basalts may also tend to have lower curvatures in the debris flow region (as reflected in larger a1 values in Table 1.3) than valleys in sedimentary rocks for similar erosion rates (Fig.

1.17a, b).

Implications for stream power law exponents

Our comparisons of USGS 30-m data to hand-extracted 1:24,000 data and to laser altimetry indicate that scatter in the 30-m data obscure scaling transitions and do not exactly reproduce source data parameters (e.g., m/n values). At low drainage areas (e.g., < 10-4 km2) much of the network may be artifactual, while at larger areas slope scatter is substantial. Therefore, 30-m DEM’s used for area-slope analysis need to be validated by comparing them to the 1:24,000 quadrangle source before they can be used to infer scaling laws. Great care should be taken to ensure that the data being fit with power laws are indeed linear in log-log space. For instance, inclusion of data that curve at low drainage areas in power law regressions decreases m/n values and increases intercept [(-∂z/∂t)/K]1/n values (e.g., Fig. 1.7). This could lead to spurious correlations between rock uplift rate and power law slope and intercept. To avoid this

problem, headwater reaches above 0.03 slope should be excluded from stream power

law analysis unless they are demonstrably influenced by fluvial incision (e.g.,

presence of strath terraces or extension of well-defined single power law).

Even m/n values extracted only from fluvial regions vary substantially in

Table 1.3. For instance, basins that follow a single power law exceedingly well (R2 values > 0.9) have m/n values that vary from 0.7-1.0 for sedimentary and metamorphic lithologies. Valleys in hard, crystalline rocks like granites tend to have m/n values (0.4-0.6) lower than those of valleys in sedimentary rocks, but this might also be an artifact of the small number of valleys I measured in granitic rocks. The range of m/n values in Table 1.3 spans those reported in the literature, from high values like 1.0 [Seidl and Dietrich, 1992; Seidl et al., 1994], to lower values like 0.1 -

0.5 [Stock and Montgomery, 1999; Snyder et al., 2000]. I have not established that each basin has uniform lithology or is at steady state, but this variation in m/n indicates that there is no single m/n value that can be extracted from topographic data for a general stream power law.

Conclusion

Field observations and map analysis demonstrate that debris flows that occur

in landscapes steep enough to produce mass failures both erode bedrock and have a

topographic signature in the form of curvature in area-slope space above 0.03-0.10

slope. Power law plots of slope versus area, widely used to examine bedrock river

incision laws, begin to over-predict valley slopes just upstream of the last strath

terrace. Above this region, the influence of debris flows increases rapidly, and is

reflected in a curved relation between slope and area on log-log plots that corresponds

to mapped debris flow runouts. This topographic signature is consistent with a

fundamentally different valley incision law by debris flows, whose form I further

explore in a forthcoming paper. Much of the world’s steepland valleys, similar in

planform appearance to fluvial networks, may be cut by debris flows. Debris flow

networks are relevant to landscape evolution because they are both extensive by

length (>80% of large steepland basins) and comprise large fractions of mainstem valley relief (25-100%). As a consequence, valleys that are predominately carved by debris flows, not rivers, bound most hillslopes in unglaciated steeplands. Debris flows limit the relief of unglaciated mountain ranges to substantially lower elevations than river incision laws would predict. Together these observations demonstrate that a debris flow incision law is needed to explore mechanistic linkages between tectonics, climate, and topography in unglaciated steeplands.

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a) 1 fluvial? 10

hillslope?

transition zone 101 debris flows?

fluvial

b) 1 10

1 10

valley slope from paper 7.5’ map uppermost strath 0.49 (+/ 0.03) S= 0.11(+/0.07)A

3 10 103 100 103 2

slope area (km )

Fig. 1.1 a) Hypothetical topographic signatures for hillslope and valley processes; area and slope are measured incrementally up valley mainstem to the drainage divide; b) area-slope data from hand measurement of 1:24,000 topographic map and field observations of strath terraces, Deer Creek, Santa Cruz Mountains. Rightmost two data points are from 1:100,000 scale maps of San Lorenzo River. The data in the lower panel appear to require more than one erosion law because a power law fit has non-random residuals.

Fig. 1.2 Debris flow valley network in an Oregon Coast Range clear-cut. The combination of elevated water pressure during a 1996 storm and reduced root strength initiated landslides at valley heads that mobilized as debris flows, scouring sediment and Tyee sandstone (white areas) along the runout. Road at top right indicates scale.

Fig. 1.3 View of bedrock valley bottom of Sullivan 1 (see Figure 1.5) in the Oregon Coast Range several months after scour by a debris flow. Note the surface parallel fractures in the Tyee Formation, some of which have been removed by the debris flow in the valley axis. In nearby untorrented valleys unsorted hillslope deposits cover the bedrock.

Fig. 1.4 Removal of Tyee Formation sandstone grains (~0.5 - 1 mm in diameter) on Sullivan 1 by abrasion caused by 1996 debris flow (see Fig. 1.5 for location). Moss in the lee of the smaller ledge indicates abrasion of less than several mm. Ledge in bottom portion of photo corresponds to removal of fractured slab 7 mm thick.

a) ↑

Fig. 1.4 Fig. 1.3 Sullivan 1

0 1 km

b N↑

0 1 km Fig. 1.5 a, b. a) Shaded relief image of high resolution airborne laser altimetry from Oregon at Coos Bay (top) and Scottsburg (bottom). Dotted lines indicate 1996/1997 debris flows, as mapped in the field. Arrows in Coos Bay panel bracket knickpoint on Sullivan Creek. Hillslopes draining to Sullivan Creek from the top portion of the image are likely deep-seated failures (as judged by the lack of larger valleys), so I choose not to use them for analysis. Deep-seated landslides also occur in the northeast quadrant of Figure 1.5b, and are a process whose occurrence in this region is in part structurally controlled [Roering et al., 1996].

↑ N a)

↑ ←

→

0 1 km

↑ b) N

↑ ←

→

0 1 km

Fig. 1.6 a, b. Valley networks with drainage areas greater than 4500 m2 using laser altimetry (red) and USGS 30-m grids (green) at a) Coos Bay and b) Scottsburg. Profiles selected to avoid regions with deep-seated failures. The 30-m data poorly represents the valley network because it results in many artifactual valleys located on hillslopes, and has spurious valleys like that crossing a ridge in Scottsburg (center left, X-symbol). Numbers refer to drainage basins used for area-slope analysis.

0 10

slope -2 10 Honeydew USGS 30-m Honeydew 7.5’ log-binned 30-m DEM 7.5’ (m/n=0.80 +/- 0.04) 30-m DEM (m/n=0.91 +/- 0.05) log-binned 30-m DEM (m/n=0.66 +/- 0.03)

-4 10 -3 -1 1 10 10 10

2 area (km )

Fig. 1.7 Comparison of USGS 30-m grid and hand extracted 1:24,000 data for Honeydew valley in the King Range, California. Sinks and adjacent points are omitted from profile, slopes calculated using forward difference, maximum fall algorithm over 2-cells. Scatter of 30-m data compared to its 1:24,000 source data indicate derivation errors leading to differences in slope and intercepts of power law regressions (shown for data below apparent scaling break at ~ 0.4 km2). Binning the data by log cycle and averaging it further alters the slope of the source data and obscures its curvature.

1 10 2

-1

) 0 4 10

-1

m/n & t-statistic curvature (1/length -3 -2 10 m/n value t-statistic curvature of fitting expression -3

-5 -4 10 -2 0 10 10 2 area (km )

Fig. 1.8 Plot of three methods to extract power law portion of area-slope plot for Deer Creek (see text). The m/n value is the slope of a power law regression applied to the data when successively larger drainage areas are pruned away for each fit. Values converge when there is no systematic curvature in the data, so that it approximates a single power law. The t-statistic is a measure of the significance of a quadratic term in a non-linear fit to the data using the same pruning. It falls to negligible magnitude (below 1) where m/n values converge (vertical dashed line), and where the curvature of equation (1.5) reaches 10-3. Together, these criteria indicate that Deer Creek has a single power law at drainage areas larger than ~4 km2.

1 0 1 0 2

0 0 0 0 0 1 1 1 1 1 1

Joe’s Canyon Silver Cr. Yucaipa Steed Rick’s Ford Aa

10 ) 2

1 2 3 3 4 2 10 Sul Rose Sul Rose Rose

1 2 1 Scott Scott 3 Sul 2 Sul Sul 1 (7.5’ data) Scott Scott 1 (7.5’ data)

3 10 1 0 0

1 2 10 10 10

10 10 slope

area (km

Fig. 1.9 Area-slope data from valleys in Oregon, Utah and California where I mapped bedrock lowering of the valley floor along the runout path of recent debris flows. Curvature in area-slope space along this runout path appears to be a signature for valley incision by debris flows. Data from Sullivan Creek, Scottsburg, and Roseburg are from high resolution laser altimetry in Oregon; Joe's Canyon, Marlow 1, Silver Creek and Yucaipa data are from 1:24,000 topography in Oregon, Utah and California. A diamond in the upper left panel identifies the approximate location of bedrock lowering shown in Figure 1.4. Also shown are data from 1:24,000 maps for basins with historic debris flow activity along their entire profile (Steed and Rick's Ford in Utah, and Aa in Maui). See Table 1.2 for fit parameters.

Taiwan-debris flows Bear-debris flows -no debris flows -no debris flows 1 10 Noyo-debris flows Deer-debris flows -no debris flows -no debris flows ↑ 1st Noyo strath ↑ 1st Deer strath Taiwan river Bear river Noyo river Deer river

-1 10 ↑ ↑

Marlow-debris flows Elder-debris flows -no debris flows -no debris flows 1 Sullivan-debris flows Honeydew-debris flows 10 -no debris flows -no debris flows ↑ 1st Honey. strath ↓ 1st Elder strath Honeydew river Elder river -1 10 ↓

↑

-3 10 -3 -1 1 -1 1 3 10 10 10 10 10 10

slope 2 area (km )

Fig. 1.10 The extent of debris flows along the mainstem as estimated by preserved deposits (open symbols) mapped in the field onto 1:24,000 topography. The zone of departure from the fluvial power law lies near the downstream end of existing debris flow deposits, and upstream from last observed strath terrace (stars or crosses). Extension of single power law (shown by lines) substantially overestimates valley slope at low drainage areas (see text for methods used to define linear portion of data). Data for each basin is bounded its downstream end by presence of the ocean (Noyo, Taiwan, Deer, Honeydew, Marlow, Sullivan) or dams (Bear). Sullivan and Marlow Creeks lack defined power law scaling, because of a combination of knickpoints and small drainage areas. They illustrate the importance of using sufficiently large basins to define fluvial trends.

m/n=0.49 (+/- 0.03) 0 10 m/n=0.28 (+/- 0.02)

slope -2 10

whole, >0 whole, <0 partial, >0 partial, <0

-2 10

-4 absolute value of residuals from power law fit 10 -3 0 3 10 10 10 2 area (km )

Fig. 1.11 a, b a) Plot of Deer Creek, Santa Cruz Mountains. Extension of a fluvial power law to step valleys is inappropriate, as shown by non-random residuals. at Also note that the trend at small drainage areas is non-linear. Catchment bedrock is sandstone, erosion rates are 0.15 - 0.3 mm/a (see text for details). b) absolute values of differences between predicted and observed slopes in a) show a non-random pattern indicating that only the lower, fluvial section is linear.

0 0 10 10

Deer Tenmile Marlow -2 -2 10 Honeydew Elder Sullivan 10 Noyo

0 0 10 10 slope

-2 Cook Franklin Howard -2 10 Cummins Indian Dry Creek 10

0 0 10 10

Big Creek Hurricane Sandymush -2 -2 10 Cane Knawls Bear 10 Alder

-3 -1 1 -1 1 -1 1 3 10 10 10 10 10 10 10 10

2 area (km )

0 0 10 10

Anghou (1:5 K) Nam Se Asahi -2 -2 10 Anghou Baay Thia 10 Chasong-gang Peinan

0 0 10 10

slope

-2 Vistula Toplodolska St. Germain -2 10 10 Golema Ter Marecchia

0 0 10 10

Marin Trapachillo Simbolar -2 -2 10 Djemaa Tulahuencito Chibalan 10 Jellamayo

-3 -1 1 -1 1 -1 1 3 10 10 10 10 10 10 10 10

2 area (km ) Fig. 1.12 a, b Data from unglaciated steepland valleys in a) the US (1:24,000) and b) around the world (1:50,000). Note that extension of linear power law trends of large drainage areas would tend to overpredict valley slope above 0.10 across a wide range of climate, rock uplift rates and lithology. See Table 1.3 for details.

Fig. 1.13 Valley network of the 100-km2 Millicoma basin, Oregon, extracted from a 10-m DEM. At a drainage area threshold of 1000 m2, 90% of the valley network length is above 0.10 gradients where debris flows are known to occur.

100000

Bear, San Gabriels fluvial extrapolation Honeydew, King Range fluvial extrapolation Deer, Santa Cruz fluvial extrapolation

1000 mabsl

10 -20000 0 20000 meters from valley head

Fig. 1.14 Plot of profiles from Bear, Honeydew and Deer Creek indicating that much of the valley relief lies in debris flow region. Shown for comparison are profiles predicted by extending slopes predicted by river incision law to valley head (defined by planform curvature from topographic maps).

rock uplift rate

10 0

slope

10 -2

(U/K)-1/n

10 -3 10 -1 10 1 area

rock uplift rate

elevation

distance from valley head

Fig. 1.15 Hypothetical response of valley network to variations in rock uplift rate/rock resistance ratio. As rock uplift rates increase, river valley slopes (solid lines) increase as intercept of the power law translates upward. Debris flow valley slopes also become steeper resulting in a more linear long- profile.

0 10

-2 10 Bear (dashed line; granitic) Anghou (ss)

-1 10

Dry (ss) Cummins (dashed line; basalt flows) -3 10 -3 -1 1 3 slope 10 10 10 10

2 area (km )

Fig. 1.16 a, b Apparent effect of rock uplift rates on valley slope in a) sandstone basins: Knawls Creek, (West Virginia) and Deer Creek, Santa Cruz Mountains, and Honeydew (California); b) granitic basins: Chasong-gang, North Korea, and Bear Creek, San Gabriels, California. Infilled symbols are data that follow a fluvial, linear power law (see text for details). Open symbols are curved, reflecting debris flow valley incision. See Table 1.3 for fit parameters.

0 10

-2 10 Knawls (~0.01 mm/a) Deer (dashed line; ~0.2 mm/a) Honeydew (4 mm/a) Big Creek (4 mm/a)

-1 10

Chasong-gang (~0.1 mm/a) Bear (~ 1 mm/a) Yucaipa (~ 1 mm/a)

-3 10 -3 -1 1 3 slope 10 10 10 10 2 area (km ) Fig. 1.17 Apparent effect of lithology on valley form. Infilled symbols are data that follow a fluvial, linear power law (see text for details). Open symbols are curved, reflecting debris flow valley incision. See Table 1.3 for parameters of both fits. Valleys in crystalline or indurated rocks (e.g., some basalts) tend to have lower long-profile curvature in both fluvial and debris flow regions. This is reflected in lower m/n values for granites and basalts versus sandstones at similar rock uplift rates, and higher values of a2 in the debris flow region (indicating lower curvature) for crystalline rocks and basalts versus sandstones.

Table 1.1. Sampling of slopes at debris flow deposition. slope confinement # flows data source location reference > 0.02 valley/fan summary literature global Costa (1984) 0.02 fan 1 field or 1:24,000 San Gabriels, CA Sharpe and Nobles (1953) 0.02 - 0.26 fan 14 survey over last 20 m Japan (Yakedake) Suwa and Okuda (1983) 0.03 - 0.05 valley/fan 1 1:24,000 Arizona Wohl and Pearthree (1991) 0.03 - 0.11 valley 9 field survey Oregon Coast Range Swanson and Lienkaemper (1978) 0.03 - 0.14 valley 7 1:24,000 Oregon Coast Range Benda and Cundy (1990) >0.04 valley/fan many 1:24,000 Appalachians, VA Morgan et al. (1999) 0.04 - 0.27 valley/fan 26 1:10,000 Calabria, Italy Sorriso-Valvo et al. (1998) > 0.05 valley/fan 448 field survey British Columbia Fannin and Rollerson (1993) 0.05 - 0.20 fan 80 1:25,000 Switzerland, alpine Rickenmann and Zimmerman (1993) 0.05 - 0.37 valley/fan summary literature? Japan Ikeya (19 89)

71 0.05 - 0.55 valley 46 1:50,000 Oregon Cascades this study, from P. Uncopher mapping 0.05 - 0.83 valley many 1:24,000 Oregon Coast Range this study, from ODFa mapping >0.07 valley 1? 1:24,000? San Gabriels, CA Scott (1971) cited in Campbell (1975) 0.07 - 0.09 fan many field or 1:24,000 San Gabriels, CA Morton and Campbell (1974) 0.07 - 0.17 fan many field survey New Zealand Pierson (1980) 0.08 - 0.24 open slope/fan 9 field survey Scandinavia Rapp and Nyberg (1981) 0.09 - 0.16 valley 3 field or 1:24,000 West Virginia Cenderelli and Kite (1998) 0.10 valley 1 field survey Maui this study 0.10 valley 1 1:24,000 Santa Monica, CA Campbell (1975) 0.10 - 0.35 open slope/fan 9 field survey Scandinavia Larsson (1982) 0.11 valley 1 field survey San Gabriels, CA this study 0.12 fan 1 field or 1:20,000 Italy Berti et al. (1999) 0.13 - 0.21 fan >4? field survey? Colorado, alpine Curry (1966) 0.14 - 0.31 valley/fan 7 1:25,000? British Columbia, glacial VanDine (1985) 0.16 - 0.20 valley/fan 4? ? Swiss alps Lewin and Warburton (1994) 0.17 - 0.24 fan 5 field or 1:25,000 British Columbia, glacial Hungr et al. (1984) 0.19 - 0.40 open slope/fan 9 survey? French alps Van Steijn et al. (1988) a: Oregon Department of Forestry

Table 1.2. Data for valleys with recent and recorded debris flows, located by USGS 1:24,000 quadrangle name.

basin location USGS 7.5' lithology average rain. erosion rate ~ date bedrock scour deposition debris flow erosion rate from:S=suspended load; R=reservoir;

a2 quadrangle (mm/a) (mm/a) features slope a0/(1+a1A ) E=fission-track/cooling; U=marine terrace; O=other

0.590 1 Sul 1 Oregon Coast R. Allegany sandstone 1500-2500 0.07-0.1 1996/1997 abrasion, plucking 0.05 1.03/(1+14.1A ) S,O-Reneau and Dietrich, 1991; Heimsath et al., 2001

0.501 1b from 7.5' data 1.05/(1+4.94A )

0.946 2 Sul 2 Oregon Coast R. Allegany sandstone 1500-2500 0.07-0.1 1996/1997 abrasion, plucking 0.04 .725/(1+54.9A ) S,O-Reneau and Dietrich, 1991; Heimsath et al., 2001

0.794 3 Sul 3 Oregon Coast R. Allegany sandstone 1500-2500 0.07-0.1 1996/1997 abrasion, plucking 0.07 .773/(1+12.4A ) S,O-Reneau and Dietrich, 1991; Heimsath et al., 2001

4 Sul 4 Oregon Coast R. Allegany sandstone 1500-2500 0.07-0.1 1996/1997 abrasion, plucking 0.09 .712/(1+24.5A1.18) S,O-Reneau and Dietrich, 1991; Heimsath et al., 2001

0.787 5 Scott 1 Oregon Coast R. Scottsburg sandstone 1500-2500 0.2 - 0.3 1996/1997 abrasion, plucking 0.11 .797/(1+8.80A ) O-Personius, 1995

0.779 5b from 7.5' data 1.04/(1+9.74A )

6 Scott 2 Oregon Coast R. Scottsburg sandstone 1500-2500 0.2 - 0.3 Pre-historic - - .830/(1+8.00A0.766) O-Personius, 1995

0.570 7 Scott 3 Oregon Coast R. Scottsburg sandstone 1500-2500 0.2 - 0.3 Pre-historic - - .859/(1+4.41A ) O-Personius, 1995

1.13 8 Silver Creek Oregon Coast R. Elk Peak sandstone 1500-2500 0.07-0.1 1996/1997 abrasion, plucking 0.05 .468/(1+7.32A ) S,O-Reneau and Dietrich, 1991; Heimsath et al., 2001

9 Rose 1 Oregon Coast R. Callahan sandstone 1000-1500 ~ 0.2 1996/1997 abrasion, plucking 0.10 .949/(1+8.25A0.868) O-Personius, 1995 72 1.97 10 Rose 2 Oregon Coast R. Callahan sandstone 1000-1500 ~ 0.2 1996/1997 abrasion, plucking 0.10 .831/(1+69.7A ) O-Personius, 1995

a 11 Rose 3 Oregon Coast R. Callahan sandstone 1000-1500 ~ 0.2 1996/1997 abrasion, plucking 0.10 - O-Personius, 1995 abrasion, plucking, 2.24 12 Yucaipa San Bernardinos Forest Falls mica schist 610-1020 ~1 1999 chips 0.11 .707/(1+7.77A ) E-Spotila et al., 1999 abrasion, plucking, 0.468 13 Joe's Canyon Wasatch (Utah) Spanish Fork Pk. quartzite 510-1020 ? 1998 chips 0.05 .817/(1+2.97A ) unknown covered 0.532 14 Steed Wasatch (Utah) Bountiful Peak gneiss 640-1270 ~ 1-2 1923, 1930 0.05-0.11 .716/(1+1.27A ), E-Armstrong et al., 1999

15 Rick's Ford Wasatch (Utah) Bountiful Peak gneiss 640-1270 ~ 1-2 1901? covered 0.04-0.10 .740/(1+22.6A0.178) E-Armstrong et al., 1999

1.20 16 Aa Maui Wailuku basalt 3810-7620 ? historic? covered 0.10 1.06/(1+16.3A ) unknown a: values for eqn. (5) did not converge

Table 1.3. Data for valleys used in area-slope analysis from contour maps: 1:24,000 scale maps. c 1/n riv er location quadrangle lithology av erage rain. erosion rate m/n [(-dz/dt)/K] debris flow scaling transitions: v alley riv er debris erosion rate ref erence from:S=suspended load; R=reservoir;

(mm/a) (mm/a) a /(1+a Aa2)area (km2) slope head (m) head (m) flow fraction E =fission-track/cooling; U =marine terrace; O =ot her 0 1 Beara San Gabriels Cry stal Lake granitic 1300-2000 0.7-1 0.57 0.431 1. 11/ ( 1+2 . 5 9 A 0.637) 7 - 10 .09 - .15 2353 1365 0.42 E -Blythe et al., 2000;O -St ock et al., unpublished Alder San Gabriels Pacifico Mntn. granitic 1300-2000 0.3-0.4 0.34 0.35 . 6 17 / ( 1+1. 8 6 A 0.820) 6 - 10 .05 - .06 1890 1561 0.17 E -Blythe et al., 2000 Sandy mush North Carolina Sandy mush biotitic granitic gneiss 1200-1800 0.05-0.08 1.01 0.455 . 9 19 / ( 1+4 . 4 4 A 0.470) 4 - 7 .08 - .09 1500 817 0.46 R -Dendy and Champion, 1978 Cane North Carolina Montreat metagrey w acke 1200-1800 0.05-0.08 1.20 1.42 .3 33 / (1+.2 71A 1.230) 7 - 15 .06 - .08 1756 1122 0.36 R -Dendy and Champion, 1978 Cook Oregon Coast Rogers Peak basalt flow s 2000-2500 0.4-0.8 0.42 0.085 1. 2 1/ ( 1+12 . 1A 0.723) 5 - 6 .02 - .04 707 280 0.60 O -Personius, 1995

Cummins Oregon Coast Yachats basalt 1500-2000 0.2 0.71 0.12 3.23/(1+24.2A0.467) 4 - 5 .03 - .04 610 146 0.76 S -Reneau and Diet rich, 1991;O -Personius, 1995 a Marlow Oregon Coast Golden Falls micac. ss (Ty ee) 1500-2500 0.07-0.1 ------S,O-Reneau and Dietrich, 1991; Heimsath et al., 2001 a Sulliv an Oregon Coast Allegany micac. ss (Ty ee) 1500-2500 0.07-0.1 ------S,O-Reneau and Dietrich, 1991; Heimsath et al., 2001 Indian Oregon Coast Cummins Peak micac. ss (Ty ee) 1500-2500 0.2 0.95 0.077 .571/ (1+9.58A 0.869) 2 - 4 .02 - .05 463 207 0.55 S -Reneau and Diet rich, 1991;O -Personius, 1995 Franklin Oregon Coast Scottsburg micac. ss (Ty ee) 1500-2000 0.2-0.3 0.73 0.132 1. 18 / ( 1+11. 9 A 0.543) 4 - 6 .04 - .07 2414 122 0.95 O -Personius, 1995 Deera Santa Cruz Mts. Castle Rock Ridge arkose,siltstone 1000-1500 0.15-0.3 0.90 0.31 .3 67/ (1+1.3 7A 0.942) 5 - 6 .05 - .09 866 463 0.46 R -Brown, 1973; S -Coat s et al., 1982; O -Perg et al., 2000 Honey dew a CA Coast Shubrick Peak grey w acke 1300-3000 4 1.21 0.824 .42 9/ (1+.44 3A 1.650) 4 - 10 .05 - .06 1109 219 0.80 U -Merrits and Vincent, 1989 Eldera CA Coast Cahto Peak grey w acke 1800-2300 0.7 1.19 0.725 . 5 16 / ( 1+2 . 5 2 A 0.262) 5 - 9 .06 - .10 1244 457 0.63 U -Merrits and Vincent, 1989 Noyoa CA Coast Burbeck grey w acke 1000-1800 0.4 0.82 0.17 . 3 13 / ( 1+. 9 5 2 A 0.836) 4 - 5 .04 - .06 780 280 0.64 U -Merrits and Vincent, 1989 Tenmile CA Coast Sherw ood Peak grey w acke 1000-2000 0.4 1.40 2.04 .2 78 / (1+.550A 1.180) 6 - 8 .04 - .14 890 305 0.66 U -Merrits and Vincent, 1989 How ard Oregon Coast Mount Peav ine w acke 2000-2400 0.1-0.2 0.46 0.169 .834/(1+4.28A0.471) 5 - 10 .04 - .14 1097 561 0.49 O -Personius, 1995 Dry Oregon Coast Father Mountain w acke 2000-2400 0.1-0.2 0.85 0.133 .730/(1+4.95A0.744) 4 - 5 0.03 610 158 0.74 O- Personius, 1995 Big North Carolina Luftee Knob ss,silt-s,m-grey w acke 1200-1800 0.05-0.08 0.28 0.124 .8 80 / (1+5.17A 0.593) 5 - 8 .03 - .15 1780 1317 0.26 R -Dendy and Champio n, 1978 Hurricane Arkansas Bidv ille ss,silt-s,shale,w acke 1120-1320 0.07 0.52 0.066 .584/(1+9.61A0.810) 3 - 5 .03 - .05 683 463 0.32 R -Dendy and Champion, 1978

0.670 R -Dendy and Champion, 1978 73 Knaw ls West VA Walkersv ille shale,silt-s,ss,ls 1020-1300 0.01-0.03 0.70 0.029 . 5 16 / ( 1+16 . 5 A ) 1 - 2 .03 - .04 433 311 0.28 Table 1.3. Data for valleys used in area-slope analysis from contour maps: 1:50,000 scale maps. 1/n riv er location quadrangle lithology av erage rain. erosion rate m/n [(-dz/dt)/K] debris flow scaling transitions: v alley riv er debris osion rate reference from:S=suspended load; R=reservoir; a2 2 E =fission-track/cooling; U =marine terrace; O =other (mm/a) (mm/a) a0/(1+a1A ) area (km ) slope head (m) head (m) flow fraction Trapachillo Ecuador NVIII-A4 granitic 600-1300b 0.7-0.75 0.08 0.048 .948/(1+3.06A0.538) 10 - 17 .04 - .16 2280 1500 0.34 O -Coltorti & Ollier, 2000; E- Steinmann et al., 1999 Jellamay o Peru 2340-III granitic ~500 0.3 0.40 0.601 1.53 /(1+2 .75A 0.455) 15 - 17 .10 - .40 5300 3325 0.37 E- Laubacher & Naser, 1994 Chasong-gang N. Korea NK-52-7-44 granite 1000-1200 0.04-0.37 0.71 0.306 .533/(1+2.28A0.372) 6 - 10 .07 - .08 1560 780 0.50 S -Yoon and Woo, 2000; E -Lim and Lee, 2000 Simbolar Argentina 2966-9-2 migmatitic gneiss 200-300 0.18-0.28 0.47 0.47 .481/(1+.479A0.995) 6 - 15 .08 - .60 3750 2925 0.22 S -Walling & Webb, 1983 Golema Greece K-34-115-1 gneiss, schist, amphib. 600-800 0.22 0.57 0.179 .352/(1+.826A0.758) 4 - 8 .09 - .10 1600 1180 0.26 R -Poulos et al., 1996 Marin Keny a 76/1 qtzites,schists,gneiss 1015-1525 0.1 0.88 1.51 .598/(1+.616A0.618) 15 .10 - .27 3260 1780 0.45 O -Roessner & Strecker, 1997 Chibalan Guatemala 2061-II schist,gneiss,marble 1000-2000 0.04-0.09 0.73 0.794 .362/(1+1.40A0.953) 9 - 16 .07 - .20 2080 1400 0.33 S -Walling & Webb, 1983 Baay Philippines 3172-I basalt/and., diorite ~3500 1.4 1.17 1.94 .321/(1+.690A0.770) 9 - 17 .05 - .10 1600 900 0.44 R -White, 1988 Thia Vietnam 5852 II clastics/v olcanics 2000-2400 0.08-0.50 0.32 0.163 .410/(1+.042A1.720) 17 - 21 .05 - .11 2920 1280 0.56 E -Maluski et al., 2001; Carter et al., 2000 Tulahuencito Chile D-85 clastics/v olcanics 300b 0.4 0.41 0.205 1. 9 1/ ( 1+ 12 .0 A 0.383) 7 - 10 .05 - .14 3600 2600 0.28 O- Munoz & Charrier, 1996 Asahi Japan NI-53-15-4/5249 II ss,slate,basalt,chert,ls 1600-2400 1.9-2.0 0.60 0.491 .6 78 / (1+.4 59 A 0.691) 12 - 20 .13 - .17 2500 1080 0.57 R -Ando et al., 1994; Takemura et al., 1997 St. Germain France 27-40 mica schist 1500-2000 0.01-0.37 0.69 0.151 .4 10 / (1+.8 53 A 2.850) 4 - 5 .04 - .06 960 520 0.46 R -Gay & Macaire, 1999; Maneux et al., 2001 Peinan Taiw an 9519-II slate,phy llite,schist 1500-3000 2-6 0.98 5.63 . 5 16 / ( 1+. 2 0 1A 0.890) 18 - 80 .08 - .12 3100 1300 0.58 S -Li, 1976; E -Liu et al., 2001 Anghoua Taiw an 9517-I argillite,ss(Lushan) 3000-4000 0.4-1.7 0.70 0.18 .682/(1+2.18A0.591) 4 - 8 .05 - .08 900 240 0.73 E -Liu et al., 2001 Ter Spain 37-10 schist, fly sch 500-1000b 0.07-0.13 0.85 1.01 . 4 15 / ( 1+ .0 7 0 A 2.420) 5 - 18 0.10 2400 1620 0.33 R -Serrat, 1999; Salas et al., 1997;O -Verges et al., 1995 Toplodolska Serbia 3481 I ss 500-1000 0.1-0.2 0.72 0.638 .520/(1+.586A0.935) 11 .06 - .02 1880 1060 0.44 R - Petkovic et al., 1999; S -Kostadinov & Markovic, 1996 Nam Se Thailand 4569-I ss/ms 1200-1400 0.01-0.09 0.17 0.066 .796/(1+4.10A0.772) 6 - 8 .03 - .14 1700 1300 0.24 R -Jantawat, 1985; S -Alford, 1992 b Marrechia Italy 278 mudstone/marls 1000-1500 0.08-0.4 0.36 0.072 ------O -van der Muelen et al., 1999;Coltorti & Pieruccini, 2000 Djemaa Algeria Oued Amizour sandstone, mudstone 1000-2000 0.1-0.26 0.98 1.42 .426/(1+.371A1.120) 10 - 20 .07 - .09 1520 780 0.49 - Errih and Bendahou, 1997; U -Morel and Meghraoui, 1996 Vistula Poland 2917 II fly sch/marl 1000-1500 0.01-0.03 0.68 0.196 .590/(1+4.49A0.794) 4 - 7 .05 - .08 1060 740 0.30 S -Lajczak, 1990 Notes: bold values indicate that pow er law regressions have R2 values greater than 0.9, italics indicate R2 values less than 0.7; a is field-checked; b is median annual rainfall; lithology abbreviations are: micac.=micaceous, ss=sandstone, amphib.=ampibolite, silt-s=siltstone, m-greyw acke=meta-greyw acke, ls=limestone, qtzites=quartzites, and=andesite, ms=mudstone.

CHAPTER 2. INCISION RATES FOLLOWING BEDROCK

EXPOSURE: THEIR IMPLICATIONS FOR PROCESS CONTROLS

ON THE LONG-PROFILES OF VALLEYS CUT BY RIVERS AND

DEBRIS FLOWS

Abstract

Until recently, published rates of bedrock valley incision came from indirect

dating of incised surfaces. A small but growing literature based on direct

measurement, however, reports short-term bedrock lowering at geologically

unsustainable rates. I report observations of bedrock lowering from erosion pins

monitored over 1 - 7 years in 10 valleys that cut indurated volcanic and sedimentary

rocks in Washington, Oregon, California and Taiwan. Most of these channels have

recently been stripped of sediment and their bedrock is exposed to bedload abrasion

and plucking. Seasonal wetting and drying also comminutes hard, intact rock into thin plates or small equant fragments that are removed by high flow. Consequent incision rates are proportional to the square of rock tensile strength, in agreement with experimental results of others. Measured rates up to cm’s per year far exceed regional long-term erosion rate estimates, even for apparently minor sediment transport rates.

Cultural artifacts on adjoining strath terraces in Washington and Taiwan indicate at least several decades of lowering at these extreme rates. These observations suggest that when stripped of sediment cover, lithologies at these sites lower at rates that far

exceed long-term rock uplift rates. This rate disparity makes it unlikely that the long-

profiles of these rivers are directly adjusted to either bedrock hardness or rock uplift

rate in the manner predicted by the stream power law, despite the observation that

their profiles are well-fit by power law plots of drainage area vs. slope. In these cases,

it may be the threshold of motion of the coarse sediment mantle rather than bedrock

hardness or rock uplift rate that controls channel slope.

By contrast, steep valleys recently scoured to bedrock by debris flows have

been buried by soil, and none of the hundreds of erosion pins I installed indicate any

post-event fluvial lowering. These results are consistent with episodic debris flows as

the primary agent of bedrock lowering in the steep parts of the channel network above

~10% slope, a process whose signature is curvature on a plot of valley area against slope in log-log space. At one site, where reaches between 4-10% slope also experienced minor fluvial lowering in addition to debris flow incision, a case could be made for a transition zone between debris flow and fluvial incision

Introduction

Over the last two decades, a theory for river incision into bedrock has

emerged which proposes that lowering rates depend on rock resistance, and either

local shear stress or stream power per unit bed area (e.g., Howard and Kerby, 1983;

Seidl and Dietrich, 1992; Sklar and Dietrich, 1998; Stock and Montgomery, 1999;

Whipple and Tucker, 1999; Whipple et al., 2000). Substituting drainage area for

discharge and channel width, this theory predicts that when rock uplift rates (U) are

balanced with incision, local channel slope varies as a power law with drainage area

A and rock erodibility:

S = (U/K)1/nA-m/n , (2.1),

where m and n are exponents in the incision law, whose values are debated (Seidl and

Dietrich, 1992; Seidl et al., 1994; Tucker and Slingerland, 1996; Stock and

Montgomery, 1999; Whipple and Tucker, 1999; Whipple at al., 2000). The intercept of this power law depends on the ratio of rock uplift rate to a measure of rock resistance. For instance, Snyder et al. (2000) have proposed that mapping the spatial variation of this ratio can be used to infer spatial patterns of rock uplift rate. Implicit is the notion that at some time scale, the rock substrate is resistant enough to remain exposed as the long-profile steepens towards a new equilibrium at higher rock uplift rates. The stream power law is widely used to model incision in steepland valleys

(e.g., Anderson, 1994; Whipple and Tucker, 1999; Whipple et al., 1999; Davy and

Crague, 2000; Willett et al., 2001). The occurrence of power law area-slope plots for bedrock-floored rivers (e.g., Fig. 2.1) and some studies (e.g., Howard and Kerby,

1983; Seidl and Dietrich, 1992; Stock and Montgomery, 1999; Whipple et al., 2000) are consistent with its use in some rivers.

Two recent discoveries suggest that the simple stream power law is incomplete, and even wrong for certain parts of valley networks. First, map-derived and high-resolution longitudinal profiles show a clear deviation from the power law

prediction at slopes greater than 0.03 – 0.10 (e.g., Fig. 2.1; Seidl and Dietrich, 1992;

Montgomery and Foufoula-Georgiou, 1993; Stock and Dietrich, 2003). Field

evidence indicates that on these steeper slopes, scour by episodic debris flows

predominates, leading to a non-linear plot of log-S against log-A (Stock and Dietrich,

2003). Consequently, in steeplands that generate debris flows, relief may be largely controlled by debris flow incision. The exact boundary between fluvial and debris flow processes, as well as the contribution of intermittent fluvial incision in the debris flow dominated portion of the channel network remain unexplored. As a result, there is ambiguity as to whether the curved area-slope signature arises solely from the action of debris flows, or a combination of fluvial and debris flow processes interacting with weathering.

The second discovery is that for a given rock uplift rate, sediment grain size and supply rather than rock resistance may strongly control local channel slope (Sklar and Dietrich, 1998; Sklar and Dietrich, 2001). Numerical modeling (Sklar and

Dietrich, 1998) and analog physical modeling (Sklar and Dietrich, 2001) demonstrate that sediment supply and size distribution influence bedrock incision by 1) providing tools of varying effectiveness for wear, and 2) creating bed coverage that prevents wear. A tradeoff between these two processes leads to a humped relation between sediment supply and wear, such that wear initially increases with supply until bed cover begins to reduce wear at high supply rates. Sklar and Dietrich (2001) propose that the extent of coverage may vary with tectonics and climate, and that grain size may be more important than rock resistance in setting channel gradients. Thus it is

not clear that concavity of channels in Fig. 2.1 can be interpreted directly in terms of equation (2.1). The interpretation of concavity from such plots is further complicated by their findings that rock resistance varies as the square of tensile strength in laboratory experiments (Sklar and Dietrich, 2001). Rocks that can wear at rates that far exceed rock uplift rates where exposed to weathering or even minor sediment loads will generate long-profiles that are not adjusted to rock strength or rock uplift rate in the simple way predicted by equation (2.1), despite the occasional occurrence of bedrock along their floors.

We explore the implications of these two new discoveries by investigating the lowering rate of exposed bedrock in Western North America and Taiwan using erosion pins installed in 10 rivers, and in 3 steepland valleys eroded by recent debris flows, and monitored over the last half-decade. I installed several thousand pins in an effort to resolve both the issue of the influence of intermittent fluvial incision along debris flow runouts, and the question of whether these bedrock-floored streams are lowering at rates greater than regional long-term estimates. I measured drainage area and slope to analyze the long-profiles containing monitoring sites, and the adjoining basins, to investigate potential topographic signatures for both cases.

Rapid Bedrock Weathering

On an opportunistic basis, I observed evidence for rapid bedrock weathering and valley floor lowering in channels in the Western U.S. and Taiwan (Table 2.1; Appendix 1).

Figures 2.2-2.3 show examples of these features. In Figure 2.2, rock breakdown is associated

with pervasive seasonal fracturing of weakly cemented siltstones and sandstones exposed to

wetting and drying. Field observations of pervasively fractured river cobbles (Mugridge and

Young, 1983) and landslide surfaces (Fujiwara, 1970) indicate rapid bedrock weathering

processes similar to those in Figure 2.2. An extensive geotechnical literature describes both field and laboratory evidence for the comminution of rock by such processes during wetting and drying (e.g., Taylor and Smith, 1986; Taylor and Cripps, 1987; Dick and Shakoor, 1992;

Santi and Shakoor, 1997). For instance, laboratory experiments designed to simulate natural exposure to rain/sun record the breakdown of basalts (Haskins and Bell, 1995), and sedimentary rocks (Mugridge and Young, 1983; Yamaguchi et al., 1988; Day, 1994; Moon and Beattie, 1995; Miscevic, 1998) over 1-20 cycles of wetting and drying. Rocks containing expandable clays (especially smectites) or zeolites are most commonly observed to fracture rapidly during wetting/drying, so most workers above explain the phenomenon as a result of

1) air breakage in voids or 2) mineral swelling or shrinking. In the first process, suction pressures of air voids in the interior create large tensional stresses that break mineral bonds leading to cracks. In the second, contraction of the rock during the drying phase creates similar tensional stresses that break mineral bonds. Expansion during rehydration then leads to comminution. Measurements showing that rock cohesion decreases with repeated wetting and drying (Kusumi et al., 1998) are consistent with this hypothesis. The volumetric percentage of clay is a reasonable parameter controlling the magnitude of swelling (e.g., Dick and Shakoor, 1992; Moon and Beattie, 1995), and cementation and local sedimentary or igneous structures are thought to influence the response as well.

By contrast, in well-cemented sandstones and volcanic rocks elsewhere, I observed

weathering features like those in Figure 2.3, skins of rock that are 10’s of cm’s in planform

dimension, and commonly one to several cm’s thick. Thin-sections of these features indicate that unlike weathering rinds, their matrix materials (CaCO3 or silica) are intact, and

secondary porosity is limited to planes that mimic the local free surface, but are not bedding.

The origin of these features remains unexplained, although their genesis may be related to

hydration processes described above. To avoid confusion with the large literature on true

weathering rinds, I use the term folia (plural of folio, Latin for leaf) to describe the features

in Figure 2.3.

Field Sites

Using features shown in Figures 2.2 and 2.3 as a guide, I selected exposed

bedrock reaches in reaches with either active fluvial transport, or recent debris flow

scour channels in the Western U.S. and Taiwan (Table 2.1). Site selection is

consequently biased towards steep bedrock-floored channels that transport sediment

that is gravel or coarser, and cut sedimentary or volcanic rocks in active tectonic

settings. At each site, I installed erosion pins to test if weathering features are

seasonally formed, and to document any resulting lowering. Where possible, I

collected bedrock samples to test if erosion rates varied with tensile strength, as

shown in flume experiments by Sklar and Dietrich (2001). At each pin installation

site (and selected surrounding basins in similar bedrock) I characterized valley

longitudinal profiles with area-slope plots. I separated longitudinal profiles into

fluvial and debris flow reaches on the basis of local field observations of processes, and analysis of area-slope plots for topographic signatures of fluvial (log-log linear) and debris flow (log-log curved) incision (Stock and Dietrich, 2003).

Olympic Mountains, Washington

Measurements since 1994 (Stock et al., 1996) indicate rapid weathering and erosion of sedimentary rocks exposed in channels on the southern margin of the

Olympic Mountains, Washington. Here the West Fork Satsop River exits the steeplands of the Eocene Crescent basalts into lowlands of Eocene through Miocene marine sedimentary rocks that unconformably overlie the basalt. Sand- and siltstone of an unnamed Eocene marine unit are the oldest of these marine sedimentary rocks, and crop out in a narrow (< 2 km wide) belt coincident with the abrupt mountain front. They are overlain by late Eocene and Oligocene marine sand- and siltstone of the Lincoln Creek Formation (Tabor and Cady, 1978), and further downstream by

Late Miocene sandstones and siltstones of the Montesano formation. Scattered outcrops of sand- and siltstone of the Miocene Astoria Formation are also present. A fission-track study by Brandon et al. (1998) indicates Neogene exhumation rates less than 1 mm/a in the meta-sedimentary core of the Olympics that diminish outwards to less than 0.3 mm/a towards the flanking basalt and sedimentary rocks. No active structures or faults are known in the lowland regions of the West Fork, although recent glacial drift covers much of the region. Pleistocene valley glaciers sourced in the Olympics left outwash terraces in the Satsop basin, whose channels have both

bedrock- and alluvium-floored reaches. Rainfall at the NOAA weather station nearest to the West Fork of the Satsop has an average value of 2660 mm/a. Gaging stations on the mainstem Satsop River recorded the 70-year flood of record during the extreme winter rainfalls of 1996-1997. Old-growth Douglas fir and cedar forest covered the land prior to historic clear-cutting in the first half of the century.

Montgomery et al. (1996) argued that many channels in the basin were alluvial prior to removal of logjams and large wood during logging.

We chose three bedrock reaches of the West Fork Satsop River, and one on a tributary called Black Creek to monitor bedrock lowering. The upstream site on the West

Fork Satsop River (Fig. 2.4a) is several hundred meters downstream of Eocene Crescent basalts in a mixed alluvial and bedrock reach cut in poorly-cemented, thin-bedded sand- and siltstones of the unnamed Eocene unit (Fig. 2.2) that strikes across the stream and dips southward. A narrow bedrock bench above the channel thalweg is exposed on both banks during base flow and a v-shaped low-flow channel is cut ~1 m deep into it. I found cut wood fragments in deposits on a bedrock surface 1.2 m above the bench, indicating historic abandonment of a ~ 100 m wide surface now covered by 1 m or more of alluvium and remnant log-jams. These deposits indicate that this reach was alluvial, at least during early post-European contact years, and probably until logging in the 1940’s-1950’s.

Approximately 2 km downstream on the Lower West Fork Satsop, I chose two sites near each other with exposed siltstone and mudstone of the Lincoln Creek Formation.

Upstream and downstream of these sites are gravel-bedded reaches with straths of varying elevation, and low flow depths of ~ 0.7 m deep. Black Creek (Fig. 2.4b) cuts poorly

cemented Late Miocene sandstones of the Montesano Formation (Tabor and Cady, 1978).

When surveyed in 1995, the channel had little alluvial cover except for where forced alluvial reaches were impounded by logjams (Montgomery et al., 1996). Low flow is less than 0.1 m deep, although I found trim-lines from a dam-break flood of ~1 m depth in 1996-1997, which removed many of the forced alluvial reaches.

In addition to West Fork Satsop River and Black Creek, I selected the nearby basins of Middle Fork Satsop, and Canyon River for long-profile analysis. The profiles of the Middle and West Fork Satsop, and Canyon River, head in basalt before crossing sand- and siltstones of the unnamed Eocene sedimentary rocks at the mountain front, and Lincoln Creek and Montesano Formations downstream. Black

Creek cuts sandstones and siltstones of the Montesano Formation.

Washington Cascades

The West Fork Teanaway River heads in glaciated Eocene sandstones of the

Swauk Formation near the crest of the Washington Cascades and flows downstream through middle Eocene basaltic, andesitic and rhyolitic rocks of the Teanaway

Formation (Tabor et al., 2000). High-relief steeplands associated with these rocks cease at a lithologic boundary with overlying Eocene micaceous sandstones and siltstones of the Roslyn Formation, into which is cut a wide, low relief valley.

Miocene Columbia River basalt flows in the region are warped up to the west towards the Cascade crest, as is a 1 Ma intracanyon andesite on the Tieton river to the south that has been incised at an average rate of ~ 0.1 mm/a at its upstream end (Donald

Swanson, Hawaiian Volcano Observatory, Hawaii, unpub. data). This local river

incision rate is approximately twice that of preliminary estimates of 0.05 mm/a for

regional long-term exhumation rates east of the Cascade crest (Ehlers et al., 2001;

Reiners et al., in press). The West Fork Teanaway basin is typically snow covered in

winter, and experiences a spring snowmelt peak in May.

Roslyn Formation sandstones are nearly continuously exposed along the lower

~3 kilometers of the West Fork Teanaway River, and in patches in the ~9 kilometers upstream. These medium- to fine-grained, white, micaceous, lithofeldspathic sandstones have weathering features like those of Figures 2.2-2.3. Above baseflow, much of the bedrock surface consists of weathered flakes ~0.01-0.1 m thick, some of which expand upward and form “tents” during the dry season. In the study area, the river has incised 1-2 m into a low relief bedrock surface, and has parabolic channel cross-section with little sediment cover. However, gravel in these reaches was abundant enough during 1936 field surveys by the Federal Bureau of Fisheries that

~65% of the streambed in the lower 11 km of the Teanaway was judged spawnable

(McIntosh et al., 1995). Descriptions and a photograph of the adjacent Middle Fork at the beginning of the 20th century (Russell, 1898) record abundant in-channel wood,

common in Pacific Northwest rivers prior to logging and stream cleaning (e.g., Sedell

and Luchessa, 1981; Collins et al., 2002). In the Teanaway, timber companies began

such activities early in the 20th century (Shideler, 1986), transporting logs by river drives (1902-1916) and railroads (1917-1930). Disappearance of alluvium along much of the West Fork Teanaway and 1-2 meters of incision into the bedrock

occurred sometime in this century, perhaps as a result of these activities. In addition

to long-profile analysis of the mainstem, I installed three cross-sections of erosion

pins from kilometer 2.0 (measured from the confluence with the Middle Fork) to

kilometer 2.6. Within the low-flow channel, beds often have ~0.1-1.0 m wide flutes.

Oregon Cascades

Walker Creek (Fig. 2.4c) dissects Oligocene-Miocene (25-35 Ma) volcanic

and volcaniclastic rocks (Sherrod and Smith, 2000) in foothills of the Western

Oregon Cascades near Eugene, an area with northwest trending high-angle faults that

have been active during the Neogene. Reservoir sedimentation surveys of Dorena

Lake (Dendy and Champion, 1978), downstream of Walker Creek, and nearby

Cottage Lake, indicate sediment yields that are equivalent to lowering rates of 0.03

and 0.05 mm/a over a period of 5-10 years, assuming commonly reported sediment

bulk density values of 1120 kg/m3 (Dendy and Champion, 1978). Locally, Walker

Creek cuts lahars in its lower reaches, and rhyolite ash flows and dacites in its upper reaches. The lahars are strongly indurated with both rounded and angular lithic fragments in a cemented, clay-rich matrix. Where exposed in the stream channel, bedrock surfaces have folia and tented folia (Fig. 2.3b) that indicate the potential for rapid erosion. A headwater portion of Walker basin was roaded and clearcut, and a consequent road-related landslide during the winter of 1996/1997 dammed the mainstem. A resulting dam-break flood reached depths of 5 m and left ~ 650 m of bedrock thalweg exposed over 1300 m from the dam-break to the downstream-most

bedrock exposure. Starting at this location, I spaced 4 cross-sections at ~ 325 m intervals upstream along the flood path. The lower three are in indurated lahar, and the uppermost cross-section is in an indurated rhyolite ashflow, which has strong secondary silica cement. Cut banks and a few preserved mid-channel deposits at the lower cross-sections along Walker Creek are composed of matrix-supported diamictons, which are likely old debris flow deposits, since glaciation did not reach these lower elevations.

We chose profiles from Walker Creek and its mainstem, Sharp’s Creek, to examine area-slope data. Sharp’s Creek traverses indurated dacite pyroclastic flows and lahar deposits in its headwaters and basalt flows in the last several hundred meters above a major tributary junction upstream of Dorena Lake.

Oregon Coast Range

Landslides during 1996/1997 El Niño storms initiated debris flows throughout the Oregon Coast Range, many of which scoured sediment from valley floors and exposed carbonate-cemented sandstones and siltstones of the Eocene Tyee Formation.

I used ground reconnaissance to locate debris flow sites in Sullivan Creek basin, near

Coos Bay. Erosion rates in this portion of the central Oregon Coast Range are thought to be between 0.1 and 0.2 mm/a on the basis of strath terrace ages (Personious, 1995), sediment yield (Reneau and Dietrich, 1991) and cosmogenic radionuclides (Heimsath et al., 2001). Here and in the nearby Marlow Creek basin, I walked debris flow runouts (dotted lines in Fig. 2.5) to map the occurrence and style of bedrock lowering

from debris flows. I observed folia and tented folia (Fig. 2.3a) along these runouts.

Although difficult to quantify systematically, I found that debris flows had removed bedrock as 1) grooves and lineations at the scale of the component rock grains and as

2) fracture-bounded blocks one to several cm’s thick, corresponding to folia. Figure

2.4 shows the locations of 20 cross-sections of 221 erosion pins placed at 0.25 m spacing over the upper 350 m of bedrock exposed and eroded by a 1997 debris flow in a tributary of Sullivan Creek (“Kate Creek”). Individual dots approximate cross- section spacing. An additional 142 pins were installed along 195 and 240 meters of two debris flow runouts in Marlow Creek, at a similar frequency. I also installed two cross-sections of erosion pins on the mainstem Sullivan Creek, which has year-round baseflow, well-defined fluvial banks and pool-riffle reaches locally. Matrix-supported deposits interbedded with fluvial deposits indicate that debris flows also occurred along this reach. I chose long-profiles for Kate creek to illustrate the curved area- slope form that I commonly observe in valleys scoured by debris flows (Stock and

Dietrich, 2003), and for Sullivan Creek, which is short and has a large knickpoint.

California Coast Range

The South Fork Eel River cuts Cretaceous marine sandstones of the

Franciscan Formation in the northern California Coast Range. Knickpoints in its longitudinal profile and strath terraces on the mainstem and tributaries (Seidl and

Dietrich, 1992) record locally transient river incision rates. Canyon walls confine the river along much of its course leading to floods of considerable depth. For instance,

trimlines from the 1964 flood of record indicate flow depths of ~4 meters at a water surface slope of ~ 0.004 near Elder Creek confluence. Average annual sediment loads estimated at 1700 t/km2 for the entire Eel basin (Milliman and Syvitski, 1992) are equivalent to basin-wide lowering rates of 0.6 mm/a, values similar to those of 0.5 mm/a estimated by inland projection of marine terrace rock uplift rates from Merrits and Vincent (1989). This basin-wide sediment yield value may overestimates

Holocene lowering rates in the headwaters of the South Fork Eel because it includes substantial increases due to anthropogenic effects (e.g., Sommerfield et al., 2002).

Consequently, long-term lowering rates are likely lower than 0.6 mm/a. I installed erosion pins on a largely bedrock cross-section (Fig. 2.4d) at the location of a USGS gauge whose daily record was discontinued in 1970 (USGS gage #11475500). This is the only site near a gaging station. A partial stage record is available for the first several years after pin installation (Fig. 2.6), however, the stage data are unreliable after 1999 (oral. comm., Tracy Allen, University of California Angelo Reserve). A strath terrace 2.3 m above the thalweg on the left bank records past bedrock river incision. I collected width and grain-size data in alluvial reaches upstream of this bedrock-dominated knickpoint area in addition to area-slope analysis.

Western Foothills, Taiwan

In September 1999, the Chelong-Pu thrust fault ruptured along ~ 200 km of eastern Taiwan during the Chi-Chi earthquake (e.g., Kao and Chen, 2000; Rubin et al., 2001). Co-seismic displacement was largest in the north end of the fault at Tachia

River, and declined to less than a meter south of Nantou (e.g., Rubin et al., 2001). A narrow (< 1km wide) belt of Chinshui shale crops out along much of the Chelong-Pu fault (Ho and Chen, 2000) where it composes waterfalls along some rivers as a consequence of the 1999 rupture. The western foothills rise to the east of the

Chelong-Pu Fault, an out-of-sequence thrust (Kao and Chen, 2000), and in this region are composed of eastward dipping monoclines of sandstone, siltstone and shale of the

Plio-Pleistocene Cholan Formation, and further eastward the Toukoshan Formation, a

Pleistocene equivalent with similar lithologies. These units are in thrust contact with older Miocene sandstone, siltstone and shale further east, which comprise the rest of the western foothills. The boundary of these foothills with the high-relief (e.g., > 1 km) region of the Central Range coincides with Eocene to Oligocene meta-sediments including shale, slate, argillite, phyllite, arkoses and quartzites which make up much of the Central range. Strath terraces occur in most of the larger rivers draining the western foothills and are widely interpreted to be of tectonic or climatic origin (e.g.,

Chen and Liu, 1991; Sung et al., 1995; Hsieh and Kneupfer, 2001; Sung et al., 1997).

Exhumation rates from apatite fission-track thermochronology referenced in Liu et al.

(2001) indicate rates of ~ 1 mm/a over the last several million years in the western foothills. Suspended loads reported for the Tachia River (Li, 1976) are equivalent to basin-wide lowering rates from 0.12 mm/a in the Central Range portion of the catchment to 0.10 mm/a near the coast, likely underestimates of lowering due to the influence of upstream dams. Rates from nearby catchments draining the Central or

Western Foothills range up to 1.1 mm/a. Yearly typhoons can drop up to a meter of water per day in the western foothills (e.g., Chang and Slaymaker, 2002).

In an effort to document the response of these knickpoints over the year following the earthquake, I surveyed river-crossing scarps in the northern sections that included four sites where the rupture exposed bedrock of the Chinshui shale

(named Tachia, Tali, Tsao-Hu and Chang-Ping on 1:50,000 geologic maps). Sites were selected in January 2000 for their range of drainage areas and minimal modification by post-earthquake engineering. At the northern edge of co-seismic rupture, I installed pins at Tachia River, which drains part of the Central Range of

Taiwan, including all of the lithologies summarized above. In the other southern basins, Chinshui shale at the rupture is followed several hundred meters upstream by

Cholan Formation, and by Toukoshan Formation. The smaller basins south of Tachia are cut back into a monocline of eastward dipping Cholan and Toukoshan units that form the eastern foothills here. The Chang-Ping basin, near the city of Nantou, also has outcrops of older Miocene sandstone and shale in its headwaters.

During our initial visit in January 2000, I noticed that siltstones and mudstones of the Chinshui shale weathered rapidly above baseflow, generating a 60-

120 mm deep zone of strongly fractured rock. In the southern basins, strath terraces are inset within modern concrete levee walls that bound one or both banks of the channel. At Tsao-Hu, hydraulic structures have collapsed over the strath, indicating strath formation after the channel was modified by engineers. Here I installed pins in a dipping bedrock ramp created by co-seismic folding that formed the only exposed

bedrock in the reach. At the other three sites I installed erosion pins many meters upstream of the fault scarp. I surveyed strath terraces and examined fill on them for historical artifacts. Baseflow in Tali, Tsao-Hu and Chang-Ping is confined to the channel thalweg, exposing wide adjacent bedrock surfaces to wetting and drying with effects that can be monitored with erosion pins.

Methods

At each study site I chose a reach of uniform bedrock with folia (Fig. 2.3) or pervasive weathering features (Fig. 2.2). I installed a cross-section of erosion pins to monitor short-term production rates of both folia and pervasive weathering features.

At each cross-section, erosion pins were spaced at equal intervals, from 0.25 m for narrow channels to 1 m for wide channels (see Table 2.1 for details). At a few sites

(Satsop and Tachia in Taiwan) coverage ends where base flow depth exceeds the drill-bit length of 100 mm. At the Olympic and Teanaway sites, additional erosion pins were installed on cross-sections a meter upstream and downstream off the main line with 1 m spacing to estimate spatial variations in lowering rate. In Taiwan and

Lower West Fork Satsop, shales were already weathered enough to emplace long nails into the bedrock using a sledgehammer. Elsewhere, I pre-drilled holes using a

Bosch rotary-impact drill and installed erosion pins of slightly larger diameter using a sledgehammer. At sites with pervasive weathering features (Taiwan, Satsop, Black

Creek), long nails (from 125- to 160-mm) were used as erosion pins because I anticipated large amounts of lowering. At sites with only folia, I used 60-mm long

hollow wall anchors with drive points because they have brackets that expand to grip

the hole upon emplacement. All erosion pins had their heads flush with the local

surface; the micro-topography of this surface limits measurement precision to ± 1

mm. To evaluate whether installation of the erosion pins affected the measured local

erosion rate: 1) at upper West Fork Satsop, I left half of the cross-section as holes of known depth in order to evaluate the influence of driving nails into the rock; and 2) I surveyed points between the nails to evaluate the influence of drilling on lowering.

Elevations of the top of each erosion pin were also surveyed and referenced to benchmarks driven into bedrock on the bank. I returned to Olympic and South Fork

Eel sites to re-measure erosion pin cross-sections two to three times, as indicated by alternate values for lowering rates in Table 2.2. Erosion rates at other sites were estimated using one return measurement.

At sites with folia, I measured the thicknesses of 100 samples by random walk within a cross-section that included both wet and dry bedrock several meters up- and down-stream of the erosion pin cross-section. A pencil tip was used to choose a sample, which was detached to measure its maximum surface normal thickness. At a few sites, I found less than

100 samples near the cross-section during our first visit (e.g., Walker Creek). At the Tsao-Hu site in Taiwan I estimated the thickness of the weathered zone by excavation of multiple folia.

At each cross-section, bedrock channel floors were measured using slope using tape and hand-level over a length of 7-10 multiples of channel width, and drainage area was determined from contour maps. I estimated channel width using recent flow line indicators,

and measured valley width as the distance between steep valley walls. At U.S. sites I

estimated baseflow using average velocity and cross-section area of inundation at the time of our visits (usually during dry summer months). I crudely estimated the size distribution of bedload that crossed our sites when I returned to measure erosion pin sections by choosing active bar tops for Wolman method point counts. Although armoring was not observed, its presence would tend to overestimate the coarse fraction of bedload. I also collected carbon samples for 14C dates from detrital charcoal in basal fluvial deposits on strath terraces near

Olympics sites.

To construct area-slope plots, I measured drainage area and slope by hand

from contoured 1:24,000 (U.S.), 1:50,000 (Taiwan) or 1:5,000 (Taiwan) scale

topographic maps using techniques described in Stock and Dietrich (2003). For long-

profiles all in one lithology (e.g., South Fork Eel, Sharp’s Creek), I separated fluvial

log-log linear data from curved data using a threshold curvature technique described

fully in Stock and Dietrich (2003). For profiles with mixed lithologies (Satsop,

Teanaway, Taiwan rivers), I separated area-slope data corresponding to lithologies in

which I had erosion pin sites. Profile concavity was estimated by regressing the log-

log linear portions in both cases with a power law. For sites with laser altimetry in

Sullivan Creek, I extracted the valley network using threshold drainage areas of 1000

m2, based on field observations of channel head location (Montgomery and Dietrich,

1992). I used a maximum fall algorithm for slope with a forward difference of two

grid cells, extracted the profile data, and averaged it to 10 m to smooth the effects of

cliffs in thick-bedded sandstones. Debris flow runouts for Marlow Creek in the

Oregon Coast Range were too short to obtain area-slope plots from USGS 7.5’ data.

To estimate rock mechanical properties associated with rapid lowering rates, I took rock samples from all of the field sites except Teanaway, and maintained field moisture conditions by keeping them saturated. For West Fork Satsop, Sullivan Creek and South Fork

Eel I successfully removed large blocks of the rock exposed at the cross-sections. These were cut into 200 mm diameter discs for abrasion mill tests of rock resistance to bedload following the methodology of Sklar and Dietrich (2001). For other sites, I either could not carry a large enough sample out (Black Creek, Teanaway), or samples proved to be too fractured to cut into large discs (Walker Creek and the Taiwan sites). Since Sklar and Dietrich (2001) have demonstrated that tensile strength is a relevant measure of rock resistance to bedload erosion,

I measured the tensile strength of the remaining samples using Brazilian tension splitting test

(e.g., Vutukuri et al., 1974). To estimate the resistance of the rock to weathering by periodic wetting and drying, I submerged samples in water overnight, and dried them at 40˚ C in an oven during the day. Following the methodology outlined in ASTM (1997), I weighed the fraction of the original block that shed during each cycle as a measure of the rate of breakdown. I chose a lower oven temperature than that recommended in ASTM (60-70˚ C) in order to approximate environmental conditions at field sites.

Results

Erosion pins

Erosion pins recorded bedrock lowering of mm’s to cm’s per year at study sites (Fig. 2.7; Table 2.2). Mean lowering rates at most sites are much larger (1-3 orders of magnitude) than long-term erosion rate estimates (Fig. 2.8; Table 2.2).

Figure 2.7 illustrates that bedrock lowering is not confined to pin sites, as it would be if installation strongly influenced lowering rate. Hand-level resurveys at West Fork

Satsop, for instance, also indicate the same magnitude of lowering away from pins.

By contrast, steep valleys scoured by debris flows before pin installation had numerous folia, but no lowering occurred in any of the 363 erosion pin sites at Kate

Creek, or Marlow tributaries between 1997 and 2001 (Fig. 2.9; Table 2.2). Repeat photography at cross-sections indicated gradual infilling (Fig. 2.9b) over scoured bedrock by hillslope sediment and vegetation, with no new folia production, or transport.

Figures 2.10-2.11 illustrate another contrast, between patchy folia production (Walker and Sullivan Creeks) and pervasive bedrock weathering above baseflow (Satsop, Black

Creek, Teanaway, Eel, Taiwan). Localized folia production in Walker and Sullivan Creeks leads to patchy removal. At sites with pervasive weathering, erosion pins record yearly bedrock lowering rates up to 100’s mm/a, consistent with seasonal production and removal of several folia depths (Table 2.2). Above baseflow, lowering is continuous across the section and occurs by entrainment of weathered product during seasonal high-flows and perhaps bedload abrasion during peak flows (and dam-break floods in the case of Black Creek).

Lowering rates decrease below the baseflow waterline, consistent with the absence or reduction in weathering rate. Non-zero lowering rates in thalwegs record bed-load abrasion rather than plucking because of the continuous pattern of lowering and absence of cavities in the smoothed bedrock surface. For instance, South Fork Eel (Fig. 2.10) had relatively continuous lowering at several mm’s per year across the erosion pin section, with an abrupt drop at baseflow boundary below which weathering is less active. Below water level, the bedrock surface is smooth and devoid of open fractures, and erosion pins are polished.

Bedload flux estimates at South Fork Eel using stage data with the Meyer-Peter and Muller equation (Figure 2.6) are two orders of magnitude larger than estimated average annual bedload fluxes (Table 2.2), consistent with excess transport capacity at this site. Historic peak discharges 2-5 times as large as those that occurred during the erosion pin monitoring (Fig.

2.6) suggest that decadal lowering rates might be substantially larger.

Mean and median lowering rates exceed 100 mm/a over 7 years of pin measurements at West Fork Satsop, 100 mm/a at Lower West Fork Satsop site 1 for a year, and 50 mm/a at Lower West Fork Satsop site 2 for 2 years. A number of pins from West Fork Satsop were entirely removed, so I can only constrain minimum lowering rates of 120 mm to 160 mm, depending on pin length. Median rates from 2 years at West Fork Satsop are 41 and >130 mm/yr, and 9 and 62 mm/yr at Black

Creek. One-year median lowering from lower sites 1 and 2 on the Satsop are 137 mm and >160 mm, respectively. At Satsop, these rates represent lowering of a platform above the thalweg, while Black Creek data represent thalweg lowering. There is an increase in incision rate at both sites in 1996-1997, coincident with high discharges

that year. In particular, large increases in lowering rate at Black Creek coincide with a dam-break flood in winter 1996. I observed smaller lowering rates below baseflow than above it during the first year at West Fork Satsop and Black Creek. Median lowering on Black Creek is 4 times greater in the zone above base flow (16 mm) than below it (4 mm). At West Fork Satsop, lowering rates also decline sharply from 70 mm above observed baseflow to less than 1 mm below it.

These trends do not appear in the second year of monitoring following much larger discharges. Revisits to West Fork Satsop and Black Creek during winter high- flows in 2001 indicated that high rates of lowering continue. Flow was too deep at the time of measurement to examine whether bedrock had remnant holes, or had lowered entirely past the original pin. Flood marks at this site indicated recent flows of ~ 1 m depth across the platform with the pins, with some quantity of bedload transport across it indicated by isolated deposition of cobbles. At Black Creek, flow was too deep to measure lowering, although I could tell that several cm’s of erosion had occurred between 1997 and 2001, with some pins entirely missing.

Teanaway sites had mean lowering rates greater than 6-28 mm over one year, more than 60 times the largest estimate for long-term lowering rate (Table 2.2). Many pins were removed entirely, although a few located high on cross-section 3 showed no lowering (Fig. 2.10). Sullivan cross-section 2 (not shown) lies entirely below baseflow, and has no folia or lowering (Table 2.2). Sullivan cross-section 1 and

Walker cross-sections 1-3 had a few sporadic folia and associated lowering in areas of shallow baseflow. Pins below baseflow were algae-covered and unabraded. Sites

without folia did not lower, and were either entirely below baseflow (Sullivan site 2)

or in strongly cemented rocks like the silicified ash-flow of Walker cross-section 4. In

Walker Creek, resurveys indicate minor deposition occurred along the path of the dam break flood since 1997, and a few plate-like folia less than a meter downstream from a source also indicate only minor sediment transport.

High rates of bedrock lowering occur at Taiwan sites (Table 2.2; Fig. 2.12). In

1 year, rebar benchmarks and all erosion pins were removed at all sites except Tachia, indicating lowering rates in excess of 125 mm/a. At Tachia, one erosion pin remained

(~47 m on cross-section), allowing us to reconstruct an approximate cross-section for a portion of the right-bank that I surveyed in 2000 (Fig. 2.12a). The differences between the initial and resurveyed cross-section indicate over 2 m of lowering in places, accomplished by a combination of weathering and bedload abrasion. At Tsao-

Hu and Chang-Ping the 1999 fault scarp was eliminated as a discrete feature over the course of a year, so it is unclear whether lowering rates at these sites were influenced by scarp retreat or not. At Tali the fault scarp remains identifiable, so that lowering around pins was not a result of scarp retreat.

Folia

The magnitude of lowering in Figures 2.10-2.11 is consistent with erosion of one to several folia, which are an average of between 9 and 15 mm thick (Fig. 2.13).

For instance, lowering rates at Black Creek are compatible with the generation and removal of an average folia thickness the first year, and several folia layers in the

second year. Larger values for Taiwan shales record formation of thick weathering

zones rather than discrete folia. Most thickness distributions are log-normal as

measured by normal quantile tests. The seasonal production of these features is

pervasive in some localities (Satsop, Black, Eel, Taiwan) and patchy in others

(Walker, Sullivan). The number of folia increased with time at Walker Creek, as

shown by larger number of folia measured at re-occupation in 2001 (Fig. 2.13) and by

repeat photography which illustrated the conversion of large sections of formerly

intact rock to folia. This increase is due in part to low flow and sediment transport

rates, as indicated by maximum stage indicators less than several decimeters over the

monitoring period (Dmax in Table 2.1). Recently transported bedload particles are also

small in size (site D50 in Table 2.1 is 40 mm).

Strath terraces

Cultural artifacts deposited on strath terraces in Washington and Taiwan indicate historic abandonment. At West Fork Satsop, the floodplain surface consists of a mosaic of low elevation channelways now overgrown with 40-50 year old alder and higher surfaces upon which cedar and fir grow and where old growth stumps occur on local high spots between abandoned channelways. I found cut wood within the alluvium on the strath, confirming that the terrace surface was a historically active depositional surface. This implies an average lowering rate of 1.2m/40-50 a, or 24 to

30 mm/a. Since logging began here in the 1940’s (oral comm., N. Phil Peterson,

Simpson Timber Co., Shelton, WA), this feature indicates sustained bedrock lowering

rates >20 mm/a, depending on exactly when incision began. Measured rates of

incision from erosion pins (>44 mm/a) are sufficient to have converted the historical floodplain into an abandoned strath terrace capped by floodplain gravels since the floodplain was logged. Downstream of Lower West Fork Satsop site 2, alluvium on

0.4 and 5 m high strath contain detrital charcoal dated to 1290 (+/- 100) and 7400 +/-

50 YBP respectively. Longer-term lowering rates from these strath terraces of 0.3-

0.7 mm/a are consistent with apatite fission track exhumation rates from Brandon et al. (1998). At Teanaway, the age of strath terraces inset ~ 1-2 m above current channel are likely historic on the basis of riparian tree ages.

In Taiwan, lowering rates in excess of 100’s of mm/a are recorded by incision below the level of historic engineering structures. Figures 2.12b and c show cross- sections and long-profiles for a reach downstream of a small retaining dam, where bedrock has been incised meters since levee construction several decades ago (oral comm., local residents). Engineering structures footed on 1-3 m high strath terraces at

Tali, Tsao-Hu and Chang-Ping are also consistent with rapid bedrock incision greater than cm/a since leveeing of these channels. Modern ceramic fragments in a fill overlying a 1.3-m high strath in the Chang-Ping River in Taiwan also indicate sustained bedrock lowering rates of >26 mm/a, assuming post-1949 emplacement.

Rock strength Table 2.1 shows tensile strengths and slake durabilities for selected sites.

Tensile strengths for poorly cemented rocks (i.e. Satsop, Black Creek, Taiwan rivers) were less than 0.3 MPa. Values for rocks with more cemented or indurated matrixes

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ranged from 2-5 MPa, consistent with measurements of tensile strength for similar lithologies elsewhere (e.g., Goodman, 1980). In Table 2.1, I characterize the rate of breakdown by showing the number of cycles required for loss of 75% of sample weight. Weak samples required only 1-2 cycles of wetting and drying to lose 75% of their initial weight by slaking (e.g., Satsop, Black creek, Taiwan samples). For instance, upon immersion after the first drying, samples from Satsop River and

Taiwan lost more than 50% of their mass in the first 5 minutes. These samples swelled rapidly as water infiltrated matrix, resulting in degassing and mm-scale compressional features along their surface. As they expanded, samples comminuted into mm-sized aggregations of grains that detached from the core and fell at its side.

By contrast, samples with tensile strengths greater than 1 MPa showed little degassing, and were intact after 30 cycles of wetting and drying. I estimated the number of cycles for these stronger rocks (e.g., Walker and Sullivan samples) by regressing mass loss against cycle number. These results are broadly consistent with order-of-magnitude differences in lowering rate recorded in the field.

Figure 2.14 illustrates the dependence of field-measured mean lowering rates measured by erosion pins on bedrock tensile strength. Although lowering rates for

Tachia, Tali and WF Satsop are minimum estimates, the power law regression with an exponent of approximately –2 is consistent with the inverse square dependency of erosion rate on tensile strength obtained experimentally by Sklar and Dietrich (2001).

Rocks with tensile strengths less than the highest range I tested of 3-5 MPa are

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lowering at rates that exceed the estimates for regional long-term lowering rates in

Table 2.2.

Area-slope analysis

Valleys traversed by debris flows (dashed lines in Figures 2.15-2.16) have area-slope plots that are curved, largely above slopes of 0.10. For instance, curved data for Kate Creek (Fig. 2.16) correspond to the runout path of the debris flow shown in Figure 2.9. Curved area-slope plots for Sharp and Walker Creeks also occur within reaches with mapped debris flow deposits. Reaches on both Kate and Walker

Creek are now being buried by colluvium and vegetation (e.g., Fig. 2.9), although they were scoured to bedrock during the 1996/97 debris flows and dam break flood on Walker.

Plots of drainage area against slope are approximately log-log linear in the weak lithologies around most fluvial sites where I have monitored rapid lowering rates, and in tributaries with similar lithologies (Fig. 2.15-2.16). With the exception of the Tali River, power law regressions of fluvial erosion pin sites have concavities between -0.75 and –1.0, and intercepts from 0.08 to 0.70. For instance, reaches cut in sand- and siltstones of the Satsop (Fig. 2.15) that weather pervasively (Fig. 2.2) plot as lines with similar slopes (-0.84 +/-0.07 and -0.78 +/-0.15) and intercepts (0.16 +/-

0.07 and 0.10 +/- 0.09). Most of these concavity estimates are higher than values of -

0.3 to -0.6 predicted by some stream power models (Whipple and Tucker, 1999), although they are within the range reported by Stock and Dietrich (2003). Power law

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intercepts for these rivers appear inconsistent with equation (2.1) because they have no apparent relation to estimates of long-term erosion rate or rock resistance characterized by tensile strength. For instance, the high intercept of Sharps Creek

(0.32) compared to South Fork Eel (0.08) does not correspond to a higher long-term erosion rate for these rocks of similar tensile strength (Table 2.1). However, substantial uncertainties in rock uplift rates and other measures of rock resistance to lowering (e.g., fracture density) do not allow us to reject this ratio as a proxy for uplift rate.

Discussion

Burial of erosion pins in Kate Creek and Marlow Creek debris flow valleys indicate that fluvial processes are not currently cutting rock or transporting all of the hillslope deposits away. Surveys of adjacent valleys without recent debris flows indicate thick colluvium burying valley floors. These accumulations indicate that rare floods do not scour these channels by fluvial processes. For instance, prior to the

1996-debris flow, the bedrock floor of Kate Creek was locally buried by a minimum of 1-3 m of colluvium (unpublished fieldwork by Montgomery). I think that burial in these steep valleys following debris flows is common because during fieldwork in soil-mantled steeplands throughout the Western U.S. I have not seen extensive exposures of bedrock in valley floors other than along recent debris flow tracks. I interpret the rapid burial of erosion pins in the Oregon sites and the dearth of extensive bedrock exposures in steepland valley floors as evidence that debris flows are the primary process lowering the rock in valleys with slopes above 0.10 and

103

curved area-slope plots. The curved area-slope plots of these valleys are therefore likely to be a signature of debris flow and weathering processes, with little fluvial contribution.

There is evidence that fluvial erosion occurs in the terminal runout areas of some debris flows, as slopes decline to ~0.10 – 0.03. For instance, bedrock lowering at Walker and Sullivan Creeks by fluvial entrainment of weathered rock occurred at sites that debris flows had previously crossed. Lowering at both sites was spatially discontinuous as indicated by the abundant folia that had not been mobilized by flow over the monitoring period. These sections are now being covered by sediment (albeit slowly) with a consequent reduction in bedrock exposure. It remains to be seen whether subsequent flows will lower bedrock extensively, or whether cover will be established so quickly that bedrock is weathered but largely uneroded. It is possible that debris flows are the agent of bedrock exposure here, but rivers are the agents of removal following exposure. In this case, the lowermost section of area-slope curvature here would record a combination of fluvial and debris flow processes, with debris flows exposing bedrock to weathering, and rivers entraining weathered products. Alternately, debris flows may dominate both exposure, and lowering during the subsequent debris flow. Future monitoring at these sites will be necessary to resolve whether cover is largely reestablished, shutting of fluvial entrainment of weathered rock.

Short term bedrock river incision rates in our lower gradient study sites far exceed long-term lowering rates inferred from geologic evidence (Fig. 2.8; Fig. 2.14;

104

Table 2.2). These high rates occurred in channel reaches largely devoid of sediment cover (e.g., Fig. 2.4), in bedrock with tensile strengths below 3-5 MPa. Not only are the rocks at each site mechanically weak, but they also show visible evidence of mechanical breakdown due to weathering such that plucking of fractured remnants may be important. Previous authors have also measured transient river incision rates in sedimentary rocks of mm’s to cm’s per year that far exceed apparent long-term erosion or rock uplift rates (Shakoor and Rodgers, 1992; Stock et al., 1996; Righter,

1997; Tinkler and Parrish, 1998; Whipple et al., 2000; Hsieh and Kneupfer, 2001).

For instance, Tinkler and Parrish (1998) describe the case of an urbanized channel whose recently exposed sedimentary rock appears to weather seasonally via wetting and drying, lowering at cm’s per year.

A strong dependence of weathering rate on rock tensile strength may partly explain the observed inverse relationship between erosion rate and tensile strength in

Figure 2.14. Given that the correlation reported by Sklar and Dietrich (2001) was for a constant sediment supply rate and grain size, conditions that seem unlikely at our field sites, the similarity between field and laboratory estimates of the regression exponent (–2) may thus be fortuitous. Despite this uncertainty, our results support findings by Sklar and Dietrich (1998; 2001) that cover strongly modulates fluvial bedrock incision.

Field evidence suggests that bedrock exposure at some field sites (most

Washington and Taiwan sites) was relatively recent, and probably due to anthropogenic activity. At other locations (e.g., Black and Sullivan Creeks and South

105

Fork Eel) abrupt local increases in slope within the same mapped lithology are consistent with transient knickpoints that may migrate upstream. In the Eel, these points (open squares in Fig. 2.16) correspond to the sudden widespread occurrence of bedrock along the channel downstream of a widely alleviated valley. High measured rates at these knickpoints may record accelerated incision rates as cover is swept off of the upstream migrating knickpoint.

In sites with evidence for anthropogenic disturbance, the removal of sediment cover appears to have coincided with the initiation of geologically unsustainable lowering rates. Gravel fill terraces at these sites record the presence of gravel bars and wood jams insulating the bedrock from weathering and abrasion prior to historic disturbance, so that the lowering rate in these rivers is plausibly limited by the frequency of bedrock exposure. A simple hypothesis based on the examples above is that in channels where the bedrock is so weak that it lowers at rates far in excess of the boundary lowering rate when exposed, slope approaches a value that is low enough that the rock bed of the river is rarely exposed to erosion for a given hydraulic geometry, peak discharge, grain size, bedform resistance and sediment supply. If so, long-profile concavities and intercepts now widely interpreted in terms of equation

(2.1) (e.g., Snyder et al., 2000; Kirby and Whipple, 2001) might arise primarily from sediment transport, rather than bedrock properties.

Conclusion

Field observations offer strong support to the interpretation by Stock and

Dietrich (2003) that debris flows dominate steep channel incision above slopes of

106

~0.10, and to the theoretical results from Sklar and Dietrich (1998; 2001) that sediment cover and grain size dominate river channel gradients. Both findings demonstrate that the stream power law is too simple, and provides insufficient insight about the mechanisms that control valley incision.

Valleys recently scoured by debris flows in the Oregon Coast Range have curved area-slope plots that are likely to be signatures for debris flow incision alone

(Stock and Dietrich, 2003), since no fluvial lowering occurred in these valleys before hillslope sediment began reburying hundreds of erosion pins. On the other hand, minor fluvial entrainment of weathered rock along the downstream-most debris flow runout at Walker Creek indicates that rivers could yet play some role in this particular transition region at slopes between 0.04 and 0.10. It remains to be seen whether reburial will prevent substantial fluvial lowering of weathered rock.

Very high incision rates of mm’s to dm’s per year in recently exposed bedrock river reaches support the argument by Sklar and Dietrich (1998; 2001) that sediment coverage dramatically inhibits erosion rates. Given that these rates appear to exceed long-term estimates of lowering rates, this result indicates that at the very least, rates of river incision in weak lithologies (< 3-5 MPa) may be limited by the frequency of exposure rather than by stream power, as is assumed in most landscape evolution models. Lowering data also provide some field verification of the dependency of bedrock lowering on the square of rock tensile strength, proposed by Sklar and

Dietrich (2001) on the basis of flume experiments.

107

We suggest that in the case of mechanically weak rocks in which the coarse sediment supply also experiences considerable breakdown during transport, the channel slope is neither set by bedrock strength nor by sediment supply, but instead primarily by the threshold motion of some characteristic grain size. The large concavities (-0.7 to –1.0) observed in our field sites may be due to the predominance of this sediment threshold of motion and to downstream fining. Where this condition occurs, there may be little variation in river long-profiles across rock uplift rates, and no direct expression of the bedrock river incision law on river longitudinal profiles.

Instead, power law plots of slope against area may reflect the long-term control by discharge, width, slope and sediment supply of an alluvial cover sufficiently thin to insulate the bed from drying, impact, or other weathering processes, rather than the rate of work on the channel bed by tools. Since coverage is largely dictated by the quantity and size distribution of sediment, as well as hydraulics, these variables may be dominant controls on even apparently bedrock-dominated river long-profiles (e.g.,

Howard, 1980; Sklar and Dietrich, 1998).

108

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114

3 10

fluvial power law region (upstream-most strath)

1 10

) 2

) 0.65 -0.84 +/- .07 -0.77 +/- .06

area (km

-1 10

(end of debris flow deposits)

Sharp Cr., OR, debris flow: S=0.74/(1+3.6A Sharp Cr., OR, river: S=0.32(+/-.10)A West Fork Satsop, river: S=0.16(+/-.07)A Satsop (basalt & glaciated) curved region of debris flows

-3 10 -1

-3

10 10 slope

Fig. 2.1 Area-slope plot for West Fork Satsop River in sandstones of the peripheral Olympic Mountains, Washington, and Sharp’s Creek in volcaniclastic rocks of the Oregon Cascades. Data from source 7.5’ contour maps, measured by hand. Power law fits weighted by inverse slope, and standard errors for parameters shown. Uncertainties for West Fork Satsop intercept shown as a range. Curved debris flow region extracted using threshold curvature of 0.001 on the 2nd derivative of equation in the legend (see also Stock and Dietrich, 2003).

115

Fig. 2.2 Pervasive fracturing of a sandstone boulder above a base-flow waterline in the West Fork Satsop River, NW Washington. Fractured rock, commonly 10-50 mm deep, is removed from exposed surfaces by seasonal high-flows, but is regenerated during spring and summer desiccation. Others have hypothesized that such features are generated by weathering during cycles of wetting and drying (see text for references).

116

Fig. 2.3 Tented folia in a) micaceous sandstones in the Oregon Coast Range (Sullivan Creek), and b) clay-rich volcanic tuff in the Oregon Cascades (Walker Creek). Both formed within several months of bedrock exposure following prolonged burial. Tented folia tend to occur preferentially above baseflow, and are arguably a result of weathering during cycles of wetting and drying. These tented folia represent cm’s of lowering, and are commonly 10’s of cm’s in area.

117

a) b)

Fig. 2.4 Cross-sections for a) West Fork Satsop, and b) Black Creek, Olympic Mountains, Washington; C) Walker Creek (site 1), Oregon Cascades and d) South Fork Eel, California Coast Range. White tape indicates cross-section of erosion pins, see Table 2.1 for site details.

118

↑

#1 #2

Kate Creek

0 1 km

Fig. 2.5 Hillshaded laser altimetry (~ 2 m horizontal resolution) from Oregon at Coos Bay. Dotted lines indicate 1996/1997 debris flows, as mapped in the field. Arrows in Coos Bay panel bracket knickpoint on Sullivan Creek. Numbers refer to erosion pin cross-sections on Sullivan. Sections on Kate are too numerous to show, but occur approximately every dot.

119

500 predicted daily bedload since pin installation 10000000 total>1 x 108 kg/m

450 d

oa 8000000 ) dl s 400 - 6000000 ) m / d be s g e t c (k 350 i 4000000 x d (cm u e fl e

pr 2000000 - g r 300 M P a 0 M 12/6/1996 12/6/1997 12/6/1998 12/6/ 1999 12/ 5/ 2000 sch

i 250

d y l i 200 erosion pins installed a 09/06/97 e d 150 ag

er 100 av 50 USGS gage abandoned 0 1/24/1941 1/23/1946 1/22/1951 1/21/1956 1/19/1961 1/18/1966 1/17/1971 1/16/1976 1/14/1981 1/13/1986 1/12/1991 1/11/1996 1/9/2001 1/8/2006 date

Fig. 2.6 Average daily discharge for South Fork Eel river at Branscomb gage (#11475500). Values from 1997-2000 are from a stage recorder operated by U.C. Angelo Reserve staff. Inset shows an illustrative calculation of bedload transport capacity past the erosion pin site for the period of stage record using the Meyer-Peter Mueller bedload equation. Excess shear stress calculated using stage data with τ*c equal to 0.047, and grain size and slope data in Table 2.1. These values are two orders of magnitude larger than regional values from sediment yield estimates of bedload, consistent with excess transport capacity at this bedrock reach.

120

c) d)

b) a)

Fig. 2.7 One to several years of bedrock lowering indicated by erosion pins in a) West Fork Satsop, b) Black Creek, c) Walker Creek (site 1), and d) South Fork Eel River. See Table 2.2 for details. Note that pin protrusion above the surface indicates pervasive lowering, not localized scour or damage from installation. Lowering in the Satsop and Eel is by detachment of cm-sized weathered fragments during high-flow. Lowering at Black and Walker Creeks is by folia generation and removal during high-flow.

121

1000 max median 100 mean geologic

lowering rate (mm/a) 0.1

0.01

li u g n p ek 2 er Ta -H o Eel lk va chia o ts re F li a S ul T ng-Pin Sa away Wa S Tsa ck C an WF a e Cha Bl Te

Fig. 2.8 A comparison of maximum estimates for long-term erosion rates with short-term erosion pin rates for rivers in Taiwan (Tachia, Tali, Tsao-Hu and Chang-Ping), Washington (West Fork Satsop, Black Creek, Teanaway 2), California (South Fork Eel) and Oregon (Sullivan 1). Short-term lowering rates on Taiwanese and Washington rivers are minimums because erosion pins were entirely removed. Except for sites in debris flow runout zones in Oregon, short-term averaged rates exceed long-term rates. In all cases, maximum observed erosion rates exceed long-term rates.

122

location of b)

Fig. 2.9 a) Runout path of Kate Creek debris flow (light areas of bedrock, starting at top middle) shortly after failure occurred in winter 1996. Note the widely exposed bedrock, which was lowered along much of the runout path during the debris flow (see also Fig. 2.5). b) Pin buried with colluvium by 2001. Most of the over two hundred erosion pins emplaced shortly after the debris flow have been buried by 2001, and indicate no bedrock erosion in the intervening years.

123

mm/a mm/a

1000 10 0.1 1000 10 0.1 ↑ ↑ ↑

↑ ↑ ↑ ↑ ↑↑ ↑↑ 1997/2001 ↑ ↑↑ no erosion baseflow highflow removed pin dam break flood ↑ Walker 1, OR

↑ 20 20 ↑

West Fork Satsop, WA ↑ ↑ ↑ ↑ meters ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑

↑ ↑ ↑ ↑↑ ↑ ↑↑ ↑ ↑↑

1995/96 1996/97 1997/2001 strath

0 0 3 3 6 6 0 0

10 0.1 1000 10 0.1 0 0 2 2

gend

ork le 1997/2001 2001/2002

est F W Black Cr., WA

see South Fork Eel, CA 0 0 ↑↑ meters

↑↑

01 01

3 3 6 6

0 0

meters meters

Fig. 2.10 Yearly lowering rates from erosion pins (right abscissa), and cross-sections (left abscissa) for South Fork Eel River, CA, West Fork Satsop River, Black Creek, Olympic Mountains, Washington, and Walker Creek (1), Oregon Cascades. See Table 2.1 for site details. Dashed vertical lines through symbols indicate maximum and minimum lowering observed around individual pins. Symbols represent mean values. Open symbols with arrows indicate minimum lowering rates from erosion pins and emplacement holes that have been entirely removed by erosion. Open triangles on cross-section indicate pins that had no lowering around them. Measurements from different years are shown with different symbols for West Fork Satsop and Black Creek. Baseflow measured at time of pin emplacement (less than line thickness at Walker 1), highflow estimated during reoccupation using stage indicators. Note the absence of pins in the Satsop thalweg, which was too deep to access with a drill. Bedrock lowering at Satsop site occurs by detachment of cm-sized weathered fragments during high-flow, and by abrasion and plucking below baseflow. Lowering at Black occurs by detachment of folia like those shown in Fig. 2.3. In these channels, lowering rates decrease rapidly approaching baseflow. Note that dam break flood stage lines for Walker Creek occurred before installation, while that of Black Creek occurred after pin installation. Large cavity in Black Creek cross-section is from an eroded concretion. Aspect ratio is the same for all cross-sections.

124

mm/a mm/a

100 1 1000 10 0.1 0 0 2 2

1997/2001 1999/2000 no erosion baseflow highflow dam break flood removed pin erosion rate ↑ 0 ↑ 0 0 meters

OR Coast Range Sullivan 1 Teanaway 3 WA Cascades 01 02 01 3 3 6 6 0 0

1 100 100 1000 10 0.1 0 0 0 2 2 2

1997/2001 1999/2000 ↑ ↑ 20 ↑ 0 0 0

↑↑ meters ↑ ↑ ↑ ↑ ↑ ↑

↑↑ WA Cascades Teanaway 2 Walker 2 OR Cascades 0 01 01 01

3 3 6 6 0

meters meters

Fig. 2.11 Yearly lowering rates from erosion pins (right abscissa) and cross-sections (left abscissa) for Walker Creek (2), Oregon Cascades, Sullivan Creek, Oregon Coast Range, and Teanaway, Washington Cascades. See Figure 2.10 caption for details. Bedrock lowering in Walker and Sullivan is by removal of local folia and tented folia (e.g., Fig. 2.3) during high-flow, and lowering magnitudes are consistent with folia depth distributions shown in Fig. 2.13. Lowering at Teanaway is by entrainment of pervasively weathered material (e.g., Fig. 2.2).

125

3 a) thalweg

-1 meters 2000 survey 2001 survey Tachia, Taiwan 12.5 cm erosion pins -3 40 50

15 b)

10 levee lb strath rb strath 5 meters

Chelong-Pu locality 0 -30 -10 10

lb strath rb strath c) thalweg levee top 10

meters

Chelong-Pu locality 0

0 100 200

meters

Fig. 2.12 Summary of recent bedrock lowering in two Taiwanese rivers cutting clay-rich indurated siltstones that weather by pervasive fracturing. a) Portion of a cross-section including right bank of Tachia River showing topography and pins in 2000, and resurveyed topography in 2001 indicating up to 3 m of lowering. Section was 20 m upstream from the 1999 fault scarp. b) Cross-section of nearby Pei-Go indicating lowering of river and strath formation following levee construction (~6-20 years ago). c) Longitudinal profile of preceding section showing bedrock thalweg in 2001, and paired left and right bank straths. Lowering increases downstream, but is pinned upstream by a sabo dam with reinforced footings.

126

100 Black Creek Marlow Creek 1 mean: 9.3+/-2.0 mm mean: 9.1+/-0.6 mm n = 210 n = 200 70

Walker Creek 1 Sullivan Creek 2 1997 mean (black): 10 +/- 1.8 mean: 15+/-1.6 mm 2001 mean (grey): 12+/- 1.6 n = 31 30 n = 49 1997 n = 100 2001

# of folia 10

Walker Creek 3 Tsao-Hu, Taiwan 1997 mean (black): 8.0 +/- 1.9 mean: 42+/-1.3 mm 2001 mean (grey): 10.7 +/- 1.72 n = 45 30 n1997 = 10 n2001 = 100

0408020 60 100 folia depth (mm)

Fig. 2.13 Thickness distributions for weathering folia measured by random walk near erosion pin cross-sections during reoccupation. Black columns are exhaustive samples of folia thicknesses at the time of pin emplacement, whose sum is usually less abundant than at reoccupation. Distributions are log-normal, with few folia below several mm, and a long tail of folia thicknesses at 100’s of mm’s. Dashed lines show log-normal mean values.

127

-1.96 (+/-0.19) c

tensile strength (MPa)

↑ dz/dt = -5.12 (+/-1.29) T mean rates may be higher

↑

0.1

0.1 1000 (mm/a) rate lowering mean

Fig. 2.14 Plot of tensile strength against average lowering rate for sites in Table 2.2. Arrows indicate minimum lowering rates at sites where many erosion pins were entirely removed. Note that sites whose rocks have tensile strengths less than 3-5 MPa are eroding at rates that appear to exceed long-term rates from geologic indicators.

128

↓ ↓

1 10

↓ ↓ ↓ ↓

-0.77(+/-0.06)

-0.97(+/-0.08)

-1 10

) debris flow: Walker CR., OR debris flow: Sharp’s CR., OR fluvial: Sharp’s Cr. S=0.32(+/-0.10)A glacial/debris flow : Teanaway, WA (volcanic and ss) fluvial: (sandstone) S=0.70(+/- 0.24)A 2

↑

1 10

↑

-0.78(+/- .15) -0.84(+/-.07)

-1 10

West Fork Satsop (ss) Black Cr. (ss, Satsop trib.) West Fork Satsop (basalt) S=0.16(+/-.07)A Middle Fork Satsop (basalt) Canyon (basalt, Satsop trib.) Mile10 (Satsop trib.) Canyon (ss, Satsop trib.) Middle Fork Satsop (ss) S=0.10(+/- .09)A

-3 10 0

-2 -2 -4

10 10 10 slope

Fig. 2.15 Plot of slope against area for sites in the first three regions of Table 2.2. Infilled squares, diamonds and triangles indicate fluvial reaches in lithologies where I have measured lowering rates with erosion pins. Note that I fit power laws only to reaches within lithologies with measured lowering rates. Open diamonds and triangles indicate the mapped extent of debris flow deposits, and were fit with an empirical slope area relation (dashed line) that curves (see Fig. 2.1 legend). Arrows indicate the location of erosion pin cross-sections, not shown for Middle Fork Satsop, or for tributary basins without pin sections. area (km

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↑

↑ ↑ 1 10

-0.80(+/- 0.15) -1.0(+/- 0.09)

-0.36(+/- 0.09)

-1

) Tali R. (conglomerate) (ss) (shale) S=0.05(+/-0.03)A Chang-Ping R. (shale) (ss) (shale & ss) Tsao-Hu R. (ss & conglomerate) (shale) S=0.13(+/- 0.05)A S=0.41(+/- 0.07)A 2

↓

1 10 ↓ ↓

-0.75(+/- 0.08)

-1

debris flow: Kate Cr. (ss) fluvial(?): Sullivan Creek (ss) debris flow: South Fork Eel R. (ss) fluvial: (ss) knickpoint: (ss) S=0.08(+/-.03)A

-3 10 0 -1 -3 -2

10 10 10 10 slope

Fig. 2.16 Plot of slope against area for the last three regions of Table 2.2. See Figure 2.15 caption for details. Erosion pin cross-sections are too dense (every ~20 m) to show on Kate Creek, see Figure 2.4 for approximate locations. Kate Creek data from laser altimetry and include runout path shown in Fig. 2.9. Note that I have excluded the downstream-most reaches of South Fork Eel (open squares) from regression because they occur in reaches influenced by a possibly transient knickpoint with common bedrock exposure (unlike alleviated reaches in the log-log linear section). area (km

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Table 2.1. Field data for sites with erosion pins

region stream litholgy tensile slake slope area Qlf field valley channel Dmax D50 2 3 strength (MPa) durability (km )(m/s) width (m) width (m) (m) (mm) Olympics, WA West Fork Satsop micaceous fine ss, siltstone .214 (.008) 1 0.023 121 ~10 ~100 22 1.1 ~40 Lower West Fork (1) siltstone NC 1 0.015 150 " ~120 ~20 ~1.5 NC Lower West Fork (2) " NC 1 0.015 150 " ~120 ~20 ~1.5 NC Black Creek micaceous med. ss .267 (.033) 2 0.060 14.7 0.18 18 18 ~1 40 Cascades, WA Teanaway (1) micaceous med. ss 0.908(.041) NC 0.008 101 0.1-0.25 ~200 25 NC NC (2) " " NC 0.008 101 " ~200 15 NC NC (3) " " NC 0.008 101 " ~200 22 NC NC Cascades, OR Walker (1) indurated lahar 2.15 (.29) ~40-900 0.08 3.22 0.016 10 10 0.19 5 (2) " " " 0.09 3.15 ~0.01 14 5 0.24 ~5 13 (3) " " " 0.08 3.00 " 18 6 0.23 ~5 1 (4) indurated rhyolite ash-flow NC NT 0.14 2.41 " 13 6 ~0.2 ~5 Oregon Coast Range Sullivan (1) micaceous med. ss 4.33 (.45) ~1000 - 0.13 3.13 ~0.5 10 10 0.36 25 (2) " " 1700 0.07 3.56 " 14 14 0.65 25 Kate Creek sections " " " 0.1-0.8 10-3-10-1 0 3 - 9-0- Marlow Creek trib.1 " " " 0.10-0.45 10-3-10-2 0 3 - 5-0- Marlow Creek trib.2 " " " 0.04-0.80 10-3-10-2 0 3 - 5-0- California Coast Range S. Fork Eel siltstone 2.68 (.12) NT 0.014 114 0.1-0.2 ~165 20 ~0.7 90 Taiwan, Western FoothillsTachia siltstone, shale .28 (.015) 1 0.013 1128 NC ~1170 104 4< NC Tali shale, siltsone, ss .14 (.044) 1 0.019 20.36 NC unconfined 16 1.6< 89 Tsao-Hu shale NC 1 0.012 12.90 NC unconfined 19 0.70< 60 Chang-Ping shale, siltsone, ss NC 1 0.033 49.10 NC unconfined 12 2.3< 87

Note: Qlf field is estimate of baseflow at visit; italics indicate order-of-magnitude estimate from measurement elsewhere; NC is not collected; NT is not tested; Numbers in parentheses in site column indicate cross-sections, increasing downstream.Slopes from reach measurement with hand-level or laser. Peak flows over monitoring period estimated from recent stage indicators. Valley width estimated by the shortest distance between opposite hillslopes in the field or on a map. Channel width is distance between banks, or distance between high-flow stage indicators if banks are absent. Dmax is maximum flow

depth along pin cross-section of high-stage flow. D50 is median gravel diameter, estimated using random walk method except for Walker Creek (sieve analysis).

Table 2.2. Erosion data for sites with erosion pins. region stream anthropogenic folia (mm) pin n pin median pin mean measur. historic strath geologic bedload flux

3 activity mode mean st dev n length (mm) spacing (m) lowering (mm/a) (mm/a) time (yrs) (mm/a) (mm/a) (mm/a) (kg/m-a) X 10 Olympics, WA West Fork Satsop logjam removal - - - - 120-160 37/49 0.50 41/>130 44/>114 1/1 20-30 - < .3 440 Lower West Fork (1) " - - - - ~200 14 0.25 137 39 1.6 - - " 600 Lower West Fork (2) " - - - - 160 28 0.5 >160 >160 1 - - " 600 Black Creek " 10-15 9.3 2.0 210 120-160 56/56 0.50 9/62 14/61 1/1 - .3-.7 " 65 Cascades, WA Teanaway (1) " NC NC NC NC 76 62 0.50-1.0 18.3 >28 1 - - ~0.05-0.10 53-110 (2) " NC NC NC NC 76 62 0.50-1.0 3.7 >6.5 1 - - " 90-180 (3) " NC NC NC NC 76 40 0.50-1.0 3.9 >7.4 1 - - " 61-120 Cascades, OR Walker (1) dam break flood 5-10/10-15 10.2/12.3 1.83/1.65 49/100 56 24 0.50 0 (0-0.5) 1.1 4 - - .03-0.05? 3-5 (2) from road-related NC NC NC NC 56 22 0.25 0 .03 4 - - " 5-8 13

2 (3) landslide 5-10/10-15 8.07/10.7 1.93/1.72 10/100 56 23 0.25 0 .54 4 - - " 5-8 (4) " - - - - 56 20 0.25 0 0 4 - - " 3-5 Oregon Coast Range Sullivan (1) debris flows from - - - - 56 16 0.50 0 0 4.1 - - 0.07-0.10 5-8 (2) clearcut 15-20 15.5 1.6 31 56 31 0.25-0.50 0 0.13 4.1 - - " 5-8 Kate Creek " 7-8 8.8 3.3 9855 56 221 0.25 0 0 4.1 - - " Marlow Creek trib.1 debris flows from 4-5 8.9 7.5 1014 56 80 0.25 0 0 4.1 - - " Marlow Creek trib.2 altered forest 4-5 6.9 6.8 705 56 62 0.25 0 0 4.1 - - " California Coast Range S. Fork Eel " - - - - 56 33 0.50 0.6/0.75 1.7/3.9 3.9 - - ~0.5-0.6 150-750 Taiwan, Tachia dam NC NC NC NC 125 56 0.50 >125 >125 1 - - 0.1-1.0 290-2900 Western Foothills Tali levee NC NC NC NC 125 40 0.50 >125 >125 1 - - " 34-340 Tsao-Hu " 45 42.5 1.4 45 125 14 0.50 >125 >125 1 - - " 18-180 Chang-Ping " NC NC NC NC 125 20 0.50 >125 >125 1 26 - " 110-1100 Note: NC is not collected; backslashes separate reoccupations of sites; folia data collected at reoccupation, except for Walker Creek where values for installation are shown first; historical lowering rates estimated from straths with cultural artifacts in their fill, strath lowering rates estimated with radiocarbon samples in their fill, and geologic estimates from sediment yield, cosmogenic radionuclides, or mineral cooling ages (see text); bedload flux per unit width estimated using geologic lowering ranges and assuming bedload is 10% of total load.

CHAPTER 3. INCISION OF STEEPLAND VALLEYS FROM

DEBRIS FLOWS: FIELD EVIDENCE AND A HYPOTHESIS FOR A

DEBRIS FLOW INCISION LAW

Abstract

The uppermost reaches of steepland valleys are prone to episodic debris flows.

Debate continues about whether the effect of this incision process and its extent are adequately represented by modified fluvial incision laws that predict power laws of drainage area against valley slope. In response, I have found that valleys recently scoured by debris flows in the western U.S. have non-power law plots of valley slope against area. Evidence for bedrock lowering by the impact of large particles entrained in the debris flow extends along these valley bottoms, disappearing near the terminal debris flow deposits. Field measurements of valley slope and bedrock weathering show a tendency for both to increase abruptly above tributaries that contribute throughgoing debris flows. Indirect measurements indicate that debris flow length and long-term event frequency increase downvalley as individual flows gain material, and as tributaries with more debris flow sources join the mainstem. I propose that long-term debris flow incision rate is proportional to the integral of solid inertial normal stresses from particle impacts along the flow, and the number of upvalley debris flow sources. I propose a crude parameterization of inertial normal stress and flow length in terms of area and slope, which leads to a model that reproduces debris flow valley long-profiles with non-power law area-slope data. The model predicts that

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downvalley increases in flow length and frequency are balanced by reductions in inertial normal stress from reduced slopes and less weathered bedrock, leading towards equilibrium lowering. Reductions in valley slope to compensate for gains in debris flow frequency and length result in a non-power law plot of slope against drainage area. Field observations and forward modeling indicate that stream power laws poorly capture steepland valley long-profiles, and that an incision law particular to debris flows is required to evolve most temperate steeplands.

Introduction

In steeplands, episodic debris flows transport hillslope sediment along valley networks superficially resembling those cut by rivers (Fig. 3.1). In soil-mantled topography, such debris flows often initiate at hollows and commonly runout to valley slopes of 0.03 or greater (see Table 1.1). Some have argued that the steep network above these reaches is cut by debris flows in a process fundamentally different from that of bedrock river incision (Seidl and Dietrich, 1992; Montgomery and Foufoula-Geourgiu, 1993; Sklar and Dietrich, 1998; Snyder et al., 2001). These workers have proposed that there is a scaling break in area slope data separating a fluvial log-log linear section with a higher rate of change of slope with drainage area

(or concavity) from data at smaller drainage areas. In Digital Elevation Models

(DEM’s), the scaling break is commonly reported at ~0.1-1 km2. The mechanistic justification for this is weak given that debris flow deposition ought not to be area dependent. Some have proposed that area-slope data above the scaling break is also log-log linear, differing only from rivers by a lower concavity (e.g., Whipple and

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Tucker, 1999; Lague et al., 2003). For instance, on the basis of 90-m DEM data from

Nepal, Lague et al. (2003) have proposed an incision law for colluvial valleys that is similar to bedrock river incision laws, differing by a lower concavity. Stock and

Dietrich (2003) found that valleys traversed by debris flows have a plot of slope against drainage area that is curved in log-log space when data are measured from contour maps, or high-resolution laser altimetry. Combining extensive field observations with high and low resolution topography from around the world, Stock and Dietrich (2003) found that curved area-slope region mapped onto valley long- profiles above ~0.03-0.10 slope, where debris flows occurred that eroded bedrock.

Although slopes between ~0.03 and 0.10 may be a combination of river and debris flow incision (Chapter 2), the network remaining above 0.10 slopes comprises much steepland relief (e.g., 25-100%) and network length (e.g., >80%). In such places, most sediment first transits debris flow valleys before arriving at rivers, and the majority of hillslopes are bounded by debris flow valleys, whose lowering rate they must approach at long time scales. Much of the landscape response to river incision is probably conditional upon debris flow valley incision.

For these reasons, a debris flow incision law should be an essential part of future landscape evolution models. However, a wide variety of solid and fluid stresses can occur during an individual debris flow (e.g., Iverson, 1997) and it may be difficult if not impossible to reduce these to one erosion law in the absence of further guidance. Field observations that point toward the relevant stresses lowering rock would provide some justification for a simplified approach. In the following paper, I

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hypothesize a debris flow incision law based on field evidence from over 16 recent debris flows for the mechanics of rock lowering by debris flows, the bulk debris flow stresses associated with such lowering, and the role of network structure and weathering. These observations are largely from soil-mantled landscapes with coarse, granular debris flows that initiated as landslides during storms (e.g., Fig. 3.2), so the resulting model is most appropriate to such sites. I do not explicitly consider earthflows, mudflows, or dry avalanches.

Storms in California, Oregon and Washington during the mid- to late 1990’s initiated many debris flows (Fig. 3.1, 3.2), providing an opportunity to view widespread evidence for bedrock erosion by debris flows. Below I propose one conceptual framework for valley networks carved by debris flows, emphasizing what is different about them from fluvial networks. I then summarize the current thinking on the solid and fluid stresses characterizing debris flows, including the uncertainties in how to estimate values from field data. I describe field methods, and discuss techniques for reconstructing flow dynamics, crude as they are. I present observations of bedrock eroded by debris flows and report field estimates of bulk stresses exerted by the debris flow on the valley floor, which are many times lower than stresses required to break most unweathered rocks. I use this discrepancy and field observations of rock damage from debris flows as evidence for a hypothesis that rock lowering rates are proportional to excursions of inertial solid stresses from large particles colliding with the valley floor. From this I develop an event law for debris flow lowering of bedrock. By considering the network properties peculiar to debris

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flows, I develop a geomorphic transport law (Dietrich et al., 2003) that parameterizes relevant variables in the event-based law in terms of topographic variables. Using forward modeling, I demonstrate that the resulting expression predicts the curved area-slope relation that I propose is a signature of debris flow incision. This is in large part the result of abrupt slope reductions at tributary junctions with large increases in the number of mobile debris flows. Although the generality of this law remains to be seen, it captures some of the essential properties that are likely shared by many debris flow networks and serves as a hypothesis to guide future flume, field and modeling efforts.

Conceptual Framework A view of debris flow valley networks

Although the planview valley network in Figure 3.1 shares properties seen in stream networks (e.g., branching), it is fundamentally different in that it is primarily scoured by episodic debris flow events initiating from point source landslides, and bulking up along a single runout path. For instance, a debris flow traveling down the mainstem of Figure 3.1 would tend to gain mass by entraining colluvium from the valley floor, which could lead to increases in bedrock lowering. Therefore, bulking rates along the runout can change lowering rates. The debris flow might also tend to slow down as valley slope declined, eventually depositing at or above 0.03 slope.

Progressive reductions in slope would tend to reduce the velocities of particles hitting the valley floor, potentially reducing rock lowering. The cumulative number of debris flow events increases with distance down the mainstem, as the number of upvalley

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debris flow sources increase. At a timescale over which many events occur (e.g., 10

Ka), the frequency of events along the mainstem can be crudely characterized by the

ratio of the number of throughgoing debris flow sources upvalley (Nt) to the average

recurrence interval of hollow failure tr, or Nt/tr. Near the valley head, bedrock might remain buried for long time periods during which weathering would reduce its strength and make it more erodible when a debris flows does occur. Down the mainstem, the accumulation of debris flow sources would lead to increased lowering rates, unless counterbalanced by less weathered rock or lower slopes.

Determining the rate at which mainstems accumulate debris flow sources requires some knowledge of planform geometry because not all landslides originating at hollows produce far-traveled debris flows. Those that transit the network to deposit at low gradients on mainstem valleys tend to originate at network tips that are connected to the mainstem by straight pathways without sharp junction angles

(Benda, 1985). For instance, field observations indicate that debris flows tend to deposit where they encounter junction angles greater than ~60-70° (Ikeya, 1981;

Benda and Cundy, 1990; Ishikawa, 1999). These events contribute to the bulking up rate of the next mobile debris flow. Benda and Dunne (1997) used the term “trigger hollows” to refer to sites whose landslides were mobile through the network because they were connected to the mainstem by paths without acute junction angles. I approximate the number of landslide sources capable of producing debris flows that are mobile along the mainstem (Nt) as the number of upvalley trigger hollows at any point along the mainstem.

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Field measurements of initial landslide volume (v0) and final debris flow fan volume (vf) indicate that debris flows tend to gain most of their mass by entraining material along the runout path (i.e. bulking up; see Table 3.1). Path-length averaged values of bulking up range from ~0.01-10 m3/m for debris flows in Oregon (e.g.,

Benda, 1990), although higher values have been reported from glaciated areas (e.g.,

Hungr et al., 1984; Rickenmann and Zimmerman, 1993). Curiously, the majority of this new material is added to the length of the debris flow, as surge head depth does not appear to vary greatly downstream in available field studies (e.g., Benda, 1990;

Mizuyama et al., 1993). The length of the granular front likely increases as material is entrained at longer runout distance, higher bulking rate and higher solids volumetric fraction. The mechanics of sediment entrainment by debris flows is largely undocumented, so we have no ability to predict bulking rate along runouts.

Tributaries with trigger hollows do become increasingly rare downvalley because acute junction angles are more common in lower reaches. This planform network tendency may result in increasingly amounts of sediment from hillslope processes and immobile debris flows accumulating along the lower reaches of mainstems. Bulking rates of mainstem debris flows would then increase downvalley approaching reaches at which even the most mobile debris flows deposit.

Unlike streams, there is little time for roughness adjustment during infrequent debris flows, so that steady, uniform flow seems exceedingly unlikely (e.g., Iverson and Denlinger, 2001). For instance, in contrast to flow in river networks, the streamwise velocities of debris flow fronts have a tendency to decrease as slope

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declines through the network. Figure 3.3 illustrates power law fits to observed velocities from debris flows on Mt. Yakedake, Japan. Little generality can be inferred from such fits other than that they represent a strong central tendency for faster debris flows on steeper slopes. This tendency has led to the attempt to parameterize velocity using flow resistance equations (e.g., Gol'din and Lyubashevskiy, 1966; Okuda et al.,

1980b; Suwa and Yamakoshi, 2000), or rheological models (e.g., Johnson, 1970;

Rickenmann and Koch, 1997). However, variations in properties not easily parameterized in these equations (like pore fluid pressure) may lead to strong variations in velocity for different flows in the same valley (e.g., Fig. 3.3), and the physical basis for the rheological models is obscure (Iverson, 1997). In the absence of detailed studies on how to parameterize frictional resistance, field data indicate a tendency for faster streamwise velocity on steeper slopes, approximated as a power law function of slope.

The long recurrence intervals at initiation sites may allow weathering processes to substantially weaken valley floor bedrock high up in the network. For while gravel bedload motion in some streams has been reported up to 4% or more of the year (e.g., Andrews and Nankervis, 1995), recurrence intervals between debris flows can be decades to thousands of years for entire basins with many debris flow sources (e.g., Orme, 1990; Yoshida et al., 1997; Harris and McDermid, 1998; Cerling et al., 1999; Eaton et al., 2003). Long-term recurrence intervals at landslide initiation sites are correspondingly greater, approaching many thousands of years near the tips of networks (e.g., Benda and Dunne, 1987; Reneau and Dietrich, 1991; Eaton et al.,

140

2003). The variation in event frequency through the network may result in a pattern in

increasingly weathered rock towards network tips, balancing the reduction in event

frequency.

A view of debris flow stresses relevant to bedrock lowering

On the basis of theory and large-scale experiments with debris flows, Iverson

(1997) summarized stresses relevant to natural, flowing mixtures of solids and fluids.

Both field and experimental evidence indicate that many debris flows are

characterized by coarser-grained, fluid-poor surge heads (e.g., Fig. 3.2), and finer-

grained, fluid-rich interiors. Static and inertial solid stresses are high in coarse flow fronts; fluid stresses, and solid-fluid interaction stresses characterize the finer-grained interior. Iverson (1997) argued that no single rheology can capture these variations, so that much previous work on rheology cannot be applied to bulk flows. On the other hand, back-calculation of stresses associated with each characteristic region of real debris flows could yield insight into the stresses causing bedrock incision.

For instance, following Iverson (1997), fluid shear forces in the fine-grained fluid interior of debris flows can be approximated as:

∂u τ ≈ν µ (3.1), f f ∂z

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where νf is volumetric fluids concentration, µ is fluid viscosity and ∂u/∂z is the shear

strain rate. For muddy water, Iverson and Denlinger (2001) and Iverson and Vallance

(2001) have proposed viscosities around 0.1 Pa s.

At coarse-grained flow fronts, peak static normal solid stresses (σs) can be

approximated using a Mohr-Coulomb expression for effective normal stress:

σs = (νsρp–νwρw)gh cos(θ) − p (3.2),

where ρp is particle density, ρw is water density, h is flow depth measured normal to the boundary, θ is slope angle and p is the nonequilibrium component of intergranular fluid pressure (Iverson and Vallance, 2001). Experiments reported in Major and

Iverson (1999) indicate that surge heads can have negligible fluid pressures, so it is likely that fluid pressure can be omitted from (3.2) if it is used to characterize the granular snout.

Inertial solid stresses arise from particle collisions that result in fluctuations about the mean flow trajectory; a property often termed granular temperature (Ogawa,

1978) by analogy to the theory of ideal gas. Some authors (e.g., Iverson and Vallance,

2001) also use the term collisional to describe this stress, emphasizing its origin from inter-particle collision. Bagnold (1954) idealized these flow conditions as two planes of spheres sliding over each other under neutrally buoyant conditions, and proposed that stresses generated by collision of these layers were proportional to the square of the velocity gradient across them because both the frequency of collisions and the

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change in momentum per collision were proportional to this gradient. Reductions in

either the frequency or momentum change per collision by fluid damping or inelastic

collisions would tend to reduce this dependency below quadratic. Kinetic theory

(Jenkins and Savage, 1983; Haff, 1983; Campbell, 1990) and laboratory experiments

(e.g., Bagnold, 1954; Savage and McKeown, 1983; Savage and Sayed, 1984; Craig et

al., 1986; Craig et al., 1987; Capart et al., 2000) validated Bagnold’s hypothesis that

normal stress resulting from the sum of these fluctuating inertial particle impacts (σi) is:

2 2 ⎛ ∂u ⎞ σ i = ai cosα iλf (λ)ρ p D p ⎜ ⎟ (3.3), ⎝ ∂z ⎠

where ai is a constant, αi is an angle determined by collision conditions, λ is linear

grain concentration, f(λ) is a function of linear concentration, Dp is particle diameter

and u is velocity. In Bagnold’s experiments, ai was 0.04, tan αi varied between 0.32 and 0.40 so that cos αi was close to 1, and f(λ)=λ. Iverson (1997) replaced the linear

concentration terms λ in (3) with a volumetric solids concentration νs, so that (3.3) is approximately

2 2 ⎛ ∂u ⎞ σ i ≈ν s ρ p D p ⎜ ⎟ (3.4). ⎝ ∂z ⎠

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Confusingly, they also report inertial stresses using both λ and νs (Iverson and

Vallance, 2001). By dimensional analysis, Campbell (1990) and Hsiau and Jang

(1998) argued that granular temperature is proportional to the last two terms of (3.4)

under non-conducting conditions.

To date the treatment of inertial normal stresses has ignored the effect of slope on 3.4. Debris flows can occur on exceedingly steep slopes (e.g., > 70°), so some modification of expression (3.4) is necessary to account for a likely reduction in particle impact frequency approaching free fall conditions. I hypothesize that at slopes well above 1, the along-slope hop-length for a particle, or layer of particles might tend to increase as 1/cos θ. This reduces the frequency of collisions in (3.4) by a cosine term:

2 2 ⎛ ∂u ⎞ σ i ≈ cos()θ ν s ρ p D p ⎜ ⎟ (3.5), ⎝ ∂z ⎠

so that impact frequency approaches zero at free fall. The cosine term plays a negligible role at slopes encountered in most inclined flume experiments to date, and many debris flow valleys lie below this slope. I include the cosine term in (3.5) to imply that at sufficiently steep slopes, debris flows become ineffective erosional agents. This effect is consistent with the absence of well-developed valley networks at very steep slopes where soil is often absent (e.g., > ~60-70°).

Limitations to calculating stresses

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There are substantial limitations to the field application of equations (3.4) or

(3.5) to calculate the inertial normal stresses that debris flows exert on valley floors.

These include uncertainty in the exponent on shear strain rate, the difficulty of

estimating shear strain rate, and the ambiguity of the relevant grain size to use for a

given distribution.

Experimental data suggest that the dependence on shear strain rate may be less

than quadratic under some conditions. For instance, at non-neutrally buoyant

conditions, gravity causes adjustments in solid volume fractions with depth to balance

the normal component of body force (McTigue, 1982), and reduces the exponent

slightly below 2 if conduction of granular temperature occurs (Hsiau and Jang, 1998;

Hsiau and Shieh, 1999). Hanes and Inman (1985) found that the addition of fluid also

reduced the exponent on ∂u/∂z to as low as 1.5. They attributed this reduction to viscous damping of impacts by pore fluids that might reduce either the frequency of impacts, or the momentum transfer per impact below linear dependencies on ∂u/∂z.

Lun and Savage (1986) predict a similar reduction for inelastic collisions.

Uncertainties in the exponent on shear strain rate may be outweighed by the practical difficulty of accurately estimating shear strain rate from field measurement.

Shear strain rate can often only be approximated as the surface velocity us divided by

flow depth h (e.g., Savage and Hutter, 1989; Iverson, 1997; Iverson and Denlinger,

2001; Iverson and Vallance, 2001) because velocity profiles are only measurable

under some experimental conditions. Experiments on flowing granular masses

(Hirano and Iwamoto, 1981; Nakashima, 1986; Davies, 1990; Cuogiang et al., 1993;

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Taylor and Hunt, 1993; Azanza et al., 1997; Capart et al., 2000; Longo and Lamberti,

2000) indicate that the linear approximation of shear strain rate can underestimate near-boundary shear strain rate values by up to an order of magnitude. This is particularly true of rough boundaries, which can increase inertial normal stresses by large factors (e.g., Hanes and Inman, 1985). Calculation of (3.4) or (3.5) from field

measurements probably significantly underestimates boundary stresses from inertial

impacts.

There is no general agreement in the literature about how to calculate inertial

normal stress in (3.4) when there is a grain size distribution. This is important because

the choice of representative grain diameter can alter inertial stress estimates from

(3.4) by orders of magnitude. For instance, Iverson (1997) and Iverson and Denlinger

(2001) use particles between 0.001 and 0.2 m diameter to characterize distributions in

natural debris flows, leading to solid inertial stresses that are more than an order of

magnitude smaller than static solid stresses for their field examples.

Given the considerable uncertainty in the literature about how to define a

representative grain size to calculate inertial stress, I sought some guidance from a

simple conceptual calculation. Figure 3.4 illustrates an attempt to estimate what

percentile of the coarse grain size distributions found at such debris flow fronts

contribute the most to inertial normal stresses by calculating the frequency-magnitude

product of expression (3.4). To do so, I used coarse-grained particle distributions

from a coarse boulder to gravel-bedded stream in the Oregon Cascades (Sharp’s

Creek from Chapter 2), collected by Wolman random walk method. I binned four

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grain-size distributions into 50 mm widths, and multiplied the number of grains in

each bin with the value of (3.5) evaluated using the grain diameter at the mid-point of

the bin. I assumed constant values for shear strain rate, density, and volume solids

fraction for each size class. In each distribution, a small percentile of the coarsest

fraction (e.g., D88-D96) resulted in the majority of the inertial normal stress. Although these fluvial grain size distributions may be less skewed than those of debris flow fronts, they illustrate a tendency for the coarsest part of the distribution (e.g., D90) to dominate loading predicted by (3.5). Because the calculation assumes the simultaneous surface impact of all of the particles with no mutual interactions, it is at best a naïve idealization of actual conditions. However, it is consistent with the notion that some coarse percentile of the grains at the flow front dominate loading. This would also be consistent with the observed relation between maximum boulder sizes transported by debris flow surges and peak acceleration of ground vibrations (Suwa et al., 1999).

Field measurements of grain size at the coarse fronts of active (Gol’din and

Lyubashevskiy, 1966; Okuda et al., 1977; Okuda et al., 1978; Okuda et al., 1979;

Watanabe and Ikeya, 1981; Suwa et al., 1984; Suwa et al., 1993) and deposited

(Suwa and Okuda, 1980; Suwa and Okuda, 1983) debris flows show that coarse- fraction mean and median grain sizes may vary from 0.1 m to several meters in diameter. On the basis of this observation and the illustrative calculation in Figure 3.4

I use propose that median grain sizes from gravel and coarser particles may be

appropriate to characterize bulk inertial normal stress at coarse-grained flow fronts,

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particularly as I am interested in those impacts that are energetic enough to erode the

valley floor by breaking bedrock. I use De to represent this crude characterization of coarse particle size.

Methods

Below I describe field methods I use to estimate the bulk flow stresses

accompanying debris flow incision of bedrock at field sites reported in Table 3.1. The

field observations are intended to lead to a simplified debris flow incision law by

connecting observations of bedrock lowering with the dominant stress causing them.

Field surveying

To record width, slope and bedrock lowering by recent debris flows, I

surveyed valley bottom profiles at 10-m increments with tape and inclinometer, and

occasionally handlevel at meter intervals. I measured debris flow width and

maximum depths using preserved trimlines, and mapped the location of scoured

bedrock and debris flow deposits (see Chapter 1 for definition). To calculate bulking

rates, I estimated initial landslide volumes and final debris flow deposit volumes, as

well as runout distance. Where present, I used debris elevation differences between

the upstream and downstream sides of trees (∆h) to estimate rough streamwise peak

flow surface velocities us:

0.5 us = (2αg∆h) (3.6),

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where the velocity head coefficient α is assumed to be 1 in the absence of field data on velocity gradients for coarse-grained debris flows. Experiments to validate this approach (Iverson et al., 1994) indicate that velocities back-calculated from (3.6) can be up to two times lower than measured surge velocities. Most of the valleys where I worked lacked well-defined channel bends that would produce measurable superelevation, so I cite back-calculated velocities in Table 3.1 as representative, if imprecise, estimates of streamwise velocity.

In Table 3.1 I calculate normal solid static stresses by assuming dry conditions in the surge head, with a volumetric solid fraction of 0.6, a particle density of 2650 kg/m3, and locally measured slopes and peak flow depths normal to the bed. I calculate fluid shear stresses by assuming a viscosity of 0.1 Pa sec for muddy water

(Iverson and Denlinger, 2001); these values are presented indirectly as the Bagnold number (NBag).

To calculate inertial normal stresses in (3.5), I assume a volumetric solid fraction of 0.6, a particle density of 2650 kg/m3, and approximate shear strain rate as us/h, where velocities are back-calculated using (3.6) and peak flow depths are locally measured. I use median boulder diameters observed in debris flow terminuses to represent particle size in (3.5), although I am aware that such estimates have great uncertainty because of the ambiguity in the correct characterization of particle diameter.

Rock weathering

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We hypothesized that the fewer the number of up-valley debris flow sources at a point in the valley network (i.e., the lower the link magnitude), the less frequently that point would be scoured by debris flows. If so, the bedrock valley floor should become increasingly weathered as one approaches the valley head. I estimated rock weathering using a type N Schmidt hammer along valleys where debris flows recently

(within 2 years) scoured to bedrock. Rebound (or R) values from this instrument represent a measure of bedrock elastic properties within a sampling volume on the order of decimeters or less (e.g., Selby, 1980). They are influenced by rock matrix conditions as well as larger-scale fractures. I collected rock weathering data only in reaches that were largely scoured to bedrock (typically > 75% of valley length) because I did not wish to bias sampling to only steep, uncovered reaches whose harder rock (e.g., cliff-forming sandstones) might be more resistant to erosion.

Starting with the landslide headscarp (link magnitude 0), I stratified sampling sites by link magnitude, sampling at two locations in each link of the runout path, equidistant from the link ends. At each of the 2 sites within the link, I took 100 R-values using a random walk over a bedrock valley floor area 10 m long by 2-4 m wide. I adjusted the exact location of these sites within each link so that I sampled sites of the same lithology down the runout track (e.g., sandstones, not a mixture of sandstones and siltstones or mudstones). I also measured 50 fracture spacings at some sites by random walk sampling. These approximate the dimensions of fractured blocks that could be entrained by debris flows.

Digital data

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We acquired laser altimetry at two sites of known debris flows in Oregon at

2.5 to 4-m average point spacing. Using the topogrid command in Arc/Info, I gridded

the data into 2 to 4-m cells, extracted the valley network with threshold drainage

areas greater than 1000 m2, and calculated slopes using a 2-cell forward difference maximum fall algorithm. I located hollows that likely generate debris flows by contouring the DEM and following continuous valleys to the highest point at which contour direction changes by greater than ~ 120 degrees (measured between relatively straight contours on either side of the valley axis). I located prominent hollows on coarser-resolution 1:24,000 contour maps using the same criteria, although these maps omit many potential debris flow sources. I used laser altimetry to define trigger hollows as valley heads above tributary junctions that join the mainstem at junction

angles less than 70˚ (Ikeya, 1981; Benda and Cundy, 1990; Ishikawa, 1999).

Cosmogenic radionuclide analysis

At a site in the San Gabriels I collected rock and sand samples for cosmogenic

radionuclide analysis of lowering rates. Rock samples were crushed, and all samples

were sieved to separate a sand-sized fraction, then washed in HF acid by Kuni

Nishiizumi (Lawrence Berkeley Labs) to separate the silica component. Robert Finkel

(Lawrence Livermore National Labs) analyzed them for isotope abundance. I

calculated basin-wide average lowering rate from catchment sands following methods

outlined by previous workers (Brown et al., 1995; Bierman and Steig, 1996; Granger

et al., 1996).

Field sites

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On an opportunistic basis, I visited valleys with recent (< 1 year-old) debris flows in the western U.S. (Table 3.1; Appendix 1) over the period 1996-2000. Debris flows were triggered by landslides, many of which initiated at hollows during intense rainfall, a process that has been studied extensively on soil-mantled landscapes (e.g.,

Dietrich and Dunne, 1978; Dietrich et al., 1986; Iverson and Major, 1986; Reneau and Dietrich, 1987). Resulting flows were composed of water and a wide range of grain sizes, including many boulders preserved in terminal flow deposits and levees.

Along the runout path I measured evidence for debris flow width, depth, slope and any evidence that could be used to reconstruct peak velocities, like differential debris elevations on objects impinged on by the flow. I used this field data to estimate stresses at the granular surge head using equations (3.1), (3.2) and (3.4) with the assumption of no fluid pressure, to estimate how surge head velocity changes with slope, and to estimate changes in surge head depth along the runout. I recorded different styles of bedrock lowering, and measured boulder sizes in some terminal levees. At sites selected for uniform lithology, I measured bedrock weathering properties and fracture spacing.

Southern California: Yucaipa, Bear, Redbox

Intense thunderstorms during July 11 and 13, 1999, triggered debris flows along the southern margin of the Valley of the Falls, San Bernardino Mountains.

Boulders in coarse granular debris flow fronts (Fig. 3.2) moved rapidly across fans at the base of Yucaipa ridge, killing two people. Three days later, I walked a large

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runout at the northern extremity of the town (Yucaipa in Table 3.1) where a boulder- rich debris flow had scoured garnet mica schists exposed on the valley floor near the fan head. I used differential mudlines on trees impinged on by the flow on the lower sloped fan to estimate minimum flow velocities for steeper, upvalley sites with microscour and block-plucking from debris flow erosion. Cliffs along the valley prevented access to the initiation source on Yucaipa ridge, which is estimated to be around lowering at ~1 mm/a on the basis of U/Th-He data (Spotila et al., 1999).

In the headwaters of the Bear River in the San Gabriel Mountains, I investigated the runout of two recent debris flows whose sand and boulder levees were still dewatering during our visit. The July 13 thunderstorm the previous day likely triggered these events. Along runouts, I observed local abrasion and block- plucking of the Mesozoic granite/diorite valley floor caused by debris flows, which also removed a pre-existing talus accumulation from valley with slopes mostly above

0.10. Differential mudlines on trees allowed us to back-calculate peak flow velocities.

Downstream of recent debris flow deposits boulder fields from older debris flow deposits fill the length of the valley for several hundred meters. Further below, potholes and runnels mark the first widespread occurrence of fluvial features, and the beginning of area-slope data that is log-log linear (Stock and Dietrich, 2003).

We collected slope and weathering data along an undated debris flow runout near Redbox gap on Highway 2. Here I collected granodiorite from the valley bed to estimate in situ lowering rates from debris flows, and catchment sand from an adjacent deposit to estimate catchment-wide rates using the cosmogenic nuclides 10Be

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and 26Al. Long-term erosion rates in this part of the San Gabriels are ~ 0.7-1 mm/a on the basis of apatite fission-track data (Blythe et al., 2000).

California Coast Ranges: Highway 9, Pescadero, Scotia

The 1996/1997 El Niño winter storms triggered hollow failures in the forested

Santa Cruz Mountains above Highway 9 that mobilized as debris flows. I investigated a flow that scoured Neogene arkoses along its runout, plucking fractured blocks from the valley bed and leaving differential mudlines on a tree. Erosion rates on the adjoining western side of the range are ~0.2-0.3 mm/a, as estimated from sediment yield (Brown, 1973) and cosmogenic radionuclide analysis of sediment (Perg et al.,

2000). A debris flow along the Pescadero River to the north (see Appendix 1) also occurred during the 1996/1997 storms, and I visited it to examine evidence for rock weathering. In the northern Coast Range near Scotia, I walked the runout of a large debris flow that destroyed houses adjacent to Highway 101. A landslide complex at the valley head failed, resulting in a debris flow that lowered chert and sandstone outcropping along the valley floor.

Utah: Joe’s Canyon

Utah State Geological Survey personnel alerted us to a 1997 debris flow that scoured Joe’s Canyon in the Mesozoic Oquirrh Formation, a quartzite in the foothills of the Wasatch near Spanish Forks. When I walked the channel it was dry, and lacked exposures of sorted sediment, defined channel banks or fluvial features like potholes

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or plunge-pools. I measured runup features to back-calculate flow front velocities and

I observed decimeter-sized blocks missing from the jointed quartzite bedrock of the valley bed along with widespread abrasion marks. Long-term erosion rates in the vicinity of the Salt Lake City segment to the north are about 1-2 mm/a on the basis of fission-track and U/Th-He data (Armstrong et al., 1999).

Oregon Coast Range: Sullivan, Scottsburg, Marlow, Silver, Elk

Winter 1996/1997 El Niño storms initiated landslides throughout the Oregon

Coast Range, many of which mobilized as debris flows that scoured sediment from valley floors and exposed carbonate-cemented sandstones and siltstones of the

Eocene Tyee Formation (Walker and MacLeod, 1991; Ryu et al., 1996). I used ground reconnaissance and maps of debris flows provided by the Oregon Department of Forestry to locate debris flow sites in or near to Elliot State Forest. High-resolution topography from laser altimetry covers two sites with recent debris flows adjacent to the southern (Sullivan) and northern (Scottsburg) boundaries of Elliot State Forest.

Figure 3.5a shows a shaded relief image of Sullivan Creek in which average topographic data spacing was 2.5 m with ~0.3 m vertical resolution; Figure 3.5b shows a similar image for Scottsburg in which average topographic data spacing was

4 m with ~0.3 m vertical resolution. Figure 3.6 illustrates that the resulting data quality rivals that of 1-m hand-level surveys for the same area, with the laser altimetry capturing variations in local valley slope that correlate with siltstone

(dashed) or massive sandstone beds. Within the Elliot State forest, I located debris

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flows in Marlow Creek, Silver Creek, and Elk Creek drainage basins. Marlow Creek sites initiated at landslides in hollows whose vegetation was predominately second- growth alder with low total root strengths (Schmidt et al., 2001; Roering et al., 2003).

The debris flow at Silver Creek occurred in a recent clear-cut. Those in Elk Creek occurred in second growth forest with low stand densities. I collected weathering data on Marlow, Sullivan and Silver Creek failures, and recorded differential mudlines preserved on trees at many of these runout sites.

The steep valleys that conveyed debris flows (>0.10 slope) lacked fluvial features like banks or sorted sediment (see Fig. 1.3) and except for minor seepage, surface water flow usually only occurs during rainfall, when Horton overland flow occurs on the bedrock exposed by 1996 debris flows or subsurface stormflow daylights. Valleys have curved area-slope plots (Fig. 3.7), a feature that Stock and

Dietrich (2003) proposed as a signature for debris flow incision. Downstream,

Sullivan and Marlow Creeks have year-round baseflow, well-defined fluvial banks and pool-riffle reaches locally. In addition to these indicators of fluvial processes, I also found older debris flow deposits along Sullivan and Marlow, indicating that past debris flows have reached these channels. Long-term erosion rates in the Sullivan basin are estimated at ~ 0.1 mm/a on the basis of sediment yield and hollow accumulation rates (Reneau and Dietrich, 1991), and cosmogenic radionuclides

(Heimsath et al., 2001). Lowering rates near the Scottsburg site are estimated at ~0.2 mm/a from radiocarbon dates on strath terraces (Personious, 1995). Reneau and

Dietrich (1991) proposed that the correspondence between sediment yield and hollow

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accumulation rates in Sullivan is evidence for approximate steady-state lowering in this basin.

Olympics: FR 23

We walked a debris flow that scoured Eocene Crescent basalts on the southern margin of the Olympic Mountains, WA, near USFS Forest Road 23 (Table 3.1). The landslide headscarp occurs in 7-m deep glacial deposits, associated with Pleistocene valley glaciers. Old-growth Douglas fir and cedar forest covered the land prior to historic clear-cutting in the first half of the century. A fission-track study by Brandon et al. (1998) indicates Neogene exhumation rates less than 1 mm/a in the meta- sedimentary core of the Olympics that diminish outwards to less than 0.3 mm/a towards the flanking basalt and sedimentary rocks.

Results

Bedrock erosion by debris flows and attendant bulk stresses

Field observations along recent debris flow runouts in Washington, Oregon,

California and Utah record patchy lowering of bedrock in a variety of styles (Figure

3.8). I found that evidence for sustained particle indentation, like grooves, is rare. For instance, Figure 3.8a records the sustained sliding indentation of an object in the Kate creek debris flow that resulted in a narrow 1-3 mm deep groove. Table 3.2 lists the dimensions of all grooves that I could find along ~ 700 m of the Kate creek runout during an exhaustive 1-m hand-level survey. It illustrates that grooves occupy far less than 1% of the scoured area. Far more common in Oregon and elsewhere are faint

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lineations caused by the removal of weakly bound particles (e.g., sand grains) from the weathered bedrock matrix (Table 3.1; Fig. 3.8b). Moss preserved in the lee of a ledge in Figure 3.8b indicates that at Kate creek this microscour was patchy and less than several multiples of the bedrock sand-grain diameter, or several mm. Local removal of weathering patinas in Figure 3.8c records similar mm-scale lowering by this process.

In contrast, a large ledge in 3.8b records the removal of a plate-like rock fragment 7 mm thick and many cm’s in lateral extent. Ledges from removal of such fracture-bounded blocks are ubiquitous in the Tyee, but related post-scour weathering features like the tent in Figure 3.8d are rare. These appear to form soon after the debris flow passage, because 363 erosion pins installed in Oregon bedrock valley bottoms several months after debris flows in winter 1996/1997 have yet to record any further tent production or lowering by such weathering (Chapter 2). I measured 9805 of fractured plates of rock, or folia, along Kate Creek (e.g., Fig. 3.8b) and found a median thickness of 7 mm, a mean thickness of 9 mm and typical plan-view dimensions of ten's of centimeters (see Table 3.1 for local values). I measured similar values along two Marlow Creek runouts, with median thicknesses of 4-7.5 mm for

1721 samples. Although the formation of such folia is incompletely understood, their patchy removal by debris flows is the largest component of bedrock lowering here because of their large dimensions and frequent occurrence. At sites without such weathering features, patchy block removal is also the predominant lowering mechanism, occurring along decimeter-scale regional fracture or joint sets. For

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instance, Figure 3.8e illustrates a fresh fracture surface resulting from the removal of

a large decimeter-sized block of quartzite by a debris flow at Joe’s Canyon Utah. At

the same cross-section, fresh fractures (Fig. 3.8f) indicate point-loading by objects

entrained in the flow, and resulting tensile failures. These kinds of features occur all

along the runouts of debris flows in Figure 3.5 and Table 3.1, down to slopes at which

these mostly small debris flows deposited in confined valleys. For instance, the dotted

lines in Figure 3.5a, b illustrate the extent of field observations of microscour and

block–plucking. In the confined valleys listed in Table 3.1, I found that bedrock

lowering occurred along debris flow runout paths up to deposition of the terminal

levee. Graphs of valley area against slope along this runout are non-linear (Fig. 3.7), as reported in Stock and Dietrich (2003).

Field back-calculations of surge head velocity (Table 3.1; Fig. 3.3) have a range not unlike values reported elsewhere (e.g., Fig. 3.3). Path-length averaged bulking values (Table 3.1) show a great range, with the full range sometimes occurring between adjacent, seemingly similar valleys (e.g., Marlow 1 & 4). Figure

3.9 illustrates that surge head depth does vary much along individual runouts, so that

these flows grow longer, rather than deeper, as they entrain material.

Table 3.1 lists static solid (3.2) and inertial normal (3.5) stresses estimated at sites where I measured surge flow depth and valley slope, and could back calculate surge velocity from field evidence of run up. At all of these sites I observed evidence for bedrock lowering by inertial impacts. My estimates of the ratio of solid inertial

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normal stresses to viscous shear stresses (called the Bagnold number by Iverson,

1997)

∂u u ν ρ D 2 ν ρ D 2 s s p p ∂z s p p h NBag = ≈ (3.7), ν f µ ν f µ

is larger than 104 for all sites, indicating the predominance of solid stresses. Solid

static normal stresses are close to values calculated using similar assumptions by

Benda (1985) for debris flows in Oregon Coast Range, and are far below MPa values

required to break intact rock. Solid inertial normal stresses are 1-2 orders of magnitude smaller than solid static values, although underestimates of ∂us/∂z from us/h may bias these estimates. Savage and Hutter (1989) used the ratio of solid inertial normal stress to total normal stress to characterize the importance of particle collisions on total stress. On the basis of experiments, they proposed that a value of

0.1 represented a crude boundary above which particle collisions dominate over

Coulomb frictional interactions. Iverson (1997) and Iverson and Vallance (2001) used a ratio of inertial to static normal stress to characterize the same transition, calling it a

Savage number. Table 3.1 reports Savage numbers defined on the basis of the original ratio of inertial to total normal stresses found in Savage and Hutter (1989), which I estimate as:

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2 2 2 ⎛ ∂u ⎞ 2 ⎛ us ⎞ ν s ρ p D p ⎜ ⎟ D p ⎜ ⎟ ⎝ ∂z ⎠ ⎝ h ⎠ NSav = ≈ (3.8) 2 2 2 ⎛ ∂u ⎞ 2 ⎛ us ⎞ ν s ρ p D p ⎜ ⎟ + ()ν ρ −ν ρ gh cos(θ ) − p D p ⎜ ⎟ + gh cos()θ ⎝ ∂z ⎠ s p w w ⎝ h ⎠

with the assumption that fluid content and pressure are negligible. Values representing averaged conditions at the coarse flow front range from ~0.01 to 0.1

(Table 3.1), suggesting that Coulomb friction forces predominate. Underestimates of shear strain rate may bias these ratios below values greater than 0.1, but even if these values are accurate, energetic point loads can occur in frictionally dominated flow.

A systematic slope pattern with trigger hollows

Trigger hollows tend to cluster at the head of basins resulting in a rapid gain in trigger hollow sources along the mainstem near the basin headwaters, and smaller gains downvalley (Fig. 3.10). Thus relative frequencies of throughgoing debris flows increase rapidly along mainstems at the basin head, and more slowly downvalley.

Field surveys along debris flow runouts illustrate a tendency for abrupt, step-like changes in slope at trigger tributary junctions (Fig. 3.11). In each case, slope decreases as a step-function with the addition of a trigger hollow tributary. Addition of non-trigger hollows that join at angles greater than 70º has a negligible effect on the slopes at these sites. The slope of the link between trigger hollows tributaries does not vary systematically, although fluctuations indicate another source of variability

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due to fracture spacing. Laser altimetry indicates a similar tendency for Scottsburg

sites (Fig. 3.12).

Locally strong forcing of slope by variations in fracture density or bedding

thickness leads to irregularities in most debris flow runout long-profiles (e.g., Fig.

3.6) that may obscure the pattern of slope adjustment described above. I have also

observed that a few widely spaced fractures may lead to local steep slopes. These

observations suggest that only large changes in link magnitude create resolvably

different slopes because lithology and fracture spacing variations may dominate local

slope variation over ten’s of meters.

A systematic weathering pattern with trigger hollows

The proportion of weak, weathered bedrock remaining on the valley floor

after a debris flow increases as link magnitude decreases at the Kate Creek failure

(Fig. 3.13). I characterized the weakest remaining portion of the bedrock using the

25th percentile of Schmidt hammer R-values (Fig. 3.14); other low percentiles yield a

similar pattern. Resolvable changes in rock strength do not persist above link

magnitude 5-7 for these basins; although it is possible that recent debris flow scour

removed evidence. This region corresponds to the upper part of the area-slope plot

where slope changes very slowly with drainage area (e.g., Fig. 3.15). An exception to

the trend of downvalley increasing rock strength occurs at a fan head at Pescadero

site, consistent with long-periods of burial at fans generating weakened rock. This field evidence of systematic increases in rock weathering with network position

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indicates that weathering is a potential adjustment to changes in frequency through the network, if it results in an increasingly deep zone of weak rock that is more susceptible to lowering during passage of a debris flow.

Long-term equilibrium lowering

Cosmogenic radionuclides indicate that debris flows are incising a granodiorite-floored valley in the San Gabriels (Redbox site) at rates of 0.75 mm/a, a value that is not statistically different from catchment-wide rates of 0.75 mm/a estimated from channel sands. These results are consistent with a balance between hillslope lowering and local valley incision by debris flows, indicating that debris flow valley incision may approach steady-state lowering at long time scales, and is not an inherently transient phenomenon. Curved area-slope data associated with debris flow runout paths need not be transient features.

Hypothesis for a Debris Flow Erosion Law

At Table 3.1 sites, lowering from abrasion and from grooving during sustained sliding contact are small multiples of the bedrock grain size (mm-scale), roughly 1-2 orders of magnitude less than individual block removal (cm- to –dm scale). Removal is most likely caused by the impact of coarse particles entrained in the flow. On the basis such field observations (Figure 3.8; Table 3.1) I hypothesize that patchy bedrock lowering along debris flows is accomplished primarily by the energetic impact of large particles in the flow with fractured bedrock. Evidence for

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patchy lowering may reflect the episodic impact of particles large enough to cause bedrock failure. Although field observations indicate the brittle failure of bedrock during debris flow passage (e.g., Stock and Dietrich, 2003), typical bulk static and inertial normal stresses from field back-calculations of (3.2) and (3.4) (e.g., Benda,

1985; Table 3.1) are of the order of ten’s of KPa at the most, 10-1000 times less than tensile strengths of many intact rocks (e.g., Table 3.1 in Goodman, 1980), although fractured rocks have lower strength. Calculations of inertial normal stresses from

(3.4) in Table 3.1 indicate that positive excursions from bulk values are required to break rocks by tensile failure in the manner shown in Figures 3.8d-e. Otherwise, rock must be substantially weakened throughout the valley network to allow failure by bulk stresses.

Excursions from bulk static normal solid stress can occur by grain-bridging, but inertial excursions by tumbling particles are more apparent in the few extant videos of bouldery debris flows from Mt. Yakedake, Japan, and from Taiwan and

Italy. In debris flows, large particles colliding with the bed have caused point loads from 0.1-10 MPa (Okuda et al., 1977; Sabo Publicity Center, 1988), sufficient to break many intact rocks (e.g., Goodman, 1980). Maximum point loads from collisions of idealized spheres can be estimated as functions of impacting particle diameter, density, elastic modulus E, Poisson’s ratio ν, and velocity by assuming elastic conditions that do not allow failure (e.g., Timoshenko and Goodier, 1951; Evans et al., 1978). Figure 3.16 illustrates the role of grain size and slope-normal velocity fluctuations on the maximum theoretical impact pressure for spherical grains of 0.1-3

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m. Point loads for this impactor size can exceed the tensile strength of many rocks

(e.g., Goodman, 1980). Similarly high point loads can occur at lower surface normal

velocities for particles with sharp edges, so the graph is intended as an illustration that

such impacts are plausible mechanisms for bedrock lowering by debris flows. I

hypothesize that such excursions become proportionally larger as bulk inertial normal

stress increases, so that a dimensionless constant K0 relates the two values. Then a rate law that characterizes debris flow incision rate into bedrock would be proportional to expression (3.5). Insofar as granular temperature is proportional to

(3.5), this hypothesis is equivalent to stating that lowering rates scale with the fluctuating component of particle velocity.

Diverse wear experiments are consistent with the use of expression (3.5) to model bedrock erosion from solid particle impacts. In a typical laboratory experiment, wear rates are modeled as the sum of many micro-mechanical failures resulting from single-particle impacts, whose intensity is a function of particle density, diameter, velocity, and impact angle (e.g., Finnie, 1960; Sheldon and Finnie,

1966; Sheldon and Kanhere, 1972; Evans et al., 1978; Hockey et al., 1978;

Wiederhorn and Lawn, 1979; Routbort et al., 1980; Wiederhorn and Hockey, 1983;

Lhymn and Wapner, 1987; Meng and Ludema, 1995; Gahr, 1997; Goretta et al.,

1999; Stack et al., 1999):

n1 m1 Wear rate = Km C(α0) (D-D0) (V-V0) (3.9)

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where Km is a material constant that includes particle density, C(α0) describes the

dependence of wear rate on attack angle α0 (e.g., Neilson and Gilchrist, 1968), D is

particle diameter, D0 is threshold diameter for erosion, V is particle velocity, V0 is

critical velocity below which there is no erosion (e.g., Hoff et al., 1974) and n and m

are exponents thought to vary from 2-6 with micro-mechanical conditions of failure

(e.g., lateral, ring, or radial crack formation, and grooving). The details of crack

formation and target microstructure lead to great variation in the optimal function

C(α) and the exponents n and m found by experiment, so these results cannot be used

to predict the exact form of a debris flow incision law. Rather, experimental results

summarized by (3.9) indicate that particle density, size and velocity are relevant to

determining lowering rates from particle impacts.

Rock discontinuity spacing and intact rock properties like tensile strength

ought to influence transient lowering rates from failure during particle impact. By

analogy to Griffith crack theory (e.g., Jaeger and Cook, 1976), I hypothesize that rock

resistance to crack growth during indentation or unloading is characterized by the

2 work done opening tensile failures (cf. Jaeger and Cook, 1976), T0 /Eeff, where T0 is tensile strength and Eeff is effective elastic modulus. Sklar and Dietrich (2001) have

demonstrated an inverse squared dependence of rock lowering rates on tensile

strength in a bedload abrasion flume, and field measurements of bedrock lowering

rate are also consistent with this relation (Stock et al., submitted). This hypothesis

predicts that transient lowering rates decrease with increasing tensile strength, and

increase with a higher Eeff that allows deeper quasi-elastic particle indentation depths

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into bedrock (ε1) for the same impact. Figure 3.17a illustrates this hypothesis under the assumption that tensile failures generated during loading propagate towards free surfaces, but it is also possible that failure occurs during unloading.

If loading is uniaxial and elastic, ε1 is defined by the compressive stress σι from an impacting particle, and the materials modulus of deformation, Eeff: ε1 =

σι/Eeff. Experimental and field data (cf. Fig. 6.5 in Lo and Hefny, 2001) indicate that

denser fracture spacing reduces Eeff, leading to deeper indentation. Rock excavation rates from tunnel boring machines and rock cutting trenchers also increase rapidly with denser fracture spacing (Franklin et al., 1971; Fowell and Smith, 1976; Aleman,

1981; Karpuz et al., 1990; Pettifer and Fookes, 1994; Thuro, 1997; Vervoort and De

Wit, 1997; Deketh et al., 1998; Thuro and Plinninger, 1999). These machines are analogous to debris flows in the sense that rock removal is accomplished by energetic impacts and point loading. I hypothesize that transient lowering rates increase with fracture density because denser discontinuities 1) reduce the modulus of deformation

Eeff, leading to deeper indentation ε1 and larger chip formation for a given impact, and

2) increase the probability of an additional free surface towards which impact-related tensile failures can migrate to, resulting in higher probabilities of block plucking over chipping. Since both effects depend upon the size of the indentor relative to the fractured block, the effect of fracture spacing on lowering rate ought to be scaled by the indentor diameter, Dp. I propose Df/(Df +Dp) as a non-dimensional measure of indentor volume, so that as fracture spacing Df is increasingly larger than particle diameter, the ratio tends towards unity for massive rocks (characterized solely by

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tensile strength and deformation modulus). This results in a rapid decline in lowering

rates as discontinuity spacing exceeds the dimensions of the impactors. Figure 3.17b

illustrates a regression of trencher data from Deketh et al. (1998) that is consistent

with use of this ratio and some measure of rock strength to characterize rock lowering

rate. On the basis of field observations and literature described above, I hypothesize

that a measure of rock resistance to lowering by particle impacts is:

T 2 ⎛ D ⎞ 0 ⎜ f ⎟ (3.10), ⎜ ⎟ Eeff ⎝ D f + D p ⎠

where To is tensile strength measured by Brazilian strength test (e.g., Vutukuri et al.,

1974; Sklar and Dietrich, 2001), Df is a measure of reach-scale fracture density (e.g.,

median fracture spacing Df of random walk count, Table 3.1) and Dp is particle diameter (which is approximated by the spacing of impact points in the excavator examples of Fig. 3.17b), or the median grain size De at bouldery surge heads of debris

flows.

Event expression

If the cumulative force of the particle impacts causing erosion scales linearly

with bulk inertial normal stresses approximated by expression (3.5) with a

generalized exponent w, transient debris flow incision rates are proportional to the

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integral of inertial normal stress along the eroding portion of a flow of unit width and

the frequency of flows f, and inversely proportional to rock resistance:

n ⎡ w ⎤ ∂z K0 K1 2 ⎛ ∂u ⎞ − = ⋅ f ⋅ L⎢cos()θ ν s ρ p De ⎜ ⎟ ⎥ (3.11), ∂t 2 ⎛ D ⎞ ⎢ ⎝ ∂z ⎠ ⎥ T0 ⎜ f ⎟ ⎣ ⎦ ⎜ ⎟ Eeff ⎝ D f + De ⎠

where K0 is a dimensionless proportionality constant relating bulk inertial normal stresses to higher excursions of inertial normal stress, K1 is a proportionality constant between rock resistance and incision rate, L is the length of the flow front with large grains capable of eroding high tensile strength rock (e.g., Fig. 3.2), n is an exponent

of unknown value and De is the median boulder diameter at a surge head. K1 has dimensions that vary with w and n so that the right side of (3.11) will have units of erosion rate (e.g., K1 is dimensionless if w is 2 and n is 1).

We approximate ∂u/∂z as us/h where us is the streamwise velocity, as measured by runup, or other field techniques, and h is flow depth at the coarse front as estimated by trimlines or terminal deposits. I treat the exponent w as a variable, although it appears likely to vary from ~1 to 2 (Hanes and Inman, 1985). A rate law whose variables could be measured for debris flows from field measurements is:

n ⎡ w ⎤ ∂z K0 K1 2 ⎛ us ⎞ − = ⋅ f ⋅ L⎢cos()θ ν s ρ p De ⎜ ⎟ ⎥ (3.12). ∂t 2 ⎛ D ⎞ ⎢ ⎝ h ⎠ ⎥ T0 ⎜ f ⎟ ⎣ ⎦ ⎜ ⎟ Eeff ⎝ D f + De ⎠

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Expression (3.12) predicts that fast, shallow, frequent flows with big rocks and long,

granular snouts, are most erosive.

A ratio of bulk solid inertial normal stresses integrated along a path of unit

width, to rock resistance, illustrates a non-dimensional number that scales with the

erosion rate predicted by (3.12):

2 ⎛ V − V ⎞ 2 ⎛ us ⎞ ⎜ f 0 ⎟ x cos()θ ν s ρ p De ⎜ ⎟ ⎜ V ⎟ x ⎝ h ⎠ ⎝ 0 ⎠ f Nerosion = (3.13), 2 ⎛ D ⎞ T0 ⎜ f ⎟ ⎜ ⎟ Eeff ⎝ D f + D p ⎠

where v0 and vf are initial failure volume and final runout volume, x is runout length, and xf is total runout length. This ratio characterizes lowering under idealized, dry, fully elastic conditions so that w is 2, and assumes that the debris flow gains volume

as it travels so that vf-v0 is non-zero. The last two terms in the numerator represent a

bulking rate non-dimensionalized by initial failure volume and multiplied by a runout

distance x. This term is meant to represent the growth of the length of the granular

flow front with bulking rate. At valleys with evidence for bedrock lowering by debris

0 2 flows, typical values for Nerosion are 10 -10 (Table 3.1). Estimated values covary with inertial normal stress and runout length because I assumed constant values for v0 (100 m3), bulking (1 m3/m), rock fracture spacing (0.5 m), tensile strength (106 Pa) and elastic modulus (109 Pa), in lieu of field measurements for these at all sites. The full

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range of values at which rock lowering does and does not occur remains to be

explored.

Parameterization of event law

Systematic change of the variable values in (3.12) might be expressed as a

topographic signature for debris flow erosion that could be measured with simple

metrics like drainage area and slope (e.g., Stock and Dietrich, 2003), or expressed as a particular long-profile shape. In the following paragraph, I propose crude topographic parameterizations for debris flow frequency, granular flow front length, flow front depth, velocity, and valley floor rock strength in order to examine the effect variations in these properties along a valley network might have on debris flow valley long-profile shape. These parameterizations are by no means unique, and they serve to illustrate our current lack of knowledge about debris flow evolution along networks.

For instance, the number of potential debris flow initiation sites tends to decrease rapidly above tributary junctions as one approaches the tip of valley networks (Fig. 3.10). If the network is to approach steady state lowering, this reduction in frequency must be balanced by a combination of reductions in rock strength or increases in erosion depth per debris flow event, either of which could have a topographic signature. The abrupt slope reduction below some tributary junctions (Figures 3.11-3.12) is one possible compensation for an increased number of events. Slope reduction would decrease streamwise velocity and resulting inertial

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normal stress, leading to a reduction in event lowering that balances in part the

increase in total number of events that the link segment experiences. I parameterize

the long-term frequency of debris flows along the mainstem as the ratio of upvalley

trigger hollows to their average failure interval: Nt/tr.

Debris flows grow in length as they entrain material, although I am not aware of any data quantifying this growth rate. I hypothesize that bulking rates also increase

downvalley where increasing numbers of tributaries joining at angles greater than 60-

70° deposit debris flows onto the mainstem. Larger downvalley bulking rates should

lead to more rapid increases in granular flow front L, modified by any systematic

changes in valley width or depth. I hypothesize that such an increase in granular flow

front can be represented by:

⎛ ⎞ a ⎜ A(x) ⎟ k v 1⎜ A ⎟ L(X ) = b 0 e ⎝ total ⎠ (3.14), w(x) ⋅ h(x)

where kb is a constant of proportionality that controls the magnitude of the bulking rate, w is debris flow width, h is surge head height, A is drainage area, Atotal is the total drainage area of the debris flow basin, and a1 is a dimensionless bulking

exponent. The first term is a ratio representing the average flow front length,

modified by kb. This length is further modified along the network as the flow entrains material deposited along the mainstem valley by hillslope processes and previous debris flow deposits. The second term expresses the spatial variation in L along the

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mainstem long-profile. I hypothesize that this growth rate is an exponential function

of drainage area, normalized by the total drainage area of the debris flow basin. The

normalization is necessary in order to yield values of L that range from several meters

at initiation to several ten’s of meters at terminal levee deposits, a range consistent

with field data (Table 3.1). Additionally, if the initial debris flow granular front is of

order 1 m, a1 cannot be larger than ~4 or terminal snout lengths will exceed those commonly observed at deposits in the field sites of Table 3.1 (1 m

in Table 3.1 could reflect variations in rock type producing coarse debris, or time

elapsed since a previous event.

Most of the material entrained by debris flows joins the body (e.g., Davies,

1990), so that flow front depth varies slowly along runouts (e.g., Fig. 3.9). Depth appears at most a weak function of drainage area:

a2 h = k2A (3.15),

where a2 is a positive number <<1 and k2 has dimensions of 1/(2a2-1) so that h is in units of length.

Figure 3.3 indicates that streamwise velocity has a tendency to decrease at gentler slopes lower in the network, although whether this happens gradually or abruptly at junction angles is unknown. I parameterize this tendency using a power law expression for slope with a variable exponent

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a3 us = k3S (3.16),

where k3 has units of velocity, and may vary greatly in time and space. I suspect that

the exponent a3 varies at least between 0.2 and 1.2, perhaps with network geometry

(i.e. junction angles). Representing velocity with this substitution assumes that

individual basins have a characteristic exponent a3, a proposition that has yet to be demonstrated. In the absence of a mechanistic understanding of velocity variation through these networks, this crude parameterization captures some spatial variation of

velocity due to slope.

Figures 3.13-3.15 indicate that systematic reductions in rock strength may

occur above junctions with trigger hollows at link magnitudes 1 to 8. These

reductions are consistent with the production of deeper rock weathering as the time

interval between debris flows increases. I hypothesize that episodic debris flows

erode more deeply into weathered bedrock carapaces, resulting in erosion rates that

balance a less frequent occurrence. Then depth and intensity of rock weathering

would be inversely proportional to the number of upvalley debris flow sources

(trigger links) up to a certain number (e.g., ~5-8 in Fig. 3.14). I hypothesize that tensile strength T0 declines towards valley heads due to longer exposure between

events as

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∂z 1 ⎛ −c N ⎞ − T (N ) = T ⎜1 − e 2 t ⎟, N ≥1 (3.17), 0 t 0 ⎜ ⎟ t ∂t ∝ ⎝ ⎠

where c2 is a constant (e.g., Fig. 3.14) that characterizes the rate of decline.

Expression (3.17) is an empirical attempt to fit the form of R-values in Figure 3.14.

Geomorphic transport law

If expressions (3.15)-(3.17) are substituted into (3.12), an expression for

debris flow incision is:

⎛ ⎞ a ⎜ A(x) ⎟ ∂z K K N k v 1⎜ A ⎟ − = 0 1 ⋅ t ⋅ b 0 e ⎝ total ⎠ ∂t 2 2 tr a T ⎛ −c N ⎞ ⎛ D f ⎞ w(x) ⋅ k A 2 0 ⎜1− e 2 t ⎟ ⎜ ⎟ 2 ⎜ ⎟ ⎜ ⎟ Eeff ⎝ ⎠ ⎝ D f + De ⎠

n w ⎡ a ⎤ ⎛ k S 3 ⎞ ⎢ 2 ⎜ 3 ⎟ ⎥ ⋅ cos()θ ν s ρ p De (3.18). ⎢ ⎜ a 2 ⎟ ⎥ ⎝ k 2 A ⎠ ⎣⎢ ⎦⎥

If rock properties, bulking coefficient kb, and debris flow width, depth, grain size and solids concentration are invariant along the runout, so that they can be characterized by a constant K2,

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⎛ ⎞ ⎜ A(x) ⎟ a ⎜ ⎟ a wn ∂z 1 Nt 1 Atotal n − = K ⋅ ⋅ ⋅ ⎝ ⎠ ⋅ cos θ S 3 3 2 e () (3.19), ∂t ⎛ −c N ⎞ tr ⎜ 2 t ⎟ ⎜1 − e ⎟ ⎝ ⎠

where K3 represents the product of K0, K1, and K2. The second term in (3.19) represents rock properties, the third term the frequency of events, the fourth term the rate of granular flow front growth due to bulking, and the last term a slope dependency on inertial normal stress. If granular temperature is a function of slope, a similar reasoning could lead to such a slope dependency. In this form, (3.19) encapsulates variables that may lead to a rate law and distinct topographic signature for debris flow incision: 1) a weathering dependency in the denominator that becomes unimportant at large link magnitude Nt (e.g., 10); 2) a dependence on the rate at which debris flow sources accumulate within the network (Nt); 3) a dependence on landslide recurrence interval (tr); 4) a bulking expression representing the length of

the erosive, coarse-grained flow front; and 5) a slope dependency that arises from

conversion of streamwise velocity to surface-normal particle impacts, and the

resulting damage mechanics (S a3ωn), counterbalanced by a decrease in impact frequency approaching free-fall [cosn(θ)].

Long-profile evolution modeling

To illustrate the debris flow incision expression, I take modern debris flow valley long-profiles and parameterize them in terms of (3.19). I erode these valleys using (3.19) for 10 Ma, a timescale that represents ~3 relief envelopes at the low

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erosion rate sites, and results in steady-state long-profiles. I vary the constant K3 in

(3.19) until it matches the boundary lowering rates shown in Table 3.3 (see Chapter 1 and 2 for rate sources) so that the lowermost points of initial and evolved long- profiles are matched to evaluate (3.19).

I use detailed long-profiles recently scoured by debris flows at Sullivan and

Scotsburg (Fig. 3.5), and coarser 1:24,000 contoured debris flow long-profiles from four sites in the western U.S. (Table 3.3) that I explored in Chapter 1. I convert these

data to 200 equally spaced elevation points using a spline. I calculate slope with a 2-

cell forward difference, and I approximate drainage area A in terms of long-profile

a distance x using the relation A=Ac + cx (Table 3.3). Ac represents a threshold drainage area above which data tend to follow a power relation cxa, and is not related

to valley head. I substitute this expression into (3.14) to calculate the increase in

granular flow front L as the flow bulks up along the runout. I characterize Nt along

each long-profile by mapping tributaries with junction angles less than 70° against

mainstem runout distance, x (see Table 3.3). The use of (3.19) assumes that debris

flow width and depth are approximately constant, which is consistent with data in

Table 3.1 and Figure 3.9. I use c2 weathering values derived from Kate Creek (Fig.

3.14). For the sake of simplicity, I assume that n=1 and w=2 in (3.19). I apply (3.19) and maintain the initial slope of the last point on the profile at each time step to simulate equilibrium lowering using finite-difference methods outlined in Stock and

Montgomery (1999). The constant slope boundary condition forces the model long- profile to approach the downvalley slope of the initial long-profile. For this reason,

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parameter values are very sensitive to lower boundary slope values. Variations from

steady state at these points because of variations in rock properties or transients will

strongly influence subsequent parameter values.

Figure 3.18 illustrates how variations in weathering (c2), bulking (a1), velocity

(a3) and stress (n) exponents influence steady-state long-profiles of Sul3. These parameter variations are referenced to a long-profile whose parameters (a1=1.0 and

a3=0.9) closely approximate the existing one using a field value of c2=0.35 from Kate

Creek and assuming that n=1 and w=2. Kinks in the long-profiles correspond to changes in the number of mobile debris flow sources, Nt. Increases in the magnitude of the weathering exponent reflect increasingly less weathered rock (see Fig. 3.14) and result in increasingly large relief as the long-profile steepens to maintain the boundary lowering rate. Increases in the bulking exponent increase the gradient in granular flow front L along the profile, leading to increasing curvature and relief as increases in L are balanced by reductions in slope to match the boundary lowering rate. By contrast, increases in exponents that are applied to slope (a3 and n) reduce the

gradient in this term along the profile, resulting in reduced steady-state relief.

Figure 3.19 illustrates the range of bulking and velocity exponents that best

reproduce existing valley long-profiles and reliefs at Table 3.3 sites. Within this field,

velocity exponents below ~0.3 poorly reproduce most initial long-profiles. Velocity

exponents above 2.0 are also unlikely because they require bulking exponents that are

unreasonably large (i.e., > 4). However, long-profile simulations summarized in Fig.

3.19 indicate that no single combination of the parameters in (3.19) explains the long-

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profile shape of all of the original valleys. For instance, for a velocity exponent of

0.9, a value allowed by all of the long-profiles, bulking exponents vary from ~0-2.1

(Fig. 3.19). It is not clear whether this variation reflects mechanistic differences

expressed by the model, or variations in the long-profiles from lithology or transient

conditions.

Figure 3.20 illustrates that (3.19) maintains several key initial long-profile

features, including abrupt slope changes at tributary junctions and reduced curvature

in the uppermost region of the long-profile. The resulting long-profiles also maintain

curved area-slope data (Figure 3.7) characteristic of debris flow valleys. This is a

consistency test that indicates that parameters in (3.19) can be arranged to yield

reasonable long-profiles. We will need to have independent means of extracting

velocity and bulking exponents before a more rigorous test of (3.19) is possible.

However, (3.19) is an improvement over fluvial models based on power law

regressions through area-slope data of Figure 3.8. These models systematically

underpredict valley relief in Figure 3.20 because they do not capture slope-area

curvature with rapid changes in slope at downvalley drainage areas. Nor do fluvial

models with constant curvature capture the tendency for linear slopes at low drainage areas that characterize most debris flow valleys (Stock and Dietrich, 2003).

Discussion

Many geomorphically relevant debris flow properties remain unquantified and

models of velocity, weathering and bulking that are more mechanistic than those

hypothesized above will be required to validate a debris flow incision law. Flume

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studies are needed to verify that inertial normal stresses are the relevant stresses

leading to bedrock erosion. Until then, (3.19) expresses in crude form the features that

are seen in the field (Figures 3.8, 3.11-3.15), like abrupt slope and weathering

reductions with the accumulation of debris flow sources. Applied to existing long-

profiles, the expression predicts equilibrium curved area-slope signatures (Fig. 3.8) as

a result of slope reductions to compensate for increases in debris flow frequency and

bulking. It also reproduces the linear long-profiles of debris flow valley where

weathering adjustments may predominate. The expression of these features is an

improvement over stream power laws calibrated by regressing area-slope data with a

power law. However, it is possible to approximate each long-profile with a stream

power law so long as substantial variation in K, m and n is allowed. These fits lack

curved area-slope data, but they can approximate relief.

The use of slope exponents between 0.8-1.2 in (3.19) results in equilibrium

long-profiles that closely match all of the existing ones, but only if bulking exponents

are varied. This variation may result from real field variation in bulking rate (e.g.,

Table 3.1 bulking variations), from transients or lithologic differences, or improper

parameterization of velocity or bulking. Those seeking to simulate long-profile

evolution using (3.19) should use slope and bulking exponents that lead to reasonable

relief for given long-profiles (e.g., values for Sul3 of a1= 1 and a3=0.9). The utility of

(3.19) is its identification of some variables that can be reasoned to influence debris flow incision rates. Below I briefly explore some of these implications of (3.19) for landscape evolution.

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Consideration of (3.19) suggests circumstances that would retard the development rate of debris flow valley networks. Litholgies that do not produce particles large enough to cause impact damage, or steep slopes that lead to greatly reduced impact frequencies could lead hillslopes without well-defined valley networks. Landslides distributed across the hillslope may compensate, perhaps leading to rocky steeplands without well-defined valley networks.

For instance, (3.19) predicts that debris flow incision rates decrease proportionally as landslide recurrence interval grows. As a thought exercise, suppose that the rivers of a steep landscape ceased lowering as rock uplift ended. Although debris flows continue to erode so long as landslides mobilize, the set elevation at the debris flow runout zone would result in gradual reduction in valley slope that migrates upvalley towards landslide sources. In its wake, debris flow incision rates decline because of lower inertial stress, leading to a reduction in hillslope angles and soil flux. This further reduces debris flow incision rate by reducing bulking rates, but landslide frequencies may not decline significantly until the reduced slope migrates to valley heads. Once this occurs, landslide failure requires increasingly extreme hydrologic events, leading to significantly lowered debris flow frequencies and lowering rates. This negative feedback process leading to longer and longer debris flow recurrence intervals may drastically reduce debris flow incision rates. In this thought experiment, valley relief above 3-10% remains substantial for long periods of time as debris flows become increasingly infrequent. Such a scenario might explain the persistence of mountain ranges (e.g., Appalachians) long after rock uplift has

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ceased. In such places, there is evidence for long recurrence intervals (e.g., 1-10 Ka) for debris flows (e.g., Woodruff, 1971; Williams and Guy, 1973; Bogucki, 1976;

Pomeroy, 1980). A frequency reduction in any event-driven erosion model would tend to preserve relief, but (3.19) predicts that relief in old landscapes is concentrated in valleys with only a few landslide sources, with abrupt relief reductions at tributary junctions that contribute mobile debris flows. In this sense, response time is strongly dependent on network structure. This hypothetical example illustrates that steepland topography may persist long after tectonism ceases if relief is dominated by debris flow valleys, and landslide recurrence interval grows after tectonic uplift ceases.

Conclusion

On the basis of field observations at recent debris flow runouts in diverse

steepland valleys above 0.03-0.10 slope, I hypothesize a debris flow incision rate law

that increases with solid inertial normal stress and length of the granular flow front,

and decreases with increasingly longer landslide recurrence intervals and harder rocks

(characterized by tensile strength and fracture spacing). One allowable parameterization of these variables in terms of topographic elements (3.19) predicts curvature of log S- log A data that depends upon the rate at which debris flow sources increase with area, the rate at the length of the granular front grows as the debris flow entrains new material from the valley bed, and the relationship of granular temperature to valley slope. Forward modeling of this expression can reproduce equilibrium long-profiles similar to real long-profiles, and have the curved area-slope

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data that I believe is a signature for valleys cut by debris flows. Much work remains to justify a debris flow incision law, like field and flume studies that explore relations between stress and rock lowering rate, and improvements in topographic parameterizations for debris flow properties like velocity and bulking rate. This effort is justified by the substantial portion of steep landscapes whose form depends on debris flow incision, and the necessity of including details of this process that are not captured by area-slope power laws.

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List of Symbols

a (-): exponent on drainage area as a power function of x a1 (-): bulking exponent a2 (-): depth exponent a3 (-): velocity exponent ai (-): constant from Bagnold (1954) A (m2): drainage area 2 Ac (m ): threshold drainage area above which data on a graph of drainage area vs. downvalley distance are well approximated by power law 2 Atotal (m ): drainage area at end of debris flow long profile c (-): constant in drainage area as a power function of x c2 (-): exponent in 3.17 characterizing the decline in weathering with increasing trigger link magnitude D0 (m): threshold particle diameter in 3.9 D (m): particle diameter in same-sized collection of grains De (m): particle diameter characterizing the most effective size at eroding bedrock from a distribution, assumed to be the median diameter of boulders at flow front Df (m): characteristic bedrock fracture spacing (e.g., median value from random walk) Dp (m): particle diameter, moment of a distribution E (Pa): elastic modulus of unfractured rock Eeff (Pa): effective elastic modulus of fractured rock f (1/yr): long-term averaged frequency of debris flows at a point in the valley network g (m/s2): gravitational constant h (m): debris flow surge head depth hw (m): effective saturation depth of debris flow k2 (f[a2]): proportionality constant between debris flow depth and source area in 3.15 k3 (f[a3]): proportionality constant between streamwise debris flow velocity and valley slope in 3.16 K0 (-): constant of proportionality relating excursions in solid inertial normal stress to bulk solid inertial normal stress K1 (f[n, w]): proportionality constant between rock strength and erosion rate in 3.11 K2 (f[K0, K1, numerous other parameters]): constant characterizing any spatially invariant properties of debris flow erosion (rock strength, debris flow width and depth, grain size, solids concentration) K3 (f[K0, K1, K2]): product of K0, K1, and K2 kb (-): coefficient of proportionality in bulking expression 3.14 Km (-): material constant in 3.9 L (m): length of debris flow granular front

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m1 (-): exponent in 3.9 n (-): exponent characterizing the erosional efficiency of inertial normal stress in 3.11 n1 (-): exponent in 3.9 NBag (-): Bagnold number (ratio of solid inertial normal stress to fluid static stress) Nerosion (-): ratio of path-integrated bulk inertial solid stresses to rock resistance NSav (-): Savage number (ratio of solid inertial normal stress to total solid stress) Nt (-): number of upvalley trigger hollows or mobile debris flow sources p (Pa): nonequilibrium component of intergranular fluid pressure S (-): valley slope T0 (Pa): rock tensile strength tr (yr): long-term recurrence interval of landsliding at a hollow u (m/s): velocity us (m/s): streamwise (along slope) velocity of debris flow V (m/s): particle velocity in 3.9 V0 (m/s): threshold particle velocity for erosion in 3.9 3 v0 (m ): landslide volume 3 vf (m ): debris flow terminal deposit volume w (m): debris flow width at surge head w(-): exponent relating shear strain rate to solid inertial normal stress; may vary with flow conditions (e.g., intensity of viscous damping or inelastic collisions) x (m): horizontal debris flow runout distance, measured along mainstem from landslide scarp xf (m): total horizontal debris flow runout distance, measured from landslide scarp α (-): velocity head coefficient from runup calculation α0 (-): particle attack angle measured from surface tangent αI (-): friction angle from Bagnold (1954) ∂u/∂z (1/s): shear strain rate of debris flow ∂z/∂t (m/yr): bedrock lowering rate ∆h (m): debris-line elevation difference from velocity runup ε1 (m): quasi-elastic particle indentation depth λ (-): Bagnold’s (1954) linear solid concentration µ (Pa s): viscosity of phase defined as fluid in debris flow ν (-): Poisson’s ratio νf (-): volumetric fluid concentration νs (-): volumetric solids concentration θ (-): valley slope angle 3 ρp (kg/m ): particle density 3 ρw (kg/m ): water density

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σi (Pa): solid normal inertial normal stress σs(Pa): solid normal static stress τf (Pa): fluid static shear stress

186

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Fig. 3.1 Debris flow valley network in an Oregon Coast Range clear-cut. The combination of elevated water pressure during a 1996 storm and reduced root strength initiated landslides at valley heads that mobilized as debris flows, scouring sediment and Tyee sandstone (white areas) along the runout. Road at top right indicates scale.

198

Fig. 3.2 Coarse-grained debris flow front in Valley of the Falls, San Bernardino Mountains, California, three days after deposition on July 13, 1999. Median diameter of boulders is approximately 0.3 m. Such coarse boulder fronts are characteristic of many sites I investigated (Table 3.1).

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2 10 Japan, Mt. Yakedake, Aug14, 1976 Aug31, 1976 Aug17, 1978 Sep4, 1978 Aug21, 1979 Sep7, 1980 Oregon Coast Range debris flows 0.84 +/- 0.16 Yakedake, V=25S 1 1.1 +/- 0.20 10 Yakedake, V=8.6S 0.26+/-0.18 Oregon, S=9.2S

velocity (m/s)

0 10

-1 10 -2 -1 0 10 10 10 slope

Fig. 3.3 Field data from Kamikamihori valley on Mt. Yakedake, Japan (Okuda et al., 1977; 1979; 1980a; 1981) and Rock Creek in Oregon, illustrating the tendency for debris flows to slow down as slope decreases. Note that this tendency exists despite the large variation in velocity for different debris flows in the same valley. Japanese data are from video camera estimates; Oregon data are back- calculated using equation (3.6).

200

0.1

1 D94D94 (2)(2) grainsize distributions from ) a 2 D93D93 (1)(1) Sharp's Cr., OR

P 3 M 100

( 4 t D88D88 (5)(5) 5 90 1 (n=127) 0.01 2 (n=127) 80 (n=112) oduc D96D96 (3)(3) 3 70 4 (n=115)

pr 5 (n=118)

r 60 e de n u D93 (4) t fi 50 t n e c

e 40 p gni

a 0.001 30 m - 20 y 10 nc 0

que 1 10 100 1000 10000

e r grain size (mm) f 0.0001 10 100 1000 10000 100000 grain-size bin midpoint (mm)

Fig. 3.4 Plot of the frequency-magnitude product of inertial normal stress estimated from (3.4), and the source grain size distributions (inset graph). I binned the distributions into 50 mm widths, and multiplied (3.4) by the number of grains in the bin, using the bin midpoint grain diameter. I assumed 3 constant values of νs (0.5), ρp (2650 kg/m ) and ∂u/∂z (10/3 1/sec). A dashed line illustrates the pattern for grain size distribution number 2. Labeled maxima correspond to the coarsest percentiles of the distribution (D88-D96), illustrating the role that a few large particles play in generating large inertial normal stresses. These results suggest the use of a coarse percentile (e.g., D90) in (3.4) to characterize the inertial normal stresses relevant to bedrock lowering by debris flows. See text for more details.

201

↑ a) N

Sul2 Kate (Sul1)

Sul3

0 1 km

A2 A3 A4 A1 b) ↑N

Scot2 Scot1

Scot3

0 1 km

Fig. 3.5 a) Shaded relief image of high-resolution airborne laser altimetry from Oregon at Coos Bay (top) and Scottsburg (bottom). Both black and white dotted lines indicate 1996/1997 debris flows and associated rock lowering, as mapped in the field. Large arrows indicate terminal deposits of debris flows that transited mainstem valleys, small arrows indicate debris flows that deposited where junction angles were greater than 60°. Wide arrows along the valley at the top of the Coos Bay panel bracket a knickpoint on Sullivan Creek. Note the less dissected landscape upvalley from the knickpoint. Dashed lines labeled A1-4 correspond to valleys in Figure 3.12. Hillslopes draining to Sullivan Creek from the top portion of the image are likely deep-seated failures (as judged by the lack of larger valleys), so I choose not to use them for analysis. Deep-seated landslides also occur in the northeast quadrant of Figure 3.5b, and are a process whose occurrence in this region is in part structurally controlled (Roering et al., 1996).

202

300

headscarp

130

↑ ↑ ↑ ↑ 150 ↑ 110 ↑

meters 310 350 390 ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ runout ↑ ↑ 1-m handlevel ↑ ↑ ↑ 1-m laser altimetry 7.5’ USGS contour map ↑ erosion pin xs

0 0 200 400 600

meters

Fig 3.6 Comparison of laser altimetry long-profile to 1-m hand-level and 7.5’ USGS topography for Kate creek. Inset illustrates influence of alternation between massive sandstone and siltstone (dashed lines) on local slope, and the accuracy with which laser altimetry captures such fine-scale variation. Erosion pin cross-sections (xs) shown by arrows.

203

0 10

) ) 0.766 1.18

0.28 0.44 -2 10 ) Scot3 S=0.16A S=0.830/(1+8.00A debris flow model Sul4 S=0.80A S=0.712/(1+24.5A debris flow model 2

-1 ) ) 10 0.787 0.770

0.33 0.39

Scot1 S=0.13A S=0.797/(1+8.80A debris flow model Sul3 S=0.08A S=0.786/(1+12.0A debris flow model

-3 10 0 -1 -2 -1

10 10 10 slope

area (km

Fig. 3.7 Area-slope data for the valleys scoured by debris flows in Figure 3.5 are unequivocally non- linear. Linear power law regressions (dashed) are shown for comparison, and used to simulate fluvial long-profile evolution in Figure 3.19. Solid lines indicate curved empirical fits to data from equation (1.5). Slope-area data from steady-state debris flow incision models in Figure 3.20 (stars) reproduces much of the curvature of the existing long-profiles.

204

Fig. 3.8 Evidence for bedrock lowering by debris flows, upvalley at top of all photos. See Table 3.1 for approximate estimation of bulk stresses at selected sites. a) Rare 1-3 mm deep groove on Kate Creek runout, indicating sustained sliding contact of particle for at least 190 mm along the bed. Adjacent 9 mm deep ledge indicates removal of a wide rock tablet following groove formation. See Table 3.2 for all groove dimensions; b) Removal of sandstone grains (~0.5 - 1 mm in diameter) on Kate Creek by abrasion. Moss in the lee of the smaller ledge indicates abrasion of less than several mm. Ledge in bottom portion of photo corresponds to removal of fractured slab 7 mm thick; c) Abrasion of weathering patina from jointed bed of Joe’s Canyon; d) Post-event weathering feature (“tent”) along Kate creek, observed ~ 1 month after debris flow. Subsequent monitoring indicated that these features were no longer forming. Note the removal of the dark weathering patina by micro-scour during debris flow; e) Failure resulting in removal of dm-sized block of quartzite at same site, indicating the predominance of the mechanism on lowering; f) tensile failure of quartzite in Joe’s Canyon debris flow, Utah.

205

10 site bulking rate 3 Marlow1 (7.5 m /m) 3 Marlow2 (0.3 m /m) 3 Marlow4 (0.03 m /m) 3 Rock Creek (2.5 m /m)

depth to thalweg (m)

0 200 600 1000 horizontal distance from headscarp (m)

Fig. 3.9 Field data from Oregon illustrating lack of systematic change in debris flow surge depths along runout paths for some of the flows listed in Table 3.1. Depths are maximum vertical distance from thalweg to trim line. Bulking rates for each event are shown in parentheses. There is no consistent increase in depth with runout distance for these events.

206

100

high resolution topography Sul1 Sul2 Sul3 Sul4 Scot1 10 Scot2 Scot3

100 lower resolution 1:24,000 topography Bear (# of debris flow sources) t Deer Noyo Sharp

1 10-3 10-2 10-1 100 101 2 drainage area (km )

Fig. 3.10 Plots of the rate at which mainstem valleys gain throughgoing debris flow sources (trigger hollows, Nt) with drainage area. Trigger hollows in the upper plot are identified using high-resolution topography from Figure 3.5. Bottom plot is a comparatively crude estimate of trigger hollow numbers from 1:24,000 contour maps of debris flow basins previously investigated in Stock and Dietrich (2003). In both plots, the number of debris flow sources is rarely characterized by a power law without non-random residuals.

207

0.9 Oregon Coast Range (ss) 5 pt. median

0.6

hillslope slope

0.3

1 3 4

San Gabriels (gr) 5 pt. median

0.7

slope hillslope 0.4

1 2 3 7 link magnitude

0.1 0 100 200 300 400 distance from headscarp (m)

Fig. 3.11 Evidence from field surveys for a step reduction in reach slope as trigger link magnitude increases (heavy vertical dashed lines). Data from debris flow runouts over rock with unusually homogenous fracture density and bedding in the Oregon Coast Range (Silver Creek) and the San Gabriels (Redbox). Note that non-trigger hollows (light dashed lines) do not substantially influence reach slope in these examples.

208

1 1 10 10 A4: N=1 (slope=0.07+/ 0.1) A2: N=1 N=2 N=3 (slope=0.16+/.02)

0 0 10 10

e p A3: N=1 (slope=.14+/.13) A1: N=1 (slope=0.03+/.02)

0 0 10 10

-1 -1 10 -3 -2 -2 -1 10 slo slope 10 10 10 10

2 area (km )

Fig. 3.12 Evidence from Scotsburg laser altimetry (Fig. 3.5b) for the influence of link magnitude N on valley slope. Slope and standard error of least squares regression shown in parentheses. Slopes of valleys with only one debris flow source (A1, A3, and A4) do not change at a statistically significant level, indicating these links have linear long-profiles. By contrast, valleys that gain more than one debris flow source (A2) have reductions in slope.

209

D25 of 100 R values

20 10

0 Nt=9 01020304050 20

0 Nt=7 01020304050 count 20 10

0 Nt=1 01020304050 40

0 headscarp 01020304050

Schmidt R values

Fig. 3.13 Distribution of Schmidt hammer rebound (R) values with link magnitude for Kate Creek (Sul1). R values are a proxy for rock tensile strength. See text for sampling details. Note the systematic increase in the proportion by area of weak, weathered rock towards landslide headscarp, as characterized by the 25th percentile of R values.

210

20 Fan head

10 Oregon ss {Kate, 27(1-e-0.35N )} -0.59N Oregon ss {Marlow, 35(1-e )} <10 Oregon ss {Silver, 27(1-e-0.60N )}

San Gabriels gr {Redbox, 29(1-e-0.31N)} Wasatch ss (Joe's Canyon) 10 S. Cruz Mntns. ss (Highway 9) (Pescadero) <10

03691215 trigger link magnitude

Fig. 3.14 A summary of field evidence for systematic increase in weak bedrock with link magnitude, approaching landslide headscarps in granite (gr) and sandstone (ss). Note the reduced R-value at the fan head fo 25th Percentile of 100 R values r Marlow Creek. R-values less than 10 are indistinguishable with Schmidt hammer, and are offset for clarity. Curves are fits to the expression in parentheses, an empirical equation that allows R values to approach the maximum measured value at large trigger link magnitude Nt. Wasatch and Santa Cruz Mountain sites have insufficient data to fit. See Table 3.1 for site details.

211

0 10 20

slope

10 erecentile of 100 R values p

25th R value 11 m laser altimetry

10-2 0 10-3 10-1 area (km2)

Fig. 3.15 R values from Figure 3.14 plotted in relation to slope and drainage area for Kate creek, illustrating common occurrence of an observable rock weathering (reduced R values) with reduced curvature of area-slope data. Slopes are averaged along-valley over 11-m intervals because this interval represents the coarsest averaging possible before curve fit changes.

212

8 10

granite, quartzite

upper limit of recorded debris flow impact pressures limestone 6 10 tuff, sandstone

weak shale surface normal velocity u n = 0.1 m/s = 0.25 m/s field values solid static normal stresss = 1.0 m/s = 2 m/s = 3 m/s 4 elastic particle collisional stress (Pa) 10 = 4 m/s = 5 m/s

-2 -1 0 10 10 10 particle diameter (m)

Fig. 3.16 Variation in maximum particle impact pressure (Pmax) with particle diameter and surface 12/5 2/5 6/5 normal velocity un from Pmax = 1720r E un , assuming elastic conditions with elastic moduli E=5 x 11 3 10 Pa, and ν=0.3 and ρrock=2650 kg/m (see eqn. 218, Timoshenko and Goodier, 1951). Note that failure of rock under impact would lead to substantially reduced impact pressures values. Dashed line indicates upper limits of impact pressures recorded in Japanese debris flows (Okuda et al., 1977; Sabo Publicity Center, 1988). Values for large particles at surface normal velocities that are still small fractions of streamwise velocities are sufficiently large to break hard crystalline rocks.

213

3 10 A) D B) p u -1.06+/-0.18 chain excavator: y = 274x ε 1 2 D (R =0.87) /hr)

tensile 1 failure 10

ε 2 case 1: E high, D >D

2 rock excavation rate (m ε deep indentation (high 1) p chipping/block removal θ Deketh et al. (1998)-chain excavator if T0 < impact stress x Fowell et al. (1976)-road header case 2: E low, D >>D eff f p -1 10 ε -1 1 shallow indentation (low 2) 10 10 chipping if T < impact stress 0 3 rock resistance (MPa): S {D /(D +D )} c f f p

Fig. 3.17.a) A model for the lowering of fractured rock by particle impact. Particles of diameter Dp impact bedrock with two different fracture spacings (dashed lines) at the same velocity ũ with a rotational component. The particles indent quasi-elastically to depths ε (shaded area) that depend on the local elastic modulus Eff. Resulting failures are shown schematically. Because Eff decreases rapidly with increasingly dense fracture spacing, the particle on the left (case 1) indents more deeply, resulting in a larger potential tensile failure, and the opportunity for block plucking along adjacent fracture surfaces. In case 2, a higher Eeff reduces indentation depth, and there are no adjacent fractures that could serve as free surfaces for block plucking. The illustration suggests that bedrock with increasingly higher tensile strength or larger fracture spacing relative to the indentor ought to fail less frequently at only the most energetic impacts. Transient lowering rates are then inversely proportional to a measure of tensile strength, and a ratio of fracture spacing to particle diameter (see text for further details). b) Mechanical rock excavation rates that are consistent with a dependency on fracture spacing and rock strength. Plot shows fractured rock excavation rates from a chain trencher and a roadheader against rock resistance, as characterized by the product of compressive rock strength Sc (often a multiple of tensile strength) and a ratio of fracture spacing Df to particle diameter Dp. Fracture spacing and compressive strength are reported in the sources, but I estimated indentor spacing from machine illustrations as 0.3 m. Excavation rates from the chain trencher (Deketh et al., 1998) are higher for smaller block sizes, and can be approximated as a linear function of the rock resistance function on the x-axis. Excavation rates from roadheader (Fowell et al., 1976) follow trend of chain-trencher at high rock resistance, but plateau at lower rock resistance values, arguably because they are limited by the roadheader’s power.

214

700

500

in 0.5 increments = 4.0 1 1 bulking: a stress exponent: n in 0.2 increments a

300

n = 0.6 = 0.0 100

1 a n = 2.0

600

in 0.1 increments in 0.1 increments 400 3 2

weathering: c slope: a

200 = 0.65 = 0.6 2 3

c a = 0.05 = 1.4 2 3

c a

0 500 300 100 300 100

(m) elevation

Fig 3.18 Different steady-state long-profiles after the application of a debris flow incision law (3.19) to

Sul3 valley (Fig. 3.5a). Each panel illustrates long-profiles perturbed from a bold line that represen distance from headscarp (m) ts a model long-profile whose bulking (a1=1.0) and velocity (a3=0.9) exponent values reproduce Sul3, given measured weathering values (c2= 0.35), and assuming a stress exponent of n=1. Kinks in the long-profiles correspond to changes in the number of debris flow sources, Nt. Increases in the magnitude of weathering and bulking exponents (top panels) lead to increased steady-state relief, while increases in exponents on slope (bottom panels) lead to reduced relief. See text for further explanation.

215

Sul1 3.5 Sul2 Sul3 Sul4 Scot1 2.5 Scot2 Scot3

1.5

, bulking exponent 1

0.5

Deer Noyo Sharp Bear -3 10

/t 3

-4 10

10-5 0.0 0.5 1.0 1.5 2.0 a , slope exponent 3 Fig. 3.19 a) Plot of bulking exponent versus velocity exponent from (3.19). These combinations resulted in model long-profiles that closely reproduced existing valley long-profiles (Fig. 3.5) after they were evolved to steady-state using the debris flow incision law. Bulking exponents must be limited to values that produce terminal granular flow fronts less than ~50 m for a conservative initiation length of 1 m (i.e. a1<~4). Most of these combinations yield a shape and relief that reasonably match the real long-profile, and I have no independent evidence to prefer one combination over another, save the observation that velocity exponents do not appear to exceed ~1.3 (Fig. 3.3). b) Plot of constant K3/tr required in (3.19) to reproduce estimated boundary lowering rates for each long- profile (see Table 3.3). Landslide recurrence interval is set to 2 Ka for all long-profiles for purposes of comparison, although much of the variation in K3 between sites may be due to unknown variations of tr.

216

800 ) )

a) -6 -5

=1.70) =0.78) 1 1

400

Sul4 fluvial (m/n=-0.44, K=3.52 x 10 debris flow (a Scot3 fluvial (m/n=-0.28, K=3.96 x 10 debris flow (a

) )

-6 -5

800

=1.02) =1.30) 1 1

400

Sul3 fluvial (m/n=-0.39, K=7.30 x 10 debris flow (a Scot1 fluvial (m/n=-0.33, K=2.05 x 10 debris flow (a

300 200 100 300 100 (m) elevation

Fig. 3.20 a) Comparison of selected long-profiles from a) laser altimetry (see Fig. 3.5) and b) contour

maps to steady-state fluvial and debris flow incision models. Dashed fluvial long-profiles distance from headscarp (m) calculated using m/n value from Figure 3.7, assuming that n=1 (e.g., Stock and Montgomery, 1999). Debris flow incision models evolved using (3.19) with a3=0.9, the lowest possible velocity exponent that results in fits to all of the valleys in Figure 3.19a. Fluvial models underestimate relief because they do not capture rapid increases in slope in the curved area-slope data of Figure 3.7, and they show profile curvature in their upper reaches that is not present in real long-profiles. Debris flow models capture abrupt slope changes at tributary junctions and linear upper sections of long-profiles, but variations in long-profile shape and lower boundary conditions of each long-profile leads to substantial variation in best-fit bulking exponent a1. Note that the large bump in the Bear long-profile is roadcast.

217

) ) -4 -5 2500 3000

2000

=0.70) =0.62) 1 1

2000 1500

Noyo fluvial (m/n=-0.233, K=2.27 x 10 debris flow (a Bear fluvial (m/n=-0.338, K=4.06 x 10 debris flow (a

1000

500

0 0 800 600 400 200

2200 1900 1600 1300

) )

4000 -5 -5

1600

=1.21) =1.95) 1 1

2000 800 Deer fluvial (m/n=-0.313, K=4.65 x 10 debris flow (a Sharp fluvial (m/n=-0.380, K=2.29 x 10 debris flow (a

0 0

900 700 500 800 600

1200 1000 (m) elevation

distance from headscarp (m)

218

Table 3.1. Field observations

location site date lithology erosion median length % bed- slope width depth vel- peak link D50 deposit bulking static inertial Nsav NBag Nerosion of features folia total /xs rock max. ocity flux mag. bould. volume normal normal event (mm) (m) (m) (m) (m/s) m3/s N(m)(m3)(m3/m) stress (Pa) stress (Pa) Olympics, WA FR 23 (3 pin xs) 1997? diabase m(icro)-scour, folia, 8 533 / 52 70 0.51 9.5 2.7 2 0.2 9990 17.0 37490 " block-plucking 18 188 0.36 11.0 3.8 3 0.2 55644 Oregon Silver Creek 1996 med. ss (Tyee) m-scour, folia, grooves, >220 /60 100 0.33 3.4 1.6 - ? 23710 Coast Range ODF#535 1996 " block-plucking 303 /201 69 0.28 9.0 2.5 7.6 >3 0.4 - 37540 2346 6.E-02 2.E+04 2.7E+01 ODF#733 1996 " " 272 /53 59 0.38 12.3 4.7 6.6 >2 0.3 - 69042 274 4.E-03 5.E+03 5.6E-01 Marlow1 1996 " m-scour, folia, block-plucking 700 /353 42 0.23 12.5 5.5 7 0.3 6000+/-2000 7.5 83303 " " 288 0.32 7.7 3.1 5 46349 " " 281 0.32 9.2 3.8 5 55867 " " 273 0.29 9.5 4.5 5 66847 " " 266 0.29 12.4 5.6 5 83724 " " 259 0.29 14.0 6.0 5 90137 " " 252 0.27 14.1 5.0 5 74532 " " 244 0.27 14.1 5.0 5 74586 " " 237 0.29 12.1 4.9 5 73899 " " 230 0.29 11.3 4.7 5 70767 " " 223 0.29 11.6 4.4 5 66202 " " 216 0.36 10.7 4.5 5 66274 " " 209 0.36 11.2 5.7 5 82858 " " 201 0.19 9.1 3.8 5 58808 " " 159 0.46 9.8 4.2 4 59590 Marlow 2 1996 " " 491 /370 77 0.17 13.0 2.6 8 0.7 ~800 0.3 39940 " " 326 0.14 16.0 2.4 8 37036 " " 122 0.27 12.0 2.5 4 37608 " m-scour, folia, grooves 66 0.55 12.0 2.0 3 27306 " m-scour, folia, block-plucking 38 0.39 11.0 2.5 3 36293 244 / 238

21 Marlow3 1996 " " 7 76 0.12 16.0 5.4 >2 0.3 660 +/- 200 1.0 83543 (10 pin xs) " " 6 14 0.49 12.6 3.8 >2 53171

9 Marlow4 1996 " " 4 192 /150 70 0.60 6.7 3.2 >2 0.3 135 0.03 43245 (8 pin xs) " " 4 143 0.60 7.3 3.6 >2 48682 " " 4 135 0.17 6.6 3.3 >2 50624 " " 4 128 0.17 8.3 3.7 >2 56088 " " 4 121 0.30 8.4 3.5 >2 51701 " " 7.5 114 0.30 7.9 4.0 >2 60284 " " 4 106 0.28 6.4 3.5 >2 52867 " " 4 99 0.28 8.4 3.5 >2 53176 " " 4 92 0.32 9.4 3.5 >2 52302 " " 4 85 0.32 9.4 3.5 >2 52554 " " 4 78 0.33 11.1 3.8 >2 55748 " " 4 71 0.33 7.8 3.0 >2 44922 " " 4 64 0.32 7.0 2.8 >2 40888 " " 4 57 0.32 6.7 3.2 >2 48003 " " 4 50 0.41 9.1 3.8 >2 0.3 55370 Kate Cr. 1996 " m-scour, folia, grooves, b.p. 7 1070 /582 76 0.07 9.0 3.0 5.8 15 0.3 ~1100 1.0 46632 533 1.E-02 7.E+03 1.3E+01 Rock Cr. #1 1996 med. ss m-scour, block-plucking 1510 /212 ~45 0.50 11.0 4.1 9.0 180 >10 0.5 2185-5395 2.5 56445 1966 3.E-02 2.E+04 3.0E+01 #2 (Yamhill Fm.) soil scour 515 0.06 19.0 2.8 7.8 150 >10 0.5 43556 3124 7.E-02 3.E+04 1.3E+02 #3 " soil scour 739 0.20 16.0 6.1 9.7 90 >10 0.5 93204 995 1.E-02 2.E+04 5.8E+01 #4 " m-scour, block-plucking 800 0.16 16.8 4.6 9.0 280 >10 0.5 70777 1524 2.E-02 2.E+04 9.6E+01 #5 " m-scour, block-plucking 921 0.30 13.1 6.6 8.2 260 >10 0.5 97758 628 6.E-03 1.E+04 4.4E+01 #6 " soil scour 990 0.20 31.0 3.9 11.6 270 >10 0.5 58826 3597 6.E-02 3.E+04 2.8E+02 #7 " soil scour 1000 0.07 40.0 5.3 7.2 450 >10 0.5 82380 735 9.E-03 1.E+04 5.9E+01 #8 soil scour 1176 0.11 32.0 4.0 5.9 240 >10 0.5 61954 871 1.E-02 1.E+04 8.1E+01 Coast Range CA Scotia 1997 chert m-scour, block-plucking ? ? 0.55 >5 >3 >10 <0.1 S. Cruz Mntns., CA Hiway9 1996? arkose m-scour, block-plucking >109 / 27 77 0.45 10.2 4.0 6.4 160 2 0.5 56838 1029 2.E-02 2.E+04 2.0E+00 Wasatch, UT Joe's #1 1998 quartzite m-scour, block-plucking 1590 /715 38 0.09 9.0 4.5 6.4 55 >10 0.4 1835 2.6 69837 520 7.E-03 9.E+03 2.2E+01 #2 " " 1135 0.13 8.5 3.0 5.9 100 >10 0.4 46356 990 2.E-02 1.E+04 6.5E+01 San Gabriels, CA Bear Cr. 1999 granodiorite m-scour, block-plucking ? ? 0.15 5.1 1.6 5.1 25 >10 0.5 24655 4114 1.E-01 3.E+04 " " ? ? 0.25 5.0 1.7 3.9 46 >10 0.5 25698 2050 7.E-02 2.E+04 Redbox 1998? " m-scour, block-plucking >225 100 >0.21 >4 >2 >7 <0.2 San Bernardino, CA Yucaipa 1999 garnet schist m-scour, block-plucking >1000 ? >0.31 >10 >4 >8.1 >10 0.3 ~4800 Notes: slope from inclinometer; width estimated from trimlines; velocity from eqn. (1); depth from field estimate of thalweg to trimline; static normal stress estimated using ρ=2560 kg/m3, and assuming volumetric solids fraction of 0.6 under dry conditions; inertial stresses from eqn. (3.5) assuming 3 du/dz ~ us/ depth and assuming solids volumetric fraction is 0.6; Savage number estimated as the ratio of inertial normal stress to total normal stress; Bagnold number estimated using viscosity of 0.1 Pa s, volume solids fraction 0.6; Nerosion calculated using bulking rate of 1m /m, initial failure 3 6 9 volume of 100 m , tensile strength of 10 Pa, Eeff of 10 Pa, and Df of 0.5 m.

Table 3.2. Dimensions of grooves in Tyee Sandstone from debris flows slope depth (mm) width (mm) length (mm) 0.20 0.7 - 0.8 3.5 - 4.0 36 0.20 2.4 - 3.7 1.4 - 1.8 101 0.08 0.4 - 1.0 2.0 - 3.0 196 0.25 4 - 5 1.5 2200 0.25 5 - 8 1.5 - 2 2160 22 0 0.25 3 - 7 1 800 1.34 2 - 3 1 105

Table 3.3. Site parameters for long-profile evolution with 3.19, assuming a3=0, c2=0.35, n=1 and w=2. a location site lithology erosion rate Ac Atotal A=cx Trigger link magnitude changes along valley long-profiles 2 2 2 (m/a) (m )(m)(m) (NtNti+1…) 1.73 Oregon Coast Range Sullivan Creek #1 sandstone 0.0001 2000 220190 4.07x 1<32>2<104>5<185>6<215>7<339>9 1.11 #2 " " 3000 146672 143x 1<84>2<114>4 1.66 #3 " " 7000 328534 5.45x 1<111>2<154>7<372>8<397>9<536>15 1.46 #4 " " 10000 203178 15.4x 1<142>2<212>4<313>8<514>9 1.45 Scottsburg #1 " 0.0002 4700 269492 17.9x 1<131>2<189>3<248>4<351>8<579>9<726>12<850>13

22 1.62 #2 " " 2000 145472 4.78x 1<148>2<277>3<387>8

1 1.73 #3 " " 5000 281132 4.10x 1<122>2<162>3<193>5<404>8<609>9 1.32 Oregon Cascades Sharp's Creek metavolcanics 0.0001 2000 6192905 83.7x 1<431>2<722>3<845>4<1103>6<1184>12<1460>13<2123>14<2282>15<2348>19<2444>31 1.54 California Coast Range Noyo River greywacke 0.0004 36000 4877795 15.6x 1<144>2<1062>3<1233>7<1341>16<1623>17<1995>47<2229>55<2385>61 1.60 Deer Creek sandstone 0.0003 2000 1768349 9.62x 1<270>2<372>4<555>6<912>13<1152>14<1599>18 1.78 San Gabriels Bear River granodiorite 0.001 3000 7573028 3.23x 1<93>2<153>3<231>4<354>7<411>8<471>12<609>20<992>23<1382>27<1640>29<2102>43<2492>57

Notes: see list of Symbols for definitions of Ac and Atotal; L is length along valley