Incision of Steepland Valleys by Debris Flows

by

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

in

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 ___________________________________________________________

Date

University of California, Berkeley

Fall, 2003

Incision of Steepland Valleys by Debris Flows

Copyright © 2003

by

Jonathan David Stock

ABSTRACT

Incision of Steepland Valleys by Debris Flows

by

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

1

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

2

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

3

valley long-profiles, and that an incision law particular to debris flows is required to

evolve most unglaciated steeplands.

4

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

i

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

ii

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)

iv

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.

v

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.

vi

TABLE OF CONTENTS

INTRODUCTION ................................................................................... 1 CHAPTER 1. VALLEY INCISION BY DEBRIS FLOWS: EVIDENCE OF A TOPOGRAPHIC SIGNATURE ........................... 6 ABSTRACT.................................................................................................. 6 INTRODUCTION.......................................................................................... 7SITE 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

ix

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

x

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

xi

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

xv

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

1

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

2

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

3

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 (

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.

5

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-

6

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

7

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:

-∂z/∂t = K1τb = K1 (ρwgRS)b (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

-∂z/∂t = ωn = (ρwgQS) n (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

8

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

S = [U/K]1/n A-m/n (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

9

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;

10

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

11

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.

12

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

13

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

14

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,

15

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

16

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

17

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

18

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.

19

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

20

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

21

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

22

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.

23

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

(a1Aa2) at large drainage area:

( )210

1 aAas

S+

= (1.5)

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

inversely proportional to curvature [and has units 1/(length2 )a2], and a2 tends towards

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

written:

24

( ) ( ) ( )[ ]

( )311

2221

2121

02

222

1

112)(a

aaa

Aa

AaAaaaAaasAf+

+−−=′′

−−

(1.6)

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 |

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

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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).

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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

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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

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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

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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

plot of erosion rate against a1 in log-log space shows a rough correlation (R2=0.77)

with curvature increasing with erosion rate. Global data in basins of sedimentary

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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

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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 lat