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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