Landscape Development in the Western Transverse Ranges, California: Insights from Mapping, Geochronology, and Modeling

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Authors DeLong, Stephen

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Link to Item http://hdl.handle.net/10150/195640 LANDSCAPE DEVELOPMENT IN THE WESTERN TRANSVERSE RANGES, CALIFORNIA: INSIGHTS FROM MAPPING, GEOCHRONOLOGY, AND MODELING

Stephen Berend DeLong

______

A Dissertation Submitted to the Faculty of the

DEPARTMENT OF GEOSCIENCES

In Partial Fulfillment of the Requirements

For the Degree of

DOCTOR OF PHILOSOPHY

In the Graduate College

THE UNIVERSITY OF ARIZONA

2006 THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE

As members of the Dissertation Committee, we certify that we have read the dissertation

prepared by Stephen B DeLong

entitled “Landscape Development in the Western Transverse Ranges, California: Insights from Mapping, Geochronology, and Modeling”

and recommend that it be accepted as fulfilling the dissertation requirement for the

Degree of Doctor of Philosophy

______Date: 4/03/06 Jon D Pelletier

______Date: 4/03/06 Jay Quade

______Date: 4/03/06 Clem Chase

______Date: 4/03/06 Phil Pearthree

Final approval and acceptance of this dissertation is contingent upon the candidate’s submission of the final copies of the dissertation to the Graduate College.

I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement.

______Date: 4/03/06 Dissertation Director: Jon D Pelletier STATEMENT BY AUTHOR

This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at the University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library.

Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgement of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however; permission must be obtained from the author.

SIGNED: Stephen B DeLong TABLE OF CONTENTS

ABSTRACT……………………………………………………………..………….5

INTRODUCTION……………………………………………………………….…7

PRESENT STUDY……………………………………………………….……….13

REFERENCES………………………………………………………………….…17

APPENDIX A: DATING ALLUVIAL DEPOSITS WITH OPTICALLLY STIMULATED LUMINESCENCE, AMS 14C AND COSMOGENIC TECHNIQUES, WESTERN TRANSVERSE RANGES, CALIFORNIA, USA………………………………………………………………………….…….20

APPENDIX B: COUPLED ALLUVIAL FAN AND AXIAL CHANNEL DEVELOPMENT IN CUYAMA VALLEY, CALIFORNIA…………………….50

APPENDIX C: GEOMORPHIC FATE OF LATE CENOZOIC BASINS IN SOUTHERN CALIFORNIA: AN EXAMPLE FROM THE UPPER CUYAMA VALLEY……………………………………………………….……..66

APPENDIX D: BEDROCK LANDSCAPE DEVELOPMENT MODELING: CALIBRATION USING FIELD STUDY, GEOCHRONOLOGY AND DEM ANALYSIS……………………………………………………………………..…96 5

ABSTRACT

Understanding how climate and tectonics have interacted to shape current landscape configuration requires application of the latest geomorphological techniques.

This dissertation presents results from a combination of field mapping, geochronology, and numerical landscape development modeling. The papers contained here focus on studies from Cuyama Valley, California, at the junction of the Coast Ranges and Western

Transverse Ranges in southern California.

Combining field observation with three geochronological techniques has led to a detailed understanding of the late Quaternary alluvial history of Cuyama Valley. The alluvial history, in turn, allows for a better understanding of important events in the history of landscape development. In the western Cuyama Valley, the timing and morphology of alluvial fans record both climatic forcing in the form of variable sediment supply from drainage basins, and tectonic forcing from ongoing tectonically driven incision of the axial Cuyama River. Fan-terrace surfaces are subparallel (older surfaces are slightly steeper) and offset systematically in relation to their ages, suggesting response to ongoing base-level incision and fluctuation in sediment supply. The fans aggraded during relatively cool and wet climate of the last glacial period, which is out-of- phase with the regional model developed in nearby desert regions.

In the upper Cuyama Valley, deposition in the Cuyama sedimentary basin ceased in the mid-Pleistocene, after which basin fill was uplifted, deformed, and beveled, forming a low-relief erosion surface on which the alluvium of San Emigdio Mesa was

deposited. Subsequent fluvial drainage network development formed the Cuyama badlands by incising into the deformed Cuyama basin sediments.

The history of the upper Cuyama Valley was used to calibrate a numerical landscape development model. Uplift rate U, bedrock erodibility K, and landslide threshold-slope Sc are related to steady-state relief, hypsometry, and drainage density for a wide range of synthetic topographies produced by a stream-power-based landscape development model. A combination of fluvial channels and threshold-slopes occurs for only a relatively narrow range of U/K between 10 and 5000 m·kyr/kyr. Using measured values for hypsometric integral, drainage density and relief, the U/K value can be further constrained, enabling K to be determined if U is known.

INTRODUCTION

This dissertation addresses fundamental questions that relate climate and tectonics to landscape development. Though the dissertation is a compilation of manuscripts with coauthors, the research design and execution is largely that of the first author.

Appendix A presents results of an intercomparison of geochronological techniques as applied to alluvial deposits. Accurate age-determination of alluvial deposits in arid and semi-arid climates is possible using a number of techniques; each with its own limitations. Most widely applied are radiocarbon dating, cosmogenic radionuclide surface-exposure dating, and optically-stimulated luminescence dating.

Radiocarbon (14C) dating relies on the presence of organic material in an interpretable context within the alluvial deposit, which is rare in dry environments. Cosmogenic radionuclide (CRN) techniques require determination of the effects of pre-depositionally inherited radionuclides and post-depositional erosion of the target deposit, and proper calibration of isotope production rates. Optically-stimulated luminescence (OSL) dating shows great promise, but is still regarded as developmental in its application to fluvial deposits. I present results of a “blind” comparison of all three techniques (with emphasis on direct comparison of radiocarbon and OSL dating by two independent laboratories) applied to late-Pleistocene to late-Holocene axial-fluvial and alluvial-fan deposits in

Cuyama Valley, in the western Transverse Ranges, California, USA. This study serves to highlight both limitations and successful applications of these techniques within a detailed case-study. This is not intend to be a comprehensive review of details of each dating technique; for a complete review of methodology and application of each

technique the reader is directed to publications such as Gosse and Phillips (2001) for

CRN techniques, Wallinga (2002) and Aitken (1998) for OSL dating, and Faure (1986)

for radiocarbon dating. This paper also does not detail the geologic interpretations made

within the wider scope of the study, but instead focuses on the comparison of the

geochronologic data.

Appendix B presents geological interpretations made from the some of the results presented in Appendix A as well as additional field mapping and topographic analysis of alluvial fans in Cuyama Valley, California. Suites of inset alluvial fan surfaces found on mountain piedmonts in arid regions record episodic alluvial episodes caused by changes in upstream sediment and water flux. These episodes of increased piedmont sedimentation (and intervening times of fluvial entrenchment and lateral erosion) are widely thought of as caused by cyclic climate change. In regions where past climates have acted on distinct catchments in similar ways, these flights of terraces are often assumed to be age-equivalent. The causes of these alluvial episodes can be diverse. In desert regions (Wells, et al., 1987; Bull, 1991; Reheis et al., 1996; Harvey, et al., 1999;

Ritter, et al., 2000; McDonald et al., 2003) and in at least one semi-arid to subhumid region (Weldon, 1986), changing hillslope vegetation and precipitation regime (increased storm intensity) during and after cool/wet to warm/dry climate transitions are most often cited as causing alluviation. In glaciated regions, drainage basin erosion by valley glaciers led to piedmont alluviation during glacial advances (Ritter et al., 1995; Gillespie et al., 1994, Harvey, 2002). Also sometimes cited is alluviation from unglaciated or minimally glaciated drainage basins during cool/wet climates due to increased effective

precipitation, fluvial transport, and possibly increased freeze-thaw and periglacial processes on high-elevation hillslopes. This is cited in the northern Basin and Range from catchments with small glaciers (Pierce and Scott, 1982), in southern Spain in what is now Mediterranean climate (Harvey, 2002), and from small, high-elevation catchments in southern California (Bull, 1991). Our limited understanding of the spatial distribution of these (and possibly other) seemingly conflicting causes of piedmont alluviation has limited our ability to put forth predictive conceptual models for the timing of alluvial episodes in diverse settings. Studies outside of desert regions, with a few exceptions are particularly lacking, which leads to the possibility of application of conceptual models of desert alluvial fan development to diverse settings in which they may not be appropriate.

Downstream base-level changes should lead to distinct topographic signatures that may replace or superpose climatic signatures in areas where axial-fluvial, marine or lacustrine systems interact with piedmonts, or regional or fault-specific uplift is occurring

(Harvey and Wells, 2002). In order to (1) better understand the causes of episodic alluviation beyond desert regions, and (2) to expand our understanding of how regional uplift and an incising axial fan-toe channel affect the topographic configuration of alluvial fan terraces, we mapped, described, and dated the Quaternary deposits of

Cuyama Valley, California.

Appendix C presents results from geochronology and field observation from the

Upper Cuyama Valley. The transition from landscape dominated by long-lived regional- scale late Cenozoic depositional basins to the formation of smaller complex structural and topographic basins occurred relatively recently in parts of southern California (Kellogg

and Minor, 2005; Page et al., 1998). There is no generally accepted model for the

geomorphic fate of these young basins, many of which stopped receiving sediment as recently as the Pleistocene. Furthermore, the details of the complex events that have created the dramatic landscapes of southern California are difficult to constrain due to the challenge of geochronology over the relevant timescales of 103 to 105 yrs. These events

can include the transition from basin filling to incision; episodic alluviation occurring at

different positions in the landscape; increasing tectonic deformation, often

accommodated on an increasingly complex structural array; and progressive regional

uplift that is spatially variable across multiple structural boundaries.

An appropriate case study in our efforts to better understand late Cenozoic landscape

development in southern California is the upper Cuyama Valley, located at the junction

between the southern Coast Ranges and western Transverse Ranges, where changes in

tectonic regime over the last few million years include increased transpression in the Big

Bend region of the San Andreas fault, expressed by complex contractional faulting and folding (Kellogg and Minor, 2005; Atwater and Stock, 1998; Page et al. 1998; Ellis, et al.

1993; White, 1992). A striking landscape feature in this area are the Cuyama Badlands, characterized by deeply incised valleys and gullied slopes cut into Neogene sedimentary strata. Associated with these incised basin strata are spatially variable tectonic deformation, erosional unconformities covered by Quaternary alluvium, and the regionally significant Big Pine fault.

Our objectives in this study were to determine the history and timing of landscape development in the upper Cuyama Valley region from the late stages of deposition in the

Cuyama basin to the present time, and to use the age of offset fluvial terraces to evaluate

the strain rate of the eastern Big Pine fault along the base of Pine Mountain. To do this,

we synthesized the current understanding of the post-Miocene history of the area and

applied cosmogenic radionuclide (CRN) surface-exposure dating and optically stimulated

luminescence (OSL) burial dating techniques to several late Quaternary alluvial deposits that are useful geologic recorders of events leading up to the current landscape configuration.

Appendix D presents the results of an effort to use the history of the upper

Cuyama Valley to calibrate a numerical bedrock landscape development model. The stream-power-law (or similar shear-stress-based methods) forms the foundation for many bedrock landscape development models (e.g., Howard, 1994; Whipple and Tucker,

1999). When stream-power-based bedrock channel development models are coupled

with hillslope process models that include threshold-landsliding and/or hillslope diffusion

components, three-dimensional landscape development modeling is possible (e.g., Tucker

et al., 2001; Howard, 1994). We were motivated by the need to understand how each

parameter in bedrock landscape development models affect model topography, and the

need to develop general techniques for calibrating landscape development models using

geologic and morphometric analyses. This motivation led us to apply a landscape

development model with a minimum of free parameters in an effort at calibration using

geologic and morphologic data from a field site in southern California.

Wide-ranging estimates for model parameters are often used in bedrock landscape

development models. Stock and Montgomery (1999) proposed a range in stream-power

law erodibility coefficient K over five orders of magnitude for varying rock types, and this wide range is often used in other modeling studies. Because the stream-power law is very sensitive to the value of K and because Snyder et al. (2000) proposed a linkage between uplift rate and K, we were interested in creating a more specific calibration technique for the stream-power law that relies on geologic constraints of uplift rate, and morphometric landscape analyses to calibrate K. Snyder et al. (2000) also provided insight regarding use of landscape morphometry to constrain the values of stream-power law exponents m and n. By integrating these studies’ findings into a fully-coupled landscape modeling environment, we hoped to further refine our understanding of the effect of model parameters as a step towards improving our ability to calibrate even more sophisticated landscape development models.

PRESENT STUDY

The methods, results, and conclusions of this study are presented in the papers appended to this dissertation. The following is a summary of the most important findings in this document.

Our multi-technique geochronological approach led to a detailed understanding of the alluvial chronology in Cuyama Valley, CA. In particular, OSL showed great utility in dating samples of all ages in this study. OSL is useful in difficult-to-calibrate radiocarbon age ranges, and in environments where detrital-aged charcoal is common or no reliable charcoal can be found. CRN techniques were moderately successful, but given our sampling strategy and limited number of samples, it was difficult to assess accuracy. Radiocarbon dating continues to show its effectiveness at providing alluvial stratigraphic ages, and though not perfect, single-grain OSL dating should now be thought of as a routine method for age-estimation of dryland alluvial-fan and axial-fluvial deposits if latest methods are employed carefully.

Though late Quaternary alluvial-fan development in desert regions of the southwestern U.S. is largely well understood and similar on a regional scale, the coupled piedmont-axial system in Cuyama Valley, CA is striking in its spatial and temporal characteristics. The preservation of at least five latest-Quaternary alluvial surfaces suggest that either drainage basins in the Sierra Madre range were particularly sensitive to cyclic climate fluctuation, or cut-and-fill cycles on the piedmont were driven by both upstream sediment supply and downstream incision driven by the axial system. Fans in

Cuyama Valley aggraded substantially during the last glacial period. A possible cause of

this was increased saturation-driven hillslope failure and sediment transfer to the

piedmont during a cool and wet climate. The late Pleistocene and Holocene has been a

time of relative stability of the north-facing, chaparral-covered slopes. The Pleistocene-

Holocene transition did appear to lead to local fan aggradation where material is sourced

from the now-unvegetated slopes of unconsolidated, possibly lacustrine, Morales

Formation on the Sierra Madre piedmont. These findings suggest further studies of piedmonts in diverse climatic and tectonic zones in the southwestern U.S. are warranted, and caution must be used when applying widely accepted models of alluvial-fan evolution beyond the regions in which they have been thoroughly tested.

Our new understanding of the upper Cuyama River geomorphic system provides a working model for the evolution of other late Cenozoic basins in coastal California.

These structural basins (such as the Salinas, Lockwood Valley, Ventura, Carrizo Plain,

Ridge, etc.) are often long-lived, but have been profoundly affected by late Cenozoic tectonic and climatic changes. Kellogg and Minor (2005) highlight the tectonic changes in adjacent Lockwood Valley, primarily using observations of Pliocene and earlier structural geology and stratigraphy. Similar traditional mapping-based approaches can be coupled with our increasing ability to establish timing of Quaternary events to lead to a rich understanding of the interactions of tectonics, erosion, deposition and climate over multiple timescales. While timing, environments of deposition, and physiography may differ greatly between basins, it seems likely that most tectonically active sedimentary basins in southern California record: 1) increased clastic deposition as contractional deformation increased beginning in the Pliocene; 2) increased tectonic uplift and

structural relief across increasingly abundant and concentrated structures within and

bordering the depositional basins, leading to basin “extinction” as basin-filling was

replaced by incision, and 3) significant climatically-controlled late Pleistocene alluviation

over a wide variety of erosional surfaces, allowing for establishment of timing in these

landscapes.

Additionally, we propose a latest-Quaternary fault-slip estimate on the Big Pine

fault of 0.7 m/kyr. This serves as a reminder of both the ongoing nature of tectonic

landscape development and the seismic potential of historically aseismic reverse faults

throughout southern California.

Three-dimensional modeling that utilizes the stream-power law for fluvial erosion

and threshold-landsliding for hillslope development allows for careful analysis of how

model parameters such as uplift rate, bedrock erosivity, threshold-slope, channel concavity and time effect landscape development. We suggest that by careful comparison of (1) actual landscape morphology via field and DEM analysis, and (2) actual landscape development process-rates from geochronology to synthetic topography derived from a numerical model with carefully controlled parameters, we can calibrate modeling efforts, and in particular, narrow our range of estimates for K. We suggest that

characterization of m/n, landslide threshold-slope, mean elevation, topographic relief, drainage density and hypsometric integral are necessary for comparison of actual topography to synthetic topography. In our study area three late-Cenozoic sedimentary units are estimated to have K values on the order of 0.3 to 0.09 m0.2-0.4kyr-1. We address

possible complications from temporal and spatial scaling, and suggest that even complex

and/or non-steady-state real topography can be compared to idealized synthetic topography with some measure of success. Work on widely different rock types and spatial scales will be necessary to further validate our results.

REFERENCES

Atwater, T., and Stock, J., 1998. Pacific-North America plate tectonics of the Neogene southwestern United States; an update, in Ernst, W.G. and Nelson, C.A., eds, Integrated earth and environmental evolution of the southwestern United States; The Clarence A. Hall, Jr. Volume: Columbia, Maryland, Bellwether Publishing, 393-420.

Aitken, M.J., 1998. An Introduction to Optical Dating. Oxford University Press. Oxford.

Bull, W.B., 1991 Geomorphic responses to climatic change. Oxford, Oxford University Press, London. 326 p.

Ellis, B.J., Levi, S., and Yeats, R.S., 1993. Magnetic stratigraphy of the Morales Formation: Late Neogene clockwise rotation and compression in the Cuyama basin, California: Tectonics, v. 11, 1170-1179.

Faure G., 1986. Principles of Isotope Geology. NewYork:. Wiley.

Gillespie, A.R., Burke, R.M. and Harden, J.W., 1994, Timing and regional paleoclimatic significance of alluvial fan deposition, western Great Basin. Geological Society of America Abstracts with Programs, 26, 6, A150–A151.

Gosse, J.C. and Phillips, F.M., 2001. Terrestrial in situ cosmogenic nuclides: theory and application. Quaternary Science Reviews, 20(14): 1475-1560

Harvey, A.M., Wigand, P.E., and Wells, S.G., 1999, Response of alluvial fan system to the late Pleistocene to Holocene climatic transition: Contrasts between the margins of pluvial Lakes Lahontan and Mojave, Nevada and California, USA: Catena v. 36, p. 255- 281.

Harvey, A.M., 2002, The role of base-level change in the dissection of alluvial fans: case studies from southwest Spain and Nevada. Geomorphology, v. 45, p. 67-87.

Harvey, A.M. and Wells, S.G., 2003, Late Quaternary variations in alluvial fan sedmentologic and geomorphic processes, Soda Lake basin, eastern Mojave Desert, California, in Enzel, Y., Wells, S.G., and Lancaster, N., eds. Paleoenvironments and paleohydrology of the Mojave and southern Great Basin Deserts: Boulder, Colorado, Geological Society of America Special Paper 368, p. 207-230.

Howard, A.D., 1994, A detachment-limited model of drainage basin evolution: Water Resources Research, v. 30, no. 7, p. 2261-2285

Kellogg, K.S., and Minor, S.A., 2005. Pliocene transpressional modification of depositional basins by convergent thrusting adjacent to the “Big Bend” of the San

Andreas fault, An example from Lockwood Valley, southern California; Tectonics, v. 24, 1-12.

McDonald, E.V., McFadden, L.D., and Wells, S.G., 2003, Regional response of alluvial fans to the Pleistocene-Holocene climatic transition, Mojave Desert, California, in Enzel, Y., Wells, S.G. and Lancaster, N., eds., Paleoenvironments and paleohydrology of the Mojave and southern Great Basin Deserts: Boulder, Colorado, Geological Society of America Special Paper 368, p. 19-205.

Page, B.M., Coleman, R.G., Thompson, G.A., 1998, OVERVIEW: Late Cenozoic tectonics of the central and southern Coast Ranges of California. Geological Society of America Bulletin 110: 846-876

Pierce, K.L., and Scott, W.E., 1982, Pleistocene episodes of alluvial-gravel deposition, southeastern Idaho, in Bonnichsen, B., and Breckenridge, R.M., eds., Cenozoic geology of Idaho: Idaho Bureau of Mines and Geology Bulletin v. 26, p. 685-702.

Reheis, M.C., Slate, J.L., Throckmorton, C.K., McGeehin, J.P., Sarna-Wojcicki, A.M., and Dengler, L., 1996, Late Quaternary sedimentation on the Leidy Creek fan, Nevada- California: Geomorphic responses to climate change: Basin Research, v. 12, p. 279-299.

Ritter, J.B., Miller, J.R., and Husek-Wulforst, J., 2000, Environmental controls on the evolution of alluvial fans in Buena Vista Valley, North Central Nevada, during late Quaternary time. Geomorphology, v.36, p. 63-87.

Ritter, J.B., Miller, J.R., Enzel Y., and Wells, S.G., 1995, Reconciling the roles of tectonism and climate in Quaternary alluvial fan evolution. Geology, v. 23, p. 245-248.

Tucker, G.E., Lancaster, S.T., Gasparini, N. M., and Bras, R. L., 2001, The Channel- Hillslope Integrated Landscape Development (CHILD) model: in Landscape Erosion and Evolution Modeling, edited by Harmon R. S. and Doe III W. W., pp. 349–388.

Snyder, N.P., Whipple, K.X., Tucker, G.E., and Merritts, D.J., 2000, Landscape response to tectonic forcing: Digital elevation model analysis of stream profiles in the Mendocino triple junction region, northern California: Geological Society of America Bulletin, v. 112, no. 8, p. 1250-1263.

Stock, J.D., and Montgomery, D.R., 1999, Geologic constraints on bedrock river incision using the stream power law: J. Geophys. Res., v. 104, no. B3, p. 4983-4993.

Wallinga, J. 2002. Optically stimulated luminescence dating of fluvial deposits: a review. Boreas, 31, pp. 303–322.

Weldon, R.J., 1986, Late Cenozoic geology of Cajon Pass; implications for tectonics and sedimentation along the San Andreas fault. Ph.D. thesis. California Institute of Technology.

Wells, S.G., McFadden, L.D., and Dohrenwend, J.C., 1987, Influence of late Quaternary climatic change on geomorphic and pedogenic processes on a desert piedmont, eastern Mojave Desert, California: Quaternary Research, v. 27, p. 130-146.

Whipple, K.X., and Tucker, G.E., 1999, Dynamics of the stream-power river incision model: Implications for height limits of mountain ranges, landscape response timescales, and research needs: J. Geophys. Res., v. 104, no. B8, p. 17661 - 17674.

White, L.A., 1992. Thermal and unroofing history of the western Transverse Ranges, California: Results from apatite fission track thermochronology. Ph.D. Thesis, University of Texas, Austin.

APPENDIX A

Submitted to Quaternary Geochronology, 2005

DATING ALLUVIAL DEPOSITS WITH OPTICALLLY-STIMULATED LUMINESCENCE, AMS 14C AND COSMOGENIC TECHNIQUES, WESTERN TRANSVERSE RANGES, CALIFORNIA, USA.

DeLong, Stephen B.1 Department of Geosciences, University of Arizona, 1040 E 4th Street, Tucson AZ 85721, USA

Arnold, Lee, J. Oxford Luminescence Research Group, School of Geography and the Environment, University of Oxford, Mansfield Rd, Oxford OX1 3TB, UK

Abstract

In an effort to better understand chronology of alluvial episodes in Cuyama Valley in the western Transverse Ranges of California, USA, we employed optically-stimulated luminescence, radiocarbon and cosmogenic radionuclide surface exposure dating methods. Twenty-one optical dates ranging from 0.01 to ~27 ka were obtained from exposures of late Holocene axial-fluvial deposits, Pleistocene-Holocene alluvial-fan deposits, and axial-fluvial sands interbedded within a late-Pleistocene alluvial-fan. These were cross-checked with thirty-seven AMS radiocarbon dates from charcoal and wood from within fluvial material and five 10Be surface exposure dates from boulders on alluvial-fan surfaces. The OSL results show generally good stratigraphic consistency, logical comparison with the radiocarbon and cosmogenic data, and appear to be the best method for accurate dating within deposits of this nature because suitable material is fairly easy to find in these environments. The radiocarbon data contained numerous

“detrital ages”, but well-bedded lenses of apparently in situ or minimally-transported

1 Corresponding author: [email protected] tel. 520-621-6003

charcoal provide reliable age estimates for the fluvial material. Radiocarbon dating of

detrital charcoal in the older alluvial-fan deposits was problematic. Our cosmogenic

surface-exposure dating was consistent stratigraphically and with our other data, but we were unable to determine its accuracy due to the limited number of samples and the possibility of inherited radionuclides and post-depositional erosion. In light of our results, we suggest that OSL dating using the latest analytical techniques combined with rigorous methods for analyzing paleodose estimates is reliable and of increasing utility in otherwise difficult-to-date coarse alluvial environments in the southwestern United States and elsewhere.

Keywords: Alluvial fans; fluvial sediment; optically-stimulated luminescence dating; radiocarbon dating; cosmogenic surface-exposure dating; Cuyama Valley, CA

1. Introduction

Accurate age-determination of alluvial deposits in arid and semi-arid climates is possible using a number of techniques; each with its own limitations. Most widely applied are radiocarbon dating, cosmogenic radionuclide surface-exposure dating, and

optically-stimulated luminescence dating. Radiocarbon (14C) dating relies on the

presence of organic material in an interpretable context within the alluvial deposit, which

is rare in dry environments. Cosmogenic radionuclide (CRN) techniques require

determination of the effects of pre-depositionally inherited radionuclides and post-

depositional erosion of the target deposit, and proper calibration of isotope production

rates. Optically-stimulated luminescence (OSL) dating shows great promise, but is still regarded as developmental in its application to fluvial deposits. This paper presents results of a “blind” comparison of all three techniques (with emphasis on direct comparison of radiocarbon and OSL dating by two independent laboratories) applied to late-Pleistocene to late-Holocene axial-fluvial and alluvial-fan deposits in Cuyama

Valley, in the western Transverse Ranges, California, USA. This study serves to highlight both limitations and successful applications of these techniques within a detailed case-study. This paper does not intend to be a comprehensive review of details of each dating technique; for a complete review of methodology and application of each technique the reader is directed to publications such as Gosse and Phillips (2001) for

CRN techniques, Wallinga (2002) and Aitken (1998) for OSL dating, and Faure (1986) for radiocarbon dating. This paper also does not detail the geologic interpretations made within the wider scope of the study, but instead focuses on the comparison of the geochronologic data.

2. Geological setting and description of lithologic units

Cuyama Valley is located at the western end of the western Transverse Ranges where they meet the southern Coast Ranges in southern California, USA, (Fig. 1). The modern climate is semi-arid (MAP = 15 to 25 cm, Mediterranean regime) and hot (MAT = 10 to

15C). Cuyama Valley is a relatively young structural valley, formed by transpression associated with the San Andreas Fault Zone which has increased since ca. 3 Ma (Ellis et

al. 1993). The valley is bounded by the Caliente Mountains to the north and the larger

Sierra Madre Mountains to the south (Fig. 2). The Sierra Madre piedmont is mosaic of

deformed and eroded late-Cenozoic basin-fill units capped in places by late-Quaternary

alluvial fans and their well-preserved planar geomorphic surfaces. The axial Cuyama

River is a meandering ephemeral channel that is incised up to 12 meters below late-

Holocene axial fluvial-terrace surfaces for over 50 km. The focus of this study was on

age-determination of the late-Pleistocene alluvial-fan deposits on the Sierra Madre

Mountain piedmont and the suite of axial-fluvial deposits along the Cuyama River.

On the Sierra Madre piedmont, there are five extensive and well-preserved alluvial- fan units preserved as a sequence of planar depositional geomorphic surfaces. We classified these as Qaf1-Qaf5 from oldest to youngest. Deposits capped by these geomorphic surfaces tend to be coarse-grained, clast-supported and bedded, indicative of fluvial processes. Sandy beds suitable for OSL dating were rare, though a large road cut through a Qaf4 unit revealed both sandy lenses in alluvium and interbedded sandy axial material. Unit Qaf5 was markedly different than the other units, as it was apparently sourced locally from reworking of a large exposure of Pleistocene lacustrine or shallow- water deposits, giving it a finer sandy texture. Organic material suitable for radiocarbon dating of these deposits is rare.

The units oriented along the axis of the valley are dominated by silty and sandy bedded sediment. Exposures of axial material are widespread over >50km of the Cuyama

River. The stratigraphy has been simplified for this paper, and we present data from four

sedimentary units, Qa1-Qa4, which represent the majority of exposed sediments preserved as axial terraces along the Cuyama River.

This paper presents geochronologic comparisons from three axial-fluvial exposures and two alluvial-fan exposures. The stratigraphic interpretations at the sites used in this paper rely on a larger dataset of radiocarbon ages and several more described stratigraphic sections from elsewhere in the study area. Detailed description of these are beyond the scope of this paper and will be presented elsewhere.

3. Methods

3.1 OSL dating

Bedded waterlain sediments were sampled using opaque ABS pipe without exposing the sediment to light during sampling. Laboratory analysis was carried out at Oxford

University by the second author. Refinement of pure coarse-grained quartz separates was undertaken using the standard laboratory preparation procedures outlined in Aitken

(1998). Individual equivalent dose (De) estimates were measured using small aliquots

(100-300 grains/disc) for all samples except 070402.01 and single grains for all samples

OSL signals were detected using a blue-sensitive EMI9235QA photomultiplier tube fitted with two U-340 filters.

Single grain and single aliquot De estimates were both calculated using the SAR protocol developed by Murray and Wintle (2000). The SAR measurement conditions adopted in this research follow those used by Arnold et al. (this issue). Single aliquot De estimates were accepted for further analysis if they displayed (i) recycling ratios within

10% of unity, (ii) OSL-IR depletion ratios >0.9 (Duller et al, 2003), (iii) thermal transfer

<5% of the natural signal. Single grain De’s were only accepted where (i) the recycling ratio Lx/Tx points were consistent with each other within their 1- errors, (ii) OSL-IR depletion ratios were >0.9, (iii) thermal transfer was <10% of the natural signal, (iv) the error on the natural test dose signal was <20%, (v) calculated De uncertainty was <30%,

(vi) the natural signal intensity was >3 times the standard deviation of the late-light background signal. The number of grains/aliquots measured and accepted can be found in

Table S1. Sample bleaching characteristics were assessed from the accepted De populations using the decision procedures approach proposed recently by Bailey and

Arnold (in press). For each sample, the final burial dose estimate was calculated using the age model deemed most suitable according to this statistical decision procedure.

Environmental dose rates were calculated using a combination of field gamma spectrometry (FGS) and inductively coupled mass spectrometry (ICP-MS). External - dose rates were calculated using FGS for all samples and ICP-MS for all samples except

OSL18-OSL22. External -dose rate contributions were calculated using ICP-MS measurements for all samples. Cosmic ray dose rate contributions were determined using the calculations of Prescott and Hutton (1994). Present-day water content values were

assumed to be representative of those pertaining to the full burial period, and were assigned relative uncertainties of ±50%.

3.2 Radiocarbon dating

Charcoal fragments from alluvial deposits were sampled for radiocarbon dating.

Preference was given to charcoal that either appeared to have burned in situ, or deposited as a large concentration, indicating minimal fluvial reworking, as these were most likely to have radiocarbon ages that represent the age of the surrounding deposit. These are referred to as “charcoal layers” in Table S3. “Detrital” charcoal, which was usually isolated fragments of charcoal within fluvial material, was also dated, though this type of

material has the potential to have ages well older than the surrounding sedimentary

deposit. In one case wood was dated, and one sample of base-soluble humates from

charcoal was dated. Samples were subjected to physical removal of visible contaminants,

a standard ABA (acid-base-acid) pretreatment, bulk combustion and CO2 extraction and

graphite target preparation under vacuum at the University of Arizona Desert Laboratory.

AMS analysis of graphite targets were performed at the NSF/Arizona AMS Facility.

Sample radiocarbon ages <21 ka were calibrated to 2-sigma calendar years using Reimer

et al. (2004) and older samples were calibrated according to Fairbanks, et al. (2005).

While proposed calibrated ages have been included in figures without error values, wide

ranges in calibrated ages exist for most samples (as reported in Table S3), and caution

must be used when using calibrated ages.

3.3 CRN surface exposure dating

Coarse-grained, extremely well-indurated sandstone boulders partially embedded in the alluvial surfaces of the Sierra Madre piedmont were sampled for 10Be surface exposure dating. These were selected with the criteria of showing no obvious signs of spallation, weathering, or past burial and excavation. Isotopic analysis of 10Be abundance in quartz was carried out at Purdue University’s PRIME Lab. These data were corrected for sample thickness and topographic shielding, and were then corrected for latitude, longitude, elevation, and past geomagnetic effects following Pigati and Lifton (2004). In order to use the most accurate cosmogenic production rate for 10Be, we also corrected the raw data of Stone’s (1998) Younger Dryas-aged samples from Scotland using the techniques in Pigati and Lifton (2004). From this we took the long-term integrated high- latitude sea-level 10Be production rate to be 4.35 atoms/g/yr. Following Partridge et al.

(2003) we use the meanlife of 10Be to be 1.93 ± 0.10 Ma, for discussion of ambiguity related to this value see note 34 therein. No corrections were made for either sample erosion or pre-depositionally inherited radionuclides. This leads to increased uncertainty in the relationship of exposure age to the age of the geomorphic surface, and the need for independent verification.

4. Results

Table S2 contains all OSL results, Table S3 contains radiocarbon results, and

Table S4 contains CRN results. The data are described at each exposure in the following sections and shown visually in the figures. In the figures, single-grain OSL ages are presented when available, though both single-grain and single-aliquot ages are included in Table S2 when available. Comparison of radiocarbon ages to OSL ages is somewhat problematic. Table S3 contains radiocarbon results including ages in 14C years, 2-sigma

calibration ranges, the median probability age in calendar years B.P. (before 1950), and

also our proposed age before 2002 which is simply the median probability age plus fifty

years rounded to the nearest 10 years. On figures, the “proposed age before 2002” is

given in calendar years without error estimates. OSL and CRN dates are presented as ka

with analytical error.

4.1 Axial exposure A1

Exposure A1 is a 12-meter arroyo-wall exposure of bedded sands, silts, and minor

gravel with no apparent soil development at ‘km 5’ (as measured from the upstream

extent of incised arroyo channel) (Fig. 3). This exposure has a disconformity halfway

down which is evidenced by a weak paleosol, and a change in sediment character from

silty, moderately consolidated material (Qa2) to overlying looser sandy material (Qa3).

Age control on this section is from three AMS radiocarbon dates and one OSL date near

the top of the section. The two younger radiocarbon dates calibrate from anywhere

between 0 to 350 calendar years before present, so OSL appears to be more useable in

this age range. However, with this caveat, the OSL and radiocarbon ages are consistent.

4.2 Axial exposure A2

Exposure A2 is at ‘km 15’, and is a wide exposure of 10-meter-thick bedded silts and

sands capped by a weakly-developed fluvent soil. At this location, we made considerable

effort to compare OSL and 14C results. The unit is made up of variable thicknesses of

Qa2 and Qa1 that overly each other across a long-wavelength angular unconformity marked by truncated bedding, paleo-hillslope deposits, a distinguishing paleosol, and onlapping overlying strata. Age control on this section is from fifteen AMS radiocarbon dates and seven OSL dates as illustrated in Figure 4.

4.3 Axial exposure A3

Exposure A3 is a 12-meter-thick conformable sequence of bedded silts, sands, gravel and cobbles capped by a weakly-developed fluvent soil at ‘km 25’. The entire exposure is unit Qa2. Age control is provided by four AMS radiocarbon dates and a single OSL sample as shown on Figure 5. The single-grain OSL date does not overlap within error with the radiocarbon dates – it is 2-300 years older. This could be from a failure of the age model determination criteria (the CAM model produces the oldest age estimate of the

six age models presented in Bailey and Arnold, (in press). A historical flood deposit adjacent to this exposure gave a single-grain OSL age of 0.01 ka and a radiocarbon age

(AA53752) of 450 cal. yrs. B.P. This radiocarbon age is certainly detrital, but could be as young as ~55 cal. yrs B.P. due to the shape of the calibration curve in this time-range.

Though we cannot be certain, we think that this deposit is the record of the significant El

Nino flood event of 1998 (Bowers, 2001). We base this conclusion on analysis of repeat aerial photograph analysis, streamflow data, and the youthful expression of the deposits in the field. This interpretation supports the utility of single-grain OSL for dating very young fluvial deposits.

4.4 Alluvial fan exposure AF1

Exposure AF1 is a gully formed in a broad swale of unit Qaf5 and possibly underlying Qaf4 (Fig. 6). This is the lowest alluvial fan surface on the Sierra Madre piedmont. Soil formation is noticeable in this dominantly fine-grained deposit, and has eliminated much of the original fluvial bedding in upper portions of the exposure. We sampled below the primary pedogenic zone from bedded sands. Exposure of sediments is generally poor, making stratigraphic interpretation difficult. Age control is provided by eight detrital radiocarbon samples which show little coherence, and four OSL dates which fall into two groups. Another OSL (070402.01) of 22.29 ± 2.12 ka from an exposure of Qaf5 or Qaf4 ~5km upstream from a sandy lens in a bouldery deposit is comparable to the oldest OSL date from the gully (OSL19) of 26.04 ± 1.97 ka. Both are

found below local unconformities in distinctively coarser material, and are likely strath remnants of Qaf4-aged material. Further discussion of the other scatter in these data can be found in Section 5.

4.5 Alluvial fan exposure AF2

Exposure AF2 is through unit Qaf4 (Fig. 7). These exposures are of interbedded tributary-derived boulder alluvial fan material and sandy axial material underlying an extensive and very well-preserved alluvial-fan surface. The fan and axial materials are easily distinguished by reddish-brown sandstone-dominated nature of the fan material and the polymict, granite-bearing nature of the finer axial material. Age control is from six OSL dates, three radiocarbon dates and two CRN surface-exposure dates. While the

OSL dates show excellent stratigraphic coherence, the radiocarbon and CRN dates show some scatter, as discussed in Section 5.

4.6 Additional alluvial fan CRN surface exposure sample sites

Two CRN ages (C011204.01 and C11204.03) were obtained from Qaf1, which is the highest and oldest extensive planar alluvial fan surface in our study area. The ages were

69±2 and 91±4 ka, indicating that either the older sample preserved inherited CRNs or the younger sample was eroded or shielded since deposition, or some combination of both. Since both appear extremely erosion-resistant and well-embedded in the alluvial

surface, we favor the former. One CRN age from a Qaf3 surface (C070403.05) gave an

age of 29.3±2.7 ka which is stratigraphically consistent. Our best estimates of ages of all

alluvial-fan surfaces fit a linear, survey-derived, age-elevation relationship determined by

projecting surface slope to their axial-valley intersection point. Assuming a relatively

constant axial-incision-rate supports the integrity of our chronology.

5. Discussion

Overall, agreement between the dating methods is good. The OSL dates appear to

have more stratigraphic consistency than the radiocarbon dates, especially for older

materials. This is unsurprising, given that radiocarbon dating in the fluvial environment

can be subject to a number of problems. The coupled OSL-radiocarbon approach allows for cross-checking of each dating method, and given enough sample density, conclusions

can be made about the accuracy of particular dates. Exposure A2 in particular is an

example of how both dating a large number of radiocarbon samples and cross-checking

with OSL and reliable “charcoal layers” can identify “detrital” radiocarbon ages, leading

to an increased understanding of actual stratigraphic ages. This could also be

accomplished by employing more careful radiocarbon sampling criteria than we did,

however this is almost always impossible in fluvial environments, where isolated detrital

charcoal is the norm.

Use of isolated and often small charcoal fragments to date older alluvial fan deposits

was problematic. Both AF1 and AF2 exposures would be less interpretable without the

complementary OSL dates. More sophisticated radiocarbon preparation such as ABOX-

SC (Bird, et al., 1999) perhaps could have improved the accuracy of our older

radiocarbon dates from the Pleistocene alluvial fans by better removing contaminants.

The five CRN surface-exposure ages from boulders on alluvial surfaces would also be difficult to rely on independently of other data, but in the context of our larger dataset, we conclude that only samples C070503.01 and C11204.03 were subject to significant inherited CRN contamination. This suggests that moderately large datasets (perhaps 3-4 per surface) of cosmogenic ages from isolated boulders on alluvial-fan surfaces can be utilized to get a sense of age succession, perhaps without the much more labor-intensive depth-profile approach. Taken with the strongly coherent OSL dates from Qaf4, we can comfortably conclude that the stratigraphic age of unit Qaf4 is between ~29 ka at >10 meters depth to ~20-22 ka at the surface. This sort of age precision is rarely possible with radiocarbon dating in these environments without serendipitous location of significant organic deposits having clear relation to the stratigraphy. The coupled OSL- radiocarbon-cosmogenic dating approach shows great promise for these types of dryland deposits.

A more difficult-to-interpret exposure was exposure AF1. Both radiocarbon and OSL ages show significant scatter (Fig. 4). The radiocarbon ages range from 13 to 30 cal. yrs

B.P. over less than 1 meter vertically and several laterally. This is indicative of reworked organic material contaminating younger sediments, which seems reasonable given that the alluvium was sourced from organic-rich Pleistocene lacustrine or shallow-water deposits preserved farther upslope on the piedmont. The OSL dates also contain scatter

between ~6 and ~28 ka. A subtle unconformity separates the three younger OSL ages (6,

7, 16.5 ka) from the two oldest ages (22, 26 ka), which is perhaps a contact between Qaf5

and older underlying Qaf4. Likely the complicated geochronological results are a

combination of geological and methodological factors. The exposure is likely a slowly-

deposited and spatially-complex deposit that cannot be clearly interpreted due to poor

exposure. The data scatter also likely indicates methodological problems; however at this

time we are unable to diagnose any specific causes of this. From this, we suggest caution

when attempting to date deposits that are not clearly interpretable in the field, as adding

problematic chorological data to difficult-to-interpret geology compounds challenge.

That said, we can place this exposure within the context of our understanding of the local stratigraphy with some confidence based on soil development, topographic position and the chronological data.

Our OSL dataset (Table S2) contains both single-grain (SG) and single-aliquot (SA) ages for most samples. It is widely accepted that single-grain analyses are favorable to single-aliquot analyses in fluvial environments (e.g., Olley et al. 2003). Comparison of the two in the context of our interpretations of the local stratigraphy provides significant support for this idea, but also some comparisons between SG and SA ages that are somewhat equivocal. The best example of clear superiority of a single-grain age comes from the dating of a very young (likely deposited in 1998) flood deposit (Qa4, OSL sample 070202.02). The OSL age of ~10 yrs would not have been possible to determine without SG techniques; the SA age was 1450 yrs, and the radiocarbon date from that deposit was a clearly-detrital 343 14C yrs B.P. SG OSL is particularly useful when dating

sediments that fall within the difficult-to calibrate, less than ~350 14C years B.P. range.

Several radiocarbon dates in this study fall into that range, and having OSL data to

compare increases the precision of dating efforts.

A closer look at other SG - SA age comparisons also support singe-grain ages as

superior. In particular, the SA OSL from exposure A1 (Fig. 3) appears to overestimate

the age of the deposit by a factor of two based on our understanding of the stratigraphy,

lack of soil development, and two radiocarbon dates from the same section. Data from

the well-dated exposure A2 (Figure 4) also supports SG use. The SG ages are both

stratigraphically consistent and very similar to the chronology suggested by the

radiocarbon dataset, whereas the SA ages contain a stratigraphic reversal (samples

070302.01 and 070302.02), and occasionally appear too old when compared to the radiocarbon dates. Somewhat less conclusive is the comparison between SA and SG ages

for OSL samples 070302.06 and 070302.07. The SG ages are possibly too young based

on the nearby radiocarbon dates (see fig. 4), but since the radiocarbon dates could include

some detrital age, the SA ages may well be too old. The one case where we can say with

a bit of confidence that the SA age appears to better represent the age of the deposit is

exposure A3 (fig. 5). There, the SG age appears too old when compared to the

radiocarbon ages, and the SA age more closely matches.

The comparison between the SG and SA ages from the early Holocene and late

Pleistocene alluvial fan deposits suggests both techniques worked similarly. All of the

SG and SA ages from the alluvial-fan exposures overlap within error.

6. Conclusions

Though our discussion tends to highlight the challenges in our study, overall our multi-technique approach led to a detailed understanding of the alluvial chronology in

Cuyama Valley, CA. In particular, OSL showed great utility in dating samples of all ages in this study. OSL is useful in difficult-to-calibrate radiocarbon age ranges, and in environments where detrital-aged charcoal is common or no reliable charcoal can be found. CRN techniques were moderately successful, but given our sampling strategy and limited number of samples, it was difficult to assess accuracy. Radiocarbon dating continues to show its effectiveness at providing alluvial stratigraphic ages, and though not perfect, single-grain OSL dating should now be thought of as a routine method for age-estimation of dryland alluvial-fan and axial-fluvial deposits if latest methods are employed carefully.

Acknowledgments

This study was performed with financial support from NSF EAR-0309518 and a

USGS EDMAP grant to JP, and generous support from the USGS Southern California

Areal Mapping Project and scholarships from the University of Arizona, Department of

Geosciences to SD. 10Be analyses were performed at PRIME Lab under a ‘seed analysis’ grant to J. Pelletier (U-Arizona). OSL analyses were supported by grants from Chevron-

Texaco and the Arizona Geological Society to SD. Thanks to M. Grace and A. Moore for field assistance. Thanks to J. Quade, J. Pigati and for guidance regarding radiocarbon

methods and for lab access. Thanks to T. Fischer for radiocarbon sample prep assistance.

AMS analyses were provided at no charge from A.T. Jull and the NSF-Arizona AMS

Facility as a student assistance grant. Thanks to J. Pigati for guidance with cosmogenic sample preparation and data analysis. Thanks to S. Mahan, USGS, for assistance with

FGS OSL dosimetry on samples OSL18-22. All field work was done on private lands, thanks to the landowners and managers whose cooperation was essential.

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Table S1. OSL analysis details Single Single grain aliquot analysis analysis Number Number Total of % aliquots Total grains of % grains Sample ID aliquots accepted accepted measured accepted accepted measured De's De's 070302.02 24 23 96 2300 37 2 070302.01 18 18 100 2000 22 1 070302.03 48 44 92 4400 82 2 070302.04 24 18 75 1600 21 1 070302.05 24 20 83 1500 30 2 070302.06 18 15 83 2300 36 2 070302.07 24 23 96 1100 27 2 070202.02 18 14 78 1500 33 2 070202.01 18 18 100 1100 20 2 070402.05 18 18 100 1800 21 1 070302.08 26 24 92 1900 73 4 070302.09 28 27 96 1000 58 6 070402.01 - - - 1900 15 1 070402.02 32 31 97 1400 29 2 070402.03 26 24 92 1500 34 2 070402.04 24 21 88 1300 20 2

Table S2. Optically-stimulated luminescence data from bedded fluvial sands, Cuyama Valley, California. Cosmic Total dose Single Grain Single Single Single Sample Exposure H O dose rate dose rate D age D age Unit 2 radiation rate D e Grain Age Aliquot D e Aliquot ID ID (%) (Gy/ka) (Gy/ka) e model* e model* (Gy/ka) (Gy/ka) (Gy) (ka) (Gy) Age (ka) 0.54 070402.05 A1 Qa3 0.8 2.81 (0.18) 1.4 (0.05) 0.18 (0.01) 4.39 (0.18) 1.26 (0.14) CAM 0.29 (0.03) 2.36 (0.54) MAM-3 (0.12) 0.74 070302.02 A2 Qa2 0.5 2.88 (0.17) 1.55 (0.06) 0.19 (0.02) 4.61 (0.18) 1.60 (0.40) MAM-4 0.35 (0.09) 3.4 (0.26) MAM-3 (0.06) 0.49 070302.01 A2 Qa2 0.8 2.7 (0.16) 1.53 (0.05) 0.18 (0.01) 4.41 (0.17) 1.91 (0.49) MAM-4 0.43 (0.11) 2.16 (0.08) MAM-3 (0.03) 0.82 070302.03 A2 Qa2 0.9 2.58 (0.15) 1.47 (0.05) 0.15 (0.01) 4.19 (.16) 2.93 (0.19) CAM 0.7 (0.05) 3.43 (0.17) MAM-3 (0.05) 070302.04 A2 Qa1 2.9 2.65 (.017) 1.44 (0.05) 0.12 (0.01) 4.21 (0.18) 4.18 (0.28) CAM 0.99 (0.08) 3.8 (0.40) MAM-3 0.9 (0.1) 1.52 070302.05 A2 Qa1 1.4 3.00 (0.18) 1.6 (0.05) 0.09 (0.01) 4.69 (0.18) 5.50 (0.37) CAM 1.17 (0.09) 7.14 (0.65) MAM-3 (0.15) 1.53 070302.06 A2 Qa1 1.5 3.02 (0.18) 1.58 (0.05) 0.08 (0.01) 4.68 (0.18) 5.67 (0.51) CAM 1.21 (0.12) 7.16 (0.65) MAM-3 (0.19) 1.78 070302.07 A2 Qa1 1.5 2.78 (0.16) 1.46 (0.05) 0.07 (0.01) 4.32 (0.17) 5.29 (0.46) CAM 1.23 (0.12) 7.66 (0.65) MAM-3 (0.17) 1.45 070202.02 A3 Qa4 12.3 2.46 (0.22) 1.63 (0.06) 0.2 (0.02) 4.29 (0.22) 0.06 (0.03) L-5% 0.01 (0.01) 6.23 (0.66) MAM-3 (0.17) 0.81 070202.01 A3 Qa2 1.4 3.00 (0.16) 1.64 (0.06) 0.08 (0.00) 4.71 (0.17) 4.65 (0.34) CAM 0.99 (0.08) 3.81 (0.63) MAM-3 (0.14) 28.96 6.85 070302.08 AF1 Qaf5 1.5 2.52 (0.15) 1.57 (0.05) 0.14 (0.01) 4.23 (0.16) 28.36 (1.21) CAM 6.71 (0.38) MAM-3 (1.16) (0.37) 30.26 6.85 070302.09 AF1 Qaf5 2.4 2.66 (0.15) 1.62 (0.06) 0.14 (0.01) 4.42 (0.17) 31.01 (1.34) CAM 7.02 (0.40) MAM-3 (1.32) (0.39) 16.51 77.94 18.3 OSL18 AF1 Qaf5 20 2.61 (0.21) 1.51 (0.07) 0.14 (0.01) 4.26 (0.22) 70.33 (4.42) CAM CAM (1.35) (5.52) (1.62) 26.04 84.11 24.21 OSL19 AF1 Qaf4 20 2.27 (0.20) 1.06 (0.05) 0.14 (0.01) 3.47 (0.21) 90.47 (4.16) MAM-4 MAM-3 (1.97) (4.39) (1.92) 22.29 070402.01 near AF1 Qaf4 0.6 2.74 (0.17) 1.51 (0.05) 0.06 (0.00) 4.3 (.18) 95.95 (8.20) CAM - - - (2.12) 23.46 111.95 23.55 070402.02 AF2 Qaf4 0.5 2.92 (0.18) 1.69 (0.06) 0.14 (0.01) 4.75 (0.19) 111.50 (6.91) MAM-4 CAM (1.73) (6.63) (1.68) 109.74 24.64 OSL22 AF2 Qaf4 20 2.88 (0.23) 1.52 (0.07) 0.05 (0.00) 4.45 (0.24) - - - CAM (9.93) (2.59) 119.97 25.36 070402.03 AF2 Qaf4 0.1 3.03 (0.18) 1.53 (0.05) 0.17 (0.01) 4.73 (0.19) 120.15 (8.23) CAM 25.4 (2.02) CAM (10.78) (2.50) 107.9 25.78 OSL20 AF2 Qaf4 20 2.64 (0.21) 1.43 (0.07) 0.11 (0.01) 4.19 (0.22) - - - CAM (12.34) (2.35) 26.87 118.66 25.19 070402.04 AF2 Qaf4 0.4 3.08 (0.19) 1.49 (0.05) 0.13 (0.01) 4.71 (0.20) 126.57 (11.19) CAM CAM (2.63) (10.19) (2.41) 128.06 27.71 OSL21 AF2 Qaf4 20 2.94 (0.22) 1.62 (0.07) 0.06 (0.00) 4.62 (0.23) - - - CAM (10.79) (2.73) *Age models were determined following procedures detailed in Bailey and Arnold (in press). CAM is Central Age Model, MAM-4 is 4- parameter Minimum Age Model, L-5% is mean of lowest 5% De values, MAM-3 is 3-parameter Minimum Age Model

Table S3. Radiocarbon data from alluvial charcoal and wood, Cuyama Valley, CA Lower Upper Proposed Age (error) median Sample Sample 14 calibration calibration age (yrs Location Unit ( C yrs probability ID Description range range before B.P.) (cal.yrs BP) (cal.yrs BP) (cal.yrs BP) 2002) AA55381 A1 Qa2 charcoal 754 (30) 665 728 689 740 AA53626 A1 Qa3 charcoal 176 (52) -3 300 170 220 AA55845 A1 Qa3 charcoal 169 (30) -2 291 178 230 AA55851 A2 Qa1 charcoal 737 (61) 558 782 684 740 AA63768 A2 Qa1 detrital charcoal 1098 (39) 929 1118 1006 1060 AA53754 A2 Qa1 charcoal 1132 (44) 957 1172 1036 1090 AA61251 A2 Qa1 charcoal 1146 (37) 969 1171 1054 1110 AA63784 A2 Qa1 charcoal layer 1176 (39) 979 1227 1102 1150 AA63783 A2 Qa1 charcoal layer 1235 (40) 1066 1267 1172 1220 AA55852 A2 Qa1 charcoal 1257 (87) 978 1307 1177 1230 AA61262 A2 Qa1 charcoal 1626 (39) 1411 1609 1517 1570 AA55853 A2 Qa1 charcoal 1676 (34) 1520 1694 1583 1640 AA53755 A2 Qa1 charcoal 1691 (48) 1421 1715 1601 1650 AA54562 A2 Qa2 charcoal 341 (48) 306 494 397 450 AA54215 A2 Qa2 charcoal 359 (43) 314 498 408 460 AA53624 A2 Qa2 charcoal 411 (63) 314 530 451 500 single piece AA61531 A2 Qa2 392 (36) 319 513 458 510 charcoal AA55375 A2 Qa2 charcoal 422 (32) 331 526 493 550 AA53753 A2 Qa2 charcoal 560 (57) 513 654 588 640 large detrital AA61265 A2 Qa2 596 (38) 538 654 602 650 charcoal AA54563 A2 Qa2 charcoal 662 (53) 547 683 620 670 AA53627 A3 Qa2 charcoal 544 (44) 509 647 558 610 AA53751 A3 Qa2 charcoal 682 (59) 547 715 640 690 AA53750 A3 Qa2 charcoal 710 (68) 546 752 664 720 AA53628 A3 Qa2 charcoal layer 706 (43) 559 724 665 720 AA53752 A3 Qa4 wood 343 (49) 307 496 398 450 AA55901 AF1 Qaf5 charcoal 10894 (82) 12785 13000 12874 12930 amalgamated AA62099 AF1 Qaf5 15600 (81) 18738 18987 18870 18920 detrital charcoal amalgamated 17810 AA61529 AF1 Qaf5 20497 21615 21045 21100 detrital charcoal (170) 19510 AA56608 AF1 Qaf5 charcoal 21457 25339 23290 23340 (720) single piece 20740 AA56609 AF1 Qaf5 24493 25417 24939 24990 charcoal (130) charcoal from 23140 27663 AA55376 AF1 Qaf5 * * 27710* 1.5m X 10cm (170) (201)* charcoal from 24970 29955 AA54561 AF1 Qaf5 * * 30010* 1.5m X 10cm (250) (525)* amalgamated 26040 31153 AA61528 AF1 Qaf5 * * 31200* detrital charcoal (270) (226)* humic acids from 16820 AA56607 AF2 Qaf4 19348 20640 19961 20010 charcoal (310) 18240 AA56606 AF2 Qaf4 charcoal 21101 22180 21692 21740 (170) 26710 31692 AA55379 AF2 Qaf4 charcoal * * 31740* (390) (319)* * Calibrated using Fairbanks, et al. (2005), standard deviation in parentheses.

Table S4. 10Be data from alluvial fans, Cuyama Valley, California

10Be† 10Be age‡ North West Elevation Sample Thickness Sample ID Unit S * (error) (error) Latitude Longitude (m) Description correction t (atoms/g) (ka)

119332 C070503.04 Qaf4 34.98 119.77 587 SS Boulder 1.044 1.0001 20.7 (1.2) (7482)

199300 C070503.01 Qaf4 34.98 119.78 589 SS Boulder 1.044 1.0001 33.2 (1.7) (11153)

185531 C070403.05 Qaf3 34.98 119.78 613 SS Boulder 1.044 1.0001 29.3 (2.7) (10270)

534734 C011204.03 Qaf1 34.93 119.82 869 SS Boulder 1.044 1.0004 69.0 (2.0) (21005)

715276 C011204.01 Qaf1 34.93 119.82 880 SS Boulder 1.083 1.0004 91.0 (4.0) (31462) *Topographic shielding factor †Corrected for chemical blank value, sample thickness and topographic shielding. Error displayed is analytical error only. †Age determined following Pigati and Lifton (2004) with a time-integrated HLSL 10Be production rate of 4.35 atoms/year. No erosion or burial assumed.

Figure 1. Location of study area in Southern California.

Figure 2. Landsat7 image of study area showing physiography, and exposure locations discussed in text.

Figure 3. Exposure A1. Radiocarbon dates shown with sample numbers as median probability calendar years before 2002. See Table S4 for actual calibration range. OSL dates shown in ka with sample numbers and analytical error in parentheses.

Figure 4. Exposure A2. Vertical exaggeration is 2X (note horizontal and vertical scales. Sample locations are surveyed with total station and projected into 2-D. Radiocarbon samples AA63784 and AA63783 are from extensive layers of charcoal and should be particularly reliable

Figure 5. Exposure A3. Radiocarbon dates shown with sample numbers as median probability calendar years before 2002. See Table S4 for actual calibration range. OSL dates shown with sample numbers and error in parentheses.

Figure 6. Exposure AF1. Radiocarbon dates shown with sample numbers as median probability calendar years before 2002. OSL dates shown with sample numbers and error in parentheses. Field assistant for scale in left photo, 30cm hammer in right photo.

Figure 7. Exposure AF2. Radiocarbon dates given as calibrated years before 2002. CRN and OSL ages shown as ka with analytical error.

APPENDIX B

Submitted to Geology, 2006

Coupled Alluvial Fan and Axial Channel Development in Cuyama Valley, California

Stephen B. DeLong* and Jon D. Pelletier University of Arizona, Department of Geosciences, 1040 E 4th Street, Tucson, AZ, 85721

ABSTRACT

The Sierra Madre Mountains piedmont in the western Transverse Ranges,

California is complex, both spatially and temporally, when compared to well-studied desert piedmonts to the east. Most desert piedmonts consist of two or three late

Pleistocene and early Holocene surfaces that converge downstream in response to stable or lacustrine-system driven fluctuating base level. In contrast, the Cuyama Valley fans are made up of at least five late Pleistocene surfaces. The timing and morphology of these fans record both climatic forcing in the form of variable sediment supply from drainage basin hillslopes, and tectonic forcing from ongoing tectonically driven incision of the axial Cuyama River. Fan-terrace surfaces are subparallel (older surfaces are slightly steeper) and offset systematically in relation to their ages, suggesting response to ongoing base-level incision and fluctuation in sediment supply. The fans aggraded during relatively cool and wet climate of the last glacial period, which is out-of-phase with the regional model developed in nearby desert regions. Saturation-driven hillslope failure during cool and wet conditions may have been the principal cause of increased sediment supply during times of fan aggradation.

INTRODUCTION

Suites of inset alluvial fan surfaces found on mountain piedmonts in arid regions record episodic alluvial episodes caused by changes in upstream sediment and water flux.

These episodes of increased piedmont sedimentation (and intervening times of fluvial entrenchment and lateral erosion) are widely thought of as caused by cyclic climate change. In regions where past climates have acted on distinct catchments in similar ways, these flights of terraces are often assumed to be age-equivalent. The causes of these alluvial episodes can be diverse. In desert regions (Wells, et al., 1987; Bull, 1991;

Reheis et al., 1996; Harvey, et al., 1999; Ritter, et al., 2000; McDonald et al., 2003) and in at least one semi-arid to subhumid region (Weldon, 1986), changing hillslope vegetation and precipitation regime (increased storm intensity) during and after cool/wet to warm/dry climate transitions are most often cited as causing alluviation. In glaciated regions, drainage basin erosion by valley glaciers led to piedmont alluviation during glacial advances (Ritter et al., 1995; Gillespie et al., 1994, Harvey, 2002). Also sometimes cited is alluviation from unglaciated or minimally glaciated drainage basins during cool/wet climates due to increased effective precipitation, fluvial transport, and possibly increased freeze-thaw and periglacial processes on high-elevation hillslopes.

This is cited in the northern Basin and Range from catchments with small glaciers (Pierce and Scott, 1982), in southern Spain in what is now Mediterranean climate (Harvey,

2002), and from small, high-elevation catchments in southern California (Bull, 1991).

The wet-to-dry climate change alluviation model has dominated the literature from the southwestern United States for the past three decades, largely due to the

influence of Bull’s (1991) detailed conceptual discussion and several well-dated sites in the Mojave and Great Basin deserts. Our limited understanding of the spatial distribution of this (and possibly other) seemingly conflicting causes of piedmont alluviation has limited our ability to put forth predictive conceptual models for the timing of alluvial episodes in diverse settings. Geochronology in the coarse-grained alluvial environments over the relevant timescales is difficult. Studies outside of desert regions, with a few exceptions are particularly lacking, which leads to the possibility of application of conceptual models of desert alluvial fan development to diverse settings in which they may not be appropriate.

(Harvey and Wells, 2003). In order to (1) better understand the causes of episodic alluviation beyond desert regions, and (2) to expand our understanding of how regional uplift and an incising axial fan-toe channel affect the topographic configuration of alluvial fan terraces, we mapped, described, and dated the Quaternary deposits of

Cuyama Valley, California.

SETTING OF ALLUVIAL FAN DEPOSITS IN CUYAMA VALLEY

Cuyama Valley is a thrust-fault bounded structural valley near the west end of the western Transverse Ranges in southern California (Fig. 1). The modern climate is hot and dry with a strongly Mediterranean precipitation regime. The valley is located

adjacent to the “Big Bend” section of the San Andreas Fault, and is experiencing ongoing but spatially complex regional uplift (White, 1992). The largest alluvial fans in the valley are sourced from the north-facing drainage basins of the Sierra Madre Range, which has an elevation range of 800-2000 meters. Vegetation on the slopes is dense oak- juniper-chaparral, with isolated stands of pine forest at high elevations. Vegetation on the fan surfaces is dominantly open grassland, which may have had more oak and juniper prior to modern grazing.

The Sierra Madre piedmont is a mosaic of planar late Quaternary alluvial fan surfaces, variably deformed Quaternary alluvium having no preserved depositional surfaces, and exposed Cenozoic sedimentary rocks. There are eight distinguishable fan- terrace levels, five of which cover significant parts of the landscape (Fig. 1). All fan surfaces are nearly planar, though the oldest surface in our study area is gullied somewhat near fluvial scarps. In order to establish the chronology of alluvial episodes in Cuyama

Valley, radiocarbon, optically stimulated luminescence, and cosmogenic radionuclide surface exposure dating were applied to these late Quaternary sedimentary deposits.

Geochronological techniques and data were detailed in DeLong and Arnold (in press,

2007) and are summarized in Table 1. The mountain-front reverse fault (South Cuyama fault zone) does not appear to offset any of the late-Pleistocene planar surfaces (Vedder and Reppening, 1975), suggesting that episodic tectonic uplift of the drainage basins relative to the piedmont zone did not occur over the timescale of alluvial fan development examined in this study.

FAN SURFACE PROFILES

Unlike most piedmonts in stable tectonic settings, the alluvial fan deposits in

Cuyama Valley generally mantle strath bedrock contacts, indicating that both episodic alluviation and ongoing tectonic uplift is occurring (Bull, 1991). In stable tectonic settings, fan-terrace longitudinal profiles tend to converge in the downstream direction because base-level has remained stable or slightly fluctuated periodically in lacustrine or marine settings (Harvey, 2002). Occasionally; however, younger fans prograde basin- ward as fan heads entrench so younger surfaces are higher distal from a mid-fan intersection point. Slope of terrace surfaces are largely a function of sediment flux and texture, because fans steepen to transport either coarser material or increased volumes of material. Sediment flux and texture are at least partially controlled by hillslope processes and climate (Harvey, et al., 1999; Ritter et al., 2000).

Figure 2 illustrates generalized end-member hypotheses for alluvial fan profile arrangement in response to both stable and fluctuating sediment supply/size and base level. In Cuyama Valley, the terraces tend to have subparallel and vertically offset longitudinal profiles near the mountain front as well as near the axial system, and older surfaces are higher than younger surfaces throughout the piedmont and have slightly steeper profiles (Fig. 3). A notable exception is the profile of the Qa5 fans that are sourced primarily from within the piedmont zone, leading to development of short, steep profiles. The amount of relief from the projection of Qa3-Qa5 surfaces to the valley axis

(in meters) is very similar to the differences in estimated age between the surfaces (in

thousands of years), suggesting that the alluvial fan system may be tracking the ongoing incision of the axial channel.

The vertical offset of the terrace surfaces suggests an axial channel incision rate of ~1 m/kyr based on estimated surface ages and the elevation of the surfaces projected to the valley axis. The extensive late Holocene valley fill is testament to the intermittent nature of this incision, but the estimated rate is generally consistent with estimates of vertical tectonic rates in the Coast Ranges (Merritts and Bull, 1989; Page et al., 1998;

Ducea et al., 2003). Base level on the Cuyama River is set by the bedrock canyon ~40 km to the west of our study area in the southern Coast Ranges. Based on our estimates of channel incision rates, the Cuyama River is nearly in equilibrium with tectonic uplift rates over the late Quaternary.

CLIMATIC AND TECTONIC IMPLICATIONS

In settings in which climate is the dominant cause of alluviation, there tends to be a suite of two and occasionally three terrace levels that are between early Holocene and late Pleistocene (~125 ka) in age (Reheis et al., 1996; Harvey, et al., 1999; Ritter, et al.,

2000; McDonald et al., 2003, Anders, et al. 2005). Even in active tectonic systems such as Cajon Pass (Weldon, 1986) and the San Emigdio mountain front (Keller, et al., 1998;

Keller et al., 2000), there are only two deposits in this age range. In Cuyama Valley, there are five distinct and spatially extensive deposits in this age range, one of which

(Qf4) is, in detail, two closely spaced geomorphic surfaces capping identical stratigraphy as indicated by continuously exposed axial facies. Of these settings, only Cuyama Valley

has a large axial channel that sets base-level for multiple tributary drainages. This raises the possibility that multiple fan surfaces do not record unique climate-change-induced alluvial events. Rather, fan aggradation may have been punctuated by episodic incision caused by downstream-forced incision even as sediment flux remained high, leading to preservation of several terrace surfaces.

Additionally, the timing of alluvial episodes in Cuyama Valley appears to be out- of-phase with other records in the Southwest. Many alluvial fans aggraded during the glacial-interglacial transition at the Pleistocene-Holocene boundary, following a period of fan entrenchment during cool, moist conditions prior to ~15-18 ka (Wells, et al., 1987;

Bull, 1991; Rehies et al., 1996; Harvey, et al., 1999; Ritter, et al., 2000; McDonald et al.,

2003). In Cuyama Valley, fan aggradation occurred between 18-30 ka, during full- glacial and the lead-up to full-glacial climates. During at least part of this time, aggradation on the main-stem Cuyama River occurred as well as evidenced by interbedded axial-fluvial material within Qaf4 deposits (DeLong and Arnold, in press 2007).

In desert regions, the leading hypothesis for lack of fan aggradation during glacial times is the stabilizing effect of increased hillslope vegetation density. The modern vegetation on the north flank of the Sierra Madre Range is dense chaparral. According to paleo-circulation pattern reconstructions such as Harvey (1999), the western Transverse

Ranges experienced cooler temperatures, and due to southward migration of the jet stream, increased precipitation from the Pacific during full-glacial conditions. This likely led to depression of the elevation of subalpine forest in the Sierra Madre Range. This change in hillslope vegetation alone seems an unlikely cause of increased sediment flux.

More likely, the change in hillslope sediment flux was related to increased mass- movement rates. Precipitation-threshold slope failures are common in southern

California, and perhaps full-glacial conditions were analogous to the increase in slope failures during El Niño conditions (Gabet, 2002), but over a longer timescale. As vegetation and moisture-driven weathering led to regolith production on steep slopes, increased precipitation may have led to saturation landsliding, which is evidenced by the dense paleo-landslide deposits preserved on the slopes of the Sierra Madre (Vedder and

Reppening, 1975).

The Pleistocene-Holocene climate change appears to have had differing effects on distinct parts of the Sierra Madre piedmont. Along Aliso Canyon, entrenchment occurred after 18 ka and there is no record of sediment storage since that time. This was likely caused by increased slope stability diminishing sediment flux, causing the channels to switch from aggradation to incision (Bull, 1991). In contrast, the western part of the map area (Fig 2) contains extensive deposits of fine-grained, possibly lacustrine (Vedder and

Reppening, 1975) Morales Formation within the piedmont. There, local fan and tributary aggradation occurred. These Qf5 deposits are striking in their resemblance to reworked

Morales Formation. If full-glacial oak-juniper scrub vegetation on the Morales

Formation on the piedmont disappeared as climate changed, the nearly unconsolidated material would have been readily eroded and redeposited as local alluvial aprons, even as the major tributaries draining the Sierra Madre Range elsewhere eroded further into the piedmont.

CONCLUSIONS

Though late Quaternary alluvial-fan development in desert regions of the southwestern

U.S. is largely well understood and similar on a regional scale, the coupled piedmont- axial system in Cuyama Valley, CA is striking in its spatial and temporal characteristics.

The preservation of at least five latest-Quaternary alluvial surfaces suggest that either drainage basins in the Sierra Madre range were particularly sensitive to cyclic climate fluctuation, or cut-and-fill cycles on the piedmont were driven by both upstream sediment supply and downstream incision driven by the axial system. Fans in Cuyama Valley aggraded substantially during the last glacial period. A possible cause of this was increased saturation-driven hillslope failure and sediment transfer to the piedmont during a cool and wet climate. The late Pleistocene and Holocene has been a time of relative stability of the north-facing, chaparral-covered slopes. The Pleistocene-Holocene transition did appear to lead to local fan aggradation where material is sourced from the now-unvegetated slopes of unconsolidated, possibly lacustrine, Morales Formation on the

Sierra Madre piedmont. These findings suggest further studies of piedmonts in diverse climatic and tectonic zones in the southwestern U.S. are warranted, and caution must be used when applying widely accepted models of alluvial-fan evolution beyond the regions in which they have been thoroughly tested.

ACKNOWLEDGMENTS

This work was supported by a USGS EDMAP grant, NSF EAR-0309518 to JP, the USGS-SCAMP, ChevronTexaco and the University of Arizona Department of

Geosciences. Thanks to the land managers of Cuyama Valley, especially J. Kelley and

A. Steinbach, for access to private lands.

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White, L. A., 1992, Thermal and Unroofing History of the Western Transverse Ranges, California: Results from Apatite Fission Track Thermochronology: unpub. PhD dissertation, University of Texas, Austin. 299 pp.

Table 1. Description and Ages of Alluvial Fan Deposits in Cuyama Valley, CA

Geomorphic Estimated Description Surface Age (ka) Qa Active alluvium < 0.01 Qya Holocene alluvium < 3†‡ Qf5 Sand-dominated alluvium 6-18*†‡ Coarse alluvium, planar surfaces, composite of two Qf4 18-30†‡# closely-spaced (<2m) parallel alluvial surfaces Qf3 Coarse alluvium, planar surface >30# Qf2 Coarse alluvium, planar surface >45? Coarse alluvium, planar surface Qf1 60-120? # with some gullying * Wide scatter in geochronological data makes age interpretation of Qf5 difficult, but landscape position, and soil development suggest younger part of age range may be better estimate. †Age estimate from AMS radiocarbon dating. ‡Age estimate from optically-stimulated luminescence dating. #Age estimate from 10Be CRN surface exposure dating Note: See DeLong and Arnold (in press, 2007) for data, techniques, and discussion of dating methods.

Figure 1. Location and generalized surficial geology of study area in southern California. Qa – active channels; Qyp – palustrine deposits; Qya – late Holocene deposits; Qf5-Qf1 – see Table 1; Qof – Quaternary alluvium, undifferentiated, lacking depositional surfaces; Qyls – recent landslides in QTmol; QTmol – fine-grained (lacustrine?) Morales Formation; QTm – coarse-grained Morales Formation; Tr – Pre-Pliocene bedrock, undifferentiated.

Figure 2. Schematic representations of fan terrace profiles in response to differing base- level and sediment-flux/texture scenarios. End-member hypothesis #1 is a generalization of terrace suites common in tectonically inactive regions where alluvial fan development is largely a response to fluctuating upstream sediment flux and texture. End-member hypothesis #2 follows Mackin’s (1948) concept of the graded stream response to downcutting.

Figure 3. Alluvial fan profiles generated using field Total Station survey and cross- checked with 10-meter DEM. Horizontal axis is distance from centerline of modern Cuyama River channel in direction of maximum fan slope. Vertical axis is distance above elevation of Cuyama River channel at same location. All profiles except Qf5 are from terrace suite flanking Aliso Canyon. Qf5 profile is from northwestern portion of map area, and relatively high slope likely related to the observation that the Qf5 alluviation is sourced from erosion of piedmont exposure of readily erodible Morales Formation. The arrangement of fan terrace profiles is suggestive of our “mixed” hypothesis from Figure 2, with vertically offset profiles at the fan-toes, and steeper older surfaces.

APPENDIX C

Submitted to Geomorphology, 2006

Geomorphic fate of late Cenozoic basins in southern California: An example from the upper Cuyama Valley

Stephen B. DeLong Department of Geosciences, University of Arizona, 1040 E 4th Street, Tucson AZ 85721, USA

Scott A. Minor United States Geological Survey, Denver CO 80225, USA

Lee J. Arnold Oxford Luminescence Research Group, School of Geography and the Environment, University of Oxford, Mansfield Rd, Oxford OX1 3TB, UK

Keywords: landscape development; neotectonics; surface exposure dating; optical dating; Cuyama Badlands; Big Pine fault

ABSTRACT

Many long-lived Cenozoic depositional basins in southern California have been affected by increased movement on local faults and increased regional-scale uplift and transpression associated with the San Andreas fault since the Pliocene.

Stratigraphic, structural and geomorphic evidence for how one of these basins responded to tectonic and climatic forcing is particularly well expressed in the upper Cuyama Valley in the western Transverse Ranges.

Plio-Pleistocene terrestrial deposition in the Cuyama sedimentary basin continued through at least ~0.76 Ma, after which basin fill was uplifted, deformed, and beveled, forming a low-relief erosion surface on which the alluvium of San

Emigdio Mesa was deposited between >70 ka and ~15 ka (with major alluviation

ending by ~28 ka). Subsequent fluvial drainage network development formed the

Cuyama badlands by incising into the deformed Cuyama basin sediments.

Localized deposition of alluvium sourced from the Pine Mountain massif occurred at the southern end of the basin near the elevation of the Cuyama River between 25 and 14 ka. This alluvium was subsequently offset ~10 m vertically by the Big Pine fault, providing a latest Quaternary vertical slip-rate estimate of ~0.7 m/ky for the

Big Pine fault in the upper Cuyama Valley. The Big Pine fault has no confirmed record of historic rupture; however based on our results, we suggest the likelihood of multiple reverse-slip rupture events since ~14 ka. Our results allow us to propose a general model for late Cenozoic landscape development in structural basins o coastal California. Though timing may vary, thick sequences of terrestrial Plio-

Pleistocene basin fill deposits have been deformed, incised, alluviated, and offset by an increasingly dense fault array. Combined analysis of stratigraphy, structure, and alluvial deposits that mantle a range of paleosurfaces allow for establishing the geomorphic history of these complex landscapes.

1. INTRODUCTION

The transition from landscape dominated by long-lived regional-scale late

Cenozoic depositional basins to the formation of smaller complex structural and topographic basins occurred relatively recently in parts of southern California (Kellogg and Minor, 2005; Page et al., 1998). There is no generally accepted model for the geomorphic fate of these young basins, many of which stopped receiving sediment as

recently as the Pleistocene. Furthermore, the details of the complex events that have created the dramatic landscapes of southern California are difficult to constrain due to the challenge of geochronology over the relevant timescales of 103 to 105 yrs. These events can include the transition from basin filling to incision; episodic alluviation occurring at different positions in the landscape; increasing tectonic deformation, often accommodated on an increasingly complex structural array; and progressive regional uplift that is spatially variable across multiple structural boundaries.

An appropriate case study in our efforts to better understand late Cenozoic landscape development in southern California is the upper Cuyama Valley, located at the junction between the southern Coast Ranges and western Transverse Ranges, where changes in tectonic regime over the last few million years include increased transpression in the Big Bend region of the San Andreas fault, expressed by complex contractional faulting and folding (Kellogg and Minor, 2005; Atwater and Stock, 1998; Page et al.

1998; Ellis, et al. 1993; White, 1992). A striking landscape feature in this area are the

Cuyama Badlands, characterized by deeply incised valleys and gullied slopes cut into

Neogene sedimentary strata. Associated with these incised basin strata are spatially variable tectonic deformation, erosional unconformities covered by Quaternary alluvium, and the regionally significant Big Pine fault.

Our objectives in this study were to determine the history and timing of landscape development in the upper Cuyama Valley region from the late stages of deposition in the

Cuyama basin to the present time, and to use the age of offset fluvial terraces to evaluate the strain rate of the eastern Big Pine fault along the base of Pine Mountain. To do this,

we synthesized the current understanding of the post-Miocene history of the area and applied cosmogenic radionuclide (CRN) surface-exposure dating and optically-stimulated luminescence (OSL) burial dating techniques to several late Quaternary alluvial deposits that are useful geologic recorders of events leading up to the current landscape configuration.

2. GEOLOGIC SETTING

Our study area (Fig. 1) is underlain by deeply-incised and moderately to strongly- deformed upper Cenozoic strata bounded on the south by Pine Mountain, to the north and east by the Mt. Piños-Mt. Abel massif, and to the west by the Cuyama River and Ozena fault. The Big Pine fault is a south-dipping oblique reverse fault (Minor, 2004) along the northern base of Pine Mountain that intersects a flight of fluvial terraces east of the prominent northward bend in the Cuyama River.

The history of post-Miocene deposition and landscape development in Cuyama

Valley is detailed in Ellis et al. (1993) and Ellis (1994). Those papers built upon contributions by Davis, (1983), Vedder, et al. (1973), and Dibblee (1987a, b) that detailed mapping, stratigraphy, and tectonic reconstructions of the upper Cuyama Valley. During the Miocene, cyclic marine transgression and regression eventually gave way to exclusively terrestrial deposition in the ancestral Cuyama basin. In our study area, the post-Miocene terrestrial deposits dominate the landscape, and consist of two mostly conformable units. The lower unit is the >1000 m-thick Quatal Formation, a clay-rich sandstone and conglomerate, and the upper unit is the >1500 m-thick Morales Formation,

a coarsening-upward sandstone and conglomerate. The Cuyama Badlands result from incision of a relatively low-relief erosion surface that formed after cessation of terrestrial deposition in the Cuyama basin. This study investigates the geomorphic fate of the basin fill deposits in response to climatic and tectonic changes.

Because the late stages of deposition in the Cuyama basin serve as the starting point for topographic development of the Cuyama Badlands, the age of the upper Morales

Formation is of particular interest. Blancan faunal remains found by Vedder (1970) in a different part of the basin indicated a Pliocene age for at least part of the Morales

Formation. Age correlation over several tens of kilometers across structural boundaries is tenuous so the Morales Formation in our study area might represent a different age.

Ellis (1994) applied paleomagnetic techniques to date the Morales Formation in several locations, including the Cuyama Badlands. Her results did not permit a unique magnetostratigraphic interpretation, but two normally-polarized samples likely correlated with either the Gauss chron (3.40-2.48 Ma) or the Olduvai subchron (1.87-1.67 Ma), and all other samples above and below had reverse polarity.

Ash located in the uppermost Morales Formation by Stone and Cossette (2000) indicate that the upper portion of the basin-fill sequence just below the paleo-erosion surface is between 1.2 and 0.76 Ma based on geochemical correlation to either the Glass

Mountain or Bishop Ash (most likely the 0.76 Ma Bishop Ash, A. Sarna-Wojcicki, written commun. 2004). This ash correlation supports the interpretation that the two normally-polarized paleomagnetic samples from the Morales Formation belong to the

Olduvai subchron, and suggests a significant part of the Morales Formation in the

Cuyama Badlands is Pleistocene in age.

The Cuyama basin likely stopped receiving sediment soon after deposition of the ash bed, and the deposits were subsequently deformed and beveled to a low-relief surface that truncates bedding, including steeply dipping beds on the northern and eastern margins of the basin. This erosional surface is mantled discontinuously by a relatively thin alluvial deposit, the largest remnant of which is San Emigdio Mesa (Fig. 2). Davis

(1983) correlated this deposit with the Riverbank Formation (0.45 – 0.13 Ma) of the northeastern San Joaquin Valley, but did not justify this in detail. This alluvial deposit, which predated formation of the Cuyama Badlands, had not been dated directly prior to this study.

More recently, alluvium was deposited across the Big Pine fault along the uppermost Cuyama River, and is now preserved as elevated fluvial terraces. This alluvium is distinguished by its nearly monomict sandstone-clast composition, derived mainly from the adjacent Pine Mountain massif. An apparent terrace offset, though coincident with the main Big Pine fault trace, had not been previously identified as a tectonic scarp offsetting an equal-aged deposit, so we applied OSL dating to alluvium on both sides of the fault trace in an effort to correlate the two deposits and estimate a late

Quaternary fault dip-slip rate.

3. METHODS

3.1 CRN Surface-Exposure Dating

We applied 10Be CRN surface-exposure dating to three boulders on the surface of

San Emigdio Mesa. Additionally, we applied OSL burial dating to 15 samples from: 1) bedded sands within alluvium of San Emigdio Mesa; 2) sandy lenses within bouldery alluvium on the terraces offset by the Big Pine fault; 3) bedded sandy axial-fluvial sediment below the bouldery alluvium; and 4) young fluvial terraces preserved along

Wagon Wheel Canyon south of the Big Pine fault (Fig 2).

For 10Be surface exposure dating, we sampled material from three flat-topped granitic boulders partially embedded in the alluvial surface of San Emigdio Mesa. These were selected with the criteria of showing no obvious signs of spallation or weathering such as nearby flakes or ongoing exfoliation, or past burial and excavation as indicated by stable microtopography and intact soil near the sample locations. Isotopic analysis of

10Be abundance in quartz was carried out at Purdue University’s PRIME Lab. These data were corrected for sample thickness and topographic shielding, and were then corrected for latitude, longitude, elevation, and past geomagnetic effects following Pigati and

Lifton (2004). In order to use the most accurate cosmogenic production rate for 10Be, we also re-corrected the raw data of Stone’s (1998) Younger Dryas-aged samples from

Scotland. From this we determined the long-term integrated high-latitude sea-level 10Be production rate to be 4.35 atoms/g/yr. Following Partridge et al. (2003) we use the

meanlife of 10Be to be 1.93 ± 0.10 Ma - for discussion of ambiguity related to this value see note 34 therein.

3.2 Optical Dating

For OSL dating, bedded sands were sampled below the main pedogenic zone in order to ensure a sample of unmixed primary sediment. Since many of the deposits of interested were bouldery alluvium, we made significant effort to locate bedded and sorted sands that were clearly deposited by subaerial streamflow. These were sampled using opaque ABS pipe without exposing the sediment to light. Dose rate measurements were made directly in the field using a portable 4-channel gamma spectrometer calibrated by personnel at the United States Geological Survey. Environmental dose rate values are calculated using the conversion factors of Adamiec and Aitken (1998) and the grain-size attenuation factors outlined in Aitken (1986). Present-day water content values are assumed to be representative of those pertaining to the full burial period, and have been assigned relative uncertainties of ±50%.

Equivalent dose (De) analysis was undertaken at the Oxford University

Luminescence Research Group Laboratories. Quartz De measurements were made using the Single Aliquot Regeneration (SAR) protocol developed by Murray and Wintle

(2000). Individual De estimates were calculated for 15 aliquots (comprised of 100-300 grains) from each of the samples. Sample bleaching characteristics were then assessed from these populations of individual De estimates using the approach suggested recently by Bailey and Arnold (in press).

4. RESULTS

4.1 Timing of San Emigdio Mesa Deposition

Table 1 shows 10Be CRN surface-exposure ages for San Emigdio Mesa. In combination with field observation, we interpret the ages to record two stages of deposition on the San Emigdio Mesa surface; a major one ending near 28 ka, and a very limited alluvial episode around 14 ka that led to localized deposition at the mouths of small, steep drainages that remained graded to the alluvial surface at that time. This interpretation is supported by field observation of distinct, localized depositional landforms of the uppermost portion of San Emigdio Mesa from which the 14.3 ka sample was collected. We realize however that three CRN dates from alluvial boulders can only lead to highly interpreted ages because correction for inherited radionuclides and correction for loss of in situ-produced nuclides due to site erosion are nearly impossible without a larger dataset. To address this, we also employed OSL dating to the same landform.

Three OSL ages from San Emigdio Mesa come from bedded sands down-fan and down-section from the CRN sampling sites. These ages and are, as expected, older than the CRN dates (Table 2), suggesting deposition occurred between 51 and 75 ka if analytical uncertainties are taken into account. Comparison of these data to the cosmogenic surface exposure data suggests a few possibilities. It is possible that the

CRN data accurately indicate that deposition continued fairly slowly after deposition of the OSL-dated sands until at least 28 ka, or erosion of boulder tops has led to an

underestimation of their true exposure age. In either case, it appears the age of the deposit forming San Emigdio Mesa is <100 ka.

4.2 Big Pine fault slip rate

In order to estimate a slip-rate on the Big Pine fault, we needed to confirm that the alluvial deposits at different elevations across the fault trace are of equal age and therefore offset tectonically. Samples OSL9-11 are from the higher terrace on the southeastern side of the fault, and samples OSL7-8, 14, and 16 are from the lower, northwest side of the fault (Figs. 3, 4). Figure 5 displays the ages and associated errors from these deposits. These data indicate that the deposits have indistinguishable ages and represent a once co-planar geomorphic surface and underlying sedimentary deposit that has been offset by dip-slip motion on the Big Pine fault. This offset is approximately 10 meters (Fig. 6), providing a latest-Quaternary slip rate estimate of ~0.7 m/kyr.

Deposits exposed stratigraphically beneath the offset alluvial terrace are dominantly moderately-deformed Eocene strata on the southeast side of the Big Pine fault, but include horizontal loose to weakly-indurated, granite-derived, sandy to bouldery, bedded alluvium on the northeast side of the Big Pine fault (Fig. 7). Though not easily distinguished from (and previously mapped as) the nearby Plio-Pleistocene

Morales Formation, OSL ages from samples OSL5, OSL6 and OSL15 indicate that sediment was deposited between ~45 and 30 ka. This suggests that the sediment was

deposited along the axis of the ancestral Cuyama River prior to the progradation of alluvium shed from Pine Mountain.

We also dated two samples (OSL12, 13) from alluvium preserved as a terrace along Wagon Wheel canyon on the southeast up-thrown block of the Big Pine fault (Fig

2). This deposit was dated at ~2 – 3.5 ka (Table 2).

5. DISCUSSION

Our geochronological data and field observations indicate dramatic landscape development over the past million years in upper Cuyama Valley. At ~0.76 Ma, coarse- grained terrestrial deposition of the Plio-Pleistocene Morales Formation was occurring in the Cuyama structural basin. Subsequent contractional faulting and folding of sediments of the Morales Formation and underlying units record the continuation of transpressional tectonism in the Cuyama Badlands area well into the middle Pleistocene. This contractional deformation initiated regionally around 3-5 Ma (Ellis et al, 1993; Davis et al. 1988; Kellogg and Minor, 2005). Pre-Morales contractional deformation in the

Cuyama Badlands area is indicated by locally derived conglomerates and sedimentary breccias in the underlying Pliocene Quatal Formation, and by a local angular unconformity at the base of the Morales Fm. (Minor, 2004).

The Morales Formation was likely deposited in a topographic setting somewhat similar to the modern landscape. The great thickness of these granite-derived terrestrial deposits suggests that the Mt Pinos/Mt. Abel crystalline massif was either already high during deposition of the Morales Formation, or that the Morales Formation records

progressive uplift and denudation of those highlands. Ellis (1994) suggested that a distinctive boulder-bed and an overall coarsening approximately two-thirds of the way up-section in the Morales Formation in the Cuyama Badlands indicates increased uplift during deposition of the Morales Formation. There is no obvious syn-depositional deformation of the Morales Formation, and because in most places it is folded similarly to the underlying Quatal Formation, it appears that tectonic deformation affected the main part of the basin mostly after cessation of sediment accumulation.

The moderate post-Morales deformation was followed by formation of a low- relief erosion surface over the area now occupied by the Cuyama Badlands. This erosion surface was then mantled by the alluvium of San Emigdio Mesa and its correlative deposits elsewhere in the upper Cuyama River drainage. This alluviation occurred since

100 ka, and perhaps since 75 ka, which is more recent than a previous estimate based on correlation to other regional deposits (Davis, 1983). Minor faults identified by Stone and

Cossette (2000) deform alluvium of San Emigdio Mesa, indicating that intra-basin deformation has continued after its deposition. Further evidence for this intra-basin deformation was documented by Dibblee (1987a) who noted that what is likely an equivalent deposit to the San Emigdio Mesa alluvium is progressively more deformed to the northwest. In that area the underlying Morales Formation is also more steeply- dipping. This further illustrates the complex and abrupt spatial variability of deformation in this area.

As pointed out by Davis (1983), the lack of a clear relationship between the San

Emigdio alluvium and any distinct mountain-front fault seems to preclude a direct local

tectonic cause for this widespread alluviation. It appears this alluviation may correlate with alluviation on the nearby northern San Emigdio Mountain front (Keller et. al, 2000) and alluviation at Cajon Creek and the San Gabriel River in the eastern Transverse

Ranges (Bull, 1991) which likely have had a somewhat similar climatic history. These are from different tectonic settings, further suggesting response to regional climatic forcing. These depositional events occurred during oxygen isotope stages 5 (OIS5) through 4 (OIS4), during a time of generally cooling climates following the OIS5e interglacial. We do not have sufficient dating resolution to evaluate whether the distinct climatic transitions during OIS5 and OIS4 forced the alluviation or whether the overall cooler, perhaps wetter climate triggered the alluviation. It is clear that alluviation occurring between ~100 and ~50 ka is a common feature in the southwestern U.S., and as our dating methods become more precise, we may be able to propose more specific hypotheses about the causes of this alluviation in diverse settings.

It is apparent from our geochronological data that the termination of alluviation on San Emigdio Mesa predates the attainment of full glacial conditions at the OIS3-2 transition. This suggests that slopes were stabilized on the granitic highlands of Mt-

Pinos/Mt. Abel during OIS2 full-glacial climate, which was the coldest climate regime of the past 100 kyr, though perhaps it had lower effective precipitation than during interglacial times (Bull, 1991). This area was not subject to glacial erosion during the last Glacial period, and apparently fluvial action and periglacial processes were not sufficient to lead to significant sediment delivery from higher elevations. During OIS2, no alluviation was recorded on San Emigdio Mesa, but as glacial conditions began to

ease by 14 ka, localized alluviation occurred, as evidenced by field observations of bar and swale topography and a single CRN exposure age on the uppermost landform on San

Emigdio Mesa, which was possibly caused by regolith removal from hillslopes during the increasingly warm and wet climates that developed during post-glacial times.

Since the deposition of the alluvium of San Emigdio Mesa and its equivalents in upper Cuyama Valley, dendritic fluvial network development has dominated. The deeply incised canyons of the Cuyama Badlands are testament to the recent regional uplift and fluvial down-cutting that is affecting this area. In the canyons of the badlands, this incision appears to have only been punctuated by fluvial aggradation over the late

Holocene. Valley floors have been aggraded during this time with up a few meters of coarse alluvium.

5.1 Big Pine Fault

The alluvial deposits flanking the Big Pine fault near the upper Cuyama River provide additional clues about the development of landscape in the study area. Our OSL ages (Table 2) indicate that widespread, but fairly thin (<10 meters thick) alluviation from Pine Mountain occurred between ~25 and 14 ka (Fig 5), which is younger than alluviation on San Emigdio Mesa sourced from Mt. Abel. Either the timing of alluviation reflects a diachronous response to climatic forcing due perhaps to differing lithology or aspect of the source terrane, the Pine Mountain alluviation was a local response to tectonic uplift of Pine Mountain along the Big Pine fault, or the dominantly bouldery, but

relatively thin deposits record a few catastrophic events, such as landslides on the north flank of Pine Mountain that led to deposition toward the valley axis.

On both sides of the Big Pine fault, the originally sub-planar depositional surface has been modified. Alluvium on the southeast, up-thrown, side of the fault is deformed and likely differentially eroded as indicated by the undulating surface and gullying. The terrace surface on the southeast side of the fault appears highest along a small ridge

(hanging-wall anticline?) adjacent to the fault scarp (Fig. 6). A broad swale that makes up the majority of the surface area is potentially a broad tectonic syncline adjacent to the back limb of the hanging-wall anticline.

On the northwest, down-dropped, part of the alluvial surface, ridges and swales are likely also of tectonic origin. A distinctive ~2-meter-high scarp (Fig. 4) oriented subparallel to both the modern fluvial scarp of the Cuyama River and to the trend of the Big

Pine fault is possibly fluvial in origin, which would indicate that a cut-and-fill episode occurred during deposition. The OSL ages of the deposit below this scarp (OSL14 and

16; Table 2) are essentially indistinguishable from those above (OSL7 and 8; Table 2), suggesting instead that the scarp may be tectonic in origin. No exposure of deformed bedded alluvium was found near this and other local geomorphic features on the alluvial deposits, precluding any clear genetic interpretation.

The axial alluvium that is exposed beneath the Pine-Mountain-derived bouldery alluvium is dominantly sandy, and contains clasts of granitic material possibly derived from the Mt Pinos/Mt. Abel uplands, the Pliocene and Oligocene Plush Ranch formation exposed upstream to the west, and/or reworked Morales Formation (Fig 7). This

alluvium, dated at approximately 45 – 30 ka suggests that the main Cuyama River was established by that time, and was depositing sediment locally as headwater reaches incised into the older basin fill deposits and underlying rocks.

The dated late Holocene alluvial fill terraces in Wagon Wheel Canyon, which is a tributary of the upper Cuyama River on the southeast up-thrown block of the Big Pine fault (OSL12, 13, see Fig. 2, and Table 2), sit ~1 meter above incised bedrock. This incised bedrock is characteristic along canyons on the southeast side of the Big Pine fault, usually below bedrock-alluvial or bedrock-colluvial contacts (Minor, 2004). Bedrock incision is often considered to be the fundamental fluvial response to tectonic uplift (Bull,

1991). This observation, in combination with the fact that overall topographic relief is higher on the southeast side of the Big Pine fault, are further evidence that tectonic uplift has occurred, and may still be occurring, on the up-thrown side of the Big Pine fault during the latest Pleistocene and Holocene.

Our ages and measurements lead us to propose a minimum late Quaternary vertical-component slip-rate on the eastern Big Pine fault of ~0.7 m/ky. Our observations of surface deformation away from the fault and Minor’s (2004) interpretation of more than one strand of the Big Pine fault in this area, suggest that the overall strain rate on the fault zone could be somewhat higher. Since our ages are depositional ages, and do not therefore date the age of surface abandonment, the time during which the 10 meters of offset occurred could have been somewhat less than 14 kyr. Also, observations of oblique slip along the eastern Big Pine fault (Minor, 1999; 2004) suggest that net slip

along the fault was somewhat greater than the vertical offset. Collectively, these factors imply a greater slip rate than the proposed 0.7 m/kyr minimum.

These conclusions have bearing on the seismic hazard associated with the Big

Pine fault. Reverse-slip recurrence intervals on historically aseismic faults are a poorly quantified hazard in southern California (Peterson et. al., 1996). We suggest that although no historical ruptures have been confirmed on the Big Pine fault, potential for future seismicity exists.

6. CONCLUSIONS

Our new understanding of the upper Cuyama River geomorphic system provides a working model for the evolution of other late Cenozoic basins in coastal California.

These structural basins (such as the Salinas, Lockwood Valley, Ventura, Carrizo Plain,

structural relief across increasingly abundant and concentrated structures within and bordering the depositional basins, leading to basin “extinction” as basin-filling was replaced by incision, and 3) significant climatically-controlled late Pleistocene alluviation over a wide variety of erosional surfaces, allowing for establishment of timing in these landscapes.

Additionally, we propose a latest-Quaternary fault-slip estimate on the Big Pine fault of 0.7 m/kyr. This serves as a reminder of both the ongoing nature of tectonic landscape development and the seismic potential of historically aseismic reverse faults throughout southern California.

7. ACKNOWLEDGEMENTS

This study was supported by NSF EAR-0309518, a USGS EDMAP grant, a

PRIME Lab seed analysis grant to J. Pelletier, support from USGS-SCAMP, Chevron-

Texaco, the Arizona Geological Society, and by Butler and Katzer scholarships to SD via the University of Arizona Department of Geosciences. Thanks to M. Grace for field assistance. Thanks to J. Pigati for guidance with CRN methods. Thanks to S. Mahan

(USGS) for assistance with OSL dosimetry. Thanks to A. King (USFS) for research permits, and private landowners for access. Thanks to J. Pelletier, E. Keller, L. Owen and an anonymous reviewer for helpful reviews of an earlier version of this manuscript.

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Murray, A.S. and Wintle A.G., 2000. Luminescence dating of quartz using an improved single-aliquot regenerative-dose procedure: Radiation Measurements v. 32, 57-73.

Page, B.M., Thompson, G.A., and Coleman, R.G., 1998. Late Cenozoic tectonics of the central and southern Coast Ranges of California: Geological Society of America Bulletin, v. 110, 846–876.

Partridge, T. C., Granger, D. E., Caffee, M. W., and Clarke, R. J., 2003. Lower Pliocene Hominid Remains from Sterkfontein: Science, v. 300, no. 5619, 607-612.

Petersen, M. D., Bryant, W.A., Cramer, C.H., Cao, T., Reichle, M.S., Frankel, A.D., Lienkaemper, J.J., McCrory, P.A., and Schwartz, D.P, 1996. Probabilistic seismic hazard assessment for the State of California California Division of Mines and Geology Open- File Report 96-08. U.S. Geol. Surv. Open-File Report. 96-706.

Pigati, J. S., and Lifton, N. A., 2004. Geomagnetic effects on time-integrated cosmogenic nuclide production with emphasis on in situ 14C and 10Be: Earth and Planetary Science Letters, v. 226, no. 1-2, 193-205.

Stone, J. O., Ballantyne, C. K., and Keith Fifield, L., 1998. Exposure dating and validation of periglacial weathering limits, northwest Scotland: Geology, v. 26, no. 7, 587-590.

Stone, P., and Cossette, P.M., 2000. Geologic map and digital database of the Apache Canyon 7.5’ quadrangle, Ventura and Kern Counties, California: U.S. Geological Survey Open-File Report 00-359, scale 1:24,000, 1 sheet, 22 p. text.

Vedder, J. G., 1970. Geologic map of the Wells Ranch and Elkhorn Hills quadrangles, San Luis Obispo and Kern Counties, California: U.S. Geological Survey Miscellaneous Geologic Investigations Map I-585, scale 1:24,000.

White, L. A., 1992. Thermal and unroofing history of the western Transverse Ranges, California: Results from apatite fission track thermochronology. Ph.D. Thesis, University of Texas, Austin.

TABLE 1. COSMOGENIC 10BE DATA AND RESULTS

Sample Sample Elevation Thickness 10Be† 10Be age‡ S * ID Description (m) t correction (103 atoms/g) (ka)

A Granitic Boulder 1575 1.0001 1.027 436 ± 14.6 32.3 ±1.0

B Granitic Boulder 1580 1.0001 1.044 179 ± 10.4 14.3 ± 0.7 C Granitic Boulder 1627 1.0001 1.027 390 ± 13.9 28.2 ± 0.9 *Topographic shielding factor †Corrected for chemical blank value, sample thickness and topographic shielding. Error displayed is analytical error only. ‡Age determined following Pigati and Lifton (2004) with a time-integrated HLSL 10Be production rate of 4.35 atoms/year. No erosion or burial assumed.

TABLE 2. OSL DATA AND RESULTS

Sample Depth Dose rate D Burial age Unit* e ID (m) (Gy/ka) (Gy) (ka) OSL2 SEM 5 4.07 ± 0.23 246.6 ± 22.1 60.6 ± 6.4 OSL3 SEM 6 4.25 ± 0.23 244.8 ± 24.3 57.5 ± 6.5 OSL4 SEM 9 4.14 ± 0.23 288.1 ± 17.3 69.5 ± 5.7

OSL5 Qaaxial 17 4.31 ± 0.23 194.4 ± 24.9 45.1 ± 6.3

OSL6 Qaaxial 16 4.10 ± 0.22 133.5 ± 16.9 32.6 ± 4.5 OSL7 QaNW 5 4.60 ± 0.25 73.0 ± 13.0 15.9 ± 3.0 OSL8 QaNW 7 4.18 ± 0.23 79.1 ± 7.8 18.9 ± 2.1 OSL9 QaSE 4 5.27 ± 0.30 75.2 ± 9.1 14.3 ± 1.9 OSL10 QaSE 3.7 4.47 ± 0.25 78.2 ± 5.6 17.5 ± 1.6 OSL11 QaSE 3 4.56 ± 0.24 110.8 ± 11.3 24.3 ± 2.8

OSL12 QaH 2 5.16 ± 0.28 15.5 ± 2.77 3.0 ± 0.6

OSL13 QaH 2 4.95 ± 0.28 11.3 ± 1.9 2.3 ± 0.4 OSL14 QaNW 3 4.37 ± 0.23 88.5 ± 16.9 20.2 ± 4.0

OSL15 Qaaxial 12 4.5 ± 0.24 141.4 ± 16.1 31.4 ± 3.9 OSL16 QaNW 6 4.26 ± 0.24 93.7 ± 8.8 22.0 ± 2.4

*SEM – alluvium of San Emigdio Mesa; Qaaxial; QaNW – Alluvial terrace NW of Big Pine Fault; QaSE – Alluvial terrace SE of Big Pine Fault; QaH – Holocene alluvium of Wagon Wheel Canyon; Qaaxial – Axial alluvium stratigraphically below QaNW

Figure 1. Location and tectonic setting of study area.

Figure 2. Shaded-relief digital elevation model showing topographic setting of study area and geochronological sample locations. Trace of Big Pine fault (white line) from Minor (1999, 2004)

Figure 3. Oblique aerial photo drape over DEM looking southwest at fluvial terraces flanking and offset by the Big Pine fault. Vertical exaggeration is approximately 2X. Stratigraphic unit symbols same as that of Table 2. OSL sample locations indicated by circles and labeled with sample IDs (squares). See Table 2 for stratigraphic depths, stratigraphic units, and OSL burial-age data. The Big Pine fault is an oblique reverse-slip fault in this area (Minor, 2004). In this view, the area to the left of the fault is the southeastern, up-thrown block.

Figure 4. Map showing geologic setting of alluvial terraces flanking the Big Pine fault (simplified from Minor, 2004).

Figure 5. OSL ages from alluvium offset by Big Pine fault. Samples indicated by closed circles and are from the southeast, up-thrown block, and the samples indicated by squares are from the down-thrown, northeastern block. Age error is indicated by vertical bars. Stratigraphic depths are given in Table 2. The deposits across the fault have indistinguishable ages based on these data.

Figure 6. Topographic profile generated from USGS 10-meter DEM of Big Pine fault scarp offsetting alluvium. Location of A – A’ is marked on Fig. 4.

Figure 7. Exposure along Cuyama River bed of Pine Mountain-derived alluvium over bedded axial-fluvial facies. Locations of OSL samples referred to in Table 2 are shown.

APPENDIX D

Submitted to Geological Society of America Bulletin, 2005

Bedrock landscape development modeling: calibration using field study, geochronology and DEM analysis

DeLong, Stephen B.2 and Pelletier, Jon D. Department of Geosciences, University of Arizona, 1040 E 4th Street, Tucson AZ 85721, USA

Arnold, Lee, Oxford Luminescence Research Group, School of Geography and the Environment, University of Oxford, Mansfield Rd, Oxford OX1 3TB, UK

Keywords: Landscape development; erosion; modeling; DEM; Cuyama Basin

ABSTRACT

Stream-power-based models of bedrock landscape development are effective at producing synthetic topography with realistic fluvial-network topology and three- dimensional topography, but are difficult to calibrate. This paper examines ways in which field observations, geochronology and DEM data can be used to calibrate a bedrock landform development model for a specific study site. We first show how uplift rate U, bedrock erodibility K, and landslide threshold-slope Sc are related to steady-state relief, hypsometry, and drainage density for a wide range of synthetic topographies produced by a stream-power-based planform landscape development model. Our results indicate that low U/K values result in low-relief, high-drainage-density, fluvially-dominated topography, and high U/K values lead to high-relief, low drainage density, mass-wasting- dominated topography. Topography made up of a combination of fluvial channels and

2 Corresponding author: [email protected]

threshold-slopes occurs for only a relatively narrow range of U/K between 10 and 5000 m·kyr/kyr. Using measured values for hypsometric integral, drainage density and relief, the U/K value can be further constrained, enabling K to be determined if U is independently known.

We applied these techniques to three sedimentary rock units in the western Transverse

Ranges in California that have experienced similar climate, uplift and incision histories.

10Be surface exposure dating and OSL burial dating data indicate that incision of initially low-relief topography there occurred during the last ~60 kyr. We estimated the ratio of drainage area and slope exponents (m/n) is from slope-area data, and inferred K values ranging from 0.09 to 0.3 m(0.2-0.4)kyr-1 for the rock types in our study area.

INTRODUCTION

The stream-power-law (or similar shear-stress-based methods) forms the foundation for many bedrock landscape development models (e.g., Howard, 1994; Whipple and Tucker,

1999). When stream-power-based bedrock channel development models are coupled with hillslope process models that include threshold-landsliding and/or hillslope diffusion components, three-dimensional landscape development modeling is possible (e.g., Tucker et al., 2001; Howard, 1994). We were motivated by the need to understand how each parameter in bedrock landscape development models affect model topography, and the need to develop general techniques for calibrating landscape development models using

geologic and morphometric analyses. This motivation led us to apply a landscape development model with a minimum of free parameters in an effort at calibration using geologic and morphologic data from a field site in southern California.

Wide-ranging estimates for model parameters are often used in bedrock landscape development models. Stock and Montgomery (1999) proposed a range in stream-power law erodibility coefficient K over five orders of magnitude for varying rock types, and this wide range is often used in other modeling studies. Because the stream-power law is very sensitive to the value of K and because Snyder et al. (2000) proposed a linkage between uplift rate and K, we were interested in creating a more specific calibration technique for the stream-power law that relies on geologic constraints of uplift rate, and morphometric landscape analyses to calibrate K. Snyder et al. (2000) also provided insight regarding use of landscape morphometry to constrain the values of stream-power law exponents m and n. By integrating these studies’ findings into a fully-coupled landscape modeling environment, we hoped to further refine our understanding of the effect of model parameters as a step towards improving our ability to calibrate even more sophisticated landscape development models.

We utilized the model of Pelletier (2004) and field data from the upper Cuyama Valley in southern California in an effort to develop a general method for calibrating the coefficient of bedrock erodibility K in the following formulation of the stream-power law:

n h h = U KAm , (1) t x

in which h is elevation, t is time, U is uplift rate and/or local base-level lowering rate, K is a constant often referred to as the “coefficient of bedrock erodibility”, A is the contributing drainage area which serves as proxy for local discharge, x is the along- channel distance and m and n are exponents (Whipple and Tucker, 1999). Our model erodes the landscape according to (1) and incorporates mass-wasting-dominated hillslope development by removing hillslope material during each time-step from cells that exceed a local landslide-threshold slope Sc. We suggest that because the model is limited to one of the simplest possible formulations of a coupled hillslope-channel landscape development model that appears to produce realistic-seeming landscapes, we are able to uniquely determine each parameter’s affect on landscape morphology. We do not suggest the model adequately captures the possible range of geomorphic processes at work on uplifting orogenic blocks.

In the first part of this study we performed model runs in which we varied the three key model parameters K, U, and landslide-threshold slope Sc systematically in order to evaluate their influence on synthetic landscape morphometry. For each set of parameters, we ran our model until steady-state was achieved and then extracted values for (1) landslide threshold-slope; (2) hypsometric integral (Strahler, 1952); (3) drainage density;

(4) topographic relief; (5) mean elevation; and (6) the nondimensional “ruggedness

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number”, which is equal to topographic relief multiplied by drainage density (Melton,

1957). By carefully controlling model parameters and characterizing resulting topographies, we were able to quantify how each model parameter affects output topography.

Next, we calibrated the parameter K for three distinct lithologic units in Southern

California by comparing model-produced synthetic morphometry against actual morphometry measured in the field and from DEM data. Geologic and geochronological data provided important constraints on this work. Incision into an alluvium-capped late

Pleistocene erosion surface has formed equal-aged drainage networks having varying morphology in several distinct rock types in the upper Cuyama Valley, California (Davis,

1983). This study area is therefore appropriate for this type of study because initial topography, age of incision, down-cutting rate, topographic relief, and landslide threshold-slope are all known and vary across three lithologies. We characterized real- world topography and compared it to our model-run outputs generated with controlled input parameters. From this we estimated best-fit values of K using data from digital elevation model analysis and geochronology. Our results apply to drainage basins having fluvially-dominated channel incision and planar landslide-dominated hillslopes.

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Previous Bedrock Landscape Development Model Calibration

Howard (1997) used a shear-stress-based landscape development model (Howard, 1994) in an effort to detail how model parameterizations affected landscape morphology and to interpret the morphology and development of badlands in Utah. This work was an important step in comparison of numerical landscape development models to actual topography, and highlighted the need for additional studies of its kind. Howard considered threshold-landsliding and diffusive hillslope development for both threshold and non-threshold shear-stress-based fluvial incision. He then applied a best-fit model choice, based primarily on relief production, to support interpretations about the erosional history of badlands near Caineville, Utah. This calibration was semi-quantitative and model run topography did not duplicate actual drainage density owing to computational limitations at the time. He did not undertake a comprehensive set of steady-state model runs to determine each model parameter’s effect on model topography, but rather focused on identifying the most likely temporal incision regime. He used a one-dimensional formulation to assess model parameterization effect on drainage density. This study serves as an excellent example of the usefulness of field-calibrated landscape development modeling, and serves as an important complement to the work presented here.

Whipple and Tucker (1999) provided an excellent review and analysis of the fundamentals of stream-power-law modeling. Attempts to calibrate the stream-power

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law have relied primarily on analysis of ‘paleo’ and modern stream profiles in a two- dimensional sense. These studies demonstrated the applicability of stream-power-law- based techniques to understanding landscape development. Howard and Kerby (1983) first formalized ideas about the relationships between discharge, slope and bedrock resistance into a stream-power law and estimated values for m and n using slope-area relationships in a badland channel. Following their general techniques, Stock and

Montgomery (1999), Seidl et al. (1994), and Rosenbloom and Anderson (1994) each calculated values for K using data from channel longitudinal profiles. In a particularly influential contribution, Stock and Montgomery (1999) integrated topographic data from varied settings in a consistent manner to provide several order-of-magnitude estimates of

K for various rock types using a number of stream-power law formulations. Their study suggested that values for K vary over as much as five orders of magnitude in different lithologies.

Snyder et al. (2000) highlighted the possible dependence of K on local values for uplift rate U by analyzing stream profiles in California with varying uplift rates as constrained by uplifting marine platforms. They found that depending on the choice of exponent n, values for K could increase by as much as six-fold in areas of higher uplift rate, even with very similar lithology. However, the processes responsible for a relationship between U and K have not been determined.

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Use of the stream power law to model bedrock incision does not take into account all details of fluvial process, and more sophisticated models have been produced to improve on the stream-power law. These refinements have been made within several landscape development models, usually in an effort to illuminate details of specific (though often common) processes at work in specific field sites. These refinements have included debris-flow incision of channels (Stock and Dietrich, 2003), saltation and abrasion-forced bedrock channel incision (Sklar and Dietrich, 2004), soil production, slope cohesion and non-mass-movement-dominated hillslopes (e.g., Roering, et al. 2001). Perhaps the most widely-published model is the CHILD model (e.g., Tucker et. al., 2001), which is a flexible and sophisticated landscape development model that includes many parameters that help to simulate many specific surface processes. Models such as these will undoubtedly form the foundation of the next generation of three-dimensional landscape development models. More sophisticated models have a larger number of parameters in need of calibration, but as we become more confident in our ability to calibrate specific mechanistic process-models, we can apply the techniques proposed in this study to better understand each parameter’s affect on large-scale topographic indicators. We believe that while our study does not calibrate the most sophisticated landscape development models available, it is an important step in our ability to do so.

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MODELING APPROACH

Most landscape development models to date have been designed such that an ideal steady-state is reached when exhumation equals uplift – leading to time-invariant topographic configuration. Recently, Pelletier (2004) showed that important long-term variation in landscape development can be captured with incorporation of a more sophisticated flow-routing algorithm. Pelletier’s model followed upon classic models developed over the past two decades (e.g. Willgoose et al. 1991; Howard, 1994; Tucker and Slingerland, 1997). For the purpose of determining whether erosional parameters can be determined from topography with a forward-modeling approach, Pelletier’s model has the advantage of requiring very few input parameters.

Following Pelletier (2004), we utilized a bedrock landform development model that solves equation (1) on a rectangular grid subject to uniform rate of combined tectonic uplift and base-level lowering having a fixed-elevation boundary condition (all material that reaches the edge of the grid is removed in each time-step). The model uses bifurcation-flow routing as a technique for calculating parameter A. This allows for long- term migration of ridges and valleys and better approximates discharge-dependent incision rates in low-relief areas such as hillslopes and valley-floors by allowing for divergent flow and thalweg widths wider than model pixel size. The model includes threshold-landsliding such that material from slopes steeper than the defined threshold- slope Sc is removed from upslope each time-step until all slopes do not exceed Sc.

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The parameters needed for each model run are grid geometry, U, K, Sc, m, n and model run-time. For calibration runs, U and Sc were approximated from geologic and topographic data and K is our primary independent variable. While the precise values of m and n are difficult to constrain, determining m/n is relatively straight-forward by regression of slope and area data. (Tucker and Whipple, 1999; Snyder et al., 2000). For the model runs performed in the effort to assess the effects of variations in K, U, and Sc on model topography, we assumed n = 1 and m = 0.5, which are commonly used values for these parameters. For calibration efforts we determined m/n from slope and area data, and assumed n = 1 (following Snyder et al. (2000)).

Characterization of Synthetic and Real Topography

In order to compare model results with geological reality, we characterized both model- derived synthetic topography and upper Cuyama River drainage basin topography according to several morphometric indicators. For characterization of real topography, we used 10m USGS DEM data and direct field observation. We used the following parameters to characterize both model topography and real topography: (1) landslide threshold-slope, which was measured in the field with an inclinometer; (2) hypsometric integral; (3) drainage density; (4) topographic relief; (5) mean elevation; and (6) the nondimensional “ruggedness number” which equals relief multiplied by drainage density.

Modeled drainage density was calculated by characterizing all parts of the grid as having

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or exceeding landslide-threshold slopes as being hillslope and all others as being part of the channel network. The drainage density is then total length of channels divided by total basin area (with units of 1/L). We normalized this to the maximum possible drainage density in order to minimize dependence on DEM pixel size. This method works well for idealized model outputs, but in actual topography variation in threshold- slope, presence of colluvial material and other topographic irregularities lead to parts of the landscape being inappropriately lumped in with the channel network. For this reason, we estimated the maximum channel slope within each lithologic unit and applied that measurement as the upper threshold for classification of cells as channels and all steeper areas as hillslopes. While this method also is not perfect, we believe it to be a reasonable approach for comparing synthetic and real topography.

RESULTS: SYNTHETIC LANDSCAPE DEVELOPMENT

To capture the full range of possible model and real-world topographies, we used a wide range of model parameters in our synthetic model runs using 15 km-square grids and 30- meter grid cells. In order to evaluate the calculated variability in K reported by Stock and

Montgomery (1999), we varied K over five orders of magnitude ranging from 10-4 to 101

-1 kyr . We varied landslide-threshold slope Sc from 20° to 40° and U from 0.1 m/kyr to 50 m/kyr. For these runs, we used a fifteen-kilometer-square grid containing 250,000 pixels.

A complete model-output dataset can be found in the GSA data repository3.

3 GSA Data Repository item, landscape development model data

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Model Behavior and Classification of Model Topography

Our model run results were synthetic landscapes that were be classified into three categories. These categories are best applied in model-space, as actual topography has more complexity than this classification scheme can adequately capture. “Type-I” synthetic topographies have dendritic drainage network morphology in which fluvial erosion dominates the entire landscape such that all slopes are below the threshold angle

Sc and topographic relief is limited; “Type-II” synthetic topographies consist of a combination of dendritic channel networks and planar threshold-slopes; and “Type-III” synthetic topographies are characterized by threshold-landsliding that outpaces fluvial erosion such that the steady-state form is made up of entirely unchanneled threshold- slopes. Figure 1 illustrates the three types of synthetic topography that result from varying K while holding other model parameters constant. Table 1 contains the key morphologic indicators extracted from those model runs. Type-III topographies are clearly not present in their idealized pyramidal form in nature, but perhaps roughly approximate mass-wasting-dominated bedrock plateaus. Type-III topographies are likely limited in nature by the tendency for large topographic loads to cause subsidence, which would offset high values of U, especially in areas of resistant bedrock. Furthermore, resistant, rapidly uplifting massifs are clearly not well-modeled by our simple model because the model does not incorporate other processes such as glacial erosion and channel debris flows, which are clearly important in many high-elevation orogenies

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worldwide. Type-II topographies are common, and simulate the geologic reality in a number of tectonically-active regimes, including the upper Cuyama drainage basin.

Type-I topographies generally do not form high relief and contain drainage divides that are eroded primarily by fluvial processes. These are perhaps similar to fluvially- dominated badland topography, but are likely highly transient over geological timescales in natural settings.. Fig. 2 shows that for all model runs (n=172), Type-II basins are formed for a relatively narrow range of values for K and U. For a given uplift rate U,

Type-II topography occurs over less than three orders of magnitude of K.

The limits of applicability of this model, and our wide-ranging model-run-output dataset, deserve clear discussion. Since our model is limited in the number of processes explicitly represented, the end-member model topographies are likely the least appropriate for such a simple model. Low-relief, low-uplift rate topographies likely are more highly dependent on non threshold-landsliding hillslope processes, as processes related to soil- formation and “diffusive” processes become important. Additionally, in areas of high uplift-rate, glacial and/or debris-flow processes likely become more important. Sobel et al, (2003) also showed that in rapidly uplifting zones having resistant lithologies, fluvial- system development can become “defeated” leading to formation of internal drainage.

This phenomena is not represented in our model, and requires the explicit representation of distinct structural boundaries. This model is most applicable to moderate-relief, moderate uplift-rate topography in which (as in our field area) field inspection indicate that threshold-landsliding and fluvial channel erosion dominate. We present the full

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dataset as a starting point for analyses of this type, and caution the reader against applying it universally without accounting for process-variation.

In order to determine how morphologic indicators depend on variables U, K, and Sc, we characterized our synthetic topography according to the morphologic indicators mean elevation, topographic relief, drainage density, ruggedness number, and hypsometric integral. In our method of calculating drainage density, Type-I topographies on 30-meter grids have achieved maximum theoretical drainage density of 0.0333 m-1 (sum of model channel pixel lengths divided by total model pixel area; the absolute value of this maximum drainage density is sensitive to model pixel geometry.), and Type-III topography has drainage density equal to zero. Our Type-II topographies have drainage density ranging from just above zero to just below 0.0333 m-1. These values can be normalized to the maximum drainage density for ease of comparison.

The size of the model grid affects the magnitude of most output morphologic characteristics, (e.g. topographic relief increases with a larger grid size). Our model results are scalable, however, and the relative value of each of the morphologic indicators remains consistent, regardless of actual grid size. For model comparison to actual topography, we ran targeted model runs on grids having the same area as our sub- sampled real DEMs in order to eliminate any ambiguity created by choice of grid size.

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Fig. 3 shows how variation in parameter K and U affected synthetic topography for selected model runs having the same threshold-slope (20°) (the full dataset from which this figure was derived can be found in the Supplemental Material). From these plots, we concluded that drainage density and mean elevation are the most useful morphometric indicators for model comparison. These indicators show monotonic change with change in model parameters U and K, whereas steady-state hypsometric integral varied little except in cases of extremely low relief, and ruggedness number depends on two indicators (drainage density and mean elevation) that tend to have an inverse relationship, leading to complex and non-monotonic variation with changes in U and K. Relief changed in the same direction as mean elevation; however mean elevation was less sensitive to local irregularities in high elevation portions of the topography. The value of

K affected drainage density, basin relief, and mean elevation most significantly. Since K is the primary control on the erodibility of a landscape, higher values of K (weaker rocks) led to limited relief development. For our highest K value (10 kyr-1), topographic relief over a 15 km-square grid was less than 100 meters; and when keeping all other parameters equal, an order-of-magnitude increase in K limited relief by as much as a factor of five. This relief limitation is related to the effect K has on drainage density. As

K increases, drainage density increased as well, and by having closely-spaced highly erosive channels, bedrock ridges could not generate substantial relief between channels.

Uplift rate also has a strong control on steady-state topography, and acts to counter K.

Higher uplift rates led to increased relief development and lower drainage density when

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all other parameters were held constant, which is consistent with the findings of Howard

(1997). An order of magnitude increase in uplift rate commonly led to a three-to-fourfold increase in model topographic relief in our model runs.

Fig. 4 illustrates results from representative model runs, highlighting the effect of the composite parameter U/K and Sc on model topography. U/K is the primary control on relief production, and increases with either high uplift rates, or with increasing rock strength (smaller K), or a combination of the two. Synthetic landscapes formed by model runs with high U/K values tended to be higher and dominated by mass-wasting processes rather than by fluvial processes. For model runs with U/K values of less than 100 m·kyr/kyr, relief was limited to less then 300 m over a 15 km-square grid. On the other end of the spectrum, model runs with U/K values more than 1000 m·kyr/kyr all had topographic relief exceeding 2500 m. Variation in model parameter Sc also affected model topography. This can also be seen in Fig. 4. Increasing the threshold-slope led to increased drainage density within Type-II topography by allowing for more closely- spaced drainage divides and narrower canyons. Though drainage density was enhanced by higher values of threshold-slope, and higher drainage density tends to correlate with lower mean elevation, we still produced higher topographic relief and higher mean elevation in our synthetic topography with higher threshold-slopes for the same value of

K. Because relief and drainage density are both positively correlated with Sc, the ruggedness number showed an extremely strong positive correlation with Sc. The magnitude of the effect on topography from variation in Sc was not nearly as strong as

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that of U or K, as it mostly controlled the geometry of the interchannel divides – higher threshold-slopes led to narrower, taller ridges. For example, model runs with U = 1.0 m/kyr and K = 0.01 kyr-1 on a 15 km-square grid showed an increase in mean elevation from ~250 m to ~300 m with an increase in Sc from 20° to 40°, while drainage density increased from 0.0017 to 0.0036 m-1.

MODEL CALIBRATION: GEOLOGICAL CONSTRAINTS

In order to calibrate any model to a specific study site, an understanding of geological reality is necessary. In our study area in southern California, this required determining the ages of key sedimentary deposits. We discuss the techniques, data, and interpretation in some detail in the next section. We build upon recent detailed mapping by USGS personnel in the study area (Minor, 2004; Kellogg and Miggins, 2002; Stone and

Cossette, 2000; Minor, 1999). Figure 5 shows the tectonic setting of our field area. The upper reaches of the Cuyama River and its tributaries form dendritic drainage networks in several different lithologic units (Fig. 6). This fluvial incision post-dates cessation of deposition in the ancestral Cuyama depositional basin, which occurred sometime since ~1

Ma as evidenced by what is likely Bishop ash (760 ka) or possibly Glass Mountain ash

(1.0 - 1.1 Ma) (Stone and Cossette, 2000) found in the uppermost part of the Cuyama basin section. Since cessation of widespread basin-filling, compressional deformation occurred in the study area which was likely caused by increasing transpression along the

“Big Bend” section of the San Andreas Fault to the northeast of the study area.

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Deformation and erosion led to formation of an undulating planation surface that truncates bedding on the top of the basin-fill sediments. This surface was subsequently overlain by a widespread, but possibly discontinuous blanket of alluvium (Davis, 1983).

Initiation of incision of the upper Cuyama River drainage basin has eroded the alluvium and underlying Cuyama Basin-fills and left alluvium as ridge-top remnants and, in its largest preserved form, as the alluvium of the San Emigdio Mesa in the headwater reaches of the Cuyama drainage network. The age of this alluviation should therefore serve as the maximum age of the development of the modern drainage network in our study area.

We attempted to calibrate the model using our understanding of late-Pleistocene landscape development in three lithologic units: (1) The Plio-Pleistocene Morales

Formation, a weakly to moderately-consolidated conglomerate and coarse sandstone unit deposited in a terrestrial environment in response to late-Cenozoic compressional tectonics (Page et al., 1998); (2) the Pliocene Quatal Formation, a generally silty to clayey terrestrial sandstone with interbedded conglomerates; and (3) the Eocene Matilija sandstone, a complex marine unit having facies of sandstone, conglomerate, siltstones, and shale (Minor, 2004). Each of these units are weak enough to have experienced significant drainage development during the late Quaternary, however enough differences exist in characteristics such as sedimentary structure, bedding attitude and material properties such that each formed somewhat different landscape morphologies in response to similar forcing.

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The most dramatic lithologic contrasts exist across the Big Pine fault, a northeast- trending oblique reverse fault that places Eocene rocks against Miocene through

Pleistocene rocks (Minor, 2004; Minor 1999). While this creates a favorable configuration of differing rock types within a single drainage basin, possible late-

Pleistocene vertical movement on the Big Pine Fault complicates our analysis somewhat by introducing possible variation in U across the Big Pine Fault. We address this by analyzing spatial relationships between equal-age alluvial deposits across the fault zone.

While our study area is referred to as the Cuyama badlands, it should be noted that much of the area does not display the classic features of badland topography. Topographic development in the three lithologic units that we studied were not characterized by densely gullied, fluvially-dominated, slopes, but were rather made up of generally planar threshold slopes and fluvial channels. It appears that coupled shallow landsliding and fluvial incision have been the dominate late-Quaternary surface processes. We found no evidence for debris-flow incision, and soil production is limited to several centimeters on vegetated slopes, which form a mosaic with more recently-failed threshold-slopes. Deep soils are limited to interchannel areas on which San Emigdio Mesa-equivalent alluvium is preserved. This limited scope of active process, the moderate relief of tens to hundreds of meters and the moderate uplift rates of 1-3 m/kyr, we believe, justifies our choice of a very simple landscape development model.

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Surface Exposure Dating, Burial Dating, Uplift Rate and Model Calibration

The alluvium that forms San Emigdio Mesa was deposited discontinuously over an undulating Pleistocene erosion surface (Davis, 1983). We correlated this alluvium with alluvial remnants preserved throughout the upper Cuyama drainage basin on both sides of the Big Pine Fault as well. These correlations are based on map relationships, similar and indicative crystalline source material, soil color, and soil texture. Soils formed on all correlative deposits tend to have 5YR color, incipient argillic or cambic B-horizon formation, and no visible petrocalcic accumulation. These alluvial deposits form a measurable datum that marks the most recent time pre-dating fluvial network incision.

We therefore use the age of the San Emigdio Mesa as an estimate for the age of the erosional landscape in the upper Cuyama region. Previous workers suggested that the alluvium of San Emigdio Mesa (the large preserved alluvial remnant that predates formation of the drainage network) (Fig. 6) was as young as late-Pleistocene in age

(Dibblee, 1972; Davis, 1983), though their correlations with dated sediments elsewhere were not justified in detail.

10Be Surface Exposure Dating

For 10Be surface exposure dating, we sampled material from three flat-topped granitic boulders partially embedded in the alluvial surface of San Emigdio Mesa (Fig. 7). These were selected with the criteria of showing no obvious signs of spallation, weathering, or

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past burial and excavation (Fig 7B). Soils developed on this alluvial surface are suggestive of long-term stability, and the lack of gullying or removal of upper fine- grained and reddened soil horizons are our criteria for lack of past burial and excavation.

Isotopic analysis of 10Be abundance in quartz was carried out at Purdue University’s

PRIME Lab according to standard procedures. These data were corrected for sample thickness and topographic shielding, and were then corrected for latitude, longitude, elevation, and past geomagnetic effects following Pigati and Lifton (2004). In order to use the most accurate cosmogenic production rate for 10Be, we also corrected the raw data of Stone’s (1998) Younger Dryas-aged samples from Scotland. From this we took the long-term integrated high-latitude sea-level 10Be production rate to be 4.35 atoms/g/yr. Using Clark et al.’s (1995) data, we followed the same procedure to calculate an integrated production rate of 4.58 atoms/g/yr, but opted to use Stone’s data because we judged it to have better independent age control. Following Partridge et al. (2003) we use the meanlife of 10Be to be 1.93 ± 0.10 Ma, for discussion of ambiguity related to this value see note 34 therein.

Our 10Be results (Table 2) indicate a late-Pleistocene age for the San Emigdio Mesa.

Sample B has a 10Be age of only 14.3 ka, which records the most recent localized deposition on the surface of the San Emigdio Mesa. Sample B is from an area that is below a set of steep, small drainages that are graded to the surface of the mesa. These drainages appear to be relatively inactive currently, and appear to have last deposited material onto the mesa during the latest Pleistocene. Our other two cosmogenic boulders

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are from areas that did not receive deposition as recently, and likely reflect the most recent widespread deposition on the alluvial surface that predated the most proximal incision. The relative proximity of the sample locations on the alluvial deposit to the sediment source area, the degree of soil formation and the youth of all exposure ages compared to previous estimates and our OSL ages (see next section) lead us to believe that inherited cosmogenic radionuclides from pre-depositional exposure are negligible.

Our 10Be data does show scatter, and this and the small number of samples necessitates the use of OSL burial dating to further support our interpretations.

OSL Burial Dating

We employed optically-stimulated luminescence (OSL) techniques to three samples of bedded alluvial sands from near the top of a ~60 m slope of nearly horizontally-bedded sandy alluvium unconformably capping deformed basin-fill on the San Emigdio Mesa.

Bedded sands were sampled below the main pedogenic zone in order to assure a sample of unmixed primary sediment (Fig. 7C). These were sampled using opaque ABS pipe without exposing the sediment to light during sampling. Dose rate measurements were made directly in the field using a portable 4-channel gamma spectrometer calibrated by personnel at the United States Geological Survey. Environmental dose rate values are calculated using the conversion factors of Adamiec and Aitken (1998) and the grain-size attenuation factors outlined in Aitken (1986). Present-day water content values are

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assumed to be representative of those pertaining to the full burial period, and have been assigned relative uncertainties of ±50%.

Equivalent dose (De) analysis was undertaken at the Oxford University Luminescence

Research Group Laboratories. Coarse-grained (125-180μm) quartz De measurements were made using the Single Aliquot Regeneration (SAR) protocol developed by Murray and Wintle (2000). Individual De estimates were calculated for 15 aliquots (comprised of

100-300 grains) from each of the three samples. Sample bleaching characteristics were then assessed from these populations of individual De estimates using the approach suggested recently by Bailey and Arnold (in press). All three of these samples were deemed to have been adequately bleached prior to deposition and burial following this analysis. Final burial dose estimates are therefore calculated using the ‘Central Age

Model’ of Galbraith et al. (1999).

Results for the three OSL samples from San Emigdio Mesa (Table 3) indicate a late-

Pleistocene depositional age for bedded sands in the San Emigdio Mesa alluvial deposit.

These dates are noticeably older than the cosmogenic ages from boulders on the surface of the deposit; however evaluation of the context of each dating method suggests that they give complementary results. Boulders on the surface of an alluvial deposit could have been deposited more recently than bedded sands exposed by fluvial incision that are below the primary soil-formation horizon. Our data suggests that at approximately 60 ka, bedded fluvial sands were being deposited on an un-incised San Emigdio Mesa, whereas

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by approximately 30 ka, deposition of coarse material was occurring in a more proximal setting and incision of the mesa was possibly occurring in more distal regions.

Application of Geochronology to Model Calibration

Since we assume that our model begins with the earliest incision into an undissected surface, it is necessary to constrain the timing of initiation of drainage network incision into the upper Cuyama basin in order to compare the basin topography with model results. It is possible that the initiation of incision predates our cosmogenic ages, since they date deposition in the upper parts of the San Emigdio Mesa alluvial deposit. Our

OSL dates are from a time when deposition was still occurring on San Emigdio Mesa, and likely throughout much of our study area. We suggest initiation of basin incision occurred during the last 60 kyr, but no more recently than approximately the last 30 kyr.

Therefore for model-run comparisons, we expect dynamic steady-state to be approached in approximately 60 kyr, especially in more distal parts of the study area.

In addition to model run-time, a key parameter needed for our model calibration is U, which is the vertical uplift rate of the landscape. In Cuyama Valley, we assume that this value is a combination of the direct tectonic uplift rate of the region and the local base- level lowering rate transmitted through the landscape from the main-stem Cuyama River.

Since the fluvial system occupies a characteristic position approximately 60-80 meters below ridge-tops and preserved alluvial caps north of the Big Pine fault, we take the

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uplift rate to be on the order of 1-2 m/kyr. On the south side of the Big Pine fault, which was likely thrusting northward during the late-Pleistocene, relief is up to 80-100 meters below the equal age datum of San Emigdio Mesa-equivalent alluvium, suggesting a higher value for U of 1-3 m/kyr depending on interpretation of the geochronologic data.

These values are comparable to other regional estimates for tectonic uplift in coastal and near-coastal California (Ducea, et al, 2003; Page et al., 1998; White, 1992).

RESULTS AND DISCUSSION

The relative simplicity of our model allows for a detailed analysis of each of the model parameters’ effect on synthetic landscape development. Many previous studies have demonstrated the stream power law’s ability to simulate bedrock channel development

(e.g., Stock and Montogmery, 1999 and references therein). By coupling this tested method to simulate channel development with a simple yet realistic process-model for hillslope development in tectonically active terrains, we believe our model appropriately simulates the primary controls on landscape development over a variety of landscape process rates and spatial scales. Furthermore, we believe our model results can be compared to actual landscapes in an effort to calibrate model parameters, and the response of synthetic landscapes to model behavior is likely mirrored to a reasonable extent in actual landscapes.

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Values of K and Relationship Between K and U

Variation in model parameter K had a profound effect on model topography. By analogy, we expect rock resistance in tectonically active areas to be a primary control on landscape morphology. Our model results indicate that K can only vary over less than three orders of magnitude in landslide-dominated tectonically active areas (as defined by model- derived Type-II topographies) (Fig. 2). The actual range of K values for various rock types in uplifting areas appears to correlate positively with U. This is perhaps consistent with the observations of Snyder et al. (2000) that K undergoes a “dynamic adjustment” to tectonic changes, though in our model K strictly controls the rock resistance to erosion at a given point regardless of uplift rate or erosive process, and does not adjust to U. Our model does not address dynamics thought to be related to change in erosional process such as sediment flux change, channel geometry change caused by increased debris flows, or increased orographic precipitation as suggested occurs with tectonic perturbation by Snyder et al. (2000). It does seem likely however that since in nature the erodibility of bedrock is related to the sediment flux over the water-rock interface

(Gilbert, 1877; Sklar and Dietrich, 2001), which is in turn a function of U in orogenic settings, we might expect a change in effective K with increased uplift rate.

In general, we found linear relationships between the upper and lower possibilities for K that form Type-II topography. Upper values for K (weak rock leading to lower-relief

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topography) in Type-II topography in our dataset follow the following relationship with

K = 0.02U 0.004 (2)

Lower values for K (resistant rock leading to higher-relief topography) in Type-II topography in our dataset follow the following relationship with U:

K = 0.002U 0.0004 (3)

Equations (2) and (3) do not strictly bind the range of parameters that form Type-II topography, but are the range of parameters that do form Type-II topography in our order-of-magnitude evaluation of landscape response to variations in K. Fig. 8 shows the range of likely K values for a range of values of U. It also shows that data from Snyder et al. (2000), which are a number of estimates for K over a range of uplift rates from coastal northern California, fell within our envelope that defines the relationship between U and

K in Type-II topography. Furthermore, we found that all our Type-II model results have

U/K values between 50 and 1000 m·kyr/kyr; all Type-I model results have U/K values of

10 m·kyr/kyr or lower and all Type-III model results have U/K values of 5000 m·kyr/kyr and above with no overlapping of topography type for each unique U/K value. We therefore conclude that in most tectonically active terrains, values for U/K should fall

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above 10 and below 5000 m·kyr/kyr. These relationships allow us to better constrain the range of possible values of K in landscapes having known uplift rate.

When the results of Stock and Montgomery (1999) are evaluated in terms of these constraints on the relationships between K and U, it may be possible to better understand the wide range of variation in their calculated values of K, which range from 10-7 m0.2yr-1

-2 0.2 -1 to 10 m yr . The lowest values they calculated for K come from tectonically quiescent and resistant crystalline rocks of Australia, the intermediate values for K come from volcanic rocks from both tectonically active California, and also Hawaii, where tectonic uplift is supplanted by addition of rock mass from lava flows so U is essentially a fairly high base-level lowering rate. Their highest values for K come from Japan, where presumably weak mudstones are evaluated for K over a very short (5 ka) period in response to a migrating knickpoint, which seems likely to be approximated by a high value for U. Likely their data reveals that in order to have a wide range of values for K, an analysis must be done of several basins with both a wide range of rock types and a wide range of uplift rates.

Model Calibration Using Real Topography

Our efforts to calibrate the stream-power law using this model provide estimates for K from the upper Cuyama region. Table 4 shows the values we measured in the field and extracted from DEMs for our three target lithologies for comparison to controlled model

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runs. For this part of our study, we ran targeted model runs on grids with the same area as our subsampled DEM grids (see Fig. 6) for each lithologic unit. Running targeted model runs required estimation of model parameters m and n. Here we rely on analysis of DEM-derived slope and area data. Following Snyder et al. (2000), in the case of steady-state landscape in which uplift rate U and coefficient of erosion K are uniform along the channel reach, eq. (1) can be solved for equilibrium slope (Se):

Se = ks A , (4)

in which

1/ n ks = (U / K) (5)

is the steepness index and

= m / n . (6)

is the concavity index. and ks in eq. (4) can be solved for using the regression of channel-slope and drainage-area data. Rearranging (4) to the form of the equation of a linear regression of the logarithm of slope and area data gives:

log S = log A + log ks , (7)

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in which S is local channel slope. Therefore m/n is approximated by the slope of the regression line on a log plot of slope area data, and the value of (U/K)1/n is the y-intercept of the regression (Snyder et al., 2000).

We used DEM-derived slope and area data in order to estimate m/n for each lithologic unit. We conservatively confined our analysis to channel reaches having drainage area greater than 104 m2, to assure that our analysis only included zones of fluvial incision and not headwater mass-movement or other geomorphic processes. Figure 9 shows our results visually. We extracted the data from the logarithm of slope of Strahler stream segments (as opposed to basin pixels or channel pixels – in an effort to reduce scatter in

DEM data) versus drainage area. Data scatter was evident and R2 values ranged from

0.27 to 0.42. Our methods differed from Snyder et. al. (2000) in how we handle the data scatter from low-order channels. They used a map-based data extraction in which each

10-meter elevation range gets a single data point along a single main channel, whereas we have included all tributaries above our drainage-are threshold, introducing scatter that served to lower our R2 values, but capturing variability in tributary channel slopes that we feel is important in a 3D model calibration. Snyder et al. (2000) performed several methods of data extraction and analysis to generate estimates for m/n, and found that both field, DEM and manual estimation from topographic maps provided similar and satisfactory estimates.

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We were able to match morphologic indicators from the upper Cuyama region with model run outputs with a good degree of success. Figure 10 shows what we believe to be our most useful comparative morphologic parameters – mean elevation and drainage density, plotted against key model parameters, and also includes our values for the three lithologic units from the upper Cuyama region. Mean elevation and drainage density were highlighted because they were the morphologic indicators that were most sensitive to model parameter changes. We sub-sampled USGS DEMs in rectangular grids which contained the largest possible areas of a single rock type for topographic characterization.

Using Figure 10 we were able to constrain the values for K for each of the lithologic units. For the Matilija Formation, we suggest an appropriate K value is on the order of

0.09 to 0.25 m0.2kyr-1; for the Quatal Formation, K appears to be between 0.1 to 0.3 m0.2kyr-1; and the Morales Formation appears to have a K value of 0.15 to 0.3 m0.4kyr-1.

These values are on the high end of the range proposed by Stock and Mongomery (2000), which is not surprising given that they are fairly poorly-indurated sedimentary units that should be among the “weakest” rocks able to support moderate-relief topography.

The techniques used by Snyder et al. (2000) also allow for an independent estimate of

U/K based on the channel steepness index. Using eq. (7), our slope and area data, and our estimates for uplift rate U from geologic data, we get estimates for K that are similar, but generally higher than our estimates based on matching morphometric indicators from targeted model runs. Using the slope and area method, K for the Morales Formation is

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between 0.4 and 0.8 m0.2kyr-1, for the Quatal Formation it is 0.4 to 0.6 m0.4kyr-1, and for the Matilija Formation, K is between 0.13 and 0.25 m0.4kyr-1. The slope and area method for calibration of K seems to work well for bedrock channel reaches, though calibrating the stream power law with only a portion of the landscape makes it susceptible to error in extraction of slope and area values from DEMs. Given that the R2 values for our slope and area are fairly low, we place more confidence in the use of our full hillslope-channel landscape development model calibration techniques. The comparative morphologic indicators we use for model calibration are simple to extract from DEMs with a minimum of error (especially mean elevation), and integrate the entire landscape into model calibration.

A possible complication in our comparison of real landscape development to synthetic landscape development is proper temporal scaling. As discussed previously, we believe our models should produce comparative topography with a model run-time of approximately 60 kyr. We approximated model run-time from geologic data, however model runs reach “dynamic steady-state” in which topographic configuration was no longer highly dependent on model run-time (Willet, 1999), so the age of the topography needs only serve as a minimum value for model run-time in steady state regimes. In order to address the possibility that the comparison landscapes in California are not appropriately approximated by steady-state model runs, we also extracted morphologic indicators as a function of time for an evolving landscape for a set of model parameters to determine how these indicators behave before steady-state is achieved.

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Our analyses of the Quatal and Matilija Formation appear robust and the modeled processes achieve steady state in accordance with our geochronological constraints. Our model runs designed to target landscape development within the Morales Formation however, has difficulty reaching a fully-dissected form by 60 ky. In addition, the actual value for hypsometric integral from the Morales Formation is 0.5, which is likely an indicator that this landscape has not quite reached a steady state form.

In order to evaluate topographic sensitivity to landscape development during the time before dynamic steady state is reached, we ran targeted model runs for a range of model run-times approaching the time it takes to achieve steady state. All of our steady-state model run landscapes of Type-II and Type-III achieved a hypsometric integral of approximately 0.32 to 0.40, and the time-evolution of the hypsometric integral, mean elevation, topographic relief and drainage density can be seen in Figure 11. These values indicate that we can make appropriate estimations for K in landscapes that are approaching, but have not yet achieved steady state. Based on this, we believe that our estimated value for K for the Morales formation is a bit too low, and that the portion of the landscape which we sub-sampled in the Morales formation has not reached its ideal form. Figure 12 shows model run output topography as they approach steady-state configuration. Noting that hypsometric integral and mean elevation lowers as steady- state is approached, and drainage density increases, we propose a better approximation for K for the Morales formation is approximately 0.2 to 0.4 m0.4kyr-1. This argument is

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supported by the observation that the San Emigdio Mesa is a preserved surface which has not yet been significantly incised, and the Morales Formation is the most proximal bedrock unit, so may have been subject to erosion for less time than the more distal

Quatal and Matilija Formations, and therefore not yet achieved steady state. This basin- scale time-transgressive nature of temporal development of hypsometric integral is illustrated in Figure 13.

While our estimates for the values of K for the three lithologic units are very similar, our model parameterization using geologic data introduced some interesting complexity that must be taken into account when comparing K values to rock properties. First, our estimation of values for the area exponent m/n from topographic data affected the erosivity of the model. Our estimate of m = 0.3 for the Morales formation limited the model’s erosiveness for a given K value, so while our estimate for K for the Morales

Formation was similar to the other lithologies, the overall erodibility of the Morales

Formation appears to be higher than the others when our estimate for m is taken into account. Secondly, our geologically-derived estimates for differing uplift rate across the

Big Pine fault affected the values for K across the fault. The Eocene Matilija Formation appears to be a more indurated, less erodible lithology, however the coupling of U and K

(Snyder et. al., 2000) leads to an estimate for K for the Matilija Formation that is only marginally lower than those for the less-indurated Quatal and Morales Formation, though the rocks seem to differ more than is suggested by the K values upon field inspection.

Finally, the differing landslide threshold-slopes affect model topography and lead to

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differing mean elevations and drainage densities for similar K values. In particular the higher threshold-slopes in the Quatal and Matilija Formations have the effect of increasing drainage density and mean elevation for a similar value of K.

These observations imply that while K may be somewhat effective at defining resistance to fluvial erosion, when using a stream-power-law-based model to model landscape development, K should not be thought of as singularly reflecting material properties of a given lithology. Material properties are also reflected in the parameters dictated by landslide threshold-slope and channel concavity (m/n). Uplift rate also affects topography independently of the material properties of the bedrock. For example, though the Quatal and Matilija Formations appear to have similar K values and threshold-slopes, the Matilija holds up a higher mean elevation and relief, presumably owing to the higher value for uplift rate we estimated from geologic data. Also, though the Morales and

Quatal Formations also appear to have a fairly similar K value, they have much different drainage density, which is likely related to the higher threshold-slope value of the Quatal

Formation, presumably caused by the finer-grained cohesive nature of the Quatal

Formation.

These observations lead us to suggest that no singular “rock-strength” parameter (e.g.

Selby, 1980) is available to characterize landscape-scale erosional behavior of a rock- type, and a more holistic approach integrating overall morphology and uplift rate is necessary in order to relate topography to lithology and vice-versa. This exercise shows

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that not only is the stream-power law extremely sensitive to changes in the value for K, in order to calibrate stream-power-law based values of K, one needs to take into account all other model parameters. Furthermore, an estimated value of K extracted using the techniques proposed in this study does not directly correlate to rock erodibility, as channel profile shape and uplift (or base-level-lowering rate) all affect modeled erosion.

Based on these results, we propose that drainage density and mean elevation (or topographic relief) can be used to uniquely infer K to within a relatively narrow range in tectonically–active landscapes with steady-state configurations if other model parameters are also carefully calibrated.

CONCLUSIONS

Three-dimensional modeling that utilizes the stream-power law for fluvial erosion and threshold-landsliding for hillslope development allows for careful analysis of how model parameters such as uplift rate, bedrock erosivity, threshold-slope, channel concavity and time effect landscape development. We suggest that by careful comparison of (1) actual landscape morphology via field and DEM analysis, and (2) actual landscape development process-rates from geochronology to synthetic topography derived from a numerical model with carefully controlled parameters, we can calibrate modeling efforts, and in particular, narrow our range of estimates for K. We suggest that characterization of m/n, landslide threshold-slope, mean elevation, topographic relief, drainage density and hypsometric integral are necessary for comparison of actual topography to synthetic

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topography. In our study area three late-Cenozoic sedimentary units are estimated to have K values on the order of 0.3 to 0.09 m0.2-0.4kyr-1. We address possible complications from temporal and spatial scaling, and suggest that even complex and/or non-steady-state real topography can be compared to idealized synthetic topography with some measure of success. Work on widely different rock types and spatial scales will be necessary to further validate our results.

ACKNOWLEDGEMENTS

This study was performed with financial support from NSF EAR-0309518, a USGS

EDMAP grant, and support from the USGS Southern California Areal Mapping Project.

10Be analyses were performed at PRIME Lab under a seed analysis grant. OSL analyses were supported by grants from Chevron-Texaco and the Arizona Geological Society.

Thanks to M. Grace, A. Moore, and M. Cline for field assistance. Thanks to J. Pigati for guidance with cosmogenic sample preparation and data analysis. Thanks to S. Mahan,

USGS, for assistance with OSL dosimetry. Thanks to G. Hilley and an anonymous reviewer for helpful reviews of an earlier version of this paper.

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Whipple, K. X., and Tucker, G. E., 1999, Dynamics of the stream-power river incision model: Implications for height limits of mountain ranges, landscape response timescales, and research needs: J. Geophys. Res., v. 104, no. B8, p. 17661 - 17674.

Willet, S. D., 1999, Orogeny and orography: The effects of erosion on the structure of mountain belts: J. Geophys. Res., v. 104 no. B12, p. 28957-28981.

136

Willgoose, G., Bras, R.L., and Rodriquez-Iturbe, I. 1991, a coupled channel network growth and hillslope evolution model, 1, Theory: Water Resources Res. v. 27, p. 1671- 1684.

137

TABLE 1. MORPHOLOGIC INDICATORS FROM TOPOGRAPHY WITH VARYING K VALUES

Mean Normalized K U Relief Hypsometric Topograp U/K -1 Sc Elevation Drainage Ruggedness (kyr ) (m/kyr) (m) Integral hy Type (m) (m) Density

0.0001 1 0.67 1678 5018 0 0.0 0.33 III 10000 0.001 1 0.67 1244 3249 0.012 1.2 0.38 II 1000 0.005 1 0.67 446 1158 0.033 1.3 0.39 II 200 0.01 1 0.67 281 782 0.075 2.0 0.36 II 100 0.1 1 0.67 36 101 1 3.4 0.36 I 10

138

TABLE 2. COSMOGENIC 10BE DATA AND RESULTS

10 † Elevation Be 10 ‡ Sample ID Sample Description Latitude Longitude S * Thickness correction Be age (ka) (m) t (atoms/g)

A Granitic Boulder 34°48'22"N 119°15'36"W 1575 1.0001 1.027 436000 ± 14600 32.3 ±1.0

B Granitic Boulder 34°49'4"N 119°15'30"W 1580 1.0001 1.044 179100 ± 10400 14.3 ± 0.7

C Granitic Boulder 34°48'53"N 119°15'5"W 1627 1.0001 1.027 390600 ± 13900 28.2 ± 0.9

*Topographic shielding factor †Corrected for chemical blank value, sample thickness and topographic shielding. Error displayed is analytical error only. †Age determined following Pigati and Lifton (2004) with a time-integrated HLSL 10Be production rate of 4.35 atoms/year. No erosion or burial assumed.

139

TABLE 3. OSL DATA AND RESULTS

Depth Dose rate D Burial age Sample ID e (m) (Gy/ka) (Gy) (ka)

SEM01 5 4.07 ± 0.23 246.6 ± 22.1 60.64 ± 6.41 SEM02 6 4.25 ± 0.23 244.8 ± 24.3 57.55 ± 6.52 SEM03 9 4.14 ± 0.23 288.1 ± 17.3 69.53 ± 5.74

140

TABLE 4. MORPHOLOGIC INDICATORS FOR TOPGRAPHY FORMED IN THREE ROCK TYPES

DEM Mean Drainage Topographic Ruggedness Hypsometric Lithologic Unit area Sc -1 Elevation 2 Density (m ) Relief (m) number Integral (km ) (m) Morales 17.6 .69 0.018 210 410 3.1 0.491 Formation Quatal 9.7 .84 0.028 70 230 4.0 0.300 Formation Matilija 2.1 .84 0.024 90 330 3.5 0.270 Formation

Note: Landslide threshold-slope Sc was measured in the field using inclinometer. All other values extracted from USGS 10-meter DEMs. See text for explanation.

141

Figure 1. Oblique shaded-relief images of synthetic topography formed by varying only model parameter K. All model runs are 15 km by 15 km, with 30 meter pixel size. Uplift rate is 1 m/kyr, threshold-slope is 0.67, m = 0.5, n = 1. See Table 1 for output morphologic indicators.

142

Figure 2. Graph indicating the resultant topography type (see text) for a range of U and K values. All model runs (n=172) are included on this figure, and no overlap between topography types was detected for pairings of U and K even with variation in Sc. Dotted lines indicate approximate transition between topography types.

143

Figure 3. Model-run results. All data are from model runs on 15 km by 15 km grids with 30m grid cell size, Sc = 20°. (A) Effect of variation of U and K on normalized drainage density. Four data series represent four uplift rates as marked. These results indicate that drainage density tends to increase with lower values for K, and decreases for higher uplift rates. (B) Graph showing effect of variation of U and K on ruggedness number. Model landscapes with the highest ruggedness was found in those Type-II topographies with highest K values and Type-I topographies with lowest K values. (C) Effect of variation of U and K on mean elevation. Each curve contains low mean-elevation Type-I topography, medium mean-elevation Type-II topography on the steepest part of the curves, and high mean-elevation Type-III topography on the upper asymptotic portion of the curves. For a given K, a larger U will lead to higher mean elevation. These results indicate that topography is extremely sensitive to changes in K over two to three orders of magnitude. (D) Effect of variation of U and K on hypsometric integral. For all model runs that resulted mean elevation higher than twenty meters, hypsometric integrals were between 0.30 and 0.40, in extremely low-relief topography, the hypsometric integral declined with increase in K and decrease in U.

144

Figure 4. Model-run results. All model runs are 15 km by 15 km, with 30 meter pixel size. (A) Relationships between U/K, Sc and normalized drainage density. U/K has dimensions of length if m = 0.5 and n = 1. Within the narrow range of U/K values that result in Type-II topography (normalized drainage density between 0 and 1), higher threshold-slope angle leads to an increase in drainage density by allowing for closer spacing of fluvial valleys, but drainage density is much more sensitive to variation in U/K than to variation in Sc. (B) Relationships between U/K, Sc and mean elevation.

145

Figure 5. Tectonic setting of study area in the Western Transverse Ranges, California, USA. Cuyama badlands are eroding late-Cenozoic sedimentary units in the study area.

146

Figure 6. Geologic and topographic setting of study area. (A) Geologic map simplified from forthcoming USGS geologic map of Cuyama 1:100,000 sheet highlighting three rock types analyzed in this study and alluvial deposits used to interpret age of initiation of drainage development. (B) Shaded-relief image of USGS DEM data showing landscape morphology. (A) and (B) or of same area at same scale.

147

Figure 7. San Emigdio Mesa and geochronological sample sites. (A) Aerial photograph of part of San Emigdio Mesa. Geochronological sample locations marked with dates (See tables 2 and 3 for complete data) generalized surficial geology indicating two distinct areas of late-Quaternary deposition as constrained by direct field observation (see Fig. 6 for location map). (B) Boulder sampled for 10Be surface exposure dating from San Emigdio Mesa, GPS unit on boulder surface is 17 cm long. (C) OSL sample location, notice faint fluvial bedding and primary pedogenic zone well above sample location. Gamma spectrometer probe is ~12 cm in diameter. (D) Setting of typical OSL sample. Alluvium unconformably overlays deformed sedimentary bedrock below. Underlying badland-forming bedrock in this photo is local exposure of Caliente Formation, which was not analyzed in this study due to limited extent in study area.

148

Figure 8. Range of U and K values in which Type-II topography is formed as in Fig. 2. Also plotted are the data from Snyder et al. (2000) from the King Range in northern California for adjacent valleys having similar rock types and variation in uplift rates. Good agreement is apparent between our model results and their field-based estimates for K. They suggested that K may be coupled with uplift rate; see text for discussion.

149

Figure 9. Slope and drainage area data extracted from 30 m USGS DEM data. Each data point represents a single strahler stream segment in order to avoid slope errors near “stair-steps” caused by DEM production from topographic maps. Vertical dashed line indicates lower drainage area bound for analysis domain. Slope of grey line indicates the negative of m/n.

150

Figure 10. Calibration of K from key morphologic parameters of our three study lithologies. Each rock type has a curve corresponding to high and low estimates for U from geologic data, and the horizontal bars are the actual values extracted from DEMs for each lithology matched to the model curves. Shaded vertical bars indicate the range of likely values for K for each rock type. Morales Formation model runs were done on a 603 by 603 cell grid with 10 meter grid cell size, m = 0.3 and n = 1. Quatal Formation model runs were done on a 309 by 309 cell grid with 10 meter grid cell size, m = 0.4 and n = 1. Matilija Formation model runs were done on a 131 by 131 cell grid with 10 meter grid cell size, m = 0.4 and n = 1. These grid geometries were chosen to match the sub

151

Figure 11. Development of drainage density, mean elevation, topographic relief, and hypsometric integral through time for a 15 km-square model run in which K = 0.04 kyr-1, m = 0.5, n = 1, U = 2 m/kyr and Sc = 0.67. Note that our technique for determining drainage density can not distinguish between and unincised low-slope plateau and a fluvial channel, so the dashed line in the top graph is interpreted from visual inspection of model topography.

152

Figure 12. Oblique shaded-relief images of the development of synthetic topography through time. Model parameters are given in Figure 10 caption.

153

Figure 13. Oblique shaded-relief image of synthetic topography that has not reached “steady-state” and a sub-sample of that topography illustrating that the hypsometric integral (the primary indicator of steady-state topography in our study) approaches that of steady-state away from a preserved plateau. Terminal steady-state hypsometric integral for this model run is ~0.35.

154

Supplemental Data

Run# U K HowLong Sc Mean Relief Drainage Roughness Hypsometric Basin U/K Elevation Density Integral Type m/kyr kyr-1 kyr dec. m m m-1 m 2 0.1 0.000001 100000 0.44 1108.7 3306 0.00000 0.00 0.335 3 100000 3 0.1 0.00001 100000 0.44 1108.7 3306 0.00000 0.00 0.335 3 10000 4 0.1 0.00001 100000 0.44 1108.8 3300 0.00000 0.00 0.336 3 10000 5 0.1 0.001 10000 0.44 255.5 757 0.00173 1.31 0.337 2 100 6 0.1 0.01 1000 0.44 36.5 102 0.03332 3.41 0.357 1 10 7 0.1 0.1 100 0.44 3.6 14 0.03333 0.48 0.284 1 1 8 0.1 1 10 0.44 0.4 13 0.03333 0.42 0.031 1 0.1 9 0.1 10 1 0.44 0.1 13 0.03333 0.44 0.005 1 0.01 11 1 0.000001 100000 0.44 1106.0 3300 0.00000 0.00 0.335 3 1000000 12 1 0.00001 100000 0.44 1106.0 3300 0.00000 0.00 0.335 3 100000 13 1 0.0001 10000 0.44 1106.0 3300 0.00000 0.00 0.335 3 10000 14 1 0.001 10000 0.44 1004.6 2747 0.00029 0.79 0.366 2 1000 15 1 0.01 1000 0.44 252.5 714 0.00171 1.22 0.353 2 100 16 1 0.1 100 0.44 36.1 100 0.03332 3.34 0.360 1 10 17 1 1 10 0.44 3.7 14 0.03333 0.45 0.271 1 1 18 1 10 1 0.44 0.4 4 0.03333 0.13 0.098 1 0.1 20 5 0.000001 100000 0.44 1099.1 3293 0.00000 0.00 0.334 3 5000000 21 5 0.00001 100000 0.44 1099.1 3293 0.00000 0.00 0.334 3 500000 22 5 0.0001 100000 0.44 1099.1 3293 0.00000 0.00 0.334 3 50000 23 5 0.001 10000 0.44 1099.1 3293 0.00000 0.00 0.334 3 5000 24 5 0.01 1000 0.44 675.2 2847 0.00042 1.21 0.365 2 500 25 5 0.1 100 0.44 148.7 425 0.00344 1.46 0.350 2 50 26 5 1 10 0.44 18.0 55 0.03333 1.84 0.327 1 5 27 5 10 1 0.44 1.9 12 0.03333 0.38 0.164 1 0.5 29 50 0.000001 100000 0.44 1110.9 3305 0.00000 0.00 0.336 3 50000000 30 50 0.00001 100000 0.44 1110.9 3305 0.00000 0.00 0.336 3 5000000 31 50 0.0001 100000 0.44 1110.9 3305 0.00000 0.00 0.336 3 500000 32 50 0.001 10000 0.44 1110.9 3305 0.00000 0.00 0.336 3 50000 33 50 0.01 1000 0.44 1110.9 3305 0.00000 0.00 0.336 3 5000 34 50 0.1 1000 0.44 698.6 1739 0.00042 0.72 0.402 2 500 35 50 1 10 0.44 148.8 419 0.00343 1.44 0.355 2 50 36 50 10 1 0.44 18.2 78 0.03333 2.58 0.235 1 5 38 0.1 0.000001 100000 0.56 1405.0 4197 0.00000 0.00 0.335 3 100000 39 0.1 0.00001 100000 0.56 1405.0 4197 0.00000 0.00 0.335 3 10000 40 0.1 0.0001 100000 0.56 1158.0 3159 0.00033 1.03 0.367 2 1000 41 0.1 0.001 10000 0.56 274.3 754 0.00201 1.52 0.364 2 100 42 0.1 0.01 1000 0.56 36.4 2 0.03333 0.08 0.363 1 10 43 0.1 0.1 100 0.56 3.6 13 0.03333 0.44 0.276 1 1 44 0.1 1 10 0.56 0.4 4 0.03333 0.14 0.091 1 0.1 45 0.1 10 1 0.56 0.1 3 0.03333 0.11 0.018 1 0.01 47 1 0.000001 1000000 0.56 1409.4 4203 0.00000 0.00 0.335 3 1000000 48 1 0.00001 100000 0.56 1409.4 4203 0.00000 0.00 0.335 3 100000 49 1 0.0001 10000 0.56 1409.4 4203 0.00000 0.00 0.335 3 10000 50 1 0.001 10000 0.56 1169.4 3218 0.00031 1.00 0.363 2 1000 51 1 0.01 10000 0.56 254.1 635 0.00183 1.16 0.400 2 100 52 1 0.1 100 0.56 36.0 98 0.03333 3.27 0.367 1 10 53 1 1 10 0.56 3.7 13 0.03333 0.45 0.276 1 1 54 1 10 1 0.56 0.4 6 0.03333 0.18 0.073 1 0.1 56 5 0.000001 100000 0.56 1396.5 4188 0.00000 0.00 0.333 3 5000000 57 5 0.00001 100000 0.56 1396.5 4188 0.00000 0.00 0.333 3 500000 58 5 0.0001 100000 0.56 1396.5 4188 0.00000 0.00 0.333 3 50000 59 5 0.001 10000 0.56 1396.5 4188 0.00000 0.00 0.333 3 5000 60 5 0.01 10000 0.56 744.2 1847 0.00047 0.86 0.403 2 500 61 5 0.1 100 0.56 155.4 478 0.00493 2.36 0.325 2 50 62 5 1 10 0.56 18.2 53 0.03333 1.75 0.346 1 5 63 5 10 1 0.56 1.9 13 0.03333 0.42 0.151 1 0.5 65 50 0.000001 100000 0.56 1408.9 4201 0.00000 0.00 0.335 3 50000000 66 50 0.00001 100000 0.56 1408.9 4201 0.00000 0.00 0.335 3 5000000 67 50 0.0001 100000 0.56 1408.9 4201 0.00000 0.00 0.335 3 500000 68 50 0.001 10000 0.56 1408.9 4201 0.00000 0.00 0.335 3 50000 69 50 0.01 1000 0.56 1408.9 4201 0.00000 0.00 0.335 3 5000 70 50 0.1 1000 0.56 779.2 1898 0.00047 0.90 0.411 2 500 71 50 1 10 0.56 156.5 459 0.00494 2.27 0.341 2 50 72 50 10 1 0.56 18.4 80 0.03333 2.66 0.230 1 5 74 0.1 0.000001 100000 0.67 1676.2 5016 0.00000 0.00 0.334 3 100000 75 0.1 0.00001 100000 0.67 1676.2 5016 0.00000 0.00 0.334 3 10000 76 0.1 0.0001 100000 0.67 1302.7 3747 0.00035 1.31 0.348 2 1000

155

77 0.1 0.001 10000 0.67 287.4 835 0.00247 2.06 0.344 2 100 78 0.1 0.01 10000 0.67 34.7 101 0.03333 3.36 0.344 1 10 79 0.1 0.1 100 0.67 3.7 12 0.03333 0.41 0.301 1 1 80 0.1 1 10 0.67 0.4 4 0.03333 0.14 0.089 1 0.1 81 0.1 10 1 0.67 0.1 3 0.03333 0.10 0.020 1 0.01 83 1 0.000001 1000000 0.67 1677.5 5018 0.00000 0.00 0.334 3 1000000 84 1 0.00001 100000 0.67 1677.5 5018 0.00000 0.00 0.334 3 100000 85 1 0.0001 10000 0.67 1677.5 5018 0.00000 0.00 0.334 3 10000 86 1 0.001 10000 0.67 1243.9 3249 0.00036 1.17 0.383 2 1000 87 1 0.01 1000 0.67 280.7 782 0.00250 1.95 0.359 2 100 88 1 0.1 100 0.67 36.3 101 0.03333 3.37 0.359 1 10 89 1 1 10 0.67 3.6 13 0.03333 0.44 0.272 1 1 90 1 10 1 0.67 0.4 6 0.03333 0.20 0.067 1 0.1

92 5 0.000001 100000 0.67 1670.7 5011 0.00000 0.00 0.333 3 5000000 93 5 0.00001 100000 0.67 1670.7 5011 0.00000 0.00 0.333 3 500000 94 5 0.0001 100000 0.67 1670.7 5011 0.00000 0.00 0.333 3 50000 95 5 0.001 10000 0.67 1670.7 5011 0.00000 0.00 0.333 3 5000 96 5 0.01 1000 0.67 830.9 2221 0.00055 1.22 0.374 2 500 97 5 0.1 100 0.67 159.3 457 0.00666 3.05 0.348 2 50 98 5 1 10 0.67 18.1 51 0.03333 1.71 0.353 1 5 99 5 10 1 0.67 1.9 11 0.03333 0.36 0.172 1 0.5 101 0.1 0.000001 100000 0.78 1949.5 5838 0.00000 0.00 0.334 3 100000 102 0.1 0.00001 100000 0.78 1949.5 5838 0.00000 0.00 0.334 3 10000 103 0.1 0.0001 100000 0.78 1384.3 3719 0.00038 1.40 0.372 2 1000 104 0.1 0.001 10000 0.78 298.6 912 0.00300 2.73 0.327 2 100 105 0.1 0.01 1000 0.78 36.3 96 0.03333 3.20 0.379 1 10 106 0.1 0.1 100 0.78 3.6 14 0.03333 0.46 0.264 1 1 107 0.1 1 10 0.78 0.4 4 0.03333 0.12 0.110 1 0.1 108 0.1 10 1 0.78 0.1 3 0.03333 0.11 0.019 1 0.01 110 1 0.000001 100000 0.78 1950.9 5839 0.00000 0.00 0.334 3 1000000 111 1 0.00001 100000 0.78 1950.9 5839 0.00000 0.00 0.334 3 100000 112 1 0.0001 100000 0.78 1950.9 5839 0.00000 0.00 0.334 3 10000 113 1 0.001 10000 0.78 1370.9 3530 0.00037 1.32 0.388 2 1000 114 1 0.01 1000 0.78 292.0 838 0.00297 2.49 0.348 2 100 115 1 0.1 1000 0.78 34.5 97 0.03333 3.22 0.358 1 10 116 1 1 10 0.78 3.6 13 0.03333 0.43 0.280 1 1 117 1 10 1 0.78 0.4 4 0.03333 0.15 0.090 1 0.1 119 5 0.000001 100000 0.78 1914.3 5743 0.00000 0.00 0.333 3 5000000 120 5 0.00001 100000 0.78 1914.3 5743 0.00000 0.00 0.333 3 500000 121 5 0.0001 100000 0.78 1914.3 5743 0.00000 0.00 0.333 3 50000 122 5 0.001 10000 0.78 1914.3 5743 0.00000 0.00 0.333 3 5000 123 5 0.01 1000 0.78 870.8 2356 0.00063 1.48 0.370 2 500 124 5 0.1 100 0.78 164.5 454 0.00878 3.98 0.363 2 50 125 5 1 10 0.78 18.3 56 0.03333 1.86 0.329 1 5 126 5 10 1 0.78 1.9 11 0.03333 0.37 0.170 1 0.5 128 50 0.000001 100000 0.78 1955.4 5845 0.00000 0.00 0.335 3 50000000 129 50 0.00001 100000 0.78 1955.4 5845 0.00000 0.00 0.335 3 5000000 130 50 0.0001 100000 0.78 1955.4 5845 0.00000 0.00 0.335 3 500000 131 50 0.001 10000 0.78 1955.4 5845 0.00000 0.00 0.335 3 50000 132 50 0.01 1000 0.78 1955.4 5845 0.00000 0.00 0.335 3 5000 133 50 0.1 100 0.78 888.5 2240 0.00060 1.34 0.397 2 500 134 50 1 10 0.78 167.0 451 0.00878 3.96 0.370 2 50 135 50 10 1 0.78 18.3 89 0.03333 2.95 0.207 1 5 137 0.1 0.000001 100000 0.89 2222.9 6660 0.00000 0.00 0.334 3 100000 138 0.1 0.00001 100000 0.89 2222.9 6660 0.00000 0.00 0.334 3 10000 139 0.1 0.0001 100000 0.89 1466.4 3612 0.00041 1.47 0.406 2 1000 140 0.1 0.001 10000 0.89 308.1 875 0.00353 3.09 0.352 2 100 141 0.1 0.01 1000 0.89 36.6 100 0.03333 3.32 0.368 1 10 142 0.1 0.1 100 0.89 3.6 13 0.03333 0.42 0.286 1 1 143 0.1 1 10 0.89 0.4 5 0.03333 0.15 0.086 1 0.1 144 0.1 10 1 0.89 0.1 3 0.03333 0.12 0.017 1 0.01 146 1 0.000001 100000 0.89 2222.2 6659 0.00000 0.00 0.334 3 1000000 147 1 0.00001 100000 0.89 2222.2 6659 0.00000 0.00 0.334 3 100000 148 1 0.0001 10000 0.89 2222.2 6659 0.00000 0.00 0.334 3 10000 149 1 0.001 10000 0.89 1449.4 3865 0.00041 1.60 0.375 2 1000 150 1 0.01 1000 0.89 297.7 814 0.00360 2.93 0.366 2 100 151 1 0.1 100 0.89 36.1 98 0.03333 3.28 0.366 1 10 152 1 1 10 0.89 3.7 13 0.03333 0.43 0.286 1 1 153 1 10 1 0.89 0.4 4 0.03333 0.15 0.091 1 0.1

156

155 5 0.000001 100000 0.89 2217.5 6654 0.00000 0.00 0.333 3 5000000 156 5 0.00001 100000 0.89 2217.5 6654 0.00000 0.00 0.333 3 500000 157 5 0.0001 10000 0.89 2217.5 6654 0.00000 0.00 0.333 3 50000 158 5 0.001 10000 0.89 2217.5 6654 0.00000 0.00 0.333 3 5000 159 5 0.01 1000 0.89 914.0 2396 0.00069 1.66 0.382 2 500 160 5 0.1 1000 0.89 164.3 432 0.01063 4.60 0.380 2 50 161 5 1 10 0.89 18.4 53 0.03333 1.77 0.347 1 5 162 5 10 1 0.89 1.9 12 0.03333 0.39 0.161 1 0.5 164 50 0.000001 100000 0.89 2228.8 6666 0.00000 0.00 0.334 3 50000000 165 50 0.00001 100000 0.89 2228.8 6666 0.00000 0.00 0.334 3 5000000 166 50 0.0001 10000 0.89 2228.8 6666 0.00000 0.00 0.334 3 500000 167 50 0.001 10000 0.89 2228.8 6666 0.00000 0.00 0.334 3 50000 168 50 0.01 1000 0.89 2228.8 6666 0.00000 0.00 0.334 3 5000 169 50 0.1 100 0.89 911.9 2587 0.00069 1.77 0.353 2 500 170 50 1 10 0.89 167.5 471 0.01135 5.35 0.355 2 50 171 50 10 1 0.89 18.4 83 0.03333 2.75 0.222 1 5 173 50 0.000001 10000 0.67 1682.1 5023 0.00000 0.00 0.335 3 50000000 174 50 0.00001 10000 0.67 1682.1 5023 0.00000 0.00 0.335 3 5000000 175 50 0.0001 1000 0.67 1682.1 5023 0.00000 0.00 0.335 3 500000 176 50 0.001 1000 0.67 1682.1 5023 0.00000 0.00 0.335 3 50000 177 50 0.01 1000 0.67 1682.1 5023 0.00000 0.00 0.335 3 5000 178 50 0.1 100 0.67 845.6 2241 0.00055 1.24 0.377 2 500 179 50 1 10 0.67 163.2 467 0.00667 3.12 0.349 2 50 180 50 10 1 0.67 18.5 82 0.03333 2.72 0.226 1 5 86_5 1 0.005 10000 0.67 446.0 1158 0.00112 1.29 0.385 2 200