Hillslope Evolution in Response to Lateral Base Level Migration by Jennifer L. Hamon submitted to the Department of Earth, Atmospheric, and Planetary Science in partial fulfillment of the requirements for the degree of Bachelor of Science at the MASSACHUSETTS INSTITUTE OFTECHNOLOGY Massachusetts Institute of Technology June 2010 June 2010SEP LZ~~L2 8 2017] LIBRARIES ARCHIVES @2010 Jennifer L. Hamon. All rights reserved. The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronic copies of this thesis document in whole or in part in any medium now known or hereafter created. Signature of Author: Signature redacted Department of Earth, Atmospheric and Planetary Science 7 May 2010 Signature redacted Certified by: Professor Taylor Perron Thesis Advisor Signature redacted Accepted by: Professor Samuel Bowring Chair, Committee on Undergraduate Program 1 Contents 1 Introduction 6 1.1 Background on Hillslope Evolution ... ....... ....... ....... .... 7 2 Analytical Model of Lateral Hillslope Migration 7 2.1 Developing the 1-D Model ....... ................................. 7 2.2 A ssum ptions ....... ....... ....... ....... ....... ..... 10 3 Case Study 11 3.1 Choosing a field site . .. .... .. .. .. .. .. 11 3.1.1 Previous work on seepage networks ...... ....... ...... ..... 12 3.1.2 Previous work on the Apalachicola Bluffs ...... ....... ....... 14 3.2 Goals of the Case Study . ......... .......... ......... ..... 15 3.3 Measuring Elevation Profiles .... ....... ....... ....... ...... 15 3.4 Numerical simulation: exploring the 2-D Effect ..... ..... ...... ..... 18 4 Data 19 4.1 Measured profiles and computed A values ... ....... ....... ....... 19 4.2 Quantifying the 2-D effect of channel width ....... ....... ....... .. 22 5 Analysis and Discussion 23 5.1 Assessing the 2-D Effect . ..... ...... ...... ..... ...... ..... 23 5.2 Distribution of A values and observed spatial relationships ...... ....... .. 25 5.3 Comparison of v with Abrams et al. [2009a] .... ...... ..... ...... .. 29 6 Concluding Remarks 30 7 Appendix 1: MATLAB functions 34 7.1 pthandler.m .... ...... ...... ..... ...... ...... ..... ... 34 7.2 strtprof.m .... ..... ...... ...... ..... ...... ...... .... 35 7.3 extractor.m . ..... ...... ...... ..... ...... ...... ..... 40 7.4 qualitycontrol.m ...... ....... ....... ....... ....... .... 42 8 Appendix 2: Data Tables 43 9 Appendix 3: Elevation Plots 44 List of Figures 1 1-D linear transport coordinate setup .. .... .... .... .... .... ..... 8 2 Elevation data for sapping network near Bristol, FL .. ...... ...... .... 12 3 Truncating measured profiles . ....... ....... ........ ....... 17 4 Schematic topography described by the 1-D linear transport model ... ....... 18 5 Representative surfaces generated by numerical hillslope evolution model . ...... 20 6 2-D effect vs. velocity .... ........ ....... ....... ....... .. 20 7 Histogram of measured A values .... ......... .......... ....... 22 2 8 Relative standard error of measured A values ........ .............. 23 9 Divergence of measured A from true A increases with v ........... ...... 24 10 Map of measured heads, colored by calculated A ...... .............. 26 11 Measured A vs geometric drainage area ............... ........... 27 12 Total curvature map, Florida seepage network .............. ........ 54 13 Gradient map, Florida seepage network ........... .............. 55 List of Tables 1 Longitudinal profile locations and extents ......... ............... 45 2 Measured A and error values ....... ......... .......... ...... 46 3 Abstract Hillslopes evolve in response to base level change, sediment production, and sediment transport. Many previous studies have focused on hillslopes undergoing vertical base level migration due to tectonic forcing and bedrock incision. Many geomorphic features, however, are characterized by lateral hillslope retreat and have not been adequately studied. Here I adapt a theory of linear diffu- sive hillslope evolution to relate the velocity of lateral hillslope retreat to the steady-state hillslope form. A case study in a Florida sapping network, in which headward migration of seepage faces in a sandy soil sets the base level for the surrounding hillslopes, provides numerous opportunities to test the analytical model by direct measurement. Measurements of hillslopes in the Florida sapping network found quantitative agreement between the predicted and observed hillslope morphology. An expected relationship between geometric drainage area and channel growth velocity was not borne out in the data, but the distribution of measured v/K ratios is consistent with what I expect based on my preferential sampling of slow-moving gently-sloped heads. Several explanations are given to explain why the expected relationship with drainage area is not observed, and suggestions for future work based on these findings is offered. 4 Acknowledgments This project would not have been possible without the help of several people. First I would like to thank Professor Taylor Perron for his help at every stage of this project. Taylor's positive attitude, guidance, and support helped keep me on track even when other things conspired to distract me. His advice- about geomorphology and about life-has been a tremendous resource. Thank you, Taylor, I could not have done this without you. Thanks to Professor Dan Rothman and members of his group, Alexander Petroff and Olivier Devauchelle, for furnishing me with the original LIDAR elevation data from the Florida Panhandle channel network. Testing the analytical model on their data proved to be a central part of this project. And, finally, I would like to thank my girlfriend Renata Cummins for her tireless support and encouragement during my writing and coding endeavors of the past several months. She endured my gripes and weird hours without complaint, and kept me fed in the chaotic final days. I love you. :) 5 1 Introduction Hillslopes evolve in response to base level change and the production and transport of sediments and soils. Base level change creates a topographic gradient while the transport of sediment leads to erosion over time [Dietrich et al., 2003]. Many 'models and field studies at the scale of individual hillslopes have focused on the response of hillslopes to vertical base level change under conditions of either tectonic uplift and subsidence [Dietrich et al., 2003, Roering et al., 1999, Burbank et al., 1996] or bedrock incision by rivers [Whipple, 2002]. However, a much less studied class of geomorphic features undergo hillslope evolution by lateral base level migration. Examples of lateral base level migration include lateral movement of meandering rivers [Nanson and Hickin, 1986, Smith, 1976], retreating escarpments and cliffs [Rosenbloom and Anderson, 1994], and headward advance of drainage networks [Dunne, 1980, Howard, 1988b]. In this thesis I will build on existing hillslope theory to address the evolution of hillslopes undergoing lateral base level change. Combining a linear diffusive transport law with a steady- state assumption and boundary conditions corresponding to lateral migration, I will formulate a 1-D analytical model that relates the measurable topography to the rate of hillslope advection. Once I have formulated the model, I will test its predictions with measurements of seepage channel heads in a Florida sapping network. Seepage channel networks are just one type of geomorphic feature that evolve in response to lateral base level migration. However, they are particularly well-suited to testing my analytical model because they occur in undissected low-relief areas in response to the approximately horizontal erosion of groundwater springs. Additionally, a single seepage channel network provides many opportunities to measure and compare lateral migration rates. The primary goal of the case study is to show that some of the channel heads have a hillslope form consistent with that predicted by the analytical model. A secondary goal will be to compute rates of headward growth at each channel tip and see whether the distribution of measured velocities is consistent with existing theories of sapping network growth. 6 1.1 Background on Hillslope Evolution In developing a mathematical description of hillslopes in seepage channels I rely fundamentally on previous work establishing the relationship between hillslope form and slope-dependent geomorphic transport laws. The occurrence of convex hillforms was first remarked upon by G.K. Gilbert 1877 [Gilbert, 1877, Dietrich et al., 2003]. Years later W.M. Davis proposed that a combination of repeated dilation and contraction would result in downhill creep of material over time and give rise to the observed convex hillform [Davis, 1892, Dietrich et al., 2003]. Gilbert eventually made the observation that Davis's dilation and contraction theory implied a direct relationship between material transport and slope [Gilbert, 1909, Dietrich et al., 2003]. The slope-dependent transport hypothesis was mathematically formalized and tested by W.E.H. Culling, whose work described how mass conservation and slope-dependent transport of individual soil particles will result in macroscopic flow analogous to Fick's Law of Diffusion [Dietrich et al., 2003, Culling, 1963, 1960, Fernandes and Dietrich, 1997]. M.J. Kirby's recognition that soil mantled hillslopes-said to be "transport limited" -evolving under certain fixed boundary conditions will come to a characteristic steady-state form independent of the initial