Analytic solution for the morphology of a soil-mantled valley undergoing steady headward growth: Validation using case studies in southeastern Arizona
The geomorphic literature contains many analytic solutions for the topographic evolution of gently sloping soil-mantled hillslopes responding to base level changes. Most of these solutions are limited to vertical base level changes and/or to simplified geometries, however. In this paper we present a...
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| Format: | Article |
| Language: | en_US |
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American Geophysical Union (AGU)
2014
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| Online Access: | http://hdl.handle.net/1721.1/85571 https://orcid.org/0000-0002-0404-8701 |
| _version_ | 1811082361138315264 |
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| author | Pelletier, Jon D. Perron, J. Taylor |
| author2 | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences |
| author_facet | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Pelletier, Jon D. Perron, J. Taylor |
| author_sort | Pelletier, Jon D. |
| collection | MIT |
| description | The geomorphic literature contains many analytic solutions for the topographic evolution of gently sloping soil-mantled hillslopes responding to base level changes. Most of these solutions are limited to vertical base level changes and/or to simplified geometries, however. In this paper we present an analytic solution for the morphology of a valley and its adjacent hillslopes undergoing steady headward growth. The mathematics of this problem were first solved by Ivantsov (1947) in the context of heat flow near a parabolic solidification boundary. Here we test whether the Ivantsov solution provides an accurate first-order prediction of the morphology of valley heads and their adjacent hillslopes by comparing the model predictions to survey data from two study sites in southeastern Arizona. The model predicts that elevation contours of valley heads are parabolas and that topographic transects normal to contour lines are error functions. High-resolution Digital Elevation Models (DEMs) were constructed for the two study sites using Real-Time Kinematic Global Positioning System (RTK-GPS) measurements and a Terrestrial Laser Scanner (TLS). Our analyses show that the model reproduces the first-order morphology of headward-growing valleys and their adjacent hillslopes. We also show that by analyzing hillslope profiles at different distances from the valley head, the model framework can be used to infer likely changes in the valley head migration rate through time. |
| first_indexed | 2024-09-23T12:01:54Z |
| format | Article |
| id | mit-1721.1/85571 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:01:54Z |
| publishDate | 2014 |
| publisher | American Geophysical Union (AGU) |
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| spelling | mit-1721.1/855712022-09-27T23:37:13Z Analytic solution for the morphology of a soil-mantled valley undergoing steady headward growth: Validation using case studies in southeastern Arizona Pelletier, Jon D. Perron, J. Taylor Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Perron, J. Taylor The geomorphic literature contains many analytic solutions for the topographic evolution of gently sloping soil-mantled hillslopes responding to base level changes. Most of these solutions are limited to vertical base level changes and/or to simplified geometries, however. In this paper we present an analytic solution for the morphology of a valley and its adjacent hillslopes undergoing steady headward growth. The mathematics of this problem were first solved by Ivantsov (1947) in the context of heat flow near a parabolic solidification boundary. Here we test whether the Ivantsov solution provides an accurate first-order prediction of the morphology of valley heads and their adjacent hillslopes by comparing the model predictions to survey data from two study sites in southeastern Arizona. The model predicts that elevation contours of valley heads are parabolas and that topographic transects normal to contour lines are error functions. High-resolution Digital Elevation Models (DEMs) were constructed for the two study sites using Real-Time Kinematic Global Positioning System (RTK-GPS) measurements and a Terrestrial Laser Scanner (TLS). Our analyses show that the model reproduces the first-order morphology of headward-growing valleys and their adjacent hillslopes. We also show that by analyzing hillslope profiles at different distances from the valley head, the model framework can be used to infer likely changes in the valley head migration rate through time. National Science Foundation (U.S.) (Grant EAR-0951672) 2014-03-10T16:06:17Z 2014-03-10T16:06:17Z 2012-05 2012-03 Article http://purl.org/eprint/type/JournalArticle 0148-0227 2156-2202 http://hdl.handle.net/1721.1/85571 Pelletier, Jon D., and J. Taylor Perron. “Analytic Solution for the Morphology of a Soil-Mantled Valley Undergoing Steady Headward Growth: Validation Using Case Studies in Southeastern Arizona.” Journal of Geophysical Research 117, no. F2 (2012). © 2012 by the American Geophysical Union https://orcid.org/0000-0002-0404-8701 en_US http://dx.doi.org/10.1029/2011jf002281 Journal of Geophysical Research Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Geophysical Union (AGU) MIT web domain |
| spellingShingle | Pelletier, Jon D. Perron, J. Taylor Analytic solution for the morphology of a soil-mantled valley undergoing steady headward growth: Validation using case studies in southeastern Arizona |
| title | Analytic solution for the morphology of a soil-mantled valley undergoing steady headward growth: Validation using case studies in southeastern Arizona |
| title_full | Analytic solution for the morphology of a soil-mantled valley undergoing steady headward growth: Validation using case studies in southeastern Arizona |
| title_fullStr | Analytic solution for the morphology of a soil-mantled valley undergoing steady headward growth: Validation using case studies in southeastern Arizona |
| title_full_unstemmed | Analytic solution for the morphology of a soil-mantled valley undergoing steady headward growth: Validation using case studies in southeastern Arizona |
| title_short | Analytic solution for the morphology of a soil-mantled valley undergoing steady headward growth: Validation using case studies in southeastern Arizona |
| title_sort | analytic solution for the morphology of a soil mantled valley undergoing steady headward growth validation using case studies in southeastern arizona |
| url | http://hdl.handle.net/1721.1/85571 https://orcid.org/0000-0002-0404-8701 |
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