{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/57667"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/57667","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Coupled length scales in eroding landscapes","abstract":"We propose a method to study natural topography by means of local transform. A nonlinear local transform Alc[h(x)] of the elevation field h(x) is used to determine a director field of anisotropy a(x). The director field is directly related to local small-scale channel-like features. From study of the correlations of these with large-scale structure of drainage basins, characteristic coupling length scales are found which indicate an important breaking of scale invariance. We also show that these length scales are related to the average sizes of the individual drainage basins. Our study demonstrates one way in which landscape patterns of unknown origin may be quantitatively analyzed to determine the kind of mechanisms that have eroded them.","abstract_html":"We propose a method to study natural topography by means of local transform. A nonlinear local transform Alc[h(x)] of the elevation field h(x) is used to determine a director field of anisotropy a(x). The director field is directly related to local small-scale channel-like features. From study of the correlations of these with large-scale structure of drainage basins, characteristic coupling length scales are found which indicate an important breaking of scale invariance. We also show that these length scales are related to the average sizes of the individual drainage basins. Our study demonstrates one way in which landscape patterns of unknown origin may be quantitatively analyzed to determine the kind of mechanisms that have eroded them.","abstract_has_math":false,"creators":["Chan, Kelvin Ka Wing, 1974-"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences","school":null,"contributors":[],"advisors":["Daniel H. Rothman."],"committee_chairs":[],"committee_members":[],"year":1999,"date_issued":"1999","date_published":"1999","updated_at":"2026-07-22T22:21:04Z","subjects":["Earth, Atmospheric, and Planetary Sciences."],"languages":["eng"],"rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. 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A nonlinear local transform Alc[h(x)] of the elevation field h(x) is used to determine a director field of anisotropy a(x). The director field is directly related to local small-scale channel-like features. From study of the correlations of these with large-scale structure of drainage basins, characteristic coupling length scales are found which indicate an important breaking of scale invariance. We also show that these length scales are related to the average sizes of the individual drainage basins. Our study demonstrates one way in which landscape patterns of unknown origin may be quantitatively analyzed to determine the kind of mechanisms that have eroded them."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["S.M."]},{"key":"dc:title","label":"Title","values":["Coupled length scales in eroding landscapes"]}]}],"canonical_facts":{"dc:contributor.advisor":["Daniel H. Rothman."],"dc:contributor.department":["Massachusetts Institute of Technology. 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From study of the correlations of these with large-scale structure of drainage basins, characteristic coupling length scales are found which indicate an important breaking of scale invariance. We also show that these length scales are related to the average sizes of the individual drainage basins. Our study demonstrates one way in which landscape patterns of unknown origin may be quantitatively analyzed to determine the kind of mechanisms that have eroded them."],"dc:description.degree":["S.M."],"dc:identifier.uri":["http://hdl.handle.net/1721.1/57667"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Earth, Atmospheric, and Planetary Sciences."],"dc:title":["Coupled length scales in eroding landscapes"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:21:04Z"}