A theory of stochastic fluvial landscape evolution

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2024-02-07 DOI:10.1098/rspa.2023.0456
G. G. Roberts, O. Wani
{"title":"A theory of stochastic fluvial landscape evolution","authors":"G. G. Roberts, O. Wani","doi":"10.1098/rspa.2023.0456","DOIUrl":null,"url":null,"abstract":"Geometries of eroding landscapes contain important information about geologic, climatic, biotic and geomorphic processes. They are also characterized by variability, which makes disentangling their origins challenging. Observations and physical models of fluvial processes, which set the pace of erosion on most continents, emphasize complexity and variability. By contrast, the spectral content of longitudinal river profiles and similarity of geometries at scales greater than approximately <jats:inline-formula> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi> </mml:mi> </mml:mrow> <mml:mn>100</mml:mn> <mml:mo> </mml:mo> <mml:mrow> <mml:mi mathvariant=\"normal\">km</mml:mi> </mml:mrow> </mml:math> </jats:inline-formula> highlight relatively simple emergent properties. A general challenge then, addressed in this manuscript, is development of a theory of landscape evolution that embraces such scale-dependent insights. We do so by incorporating randomness and probability into a theory of fluvial erosion. First, we explore the use of stochastic differential equations of the Langevin type, and the Fokker–Planck equation, for predicting migration of erosional fronts. Second, analytical approaches incorporating distributions of driving forces, critical thresholds and associated proxies are developed. Finally, a linear programming approach is introduced, that, at its core, treats evolution of longitudinal profiles as a Markovian stochastic problem. The theory is developed essentially from first principles and incorporates physics governing fluvial erosion. We explore predictions of this theory, including the natural growth of discontinuities and scale-dependent evolution, including local complexity and emergent simplicity.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","FirstCategoryId":"103","ListUrlMain":"https://doi.org/10.1098/rspa.2023.0456","RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 0

Abstract

Geometries of eroding landscapes contain important information about geologic, climatic, biotic and geomorphic processes. They are also characterized by variability, which makes disentangling their origins challenging. Observations and physical models of fluvial processes, which set the pace of erosion on most continents, emphasize complexity and variability. By contrast, the spectral content of longitudinal river profiles and similarity of geometries at scales greater than approximately 100 km highlight relatively simple emergent properties. A general challenge then, addressed in this manuscript, is development of a theory of landscape evolution that embraces such scale-dependent insights. We do so by incorporating randomness and probability into a theory of fluvial erosion. First, we explore the use of stochastic differential equations of the Langevin type, and the Fokker–Planck equation, for predicting migration of erosional fronts. Second, analytical approaches incorporating distributions of driving forces, critical thresholds and associated proxies are developed. Finally, a linear programming approach is introduced, that, at its core, treats evolution of longitudinal profiles as a Markovian stochastic problem. The theory is developed essentially from first principles and incorporates physics governing fluvial erosion. We explore predictions of this theory, including the natural growth of discontinuities and scale-dependent evolution, including local complexity and emergent simplicity.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
随机河流地貌演变理论
侵蚀地貌的几何形状包含有关地质、气候、生物和地貌过程的重要信息。侵蚀地貌还具有多变性的特点,这就给厘清侵蚀地貌的起源带来了挑战。大多数大陆的侵蚀过程都是由河川过程决定的,对河川过程的观测和物理模型都强调其复杂性和多变性。相比之下,河流纵向剖面的频谱内容和大于约 100 公里尺度的几何形状的相似性则突出了相对简单的新兴特性。因此,本手稿所要解决的一个普遍挑战,就是发展一种景观演化理论,将这些与尺度相关的见解纳入其中。为此,我们将随机性和概率纳入了河流侵蚀理论。首先,我们探讨了如何利用朗格文随机微分方程和福克-普朗克方程来预测侵蚀前沿的迁移。其次,我们开发了包含驱动力分布、临界阈值和相关代用指标的分析方法。最后,介绍了一种线性规划方法,其核心是将纵向剖面的演变视为马尔可夫随机问题。该理论基本上是从第一性原理出发,并结合了控制河川侵蚀的物理学原理。我们探讨了这一理论的预测结果,包括不连续性的自然增长和规模依赖性演变,包括局部复杂性和出现的简单性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
期刊最新文献
On the well-posedness of Eringen’s non-local elasticity for harmonic plane wave problems On the stability of prestressed beams undergoing nonlinear flexural free oscillations A cluster of N -bubbles driven along a channel at high imposed driving pressure: film orientations and bubble pressures Enhanced interfacial capture with an elliptical cylinder A Comment on: ‘Wind tunnel evaluation of novel drafting formations for an elite marathon runner’ (2023), by Marro M et al.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1