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Chaos in a simple model of a delta network

Salter, Gerard and Voller, Vaughan R. and Paola, Chris (2020) Chaos in a simple model of a delta network. Proceedings of the National Academy of Sciences of the United States of America, 117 (44). pp. 27179-27187. ISSN 0027-8424. https://resolver.caltech.edu/CaltechAUTHORS:20201020-095208643

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Abstract

The flux partitioning in delta networks controls how deltas build land and generate stratigraphy. Here, we study flux-partitioning dynamics in a delta network using a simple numerical model consisting of two orders of bifurcations. Previous work on single bifurcations has shown periodic behavior arising due to the interplay between channel deepening and downstream deposition. We find that coupling between upstream and downstream bifurcations can lead to chaos; despite its simplicity, our model generates surprisingly complex aperiodic yet bounded dynamics. Our model exhibits sensitive dependence on initial conditions, the hallmark signature of chaos, implying long-term unpredictability of delta networks. However, estimates of the predictability horizon suggest substantial room for improvement in delta-network modeling before fundamental limits on predictability are encountered. We also observe periodic windows, implying that a change in forcing (e.g., due to climate change) could cause a delta to switch from predictable to unpredictable or vice versa. We test our model by using it to generate stratigraphy; converting the temporal Lyapunov exponent to vertical distance using the mean sedimentation rate, we observe qualitatively realistic patterns such as upwards fining and scale-dependent compensation statistics, consistent with ancient and experimental systems. We suggest that chaotic behavior may be common in geomorphic systems and that it implies fundamental bounds on their predictability. We conclude that while delta “weather” (precise configuration) is unpredictable in the long-term, delta “climate” (statistical behavior) is predictable.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1073/pnas.2010416117DOIArticle
https://www.pnas.org/content/suppl/2020/10/16/2010416117.DCSupplementalPublisherSupporting Information
https://github.com/salterg/bifurcation_networkRelated ItemData
ORCID:
AuthorORCID
Salter, Gerard0000-0001-6426-0133
Voller, Vaughan R.0000-0001-8116-1567
Additional Information:© 2020 the Author(s). Published by PNAS. This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND). Edited by Andrea Rinaldo, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland, and approved September 17, 2020 (received for review May 22, 2020). PNAS first published October 19, 2020. This material is based upon work supported by NSF Graduate Research Fellowship Grant 00039202. We thank Rick Moeckel, Crystal Ng, and Andy Wickert for helpful discussions and two reviewers for constructive comments. Data Availability: Model code data have been deposited in GitHub (https://github.com/salterg/bifurcation_network). Author contributions: G.S., V.R.V., and C.P. designed research; G.S. performed research; G.S., V.R.V., and C.P. analyzed data; and G.S., V.R.V., and C.P. wrote the paper. The authors declare no competing interest. This article is a PNAS Direct Submission. This article contains supporting information online at https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.2010416117/-/DCSupplemental.
Funders:
Funding AgencyGrant Number
NSFDGE-00039202
Subject Keywords:prediction; bifurcation; attractor; geomorphic models
Issue or Number:44
Record Number:CaltechAUTHORS:20201020-095208643
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20201020-095208643
Official Citation:Chaos in a simple model of a delta network. Gerard Salter, Vaughan R. Voller, Chris Paola. Proceedings of the National Academy of Sciences Nov 2020, 117 (44) 27179-27187; DOI: 10.1073/pnas.2010416117
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106166
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:20 Oct 2020 17:23
Last Modified:04 Nov 2020 18:22

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