Chaos in a simple model of a delta network

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)27179-27187
Number of pages9
JournalProceedings of the National Academy of Sciences of the United States of America
Volume117
Issue number44
DOIs
StatePublished - Nov 3 2020

Bibliographical note

Funding Information:
ACKNOWLEDGMENTS. 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.

Keywords

  • Attractor
  • Bifurcation
  • Geomorphic models
  • Prediction

PubMed: MeSH publication types

  • Journal Article
  • Research Support, U.S. Gov't, Non-P.H.S.

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