Ocean Dynamics

, Volume 69, Issue 2, pp 145–156 | Cite as

Extension of sea surface temperature unpredictability

  • Marat AkhmetEmail author
  • Mehmet Onur Fen
  • Ejaily Milad Alejaily


The sea surface temperature (SST) variability is clearly affected by global climate patterns, which involve large-scale ocean-atmosphere fluctuations similar to the El Niño-Southern Oscillation (ENSO). We give mathematical arguments for the SST to be unpredictable over oceans. Sensitivity (unpredictability) is the core ingredient of chaos. Several researches suggested that the ENSO might be chaotic. It was Vallis (Science 232:243–245, 1986) who revealed unpredictability in ENSO by reducing his model to the Lorenz equations. We discuss the unpredictability for SST as an extendable phenomenon through coupled Vallis ENSO models and advection equations by using theoretical as well as numerical analyses. To perform theoretical research, we apply our recent results on replication of chaos and unpredictable solutions of differential equations, while for numerical analysis, we combine results on unpredictable solutions with numerical analysis of chaos in the advection equation.


Sea surface temperature Unpredictability extension El Niño-Southern Oscillation Vallis model Advection equation 



The authors wish to express their sincere gratitude to the referees for the helpful criticism and valuable suggestions, which helped significantly improve the paper.

Funding information

The third author is financially supported by a scholarship from the Ministry of Education, Libya.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Marat Akhmet
    • 1
    Email author
  • Mehmet Onur Fen
    • 2
  • Ejaily Milad Alejaily
    • 1
  1. 1.Department of MathematicsMiddle East Technical UniversityAnkaraTurkey
  2. 2.Department of MathematicsTED UniversityAnkaraTurkey

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