Abstract
A new technique to derive delay models from systems of partial differential equations, based on the Mori-Zwanzig (MZ) formalism, is used to derive a delay-difference equation model for the Atlantic Multidecadal Oscillation (AMO). The MZ formalism gives a rewriting of the original system of equations, which contains a memory term. This memory term can be related to a delay term in a resulting delay equation. Here, the technique is applied to an idealized, but spatially extended, model of the AMO. The resulting delay-difference model is of a different type than the delay differential model which has been used to describe the El Ninõ Southern Oscillation. In addition to this model, which can also be obtained by integration along characteristics, error terms for a smoothing approximation of the model have been derived from the MZ formalism. Our new method of deriving delay models from spatially extended models has a large potential to use delay models to study a range of climate variability phenomena.
| Original language | English |
|---|---|
| Article number | 20200659 |
| Pages (from-to) | 1-21 |
| Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
| Volume | 477 |
| Issue number | 2246 |
| DOIs | |
| Publication status | Published - 17 Feb 2021 |
Bibliographical note
Funding Information:Data accessibility. The codes supporting this article have been uploaded as part of the electronic supplementary material. Authors’ contributions. S.K.J.F., C.Q. and H.A.D. designed the study. The work was carried out mainly by S.K.J.F. and C.Q. J.S. designed the analysis and comparison of the delay models in §5. All authors contributed to the work, discussed the results and read and approved the manuscript. Competing interests. We declare we have no competing interests. Funding. This work was supported by funding from the European Union Horizon 2020 research and innovation programme for the ITN CRITICS under grant agreement no. 643073 (C.Q., J.S. and H.A.D.). S.K.J.F. was supported by the Centre for Doctoral Training in Mathematics of Planet Earth, UK EPSRC funded (grant no. EP/L016613/1) and J.S. by EPSRC grants nos. EP/N023544/1 and EP/N014391/1. Acknowledgements. We thank Bruno Deremble and the anonymous reviewer for their constructive comments. S.K.J.F. thanks the University of Exeter for hosting her for five months in 2018.
Publisher Copyright:
© 2021 The Author(s).
Funding
Data accessibility. The codes supporting this article have been uploaded as part of the electronic supplementary material. Authors’ contributions. S.K.J.F., C.Q. and H.A.D. designed the study. The work was carried out mainly by S.K.J.F. and C.Q. J.S. designed the analysis and comparison of the delay models in §5. All authors contributed to the work, discussed the results and read and approved the manuscript. Competing interests. We declare we have no competing interests. Funding. This work was supported by funding from the European Union Horizon 2020 research and innovation programme for the ITN CRITICS under grant agreement no. 643073 (C.Q., J.S. and H.A.D.). S.K.J.F. was supported by the Centre for Doctoral Training in Mathematics of Planet Earth, UK EPSRC funded (grant no. EP/L016613/1) and J.S. by EPSRC grants nos. EP/N023544/1 and EP/N014391/1. Acknowledgements. We thank Bruno Deremble and the anonymous reviewer for their constructive comments. S.K.J.F. thanks the University of Exeter for hosting her for five months in 2018.
Keywords
- Atlantic Multidecadal Oscillation
- conceptual models
- delay model
- Mori-Zwanzig
- reduction methods