Derivation of Delay Equation Climate Models Using the Mori-Zwanzig Formalism

Models incorporating delay have been frequently used to understand climate variability phenomena, but often the delay is introduced through an ad-hoc physical reasoning, such as the propagation time of waves. In this paper, the Mori-Zwanzig formalism is introduced as a way to systematically derive delay models from systems of partial differential equations and hence provides a better justification for using these delay-type models. The Mori-Zwanzig technique gives a formal rewriting of the system using a projection onto a set of resolved variables, where the rewritten system contains a memory term. The computation of this memory term requires solving the orthogonal dynamics equation, which represents the unresolved dynamics. For nonlinear systems, it is often not possible to obtain an analytical solution to the orthogonal dynamics and an approximate solution needs to be found. Here, we demonstrate the Mori-Zwanzig technique for a two-strip model of the El Nino Southern Oscillation (ENSO) and explore methods to solve the orthogonal dynamics. The resulting nonlinear delay model contains an additional term compared to previously proposed ad-hoc conceptual models. This new term leads to a larger ENSO period, which is closer to that seen in observations.Comment: Submitted to Proceedings of the Royal Society A, 25 pages, 10 figure

Die makro-ekonomiese verband tussen die openbare en privaatsektor in Suid-Afrika.

Die dualistiese karakter van die Suid-Afrikaanse volkshuishouding bring die regering voor feitlik ongekende vraagstukke te staan en bemoilik sy rol as skepper van sosiaal-ekonomiese orde in beslissende mate. ... Zie: Samenvattin

Derivation of Delay Equation Climate Models Using the Mori-Zwanzig Formalism

This is the author accepted manuscript. The final version is available from The Royal Society via the DOI in this record.Data access: The codes supporting this article have been uploaded as part of the supplementary material. They can also be found on the online repository figshare: https://doi.org/10.6084/m9.figshare.8085683.v1Models incorporating delay have been frequently used to understand climate variability phenomena, but often the delay is introduced through an ad-hoc physical reasoning, such as the propagation time of waves. In this paper, the Mori-Zwanzig formalism is introduced as a way to systematically derive delay models from systems of partial differential equations and hence provides a better justification for using these delay-type models. The Mori-Zwanzig technique gives a formal rewriting of the system using a projection onto a set of resolved variables, where the rewritten system contains a memory term. The computation of this memory term requires solving the orthogonal dynamics equation, which represents the unresolved dynamics. For nonlinear systems, it is often not possible to obtain an analytical solution to the orthogonal dynamics and an approximate solution needs to be found. Here, we demonstrate the Mori-Zwanzig technique for a two-strip model of the El Nino Southern Oscillation (ENSO) and explore methods to solve the orthogonal dynamics. The resulting nonlinear delay model contains an additional term compared to previously proposed ad-hoc conceptual models. This new term leads to a larger ENSO period, which is closer to that seen in observations.European Union Horizon 2020Dutch Science Foundation (NWOEngineering and Physical Sciences Research Council (EPSRC

A Bayesian Approach to Atmospheric Circulation Regime Assignment

The standard approach when studying atmospheric circulation regimes and their dynamics is to use a hard regime assignment, where each atmospheric state is assigned to the regime it is closest to in distance. However, this may not always be the most appropriate approach as the regime assignment may be affected by small deviations in the distance to the regimes due to noise. To mitigate this we develop a sequential probabilistic regime assignment using Bayes Theorem, which can be applied to previously defined regimes and implemented in real time as new data become available. Bayes Theorem tells us that the probability of being in a regime given the data can be determined by combining climatological likelihood with prior information. The regime probabilities at time $t$ can be used to inform the prior probabilities at time $t+1$, which are then used to sequentially update the regime probabilities. We apply this approach to both reanalysis data and a seasonal hindcast ensemble incorporating knowledge of the transition probabilities between regimes. Furthermore, making use of the signal present within the ensemble to better inform the prior probabilities allows for identifying more pronounced interannual variability. The signal within the interannual variability of wintertime North Atlantic circulation regimes is assessed using both a categorical and regression approach, with the strongest signals found during very strong El Ni\~no years.Comment: Accepted for publication in Journal of Climat