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

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

Global Tipping Points Report 2023: Ch1.5: Climate tipping point interactions and cascades.

This chapter reviews interactions between climate tipping systems and assesses the potential risk of cascading effects. After a definition of tipping system interactions, we map out the current state of the literature on specific interactions between climate tipping systems that may be important for the overall stability of the climate system. For this, we gather evidence from model simulations, observations and conceptual understanding, as well as archetypal examples of palaeoclimate reconstructions where propagating transitions were potentially at play. This chapter concludes by identifying crucial knowledge gaps in tipping system interactions that should be resolved in order to improve risk assessments of cascading transitions under future climate change scenarios

Climate tipping point interactions and cascades: A review

Climate tipping elements are large-scale subsystems of the Earth that may transgress critical thresholds (tipping points) under ongoing global warming, with substantial impacts on the biosphere and human societies. Frequently studied examples of such tipping elements include the Greenland Ice Sheet, the Atlantic Meridional Overturning Circulation (AMOC), permafrost, monsoon systems, and the Amazon rainforest. While recent scientific efforts have improved our knowledge about individual tipping elements, the interactions between them are less well understood. Also, the potential of individual tipping events to induce additional tipping elsewhere or stabilize other tipping elements is largely unknown. Here, we map out the current state of the literature on the interactions between climate tipping elements and review the influences between them. To do so, we gathered evidence from model simulations, observations, and conceptual understanding, as well as examples of paleoclimate reconstructions where multi-component or spatially propagating transitions were potentially at play. While uncertainties are large, we find indications that many of the interactions between tipping elements are destabilizing. Therefore, we conclude that tipping elements should not only be studied in isolation, but also more emphasis has to be put on potential interactions. This means that tipping cascades cannot be ruled out on centennial to millennial timescales at global warming levels between 1.5 and 2.0 ◦C or on shorter timescales if global warming surpassed 2.0 ◦C. At these higher levels of global warming, tipping cascades may then include fast tipping elements such as the AMOC or the Amazon rainforest. To address crucial knowledge gaps in tipping element interactions, we propose four strategies combining observation-based approaches, Earth system modeling expertise, computational advances, and expert knowledge

Detection of interannual ensemble forecast signals over the North Atlantic and Europe using atmospheric circulation regimes

To study the forced variability of atmospheric circulation regimes, the use of model ensembles is often necessary for identifying statistically significant signals as the observed data constitute a small sample and are thus strongly affected by the noise associated with sampling uncertainty. However, the regime representation is itself affected by noise within the atmosphere, which can make it difficult to detect robust signals. To this end we employ a regularised k-means clustering algorithm to better identify the signal in a model ensemble. The approach allows for the identification of six regimes for the wintertime Euro-Atlantic sector and leads to more pronounced regime dynamics, compared to results without regularisation, both overall and on sub-seasonal and interannual timescales. We find that sub-seasonal variability in the regime occurrence rates is mainly explained by changes in the seasonal cycle of the mean climatology. On interannual timescales relations between the occurrence rates of the regimes and the El Nino Southern Oscillation (ENSO) are identified. The use of six regimes captures a more detailed response of the circulation to ENSO compared to the common use of four regimes. Predictable signals in occurrence rate on interannual timescales are found for the two zonal flow regimes, namely a regime consisting of a negative geopotential height anomaly over the Norwegian Sea and Scandinavia, and the positive phase of the NAO. The signal strength for these regimes is comparable between observations and model, in contrast to that of the NAO-index where the signal strength in the observations is underestimated by a factor of two in the model. Our regime analysis suggests that this signal-to-noise problem for the NAO-index is primarily related to those atmospheric flow patterns associated with the negative NAO-index as we find poor predictability for the corresponding NAO- regime

Climate tipping point interactions and cascades: a review

Climate tipping elements are large-scale subsystems of the Earth that may transgress critical thresholds (tipping points) under ongoing global warming, with substantial impacts on the biosphere and human societies. Frequently studied examples of such tipping elements include the Greenland Ice Sheet, the Atlantic Meridional Overturning Circulation (AMOC), permafrost, monsoon systems, and the Amazon rainforest. While recent scientific efforts have improved our knowledge about individual tipping elements, the interactions between them are less well understood. Also, the potential of individual tipping events to induce additional tipping elsewhere or stabilize other tipping elements is largely unknown. Here, we map out the current state of the literature on the interactions between climate tipping elements and review the influences between them. To do so, we gathered evidence from model simulations, observations, and conceptual understanding, as well as examples of paleoclimate reconstructions where multi-component or spatially propagating transitions were potentially at play. While uncertainties are large, we find indications that many of the interactions between tipping elements are destabilizing. Therefore, we conclude that tipping elements should not only be studied in isolation, but also more emphasis has to be put on potential interactions. This means that tipping cascades cannot be ruled out on centennial to millennial timescales at global warming levels between 1.5 and 2.0 ∘C or on shorter timescales if global warming surpassed 2.0 ∘C. At these higher levels of global warming, tipping cascades may then include fast tipping elements such as the AMOC or the Amazon rainforest. To address crucial knowledge gaps in tipping element interactions, we propose four strategies combining observation-based approaches, Earth system modeling expertise, computational advances, and expert knowledge