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Register a new userA simple conceptual model of abrupt glacial climate events
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Here we use a very simple conceptual model in an attempt to reduce essential parts of the complex nonlinearity of abrupt glacial climate changes (the so-called Dansgaard-Oeschger events) to a few simple principles, namely (i) a threshold process, (ii) an overshooting in the stability of the system and (iii) a millennial-scale relaxation. By comparison with a so-called Earth system model of intermediate complexity (CLIMBER-2), in which the events represent oscillations between two climate states corresponding to two fundamentally different modes of deep-water formation in the North Atlantic, we demonstrate that the conceptual model captures fundamental aspects of the nonlinearity of the events in that model. We use the conceptual model in order to reproduce and reanalyse nonlinear resonance mechanisms that were already suggested in order to explain the characteristic time scale of Dansgaard-Oeschger events. In doing so we identify a new form of stochastic resonance (i.e. an overshooting stochastic resonance) and provide the first explicitly reported manifestation of ghost resonance in a geosystem, i.e. of a mechanism which could be relevant for other systems with thresholds and with multiple states of operation. Our work enables us to explicitly simulate realistic probability measures of Dansgaard-Oeschger events (e.g. waiting time distributions, which are a prerequisite for statistical analyses on the regularity of the events by means of Monte-Carlo simulations). We thus think that our study is an important advance in order to develop more adequate methods to test the statistical significance and the origin of the proposed glacial 1470-year climate cycle.
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We propose a conceptual model which generates abrupt climate changes akin to Dansgaard-Oeschger events. In the model these abrupt climate changes are not triggered by external perturbations but rather emerge in a dynamic self-consistent model through complex interactions of the ocean, the atmosphere and an intermittent process. The abrupt climate changes are caused in our model by intermittencies in the sea-ice cover. The ocean is represented by a Stommel two-box model, the atmosphere by a Lorenz-84 model and the sea-ice cover by a deterministic approximation of correlated additive and multiplicative noise (CAM) process. The key dynamical ingredients of the model are given by stochastic limits of deterministic multi-scale systems and recent results in deterministic homogenisation theory. The deterministic model reproduces statistical features of actual ice-core data such as non-Gaussian $alpha$-stable behaviour. The proposed mechanism for abrupt millenial-scale climate change only relies on the existence of a quantity, which exhibits intermittent dynamics on an intermediate time scale. We consider as a particular mechanism intermittent sea-ice cover where the intermittency is generated by emergent atmospheric noise. However, other mechanisms such as freshwater influxes may also be formulated within the proposed framework.
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Tipping elements in the climate system are large-scale subregions of the Earth that might possess threshold behavior under global warming with large potential impacts on human societies. Here, we study a subset of five tipping elements and their interactions in a conceptual and easily extendable framework: the Greenland and West Antarctic Ice Sheets, the Atlantic Meridional Overturning Circulation (AMOC), the El-Nino Southern Oscillation (ENSO) and the Amazon rainforest. In this nonlinear and multistable system, we perform a basin stability analysis to detect its stable states and their associated Earth system resilience. Using this approach, we perform a system-wide and comprehensive robustness analysis with more than 3.5 billion ensemble members. Further, we investigate dynamic regimes where some of the states lose stability and oscillations appear using a newly developed basin bifurcation analysis methodology. Our results reveal that the state of four or five tipped elements has the largest basin volume for large levels of global warming beyond 4 {deg}C above pre-industrial climate conditions. For lower levels of warming, states including disintegrated ice sheets on West Antarctica and Greenland have higher basin volume than other state configurations. Therefore in our model, we find that the large ice sheets are of particular importance for Earth system resilience. We also detect the emergence of limit cycles for 0.6% of all ensemble members at rare parameter combinations. Such limit cycle oscillations mainly occur between the Greenland Ice Sheet and AMOC (86%), due to their negative feedback coupling. These limit cycles point to possibly dangerous internal modes of variability in the climate system that could have played a role in paleoclimatic dynamics such as those unfolding during the Pleistocene ice age cycles.
Holm (ASR, 2018) claims that Scafetta (ASR 57, 2121-2135, 2016) is irreproducible because I would have left undocumented the values of two parameters (a reduced-rank index p and a regularization term) that he claimed to be requested in the Magnitude Squared Coherence Canonical Correlation Analysis (MSC-CCA). Yet, my analysis did not require such two parameters. In fact: 1) using the MSC-CCA reduced-rank option neither changes the result nor was needed since Scafetta (2016) statistically evaluated the significance of the coherence spectral peaks; 2) the analysis algorithm neither contains nor needed the regularization term. Herein, I show that Holm could not replicate Scafetta (2016) because he used different analysis algorithms. In fact, although Holm claimed to be using MSC-CCA, for his figures 2-4 he used a MatLab code labeled gcs_cca_1D.m (see paragraph 2 of his Section 3), which Holm also modified, that implements a different methodology known as the Generalized Coherence Spectrum using the Canonical Correlation Analysis (GCS-CCA). This code is herein demonstrated to be unreliable under specific statistical circumstances such as those required to replicate Scafetta (2016). On the contrary, the MSC-CCA method is stable and reliable. Moreover, Holm could not replicate my result also in his figure 5 because there he used the basic Welch MSC algorithm by erroneously equating it to MSC-CCA. Herein I clarify step-by-step how to proceed with the correct analysis, and I fully confirm the 95% significance of my results. I add data and codes to easily replicate my results.
North Atlantic climate during glacial times was characterized by large-amplitude switchings, the Dansgaard-Oeschger (DO) events, with an apparent tendency to recur preferably in multiples of about 1470 years. Recent work interpreted these intervals as resulting from a subharmonic response of a highly nonlinear system to quasi-periodic solar forcing plus noise. This hypothesis was challenged as inconsistent with the observed variability in the phase relation between proxies of solar activity and Greenland climate. Here we reject the claim of inconsistency by showing that this phase variability is a robust, generic feature of the nonlinear dynamics of DO events, as described by a model. This variability is expected from the fact that the events are threshold crossing events, resulting from a cooperative process between the periodic forcing and the noise. This process produces a fluctuating phase relation with the periodic forcing, consistent with proxies of solar activity and Greenland climate.
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