Hans van Haren, Sebastiano Piccolroaz, Marina Amadori, Marco Toffolon, Henk A. Dijkstra
Deep water circulation and mixing processes in deep lakes are largely unknown, although they are responsible for the transport of matter, nutrients and pollutants. Such a lack of knowledge cannot be reliably provided by numerical hydrodynamic modelling studies because detailed observations are typically not available to validate them. To overcome some of these deficiencies, a dedicated yearlong mooring comprising 100 high-resolution temperature sensors and a single current meter were located in the deeper half of the 344 m deepest point of the subalpine Lake Garda (Italy). The observations show peaks and calms of turbulent exchange, besides ubiquitous internal wave activity. In late winter, northerly winds activate episodic deep convective overturning, the dense water being subsequently advected along the lake-floor. Besides deep convection, such winds also set-up seiches and inertial waves that are associated with about 100 times larger turbulence dissipation rates than that by semidiurnal internal wave breaking observed in summer. In the lower 60 m above the lake-floor however, the average turbulence dissipation rate is approximately constant in value year-around, being about 10 times larger than open-ocean values, except during deep convection episodes.
Peter D. Nooteboom, Qing Yi Feng, Cristóbal López, Emilio Hernández-García, Henk A. Dijkstra
The skill of current predictions of the warm phase of the El Niño Southern Oscillation (ENSO) reduces significantly beyond a lag of six months. In this paper, we aim to increase this prediction skill at lags up to one year. The new method to do so combines a classical Autoregressive Integrated Moving Average technique with a modern machine learning approach (through an Artificial Neural Network). The attributes in such a neural network are derived from topological properties of Climate Networks and are tested on both a Zebiak-Cane-type model and observations. For predictions up to six months ahead, the results of the hybrid model give a better skill than the CFSv2 ensemble prediction by the National Centers for Environmental Prediction (NCEP). Moreover, results for a twelve month lead time prediction have a similar skill as the shorter lead time predictions.
Niels Drost, Jason Maassen, Maarten A. J. van Meersbergen, Henri E. Bal, F. Inti Pelupessy, Simon Portegies Zwart, Michael Kliphuis, Henk A. Dijkstra, Frank J. Seinstra
High-performance scientific applications require more and more compute power. The concurrent use of multiple distributed compute resources is vital for making scientific progress. The resulting distributed system, a so-called Jungle Computing System, is both highly heterogeneous and hierarchical, potentially consisting of grids, clouds, stand-alone machines, clusters, desktop grids, mobile devices, and supercomputers, possibly with accelerators such as GPUs. One striking example of applications that can benefit greatly of Jungle Computing Systems are Multi-Model / Multi-Kernel simulations. In these simulations, multiple models, possibly implemented using different techniques and programming models, are coupled into a single simulation of a physical system. Examples include the domain of computational astrophysics and climate modeling. In this paper we investigate the use of Jungle Computing Systems for such Multi-Model / Multi-Kernel simulations. We make use of the software developed in the Ibis project, which addresses many of the problems faced when running applications on Jungle Computing Systems. We create a prototype Jungle-aware version of AMUSE, an astrophysical simulation framework. We show preliminary experiments with the resulting system, using clusters, grids, stand-alone machines, and GPUs.
Jan P. Viebahn, Anna S. von der Heydt, Dewi Le Bars, Henk A. Dijkstra
The climate impact of ocean gateway openings during the Eocene-Oligocene transition is still under debate. Previous model studies employed grid resolutions at which the impact of mesoscale eddies has to be parameterized. We present results of a state-of-the-art eddy-resolving global ocean model with a closed Drake Passage, and compare with results of the same model at non-eddying resolution. An analysis of the pathways of heat by decomposing the meridional heat transport into eddy, horizontal, and overturning circulation components indicates that the model behavior on the large scale is qualitatively similar at both resolutions. Closing Drake Passage induces (i) sea surface warming around Antarctica due to changes in the horizontal circulation of the Southern Ocean, (ii) the collapse of the overturning circulation related to North Atlantic Deep Water formation leading to surface cooling in the North Atlantic, (iii) significant equatorward eddy heat transport near Antarctica. However, quantitative details significantly depend on the chosen resolution. The warming around Antarctica is substantially larger for the non-eddying configuration (5.5{degree sign}C) than for the eddying configuration (2.5{degree sign}C). This is a consequence of the subpolar mean flow which partitions differently into gyres and circumpolar current at different resolutions. We conclude that for a deciphering of the different mechanisms active in Eocene-Oligocene climate change detailed analyses of the pathways of heat in the different climate subsystems are crucial in order to clearly identify the physical processes actually at work.
Alexis Tantet, Mickaël D. Chekroun, Henk A. Dijkstra, J. David Neelin
The spectrum of the generator (Kolmogorov operator) of a diffusion process, referred to as the Ruelle-Pollicott (RP) spectrum, provides a detailed characterization of correlation functions and power spectra of stochastic systems via decomposition formulas in terms of RP resonances. Stochastic analysis techniques relying on the theory of Markov semigroups for the study of the RP spectrum and a rigorous reduction method is presented in Part I. This framework is here applied to study a stochastic Hopf bifurcation in view of characterizing the statistical properties of nonlinear oscillators perturbed by noise, depending on their stability. In light of the Hörmander theorem, it is first shown that the geometry of the unperturbed limit cycle, in particular its isochrons, is essential to understand the effect of noise and the phenomenon of phase diffusion. In addition, it is shown that the spectrum has a spectral gap, even at the bifurcation point, and that correlations decay exponentially fast. Explicit small-noise expansions of the RP eigenvalues and eigenfunctions are then obtained, away from the bifurcation point, based on the knowledge of the linearized deterministic dynamics and the characteristics of the noise. These formulas allow one to understand how the interaction of the noise with the deterministic dynamics affect the decay of correlations. Numerical results complement the study of the RP spectrum at the bifurcation, revealing useful scaling laws. The analysis of the Markov semigroup for stochastic bifurcations is thus promising in providing a complementary approach to the more geometric random dynamical system approach. This approach is not limited to low-dimensional systems and the reduction method presented in part I is applied to a stochastic model relevant to climate dynamics in part III.
Alexis Tantet, Valerio Lucarini, Frank Lunkeit, Henk A. Dijkstra
The destruction of a chaotic attractor leading to rough changes in the dynamics of a dynamical system is studied. Local bifurcations are characterised by a single or a pair of characteristic exponents crossing the imaginary axis. The approach of such bifurcations in the presence of noise can be inferred from the slowing down of the correlation decay. On the other hand, little is known about global bifurcations involving high-dimensional attractors with positive Lyapunov exponents. The global stability of chaotic attractors may be characterised by the spectral properties of the Koopman or the transfer operators governing the evolution of statistical ensembles. It has recently been shown that a boundary crisis in the Lorenz flow coincides with the approach to the unit circle of the eigenvalues of these operators associated with motions about the attractor, the stable resonances. A second type of resonances, the unstable resonances, is responsible for the decay of correlations and mixing on the attractor. In the deterministic case, those cannot be expected to be affected by general boundary crises. Here, however, we give an example of chaotic system in which slowing down of the decay of correlations of some observables does occur at the approach of a boundary crisis. The system considered is a high-dimensional, chaotic climate model of physical relevance. Moreover, coarse-grained approximations of the transfer operators on a reduced space, constructed from a long time series of the system, give evidence that this behaviour is due to the approach of unstable resonances to the unit circle. That the unstable resonances are affected by the crisis can be physically understood from the fact that the process responsible for the instability, the ice-albedo feedback, is also active on the attractor. Implications regarding response theory and the design of early-warning signals are discussed.
Sacha Sinet, Anna S. von der Heydt, Henk A. Dijkstra
The Atlantic Meridional Overturning Circulation (AMOC) and polar ice sheets are coupled tipping elements, allowing for potential cascading tipping events in which tipping is facilitated by their mutual interactions. However, while an AMOC destabilization driven by Greenland Ice Sheet (GIS) meltwater release is well documented, the consequences of a West Antarctic Ice Sheet (WAIS) tipping on the AMOC remain unclear. In the Earth System Model of Intermediate Complexity CLIMBER-X, we perform experiments where meltwater fluxes representing plausible tipping trajectories of the GIS and WAIS are applied. We find that WAIS meltwater input can increase the AMOC resilience to GIS meltwater. In particular, we show that this stabilizing effect can cause the AMOC recovery and, for the first time in a comprehensive model, totally prevent an AMOC collapse. Moreover, we find this stabilzation to occur for ice sheet tipping trajectories that are relevant under high future greenhouse gas emission scenarios.
Swinda K. J. Falkena, Henk A. Dijkstra, Anna S. von der Heydt
The subpolar gyre is at risk of crossing a tipping point under future climate change associated with the collapse of deep convection. As such tipping can have significant climate impacts, it is important to understand the mechanisms at play and how they are represented in modern climate models. In this study we use causal inference to investigate the representation of several proposed mechanisms of subpolar gyre variability in CMIP6 models. As expected, an increase in sea surface salinity or a decrease in sea surface temperature leads to an increase in mixed layer depth in nearly all CMIP6 models due to an intensification of deep convection. However, the effect of convection to modify sea surface temperature due to re-stratification is less clear. In most models the deepening of the mixed layer caused by an increase of sea surface salinity, does result in a cooling of the water at intermediate depths. The feedback from the subsurface temperature through density to the strength of the subpolar gyre circulation is more ambiguous, with fewer models indicating a significant link. Those that do show a significant link, do not agree on its sign. The CMIP6 models that have the expected sign for the links from density to the subpolar gyre strength and on to sea surface salinity, are also the models in which abrupt shifts in the subpolar gyre region have been found in climate change scenario runs. One model (CESM2) contains all proposed mechanisms, with both a negative and delayed positive feedback loop being significant.
Lucas Esclapez, Valérian Jacques-Dumas, Reyk Börner, Laurent Soucasse, Henk A. Dijkstra
Calculating transition probabilities between different states of multistable climate tipping systems is computationally challenging in high-dimensional models. Targeted algorithms, such as the Trajectory-Adaptive Multilevel Splitting (TAMS) method, require an adequate score function to be successful, i.e., to provide an estimate of a transition probability with an acceptable variance when only a relatively small ensemble of model trajectories can be computed. Here, we present a data-driven method to derive a score function based on projecting the model dynamics in a reduced state space. Using a spatially two-dimensional partial differential equation model of the Atlantic Meridional Overturning Circulation, we show that this score function performs better than currently available ones. Using the new score function, transition probabilities can be determined with low variance, even in the case of small noise amplitudes. Besides purely noise-induced transitions, we also consider the scenario of combined stochastic and time-dependent deterministic forcing, presenting a strategy to efficiently simulate AMOC tipping events in global ocean and climate models subject to transient climate change.
Andrea A. Cimatoribus, Sybren S. Drijfhout, Henk A. Dijkstra
A global hybrid coupled model is developed, with the aim of studying the effects of ocean-atmosphere feedbacks on the stability of the Atlantic meridional overturning circulation. The model includes a global ocean general circulation model and a statistical atmosphere model. The statistical atmosphere model is based on linear regressions of data from a fully coupled climate model on sea surface temperature both locally and hemispherically averaged, being the footprint of Atlantic meridional overturning variability. It provides dynamic boundary conditions to the ocean model for heat, freshwater and wind-stress. A basic but consistent representation of ocean-atmosphere feedbacks is captured in the hybrid coupled model and it is more than ten times faster than the fully coupled climate model. The hybrid coupled model reaches a steady state with a climate close to the one of the fully coupled climate model, and the two models also have a similar response (collapse) of the Atlantic meridional overturning circulation to a freshwater hosing applied in the northern North Atlantic.
Andrea A. Cimatoribus, Matthijs den Toom, Sybren S. Drijfhout, Henk A. Dijkstra
The sensitivity of the Atlantic Meridional Overturning Circulation (AMOC) to changes in basin integrated net evaporation is highly dependent on the zonal salinity contrast at the southern border of the Atlantic. Biases in the freshwater budget strongly affect the stability of the AMOC in numerical models. The impact of these biases is investigated, by adding local anomaly patterns in the South Atlantic to the freshwater fluxes at the surface. These anomalies impact the freshwater and salt transport by the different components of the ocean circulation, in particular the basin--scale salt--advection feedback, completely changing the response of the AMOC to arbitrary perturbations. It is found that an appropriate dipole anomaly pattern at the southern border of the Atlantic Ocean can collapse the AMOC entirely even without a further hosing. The results suggest a new view on the stability of the AMOC, controlled by processes in the South Atlantic.
Henk A. Dijkstra, Rene M. van Westen
It is known that global climate models (GCMs) have substantial biases in the surface freshwater flux which forces the ocean component of these models. Using numerical bifurcation analyses on a global ocean model, we study here the effect of a specific freshwater flux bias on the multiple equilibrium regime of the Atlantic Meridional Overturning Circulation (AMOC). We find that a (positive) freshwater flux bias over the Indian Ocean shifts the multiple equilibrium regime to larger values of North Atlantic freshwater input but hardly affects the associated hysteresis width. The magnitude of this shift depends on the way the anomalous North Atlantic freshwater flux is compensated. We explain the changes in bifurcation diagrams using the freshwater balance over the Atlantic basin. The results suggest that state-of-the-art GCMs may have an AMOC multiple equilibrium regime, but that it is located in a parameter regime that is considered unrealistic and hence is not explored.
René M. van Westen, Henk A. Dijkstra
We study hysteresis properties of the Atlantic Meridional Overturning Circulation (AMOC) under a slowly-varying North Atlantic (20$^{\circ}$N -- 50$^{\circ}$N) freshwater flux forcing in state-of-the-art Global Climate Model (GCM), the Community Earth System Model. Results are presented of a full hysteresis simulation ($4,400$ model years) and show that there is a hysteresis width of about $0.4$ Sv. This demonstrates that an AMOC collapse and recovery do not only occur in conceptual and idealised climate models, but also in a state-of-the-art GCM. The AMOC recovery is about a factor six faster than the AMOC collapse and this asymmetry is due to the major effect of the North Atlantic sea-ice distribution on the AMOC recovery. The results have implications for projections of possible future AMOC behaviour and for explaining relatively rapid climate transitions in the geological past.
Qing Yi Feng, Jan P. Viebahn, Henk A. Dijkstra
The Atlantic Meridional Overturning Circulation (MOC) is a crucial part of the climate system because of its associated northward heat transport. The present-day MOC is sensitive to freshwater anomalies and may collapse to a state with a strongly reduced northward heat transport. A future collapse of the Atlantic MOC has been identified as one of the most dangerous tipping points in the climate system. It is therefore crucial to develop early warning indicators for such a potential collapse based on relatively short time series. So far, attempts to use indicators based on critical slowdown have been marginally successful. Based on complex climate network reconstruction, we here present a promising new indicator for the MOC collapse that efficiently monitors spatial changes in deep ocean circulation. Through our analysis of the performance of this indicator we formulate optimal locations of measurement of the MOC to provide early warning signals of a collapse. Our results imply that an increase in spatial resolution of the Atlantic MOC observations (i.e., at more sections) can improve early detection, because the spatial coherence in the deep ocean arising near the transition is better captured.
Anna S. von der Heydt, Peter Köhler, Roderik S. W. van de Wal, Henk A. Dijkstra
Palaeo data have been frequently used to determine the equilibrium (Charney) climate sensitivity $S^a$, and - if slow feedback processes (e.g. land ice-albedo) are adequately taken into account - they indicate a similar range as estimates based on instrumental data and climate model results. Most studies implicitly assume the (fast) feedback processes to be independent of the background climate state, e.g., equally strong during warm and cold periods. Here we assess the dependency of the fast feedback processes on the background climate state using data of the last 800 kyr and a conceptual climate model for interpretation. Applying a new method to account for background state dependency, we find $S^a=0.61\pm0.06$ K(Wm$^{-2}$)$^{-1}$ using the latest LGM temperature reconstruction and significantly lower climate sensitivity during glacial climates. Due to uncertainties in reconstructing the LGM temperature anomaly, $S^a$ is estimated in the range $S^a=0.55-0.95$ K(Wm$^{-2}$)$^{-1}$.
Swinda K. J. Falkena, Courtney Quinn, Jan Sieber, Jason Frank, Henk A. Dijkstra
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.
Mikael L. A. Kaandorp, Henk A. Dijkstra, Erik van Sebille
Field studies have shown that plastic fragments make up the majority of plastic pollution in the oceans in terms of abundance. How quickly environmental plastics fragment is not well understood, however. Here, we study this fragmentation process by considering a model which captures continuous fragmentation of particles over time in a cascading fashion. With this cascading fragmentation model we simulate particle size distributions (PSDs), specifying the abundance or mass of particles for different size classes. The fragmentation model is coupled to an environmental box model, simulating the distributions of plastic particles in the ocean, coastal waters, and on the beach. We compare the modelled PSDs to available observations, and use the results to illustrate the effect of size-selective processes such as vertical mixing in the water column and resuspension of particles from the beach into coastal waters. The model quantifies the role of fragmentation on the marine plastic mass budget: while fragmentation is a major source of (secondary) plastic particles in terms of abundance, it seems to have a minor effect on the total mass of particles larger than 0.1 mm. Future comparison to observed PSD data allow us to understand size-selective plastic transport in the environment, and potentially inform us on plastic longevity.
Mu Mu, Liang Sun, Henk A. Dijkstra
Within a simple model context, the sensitivity and stability of the thermohaline circulation to finite amplitude perturbations is studied. A new approach is used to tackle this nonlinear problem. The method is based on the computation of the so-called Conditional Nonlinear Optimal Perturbation (CNOP) which is a nonlinear generalization of the linear singular vector approach (LSV). It is shown that linearly stable thermohaline circulation states can become nonlinearly unstable and the properties of the perturbations with optimal nonlinear growth are determined. An asymmetric nonlinear response to perturbations exists with respect to the sign of finite amplitude freshwater perturbations, on both thermally dominated and salinity dominated thermohaline flows. This asymmetry is due to the nonlinear interaction of the perturbations through advective processes.
Qing Yi Feng, Henk A. Dijkstra
Most of the existing prediction methods gave a false alarm regarding the El Niño event in 2014. A crucial aspect is currently limiting the success of such predictions, i.e. the stability of the slowly varying Pacific climate. This property determines whether sea surface temperature perturbations will be amplified by coupled ocean-atmosphere feedbacks or not. The so-called Bjerknes stability index has been developed for this purpose, but its evaluation is severely constrained by data availability. Here we present a new promising background stability index based on complex network theory. This index efficiently monitors the changes in spatial correlations in the Pacific climate and can be evaluated by using only sea surface temperature data.
Andrew Keane, Alexandre Pohl, Henk A. Dijkstra, Andy Ridgwell
The global ocean circulation plays a pivotal role in the regulation of the Earth's climate. The specific pattern and strength of circulation also determines how carbon and nutrients are cycled and via the resulting distribution of dissolved oxygen, where habitats suitable for marine animals occur. However, evidence from both geological data and models suggests that state transitions in circulation patterns have occurred in the past. Understanding the controls on marine environmental conditions and biodiversity requires a full appreciation of the nature and drivers of such transitions. Here we present stable millennial oscillations of meridional overturning circulation in an Earth system model of intermediate complexity, cGENIE, that appear to only occur in the presence of a circumpolar current. To demonstrate that a circumpolar current can act as a driver of stable oscillations, we adapt a simple ocean box model to include a delayed feedback to represent the effect of a circumpolar current on meridional overturning circulation. We investigate the millennial oscillatory solutions that arise in the box model by bifurcation analysis and show that the model can reproduce the same bifurcation structure observed in the Earth system model. Our results provide new insights into the nature of oscillations that could have occurred under certain continental configurations in the geological past, and also highlight the potential influence of the changing Antarctic circumpolar current speed on the stability of the Atlantic meridional overturning circulation.