Multistability and intermediate tipping of the Atlantic Ocean circulation.

Tipping points (TP) in climate subsystems are usually thought to occur at a well-defined, critical forcing parameter threshold, via destabilization of the system state by a single, dominant positive feedback. However, coupling to other subsystems, additional feedbacks, and spatial heterogeneity may promote further small-amplitude, abrupt reorganizations of geophysical flows at forcing levels lower than the critical threshold. Using a primitive-equation ocean model, we simulate a collapse of the Atlantic Meridional Overturning Circulation (AMOC) due to increasing glacial melt. Considerably before the collapse, various abrupt, qualitative changes in AMOC variability occur. These intermediate tipping points (ITP) are transitions between multiple stable circulation states. Using 2.75 million years of model simulations, we uncover a very rugged stability landscape featuring parameter regions of up to nine coexisting stable states. The path to an AMOC collapse via a sequence of ITPs depends on the rate of change of the meltwater input. This challenges our ability to predict and define safe limits for TPs.

Risk of tipping the overturning circulation due to increasing rates of ice melt.

Central elements of the climate system are at risk for crossing critical thresholds (so-called tipping points) due to future greenhouse gas emissions, leading to an abrupt transition to a qualitatively different climate with potentially catastrophic consequences. Tipping points are often associated with bifurcations, where a previously stable system state loses stability when a system parameter is increased above a well-defined critical value. However, in some cases such transitions can occur even before a parameter threshold is crossed, given that the parameter change is fast enough. It is not known whether this is the case in high-dimensional, complex systems like a state-of-the-art climate model or the real climate system. Using a global ocean model subject to freshwater forcing, we show that a collapse of the Atlantic Meridional Overturning Circulation can indeed be induced even by small-amplitude changes in the forcing, if the rate of change is fast enough. Identifying the location of critical thresholds in climate subsystems by slowly changing system parameters has been a core focus in assessing risks of abrupt climate change. This study suggests that such thresholds might not be relevant in practice, if parameter changes are not slow. Furthermore, we show that due to the chaotic dynamics of complex systems there is no well-defined critical rate of parameter change, which severely limits the predictability of the qualitative long-term behavior. The results show that the safe operating space of elements of the Earth system with respect to future emissions might be smaller than previously thought.

Multiscale measures of phase-space trajectories.

Characterizing the multiscale nature of fluctuations from nonlinear and nonstationary time series is one of the most intensively studied contemporary problems in nonlinear sciences. In this work, we address this problem by combining two established concepts-empirical mode decomposition (EMD) and generalized fractal dimensions-into a unified analysis framework. Specifically, we demonstrate that the intrinsic mode functions derived by EMD can be used as a source of local (in terms of scales) information about the properties of the phase-space trajectory of the system under study, allowing us to derive multiscale measures when looking at the behavior of the generalized fractal dimensions at different scales. This formalism is applied to three well-known low-dimensional deterministic dynamical systems (the Hénon map, the Lorenz '63 system, and the standard map), three realizations of fractional Brownian motion with different Hurst exponents, and two somewhat higher-dimensional deterministic dynamical systems (the Lorenz '96 model and the on-off intermittency model). These examples allow us to assess the performance of our formalism with respect to practically relevant aspects like additive noise, different initial conditions, the length of the time series under study, low- vs high-dimensional dynamics, and bursting effects. Finally, by taking advantage of two real-world systems whose multiscale features have been widely investigated (a marine stack record providing a proxy of the global ice volume variability of the past 5×106 years and the SYM-H geomagnetic index), we also illustrate the applicability of this formalism to real-world time series.

Role of helicity in triad interactions in three-dimensional turbulence investigated by a new shell model.

Fully developed homogeneous isotropic turbulence in two dimensions is fundamentally different from that in three dimensions. In two dimensions, the simultaneous inviscid conservation of both kinetic energy and enstrophy within the inertial range of scales leads to a forward cascade of enstrophy and a reverse cascade of energy. In three dimensions, helicity, the integral of the scalar product of velocity and vorticity, is also an inviscid flow invariant along with the energy. Unlike the enstrophy, however, the helicity does not block the forward cascade of energy to small scales. Energy and helicity are conserved not only globally but also within each nonlinear triadic interaction between three plane waves in the spectral form of the Navier-Stokes equation (NSE). By decomposing each plane wave into two helical modes of opposite helicities, each triadic interaction is split into a set of eight helical triadic interactions between helical modes [F. Waleffe, Phys. Fluids A 4, 350 (1992)PFADEB0899-821310.1063/1.858309]. Recently it was found that a subset of these helical interactions, which render both signs of helicity separately conserved (enstrophy-like), leads to an inverse cascade of (part of) the energy [L. Biferale et al., Phys. Rev. Lett. 108, 164501 (2012)PRLTAO0031-900710.1103/PhysRevLett.108.164501]. Motivated by this finding we introduce a new shell model, obtained from the NSE expressed in the helical basis, allowing the eight helical interactions to be coupled as in the NSE and their relative contributions evaluated as a function of both the net helicity input and triad geometry. By numerically integrating the new model, we find that the intermittency of the energy cascade decreases with the net helicity input. Studying the partitioning of the energy cascade between the eight helical interactions, we find that the decrease in intermittency is related to a shift in the dominating helical interactions when helically forced, two of which exhibit a larger cascade intermittency than the other six interactions. Among the relatively local triad geometries considered here, the partitioning of the energy and helicity cascades between the eight helical interactions shows no sign of change with triad geometry.

Contrasting scaling properties of interglacial and glacial climates.

Understanding natural climate variability is essential for assessments of climate change. This is reflected in the scaling properties of climate records. The scaling exponents of the interglacial and the glacial climates are fundamentally different. The Holocene record is monofractal, with a scaling exponent H∼0.7. On the contrary, the glacial record is multifractal, with a significantly higher scaling exponent H∼1.2, indicating a longer persistence time and stronger nonlinearities in the glacial climate. The glacial climate is dominated by the strong multi-millennial Dansgaard-Oeschger (DO) events influencing the long-time correlation. However, by separately analysing the last glacial maximum lacking DO events, here we find the same scaling for that period as for the full glacial period. The unbroken scaling thus indicates that the DO events are part of the natural variability and not externally triggered. At glacial time scales, there is a scale break to a trivial scaling, contrasting the DO events from the similarly saw-tooth-shaped glacial cycles.