Showing papers by "Peter D. Ditlevsen published in 2016"

Lessons on Climate Sensitivity From Past Climate Changes

Abstract: Over the last decade, our understanding of climate sensitivity has improved considerably. The climate system shows variability on many timescales, is subject to non-stationary forcing and it is most likely out of equilibrium with the changes in the radiative forcing. Slow and fast feedbacks complicate the interpretation of geological records as feedback strengths vary over time. In the geological past, the forcing timescales were different than at present, suggesting that the response may have behaved differently. Do these insights constrain the climate sensitivity relevant for the present day? In this paper, we review the progress made in theoretical understanding of climate sensitivity and on the estimation of climate sensitivity from proxy records. Particular focus lies on the background state dependence of feedback processes and on the impact of tipping points on the climate system. We suggest how to further use palaeo data to advance our understanding of the currently ongoing climate change.

Contrasting scaling properties of interglacial and glacial climates.

Abstract: Natural climate variability and persistency are reflected in the scaling properties of climate records. Here, the authors show that the scaling properties of interglacial and glacial climates are distinctively different: The former is monofractal while the latter is multifractal with much longer range memory.

A conceptual model for glacial cycles and the middle Pleistocene transition

Abstract: Milankovitch’s astronomical theory of glacial cycles, attributing ice age climate oscillations to orbital changes in Northern-Hemisphere insolation, is challenged by the paleoclimatic record. The climatic response to the variations in insolation is far from trivial. In general the glacial cycles are highly asymmetric in time, with slow cooling from the interglacials to the glacials (inceptions) and very rapid warming from the glacials to the interglacials (terminations). We shall refer to this fast-slow dynamics as the “saw-tooth” shape of the paleoclimatic record. This is non-linearly related to the time-symmetric variations in the orbital forcing. However, the most pronounced challenge to the Milankovitch theory is the middle Pleistocene transition (MPT) occurring about one million years ago. During that event, the prevailing 41 kyr glacial cycles, corresponding to the almost harmonic obliquity cycle were replaced by longer saw-tooth shaped cycles with a time-scale around 100 kyr. The MPT must have been driven by internal changes in climate response, since it does not correspond to any apparent changes in the orbital forcing. In order to identify possible mechanisms causing the observed changes in glacial dynamics, it is relevant to study simplified models with the capability of generating temporal behavior similar to the observed records. We present a simple oscillator type model approach, with two variables, a temperature anomaly and a climatic memory term. The generalization of the ice albedo feedback is included in terms of an effective multiplicative coupling between this latter climatic memory term (representing the internal degrees of freedom) and the external drive. The simple model reproduces the temporal asymmetry of the late Pleistocene glacial cycles and suggests that the MPT can be explained as a regime shift, aided by climatic noise, from a period 1 frequency locking to the obliquity cycle to a period 2–3 frequency locking to the same obliquity cycle. The change in dynamics has been suggested to be a result of a slow gradual decrease in atmospheric greenhouse gas concentration. The critical dependence on initial conditions in the (non-autonomous) glacial dynamics raises fundamental questions about climate predictability.

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

Abstract: 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)]. 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)]. 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.

Pseudo-invariants causing inverse energy cascades in three-dimensional turbulence

Abstract: Three-dimensional (3D) turbulence is characterized by a dual forward cascade of both kinetic energy and helicity, a second inviscid flow invariant, from the integral scale of motion to the viscous dissipative scale. In helical flows, however, such as strongly rotating flows with broken mirror symmetry, an inverse energy cascade can be observed analogous to that of two-dimensional turbulence (2D) where a second positive-definite flow invariant, enstrophy, unlike helicity in 3D, effectively blocks the forward cascade of energy. In the spectral-helical decomposition of the Navier-Stokes equation it has previously been show that a subset of three-wave (triad) interactions conserve helicity in 3D in a fashion similar to enstrophy in 2D, thus leading to a 2D-like inverse energy cascade in 3D. In this work, we show both theoretically and numerically that an additional subset of interactions exist conserving a new pseudo-invariant in addition to energy and helicity, which contributes either to a forward or inverse energy cascade depending on the specific triad interaction geometry.

Three types of nonlinear resonances

Abstract: We analyse different types of nonlinear resonances in a weakly damped Duffing oscillator using bifurcation theory techniques. In addition to (i) odd subharmonic resonances found on the primary branch of symmetric periodic solutions with the forcing frequency and (ii) even subharmonic resonances due to symmetry-broken periodic solutions that bifurcate off the primary branch and also oscillate at the forcing frequency, we uncover (iii) novel resonance type due to isolas of periodic solutions that are not connected to the primary branch. These occur between odd and even resonances, oscillate at a fraction of the forcing frequency, and give rise to a complicated resonance `curve' with disconnected elements and high degree of multistability. We use bifurcation continuation to compute resonance tongues in the plane of the forcing frequency vs. the forcing amplitude for different but fixed values of the damping rate. In this way, we demonstrate that identified here isolated resonances explain the intriguing structure of "patchy tongues" observed for week damping and link it to a seemingly unrelated phenomenon of "bifurcation superstructure" described for moderate damping.