State-dependence of climate sensitivity: attractor constraints and palaeoclimate regimes

Equilibrium climate sensitivity (ECS) is a key predictor of climate change. However, it is not very well constrained, either by climate models or by observational data. The reasons for this include strong internal variability and forcing on many time scales. In practise this means that the 'equilibrium' will only be relative to fixing the slow feedback processes before comparing palaeoclimate sensitivity estimates with estimates from model simulations. In addition, information from the late Pleistocene ice age cycles indicates that the climate cycles between cold and warm regimes, and the climate sensitivity varies considerably between regime because of fast feedback processes changing relative strength and time scales over one cycle. In this paper we consider climate sensitivity for quite general climate dynamics. Using a conceptual Earth system model of Gildor and Tziperman (2001) (with Milankovich forcing and dynamical ocean biogeochemistry) we explore various ways of quantifying the state-dependence of climate sensitivity from unperturbed and perturbed model time series. Even without considering any perturbations, we suggest that climate sensitivity can be usefully thought of as a distribution that quantifies variability within the 'climate attractor' and where there is a strong dependence on climate state and more specificially on the 'climate regime' where fast processes are approximately in equilibrium. We also consider perturbations by instantaneous doubling of CO$_2$ and similarly find a strong dependence on the climate state using our approach.Comment: 32 pages, 10 figure

Extreme sensitivity and climate tipping points

A climate state close to a tipping point will have a degenerate linear response to perturbations, which can be associated with extreme values of the equilibrium climate sensitivity (ECS). In this paper we contrast linearized (`instantaneous') with fully nonlinear geometric (`two-point') notions of ECS, in both presence and absence of tipping points. For a stochastic energy balance model of the global mean surface temperature with two stable regimes, we confirm that tipping events cause the appearance of extremes in both notions of ECS. Moreover, multiple regimes with different mean sensitivities are visible in the two-point ECS. We confirm some of our findings in a physics-based multi-box model of the climate system.Comment: 11 figure

Response maxima in modulated turbulence

Isotropic and homogeneous turbulence driven by an energy input modulated in time is studied within a variable range mean-field theory. The response of the system, observed in the second order moment of the large-scale velocity difference D(L,t)=>~Re(t)^2$, is calculated for varying modulation frequencies w and weak modulation amplitudes. For low frequencies the system follows the modulation of the driving with almost constant amplitude, whereas for higher driving frequencies the amplitude of the response decreases on average 1/w. In addition, at certain frequencies the amplitude of the response either almost vanishes or is strongly enhanced. These frequencies are connected with the frequency scale of the energy cascade and multiples thereof.Comment: 11 pages, 6 figure

High continuous bandwidth multichannel acquisition system

Multichannel data acquisition has been a keystone of 7 ONR sponsored Arctic acoustic research programs conducted jointly by WHOI and MIT investigators from 1978 through 1989. This report describes the status and capability of the most recent system developed at WHOI for the purpose of acquiring digital data from up to 64 channels at sampling rates up to 20 kH per channel with data bandwidth to 5120 Hz. ONR funded the development of and use of this system and its prototye for 2 Arctic field experiments, PRUDEX 87 and CEAREX 89. It was most recently use during the Heard Island Feasibility Experiment in February 1991. Of note are the auto-gain ranging capabilty offering a dynamic measurement range of greater than 120 dB, the continuous storage capability of up to 200,000 samples per second to a Small Computer System Interface (SCSI) device, typically optical disk, and easy expandability with additional identical chanels connected in parallel.Funding was provided by the Office of Naval Research under Contract No. N00014-91-J-1296

Ripple Effects: The Unintended Change to Jurisdictional Pleading Standards After Iqbal

This Note describes a little-observed ripple effect of the new pleading standard announced in Iqbal, the antiterrorism case whose holding swept broadly and changed the ground rules for considering allegations in so-called 12(b)(6) motions for all civil cases. This Note examines the interplay between the Twombly/Iqbal doctrine and federal courts’ practical approach to subject-matter jurisdiction. Part II describes the background jurisprudence on subject-matter jurisdiction, including the sharp line the Supreme Court has consistently re-drawn between claims lacking merit and those lacking jurisdictional basis, from Bell v. Hood through Arbaugh v. Y & H Corp. The consistent theme of this jurisprudence is that courts should not conflate merits and jurisdictional questions, and that judges should readily activate the court’s jurisdiction in response to a simple allegation in the complaint. Part III then describes the recent change to pleading standards on the merits of a claim. It explains the origins, factual context, and doctrinal bases of the altered pleading standard introduced in Iqbal and Twombly. These rationales do not, in most cases, apply to motions to dismiss for lack of subject-matter jurisdiction. In Part IV, lower-court case law reveals that since 2009, in practice, the Iqbal standard has been interfering with the agenda of Arbaugh, in a way that the Supreme Court did not intend. Federal judges, in their eagerness to apply the novel pleading standard of Iqbal, have neglected the jurisdictional teachings of the Supreme Court in the Arbaugh line of cases. As a result, since Iqbal an erroneous 12(b)(1) standard has propagated rapidly through circuit and lower courts.If the application of Iqbal to jurisdictional pleadings is an error, as this Note maintains and as recent Supreme Court reaffirmations of Arbaugh suggest, it may prove difficult to eradicate. Part V addresses the ineffectiveness of circuit courts and the rules-based system in correcting such mistakes

Elasticity of cross-linked semiflexible biopolymers under tension

Aiming at the mechanical properties of cross-linked biopolymers, we set up and analyze a model of two weakly bending wormlike chains subjected to a tensile force, with regularly spaced inter-chain bonds (cross-links) represented by harmonic springs. Within this model, we compute the force-extension curve and the differential stiffness exactly and discuss several limiting cases. Cross-links effectively stiffen the chain pair by reducing thermal fluctuations transverse to the force and alignment direction. The extra alignment due to cross-links increases both with growing number and with growing strength of the cross-links, and is most prominent for small force f. For large f, the additional, cross-link-induced extension is subdominant except for the case of linking the chains rigidly and continuously along their contour. In this combined limit, we recover asymptotically the elasticity of a weakly bending wormlike chain without constraints, stiffened by a factor four. The increase in differential stiffness can be as large as 100% for small f or large numbers of cross-links.Comment: 11 pages, 6 figures, submitted to PR

On the sound of snapping shrimp

Fluid dynamics video: Snapping shrimp produce a snapping sound by an extremely rapid closure of their snapper claw. Our high speed imaging of the claw closure has revealed that the sound is generated by the collapse of a cavitation bubble formed in a fast flowing water jet forced out from the claws during claw closure. The produced sound originates from the cavitation collapse of the bubble. At collapse a short flash of light is emitted, just as in single bubble sonoluminescence. A model based on the Rayleigh-Plesset equation can quantitatively account for the visual and acoustical observations.Comment: Fluid dynamics vide