Exploring the Lyapunov instability properties of high-dimensional atmospheric and climate models

The stability properties of intermediate-order climate models are investigated by computing their Lyapunov exponents (LEs). The two models considered are PUMA (Portable University Model of the Atmosphere), a primitive-equation simple general circulation model, and MAOOAM (Modular Arbitrary-Order Ocean-Atmosphere Model), a quasi-geostrophic coupled ocean–atmosphere model on a β-plane. We wish to investigate the effect of the different levels of filtering on the instabilities and dynamics of the atmospheric flows. Moreover, we assess the impact of the oceanic coupling, the dissipation scheme, and the resolution on the spectra of LEs. The PUMA Lyapunov spectrum is computed for two different values of the meridional temperature gradient defining the Newtonian forcing to the temperature field. The increase in the gradient gives rise to a higher baroclinicity and stronger instabilities, corresponding to a larger dimension of the unstable manifold and a larger first LE. The Kaplan–Yorke dimension of the attractor increases as well. The convergence rate of the rate function for the large deviation law of the finite-time Lyapunov exponents (FTLEs) is fast for all exponents, which can be interpreted as resulting from the absence of a clear-cut atmospheric timescale separation in such a model. The MAOOAM spectra show that the dominant atmospheric instability is correctly represented even at low resolutions. However, the dynamics of the central manifold, which is mostly associated with the ocean dynamics, is not fully resolved because of its associated long timescales, even at intermediate orders. As expected, increasing the mechanical atmosphere–ocean coupling coefficient or introducing a turbulent diffusion parametrisation reduces the Kaplan–Yorke dimension and Kolmogorov–Sinai entropy. In all considered configurations, we are not yet in the regime in which one can robustly define large deviation laws describing the statistics of the FTLEs. This paper highlights the need to investigate the natural variability of the atmosphere–ocean coupled dynamics by associating rate of growth and decay of perturbations with the physical modes described using the formalism of the covariant Lyapunov vectors and considering long integrations in order to disentangle the dynamical processes occurring at all timescales

Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach

In this paper we consider the problem of deriving approximate autonomous dynamics for a number of variables of a dynamical system, which are weakly coupled to the remaining variables. In a previous paper we have used the Ruelle response theory on such a weakly coupled system to construct a surrogate dynamics, such that the expectation value of any observable agrees, up to second order in the coupling strength, to its expectation evaluated on the full dynamics. We show here that such surrogate dynamics agree up to second order to an expansion of the Mori-Zwanzig projected dynamics. This implies that the parametrizations of unresolved processes suited for prediction and for the representation of long term statistical properties are closely related, if one takes into account, in addition to the widely adopted stochastic forcing, the often neglected memory effects.Comment: 14 pages, 1 figur

A case of labial fusion and urinary pseudo-incontinence in an elderly woman. A surgical treatment and a review

Labial fusion is defined as either partial or complete adherence of the labia minora (1), and also called vulvar fusion, adhesions of the labia minor or conglutination of the labia minora and sinechia of the vulva. The complete and severe labial fusion is a rare pathology with a small number of cases reported in the literature in adults. We present a case report of a postmenopausal woman who presented with voiding difficulty and incontinence and was treated by surgical division of the adhesions and immediate resolution of the urinary incontinence confirmed by multichannel urodynamic test postoperatively

A case of labial fusion and urinary pseudo-incontinence in an elderly woman. A surgical treatment and a review

Labial fusion is defined as either partial or complete adherence of the labia minora (1), and also called vulvar fusion, adhesions of the labia minor or conglutination of the labia minora and sinechia of the vulva. The complete and severe labial fusion is a rare pathology with a small number of cases reported in the literature in adults. We present a case report of a postmenopausal woman who presented with voiding difficulty and incontinence and was treated by surgical division of the adhesions and immediate resolution of the urinary incontinence confirmed by multichannel urodynamic test postoperatively

Efficacy of isothiocyanate-based compounds on different forms of persistent pain.

Current pharmacotherapy for persistent pain related to neuropathy or articular diseases is unsatisfactory, due to the large number of unresponsive patients and side effects. Isothiocyanates (ITCs) are a class of natural or synthetic compounds characterized by the general formula R-NCS. ITCs show antihyperalgesic effects in models of central and peripheral nervous tissue injury and anti-inflammatory properties. The pharmacodynamics are strictly related to the release of the gasotransmitter hydrogen sulfide (H2S) from their moiety. In particular, phenyl ITC (PITC) and 3-carboxyphenyl ITC (3C-PITC) exhibit interesting slow H2S-release properties suitable for treating painful pathology. The aim of the present work was to evaluate the efficacy of PITC and 3C-PITC against mechanical hyperalgesia and spontaneous pain induced by nerve injury and osteoarthritis

Predicting climate change using response theory: global averages and spatial patterns

The provision of accurate methods for predicting the climate response to anthropogenic and natural forcings is a key contemporary scientific challenge. Using a simplified and efficient open-source general circulation model of the atmosphere featuring O(105105) degrees of freedom, we show how it is possible to approach such a problem using nonequilibrium statistical mechanics. Response theory allows one to practically compute the time-dependent measure supported on the pullback attractor of the climate system, whose dynamics is non-autonomous as a result of time-dependent forcings. We propose a simple yet efficient method for predicting—at any lead time and in an ensemble sense—the change in climate properties resulting from increase in the concentration of CO22 using test perturbation model runs. We assess strengths and limitations of the response theory in predicting the changes in the globally averaged values of surface temperature and of the yearly total precipitation, as well as in their spatial patterns. The quality of the predictions obtained for the surface temperature fields is rather good, while in the case of precipitation a good skill is observed only for the global average. We also show how it is possible to define accurately concepts like the inertia of the climate system or to predict when climate change is detectable given a scenario of forcing. Our analysis can be extended for dealing with more complex portfolios of forcings and can be adapted to treat, in principle, any climate observable. Our conclusion is that climate change is indeed a problem that can be effectively seen through a statistical mechanical lens, and that there is great potential for optimizing the current coordinated modelling exercises run for the preparation of the subsequent reports of the Intergovernmental Panel for Climate Change