Lyapunov analysis of multiscale dynamics: the slow bundle of the two-scale Lorenz 96 model

We investigate the geometrical structure of instabilities in the two-scale Lorenz 96 model through the prism of Lyapunov analysis. Our detailed study of the full spectrum of covariant Lyapunov vectors reveals the presence of a slow bundle in tangent space, composed by a set of vectors with a significant projection onto the slow degrees of freedom; they correspond to the smallest (in absolute value) Lyapunov exponents and thereby to the longer timescales. We show that the dimension of the slow bundle is extensive in the number of both slow and fast degrees of freedom and discuss its relationship with the results of a finite-size analysis of instabilities, supporting the conjecture that the slow-variable behavior is effectively determined by a nontrivial subset of degrees of freedom. More precisely, we show that the slow bundle corresponds to the Lyapunov spectrum region where fast and slow instability rates overlap, “mixing” their evolution into a set of vectors which simultaneously carry information on both scales. We suggest that these results may pave the way for future applications to ensemble forecasting and data assimilations in weather and climate models

Does the Danube exist? Versions of reality given by various regional climate models and climatological datasets

We present an intercomparison and verification analysis of several regional climate models (RCMs) nested into the same run of the same Atmospheric Global Circulation Model (AGCM) regarding their representation of the statistical properties of the hydrological balance of the Danube river basin for 1961-1990. We also consider the datasets produced by the driving AGCM, from the ECMWF and NCEP-NCAR reanalyses. The hydrological balance is computed by integrating the precipitation and evaporation fields over the area of interest. Large discrepancies exist among RCMs for the monthly climatology as well as for the mean and variability of the annual balances, and only few datasets are consistent with the observed discharge values of the Danube at its Delta, even if the driving AGCM provides itself an excellent estimate. Since the considered approach relies on the mass conservation principle and bypasses the details of the air-land interface modeling, we propose that the atmospheric components of RCMs still face difficulties in representing the water balance even on a relatively large scale. Their reliability on smaller river basins may be even more problematic. Moreover, since for some models the hydrological balance estimates obtained with the runoff fields do not agree with those obtained via precipitation and evaporation, some deficiencies of the land models are also apparent. NCEP-NCAR and ERA-40 reanalyses result to be largely inadequate for representing the hydrology of the Danube river basin, both for the reconstruction of the long-term averages and of the seasonal cycle, and cannot in any sense be used as verification. We suggest that these results should be carefully considered in the perspective of auditing climate models and assessing their ability to simulate future climate changes.Comment: 25 pages 8 figures, 5 table

Crystal plasticity simulation of the effect of grain size on the fatigue behavior of polycrystalline Inconel 718

A microstructure-based model that accounts for the effect of grain size has been developed to study the effect of grain size on the fatigue life of Inconel 718 alloys. The fatigue behavior of two alloys with different grain size was determined by means of uniaxial cyclic deformation tests under fully-reversed deformation ($R_\varepsilon$ = -1) at 400$^\circ$C in the low cycle fatigue regime. The model was based in the determination of the fatigue indicator parameter (based on the local crystallographic strain energy dissipated per cycle) by means of computational homogenization of a representative volume element of the microstructure. The mechanical response of the single crystal within the polycrystal was modelled through a phenomenological crystal plasticity model which was modified to account for the effect of grain size on the monotonic and cyclic hardening/softening mechanisms. The microstructure-based crack initiation model parameters were calibrated from the experimental tests of the material with fine grain size. The results of the fatigue simulations were in good agreement with the experimental results in terms of the cyclic stress-strain curves and of the number of cycles for fatigue crack initiation. The model did not show any grain size effect on the fatigue life for the largest cyclic strain ranges while the predicted fatigue life predicted was considerably longer in the case of the microstructure with fine grain size for the lowest strain ranges, in quantitative agreement with experimental data. These differences were attributed to changes in the deformation modes between homogeneous plastic deformation at large cyclic strain ranges and localized plasticity in a few grains at low cyclic strain ranges

Testing the validity of THz reflection spectra by dispersion relations

Complex response function obtained in reflection spectroscopy at terahertz range is examined with algorithms based on dispersion relations for integer powers of complex reflection coefficient, which emerge as a powerful and yet uncommon tools in examining the consistency of the spectroscopic data. It is shown that these algorithms can be used in particular for checking the success of correction of the spectra by the methods of Vartiainen et al [1] and Lucarini et al [2] to remove the negative misplacement error in the terahertz time-domain spectroscopy.Comment: 17 pages, 4 figure

The impact of oceanic heat transport on the atmospheric circulation

A general circulation model of intermediate complexity with an idealized Earth-like aquaplanet setup is used to study the impact of changes in the oceanic heat transport on the global atmospheric circulation. Focus is on the atmospheric mean meridional circulation and global thermodynamic properties. The atmosphere counterbalances to a large extent the imposed changes in the oceanic heat transport, but, nonetheless, significant modifications to the atmospheric general circulation are found. Increasing the strength of the oceanic heat transport up to 2.5 PW leads to an increase in the global mean near-surface temperature and to a decrease in its equator-to-pole gradient. For stronger transports, the gradient is reduced further, but the global mean remains approximately constant. This is linked to a cooling and a reversal of the temperature gradient in the tropics. Additionally, a stronger oceanic heat transport leads to a decline in the intensity and a poleward shift of the maxima of both the Hadley and Ferrel cells. Changes in zonal mean diabatic heating and friction impact the properties of the Hadley cell, while the behavior of the Ferrel cell is mostly controlled by friction. The efficiency of the climate machine, the intensity of the Lorenz energy cycle and the material entropy production of the system decline with increased oceanic heat transport. This suggests that the climate system becomes less efficient and turns into a state of reduced entropy production as the enhanced oceanic transport performs a stronger large-scale mixing between geophysical fluids with different temperatures, thus reducing the available energy in the climate system and bringing it closer to a state of thermal equilibrium

The exploitation of wild plants in Neolithic North Africa. Use-wear and residue analysis on non-knapped stone tools from the Haua Fteah cave, Cyrenaica, Libya

The North African region offers up essential data for the study of the origins of the earliest forms of plant exploitation. Data available from several Saharan and coastal areas in the region have revealed that the arrival of domestic wheat and barley from the Levant during the Mid Holocene did not replace the exploitation of autochthonous wild plants, especially grasses. The Neolithic layers of the Haua Fteah cave, in Cyrenaica (Northern Libya), have so far produced archaeobotanical assemblages exclusively made up of wild species. This paper investigates production and use of non-knapped stone tools, mainly grinding stones, from the Holocene sequence of the Haua Fteah Cave. The presence of grinding stones may indicate a certain level of behavioural change and the adoption of new economic strategies, relying more strongly on plant exploitation. This assumption has been tested using an integrated approach of use-wear and residue analysis. These methods allowed us to obtain significant new information as to how tools were originally used. Use-wear analysis was carried out adopting a low power approach; such study was complemented by residue analysis, in particular starch granules analysis, only rarely applied in North African contexts. This combined approach was carried out on a selected sample of tools, in order to test survival of plant micro-remains and, where possible, the types of plants processed by the Holocene communities in the cave. Here we confirm the lack of evidence of domesticated crops and the presence of starch granules only belonging to wild plants. The importance of wild plants in the economy of North African prehistoric groups has often been underestimated, on the assumption that they were replaced by the Near Eastern domesticated crops and animals once they were firstly introduced in North Africa. The results of our study show a different picture, confirming the role of the wild species as an important food source during the Holocene.his research was conducted as a part of the Marie Skłodowska-Curie Project FP7-People-2012-IEF ‘AGRINA’, funded by the European Commission. We gratefully acknowledge the permission and support of the Department of Antiquities of Libya to undertake the Cyrenaican Prehistory Project and the financial support from the European Research Grant (grant number 230421) and the Society for Libyan Studies.This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.quaint.2015.11.10

Crisis of the chaotic attractor of a climate model: a transfer operator approach

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

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