arXiv subjects

Valerio Lucarini

Publications and source records attributed to Valerio Lucarini.

At least 163 records · Page 9Linked to original sources

arXiv2010

Energetics of PCMDI/CMIP3 Climate Models: Energy Budget and Meridional Enthalpy Transport

We analyze the PCMDI/CMIP3 simulations performed by climate models (CMs) using pre-industrial and SRESA1B scenarios. Relatively large biases are present for most CMs when global energy budgets and when the atmospheric, oceanic, and land budgets are considered. Apparently, the biases do not result from transient effects, but depend on the imperfect closure of the energy cycle in the fluid components and on inconsistencies over land. Therefore, the planetary emission temperature is underestimated. This may explain the CMs' cold bias. In the pre-industrial scenario, CMs agree on the location in the mid-latitudes of the peaks of the meridional atmospheric enthalpy transport, while large discrepancies exist on the intensity. Disagreements on the location and intensity of the oceanic transport peaks are serious. With increased $CO_2$ concentration, a small poleward shift of the peak and an increase in the intensity of the atmospheric transport of up to 10% are detected in both hemispheres. Instead, most CMs feature a decrease in the oceanic transport intensity in the northern hemisphere and an equatorward shift of the peak in both hemispheres. The Bjerkens compensation mechanism is active both on climatological and interannual time scales. The peak of the total meridional transport is typically around $35^\circ$ in both hemispheres and scenarios, whereas disagreements on the intensity are relevant. With increased $CO_2$ concentration, the total transport increases by up to 10%, thus contributing to polar amplification. Advances in the representation of physical processes are definitely needed for providing a self-consistent representation of climate as a non-equilibrium thermodynamical system.

physics.ao-ph↗

arXiv2010

A Statistical Mechanical Approach for the Computation of the Climatic Response to General Forcings

The climate belongs to the class of non-equilibrium forced and dissipative systems, for which most results of quasi-equilibrium statistical mechanics, including the fluctuation-dissipation theorem, do not apply. We show for the first time how the Ruelle linear response theory, developed for studying rigorously the impact of perturbations on general observables of non-equilibrium statistical mechanical systems, can be applied to analyze the climatic response. We choose as test bed the Lorenz 96 model, which has a well-recognized prototypical value. We recapitulate the main aspects of the response theory and propose some new results. We then analyze the frequency dependence of the response of both local and global observables to perturbations with localized as well as global spatial patterns. We derive analytically the asymptotic behaviour, validity of Kramers-Kronig relations, and sum rules for the susceptibilities, and related them to parameters describing the unperturbed properties of the system. We verify the theoretical predictions from the outputs of the simulations with great precision. The theory is used to explain differences in the response of local and global observables, in defining the intensive properties of the system and in generalizing the concept of climate sensitivity to all time scales. We also show how to reconstruct the linear Green function, which maps perturbations of general time patterns into changes in the expectation value of the considered observable. Finally, we propose a general methodology to study Climate Change problems by resorting to few, well selected simulations and discuss the specific case of surface temperature response to changes of the $CO_2$ concentration. This approach may provide a radically new perspective to study rigorously the problem of climate sensitivity and climate change.

cond-mat.stat-mech↗

arXiv2009

Thermodynamic Analysis of Snowball Earth Hysteresis Experiment: Efficiency, Entropy Production, and Irreversibility

We present an extensive thermodynamic analysis of a hysteresis experiment performed on a simplified yet Earth-like climate model. We slowly vary the solar constant by 20% around the present value and detect a substantial bistability: for a large range of values the realization of snowball (SB) or of warm (W) climate conditions depend on the history of the system. Using recent results on the global climate thermodynamics, we show that that the two regimes feature radically different properties. The efficiency of the climate machine increases with decreasing solar constant in W climate conditions, whereas the opposite takes place in the SB regime. Instead, entropy production is increasing with the solar constant in both branches of climate conditions, and its value is about 4 times as large in the W branch than in the corresponding C state. Finally, the degree of irreversibility of the system is much higher in the W conditions, with an explosive growth in the upper range of the considered values of solar constants. Whereas in the SB regime a dominating role is played by changes in the meridional albedo contrast, in the W climate regime changes in the intensity of latent heat fluxes are crucial for determining the observed properties. This substantiates the importance of addressing correctly the variations of the hydrological cycle in a changing climate. An interpretation of the transitions at the boundary of the bistable region based upon macro-scale thermodynamic properties is also proposed. Our results support the adoption of a new generation of diagnostic tools based on the 2nd law of thermodynamics for auditing climate model and outline a set of parameterizations to be used in conceptual and intermediate complexity models or for the reconstruction of the past climate conditions.

physics.ao-ph↗

arXiv2009

Thermodynamic Efficiency and Entropy Production in the Climate System

We present a new outlook on the climate system thermodynamics, studying some of its macroscopic properties in terms of the 1st and 2nd laws of thermodynamics. We review and clarify the notion of efficiency of the climate system by constructing formally an equivalent Carnot engine with efficiency eta, and show how the Lorenz energy cycle can be framed in a macro-scale thermodynamic context. Then, by exploiting the 2nd law, we prove that the lower bound to the entropy production is eta times the integrated absolute value of the internal entropy fluctuations. An exergetic interpretation is also proposed. Finally, the controversial maximum entropy production principle is re-interpreted as requiring the joint optimization of heat transport and mechanical work production. These results provide new tools for climate change analysis and for climate models' validation.

physics.ao-ph↗

arXiv2008

Symmetry-break, mixing, instability, and low frequency variability in a minimal Lorenz-like system

Starting from the classical Saltzman 2D convection equations, we derive via a severe spectral truncation a minimal 10 ODE system which includes the thermal effect of viscous dissipation. Neglecting this process leads to a dynamical system which includes a decoupled (generalized) Lorenz system. The consideration of this process breaks an important symmetry, couples the dynamics of fast and slow variables, ensuing modifications of the structural properties of the attractor and of the spectral features. When the relevant nondimensional number (Eckert number Ec) is different from zero, the system is ergodic and hyperbolic, the slow variables feature long term memory with 1/f 3/2 power spectra, and the fast variables feature amplitude modulation on time scale of 1/Ec. Increasing the strength of the thermal-viscous feedback has a stabilizing effect, as both the metric entropy and the Kaplan-Yorke attractor dimension decrease monotonically with Ec. The analyzed system features very rich dynamics: it overcomes some of the limitations of the Lorenz system and might have prototypical value in relevant processes in complex systems dynamics, such as the interaction between slow and fast variables. the presence of long term memory and the associated extreme value statistics. Analysis shows how, neglecting the coupling of slow and fast variables only on the basis of scale analysis can be catastrophic. In fact, this leads to spurious invariances that affect essential dynamical properties (ergodicity, hyperbolicity) and that cause the model losing ability in describing intrinsically multiscale processes.

nlin.CD↗

arXiv2008

Evidence of dispersion relations for the nonlinear response of the Lorenz 63 system

Along the lines of the nonlinear response theory developed by Ruelle, in a previous paper we have proved under rather general conditions that Kramers-Kronig dispersion relations and sum rules apply for a class of susceptibilities describing at any order of perturbation the response of Axiom A non equilibrium steady state systems to weak monochromatic forcings. We present here the first evidence of the validity of these integral relations for the linear and the second harmonic response for the perturbed Lorenz 63 system, by showing that numerical simulations agree up to high degree of accuracy with the theoretical predictions. Some new theoretical results, showing how to obtain recursively harmonic generation susceptibilities for general observables, are also presented. Our findings confirm the conceptual validity of the nonlinear response theory, suggest that the theory can be extended for more general non equilibrium steady state systems, and shed new light on the applicability of very general tools, based only upon the principle of causality, for diagnosing the behavior of perturbed chaotic systems and reconstructing their output signals, in situations where the fluctuation-dissipation relation is not of great help.

cond-mat.stat-mech↗

arXiv2008

Three-dimensional Random Voronoi Tessellations: From Cubic Crystal Lattices to Poisson Point Processes

We perturb the SC, BCC, and FCC crystal structures with a spatial Gaussian noise whose adimensional strength is controlled by the parameter a, and analyze the topological and metrical properties of the resulting Voronoi Tessellations (VT). The topological properties of the VT of the SC and FCC crystals are unstable with respect to the introduction of noise, because the corresponding polyhedra are geometrically degenerate, whereas the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. For weak noise, the mean area of the perturbed BCC and FCC crystals VT increases quadratically with a. In the case of perturbed SCC crystals, there is an optimal amount of noise that minimizes the mean area of the cells. Already for a moderate noise (a>0.5), the properties of the three perturbed VT are indistinguishable, and for intense noise (a>2), results converge to the Poisson-VT limit. Notably, 2-parameter gamma distributions are an excellent model for the empirical of of all considered properties. The VT of the perturbed BCC and FCC structures are local maxima for the isoperimetric quotient, which measures the degre of sphericity of the cells, among space filling VT. In the BCC case, this suggests a weaker form of the recentluy disproved Kelvin conjecture. Due to the fluctuations of the shape of the cells, anomalous scalings with exponents >3/2 is observed between the area and the volumes of the cells, and, except for the FCC case, also for a->0. In the Poisson-VT limit, the exponent is about 1.67. As the number of faces is positively correlated with the sphericity of the cells, the anomalous scaling is heavily reduced when we perform powerlaw fits separately on cells with a specific number of faces.

cond-mat.stat-mech↗

arXiv2007

Response Theory for Equilibrium and Non-Equilibrium Statistical Mechanics: Causality and Generalized Kramers-Kronig relations

We consider the general response theory proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions allows for writing a set of Kramers-Kronig relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of observable susceptibilities obey Kramers-Kronig relations. Specific results are provided for arbitrary order harmonic response, which allows for a very comprehensive Kramers-Kronig analysis and the establishment of sum rules connecting the asymptotic behavior of the susceptibility to the short-time response of the system. These results generalize previous findings on optical Hamiltonian systems and simple mechanical models, and shed light on the general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks for any experimental and model generated dataset. In order to connect the response theory for equilibrium and non equilibrium systems, we rewrite the classical results by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. We briefly discuss how these results, taking into account the chaotic hypothesis, might be relevant for climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, Kramers-Kronig relations might be more robust tools for the definition of a self-consistent theory of climate change.

cond-mat.stat-mech↗

arXiv2007

From symmetry break to Poisson point process in 2D Voronoi tessellations: the generic nature of hexagons

We bridge the properties of the regular square and honeycomb Voronoi tessellations of the plane to those of the Poisson-Voronoi case, thus analyzing in a common framework symmetry-break processes and the approach to uniformly random distributions of tessellation-generating points. We consider ensemble simulations of tessellations generated by points whose regular positions are perturbed through a Gaussian noise controlled by the parameter alpha. We study the number of sides, the area, and the perimeter of the Voronoi cells. For alpha>0, hexagons are the most common class of cells, and 2-parameter gamma distributions describe well the statistics of the geometrical characteristics. The symmetry break due to noise destroys the square tessellation, whereas the honeycomb hexagonal tessellation is very stable and all Voronoi cells are hexagon for small but finite noise with alpha<0.1. For a moderate amount of Gaussian noise, memory of the specific unperturbed tessellation is lost, because the statistics of the two perturbed tessellations is indistinguishable. When alpha>2, results converge to those of Poisson-Voronoi tessellations. The properties of n-sided cells change with alpha until the Poisson-Voronoi limit is reached for alpha>2. The Desch law for perimeters is confirmed to be not valid and a square root dependence on n is established. The ensemble mean of the cells area and perimeter restricted to the hexagonal cells coincides with the full ensemble mean; this might imply that the number of sides acts as a thermodynamic state variable fluctuating about n=6; this reinforces the idea that hexagons, beyond their ubiquitous numerical prominence, can be taken as generic polygons in 2D Voronoi tessellations.

cond-mat.stat-mech↗

arXiv2006

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.

physics.ao-ph↗

arXiv2006

Extreme Value Statistics of the Total Energy in an Intermediate Complexity Model of the Mid-latitude Atmospheric Jet. Part II: trend detection and assessment

A baroclinic model for the atmospheric jet at middle-latitudes is used as stochastic generator of non-stationary time series of the total energy of the system. A linear time trend is imposed on the parameter $T_E$, descriptive of the forced equator-to-pole temperature gradient and responsible for setting the average baroclinicity in the model. The focus lies on establishing a theoretically sound framework for the detection and assessment of trend at extreme values of the generated time series. This problem is dealt with by fitting time-dependent Generalized Extreme Value (GEV) models to sequences of yearly maxima of the total energy. A family of GEV models is used in which the location $μ$ and scale parameters $σ$ depend quadratically and linearly on time, respectively, while the shape parameter $ξ$ is kept constant. From this family, a model is selected by using diagnostic graphical tools, such as probability and quantile plots, and by means of the likelihood ratio test. The inferred location and scale parameters are found to depend in a rather smooth way on time and, therefore, on $T_E$. In particular, power-law dependences of $μ$ and $σ$ on $T_E$ are obtained, in analogy with the results of a previous work where the same baroclinic model was run with fixed values of $T_E$ spanning the same range as in this case. It is emphasized under which conditions the adopted approach is valid.

physics.ao-ph↗

arXiv2006

Does the subtropical jet catalyze the mid-latitude atmospheric regimes?

Understanding the atmospheric low-frequency variability is of crucial importance in fields such as climate studies, climate change detection, and extended-range weather forecast. The Northern Hemisphere climate features the planetary waves as a relevant ingredient of the atmospheric variability. Several observations and theoretical arguments seem to support the idea that winter planetary waves indicator obey a non-Gaussian statistics and may present a multimodal probability density function, thus characterizing the low-frequency portion of the climate system. We show that the upper tropospheric jet strength is a critical parameter in determining whether the planetary waves indicator exhibits a uni- or bimodal behavior, and we determine the relevant threshold value of the jet. These results are obtained by considering the data of the NCEP-NCAR and ECMWF reanalyses for the overlapping period. Our results agree with the non-linear orographic theory, which explains the statistical non-normality of the low-frequency variability of the atmosphere and its possible bimodality.

physics.ao-ph↗

arXiv2006

Intercomparison of the northern hemisphere winter mid-latitude atmospheric variability of the IPCC models

We compare, for the overlapping time frame 1962-2000, the estimate of the northern hemisphere (NH) mid-latitude winter atmospheric variability within the XX century simulations of 17 global climate models (GCMs) included in the IPCC-4AR with the NCEP and ECMWF reanalyses. We compute the Hayashi spectra of the 500hPa geopotential height fields and introduce an integral measure of the variability observed in the NH on different spectral sub-domains. Only two high-resolution GCMs have a good agreement with reanalyses. Large biases, in most cases larger than 20%, are found between the wave climatologies of most GCMs and the reanalyses, with a relative span of around 50%. The travelling baroclinic waves are usually overestimated, while the planetary waves are usually underestimated, in agreement with previous studies performed on global weather forecasting models. When comparing the results of various versions of similar GCMs, it is clear that in some cases the vertical resolution of the atmosphere and, somewhat unexpectedly, of the adopted ocean model seem to be critical in determining the agreement with the reanalyses. The GCMs ensemble is biased with respect to the reanalyses but is comparable to the best 5 GCMs. This study suggests serious caveats with respect to the ability of most of the presently available GCMs in representing the statistics of the global scale atmospheric dynamics of the present climate and, a fortiori, in the perspective of modelling climate change.

physics.ao-ph↗

arXiv2006

Extreme Value Statistics of the Total Energy in an Intermediate Complexity Model of the Mid-latitude Atmospheric Jet. Part I: Stationary case

A baroclinic model for the atmospheric jet at middle-latitudes is used as a stochastic generator of time series of the total energy of the system. Statistical inference of extreme values is applied to yearly maxima sequences of the time series, in the rigorous setting provided by extreme value theory. In particular, the Generalized Extreme Value (GEV) family of distributions is used here. Several physically realistic values of the parameter $T_E$, descriptive of the forced equator-to-pole temperature gradient and responsible for setting the average baroclinicity in the atmospheric model, are examined. The location and scale GEV parameters are found to have a piecewise smooth, monotonically increasing dependence on $T_E$. This is in agreement with the similar dependence on $T_E$ observed in the same system when other dynamically and physically relevant observables are considered. The GEV shape parameter also increases with $T_E$ but is always negative, as \textit{a priori} required by the boundedness of the total energy of the system. The sensitivity of the statistical inference process is studied with respect to the selection procedure of the maxima: the roles of both the length of maxima sequences and of the length of data blocks over which the maxima are computed are critically analyzed. Issues related to model sensitivity are also explored by varying the resolution of the system.

physics.geo-ph↗

arXiv2005

Physical and Mathematical Properties of a Quasi-Geostrophic Model of Intermediate Complexity of the Mid-Latitudes Atmospheric Circulation

A quasi-geostrophic intermediate complexity model is considered, providing a schematic representation of the baroclinic conversion processes which characterize the physics of the mid-latitudes atmospheric circulation. The model is relaxed towards a given latitudinal temperature profile, which acts as baroclinic forcing, controlled by a parameter TE determining the forced equator-to-pole temperature gradient. As TE increases, a transition takes place from a stationary regime to a periodic regime, and eventually to an earth-like chaotic regime where evolution takes place on a strange attractor. The dependence of the attractor dimension, metric entropy, and bounding box volume in phase space is studied by varying both TE and model resolution. The statistical properties of observables having physical relevance, namely the total energy of the system and the latitudinally averaged zonal wind, are also examined. It is emphasized that while the attractor's properties are quite sensitive to model resolution, the global physical observables depend less critically on it. For more detailed physical observables, such as the latitudinal profiles of the zonal wind, model resolution again may be critical: the effectiveness of the zonal wind convergence, acting as barotropic stabilization of the baroclinic waves, heavily relies on the details of the latitudinal structure of the fields. The necessity and complementarity of both the dynamical systems and physical approach is underlined.

physics.ao-ph↗

arXiv2005

Detection and correction of the misplacement error in THz Spectroscopy by application of singly subtractive Kramers-Kronig relations

In THz reflection spectroscopy the complex permittivity of an opaque medium is determined on the basis of the amplitude and of the phase of the reflected wave. There is usually a problem of phase error due to misplacement of the reference sample. Such experimental error brings inconsistency between phase and amplitude invoked by the causality principle. We propose a rigorous method to solve this relevant experimental problem by using an optimization method based upon singly subtractive Kramers-Kronig relations. The applicability of the method is demonstrated for measured data on an n-type undoped (100) InAs wafer in the spectral range from 0.5 up to 2.5 THz.

cond-mat.mtrl-sci↗

arXiv2004

Hayashi Spectra of the Northern Hemisphere Mid-latitude Atmospheric Variability in the NCEP and ERA 40 Reanalyses

We compare 45 years of the reanalyses of NCEP-NCAR and ECMWF in terms of their representation of the mid-latitude winter atmospheric variability for the overlapping time frame 1957-2002. We adopt the classical approach of computing the Hayashi spectra of the 500 hPa geopotential height fields. Discrepancies are found especially in the first 15 years of the records in the high-frequency-high wavenumber propagating waves and secondly on low frequency-low wavenumber standing waves. This implies that in the first period the two datasets have a different representation of the baroclinic available energy conversion processes. In the period starting from 1973 a positive impact of the aircraft data on the Euro-Atlantic synoptic waves has been highlighted. Since in the first period the assimilated data are scarcer and of lower quality than later on, they provide a weaker constraint to the model dynamics. Therefore, the resulting discrepancies in the reanalysis products may be mainly attributed to differences in the models' behavior.

physics.ao-ph↗

arXiv2004

Thermohaline circulation stability: a box model study - Part I: uncoupled model

A thorough analysis of the stability of the uncoupled Rooth interhemispheric 3-box model of thermohaline circulation (THC) is presented. The model consists of a northern high latitudes box, a tropical box, and a southern high latitudes box, which respectively correspond to the northern, tropical and southern Atlantic ocean. We adopt restoring boundary conditions for the temperature variables and flux boundary conditions for the salinity variables. We study how the strength of THC changes when the system undergoes forcings that are analogous to those of global warming conditions by applying to the equilibrium state perturbations to the moisture and heat fluxes into the three boxes. In each class of experiments, we determine, using suitably de- fined metrics, the boundary dividing the set of forcing scenarios that lead the system to equilibria characterized by a THC pattern similar to the present one, from those that drive the system to equilibria with a reversed THC. Fast increases in the moisture flux into the northern high-latitude box are more effective than slow increases in leading the THC to a breakdown, while the increases of moisture flux into the southern high-latitude box strongly inhibits the breakdown and can prevent it, in the case of slow increases in the Northern Hemisphere. High rates of heat flux increase in the North Hemisphere destabilize the system more effectively than low ones, and increases in the heat fluxes in the Southern Hemisphere tend to stabilize the system.

physics.ao-ph↗