Climate response to external perturbation for the Lorenz 96 model (Lucarini and Sarno, Nonlin. Proc. Geophys. 2011) | In recent years, many exciting advances have been made in statistical mechanics. The aim is to explain the thermodynamic behaviour of complex systems, starting from a low-level physical description. Although the equilibrium theory of statistical mechanics in terms of canonical distributions is by now well-developed, the question remains whether an equivalent concept can be found for systems that are driven out of equilibrium. Examples of recent advances are the development of a linear response theory, describing the effect of a small perturbation on a system, and the application of large deviation theory, giving rise to the so-called fluctuation theorem describing symmetries in the non-equilibrium entropy production rates. We investigate applications of the theory on climate systems, to understand the non-equilibrium character of the climate, as well as provide a physical interpretation of theoretical concepts. We also investigate applications of some techniques from the underlying language of dynamical system, such as the Nambu extension of Hamiltonian mechanics. |

Using extremes of specific observables we are able to reconstruct the geometrical properties of multifractal objects for a vast range of values of the cascade parameter p (Lucarini et al. 2011) | The attention of the scientific community to the problem of understanding extreme values theory is growing, also because this theory is crucial in a wide class of applications for defining risk factors such as those related to instabilities in the financial markets and to natural hazards related to seismic, climatic and hydrological extreme events. Even if the probability of extreme events decreases with their magnitude, the damage that they may bring increases rapidly with the magnitude as does the cost of protection against them. From a theoretical point of view, extreme values of observables are related to large fluctuations of the corresponding underlying system. Extremes are also shown to provide new ways to investigate dynamical systems and characterize the geometrical properties of the underlying attractors. The aim of our research projects in this field is to provide theoretical and numerical tools for the application of extreme value theory in many situations of practical interest, where the phenomena can be modeled through dynamical systems. Moreover, by studying the behaviour of extreme fluctuations for systems close to their tipping points, we aim to provide new theoretical advancements in the understanding of high-dimensional systems that feature a complex and chaotic behaviour. |

Minimal conceptual diagram for the material entropy production of a planetary system. Boxes 1 and 2 represent warm (low latitudes) and cold (high latitudes) fluid domains, coupled by enthalpy transport. Boxes 3 and 4 represent warm (low latitudes) and cold (high latitudes) surface domains, coupled vertically to the corresponding fluid boxes, but not to each other. The dashed rectangle encloses the reduced two-box model usually considered in previous literature. | The climate is an important example of a non-equilibrium steady state system. The non-equilibrium nature of the climate means that a variety of irreversible processes must take place within it, whereas the steady characteristics impliy that a time-independent balance must exist for some relevant quantities (e.g. energy, angular momentum, water, entropy). The quantity that describes the irreversibility of climatic processes is the entropy production. Furthermore, the general circulation of the atmosphere and the oceans redistributes the equatorial surplus of radiative energy towards the polar regions (meridional heat transport), generating wind motion (Hadley cell and baroclinic waves), which is then dissipated into frictional heating. The climate circulation therefore converts heat into kinetic energy thus acting as a heat engine, to which it is possible to associate a net energy input, a net energy output, mechanical work performed and a Carnot-like efficiency. It is therefore natural to pursue a thermodynamic approach based on the macroscopic theory of non-equilibrium thermodynamics (de Groot and Mazur, 1962) which brings together the concepts of entropy production, energy fluxes and efficiency for addressing the big picture of a system as complex as the climate and providing new validation metrics for climate models. |

# Long term memory

LTM time series (black circled: hindcast; red: leave-one-out forecast) promise higher forecast skills than red noise (gray lines: hindcast): an example forecast with correlation scores at 2-, 4-, 6-, ... 20-yr scales. Gray lines show hindcasts of 100 red noise surrogates generated using the lag-1 autocorrelation coefficient from the example LTM time series. The dash-dotted line denotes the 95% confidence level; "*" denotes the mean of the correlation scores of all 100 ensembles (gray lines)(Zhu et al. 2010). |
Temporal variability of dynamical systems like weather or climate is conveniently characterized by its memory, which is closely related to the predictability of the system: while short-term memory shows finite integral correlation time-scale and is related to exponentially decaying auto-correlation between initial and future states, long-term memory (LTM) characterized by an infinite integral time-scale has a non-integrable power-law autocorrelation. LTM has been found in the Earth's surface temperature records extending from annual cycles to Milankovitch cycles suggesting climate processes are intimately coupled and understanding variability at any one timescale requires some understanding of the whole. This continuum variability is different from the Brownian motion analog which has been used so far as the paradigm to explain climate system response to white noise atmospheric forcing, calling up new concepts and new understandings. In practice, LTM conveys great implications for long-term climate forecasts and extreme events, for example, we have demonstrated that climate records with LTM promise higher forecast skills than its red noise surrogates, and we are also trying to establish and understand links between LTM and the statistics of extreme events. |

Two-layer quasi-geostrophic model | the basic tool to understand the fundamental features of mid latitude weather conditions and its instabilities. It is a beta channel and it allows computational analysis of parametric dependencies as well as the analysis of short term growth of instabilities | |

SAM | Shallow Atmosphere Model based on the shallow water equations, it is a model to be used to study planetary circulation phenomena which areessentially two-dimensional. | |

PUMA | Portable University Model of the Atmosphere, an atmospheric circulation model consisting of a dynamical core based on the Primitive Equations with simple parametrisations for friction and diabatic heating (Rayleigh friction, Newtonian cooling). | |

Moist PUMA | a version of PUMA which includes moisture physics and a simplified parameterization scheme for the boundary layer and cloud physics | |

PUMA/grey atmosphere | the PUMA model with the inclusion of a very simple radiative scheme and a simple model for the surface | |

| PlanetSimulator | a coupled system of climate components for Earth, Mars and other planets developed as a model of intermediate complexity. |

HadCM3 | and its low-resolution version, FAMOUS, a state-of-the-art atmospheric-ocean coupled general circulation model with advanced physical parametrisations developed by the UK Met Office-Hadley Centre. |

Elaborate diagnostics (data analysis) is indispensable to characterize and to understand the climate system, its variability and its sensitivity to internal or external perturbations. In addition, thorough diagnostics is needed to evaluate and to improve climate models. Successful climate diagnostics implies the analysis of quantities which optimally represent the phenomena or the processes under consideration. The applied methodologies may range from computing simple diagnostics like spatial/temporal averages and standard deviation, to assessing regional budgets of energy or water mass, to employing sophisticated statistical or physical methods like, e.g., extreme value statistics, spectral analysis, or wave-mean flow interaction diagnostics. Conceptual models or theoretical concepts may help to link the results to the underlying physical, and, on the other hand, may help to select the appropriate diagnostics. | |||||

| |||||