Significance: We propose an algorithm to sample rare events in climate models with a computational cost from 100 to 1,000 times less than direct sampling of the model. Applied to the study of extreme heat waves, we estimate the probability of events that cannot be studied otherwise because they are too rare, and we get a huge ensemble of realizations of an extreme event. Using these results, we describe the teleconnection pattern for the extreme European heat waves. This method should change the paradigm for the study of extreme events in climate models: It will allow us to study extremes with higher-complexity models, to make intermodel comparison easier, and to study the dynamics of extreme events with unprecedented statistics.

The climate is a forced and dissipative nonlinear system featuring nontrivial dynamics on a vast range of spatial and temporal scales. The understanding of the climate's structural and multiscale properties is crucial for the provision of a unifying picture of its dynamics and for the implementation of accurate and efficient numerical models. We present some recent developments at the intersection between climate science, mathematics, and physics, which may prove fruitful in the direction of constructing a more comprehensive account of climate dynamics. We describe the Nambu formulation of fluid dynamics and the potential of such a theory for constructing sophisticated numerical models of geophysical fluids. Then, we focus on the statistical mechanics of quasi-equilibrium flows in a rotating environment, which seems crucial for constructing a robust theory of geophysical turbulence. We then discuss ideas and methods suited for approaching directly the nonequilibrium nature of the climate system. First, we describe some recent findings on the thermodynamics of climate, characterize its energy and entropy budgets, and discuss related methods for intercomparing climate models and for studying tipping points. These ideas can also create a common ground between geophysics and astrophysics by suggesting general tools for studying exoplanetary atmospheres. We conclude by focusing on nonequilibrium statistical mechanics, which allows for a unified framing of problems as different as the climate response to forcings, the effect of altering the boundary conditions or the coupling between geophysical flows, and the derivation of parametrizations for numerical models.

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(\(10^5\)) 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 CO\(_2\) 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.

Climate change impacts are non uniformly distributed over the globe. Mountains have a peculiar response to large scale variations, documented by elevation gradients of surface temperature increase observed over many mountain ranges in the last decades. Significant changes of precipitation are expected in the changing climate and orographic effects are important in determining the amount of rainfall at a given location. It thus becomes particularly important to understand how orographic precipitation responds to global warming and to anthropogenic forcing. Here, using a large rain gauge dataset over the European Alpine region, we show that the distribution of annual precipitation among the lowlands and the mountains has varied over time, with an increase of the precipitation at the high elevations compared to the low elevations starting in the mid 20 century and peaking in the 1980s. The simultaneous increase and peak of anthropogenic aerosol load is discussed as a possible source for this interdecadal change. These results provide new insights to further our understanding and improve predictions of anthropic effects on mountain precipitations, which are fundamental for water security and management.