Title: Evidence for human influence on climate and implications for climate forecasting.

Summary: To be announced

Title: Energy balance models in climate dynamics (tentative).

Summary: To be announced

Title: The nonlinear dynamics of large-scale atmospheric flows.

Summary:

This course will first introduce the basic laws that govern atmospheric motions on the planetary scale, i.e., the motions of a fluid in the presence of rotation and stratification. Next, observational evidence will be described for persistent and recurrent departures from the climatological mean of these motions and multiple regimes of atmospheric flows will be modeled.

Finally, oscillatory behavior of such flows - on the time scale of weeks-to-months - will be described and analyzed. The dynamical systems approach to the study of low-frequency variability of the atmosphere will be used throughout to analyze the models formulated and their solutions. The course will conclude with a discussion of perspectives for extended-range predictability of atmospheric motions in mid-latitudes.

Title: Transport, stirring and mixing in atmospheric chemistry and dynamics.

Summary:

The lectures will introduce fundamental ideas on transport, stirring and mixing, including relevant mathematical models. The extent to which transport and mixing in the atmosphere is captured by the `large-scale flow' paradigm (chaotic advection and Batchelor turbulence) will be discussed. Potential vorticity will be introduced as a dynamical tracer, allowing description of the dynamics of the atmosphere in terms of transport and mixing. The structure of transport barriers and mixing regions in kinematic and dynamically consistent flows and theories for tracer microstructure in two- dimensional and `layerwise two-dimensional' flows will be described.

These ideas will then be used to describe different aspects of the observed structure of the atmosphere, including transport and mixing of chemical species in troposphere and stratosphere and a dynamical theory for the structure of the extratropical troposphere and tropopause.

Title: Modeling ocean mixing.

Summary:

The ocean is a highly inhomogeneous medium, characterized by spatial and temporal contrasts in temperature and salinity, as well as in chemical composition and in the distribution of biological agents. The inhomogeneity of the ocean, however, is not static, but follows from a dynamical equilibrium, in which contrasts are permanently being created and attenuated. Local processes that generate contrasts include evaporation and rain, freezing and melting of sea--ice, river inflows, and volcanic activity. Attenuation is mainly due to mixing processes, such as turbulent diffusion, breaking waves, and stirring by surface winds, ocean currents, and planetary tides interacting with the ocean's bottom and lateral morphology. The dynamical equilibrium emerging from the balance of these processes is a determining factor to the Earth's climate: slight changes in the properties of the upper layers of the ocean, in particular, can lead to significant variations of its ice--coverage, of local patterns of convection and rain and, ultimately, to dramatic changes in the global patterns of surface temperature, humidity and prevailing winds.

Yet the quantification, and even the identification of some of the critical processes involved in this dynamical balance, remain to a large degree incomplete. The mixing side of the balance is particularly elusive, due to its vast distribution over whole basins, to the difficulties inherent to its observation and measurement, to its highly anisotropic nature, and to the incompletely understood physics of its underlying processes, such as turbulent diffusion, shear and convective instabilities, and wave overturning. State-of-the-art computational ocean circulation models typically parameterize these processes, introducing empirical closures designed to fit as well as possible the [sparse] available experimental and observational data.

Such an approach, driven by necessity, may yield large errors in the prediction of climatic changes, since the adjustment of parameters to match features of today's climate may fail to capture those of tomorrow's.

This course will describe various approaches to the mathematical modeling of ocean mixing. These include models of nonlinear turbulent diffusion, mixing by internal breaking waves, and descriptions of mixing based on statistical physics.