C6

Stick-slip behavior is a distinguishing characteristic of the flow of Whillans Ice Stream. Distinct from stick-slip on northern hemisphere glaciers, which is generally attributed to supraglacial melt, the behavior is thought be be controlled by fast processes at the bed and by tidally-induced stress. Modelling approaches to studying this phenomenon typically consider ice to be an elastically-deforming solid (e.g. Winberry et al, 2008; Sergienko et al, 2009). However, there remains a question of whether irreversible, i.e. viscous, deformation is important to the stick-slip process; and furthermore whether the details of stick-slip oscillations are important to ice stream evolution on longer time scales (years to decades).

To address this question I use two viscoelastic models of varying complexity. The first is a modification to the simple block-and-slider models traditionally used to examine earthquake processes on a very simplistic fashion. Results show that the role of viscosity in stick-slip depends on the dominant stress balance. These results are then considered in the context of a continuum description of a viscoelastic ice stream with a rate-weakening base capable of exhibiting stick-slip behavior. With the continuum model we examine the spatial and temporal aspects of stick-slip, their dependence on viscous effects, and how this behavior impacts the mean flow. Different models for the evolution of basal shear stress are examined in the experiments, with qualitatively similar results. A surprising outcome is that tidal effects, while greatly affecting the spectrum of the stick-slip cycle, may have relatively little effect on the mean flow.

Clouds play a key role in the climate system. Driven by radiation, clouds power the hydrological cycle and global atmospheric dynamics. In addition, clouds fundamentally affect the global radiation balance by reflecting solar radiation back to space and trapping longwave radiation. The response of clouds to global warming remains poorly understood and is strongly regime dependent. In addition, anthropogenic aerosols influence clouds, altering cloud microphysics, dynamics and radiative properties. In this presentation I will review progress and limitations of our current understanding of the role of clouds in climate change and discuss the state of the art of the representation of clouds and aerosol-cloud interactions in global climate models, from (slightly) better constrained stratiform clouds to new frontiers: the investigation of anthropogenic effects on convective clouds.

Many years ago, Mark Kac was consulted by biologist colleague Lamont Cole regarding field-based observations of animal populations that suggested the existence of 3-4 year cycles in going from peak to peak. Kac provided an elegant argument for how purely random sequences of numbers could yield a mean value of 3 years, thereby establishing the notion that pattern can seemingly emerge in random processes. (This does not, however, mean that there could be a largely deterministic cause of such population cycles.)

By extending Kac's argument, we show how the distribution of cycle length can be analytically established using methods derived from random graph theory, etc. We will examine how such distributions emerge in other natural settings, including large earthquakes as well as colored Brownian noise and other random models and, for amusement, the Standard & Poor's 500 index for percent daily change from 1928 to the present.

We then show how this random model could be relevant to a variety of spatially-dependent problems and the emergence of clusters, as well as to memory and the aphorism "bad news comes in threes." The derivation here is remarkably similar to the former and yields some intriguing closed-form results. Importantly, the centroids or "centers of mass" of these clusters also yields clusters and a hierarchy then emerges. Certain "universal" scalings appear to emerge and scaling factors reminiscent of Feigenbaum numbers. Finally, as one moves from one dimension to 2, 3, and 4 dimensions, the scaling behaviors undergo modest change leaving this scaling phenomena qualitatively intact.

Finally, we will show how that an adaptation of the Langevin equation from statistical physics provides not simply a null-hypothesis for matching the observation of 3-4 year cycles, but a remarkably simple model description for the behavior of animal populations.