Session L3: The Physics of Climate and Climate Change

The Disordered Kinetics of Earth's Carbon Cycle

The carbon cycle describes the transformations of carbon as it cycles through living organisms and the physical environment. In its simplest form, the cycle amounts to a loop between photosynthesis and respiration. Photosynthesis produces organic carbon and molecular oxygen from carbon dioxide and water. Respiration reverses the process by oxidation of organic carbon. The duration of the cycle spans a vast range of time scales: from days or less for fast-growing plankton in the oceans, to hundreds of millions of years or more for the small fraction of organic matter that is buried as rock. The rates at which the cycle is closed set atmospheric carbon dioxide levels at short time scales and oxygen levels at geologic time scales. Respiration rates thereby influence not only climate---by the determination of equilibrium carbon dioxide concentrations---but also biological evolution---because the oxygenation of Earth's atmosphere must have preceded the advent of aerobic metabolism. We review recent advances in the understanding of the rates that control the carbon cycle, with emphasis on the respiratory back-reaction. Given considerable biological, chemical, and environmental variation, it comes as no surprise that measurements of rates vary greatly. Observations suggest, however, some surprising simplicity: for example, the rates of microbial consumption of organic matter in sediments and soils slow down systematically like the inverse of the age of the organic matter. This aging effect can be quantitatively understood as the macroscopic observation of microscopically disordered kinetics. The disorder can arise purely physically as the consequence of a reaction-diffusion process in porous media, but any combination of physical, chemical, and biological parameters that yield a wide range of rates suffices. A predicted practical consequence is a slow, logarithmic decay of organic matter in sediments and soils, which compares well with measurements. Further observations suggest that the effects of such disordered kinetics extends to inorganic processes as well. The carbon cycle thus appears not as a simple reaction network defined by a single set of rates, but rather as complex network in which the rates of specific reactions can be widely dispersed. We conclude by briefly discussing implications for short-term climate and long-term evolution.   

The Quantum and Fluid Mechanics of Global Warming

Quantum physics and fluid mechanics are the foundation of any understanding of the Earth's climate. In this talk I invoke three well-known aspects of quantum mechanics to explore what will happen as the concentrations of greenhouse gases such as carbon dioxide continue to increase. Fluid dynamical models of the Earth's atmosphere, demonstrated here in live simulations, yield further insight into past, present, and future climates. Statistics of geophysical flows can, however, be ascertained directly without recourse to numerical simulation, using concepts borrowed from nonequilibrium statistical mechanics\footnote{J. B. Marston, E. Conover, and Tapio Schneider, ``Statistics of an Unstable Barotropic Jet from a Cumulant Expansion,'' arXiv:0705.0011, J. Atmos. Sci. (in press).}. I discuss several other ways that theoretical physics may be able to contribute to a deeper understanding of climate change\footnote{J. Carlson, J. Harte, G. Falkovich, J. B. Marston, and R. Pierrehumbert, ``Physics of Climate Change'' 2008 Program of the Kavli Institute for Theoretical Physics.}.   

Geostrophic Turbulence and the stability of Ocean models

Despite multiple efforts, predictions of climate change remain uncertain. Where precision is an issue (e.g., in a climate forecast), only ensembles of simulations made across model families which differ for parameterizations, discrete algorithms and parameter choices allow an estimate of the level of imprecision. Is this the best we can do? Or is it at least conceptually possible to reduce these uncertainties? Focusing on ocean models in idealized domains we describe chaotic space-time patterns and equilibrium distributions that mimic nature. Using the Navier-Stokes equations for barotropic flows as a zero-order approximation of analogous flow pattern, we then investigate if is possible, in this overly-simplified set-up, for which smooth-solutions exist, to bound the uncertainty associated with the numerical domain discretization (i.e. with the limitation imposed by the Reynolds number range we can explore). To do so we analyze a series of stationary barotropic turbulence simulations spanning a range of Reynolds number of 10$^{4}$.   

Heat waves, climate change and eggplant harvests - simple models of climate systems

I discuss a simple box model of soil-vegetation-atmosphere interactions that we recently introduced to study the insurgence of summer droughts at continental midlatitudes (D'Andrea et al, GRL 2006, Baudena et al, AWR 2007). I show that the model possesses multiple equilibria and that, for the same synoptic forcing, soil moisture at the beginning of summer and vegetation cover play a primary role in determining which equilibrium will be reached. We also observe a difference in the drought climatologies associated respectively with the dynamics of natural vegetation, capable of adapting to the prevailing soil moisture conditions, and with cultivated vegetation such as eggplant, that cannot spontaneously modify its areal extent. I conclude with some speculations on a conceptual model of the interaction between vegetation and climate at global scale. The results discussed in this talk are the product of joint work with Fabio D'Andrea (ENS, Paris) and Mara Baudena (ISAC-CNR).   

Physical Problems in Modeling the Global Ocean

Understanding and modeling the physical ocean circulation is of primary importance for both enhancing the science of the ocean, and for providing rational projections of future climate. This talk aims to outline fundamental physical and numerical aspects of ocean climate modeling. We highlight features associated with representing elements of the continuum ocean fluid using a discrete model lattice. A major challenge of this representation includes the parameterization of scales which are unresolved by the simulation. This subgrid-scale problem is ubiquitous in computational fluid dynamics, and forms a major focus of ongoing research and development with ocean climate models. Another challenge involves developing robust numerical methods whose truncation errors do not adversely corrupt the quasi-ideal nature of much of the ocean circulation outside of boundary layers. Progress has been made on both fronts, with improvements arising from better understanding of the ocean, smarter methods used to simulate the ocean, and enhancements in computational power.