| We seek to understand the evolution of ordered states in the Earth's atmosphere on different spatial scales. The use of thermodynamic entropy to describe atmospheric order is examined in the context of cloud morphogenesis. An expression is derived for the entropy deficit of a system of cloudy air, as compared to the equilibrium state that the system would reach in isolation. This expression is applied to a numerical model of the entrainment process, intended to model the transition from marine stratus to cumulus clouds. In the model, the entropy decrease in the transition is near the maximum allowed by the second law of thermodynamics. The limiting factor in the second law constraint is the observed total throughput, over the history of the process, in the water cycle of evaporation from the warm sea surface and precipitation from the cold clouds.;Another view of atmospheric self-organization, based on the intrinsic dynamics of the evolving system, arises from the phenomenon of synchronized chaos, previously more familiar in low-order or engineered systems. It is shown that chaotic numerical models of the vacillation of the atmospheric circulation between blocked and zonal flow in the Northern and Southern hemisphere midlatitudes tend to synchronize, when coupled in a way that represents the exchange of Rossby waves through the upper-tropospheric tropical "westerly ducts," which re-open each winter. The time-dependent coefficients of the Rossby wave modes play the role of the shared variables, and the coefficients of the zonal flow modes play the role of the un-shared variables in the chaotic synchronization paradigm. The two hemispheric subsystems fall into synchronized motion along their strange attractors for sufficiently large coupling coefficients linking corresponding modes in the two hemispheres. For smaller couplings the system alternates at irregular intervals between synchronized and de-synchronized motion. At physical coupling values, which are smaller yet, there are no distinct periods of synchronization, but trajectories in phase-space tend to hug the synchronization manifold more closely than they do in the uncoupled case.;Such partial synchronization is manifest in the model as a tendency for the two hemispheric subsystems to occupy the same dynamical regime, corresponding to blocked or zonal flow, simultaneously. The resulting correlations are enhanced by the annual cycle in thermal forcing, which lends directionality to the coupling, with the summer hemisphere effectively driven by the winter hemisphere. The interhemispheric correlations predicted by the model are actually seen in observed data. The partial synchronization paradigm may explain and/or predict other teleconnection patterns linking remote parts of the Earth's climate. |
