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The global climate systemties togethermany physical variables, such as flow velocity, density, pressure, temperature, to name a few. The core equations of the climate system are the primitive evolution equations of the atmosphere and ocean (Lions et al., 1992a;b; 1993a;b; 1995; Majda, 2003), which directly involve the flow velocity (or, alternatively, streamfunction and vorticity), density and pressure. To incorporate the effects of other relevant physical processes which supply the energy to or draw it from the motion of the flow, the primitive equations are coupled to other physical processes through temperature, water vapor, ocean surface pressure, and other variables. The coupling terms often preserve energy balance, that is, at any moment, the sum of energy transfer rates between all coupled processes is zero. The main difficulty in the study of the behavior of primitive equations lies in the nonlinearity of the dynamics of velocity or streamfunction-vorticity in the advection term. The nonlinearity of the primitive equations is also the main source of chaos and lack of predictability for long times in the weather and climate prediction. As has first been recognized by Lorenz (1963), even a simple three-variable nonlinear dynamical system (the so-called Lorenz attractor), based on the idealized convection cell with cooling at the top and heating at the bottom, exhibits extreme sensitivity to initial conditions. Nowadays, the Lorenz attractor is considered a canonical textbook example of chaos in a nonlinear dynamical system, with many illustrations depicting two nearly identical initial conditions evolving into two unrelated trajectories after a short period of time. In more complex dynamical systems with advection terms, nonlinear chaos develops in much more sophisticated fashion, making long-term forecasts difficult and uncertain.





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Modern Climatology, whole system, historical statistics, variability, atmosphere, prediction


Climate | Earth Sciences


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