Abstract
Some issues which are relevant for the recent state in climate modeling have been considered. A detailed overview of literature related to this subject is given. The concept in modeling of climate, as a complex system, seen through Gödel’s theorem and Rosen’s definition of complexity and predictability is discussed. Occurrence of chaos in computing the environmental interface temperature from the energy balance equation given in a difference form is pointed out. A coupled system of equations, often used in climate models, was analyzed. It is shown that the Lyapunov exponent mostly has positive values allowing presence of chaos in this system. The horizontal energy exchange between environmental interfaces, which is described by the dynamics of driven coupled oscillators, was analyzed. Their behavior and synchronization, when a perturbation is introduced in the system, as a function of the coupling parameter, the logistic parameter, and the parameter of exchange, were studied calculating the Lyapunov exponent under simulations with the closed contour ofN=100environmental interfaces. Finally, we have explored possible differences in complexities of two global and two regional climate models using their air temperature and precipitation output time series. The complexities were obtained with the algorithm for calculating the Kolmogorov complexity.
Highlights
Among the most interesting and fascinating phenomena that are predicted/predictable is the chaotic ocean/atmosphere/land system called weather and its longtime average, climate
He was the first person in the scientific world who explicitly pointed out the following points related to the nonlinear dynamics in atmospheric motion: (i) question of prediction and predictability, (ii) importance of understanding the nonlinearity in modeling procedure, (iii) demand for discovery of chaos, and (iv) careful consideration of sensitivity of differential equations in modeling system on initial conditions
The following topics have been set in the focus: (1) dynamics of error growth; (2) linear and nonlinear systems; (3) predictability of systems with many scales; (4) limit of predictability; (5) weather predictability (growth of errors in General Circulation Models (GCMs) based on Lorenz’s analysis); (6) predictability from analogs; (7) climate predictability and potential predictability; (8) seasonal mean predictability; and (9) El Nino-Southern Oscillation (ENSO) chaos, predictability of coupled models, and decadal modulation of predictability [6,7,8,9,10,11,12,13,14,15,16,17,18]
Summary
Among the most interesting and fascinating phenomena that are predicted/predictable is the chaotic ocean/atmosphere/land system called weather and its longtime average, climate. To our mind there is a significant space for “improvement” of models and their capabilities to provide good forecasts It can be done only if the modeling attempts are directed towards the following steps: from structures and states to processes and functions; from self-correcting to self-organizing systems; from hierarchical steering to participation; from conditions of equilibrium to dynamic balances of nonequilibrium; from single trajectories to bundles of trajectories; from linear causality to circular causality; from predictability to relative chance; from order and stability to instability, chaos, and dynamics; from certainty and determination to a larger degree of risk, ambiguity, and uncertainty; from reductionism to emergentism; from being to becoming.
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