Nonlinear processes in the Earth's atmosphere: dynamic chaos

S.G.Chezganova

KSTU of A.N.Tupolev name

Institute of Machnery and Information Technology

Zelenodolsk, Russia

In the dynamic chaos of hidden order.

Unexpected, weird, poorly understood,

represents the "fine structure, lurking

in a disorderly flow information".

James Gleick.

Nowadays, when we see climate change over the Earth and understand that this will lead to unpredictable consequences, especially important to investigate nonlinear processes in the Earth's atmosphere and, in particular, the dynamic chaos. Maybe this will help locally managed element, since the system with chaotic dynamics, while maintaining the type of movement, notably responsive to weak external stimuli. In general, the system with chaos exhibit good handling and flexibility.

The concept of is widely used to characterize complex motions. The first example of dynamic chaos was introduced in the work of Edward Lorenz to describe the convective motion in the atmosphere to predict the weather in 1963. Even earlier, in 1960, Lorenz constructed a weather model. The model is a set of numbers - the values of several variables (temperature, atmospheric pressure, wind speed) at a given time. Lorenz chose twelve equations describing the relationship between these variables. It turned out that the model of which is completely eliminated by chance, with the same initial values gives completely different results (due to the different number of decimals in the input data). System proved to be very sensitive to the slightest effect on it. In the above article, Lorentz considered a similar but more simple model - a system of three ordinary nonlinear differential equations describing the convective motion in the atmosphere, and for visual display behavior of the system to construct the phase portrait. It was found that for certain values of parameters in this system, there is a two-dimensional attracting set of complex structures - the attractor. In other words, there are exponentially unstable regimes that generate complex nonlinear processes. The numerical analysis showed that for sufficiently large temperature gradient behavior of the solution is so complicated that the corresponding movements are perceived as chaotic, and therefore introduced a new concept of "dynamic chaos".

Weather Lorenz model included three variables (temperature, barometric pressure, wind speed) at a given time. Next will be considered only one variable - the wind speed.

In this paper we study the time series of wind speed is carried out in terms of modern nonlinear dynamics. It is assumed that the ionosphere behaves as a deterministic (the unique relationship of cause and effect) of a nonlinear system that allows us to calculate the characteristics of time series.

Time series of wind speed values characterizes the motion in the atmosphere, after appropriate treatment can be assessed for future time series values, which is important for solving problems related to the research of atmospheric dynamics.

Application of the theory of nonlinear systems with chaotic behavior is the prediction of the dynamics they generate time series. Like most systems because of their complexity, the ionosphere can be modeled with sufficient accuracy. However, it can be described on the basis of observation. The observed wind speed (time series) - is a function of time at which the judge about the process in the ionosphere. If there has been some way to process, then under certain conditions it is possible to assess the future value of the time series, knowing only the previous values.

In the modern theory of dynamical systems can distinguish the noise (random process) from the deterministic behavior. Based on some additional definitions to the observed one can determine the so-called correlation dimension. If you find that capacity - the quantity is finite, then (under certain conditions yet) is described by the observed finite system of ordinary differential equations. If you continue to succeed (at least partially) recover the explicit form of these equations, the prediction becomes possible. Thus, the only observable is possible to recover many of the properties of the dynamic behavior of the system and get an idea of its attractor.

Study the characteristics of time series of wind speed in the atmosphere showed the presence of complex chaotic motions of the dynamic chaos. The dynamic (deterministic) chaos in time series of the velocity of the western and northern winds in the meteor zone D-layer of the ionosphere. We calculate the characteristics of time series of wind speed, such as the Hurst exponent, correlation dimension, the autocorrelation function. Graphs of variation of the Hurst exponent for the northern and western winds. Found a finite dimension, slowly decaying autocorrelation function, the value of Hurst parameter, and other properties of time series indicate the presence of chaotic dynamics in the behavior of the horizontal component of wind velocity. The resulting information can then be used to reconstruct the structure of the system of equations describing the time series of wind speed. Previously can be seen that the corresponding system of equations belongs to a class of nonlinear dissipative dynamical systems with phase space dimension 2 <n <12 (upper bound estimate is overstated).