Rr hi

with a period much larger than t0x but much smaller than t0y. In doing so we obtain where the overbar symbolizes time averaging.

We replace averaging over time by averaging over an ensemble of all possible realizations of the fast variable x at a fixed value of the slow variable y and parametrize the variable x appearing in <{jf;(y, x)> (here angle brackets mean probability averaging) in terms of y. First we recollect that gfy, x) differs from <#,-(y, x)> by the fluctuation term g[ describing the contribution to the dispersion of the variable y from all high-frequency disturbances of the variable x and disturbances from the range t0x « t « t0y of the spectral minimum, that is, disturbances which are determined by the interaction of the fast and slow components and, together with high-frequency disturbances, form white noise. Thus, parametrizing <#;(y, x)> in the form <0;(y, x)> = Qiiy) + g'h we arrive at the equation

From (5.1.4) it follows that the evolution of the slow component of the climatic system from any initial state will be described not by one curve in a phase space of parameters yh but by a family of curves complying with all possible random disturbances g[. It is precisely this fact which is the main difference between deterministic and stochastic models. The former does not take into account the existence of random disturbances at all, the latter takes it into account in one form or another.

Let us discuss the basic ideas and principles of construction of deterministic models which have played an extremely important role in the climate theory and have still not exhausted their usefulness. One of the restrictions of these models is the difficulty of interpreting results obtained in the absence of numerical experiments carried out for various combinations of internal and external model parameters. The similarity theory of the circulation of planetary atmospheres developed by Golitsyn (1973) and then modified by Zilitinkevich and Monin (1977) as applied to the case of the global ocean-atmosphere interaction may be quite useful in this respect.

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