Investigating chaos in ozone layer depletion at Pakistan air space

Phenomena like, atmospheric pollution, temperature variability, global warming, or ozone layer depletion (OLD) may be analyzed for forecasts etc. by solving the primitive dynamic equations along with the continuity and energy ones. The environmental variables actually observed are the consequences of thousand of events, some of which may be poorly defined or imperfectly understood. However, such atmospheric models of meteorological phenomena are simplistic in their nature, in the sense of largely hiding the character of nature as it dasiareallypsila is. This failure of reaching an exact solution and the fact that environmental phenomena nearly always include random components prompt us to leave the purely deterministic approach and invoke instead pseudo-randomness or randomness (stochasticity). In globally coupled dynamical systems, the law of large numbers is violated but the central limit theorem holds. The ozone reduction is predictable and models can be used to provide predictions of OLD due to human activities. One may argue that the consistency resulting from model application - such as the ability to describe the OLD and its seasonal variations, the reproducibility of predictions, and reasonable consistency between different models - could be a property of the models rather than of the OLD. For instance consider the Milankovitch forcing arising from changes in the distribution of solar radiation over the Earth because of variations in the Earth´s orbit. If we turn to the past record of OLD we see that changes in ozone as a result of the increase of CFCs are also driven by changes in the radiative regime at the top of the atmosphere. This study attempts time series modeling via fluctuating dynamics of ozone layer for the study of OLD which has not been attempted earlier. Our investigations produce quantitative results that describe the relation of synoptic meteorological conditions to regional OLD. In this communication analysis of bispectrum properties, corr- elation dimension and lyapunov exponent for fluctuating OLD phenomenon have been carried out in order to test the existence of some degree of chaos in discrete time series. This analysis, based on the study of correlation properties, can be considered as a first contribution in understanding the fluctuating dynamics of OLD phenomenon in order to obtain a coherent representation of this complex dynamical system.