For the first time, functioning of the planetary climate system is considered in terms of the self-organization laws with account of positive and negative feedbacks. It is shown that the maximum risks in the development of positive feedbacks that can lead the climate system to a planetary catastrophe, are associated with an unprecedented increase in the concentration of methane in the atmosphere. Over the last 30 years, its concentration in the atmosphere has increased by 2.5 times and continues to grow exponentially. In this review, we show that today the principal source for increase of methane concentration in the atmosphere is the self-accelerating decomposition of methane hydrates in the cryosphere of the Northern Hemisphere. In the history of the Earth, the emissions of methane into the atmosphere due to mass decomposition of methane hydrates led to climate-induced biosphere catastrophes. Paleo-reconstruction analysis of greenhouse gas concentrations in the atmosphere and its temperature over the last 420,000 years has allowed us to conclude that the self-organizing planetary climate system is currently in a state of dynamic chaos (close to the bifurcation point). This means that even a relatively weak impact on it, also of anthropogenic characters, is able to affect the planetary climate system to select its future development trajectory.
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