Astronomical forcing and mathematical theory of glacial-interglacial cycles

Abstract. There are three important features of a proxy time series recorded during the Late Pleistocene. They are: 1) 100 000-year cycle as a dominant control of global glacial-interglacials through the late Quaternary, 2) fluctuations with periods of about 40 and 20 thousand years (their contribution to dispersion is no more than 20%), 3) ''Red-noise'' behavior of the time series. Direct influence of the insolation change created by fluctuations of the eccentricity is too weak to cause the observed 100 000-year climate fluctuations. Therefore, other mechanisms of such a rhythm are proposed. On the basis of the equation of the heat budget, the equation describing dynamics of zonally averaged temperature is developed. Various combinations of terms of this equation are discussed. They present a linear response to the Milankovitch periodicity, the Langeven stochastic equation, the equation of delay oscillator, the stochastic equation of spontaneous transitions, and the equation of stochastic resonance.

Orbitally-induced changes in the solar energy flux received by the Earth play an important role as a mechanism starting process of climate changes which is supported and intensified by different feedbacks within the climate system. Positive anomalies of solar radiation serve as a mechanism causing reorganization of the climate only in rare cases when inclination of Earth axis of rotation increases and, simultaneously, perihelion takes place during the summer time (for the Northern Hemisphere).