A simple physical model for glacial cycles

Abstract. Glacial cycles are the norm in Pleistocene climate variability. Models of varying degree of complexity have been used to answer the question of what causes the nonlinear response of the climate system to the periodic forcing from the Sun. At one end of the spectrum of complexity are comprehensive models which aim to represent all involved processes in a realistic manner. However, their high computational cost precludes their use in the ultra-long simulations needed. At the other end are conceptual models which are computationally less demanding but which generally lack a physical basis. Most of them yield good results in terms of capturing the shape and patterns of glacial cycles as indicated by the geological record, thus making it very difficult to identify the underlying mechanisms. Here we present a conceptual model that aims to physically represent the interaction between the climate and the Northern Hemisphere ice sheets while eliminating spatial dimensions in some of the fundamental ice-sheet thermodynamic and dynamic equations. To this end, we describe the Physical Adimensional Climate Cryosphere mOdel (PACCO) from its simplest to its most complex configuration. We discuss separately the implications of different fundamental mechanisms such as ice-sheet dynamics and thermodynamics, glacial isostatic adjustment and ice-sheet albedo aging for our model. We conclude that ice-sheet dynamics and a delayed isostatic response are sufficient to produce resonance around periodicities of 100 kyr, although the forcing has a spectrum concentrated around lower values. In addition, ice-sheet thermodynamics and ice aging separately enhance the model nonlinearities to provide 100 kyr periodicities in good agreement with reconstructions. However, we found that it is easier to reproduce the late Pleistocene glacial cycles using the simpler process of ice aging. Overall, PACCO is a valuable tool for analyzing the different hypotheses present in the literature.