A climate model with cryodynamics and geodynamics

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Abstract
We present a highly simplified, zero‐dimensional model of the climatic system. The model attempts to incorporate mechanisms important on the time scale of glaciation cycles, namely, 104–105 years. In particular, the radiation balance of the ocean‐atmosphere, the plastic flow of continental ice sheets, and the viscous flow of the upper mantle are taken into account. The stress is on the interaction between the cryosphere (ice sheets) and the asthenosphere (upper mantle), which had not been taken into account in previous energy‐balance or ice‐sheet models of climate (Weertman, 1976; Källén et al., 1979). The model exhibits free, self‐sustained oscillations of an amplitude and period comparable to those found in the paleoclimatic record of glaciations, viz., O(10 deg K) and O(104 years), respectively. Such oscillations had already been found in the simpler model of Källén et al. (1978, 1979). The fact that nonlinear, self‐sustained oscillations also obtain for the present, slightly more complex model is interesting: it offers mild support to the idea that unforced oscillations can actually exist in the real climatic system itself. These oscillations are characterized by a quarter‐phase lag between ice extent and global temperature. Given that the climatic system is a nonlinear oscillator with a period of O(104 years), it is expected that astronomical forcing at 19,000, 23,000 and 41,000 years will lead to subharmonic oscillations with a period close to 100,000 years, the dominant period of glaciation cycles. Such effects have already been noticed in the work of Birchfield and Weertman (1978) with an even simpler model, including only glacial dynamics. The careful study of the interplay between internal mechanisms and external forcing with comparable time scales represents an interesting challenge to the theory of ice ages. The results of such theoretical studies can also provide guidance for observational work. In particular, periodicities of O(104 years) in the climate record and phase lags between ice volume and temperature appear to be supported by the most recent paleogeochemical investigations (Ruddiman and Mclntyre, 1981).