Ice-covered. Earth

0£ 0.9 1.0 11 12 So/% Figure 5.3 Dependence of the southern ice edge location on S0/S° for the one-dimensional model (diffusion approximation), according to North et al. (1981).

as the regimes of ice-free and ice-covered Earth, are stable, and that the remaining regimes belonging to segments of the curve in Figure 5.3 with negative values of the derivatives d(SQ/So)/dxs are unstable. This suggests that the last two regimes cannot be realized in the process of modern climate evolution.

The most striking difference between Figure 5.2 and Figure 5.3 takes place in the regime of total glaciation when S0/S° > 1.1 and in the regime of ice-free Earth when S0/Sq < 1.1: the diffusive approximation predicts the branching of solutions, the transport approximation predicts their merging. Also, on the diffusive approximation the derivative d(SQ/So)/dxs for xs ss 0.95 changes sign, so a gradual increase in S0/Sq from S0/So = 1 is accompanied at first by smooth and then, after the derivative 3(S0/Sq)/3x passes the point of changing sign, by an abrupt increase in xs (decrease in the polar glaciation area) reminiscent of a jump-like transition to the regime of ice-free Earth. According to North et al. (1981), the marked peculiarity of the solution disappears when taking into account the dependence of the diffusion coefficient on the meridional temperature gradient and when retaining higher modes in the expansion (5.4.12), and therefore it should be qualified only as artefact, stipulated by the limitation of assumptions forming the basis of the model.

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