## Polar ice cap instability in energybalance climate models

This best-known example of a catastrophe in climatology is found in energy-balance climate models. Budydo (1969) and Sellers (1969) demonstrated, in a one-dimensional model, a catastrophic transition from a globe that has ice in the polar regions only to an ice-covered globe by lowering the solar constant by a few percent. A description of this catastrophe can be found in textbooks on climatology, such as Hartmann (1994).

### Abrupt climate changes

Ocean-atmosphere interaction gives rise to additional catastrophes. The onset of an ice age, a long-term drought, and abrupt changes in ocean general circulation are some examples.

### Barotropic and baroclinic instabilities

The textbook explanation for these instabilities presents only a linear growth rate depiction based on linear analyses, which is of limited use. The linear analysis approach starts from a basic (quasi-)equilibrium state, such as Si, S2 and S3 in Fig. 3, adds perturbation and determines if the perturbation can grow and, if so, its growth rate. If a state such as S2 in Fig. 3 is unstable, the perturbation will then grow at a constant growth rate, and can be of either sign. The obvious limitations of linear analysis are that the unstable equilibrium is not physically realizable and that the analysis is valid only for a very short period of time, before nonlinear effects become sizeable. Therefore, to get a more complete picture of these instabilities, one should turn to the concept of a catastrophe. In studying these instabilities as catastrophes, one needs to ask what the equilibria are before and after these instabilities and what the forcings sustaining the equilibria are, in order to arrive at a complete picture of the whole life span of the phenomenon. In a catastrophe, the growth rate is initially zero, when the system loses its equilibrium, and then increases and finally decreases over the life span of the catastrophe. The growth can be in one direction only. The trigger in a triggered catastrophe has to be in the same direction as the growth of the catastrophe.

### Middle-latitude explosive cyclogenesis

This is a good research topic. Linear baroclinic instability studies (Sec. 6.e of Hoskins et al., 1985) are not adequate to explain cyclo-genesis, owing to its nonlinear nature and the convective heating involved.

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