In addition to the proposed work with complex numerical models, it can be of great utility to reduce the system to low-order, box, and conceptual models. This complementary approach has been successfully applied to a number of questions regarding feedback mechanisms and the basic dynamical behavior (Lohmann et al., 1996b; Lohmann and Schneider, 1999; Timmermann and Lohmann, 2000 - pdf 156 KB). For the determination of first exit times between climate attractors, concepts of `Large deviation theory' (Freidlin, 1999) can be introduced into climate research. In some cases, e.g. the stochastic climate model of Hasselmann (1976), such models can provide a null hypothesis for the complex system.

The transition from highly complex equations to a low-order description of climate is an important topic of research. In his recent book 'Dynamical Paleoclimatology', Saltzman (2002) formulated a dynamical system approach in order to differentiate between fast-response and slow-response variables. In statistical mechanics, a similar approach is formulated by Mori-Zwanzig, in which the phase space is coarse grained in space and time (this formalism can also be applied to dissipative systems; Chorin et al., 2000). As an alternative to this method, one can try to derive a phenomenologically based climate theory. This can be based on fundamental and derived modes in climate theory for interannual to millennial timescales (Dima and Lohmann, 2004). This approach can be formulated in terms of superposition and selection of certain modes of climate variability. Interestingly, these modes can also be obtained in well dated proxy data from Cariaco basin and Greenland ice cores.

Examples:

• Noise-Induced Transitions in a simplified model of the thermohaline circulation pdf (156 KB)
• Stability of the thermohaline circulation in a simple coupled model
  
• Fundamental and derived modes of climate variability