Error Dynamics and Coupling Procedures in Mathematical Climate System Models

The mathematical hypothesis concerning the external character of perturbations is critically examined in the special case of a climate system model. The importance of embedding such models into a perturbation space with L 1 -structure for the analysis of error and model stability is demonstrated. 1. TOPOLOGICAL EMBEDDING OF MATHEMATICAL MODELS Since there are many real dynamic systems on which controlled experiments cannot be carried out, it is important to construct an appropriate model of a "proxy system" on which such experiments can be conducted. A classic example of such a dynamic system is the atmosphereactive -layers (AAL) system. As a result of increasing computational power of modern computers, improvements in measuring techniques and achievements in the development of effective numerical procedures, a number of mathematical models for the proxy AAL system are currently available (see references in [4]). As a rule, such models require a large datasets of initial conditions ..