Mathematical modelling is one of the most powerful methods for the study and understanding of the Earth’s climate system and its components. Modern climate models used in variety of applications are derived from a set of multi-dimensional non-linear differential equations in partial derivatives, which describe dynamical, physical and chemical processes and cycles in the climate system. Climate models are mostly deterministic with a large-phase space dimension containing a vast number of parameters that have various meanings. Most of them are not well-known a priori and, hence, are not well defined. Parameter errors and their time and space variabilities generate parametric uncertainty. Some model parameters describe external forcing that can strongly influence the climate model behaviour. It is, therefore, very important to estimate the influence of variations in parameters on the model behaviour and results of simulations. Questions like these can be answered by performing sensitivity analysis. This chapter considers various methods of sensitivity analysis that can be used: first, to estimate the influence of model parameter variations on its behaviour; second, to identify parameters of climate models and third, to study the model response to external forcing.
Part of the book: Topics in Climate Modeling
Climate system consisting of the atmosphere, ocean, cryosphere, land and biota is considered as a complex adaptive dynamical system along with its essential physical properties. Since climate system is a nonlinear dissipative dynamical system that possesses a global attractor and its dynamics on the attractor are chaotic, the prediction of weather and climate change has a finite time horizon. There are two kinds of predictability of climate system: one is generated by uncertainties in the initial conditions (predictability of the first kind) and another is produced by uncertainties in parameters that describe the external forcing (predictability of the second kind). Using the concept of the ‘perfect’ climate model, two kinds of predictability are considered from the standpoint of the mathematical theory of climate.
Part of the book: Dynamical Systems