Climate models are based on mathematical representations, which attempt to reproduce the behaviour of the Earth's climate system (Trenberth 1992). As outlined in Sect. 2.1 the climate system is composed of a number of subcompartments (e.g. the atmosphere, hydrosphere, cryosphere, and biosphere), each component is a nonlinear system in itself and is associated with a characteristic time scale.
The representations of climate models attempt to account for the most important external and internal forcings, they also try to include the most important processes which are involved in feedbacks within the system. The models are based on physical principles such as the conservation of energy, momentum, and mass. Although the fundamental principles appear to be robust, computational limits preclude their numerical solution on all scales which include the many processes that are important in the climate system. For these processes, modellers have to rely on parame-terisations which try to capture the fundamental phenomenology of a small scale process. For more details on the state-of-the-art of climate modelling see, e.g. Washington and Parkinson (2005), Kiehl and Ramanathan (2006), or Donner and Large (2008).
Current climate models simulate the atmosphere, with a prescribed atmospheric composition and incoming solar radiation, and include explicit modelling of the ocean's general circulation and sea-ice dynamics, and relevant land processes. By way of interfaces the subcomponents can exchange energy, momentum, and mass. A typical horizontal grid resolution of today's global atmospheric models is about 180 km; regional climate models on the other hand, capture only part of the globe, and typically work with a 25-50 km horizontal grid resolution. In the vertical dimension, the resolution decreases with the distance from the Earth's surface and ranges from a few decametres to a few kilometres. Among the most important feedbacks climate models have to cope with is the water vapour and the cloud feedbacks as well as the snow, sea and land-ice albedo feedbacks, which also need to be mentioned. Cloud feedbacks can be substantial for the overall performance of a climate model, but the sign and the magnitude of the global mean cloud feedback depends on so many factors that it remains very uncertain (Stephens 2005; Bony et al. 2006).
Climate models are far from perfect, but they are unmatched in their ability to quantify otherwise qualitative hypotheses. More than a dozen facilities worldwide develop and maintain state-of-the-art climate models and comprehensive model comparisons have been conducted using the present-day climate as a primary test bed. These models have successfully captured fundamental aspects of air, ocean, and sea-ice circulations as well as their variability. In recent climate studies (i.e. IPCC 2007a), results of ensembles of a number of models have been reported (such as outlined in Sect. 5.3.). Interestingly however, comparison studies have revealed that the average across a number of models outperformed any given single model. Climate models are evolving more and more into Earth system models, which include chemical and biological processes (e.g. vegetation dynamics) as well as simple socio-economic sub-models.
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