Modelling the climate system 16 Current understanding of the physics (and increasingly the chemistry and biology) of the climate system is represented in a mathematical form in climate models, which are used to simulate past climate and provide projections of possible future climate change. Climate models are also used to provide quantitative estimates to assist the attribution of observed climate change to a particular cause or causes. 17 Climate models vary considerably in complexity. The simplest can be described by a few equations, and may represent the climate by global-average surface temperature alone. The most complicated and computer-intensive models represent many details of the interactions between components of the climate system. These more complex models represent variations in parameters such as temperature, wind and humidity with latitude, longitude and altitude in the atmosphere, and also represent similar variations in the ocean. In complex climate models climate sensitivity emerges as an output; in the simpler calculations it is specified either as an input or it emerges as a consequence of simplified (but plausible) assumptions. 18 By applying established laws of fluid dynamics and thermodynamics, the more complex climate models simulate many important weather phenomena that determine the climate. However, limitations of computer power mean that these models cannot directly represent phenomena occurring at small scales. For example, individual clouds are represented by more approximate methods. Since there are various ways to make these approximations, the representation can vary in climate models developed at different climate institutes. The use of these different approximations leads to a range of estimates of climate sensitivity, especially because of differences between models in the response of clouds to climate change. There are intensive efforts to compare the models with observations and with each other. The spread of results from these models gives useful information on the degree of confidence in the reliability of projections of climate change. 19 Unlike weather-forecast models, climate models do not seek to predict the actual weather on a particular day at a particular location. The more complex models do however simulate individual weather phenomena, such as mid-latitude depressions and anticyclones, and aim to give simulations of possible weather sequences much farther into the future than weather forecast models. From such simulations, one can derive the characteristics of climate likely to occur in future decades, including mean temperature and temperature extremes. The Royal Society Climate change: a summary of the science I September 2010 I 4 Changes in global-average surface temperature 20 Measurements suitable for showing how surface temperature has changed with time across the world became available around 1850. Analyses of these data, in a number of institutes, try to take into account changing distributions of measurements, changing observation techniques, and changing surroundings of observing stations (e.g. some stations become more urban with time, which can make measurements from them less representative of wider areas).