Calculations of global warming prepared in or before 2001 from a range of climate models under the SRES A2 emissions scenario, which assumes no action is taken to reduce emissions and regionally divided economic development.
The geographic distribution of surface warming during the 21st century calculated by the HadCM3 climate model if a business as usual scenario is assumed for economic growth and greenhouse gas emissions. In this figure, the globally averaged warming corresponds to 3.0 ?C (5.4 ?F).The main tools for projecting future climate changes are mathematical models based on physical principles including fluid dynamics, thermodynamics and radiative transfer.

Although they attempt to include as many processes as possible, simplifications of the actual climate system are inevitable because of the constraints of available computer power and limitations in knowledge of the climate system. All modern climate models are in fact combinations of models for different parts of the Earth. These include an atmospheric model for air movement, temperature, clouds, and other atmospheric properties; an ocean model that predicts temperature, salt content, and circulation of ocean waters; models for ice cover on land and sea; and a model of heat and moisture transfer from soil and vegetation to the atmosphere. Some models also include treatments of chemical and biological processes.

Warming due to increasing levels of greenhouse gases is not an assumption of the models; rather, it is an end result from the interaction of greenhouse gases with radiative transfer and other physical processes. Although much of the variation in model outcomes depends on the greenhouse gas emissions used as inputs, the temperature effect of a specific greenhouse gas concentration varies depending on the model used. The representation of clouds is one of the main sources of uncertainty in present-generation models.

Global climate model projections of future climate most often have used estimates of greenhouse gas emissions from the IPCC Special Report on Emissions Scenarios. In addition to human-caused emissions, some models also include a simulation of the carbon cycle; this generally shows a positive feedback, though this response is uncertain. Some observational studies also show a positive feedback. Including uncertainties in future greenhouse gas concentrations and climate sensitivity, the IPCC anticipates a warming of 1.1 ?C to 6.4 ?C by the end of the 21st century, relative to 1980�1999.

Models are also used to help investigate the causes of recent climate change by comparing the observed changes to those that the models project from various natural and human-derived causes. Although these models do not unambiguously attribute the warming that occurred from approximately 1910 to 1945 to either natural variation or human effects, they do indicate that the warming since 1970 is dominated by man-made greenhouse gas emissions.
The physical realism of models is tested by examining their ability to simulate current or past climates. Current climate models produce a good match to observations of global temperature changes over the last century, but do not simulate all aspects of climate. Not all effects of global warming are accurately predicted by the climate models used by the IPCC. For example, observed Arctic shrinkage has been faster than that predicted.