Current climate models work by attempting to simulate the weather from first principles. In effect they are weather forecast models run for decades to centuries and in some cases millennia, typically representing scales of 200km or greater. Scales below this need to be parameterized in terms of the large scale flow, and these parameterizations lead to uncertainty in future warming.
Observational datasets of climate change are created by combining observations originally made for other purposes. Observing practice has not remained constant over the 20th (or earlier) centuries, and this introduces bias which if not corrected leads to an incorrect view of 20th century climate change. Two examples will be discussed: the record of surface temperature and the upper-air radiosonde network.
Using models and observations I will illustrate how the 4th IPCC assessment report reached the conclusion that “Most of the observed increase in global average temperatures since the mid-20th century is very likely due to the observed increase in anthropogenic greenhouse gas concentrations”.