Models are simply hypotheses that are run on a machine instead of in a human brain.
Having said that, all computer used in science do have to be validated. This is standard practice.
Coby Beck writes:
.. in 1988, James Hansen of NASA GISS fame predicted that the temperature would climb over the next 12 years, with a possible brief episode of cooling in the event of a large volcanic eruption.
He made this prediction in a landmark paper and before a Senate hearing, which marked the official "coming out" to the general public of the dangers of Anthropogenic Global Warming. 12 years later, he was proven remarkably correct, requiring an adjustment only for the timing difference between the simulated future volcanic eruption and the actual eruption of Mount Pinatubo.
- the warming at the surface should be accompanied by cooling of the stratosphere and this has indeed been observed
- as well as surface temperatures warming, models have long predicted warming of the lower, mid and upper troposphere even while satellite readings seemed to disagree. But it turns out the satellite analysis was full of errors and on correction, this warming has been observed
- models expect warming of ocean surface waters as is now observed
- models predict an energy imbalance between incoming sunlight and outgoing infrared radiation. This has been detected
- models predict sharp and short lived cooling of a few tenths of a degree in the event of large volcanic eruptions and Mount Pinatubo confirmed this.
- models predict an amplification of warming trends in the Arctic region and this is happening
Here is another presentation of this data, in more detail.
Deniers often claim that the models do not take clouds into account. Not true.
All of the Atmospheric Global Climate Models used for the kind of climate projections reported on by the IPCC take the effects of clouds into account. You can read a discussion about cloud processes and feedbacks in the IPCC TAR.
It is true however that clouds are one of the largest sources of uncertainty in the GCM's. They are very complicated to model because they have both positive feedbacks, preventing surface heat from escaping back into space and negative feedbacks, reflecting incoming sun light before it can even reach the surface. The precise balance of these opposing effects depends on the time of day, the time of year, the cloud's altitude, the size of the water droplets and/or ice particles forming the clouds, the latitude, the current air temperature and the cloud's size and shape. On top of that, different types of clouds will interact, amplifying or mitigating each other's effect as they co-exist in different layers of the atmosphere. There are also latent heat considerations as water vapour condenses during cloud formation and precipitation events and as water droplets evaporate when clouds dissipate.