This is an interesting question, and I think the short answer is, no. 'Reliability' perhaps means that they are somehow 'proven' to work, like weather forecasts I tend to trust even knowing that sometimes they are less correct or that your car will start in the morning, but since we don't know the future we cannot really get this proof. The things we place scientific trust in as future climate predictions are the phenomena where there is a sound physical understanding, observational evidence, and are robust across many models. Examples of the latter could be that the Arctic region will warm more than the rest of the world, that it will rain more in the global average and that extreme precipitation will increase. 

Are you looking for something like this?

https://www.researchgate.net/publication/257411712_How_well_do_CMIP5_Earth_System_Models_simulate_present_climate_conditions_in_Europe_and_Africa

Article How well do CMIP5 Earth System Models simulate present clima...

Thank you very much Eduardo ! Are there studies on error variability and uncertainty estimations for the future per decade?

I really don't know, I'm not familiar with the topics, I've just remembered that I had read some months ago a paper somehow related with your question

This is an interesting question, and I think the short answer is, no. 'Reliability' perhaps means that they are somehow 'proven' to work, like weather forecasts I tend to trust even knowing that sometimes they are less correct or that your car will start in the morning, but since we don't know the future we cannot really get this proof. The things we place scientific trust in as future climate predictions are the phenomena where there is a sound physical understanding, observational evidence, and are robust across many models. Examples of the latter could be that the Arctic region will warm more than the rest of the world, that it will rain more in the global average and that extreme precipitation will increase. 

The climate models need to be improved. One problem is that they are unable to simulate the decadal to multi-decadal variations in large-scale climate, and the second problem is the relatively large uncertainty with sensitivity of the climatic system which currently ranges from 1.2 C to 5.0 C. Cautions has to be paid when to make projections of the climate change and variability using the models.

George. The best available answer to your question is still probably in the IPCC AR5 Working Group 1 report, especially chapters 9-11. Lots to read! This is freely available at http://www.ipcc.ch/report/ar5/wg1/.

I have my aproach that diverges from the rest, the rest does not understand the underlying dynamics, I have writen and documented and detailed described that, and discovered the mechanisms involved

https://www.researchgate.net/profile/Dimis_Poulos

In reply to Guoyu Ren (July 27), it is not really true that CMIP5 models cannot simulate decadal to multi-decadal variability to a useful extent. Many do simulate moderately realistically both the AMO and the PDO/IPO in control runs, though it remains true that these models cannot predict the phasing of these phenomena beyond a few years ahead at most. This new ability is important for the emerging science of decadal prediction where the natural component of predictability is important.  

There is a considerable literature on model simulations of decadal to multi-decadal  variability. A good place to start is Chapter 9 of the AR5, section 9.5.3.3.2 for the AMO and section 9.5.3.6 for the IPO/PDO. Chapter 14 of the same report has further details, as do other chapters especially chapter 10 on decadal prediction. There is a large bibliography in these chapters; these fairly short sections contain enough references to explore this literature. (See the IPCC web reference at my reply July 28).

To disagree with Dimis Poulos, these results do suggest that the basic ocean-atmosphere dynamics of CMIP5 models is on the correct lines, if still needing much improvement. Indeed more recent work shows that an important limitation on CMIP5 models was their relatively low horizontal and vertical resolution. This is largely a reflection of limited computer power. This is increasing quite fast since these AR5 was written. Early indications are that higher resolution will improve some of the better CMIP5 models' ability to simulate the natural variability of the climate system in many ways besides decadal variability.