"All models are wrong but some are useful". I am not against the concept of anthropogenic climate change because climate models may not be strong source of information for climate change. Observation data in the last 30 years or more are enough to prove that human related emissions are affecting the radiative and thermal properties of land, ocean and atmosphere. This question is about climate models which are based on approximations in so many ways. I am deeply concerned that most modelers tune their models for the right or wrong reasons to produce "quality" publications on peer-reviewed journals. They seem to say, "look at my model, it perfectly reproduced what is observed". But we know that, there are so many approximations for turbulence, micro-physics, land surface fluxes, and so forth. The numerical solution approximation by itself imposes serious limit to the accuracy of climate models. Some manuscripts that I found are "too accurate to be true". Then my question is how accurate can a climate model be? Are there methods to check the accuracy of those publications claiming to be true?
Edit: This question is broad and it requires broad answer based on uncertainties imposed on climate models by approximations at each level of the model development and indicate the maximum achievable accuracy level. In my mind something like the following conceptual figure.