The model curve does not match the temperature record curve. The model temp rates do not follow the measurements, or match the values. If they wish to make policy decisions, then they should clean it up first. To answer you specific question, it is not simply a threshold, but also shape. Does it fit the measurements? No?, start over.
The validation and verification for these are a expert-subjective judgement. That means the models are not judged against a performance specification like a control system model would be, but by the expert opinion of the development team of its output compared to previous versions and measured data. There are no objective measures for this, the closest you can get is an outwardly looking objective opinion which is really a subjective decision based on invisible and subjective scoring. It is in reality a “that looks about right” process cloaked in an opaque process that is designed to appear objective, but is not.
Again, if they are to be used to make policy decisions, fix them so that they at least fit the measured data. If they are to be used only in research, they can do whatever they wish with them. They still have utility in that they may provide clues to processes that may not be measured directly.