Enrico Fermi's elephant and climate models

Freeman Dyson once related an anecdote about physical modelling:

... I asked Fermi whether he was not impressed by the agreement between our calculated numbers and his measured numbers. He replied, “How many arbitrary parameters did you use for your calculations?” I thought for a moment about our cut-off procedures and said, “Four.” He said, “I remember my friend Johnny von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk.” With that, the conversation was over. I thanked Fermi for his time and trouble,and sadly took the next bus back to Ithaca to tell the bad news to the students. ...
Since global climate is so highly complex and poorly understood, to make them 'work' climate models are necessarily loaded with arbitray parameters.