Mathematical models of the Earth System are evolving rapidly, and are becoming more insighful, more accurate, and more complex as the Earth's fundamental natural processes are better understood. However, each model has its own strengths and weaknesses, depending on the choice of algorithms embedded therein, and the nature of the data necessary to initialize them.
Models are often run 'backwards in time' to test their skill against historical records - that is, as a check of the model's accuracy to predict past scenarios. They are then run 'forwards' to forecast future events.
A discussion of various models and modeling issues is contained in the following papers: