Mathematical models of the Earth System, the Solar System, and indeed the entire Cosmos are evolving rapidly, and are becoming more insighful, more accurate, and more complex as the 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 it.
Models are often run 'backwards in time' to test their skill against historical records - that is, as a check of the models' accuracy to predict past scenarios. They are then ran 'forwards' to forecast future events.
A discussion of various models and modeling issues is contained in the following material, sorted by category: