The climatic history of the Earth through geological time can only be understood successfully by complementary use of geophysical data and evolutionary models. A numerical model of the evolution of the Earth's surface/atmosphere system is presented which characterizes the global climate by the average surface temperature, TJ. Recent geological data verify the existence of liquid water on the surface of the Earth 3.8 aeons ago and thus provide error bounds on TJ. The computer model includes explicit calculation of the "greenhouse increment" of surface temperature due to gaseous absorption. Data relating to the type and amount of gases in the early atmosphere are derived from geological evidence. Previous debate regarding the exact nature of the early atmosphere seems to be resolved by the results of the model described here. The numerical model is discussed in detail and validated in terms of our present knowledge of the Earth's evolution.