Perhaps more interesting to me than UNIVAC itself is the system by which all the weather data it crunched was brought to it in the first place. Without the Internet, how was weather data transmitted across the country? Wireless ground stations? Primitive digital telephony? Simple synchronous voice communication? And after that, how was it fed into the machine? I assume not all weather stations in 1956 had adopted a standardized method of storing data.
If you can't bring the data to the machine, it can't tell you anything interesting about it.