Shenmue was one of the first games to give players a taste of what a living, breathing simulation of the world looked like in video game form. Long before the likes of The Elder Scrolls or GTA would later get all the credit for doing the same thing, this game was pioneering the systems that would come to signify a lifelike open world, and the developers accomplished them by putting a frankly preposterous amount of detail into every little thing.
However, the developers occasionally went a little overboard when it came to authentically capturing the minutia of the world they were creating. In fact, on a second playthrough you can change the way the weather works, and if you choose the "actual weather" option in the settings, the game will use real forecasts from 1986-7 Yokosuka (where the title is set) to dictate how the weather should be at any point in the game.
The devs could have just had any old weather system in place and it wouldn't have made a difference, but for some reason they thought that mimicking the actual forecasts from the time would make the world feel that bit more real.