There is no info about that directly in the game. It depends on where you are exactly. (most important lattitude) But you should be able to measure your lattitude and longitude coordinates on the map (1 degree for every 120km in both directions), and deduce your timezone from it (IIRC SH3 has it's timezones shifted by 7.5 degrees from the real timezones or does something buggy with it... better test it out beforehand). With that and the time on the clock you should then be able to deduce Universal Time Coordinated (UTC). It seems the clock adjusts the timezone automatically (hours only) as you move to keep it it check roughly with local solar time. Definately not realistic, but so it is. Then you should have all the information to input it on some kind of sunrise/sunset calculator website.
Like this:
http://www.srrb.noaa.gov/highlights/...e/sunrise.html
Oops, I forgot to mention... SH3 switches day/night state when the sun is halveway visible. But real life definitions of sun/moon-rise and -set is when the upper edge of the sun/moon is on the horizon. So at the times when it is barely visible. So you need to take into account some minutes after sunrise and before sunset if you need to be accurate.