Love to get the transliterate Hanja versions of both the 일기s, weather and diary. Could you help?
I suspect the
일기 (weather) stands for "work/study on the atmosphere" or something similar; whereas,
일기 (diary) stands for daily record/register.
Unfortunately, I can only follow my gut instincts as I don't know Chinese.
일기 is a Hanja (Sino-korean) word meaning "daily recording". By itself, it stands for diary/journal
When used to speak about the weather, it means a daily recording of the 날씨, weather i.e. of the state of the atmosphere at a particular place and time. (날씨 is a pure Korean word.). In other words,
일기 예보 is short for 날씨 일기 예보.
(1) typo: "기상" [lit. Atmospheric phenomena]
(2) [To be nitty gritty]
기상 예보관 = ("real") weather forecaster (i.e. weather data analyst; sometimes, referred to as meteorologist).
while (according to Naver dict.),
일기 예보관 = 기상 통보관 = Lit. weather report broadcaster = weatherman or woman (i.e. one who broadcasts to the public the analysis reported by the 기상 예보관).