If we consider the scale of the day from the first hours until nightfall, being noon as its name indicates it medium, then the sentence of " half-day for down " It refers to the hours of the afternoon and evening.
Half day down means before 12:00 example 8 9 10 etc. By that are before noon if after 12:00 would be half a day up ok
It is a colloquial way of saying: after noon, passed Meridian, after 12 PM, etc.