Beyond the animal it carries, a branch enters three fixed sets of relations that the almanac and the fate-calculation tradition use constantly. Hai belongs to the trio Hai, Mao and Wei, one of the four groups of three branches spaced four apart which are read as combining into Wood. It clashes with Si, the branch six places away, and it forms one of the six harmonies with Yin. These relations are properties of position in the twelve, not of the animal.
The branches also do more work than the year cycle they are best known for. They divide the day into twelve double hours, so Hai names a period of two hours as well as a year and a month; they mark the twelve directions of the compass, Hai standing at north-northwest; and they carry the twelve stations against which the movement of Jupiter was tracked, which is one proposed origin for the twelve-year cycle itself.
The stem-and-branch day count is the longest continuously running day count known. Numbering days by ganzhi begins in the Shang inscriptions and has run without acknowledged interruption since, through every dynastic change and every calendar reform, because the cycle of sixty is independent of any astronomical quantity and therefore needs no correction. Chinese historical dates from the classical period onward can be checked against it.
Hai is the twelfth and last branch and opens the winter in the month assignment. Because ten and twelve have a common factor of two, only half the possible stem and branch pairings occur: a yang stem always meets an odd-numbered branch and a yin stem an even-numbered one, so the cycle is sixty rather than 120, and Hai, standing twelfth, always carries a yin stem.
Sources Chinese Mathematical Astrology: Reaching Out to the StarsHo Peng Yoke with The Chinese Sexagenary Cycle and the Ritual Origins of the CalendarAdam Smith