Many nile valley civilizations followed what is documented as the ancient Egyptian system(though its origins are most likely further south up the nile.) This is the root of what got carried over into the more modern Egyptian coptic and Ethiopian Orthodox calender.

Here is some basic info.

"The calendar system of ancient Egypt is unique to both the cosmology of the Egyptians and their religion. Unlike the modern Julian calendar system, with it's 365 days to a year, the Egyptians followed a calendar system of 360 days, with three seasons, each made up of 4 months, with thirty days in each month. The seasons of the Egyptians corresponded with the cycles of the Nile, and were known as Inundation (pronounced akhet which lasted from June 21st to October 21st), Emergence (pronounced proyet which lasted from October 21st to February 21st), and Summer (pronounced shomu which lasted from February 21st to June 21st).

The beginning of the year, also called "the opening of the year", was marked by the emergence of the star Sirius, in the constellation of Canis Major. The constellation emerged roughly on June 21st., and was called "the going up of the goddess Sothis". The star was visible just before sunrise, and is still one of the brightest stars in the sky, located to the lower left of Orion and taking the form of the dogs nose in the constellation Canis Major.

Though the Egyptians did have a 360 day calendar, in a literal sense they did have a 365 day calendar system. The beginning of the year was marked by the addition of five additional days, known as "the yearly five days". These additional five days, were times of great feasting and celebration for the Egyptians, and it was not uncommon for the Egyptians to rituals, and other celebratory dealings on these days. The Egyptian calendar also took on other important functions within Egyptian life specifically in dealing with the astrology of the people."

from: http://www.mnsu.edu/emuseum/prehistory/egypt/dailylife/calendar.html