The calendar provided to us by the Torah (Five Books of Moses) is a solar-corrected lunar calendar. It is lunar in that each month begins with the sighting of the new moon. It is solar-corrected in that is uses an agricultural event to correct for the solar year. Each year during the twelfth biblical month Karaite religious authorities (as ancient pre-talmudic Israelites used to) go out to the fields to observe the barley crop. There is a certain state of the barley when it becomes green and begins to ripen, this is called the “aviv” (or abib). In Egypt, 3500 years ago the volcanic hail from Santorini (fire and ice) fell on Egypt when the barley had reached aviv (Breshit [Genesis] 9:31-34).
If the aviv is not sighted during the twelfth biblical month a thirteenth month begins at the new moon. When the aviv is sighted the first biblical month begins at the sighting of the next new moon. Fourteen days pass before we begin the holiday Chag Hamatzot (the pilgrimage festival of the unleavened bread otherwise known as passover).