Q. How can you determine when a 13th month comes, and when the Biblical New Year starts?
A. 2003, 2005, 2008, 2011, 2014 and 2016 were all years in which a 13th month was added. We've noticed for many years now that Yahweh has apparently honored the Jews’ calculations by keeping things close. Typically within a few days for Passover, Days of Unleavened Bread, Pentecost, etc. This would keep us all thinking about these days roughly at the same time.
In calculating future years, to when the Biblical New Years are expected to be, we use as a reference work called, The Comprehensive Hebrew Calendar, by Arthur Spier. It takes the calculated Hebrew calendar out to the year 2100. We also use the United States Naval Observatory (USNO) to determine when new moons are expected to appear, as they are mathematically predictable.
With all of this said, we still continue to follow the Biblical and historical standard of visually confirming a few days before the new moon the abib barley in Israel (Deut. 11:10-13; 16:1). As we understand, there should be two or three fields (Exod. 9:31; Lev. 23:10; 2 Cor. 13:1) of natural or wild barley (hordeum spontaneum) in an early harvestable firm dough stage (Lev. 2:14) before the beginning of months (Exod. 12:2).
Today, with no operational Levitical priesthood active and no standing Temple, we do not see the wave sheaf (Lev. 23: 10-11) being performed; even though it’s law, along with others, help us in our principle understanding of when the Biblical New Year is to start. This in turn allows us to keep the holy convocations, which are to be kept forever, with or without a physical Temple and within or outside of Jerusalem (John 4:19-24).
For further information see our free in-depth booklet called, Biblical Holy Days: Yesterday, Today, Forever.