Brendan Low

“a leap month could also be decreed before Nisan if the crops had been delayed by exceptionally bad weather (since the firstfruits of barley had to be ready for presentation in the temple on Nisan
16), or if the lambs were too young. Think of the power this gave the Sanhedrin. I have many times wished for the ability to decree an extra
month as I approached a deadline. However, there is no power without
responsibility, and think of the criticism that would be heaped on the Sanhedrin if they decreed an extra month unnecessarily so that the barley was then over-ripe, and the harvest was lost.

...

Unfortunately we possess no historical records of the proclamation of leap months in the period AD 26–36. It is therefore possible
that in some years Nisan was one month later than given in the tables
in this chapter because of exceptionally severe weather. Waddington
has repeated his series of calculations assuming that a leap month
was proclaimed in each year in the period AD 26–36 because of bad
weather. The calculations, given in our Nature paper, show that in
the period AD 26–36, if Nisan was one month later, Nisan 14 would
not fall on a Friday in any year, and Nisan 15 would only fall on a
Friday in AD 34 (April 23). Thus we have fully taken into account in
our calculations the possibility of leap years.”
― Sir Colin J. Humphreys