Biblical chronology

Traditionally, the royal chronologies in Kings and Chronicles appear to be a hopeless jumble to modern readers. The solution required distinctions in terms of different calendars at different times and places, regnal years, and coregencies. This was facilitated by biblical archeology, which provided a cross-check in terms of ancient Near Eastern calendrical methods. So what initially seems to be irresolvable discrepancies turns out to be a witness to the minute factual accuracy of Kings and Chronicles. 

The official start of the new year was different in Judah (Tishri) than in Israel (Nisan). Judah initially used accession year reckoning whereas Israel used non-accession year reckoning. For a while Judah switched to non-accession year reckoning before switching back to accession year reckoning. Israel eventually changed to accession year reckoning. For Judah, there was the matter of coregencies. 

By recognizing that Uzziah's reign was reckoned according to Judah's Tishri-based year while the northern kingdom observed a Niasan-based year for its kings, what otherwise seem to be occasional discordancies in the synchronisms all fall into place. This six-month difference in when the year began then provided to be a useful aid in determining the half-year in which some of these kings terminated their reign, and in the the cases of Jeroboam II through Shallum, the actual month of the kings' death could be determined…The basic data that allows this kind of precision in dating could never have been provided by a late-date editor; the data must have come from contemporary accounts, probably from the official court records of these two kingdoms. A. Steinmann, From Abraham to Paul: A Biblical Chronology (Concordia 2011), 128, 139-40; cf. 38-39.