A. Malamat discusses the chronology for the fall of Jerusalem.
A. Malamat, “The Last Kings of Judah and the Fall of Jerusalem: An Historical—Chronological Study,” Israel Exploration Journal 18, no. 3 (1968):137–156
The new data seem to weigh in favour of a Tishri reckoning, which would in any event, in our opinion, better suit the overall chronological context of the latter years of the kingdom of Judah, and all the more so the series of dates for the reign of Zedekiah and the destruction of the First Temple (see references above, n. 20). Only by reckoning Zedekiah's first year from Tishri, 597 B.C. (the period from Adar to Tishri being his accession year) can we reconcile the evidence of the Chronicle, the biblical synchronisms between the regnal years of Zedekiah and those of Nebuchadnezzar, and the dates in the Book of Ezekiel for the final conquest of Jerusalem. Thus, Zedekiah's 1st official year overlapped the second half of Nebuchadnezzar's 8th year which began in Nisan 597 B.C., and the first half of this 9th year. Hence, Zedekiah's 10th year partly overlapped Nebuchadnezzar's 17th year, but also the first part of his 18th (Jer. 32:1), and the summer of Zedekiah's 11th year (during which Jerusalem was destroyed)—2 Kings 25:2; Jer. 1:3; 39:2; 52:5-6) fell already within the 19th year of Nebuchadnezzar's reign (2 Kings 35:8; Jer. 52:12), all in full accord with the data given in the Bible (see the diagram below, p. 156).
However, a series of synchronisms entirely conflicting with the biblical evidence would result from reckoning from Zedekiah's official reign from Nisan 597 B.C., a mere few weeks after his accession. Zedekiah's 1st year would then correspond to Nebuchadnezzar's 8th year in its entirety, and his 10th and 11th years with Nebuchadnezzar's 17th and 18th; thus, only his 12th year would correspond to Nebuchadnezzar's 19th year. In order to uphold these biblical synchronisms, scholars have chosen between two possibilities: (a) the unlikely assumption that the biblical chronologers retarted their reckoning of Nebuchadnezzar's reign by one year, i.e. from Nisan 604 to Nisan 605 B.C., in a sort of antedating non-accession-year method, in contrast to the official reckoning in both Babylonia and Judah; (b) advancing the date of Zedekiah's first regional year to Nisan 596 (some thirteen months after the removal of Jehoiachin!), assuming that he was enthroned only after 1 Nisan 597 B.C., the period of his reign up to Nisan 596 being considered his accession year. As stated above, the assumption (which per se does not conflict with a Tishri reckoning) not only contradicts the evidence of the Babylonian Chronicle, but the biblical testimony as well.