The 'climatic changes' caused by Saul's death come from a literal interpretation of II Samuel 1: 21, but Tasso probably highlights this episode because it had already been powerfully reused by Dante, Purgatorio 12: 40-42.
The description in which Saul's beheaded body is "fixed onto a tree" is wrong, instead. According to I Samuel 31: 9-10, ". . . they cut off his head and stripped off his armor, and sent word throughout the land of the Philistines, to proclaim it in the temple of their idols and among the people. Then they put his armor in the temple of the Ashtoreths, and they fastened his body to the wall of Beth Shan" (NKJV), nor did the then commonly used Latin Vulgate read otherwise, nor does the parallel text of I Chronicles 10: 9-10 report such a detail. Tasso's literary - and maybe also Freudian - slip belongs to the general 'Vikingalization' his poetry undergoes in the last period of his life, with Il Re Torrismondo and Gerusalemme Conquistata. Quite often, in fact, in GC bodies and heads of men or bears, killed by warriors or hunters and fixed onto trees appear.
A minor remark: in the Bible we can read both pro-Saul and anti-Saul passages. Tasso sides with the first, terming "noble" the king's head.
To be continued . . .