Why does it say that the trees will know?
Radak: Because Malchus Beis David is compared to a cedar, it compares kings of the nations to forest trees.
Malbim: They will know that everything was with Hashgachah. He lowered Tzidkiyah, who was a tall, moist tree, and raised Yechanyah, who was a low, dry tree. It was written about him in the creed of Bavel that his seed may not rule over Beis Yisrael 1 .
Malbim (Yirmeyah 22:30) learns this from that verse "Lo Yitzlach mi'Zar'o... u'Moshel Od bi'Yhudah."
What is the tall tree?
Rashi: It is the Kasdim (Radak #1 - Melech Bavel), who were ruling in Yisrael.
Radak #2: It is Tzidkiyah.
What low tree will be raised?
Radak #1: It is Melech Yehudah, i.e. Zerubavel.
Radak #2: It is Yehoyachin. He was lowly in Galus, and Hashem raised him. Evil Merudach removed him from jail, and permit his chair above the kings with him.
What moist tree did He dry?
Rashi: Tzidkiyah and his seed.
Radak #1: Melech Yehudah.
Radak #2: It is Tzidkiyah.
What dry tree will He make sprout?
Rashi: Yehoyachin, who was exiled without sons in Bavel, will be exiled to Bavel. He will be the ruling officer of Yehudah. Radak - he had no children when he was exiled. Afterwards, he fathered children in jail - Asir and She'alti'el. He became a moist tree.
Why does it say "Dibarti v'Asisi"?
Malbim: when Hashem says that He will do good, He does not retract. With the Dibur, it is finished. For evil, speech is not tied to action. Hashem looks forward to his Teshuvah, and the decree will be nullified.