The Haftarah of Noach is taken from Yeshayahu . This chapter makes up the Haftarot for two of the Sheva d’Nechemta, the Haftarot of Comfort read after Tisha B’Av: #3, Re’eh and #5, Ki Teitzei.
Linear annotated translation of the Haftarah of Noach
Noach is explicitly mentioned in the Haftarah, making it a natural choice. But what is his relevance to comforting Jerusalem?