The Holy Spirit came down when the Lord was baptized, that the dignity of Him who was baptized might not be hidden;…’the heavens were opened, and he saw the Spirit of God descending as a dove, and lighting upon Him’ (Matt. 3:16)…Of this dove, the dove of Noah, according to some, was in part a figure. For as in his time by means of wood and of water there came salvation to themselves, and the beginning of a new generation, and the dove returned to him towards evening with an olive branch; thus, they say, the Holy Spirit also descended upon the true Noah, the Author of the second birth…The spiritual dove, therefore, as some interpret, came down at the season of His baptism, that He might show that it is He who by the wood of the Cross saves them who believe, He who at eventide should grant salvation through His death.
-St Cyril of Jerusalem (Catechetical Lectures: Lecture 17 no. 9-10)