First off there is no scripture to support that Jesus was actually submerged. The verses that are used state:
Matthew 3:16 As soon as Jesus was baptized, he went up out of the water. At that moment heaven was opened, and he saw the Spirit of God descending like a dove and lighting on him.
Mark 1:10 As Jesus was coming up out of the water, he saw heaven being torn open and the Spirit descending on him like a dove.
The Jordan is a river and you must "come up" out of the river because you must go down the banks to go into the river. If Jesus was in fact fully submerged then there is a possibility that he would have floated off once he was pushed under. The body is very buoyant as anyone knows.
The big clincher he is that in the book of Acts 8 Phillip baptizes the Eunuch and "They" came out of the water. So are we to believe that Phillip was under the water with the Eunuch?
Acts 8:36 As they traveled along the road they came to some water, and the eunuch said, "Look, there is water. What is to prevent my being baptized?" ( The oldest and best manuscripts of Acts omit this verse, which is a Western text reading: "And Philip said, "If you believe with all your heart, you may.' And he said in reply, "I believe that Jesus Christ is the Son of God.' ") 38 Then he ordered the chariot to stop, and Philip and the eunuch both went down into the water, and he baptized him. 39 When they came out of the water, the Spirit of the Lord snatched Philip away, and the eunuch saw him no more, but continued on his way rejoicing.
There are also there verses:
Ezechiel 36:25 "Then I will sprinkle clean water on you, and you will be clean; I will cleanse you from all your filthiness and from all your idols. 26 "Moreover, I will give you a new heart and put a new spirit within you; and I will remove the heart of stone from your flesh and give you a heart of flesh.. 27 "I will put My Spirit within you and cause you to walk in My statutes, and you will be careful to observe My ordinances.