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Subsurface Ice? You mean like subsurface where all the magma rotates around and bubbles up.. Or are we mixing our theories? Water at the subsurface level would be under great pressure which would tend to have it hot, not cold.

I would argue that we've likely lost water rather than gaining it. But, I also would argue against plate techtonics. It isn't a given, it isn't observeable nor do the physics seem to work. But that's another story. cubic miles of ice and water don't just get out of the way and hide in places that can't support them or don't make sense. Ice doesn't stay ice in warm climate just because a mountain top seems like a reasonable place for a mile of extra ice to hide. That isn't the way it works. 70 percent of the earth is covered by water. Remove the volume down to the tributaries extending toward the ocean floor then tell me where you can hide that volume of water without it being problematic. I can; but, can you.

esquirette got the right answer.

Genesis 7

4 For yet seven days, and I will cause it to rain upon the earth forty days and forty nights; and every living substance that I have made will I destroy from off the face of the earth.
5 And Noah did according unto all that the LORD commanded him.
6 And Noah was six hundred years old when the flood of waters was upon the earth.
7 And Noah went in, and his sons, and his wife, and his sons' wives with him, into the ark, because of the waters of the flood.
8 Of clean beasts, and of beasts that are not clean, and of fowls, and of every thing that creepeth upon the earth,
9 There went in two and two unto Noah into the ark, the male and the female, as God had commanded Noah.
There went in two and two unto Noah into the ark, the male and the female, as God had commanded Noah.
10 And it came to pass after seven days, that the waters of the flood were upon the earth.
11 In the six hundredth year of Noah's life, in the second month, the seventeenth day of the month, the same day were all the fountains of the great deep broken up, and the windows of heaven were opened.
12 And the rain was upon the earth forty days and forty nights.
13 In the selfsame day entered Noah, and Shem, and Ham, and Japheth, the sons of Noah, and Noah's wife, and the three wives of his sons with them, into the ark;
14 They, and every beast after his kind, and all the cattle after their kind, and every creeping thing that creepeth upon the earth after his kind, and every fowl after his kind, every bird of every sort.
15 And they went in unto Noah into the ark, two and two of all flesh, wherein is the breath of life.
16 And they that went in, went in male and female of all flesh, as God had commanded him: and the LORD shut him in.
17 And the flood was forty days upon the earth; and the waters increased, and bare up the ark, and it was lift up above the earth.
18 And the waters prevailed, and were increased greatly upon the earth; and the ark went upon the face of the waters.
19 And the waters prevailed exceedingly upon the earth; and all the high hills, that were under the whole heaven, were covered.
20 Fifteen cubits upward did the waters prevail; and the mountains were covered.
21 And all flesh died that moved upon the earth, both of fowl, and of cattle, and of beast, and of every creeping thing that creepeth upon the earth, and every man:
22 All in whose nostrils was the breath of life, of all that was in the dry land , died.
23 And every living substance was destroyed which was upon the face of the ground, both man, and cattle, and the creeping things, and the fowl of the heaven; and they were destroyed from the earth: and Noah only remained alive , and they that were with him in the ark.
24 And the waters prevailed upon the earth an hundred and fifty days.

Genesis 8

1 And God remembered Noah, and every living thing, and all the cattle that was with him in the ark: and God made a wind to pass over the earth, and the waters asswaged;
2 The fountains also of the deep and the windows of heaven were stopped, and the rain from heaven was restrained;
3 And the waters returned from off the earth continually: and after the end of the hundred and fifty days the waters were abated.
4 And the ark rested in the seventh month, on the seventeenth day of the month, upon the mountains of Ararat.
5 And the waters decreased continually until the tenth month: in the tenth month , on the first day of the month, were the tops of the mountains seen.