I read it as:
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It is a scientific fact that water is among the few substances that expand when they freeze.
Water expand when freezed.
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This explains why ice floats in liquid water; because it is less dense than the water around it, the buoyant force pushes it to the surface.
ice floats on water,because it's less dense than water so buoyant force pushes it to surface.
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Larger differences in density create stronger buoyant forces.
larger the difference greater the buoyant force.
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This fact also accounts for the observation that melting ice does not cause the level of the surface of the water in which it is floating to change
for this reason, when floating ice melts it does not raise water level.
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While some of the ice protrudes above the surface, melting causes the volume of what was the ice cube to decrease so that the newly melted water exactly fills the space that the frozen ice cube occupied under the surface
A floating ice cube if melted fills the same space it occupied under the surface.
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There are those who would use these facts to declare that the melting of the polar ice caps would not contribute to sea level rise, but this is an example of the saying that “a little knowledge is a dangerous thing.”
Author disagrees with it, saying these facts people claims that polar ice caps will not raise water level.
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First, the southern polar cap is not floating on the surface of the ocean, but rather is supported by the Antarctic land mass.
Why author disagrees, it's because the polar ice cap rather than floating freely on the water is actually supported by land-mass beneath. So buoyant foce won't be applied here.
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As a result, the portions of this ice cap that are submerged displace far less ocean water than would be displaced by a floating cap.
For this, ice cap submerged doesn't displace the same space as in case of floating 'ice cube' mentioned above.
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Additionally, the ocean water is salty while the ice caps are fresh.
Furthermore, ocean water is salty, and ice caps are fresh water source.
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Consequently, ocean water is more dense than fresh water, which means that it generates larger buoyant forces and so can support a larger ice cap than fresh water would.
Why does it matter if it's ocean water or fresh water ? another reason for raised water level, it's because ocean water being salty and heavy exerts greater buoyant force than fresh water.
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For both of these reasons, melting of the polar ice caps would in fact cause nontrivial sea level rise.
For this reason melting polar ice caps raises sea level.