In this article, scientists have proposed a way to regrow the Arctic icecap by pumping and freezing arctic seawater. As far as I can gather, they suggest that if seawater is pumped up onto depressions in the remaining ice, the seawater will freeze and thicken the floating ice. My question by analogy is: if I place a large ice cube in a glass and then add a smaller amount of nearly freezing cold seawater to the glass, will the seawater freeze, or will the ice cube melt?
Does it depend on the relative quantities of ice and seawater? Does the fact that seawater freezes at a lower temperature than pure water have any relevance?
I guess it does not matter if the seawater freezes or not. If you pump water out of the ocean onto land, that will reduce the ocean's level (slightly), which I guess is the end result they are looking for. However, if you pump the water onto floating ice, the ice will sink a little bit and displace more water, and that would make no change to the sea level.
Would the ideas suggested in the article make any significant and cost-effective reduction in the rise of sea levels worldwide?
The following points are a summary of the comments and answers so far (and some related questions) which I think are pertinent:
Ice floating in pure water does not change the level when it melts.
Ice floating in seawater does slightly increase the sea level, but the effect is slight.
The main cause of sea level rise appears to be thermal expansion of seawater with increasing temperatures.
Ice that is on land, such as in parts of Greenland and Antarctica and on mountain tops, obviously does raise sea levels when it melts.
Removing water from the sea and supporting the water on top of ice that is floating on the sea does not change the sea level at all.
Increasing the area of floating ice does increase the amount of sunlight that is reflected and indirectly may reduce temperatures and the rate of sea level rise (slightly).
I think the observation by Dale M in his answer that pumping water up onto the surface of ice exposes the water to very cold air and would freeze the pumped seawater is very valid. I also think the surface ice is most likely below $0 \ ^{\circ} \text{C}$ and if the mass of ice is greater than that of the pumped water, the water will lose more thermal energy than the ice gains. It does seem possible that it is technically possible to freeze the water by pumping it onto the surface of the ice.
However, pumping the seawater onto the top of the mostly floating ice in the Arctic seems to be the least effective place to carry out the operation. See point 5.
P.S. One thing no one has mentioned so far is the heat created when creating the energy to pump the water. The article does mention using a hydrogen powered generator, presumably to reduce pollution from burning fossil fuels, but no mention is made of the heat put into the atmosphere from burning fuel to power the generator or the heat put into the pumped water due to pumping it. I guess the power source would have to be solar (probably not very practical when there is very little sunlight for about 6 months) or wind power.