Dedesertification of the mid-oceans

Many parts of the oceans, most notably the South Pacific Gyre, are biological deserts. Unlike the land deserts most commonly associated with the word, it's the micronutrients rather than water that's lacking. The most fertile areas of the oceans are where rivers flow into the sea, providing micronutrients that have been eroded from the land, and where currents bring up nutrients from the ocean floors.

So, can we dedesertify these mid-ocean areas by piping water from the lower layers or the ocean floor? Imagine a floating platfrom, with solar and wind power generation powering a pump connected to a long pipe that descends into the depths.

It may even be possible to power the movement of water purely using the heating of the water by the sun. For example, consider that the pipe has a one-way valve (i.e. up only). The cold water is drawn up, then expands, overflowing the edges of the container. The sun then evaporates some of the water, causing lower pressure, which then sucks up more water.