Where is all the water going?

The news is full of how seawater is being sprayed on the stricken reactors and cooling pools of "spent" fuel at the Fukushina plant in Japan. Here's a CNN story about it today. A couple of grafs from the story:

The tsunami that followed the 9.0-magnitude earthquake March 11 damaged electrical components and coolant pumps in units No. 1 and 2. Those are two of the three units now believed to have suffered damage to their reactor cores, Muto said. 

Reactor No. 2 suffered more damage than No. 1, and the earliest those parts can be replaced is Wednesday, Muto said. The cause of the damage was unclear, but seawater was pumped in previously to cool the reactors as an emergency measure after the earthquake. 

Reactors No. 3 and 4 were still being evaluated to determine which parts need repair or replacement, he said, adding that restoring lighting and air conditioning was a priority so crews can work from inside and gather further data.

Water was sprayed on the damaged housing of reactor No. 3 for about 50 minutes on Tuesday, and seawater was still being injected into the reactor core, Japan's Nuclear and Industrial Safety Agency said. Workers plan to spray over reactor No. 4 for three hours on Tuesday as well.

The question arises: if they continue to pump water on the reactors and the cooling ponds, where is it going? I think there are two choices, and two choices only: radioactive steam, or radioactive groundwater.