If we were to terraform Mars would Mars slowly lose its water i.e., some of the water would sink deep into the dry Martian crust or combine with other elements in the soil? Mars has been dry for billions of years!
NASA's MAVEN isotopically analyzed Mars' atmosphere, and found that 4.5 billion years ago it was close to earth density. Given a consistent loss rate, an Earth-like atmosphere would take tens of millions of years to erode, at least. Ref: http://svs.gsfc.nasa.gov/12557. IF we could put a significant atmosphere on Mars, it would likely create a host of ecological problems. Example: dust storms; multiply martian dust storms by a factor of 100 because of the far thicker atmosphere. Invasive organisms could create a toxic and even dangerous environment. The list of disasters could be quite extensive, it is doubtful that responsible authorities would even risk it.
Assuming terraforming (martiaforming?) means increasing atmospheric pressure and density to support human and plant life without protection, then my educated guess is that water now frozen would form water vapor. Over time this would escape into space.
Current consensus among scientists seems to be that Mars once had oceans. The atmosphere along with the water (vapor) got lost because Mars is subject to deeply penetrating solar wind, which effectively "blew away" the atmosphere over eons. Two factors make this effect much larger on Mars than on Earth:
- Mars does not have a strong magnetic field deflecting solar wind charged particles to the poles.
- Only about 1/3 of Earth gravity, so atmospheric particles need less energy to escape.
I'm quite skeptical that terraforming will ever work. On Mars it could be a non-terminating effort: you'd need to constantly resupply the lost atmosphere. I wonder what Sisyphus would have to say...
To contradict myself right away, lets think big. Missing magnetic field? Superconducting coils along the equator! Or kickstart an iron core into rotation. If there's no iron core, make one. That's a piece of cake for people talking Dyson spheres and Kardashev types.
Actually, it should be possible to prevent Mars from losing its water, or at least keep its water loss to a suitably low rate. In an atmosphere, there's something called a cold trap, the coldest layer of the atmosphere (relevant links: 1, 2). It causes water vapour to condense and thus prevents it from rising into the upper atmosphere. If the water did reach the upper atmosphere, it would be exposed to UV rays and hence split into hydrogen and oxygen (photolysis), and the light hydrogen would soon escape the atmosphere. Thus a cold trap prevents water being lost. For a cold trap to occur, there need to be gases with low boiling points like N2, CO2 and O2; these would be added to the atmosphere anyway as part of terraforming. You'd also want to protect the atmosphere, which you could do using an artificial magnetosphere.