There's little doubt that, at least early in its history, Mars had significant quantities of liquid water. Everything from mineral deposits to ancient shorelines and river-like features indicate that the watery period peaked near the border between the planet's Noachian and Hesperian epochs, about 3.5 billion years ago. There has been some debate, however, about just how much water was present at that time. A paper published over the weekend in Nature Geoscience argues that there was enough to cover the planet's northern pole in an ocean.
The logic of the analysis is pretty simple, and applies the sort of reasoning we use for determining the Earth's historic ocean levels. In short, you look for geologic features indicative of a shoreline, and see if they line up at the same altitude. In this case, the two authors used a database that tracks the appearance of river deltas on the Martian surface, and uses the Mars Observer Laser Altimeter dataset to get elevations for each of them. If an ancient ocean existed, these features should exist within a narrow range.
On a first pass, the data didn't look very promising, as the mean elevation of the 52 deltaic deposits under consideration varied widely (the standard deviation was over a kilometer). But the authors went through and analyzed each deposit individually, and found that many were associated with a local basin, such as a large crater. Only a third of the features were associated with the outflow of water into the basin that covers the northern hemisphere of the planet, and these were tightly clustered in elevation (a mean elevation of of -2,540m with a standard deviation of 177m).
The authors point out that this is exactly what you'd see if you were looking at an ancient shoreline, writing, "Therefore, the deposits topographically connected to the site occupied by the putative ocean define the closest approximation of an equipotential surface as would be expected if they formed in a single large body of standing water encompassing the northern hemisphere of Mars."
Data from outside the region suggests that there might have been a planet-wide water table in the crust, as there are almost no valleys below the shoreline level that date from the Noachian, even in areas well removed from the northern basin. That changes in more recent eras, suggesting a gradual loss of water planet-wide.
Cumulatively, there seems to have been a lot of water involved—the authors estimate that over 108 cubic kilometers may have been present, with 36 percent of the planet's surface covered in water.
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