And the more recent ones seem to be concentrated around Mars' relatively small centers of longer-lasting volcanism, some of which stayed active well into the Amazonian age -- one small part of the Martian surface where there unquestionably WAS surface liquid water for quite a while.

However, other scientists insist that they look more as if they were formed by fairly widespread liquid-water flows -- maybe even of surface runoff. The very fact that they're so old means that many of them may since have been completely eroded away or covered up by blankets of the fine, dry dust and sand moved around on Mars' surface by the wind for eons.

And the visible-light camera that makes up the second part of THEMIS -- whose 19-meter resolution is intermediate between the very high-resolution but limited-area photos taken by Mars Global Surveyor's big telephoto camera, and the vastly wider-angle photos taken by the 1970s Viking Orbiters -- has revealed that many of them have far more and finer branches than had been thought, now blurred into gentle hard-to-see gullies, which suggests that many of them really may have been formed largely by surface runoff rather than "sapping" by smaller underground water flows.

But that surface runoff may still have been pretty limited in both time and scope -- even at their best, the valley networks seem certain to always have been far scarcer than the riverbeds that exist on Earth, and they seem to be concentrated mostly on just some parts of the ancient highlands that cover Mars' southern hemisphere.

One theory is that most of Noachian Mars' overall surface was indeed considerably below freezing all the time -- but that the much greater geothermal warmth from the still-cooling early planet provided enough warmth in some limited places to raise warm liquid water out of the planet's lower crust so that it then flowed along on or near the surface for fairly long distances before totally refreezing, for so long as volcanic warmth remained high in that area. But this has some trouble explaining why the valley networks tend to flow mostly from high-altitude terrain, where it would be hard for the liquid water to ascend high enough.

Another theory, recently described by Michael Carr of the US Geological Service, revolves around the undoubted fact that early Mars -- like present-day Mars -- was, unlike the Earth, slowly "rocking" back and forth in its degree of spin-axis tilt, over cycles lasting about a hundred thousand years. (More on this in my next chapter.)

During the intermittent periods when its tilt was especially extreme -- over 35 degrees, and occasionally even as high as 60 degrees -- one polar region at a time would be tilted continually toward the Sun for months at a time, and would therefore rise in temperature well above freezing even during the Sun's fainter early days.

This would thaw the surface ice in that region, and it would in fact evaporate a lot of the resultant water into vapor which would refreeze as frost or snow at Mars' lower-latitude regions nearer the equator, which during these periods would actually be colder than the Sun-facing pole. During these periods, Mars had two middle-latitude "ice belts" rather than two polar ice caps. (During its rarer episodes of most extreme tilt, it may have a single ice belt around its equator, which would have been its coldest area then on a year-round basis.)

Then, as Mars' degree of axial tilt slowly decreased again, its low-latitude regions would once again warm up, and the accumulated ice and snow there would evaporate and move back to the poles to refreeze. It seems very likely that throughout Mars' history, its surface supply of water ice has thus been migrating back and forth between its poles and its lower latitudes as the planet's degree of tilt rocks slowly back and forth. And so, during the Noachian age, snow layers dozens of meters thick may have fallen in the higher-altitude parts of a Martian surface region as the amount of solar heating diminished there and water vapor migrated there from other parts of the planet that were warming up. Then, as Mars' hundred-thousand-year "obliquity cycle" caused the colder region to begin warming up again, the snow would evaporate away and move back to high-altitude regions in the once-again colder parts of the planet.

Would such re-warming snow layers at first produce large amounts of meltwater at their top from the sunlight's growing warmth, which would trickle down to the bottom of the snow layer and then run along the surface to gradually carve the valley networks?

Unfortunately, calculations indicate not -- because the meltwater formed by the sun at the top of the snow would tend to refreeze after trickling only a small distance down through the thick snow layer. It would be able to reach the ground only during the brief final days of the snow layer, when the layer was thin. Instead, most of the snowbank would end up eventually getting evaporated directly into the air, as water vapor, from the top down as the region's warmth increased.

But early Mars, still cooling down from its formation, was also emitting a lot more geothermal heat from its interior than it is today -- and if a snowbank was dozens of meters thick, its insulating effect might allow the snow at the very bottom to be melted by this geothermal heat flow instead and trickle along the surface for all of the tens of thousands of years that the snow layer existed. This might indeed be long enough to gradually carve the valley networks -- with repeated flows of this geothermally melted snow water trickling down the same channels again and again at 100,000-year intervals and further deepening them. And this would also explain why the valley networks tend to start in Mars' higher-altitude hills, where the snowfall would be deepest.