There is almost certainly ice water on the surface of the moon, hiding in the cold, dark places near the north and south poles, a new study shows.

Scientists had thought there was water up there, but now we have some of the most definitive proof to date. It appears that this ice — very muddy ice, mixed with a lot of lunar dust — exists inside craters where direct sunlight does not reach it.

But we still do not know how deep it goes, or exactly how it got there.

The authors of the study, published Monday in Proceedings of the National Academy of Sciences, said the findings are exciting because they call for further exploration of our rocky satellite. The ice could be a resource for human visitors — perhaps to drink, or even to make rocket fuel.

Shuai Li, the lead author and a planetary scientist at the University of Hawaii at Manoa, said that despite decades of lunar research, scientists have had trouble exploring the polar regions, in part because the craters are so dark. “So there aren’t too many measurements,” he said. “But a lot of things are going on there.”

Researchers estimate that the exposed ice covers only 3.5 percent of the craters’ shadowy areas. They don’t know whether the water runs deep, like the tips of buried icebergs, or is as thin as a layer of frost.

The data used by Li and his team had been collected by NASA’s Moon Mineralogy Mapper, which hitched a ride on Chandrayaan 1, India’s first lunar probe, in 2008 and 2009.

The instrument was able to map most of the moon’s surface, but data from the permanent shadows — inside some of the craters near the poles — were hard for researchers to work with. So Li and his team were creative and patient. They peered into dark craters using traces of sunlight that had bounced off crater walls. They analyzed the spectral data to find places where three specific wavelengths of near-infrared light were absorbed, indicating ice water. They performed rigorous analysis to make sure their results were uncorrupted by anomalies or instrument errors.

Ralph Milliken, a study author and an associate professor at Brown University, said he “had a healthy dose of skepticism” when Li approached him with the idea of sifting through old data to look for clues in infrared. But he soon came around. “I consider this to be the most convincing evidence that you actually do have true water ice at the uppermost surface — what we call the optical surface — of the moon,” he said of the study.

Scientists have researched extraterrestrial water before — on Mercury, for example, or the large asteroid Ceres. But the moon has been difficult. Radar can be unreliable when the ice water is muddied by sediment, and some spectroscopic analyses could not distinguish between water and hydrogen.

Rachel L.P. Klima, a senior staff scientist at the Johns Hopkins University Applied Physics Laboratory, said Li’s results were impressive. “We’ve had all of these kind of circumstantial things that hinted at ice on the moon — different data sets — but there really was not a robust observation that could only be attributed to ice,” she said. “This is, in my opinion, the first evidence that there’s really no other way to explain.”

“We’re really pushing the boundaries,” Milliken said of the methodology. “I could imagine, now that we know this does work, you could easily go and design an instrument that is tailored to these more difficult conditions and that would open even more doors.”