The water appears to be present day and night, though it is not necessarily easily accessible, they said.
The findings may help understand the origin of the Moon's water and how easy it would be to use as a resource.
If the Moon has enough water, and if it is reasonably convenient to access, future explorers might be able to use it as drinking water or to convert it into hydrogen and oxygen for rocket fuel or oxygen to breathe.
"The presence of water doesn't appear to depend on the composition of the surface, and the water sticks around," said Bandfield, lead author of the study published in the journal Nature Geoscience.
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The results contradict some earlier studies, which had suggested that more water was detected at the Moon's polar latitudes and that the strength of the water signal waxes and wanes according to the lunar day (29.5 Earth days).
In planetary science, a cold trap is a region that's so cold, the water vapour and other volatiles which come into contact with the surface will remain stable for an extended period of time, perhaps up to several billion years.
The debates continue because of the subtleties of how the detection has been achieved so far. The main evidence has come from remote-sensing instruments that measured the strength of sunlight reflected off the lunar surface.
However, the surface of the Moon also can get hot enough to "glow," or emit its own light, in the infrared region of the spectrum.
The challenge is to disentangle this mixture of reflected and emitted light. To tease the two apart, researchers need to have very accurate temperature information.
Researchers came up with a new way to incorporate temperature information, creating a detailed model from measurements made by the Diviner instrument on NASA's Lunar Reconnaissance Orbiter (LRO).
The finding of widespread and relatively immobile water suggests that it may be present primarily as OH, a more reactive relative of water that is made of one oxygen atom and one hydrogen atom.
OH, also called hydroxyl, doesn't stay on its own for long, preferring to attack molecules or attach itself chemically to them. Hydroxyl would therefore have to be extracted from minerals in order to be used.
"By putting some limits on how mobile the water or the OH on the surface is, we can help constrain how much water could reach the cold traps in the polar regions," said Michael Poston of the Southwest Research Institute in the US.
Sorting out what happens on the Moon could also help researchers understand the sources of water and its long-term storage on other rocky bodies throughout the solar system.
The researchers are still discussing what the findings tell them about the source of the Moon's water.