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The New York Times article Ice on the Surface of the Moon? Almost Certainly, New Research Shows talks about the recent paper published in PNAS Direct evidence of surface exposed water ice in the lunar polar regions where decade-old data has been reanalyzed very thoroughly.

The paper seems to be open access, at least when clicked through the NYTimes.

When I look at the spectra in Figure 1 (shown below) I just don't see any difference between them in the three bands used to zero-in on water.

Can someone explain how to see the difference between water-containing and non-water-containing pixels? Or is the difference only detectable algorithmically?

I just don't see how to get to the NYTimes' "Almost certainly, new research shows."

The data used by Dr. Li and his team was not new. It 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 — was a little bit patchy, and hard for researchers to work with.

So Dr. 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 statistical analysis to make sure their results were uncorrupted by coincidental anomalies or instrument errors.

Ralph E. Milliken, a study author and an associate professor in the department of earth, environmental and planetary sciences at Brown University, said he “had a healthy dose of skepticism” when Dr. Li approached him with the idea of sifting through old data to look for clues in infrared. But he soon came around.

Figures from the paper in PNAS.

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First, they build the case for the positive detections to not be the result of noise:

In contrast, ∼0.2% of shaded M (3) data showed positive detections (SI Appendix, Fig. S2C). The average spectrum of positive detections of the random data (SI Appendix, Fig. S3) is distinct from those observed in the M (3) data (Fig. 1), indicating that a population of random noise of a size similar to that of the M (3) data is highly unlikely to produce ice-like spectra.

Then, they conducted a null hypothesis test regarding what categories of absorption the pixels showed:

A null hypothesis test was conducted to show that the prediction of a third ice-like absorption based on detection of the other two is significant (SI Appendix, Tables S2 and S3).

[...]

the third ice-like absorption was always observed in the average spectra of the positive pixels (SI Appendix, Fig. S4). It is thus statistically significant to conclude that the three absorptions near 1.3, 1.5, and 2.0 μm occur simultaneously in a subset of the M (3) data, which is consistent with the presence of water ice in these pixels.

So, the paper authors concluded "direct and definitive evidence for surface-exposed water ice in the lunar polar regions" in their Significance section.

In summary, ice absorbs radar wavelengths. The absorptions detected were statistically meaningful--that is, the paper authors concluded that it was "highly unlikely" to be noise and "definitive evidence" of ice.

To see this on the chart at the end of the question, you look in the three ranges shown. Notice how there are peaks in those bands for pixels with no ice, but in the three moon readings shown there are troughs, as there are in the known ice reading from Earth.

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