Every once in a while, nature produces something with captivating fragility. Such is the case with Zen stones, which seemingly hover above frozen lakes, their masses supported by thin, sometimes nearly invisible, pedestals of ice. Researchers have now determined the physics underpinning the formation of Zen stones using laboratory experiments and numerical simulations. Sublimation of ice plays a key role, the team discovered, which puts Zen stones in rare company with other sublimation-sculpted natural features such as penitentes.
The best place to find Zen stones is on Siberia’s Lake Baikal, where it’s consistently cold and dry in the wintertime and the lake’s surface freezes. But they’re hardly commonplace, said team member Nicolas Taberlet, a physicist at the University of Lyon in France. “Even on Lake Baikal, they’re rare.”
In recent years, Zen stones have been popularized by nature photographers. Olga Zima, a photographer from Siberia, captured an image of a Zen stone on Lake Baikal that took top honors in a recent “Best of Russia” photo competition. This shot evokes a sense of calm, she said. “It symbolizes the balance of nature.”
Despite the beauty of Zen stones, a convincing explanation of their formation has remained elusive. Theories abound on personal websites and blogs, but those ideas represent mostly guesswork, said Jeff Moore, a planetary geologist at NASA Ames Research Center in Moffett Field, Calif., not involved in the research. “It was idle speculation.”
In particular, one long-standing idea has been that Zen stones form when the ice around them melts. But that notion doesn’t make sense, said Moore, because meltwater would likely destabilize the fragile structures. “Running water will tend to undermine the pedestal.”
In 2017, Taberlet and his colleague Nicolas Plihon, a physicist at the French National Centre for Scientific Research, began reproducing Zen stones in the laboratory. Their motivation was a desire to explain a rare natural formation, said Taberlet. “It’s mostly for the beauty of understanding something interesting.”
Zen in the Laboratory
The researchers placed a metal disk 30 millimeters in diameter—simulating a stone—atop a block of ice. Taberlet and Plihon then enclosed the entire experimental setup in a freeze dryer, which functioned by pumping out air to reduce the humidity in its refrigerator-sized chamber and facilitate sublimation.
Taberlet and Plihon found that ice not covered by the disk sublimated at a rate of roughly 8–10 millimeters per day. The energy responsible for that sublimation came from the nearly uniform infrared radiation originally emitted by the freeze dryer’s outer walls, which were at room temperature, the team concluded. A similar process is at work in nature, Taberlet and Plihon suggested, because significant cloud cover over Lake Baikal in winter tends to scatter sunlight, reducing its directionality.
The ice directly beneath the disk sublimated less rapidly, resulting in the formation of the pedestals characteristic of Zen stones in nature, the researchers found. Taberlet and Plihon concluded that the rocks that top Zen stones function like miniature umbrellas, shielding the ice beneath them from infrared radiation and thereby lowering the rate of sublimation. “The ice far from the rock disappears, and the rock itself protects the ice directly underneath,” said Taberlet.
To explain another feature of Zen stones—the characteristic depressions that persist directly beneath their rocks and are influenced by their shapes—the researchers turned to numerical modeling. They showed that these depressions can be explained by the far-infrared emission of the rock itself. That energy is responsible for a localized uptick in the sublimation rate in the immediate vicinity of the rock, the team proposed.
In the future, Taberlet and Plihon hope to study in more detail how Zen stones form in their natural environment. They’d like to place rocks on the frozen surface of Lake Baikal and film the formation of Zen stones over several weeks. Seeing these features grow in nature would be logical follow-up, said Taberlet. “That’d be the next step.”
—Katherine Kornei (@KatherineKornei), Science Writer