After the eruption of Mount Pinatubo, scientists took seven snapshots of the atmosphere. Each snapshot is a map of concentrations of various substances. The goal is to figure out which substance turns into which. But how do you infer causation from seven frames when there are more substances than time points?

M-CaStLe looks at each point on the map and its eight neighbors. Such a set of nine cells is called a neighborhood. On the map, there are thousands of these windows, and all of them are considered repeats of the same mechanism. Instead of seven observations over time, the method gets thousands of observations in space. Each window is like a view of the same clockwork from a different angle.

The method was tested on synthetic data where the true relationships are known. It found them with accuracy above 0.9. For the Pinatubo data, M-CaStLe reconstructed the chain: SO2 gas turns into H2SO4, which then becomes SO4. Standard analysis of averaged time series found no relationships at all. On El Niño data, the method showed that ocean temperature affects convection, but not the other way around.

Seven snapshots of the sky turned out to be enough to see the hidden gears. Thousands of windows into the same mechanism add up to a clear picture of causation.