In 1988, water temperatures in the Pacific Ocean began to change in a coordinated way: if it warmed in one place, it also warmed in a neighboring spot. These coincidences can be drawn as a network, where points in space are connected by threads if their behavior is similar. While everything is calm, the network consists of small islands. But before abrupt changes, the islands start to merge, and at some point a single large continent of connections emerges. This moment arrives before the change itself.
An even earlier signal can be obtained by watching small groups of points. In a random network, the probability that a random point belongs to a cluster of two points reaches its maximum long before the large continent appears. For a lake that might suddenly turn turbid from fertilizers, this peak occurs at a value of 0.635, while the transition itself happens at 0.658. The difference is small, but it buys time for preparation.
The method was tested on ocean data. It detected precursors of the 1988 El Niño 240 days before, and the 2009 El Niño 115 days before the official onset. Previously, such warnings either came too late or required precise knowledge of the model. The new approach uses only measurements that can be collected from sensors. It does not explain why the system changes, but simply notices that its parts have become too synchronized. When small islands of correlations start to merge into a continent, it is worth listening: the ocean is already whispering about what will soon shout.
For the lake model, the peak of probability c₂ occurs at p=0.635, while the transition itself occurs at p=0.658: a difference of 0.023 in the parameter, which corresponds to a noticeable lead time.
The idea of predicting a catastrophe from growing correlations echoes the concept of the 'psychohistory' from Isaac Asimov's 'Foundation' series, where Hari Seldon predicts the fall of the Empire through statistical patterns.