Every winter, the Pacific Ocean warms slightly off the coast of Peru, and every summer it cools. This rhythm is set by the gears of the climate machine, but some turn fast, others slow, and still others speed up or stall. Linear inverse models have helped us glimpse these gears in data for decades, but they were blind to seasonal changes in pace. The new work adds a calendar to the clockwork.
Previously, the model assumed the climate system behaves the same way every month. But El Niño builds strength in spring and fall, and fades in winter. The researchers examined the mathematical foundations of a model that accounts for such periodicity. They broke it into two variants, much as a watchmaker disassembles a mechanism into two components: one responsible for the smooth rotation of the hands, the other for the random jolts that disrupt the movement.
Numerical experiments on synthetic data showed that e-CS-LIM matches the truth almost perfectly, whereas the old model shifted the phase by about 0.05 of a period, as if June readings were attributed to early July. For the real Niño 3.4 index, the model revealed that the dynamics vary sinusoidally, and the strength of random jolts has two peaks: in spring and fall. This explains why El Niño tends to originate in those seasons.
Now researchers can choose the tool for the task: e-CS-LIM for precise description of motion, l-CS-LIM for estimating random impacts. Previously, it was unclear how to correctly separate these contributions in seasonal data. Now the climate clockwork can not only be heard but also taken apart screw by screw, knowing which screw does what.
The original CS-LIM produced a systematic phase shift, which the authors eliminated by simply shifting the time coordinate by half a step.