Ocean currents intertwine like sticky spider silk: every disturbance leaves a trace that does not vanish instantly. Climatologists have been used to treating random jolts in this web as invisible and memoryless, but new research shows that noise has memory, and that memory strengthens connections between distant nodes.

The author built a linear inverse model in which random forcing can be either white noise without memory or colored noise with a characteristic correlation time. Instead of directly computing derivatives as in Liang's method, the dynamics are extracted by minimizing the difference between the observed correlation function and the theoretical one. For white noise, the norm of the difference is minimized over a window of four months; for colored noise, the memory time is additionally fitted. The initial guess comes from the matrix logarithm of the correlation function at different lags. Then, using the Liang-Kleeman formula, the information flow between variables is computed, serving as a measure of causality.

The method was applied to sea surface temperature data from the Pacific Ocean and the Indian Ocean Dipole index for 1958–2010. All approaches show mutual but asymmetric causality: the Pacific stabilizes the dipole, while the dipole excites the Pacific. The information flow map resembles the structure of El Niño. Accounting for colored noise yields stronger flows, especially in the Niño 3 region. There, noise memory reaches two months, which is fifty percent longer than in the rest of the ocean. Observed autocorrelations are concave at zero, confirming the presence of noise memory.

This work is the first to apply a linear inverse model with colored noise to a causality problem in climate, and it explicitly separates the contributions of dynamics and correlations. This is not just a refinement of Liang's method but a fundamentally more complete picture: the memory of random perturbations changes causal links. The method could improve forecasts of El Niño and the Indian Ocean Dipole, which is important for agriculture, water resources, and the economies of countries dependent on these phenomena. It is also applicable in other fields where noise has memory, such as finance or neuroscience.

The sticky web of ocean connections turns out to be even more tenacious than thought: a disturbance that hits the Niño 3 node lingers there longer than a seasonal cycle. Noise memory, like a viscous thread, stretches the influence of El Niño on the Indian Ocean Dipole and back. Now climatologists can see where the web does not break but merely sags slightly under the weight of randomness.