Studying Pacific sea surface temperature variability has long relied on linear methods, such as principal component analysis, which require orthogonal modes and maximize explained variance. However, modes like El Niño, the Pacific Decadal Oscillation, and the Pacific Meridional Mode overlap spatially and interact nonlinearly, so linear decompositions provide only a partial picture. Related work in the archive uses Fourier transforms, filtering, and signal processing to separate timescales, but these often require predefined frequency bands or geographic regions. This work stands apart: it applies deep learning with physically motivated constraints to separate modes by their characteristic timescales without predetermined filters.
The authors built a Knowledge-Guided AutoEncoder (KGAE) based on a variational autoencoder with five latent dimensions. Input data were monthly sea surface temperature (SST) anomalies in the Pacific from the ERA5 reanalysis, spanning 1940 to 2023, with trend and seasonal cycle removed beforehand. The loss function included several additional terms: a penalty for overlapping power spectra between latent dimensions, a penalty for spatial correlation when spectral overlap exists, and an incentive for each latent dimension to have a unimodal spectrum. Uncertainty was assessed using an ensemble of 100 randomly initialized models and cross-validation with alternating temporal slices to preserve access to low-frequency variability. Decoder sensitivity was analyzed via finite differences in latent space, allowing separation of linear and nonlinear responses.
KGAE identified three dominant modes of variability: a decadal mode with periods of 10–20 years, an interannual mode with periods of 3–7 years, and a quasi-biennial mode with a period of about 2 years. The spatial patterns of these modes were robust to random initialization and data subsampling. The decadal mode resembles the Pacific Decadal Oscillation (PDO) in spatial structure, with a correlation of about 0.84 over the basin and 0.92 in the North Pacific, while in the tropics it resembles the negative phase of the North Pacific Gyre Oscillation (NPGO) with a correlation of about -0.88. The interannual mode is closely linked to the Niño-3.4 index (time series correlation about 0.82) and to indices of eastern and central El Niño types (spatial correlations about 0.80–0.81). The quasi-biennial mode correlates most strongly with the eastern Pacific index (about 0.84), but its spectrum is concentrated at shorter periods than standard El Niño indices. Nonlinear interaction analysis showed that the decadal mode modulates the response of the interannual mode, and this modulation correlates strongly with the Pacific Meridional Mode (PMM) pattern, with a correlation of about -0.86 over the basin. Joint composites showed that when the decadal and interannual modes have the same sign, anomalies resemble central Pacific El Niño (correlation with the C-index about 0.95), while opposite signs yield weaker eastern Pacific-like anomalies. Seasonal analysis revealed that the quasi-biennial mode strengthens from July to November, and the interannual mode from November to January, matching the development and maturation phases of El Niño. Applying KGAE to the E3SM2 and CESM2 climate models showed that CESM2 overestimates the frequency of central Pacific El Niño events and has a biased seasonal cycle of phase transitions.
This work differs from neighboring studies by using deep learning with physically motivated constraints instead of linear decompositions or predefined filters to simultaneously separate spatial and temporal scales. This allows direct characterization of nonlinear interactions between modes, which traditional methods ignore. The results confirm that decadal variability modulates El Niño type and that the quasi-biennial mode is linked to its development and decay, consistent with known mechanisms, but now shown for the first time with a unified method without a priori assumptions.
The KGAE method can be extended to multivariate data, including for example atmospheric pressure, wind, and ocean heat content, to explore coupled modes of the entire climate system. It could also be applied to other basins or the global ocean. Explicitly modeling time-varying spectral power and separating internal variability from forced signals remain open challenges. In the long run, KGAE may help improve long-term El Niño forecasts by isolating more predictable components.
The method could be useful for assessing the realism of climate models and for improving seasonal and decadal forecasts. It also offers a new way to analyze nonlinear interactions in the climate system.
A next step could be incorporating additional variables into KGAE, such as upper-ocean heat content, and applying it to forecasting tasks to test whether mode separation improves El Niño predictability.
This work directly addresses the unresolved problem of separating internal climate variability from forced signals, as well as the question of how independent Pacific decadal variability is from interannual variability. It also touches on the predictability of El Niño, particularly the spring predictability barrier, which is shown to be concentrated in the quasi-biennial mode.
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The authors developed a Knowledge-Guided AutoEncoder (KGAE) to separate modes of sea surface temperature variability in the Pacific Ocean without predefined filters. The model extracted decadal, interannual, and quasi-biennial modes, and decoder sensitivity analysis revealed that the decadal mode is linked to the modulation of El Niño type, while the quasi-biennial mode is associated with its development and decay. The method also uncovered systematic errors in the E3SM2 and CESM2 climate models.
Where its strength is
The strength of the work lies in using physically motivated constraints in the loss function (penalties for spectral overlap, spatial correlation, and encouragement of spectral unimodality), which yielded interpretable and stable modes without predefined filters. Sensitivity analysis in the latent space allows exploring nonlinear responses that linear methods cannot capture.
Where it could go next
Worth trying
Why this may matter
Separating Pacific Ocean variability modes using deep learning without predefined filters paves the way for a more accurate understanding of nonlinear interactions in the climate system, which could improve both climate model diagnostics and forecasting of phenomena like El Niño.
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.52, against a usual 0.64. It looks like few have drilled nearby.
The spring predictability barrier for El Niño, known since the 1980s, turns out in this work to apply only to the quasi-biennial mode, while the interannual mode retains predictability longer.
The idea of decomposing a complex signal into hidden independent components recalls science fiction attempts to decipher alien messages by extracting structure from noise. In Carl Sagan's novel Contact, the signal contains nested layers of information that unfold as analysis proceeds, much as KGAE uncovers hidden modes in ocean temperature.