El Niño–Southern Oscillation (ENSO) and the Pacific Decadal Oscillation (PDO) have been studied for decades as separate climate phenomena, even though their spatial patterns are strikingly similar. Neighboring papers in the archive deal with quantum fluctuations, numerical methods for the Dirac equation, and El Niño prediction, but this article stands apart: it directly attacks the methodological problem that has hindered seeing the connection between ENSO and the PDO. The classical EOF method, proposed by Lorenz in 1956, produces static maps that do not reflect evolution over time. This has fueled a debate: is the PDO an independent phenomenon or merely a low-frequency response to ENSO? The work offers a new tool capable of separating contributions from different time scales and showing their spatial dynamics.
The author used monthly sea surface temperature data (ERSSTv4) from 1880 to 2015 for two representative points: point A at the equator (0°, 130°W) and point B in the North Pacific (42°N, 130°W). Each time series was subjected to the Extreme-point Symmetric Mode Decomposition (ESMD), which extracts intrinsic modes with time-varying periods. To validate the decomposition, the sum of modes 2–5 at point A was compared with the known Niño-3.4 index; the correlation was 0.84. An integrated version of ESMD was then developed: for each grid point, the decomposition was performed, the number of modes was unified to five, and spatial maps of each mode were constructed at fixed time instants. This made it possible to track how warm and cold anomalies move across the Pacific Ocean.
The decomposition revealed six main temporal modes. The first mode corresponds to the seasonal cycle with amplitudes of 2.5°C at the equator and 7.0°C in the North Pacific. The residual reflects global warming: over the last 50 years, the increase was 0.65°C in the tropics and 0.58°C in the extratropics. For ENSO, the key modes are modes 2 and 3 with average periods of 2.6 and 5.5 years (quasi-quadrennial and quasi-decadal). For the PDO, modes 3, 4, and 5 are important, with periods of 5.1, 11, and 22 years, as well as mode 6 with a period of about 50 years, but its amplitude is the smallest. The quasi-decadal mode (about 5 years) is present in both phenomena and appears to be responsible for the "ENSO-like" variability of the PDO. The integrated ESMD for the 1997–2000 episode showed how the warm El Niño anomaly gives way to cold La Niña, while in the North Pacific a shift from a warm to a cold regime occurs simultaneously.
This work differs from neighboring studies in that it offers not just a statistical analysis but a method that yields evolving spatial patterns over time. This is the first attempt to apply ESMD to sea surface temperature data to separate the contributions of ENSO and the PDO. If classical EOF gives static maps that cannot be matched with dynamics, the integrated ESMD shows how anomalies move and change sign. This provides a fresh perspective on the long-standing debate about the independence of the PDO: the quasi-decadal mode is common, supporting the hypothesis that the PDO is partly a response to ENSO, but it also has its own decadal and interdecadal components.
The ESMD method can be extended to other climate indices and regions, as well as to the joint analysis of multiple variables such as temperature, pressure, and precipitation. The integrated version opens the way to building dynamical forecasts that account for the evolution of spatial patterns. In the future, one could investigate how global warming affects the amplitudes and periods of the identified modes, especially the quasi-decadal mode linking ENSO and the PDO.
The results are important for climatology, oceanography, and forecasting of extreme weather events associated with ENSO and the PDO. The method may be useful to ecologists and natural resource managers, as the PDO affects the productivity of marine ecosystems.
The next step could be to apply the integrated ESMD to the entire Pacific region to objectively determine the timing of PDO regime shifts. It is also worth testing hypotheses about the connection of the quasi-decadal mode with the Kuroshio and Oyashio currents.
In climatology, the question remains unresolved as to whether the PDO is an independent phenomenon or merely a low-frequency response to ENSO. This work contributes by showing that both phenomena share a common quasi-decadal mode, but the PDO has additional decadal and interdecadal components. This is consistent with the view of the PDO as a combination of different physical processes rather than a single mode.
The ESMD method was developed earlier by the author and patented in China in 2019 as the "Integrated ESMD method for spatiotemporal data analysis."