Fig. 2

Examples of white and red noise: sea level pressure (SLP) and sea surface temperatures (SSTs). a Leading EOF of detrended monthly SLP anomalies in the North Pacific (between 20 and 60°N; area-weighted) during 1959–2022 displayed as regression coefficients in physical units [hPa per standard deviation] using ERA5 reanalysis (Hersbach et al. 2020), capturing variability of the Aleutian Low. b Leading EOF of detrended monthly SST anomalies in the North Pacific (between 20 and 60°N; area-weighted) during the same time period displayed as regression coefficients in physical units [K per standard deviation] using ERSSTv5 data (Huang et al. 2017), capturing the characteristic PDO pattern. c Power spectral density [PSD; using the Multi-Taper Method (MTM) with 3 tapers and nfft = 1024 (Thomson 1982)] of the normalized leading principal components (PCs) of North Pacific SLP anomalies (grey line) and North Pacific SST anomalies (black line) corresponding to the EOFs shown in a, b, respectively. The AR(1) fit (solid orange and red lines) as well as the 99% confidence levels (CL; dashed orange and red lines) for potential spectral peaks were calculated from the respective percentile at each frequency of 10,000 power spectra generated from discrete AR(1) processes with the same lag(-1) autocorrelation r and data length as the respective PC time series (\({\lambda }^{-1}=\sim 8.1\) months for SST PC1 and \({\lambda }^{-1}=\sim 0.7\) months for SLP PC1). The SLP PC1 spectrum is almost white (i.e., characterized by a very fast decorrelation timescale) whereas the SST PC1 exhibits a Lorentzian spectrum (i.e., red at high frequencies and white at low frequencies). The predicted -2 power law slope in log–log space of red noise at high frequencies is indicated by the thin black line. The vertical dashed grey lines indicate the frequencies beyond which the spectra are expected to be approximately white for each \(\lambda\)