The time-frequency domain analysis of the sea surface temperature (SST) in the tropical western Indian Ocean was conducted using wavelet analysis, cross wavelet transform (XWT), the Mann–Kendall (MK) test, and other methods based on COBE-SST data for the last 50 years (1974–2020). From the perspective of time-frequency combination, examining the data of precipitation, sea surface heat flux, total cloud cover, and long-wave radiation, helped contribute to exploring the periodic changes of SST. Moreover, the Western Hemisphere Warm Pool (WHWP) was selected to analyze the role of SST from 1974 to 2020. Present results have demonstrated that the SST in the western Indian Ocean was in a stage of rising, particularly in 1998. According to the fast Fourier transform of the filtered SST time series, the tropical western Indian Ocean SST has a short period of 3–6 years, a medium period of about 10 years, and a long period of 40 years. The SST in the tropical western Indian Ocean has a resonance period of 2–6 years with precipitation, a resonance period of 2–6 years with sea surface heat flux, a resonance period of 4–5 years with total cloud cover, and a resonance period of 2–5 years with long-wave radiation. Importantly, SST was negatively associated with precipitation, total cloud cover, and long-wave radiation, and positively for sea surface heat flux before 1997. Seasonal migration activities are significantly correlated with the WHWP and the tropical western Indian Ocean SST. The spatial lattice point correlation coefficient is generally from 0.6 to 0.9, and the inter-annual serial correlation value is more than 0.89. Furthermore, the two exist with a resonance period of 2–5 years.

To comprehensively explore the characteristics of global SST anomalies, a novel time–frequency combination method, based on the COBE data and NCEP/NCAR reanalysis products in the past 100 years, was developed. From the view of the time domain, the global SST generally showed an upward trend from 1920 to 2019, the upward trend was significant after 1988, and the growth mutation occurred in 1930, according to the Mann–Kendall (MK) mutation test. Moreover, we extracted spatiotemporal modes of SST anomalies’ variability by empirical orthogonal function (EOF) analysis and obtained global spatial EOFs that closely correspond to regionally defined climate modes. Our results demonstrated that El Niño–Southern Oscillation (ENSO) is the typical character for the first mode of SST anomaly EOF, and Atlantic multidecadal oscillation (AMO) for the second. From the view of the frequency domain, our data suggested that there is a multi-period nesting phenomenon in global SST variations, in which the first main cycle with the most obvious oscillation was a 30-year cycle and changed in 20-year cycles, and the second cycle was a 15-year cycle and changed in 10-year cycles through wavelet analysis. As for the perspective of time–frequency characteristics, the dominant period of ENSO in the first mode of EOF is 4 years, obtained through filtering and cross wavelet transform. In addition, SST anomalies will maintain an upward trend for the next 60 months, according to the seasonal autoregressive integrated moving average (SARIMA) model, which has the potential value for predicting ENSO.