Abstract This study investigated trends in satellite-based chlorophyll-a (Chl-a; 1998–2022), sea surface temperature (SST; 1982–2022), and sea level anomaly (SLA; 1993–2021) from the European Space Agency’s Climate Change Initiative records, integrating time series decomposition and spectral analysis. Trends in parameters signify prolonged increases, decreases, or no changes over time. These are time series in the same space as original parameters, excluding seasonalities and noise, and can exhibit nonlinearity. Trend rates approximate the pace of change per time unit. We quantified trends using conventional linear-fit and three incrementally advancing methods for time series decomposition: simple moving average (SMA), seasonal-trend decomposition using locally estimated scatterplot smoothing (STL), and multiple STL (MSTL), across the global ocean, the Bay of Bengal, and the Chesapeake Bay. Challenges in decomposition include specifying accurate seasonal periods that are derived here by combining Fourier and Wavelet Transforms. Globally, SST and SLA trend upwards, and Chl-a has no significant change, yet regional variations are notable. We highlight the advantage of extracting multiple periods with MSTL and, more broadly, decomposition’s role in disentangling time-series components (seasonality, trend, noise) without resorting to monotonic functions, thereby preventing overlooking episodic events. Illustrations include extreme events temporarily counteracting background trends, e.g., the 2010–2011 SLA drop due to La Niña-induced rainfall over land. The continuous analysis clarifies the warming hiatus debate, affirming sustained warming. Decadal trend rates per grid cell are also mapped. These are ubiquitously significant for SST and SLA, whereas Chl-a trend rates are globally low but extreme across coasts and boundary currents.