Weather prediction systems rely on the vast amounts of data continuously generated by Earth modeling and monitoring systems, and efficient data analysis techniques are needed to track changes and compare datasets. Here we show that a nonlinear quantifier, the spatial permutation entropy (SPE), is useful to characterize spatio-temporal complex data, allowing detailed analysis at different scales. Specifically, we use SPE to analyze ERA5 and NOAA OI v2 sea surface temperature (SST) anomalies in two key regions, Nino3.4 and Gulf Stream. We perform a quantitative comparison of these two SST products and find that SPE detects differences at short spatial scales (<1 degree). We also identify several transitions, including a transition that occurs in 2007 when ERA5 changed its sea–surface boundary condition to OSTIA, in 2013 when OSTIA updated the background error covariances, and in 2021 when NOAA SST changed satellite, from MeteOp–A to MeteOp–C. We also show that these transitions are not detected by standard distance and cross-correlation methods.