Analysis of spatio temporal geophysical data using spatial entropy: application to comparison of SST datasets

Abstract. Efficient data analysis techniques are urgently needed due to the large amount of data continuously generated by Earth modeling and monitoring systems. We show that the spatial permutation entropy (SPE) is a valuable technique to characterize spatio-temporal geophysical data, allowing detailed analysis at different scales. Specifically, we show that SPE is able to uncover differences in two sea surface temperature (SST) products, in two relevant geographical regions: the equatorial Pacific (Niño3.4) and the Gulf Stream. SPE is calculated as the entropy of the probabilities of occurrences of symbols that are defined along two orientations, west-east (WE) or north-south (NS), and either in consecutive grid points, or separated by a lag, δ. We find substantial differences between the analyzed datasets, for the WE orientation with δ = 1, that gradually disappear as δ increases. We also identify two transitions, one in year 2007 when ERA5 changed its sea–surface boundary condition to OSTIA, and the second one in 2021 when NOAA changed satellite, from MeteOp–A to MeteOp–C. These transitions were not detected when using conventional data analysis tools, which demonstrates that SPE is a valuable tool for the analysis of 2D geophysical data.