the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 16 Dec 2024
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.
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RC1: 'Comment on esd-2024-37', Anonymous Referee #1, 16 Jan 2025
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The manuscript introduces a permutation method, together with the computation of the associated entropy, to analyze Sea- Surface Temperature (SST) datasets in two regions of the world, the Gulf stream region and the El-Nino region. Two datasets are used for the analysis, the NOAA optimal interpolation and the ERA5 with a monthly sample. The Indices of changes in the datasets are reported related to changes in the sources of observations used. It is claimed that these are not detected with other methods. I think that the method has merits but the work is at a very preliminary stage, and I cannot therefore recommend publication. My points follow:
- As the focus is on the introduction of a method of detection of changes, a proper statistical test should be designed. This is not performed and the indices of changes are guessed based on eye evaluation. The claim that it is better than other methods is not substantiated. Other even simpler methods could be designed for that purpose (for instance taking averages of certain fields in these regions). This is a necessary step if the purpose is to detect changes.
- The number of points in the datasets is very small (probably around a few hundreds of values at each grid point). The authors are using permutations of 4 symbols, leading to 24 different bins for the estimation of the probabilities. It means that a number of events falling in each bin is small, and therefore the estimates of probabilities and the corresponding entropy is affected by large uncertainties. This aspect is not evaluated and no sensitivity test is made. This is also a necessary step to clarify the usefulness of the method.
- Figure 3 is probably the most interesting as illustrating the potential long term changes in the dynamics of the climate system (that could be also detected with other methods). But the interpretation of the trends (and the possible implications of the entropy changes) is left for future study. In view of the weakness of the development of the method discussed in the two previous points, it would have been important to provide a deep and detailed analysis of the origin of these trends in the entropy. This exercise is not done and therefore the conclusions of the work on the physical aspects is weak.
Overall, I think that the work is too preliminary. A more extensive development of the testing method (and associated uncertainties) is necessary as the method has already been introduced some time ago, and a detailed and more extensive analysis of the physical origin of the trends is necessary.
Citation: https://doi.org/10.5194/esd-2024-37-RC1
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