Articles | Volume 17, issue 3
https://doi.org/10.5194/esd-17-533-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/esd-17-533-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Detecting transitions and quantifying differences in two SST datasets using spatial permutation entropy
Departament de Física, Universitat Politècnica de Catalunya, Rambla Sant Nebridi 22, Terrassa 08222, Barcelona, Spain
Giulio Tirabassi
Departament de Informàtica, Matemàtica Aplicada i Estadística, Universitat de Girona, Carrer de la Universitat de Girona 6, Girona 17003, Spain
Cristina Masoller
Departament de Física, Universitat Politècnica de Catalunya, Rambla Sant Nebridi 22, Terrassa 08222, Barcelona, Spain
Marcelo Barreiro
Departamento de Ciencias de la atmósfera y Física de los Océanos, Facultad de Ciencias, Universidad de la República, Montevideo, 11400, Uruguay
Related authors
Juan Gancio, Giulio Tirabassi, Cristina Masoller, and Marcelo Barreiro
Earth Syst. Dynam. Discuss., https://doi.org/10.5194/esd-2024-37, https://doi.org/10.5194/esd-2024-37, 2024
Manuscript not accepted for further review
Short summary
Short summary
We propose the use of the spatial permutation entropy (SPE) as a versatile tool to quantify differences between the sea surface temperature (SST) data set of NOAA OI v2, and the SST used in the ERA5 reanalysis. Focusing on monthly SST anomalies in Niño3.4 region and in the Gulf Stream region, we show that SPE identifies differences in short spatial scales, which vary over time and which can be attributed to the methods and data used to construct SSTs.
Camila de Mello, Marcelo Barreiro, and Madeleine Renom
Ocean Sci., 22, 1169–1182, https://doi.org/10.5194/os-22-1169-2026, https://doi.org/10.5194/os-22-1169-2026, 2026
Short summary
Short summary
We show for the first time that coastal upwelling occurs along the Uruguayan coast throughout the year, not only in summer. Using an ocean model and observations, we identify events that cannot be detected from temperature alone outside the warm season. These findings improve our understanding of local ocean conditions and their potential effects on marine communities.
Juan Gancio, Giulio Tirabassi, Cristina Masoller, and Marcelo Barreiro
Earth Syst. Dynam. Discuss., https://doi.org/10.5194/esd-2024-37, https://doi.org/10.5194/esd-2024-37, 2024
Manuscript not accepted for further review
Short summary
Short summary
We propose the use of the spatial permutation entropy (SPE) as a versatile tool to quantify differences between the sea surface temperature (SST) data set of NOAA OI v2, and the SST used in the ERA5 reanalysis. Focusing on monthly SST anomalies in Niño3.4 region and in the Gulf Stream region, we show that SPE identifies differences in short spatial scales, which vary over time and which can be attributed to the methods and data used to construct SSTs.
Riccardo Silini, Sebastian Lerch, Nikolaos Mastrantonas, Holger Kantz, Marcelo Barreiro, and Cristina Masoller
Earth Syst. Dynam., 13, 1157–1165, https://doi.org/10.5194/esd-13-1157-2022, https://doi.org/10.5194/esd-13-1157-2022, 2022
Short summary
Short summary
The Madden–Julian Oscillation (MJO) has important socioeconomic impacts due to its influence on both tropical and extratropical weather extremes. In this study, we use machine learning (ML) to correct the predictions of the weather model holding the best performance, developed by the European Centre for Medium-Range Weather Forecasts (ECMWF). We show that the ML post-processing leads to an improved prediction of the MJO geographical location and intensity.
Cited articles
Allen, A., Markou, S., Tebbutt, W., Requeima, J., Bruinsma, W. P., Andersson, T. R., Herzog, M., Lane, N. D., Chantry, M., Hosking, J. S., and Turner, R. E.: End-to-end data-driven weather prediction, Nature, 641, 1172–1179, https://doi.org/10.1038/s41586-025-08897-0, 2025. a
Azami, H. and Escudero, J.: Amplitude-aware permutation entropy: illustration in spike detection and signal segmentation, Comput. Meth. Prog. Bio., 128, 40–51, https://doi.org/10.1016/j.cmpb.2016.02.008, 2016. a
Barreiro, M., Marti, A. C., and Masoller, C.: Inferring long memory processes in the climate network via ordinal pattern analysis, Chaos: An Interdisciplinary Journal of Nonlinear Science, 21, 013101, https://doi.org/10.1063/1.3545273, 2011. a
Boaretto, B. R., Budzinski, R. C., Rossi, K. L., Masoller, C., and Macau, E. E.: Spatial permutation entropy distinguishes resting brain states, Chaos Soliton. Fract., 171, 113453, https://doi.org/10.1016/j.chaos.2023.113453, 2023. a
Boers, N., Goswami, B., Rheinwalt, A., Bookhagen, B., Hoskins, B., and Kurths, J.: Complex networks reveal global pattern of extreme-rainfall teleconnections, Nature, 566, 373, https://doi.org/10.1038/s41586-018-0872-x, 2019. a
Bulgin, C. E., Merchant, C. J., and Ferreira, D.: Tendencies, variability and persistence of sea surface temperature anomalies, Sci. Rep.-UK, 10, 7986, https://doi.org/10.1038/s41598-020-64785-9, 2020. a
Celik, T.: Spatial mutual information and PageRank-based contrast enhancement and quality-aware relative contrast measure, IEEE T. Image Process., 25, 4719–4728, https://doi.org/10.1109/TIP.2016.2599103, 2016. a
Comunian, A., Giudici, M., and Panzeri, A.: A Bayesian approach to map oceanic structures, with an application to the Gulf Stream, J. Marine Syst., 253, 104175, https://doi.org/10.1016/j.jmarsys.2025.104175, 2026. a
Dai, A.: The diurnal cycle from observations and ERA5 in surface pressure, temperature, humidity, and winds, Clim. Dynam., 61, 2965–2990, https://doi.org/10.1007/s00382-023-06721-x, 2023. a
Deza, J. I., Barreiro, M., and Masoller, C.: Inferring interdependencies in climate networks constructed at inter-annual, intra-season and longer time scales, Eur. Phys. J. Special Topics, 222, 511–523, https://doi.org/10.1140/epjst/e2013-01856-5, 2013. a, b
Díaz, N., Barreiro, M., and Rubido, N.: Data driven models of the Madden-Julian Oscillation: understanding its evolution and ENSO modulation, npj Climate and Atmospheric Science, 6, 203, https://doi.org/10.1038/s41612-023-00527-8, 2023. a
Dijkstra, H. A., Hernandez-Garcia, E., Masoller, C., and Barreiro, M.: Networks in Climate, Cambridge University Press, https://doi.org/10.1017/9781316275757, 2019. a
Dong, S. and Kelly, K. A.: Heat budget in the Gulf Stream region: the importance of heat storage and advection, J. Phys. Oceanogr., 34, 1214–1231, https://doi.org/10.1175/1520-0485(2004)034<1214:HBITGS>2.0.CO;2, 2004. a
Donlon, C. J., Martin, M., Stark, J., Roberts-Jones, J., Fiedler, E., and Wimmer, W.: The Operational Sea Surface Temperature and Sea Ice Analysis (OSTIA) system, Remote Sens. Environ., 116, 140–158, https://doi.org/10.1016/j.rse.2010.10.017, 2012. a
Fadlallah, B., Chen, B., Keil, A., and Príncipe, J.: Weighted-permutation entropy: a complexity measure for time series incorporating amplitude information, Phys. Rev. E, 87, 022911, https://doi.org/10.1103/PhysRevE.87.022911, 2013. a, b
Falasca, F., Crétat, J., Braconnot, P., and Bracco, A.: Spatiotemporal complexity and time-dependent networks in sea surface temperature from mid-to late Holocene, Eur. Phys. J. Plus, 135, 392, https://doi.org/10.1140/epjp/s13360-020-00403-x, 2020. a
Gancio, J.: juangancio/climate-spatial-analysis: Supporting code for EDS submission: “Detecting transitions and quantifying differences in two SST datasets using spatial permutation entropy” (v2.0.0), Zenodo [code], https://doi.org/10.5281/zenodo.17250157, 2025. a
Gancio, J.: Supplemental videos for ESD article “Detecting transitions and quantifying differences in two SST datasets using spatial permutation entropy”, Zenodo [video], https://doi.org/10.5281/zenodo.19051869, 2026. a
Gancio, J., Masoller, C., and Tirabassi, G.: Permutation entropy analysis of EEG signals for distinguishing eyes-open and eyes-closed brain states: comparison of different approaches, Chaos, 34, 043130, https://doi.org/10.1063/5.0200029, 2024. a
Garreau, D. and Arlot, S.: Consistent change-point detection with kernels, Electron. J. Stat., 12, 4440–4486, https://doi.org/10.1214/18-EJS1513, 2018. a
Good, S., Fiedler, E., Mao, C., Martin, M. J., Maycock, A., Reid, R., Roberts-Jones, J., Searle, T., Waters, J., While, J., and Worsfold, M.: The current configuration of the OSTIA system for operational production of foundation sea surface temperature and ice concentration analyses, Remote Sens.-Basel, 12, 720, https://doi.org/10.3390/rs12040720, 2020. a
Gupta, S., Boers, N., Pappenberger, F., and Kurths, J.: Complex network approach for detecting tropical cyclones, Clim. Dynam., 57, 3355–3364, https://doi.org/10.1007/s00382-021-05871-0, 2021. a
Haynes, K., Eckley, I. A., and Fearnhead, P.: Computationally efficient changepoint detection for a range of penalties, J. Comput. Graph. Stat., 26, 134–143, https://doi.org/10.1080/10618600.2015.1116445, 2017. a
Hersbach, H., Bell, B., Berrisford, P., Hirahara, S., Horányi, A., Muñoz-Sabater, J., Nicolas, J., Peubey, C., Radu, R., Schepers, D., Simmons, A., Soci, C., Abdalla, S., Abellan, X., Balsamo, G., Bechtold, P., Biavati, G., Bidlot, J., Bonavita, M., De Chiara, G., Dahlgren, P., Dee, D., Diamantakis, M., Dragani, R., Flemming, J., Forbes, R., Fuentes, M., Geer, A., Haimberger, L., Healy, S., Hogan, R. J., Hólm, E., Janisková, M., Keeley, S., Laloyaux, P., Lopez, P., Lupu, C., Radnoti, G., de Rosnay, P., Rozum, I., Vamborg, F., Villaume, S., and Thépaut, J. N.: The ERA5 global reanalysis, Q. J. Roy. Meteor. Soc., 146, 1999–2049, https://doi.org/10.1002/qj.3803, 2020. a, b, c
Hersbach, H., Bell, B., Berrisford, P., Biavati, G., Horányi, A., Muñoz Sabater, J., Nicolas, J., Peubey, C., Radu, R., Rozum, I., Schepers, D., Simmons, A., Soci, C., Dee, D., and Thépaut, J.-N.: ERA5 monthly averaged data on single levels from 1940 to present, Copernicus Climate Change Service (C3S) Climate Data Store (CDS) [data set], https://doi.org/10.24381/cds.f17050d7, 2023. a
Huang, B., Liu, C., Banzon, V., Freeman, E., Graham, G., Hankins, B., Smith, T., and Zhang, H.-M.: Improvements of the daily optimum interpolation sea surface temperature (DOISST) version 2.1, J. Climate, 34, 2923–2939, https://doi.org/10.1175/JCLI-D-20-0166.1, 2021. a, b, c
Huang, B., Yin, X., Carton, J. A., Chen, L., Graham, G., Liu, C., Smith, T., and Zhang, H.-M.: Understanding differences in sea surface temperature intercomparisons, J. Atmos. Ocean. Tech., 40, 455–473, https://doi.org/10.1175/JTECH-D-22-0081.1, 2023. a, b, c, d
Ikuyajolu, O. J., Falasca, F., and Bracco, A.: Information entropy as quantifier of potential predictability in the tropical Indo-Pacific basin, Frontiers in Climate, 3, 675840, https://doi.org/10.3389/fclim.2021.675840, 2021. a
Jonasson, O., Gladkova, I., Ignatov, A., and Kihai, Y.: Progress with development of global gridded super-collated SST products from low Earth orbiting satellites (L3S-LEO) at NOAA, in: Ocean Sensing and Monitoring XII, Vol. 11420, SPIE, https://doi.org/10.1117/12.2551819, 5–22, 2020. a, b
Khapalova, E. A., Jandhyala, V. K., Fotopoulos, S. B., and Overland, J. E.: Assessing change-points in surface air temperature over Alaska, Frontiers in Environmental Science, 6, 121, https://doi.org/10.3389/fenvs.2018.00121, 2018. a
Killick, R., Fearnhead, P., and Eckley, I. A.: Optimal detection of changepoints with a linear computational cost, J. Am. Stat. Assoc., 107, 1590–1598, https://doi.org/10.1080/01621459.2012.737745, 2012. a, b
Krouma, M., Specq, D., Magnusson, L., Ardilouze, C., Batté, L., and Yiou, P.: Improving subseasonal forecast of precipitation in Europe by combining a stochastic weather generator with dynamical models, Q. J. Roy. Meteor. Soc., https://doi.org/10.1002/qj.4733, 2024. a
Kumar, R. and Bhandari, A. K.: Spatial mutual information based detail preserving magnetic resonance image enhancement, Comput. Biol. Med., 146, 105644, https://doi.org/10.1016/j.compbiomed.2022.105644, 2022. a
Leyva, I., Martínez, J. H., Masoller, C., Rosso, O. A., and Zanin, M.: 20 years of ordinal patterns: Perspectives and challenges, Europhysics Letters, 138, 31001, https://doi.org/10.1209/0295-5075/ac6a72, 2022. a
Messori, G., Caballero, R., and Faranda, D.: A dynamical systems approach to studying midlatitude weather extremes, Geophys. Res. Lett., 44, 3346–3354, https://doi.org/10.1002/2017GL072879, 2017. a
Muñoz-Guillermo, M.: Multiscale two-dimensional permutation entropy to analyze encrypted images, Chaos: An Interdisciplinary Journal of Nonlinear Science, 33, 013112, https://doi.org/10.1063/5.0130538, 2023. a
Novi, L., Bracco, A., Ito, T., and Takano, Y.: Evolution of oxygen and stratification and their relationship in the North Pacific Ocean in CMIP6 Earth system models, Biogeosciences, 21, 3985–4005, https://doi.org/10.5194/bg-21-3985-2024, 2024. a
Paluš, M., Chvosteková, M., and Manshour, P.: Causes of extreme events revealed by Rényi information transfer, Science Advances, 10, eadn1721, https://doi.org/10.1126/sciadv.adn1721, 2024. a
Parfitt, R. and Czaja, A.: On the contribution of synoptic transients to the mean atmospheric state in the Gulf Stream region, Q. J. Roy. Meteor. Soc., 142, 1554–1561, https://doi.org/10.1002/qj.2689, 2016. a
Politi, A.: Quantifying the dynamical complexity of chaotic time series, Phys. Rev. Lett., 118, 144101, https://doi.org/10.1103/PhysRevLett.118.144101, 2017. a
Prado, T., Corso, G., dos Santos Lima, G., Budzinski, R., Boaretto, B., Ferrari, F., Macau, E., and Lopes, S.: Maximum entropy principle in recurrence plot analysis on stochastic and chaotic systems, Chaos: An Interdisciplinary Journal of Nonlinear Science, 30, https://doi.org/10.1063/1.5125921, 2020. a
Reynolds, R. W., Smith, T. M., Liu, C., Chelton, D. B., Casey, K. S., and Schlax, M. G.: Daily high-resolution-blended analyses for sea surface temperature, J. Climate, 20, 5473–5496, https://doi.org/10.1175/2007JCLI1824.1, 2007. a
Ribeiro, H. V., Zunino, L., Lenzi, E. K., Santoro, P. A., and Mendes, R. S.: Complexity-entropy causality plane as a complexity measure for two-dimensional patterns, PLoS One, 7, 1–9, https://doi.org/10.1371/journal.pone.0040689, 2012. a
Roberts-Jones, J., Bovis, K., Martin, M. J., and McLaren, A.: Estimating background error covariance parameters and assessing their impact in the OSTIA system, Remote Sens. Environ., 176, 117–138, https://doi.org/10.1016/j.rse.2015.12.006, 2016. a
Rocha, R. V. and de Souza Filho, F. d. A.: Mapping abrupt streamflow shift in an abrupt climate shift through multiple change point methodologies: Brazil case study, Hydrolog. Sci. J., 65, 2783–2796, https://doi.org/10.1080/02626667.2020.1843657, 2020. a
Schlemmer, A., Berg, S., Shajahan, T., Luther, S., and Parlitz, U.: Quantifying spatiotemporal complexity of cardiac dynamics using ordinal patterns, in: 2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), IEEE, https://doi.org/10.1109/EMBC.2015.7319283, 4049–4052, 2015. a
Schlemmer, A., Berg, S., Lilienkamp, T., Luther, S., and Parlitz, U.: Spatiotemporal permutation entropy as a measure for complexity of cardiac arrhythmia, AIP Conf. Proc., 6, 39, https://doi.org/10.3389/fphy.2018.00039, 2018. a
Schreiber, T. and Schmitz, A.: Improved surrogate data for nonlinearity tests, Phys. Rev. Lett., 77, 635–638, https://doi.org/10.1103/PhysRevLett.77.635, 1996. a, b, c
Seidov, D., Mishonov, A., Reagan, J., and Parsons, R.: Multidecadal variability and climate shift in the North Atlantic Ocean, Geophys. Res. Lett., 44, 4985–4993, https://doi.org/10.1002/2017GL073644, 2017. a
Sigaki, H. Y. D., Perc, M., and Ribeiro, H. V.: History of art paintings through the lens of entropy and complexity, PNAS, 115, E8585–E8594, https://doi.org/10.1073/pnas.1800083115, 2018. a
Sigaki, H. Y. D., de Souza, R. F., de Souza, R. T., Zola, R. S., and Ribeiro, H. V.: Estimating physical properties from liquid crystal textures via machine learning and complexity-entropy methods, Phys. Rev. E, 99, 013311, https://doi.org/10.1103/PhysRevE.99.013311, 2019. a
Tarozo, M. M., Pessa, A. A. B., Zunino, L., Rosso, O. A., Perc, M., and Ribeiro, H. V.: Two-by-two ordinal patterns in art paintings, PNAS Nexus, 4, pgaf092, https://doi.org/10.1093/pnasnexus/pgaf092, 2025. a
Tirabassi, G. and Masoller, C.: Entropy-based early detection of critical transitions in spatial vegetation fields, P. Natl. Acad. Sci. USA, 120, e2215667120, https://doi.org/10.1073/pnas.2215667120, 2023. a
Tirabassi, G., Duque-Gijon, M., Tiana-Alsina, J., and Masoller, C.: Permutation entropy-based characterization of speckle patterns generated by semiconductor laser light, APL Photonics, 8, 126112, https://doi.org/10.1063/5.0169445, 2023. a
Titchner, H. A. and Rayner, N. A.: The Met Office Hadley Centre sea ice and sea surface temperature data set, version 2: 1. Sea ice concentrations, J. Geophys. Res.-Atmos., 119, 2864–2889, https://doi.org/10.1002/2013JD020316, 2014. a
Todd, R. E. and Ren, A. S.: Warming and lateral shift of the Gulf Stream from in situ observations since 2001, Nat. Clim. Change, 13, 1348–1352, https://doi.org/10.1038/s41558-023-01835-w, 2023. a
Truong, C., Oudre, L., and Vayatis, N.: Selective review of offline change point detection methods, Signal Process., 167, 107299, https://doi.org/10.1016/j.sigpro.2019.107299, 2020. a, b
Vries, H. D., Scher, S., Haarsma, R., Drijfhout, S., and Delden, A. V.: How Gulf-Stream SST-fronts influence Atlantic winter storms: results from a downscaling experiment with HARMONIE to the role of modified latent heat fluxes and low-level baroclinicity, Clim. Dynam., 52, 5899–5909, https://doi.org/10.1007/s00382-018-4486-7, 2019. a
Wang, S. and Fan, F.: Analysis of the response of long-term vegetation dynamics to climate variability using the Pruned Exact Linear Time (PELT) Method and Disturbance Lag Model (DLM) based on remote sensing data: a case study in Guangdong Province (China), Remote Sens.-Basel, 13, 1873, https://doi.org/10.3390/rs13101873, 2021. a
Wills, R. C. J., Dong, Y., Proistosecu, C., Armour, K. C., and Battisti, D. S.: Systematic climate model biases in the large-scale patterns of recent sea-surface temperature and sea-level pressure change, Geophys. Res. Lett., 49, e2022GL100011, https://doi.org/10.1029/2022GL100011, 2022. a
Xie, S.-P., Deser, C., Vecchi, G. A., Ma, J., Teng, H., and Wittenberg, A. T.: Global warming pattern formation: sea surface temperature and rainfall, J. Climate, 23, 966–986, https://doi.org/10.1175/2009JCLI3329.1, 2010. a
Yao, L., Lu, J., Xia, X., Jing, W., and Liu, Y.: Evaluation of the ERA5 sea surface temperature around the Pacific and the Atlantic, IEEE Access, 9, 12067–12073, https://doi.org/10.1109/ACCESS.2021.3051642, 2021. a
Zeng, X. and He, R.: Gulf Stream variability and a triggering mechanism of its large meander in the South Atlantic Bight, J. Geophys. Res.-Oceans, 121, 8021–8038, https://doi.org/10.1002/2016JC012077, 2016. a
Short summary
In this work, we apply a novel quantifier, the spatial permutation entropy, to sea surface temperatures obtained from two commonly used products: ERA5 and NOAA OI v2 (NOAA Optimal Interpolation version 2). We report small scale differences between these products, as well as persistent trends at the large scale, which could be a consequence of global warming. We also report sudden changes that were not uncovered before, which correlate with different changes in the methodology or data sources of the products.
In this work, we apply a novel quantifier, the spatial permutation entropy, to sea surface...
Altmetrics
Final-revised paper
Preprint