Articles | Volume 20, issue 6
https://doi.org/10.5194/os-20-1567-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Special issue:
https://doi.org/10.5194/os-20-1567-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
02 Dec 2024
Research article |
| 02 Dec 2024
| 02 Dec 2024
Ensemble reconstruction of missing satellite data using a denoising diffusion model: application to chlorophyll a concentration in the Black Sea
GeoHydrodynamics and Environment Research (GHER), FOCUS, University of Liège, Liège, Belgium
Julien Brajard
Nansen Environmental and Remote Sensing Center and Bjerknes Centre for Climate Research, Bergen 5007, Norway
Aida Alvera-Azcárate
GeoHydrodynamics and Environment Research (GHER), FOCUS, University of Liège, Liège, Belgium
Bayoumy Mohamed
GeoHydrodynamics and Environment Research (GHER), FOCUS, University of Liège, Liège, Belgium
Charles Troupin
GeoHydrodynamics and Environment Research (GHER), FOCUS, University of Liège, Liège, Belgium
Jean-Marie Beckers
GeoHydrodynamics and Environment Research (GHER), FOCUS, University of Liège, Liège, Belgium
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Earth-observing satellites provide routine measurement of several ocean parameters. However, these datasets have a significant amount of missing data due to the presence of clouds or other limitations of the employed sensors. This paper describes a method to infer the value of the missing satellite data based on a convolutional autoencoder (a specific type of neural network architecture). The technique also provides a reliable error estimate of the interpolated value.
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Zikang He, Julien Brajard, Yiguo Wang, Xidong Wang, and Zheqi Shen
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Matjaž Zupančič Muc, Vitjan Zavrtanik, Alexander Barth, Aida Alvera-Azcarate, Matjaž Ličer, and Matej Kristan
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Accurate sea surface temperature data (SST) is crucial for weather forecasting and climate modeling, but satellite observations are often incomplete. We developed a new method called CRITER, which uses machine learning to fill in the gaps in SST data. Our two-stage approach reconstructs large-scale patterns and refines details. Tested on Mediterranean, Adriatic, and Atlantic seas data, CRITER outperforms current methods, reducing errors by up to 44 %.
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Simon Driscoll, Alberto Carrassi, Julien Brajard, Laurent Bertino, Einar Ólason, Marc Bocquet, and Amos Lawless
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Manal Hamdeno, Aida Alvera-Azcárate, George Krokos, and Ibrahim Hoteit
Ocean Sci., 20, 1087–1107, https://doi.org/10.5194/os-20-1087-2024, https://doi.org/10.5194/os-20-1087-2024, 2024
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Our study focuses on the characteristics of MHWs in the Red Sea during the last 4 decades. Using satellite-derived sea surface temperatures (SSTs), we found a clear warming trend in the Red Sea since 1994, which has intensified significantly since 2016. This SST rise was associated with an increase in the frequency and days of MHWs. In addition, a correlation was found between the frequency of MHWs and some climate modes, which was more pronounced in some years of the study period.
Cyril Palerme, Thomas Lavergne, Jozef Rusin, Arne Melsom, Julien Brajard, Are Frode Kvanum, Atle Macdonald Sørensen, Laurent Bertino, and Malte Müller
The Cryosphere, 18, 2161–2176, https://doi.org/10.5194/tc-18-2161-2024, https://doi.org/10.5194/tc-18-2161-2024, 2024
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Sea ice forecasts are operationally produced using physically based models, but these forecasts are often not accurate enough for maritime operations. In this study, we developed a statistical correction technique using machine learning in order to improve the skill of short-term (up to 10 d) sea ice concentration forecasts produced by the TOPAZ4 model. This technique allows for the reduction of errors from the TOPAZ4 sea ice concentration forecasts by 41 % on average.
Pamela Linford, Iván Pérez-Santos, Paulina Montero, Patricio A. Díaz, Claudia Aracena, Elías Pinilla, Facundo Barrera, Manuel Castillo, Aida Alvera-Azcárate, Mónica Alvarado, Gabriel Soto, Cécile Pujol, Camila Schwerter, Sara Arenas-Uribe, Pilar Navarro, Guido Mancilla-Gutiérrez, Robinson Altamirano, Javiera San Martín, and Camila Soto-Riquelme
Biogeosciences, 21, 1433–1459, https://doi.org/10.5194/bg-21-1433-2024, https://doi.org/10.5194/bg-21-1433-2024, 2024
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The Patagonian fjords comprise a world region where low-oxygen water and hypoxia conditions are observed. An in situ dataset was used to quantify the mechanism involved in the presence of these conditions in northern Patagonian fjords. Water mass analysis confirmed the contribution of Equatorial Subsurface Water in the advection of the low-oxygen water, and hypoxic conditions occurred when the community respiration rate exceeded the gross primary production.
Francesca Doglioni, Robert Ricker, Benjamin Rabe, Alexander Barth, Charles Troupin, and Torsten Kanzow
Earth Syst. Sci. Data, 15, 225–263, https://doi.org/10.5194/essd-15-225-2023, https://doi.org/10.5194/essd-15-225-2023, 2023
Short summary
Short summary
This paper presents a new satellite-derived gridded dataset, including 10 years of sea surface height and geostrophic velocity at monthly resolution, over the Arctic ice-covered and ice-free regions, up to 88° N. We assess the dataset by comparison to independent satellite and mooring data. Results correlate well with independent satellite data at monthly timescales, and the geostrophic velocity fields can resolve seasonal to interannual variability of boundary currents wider than about 50 km.
Georges Baaklini, Roy El Hourany, Milad Fakhri, Julien Brajard, Leila Issa, Gina Fifani, and Laurent Mortier
Ocean Sci., 18, 1491–1505, https://doi.org/10.5194/os-18-1491-2022, https://doi.org/10.5194/os-18-1491-2022, 2022
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We use machine learning to analyze the long-term variation of the surface currents in the Levantine Sea, located in the eastern Mediterranean Sea. We decompose the circulation into groups based on their physical characteristics and analyze their spatial and temporal variability. We show that most structures of the Levantine Sea are becoming more energetic over time, despite those of the western area remaining the most dominant due to their complex bathymetry and strong currents.
Alexander Barth, Aida Alvera-Azcárate, Charles Troupin, and Jean-Marie Beckers
Geosci. Model Dev., 15, 2183–2196, https://doi.org/10.5194/gmd-15-2183-2022, https://doi.org/10.5194/gmd-15-2183-2022, 2022
Short summary
Short summary
Earth-observing satellites provide routine measurement of several ocean parameters. However, these datasets have a significant amount of missing data due to the presence of clouds or other limitations of the employed sensors. This paper describes a method to infer the value of the missing satellite data based on a convolutional autoencoder (a specific type of neural network architecture). The technique also provides a reliable error estimate of the interpolated value.
Malek Belgacem, Katrin Schroeder, Alexander Barth, Charles Troupin, Bruno Pavoni, Patrick Raimbault, Nicole Garcia, Mireno Borghini, and Jacopo Chiggiato
Earth Syst. Sci. Data, 13, 5915–5949, https://doi.org/10.5194/essd-13-5915-2021, https://doi.org/10.5194/essd-13-5915-2021, 2021
Short summary
Short summary
The Mediterranean Sea exhibits an anti-estuarine circulation, responsible for its low productivity. Understanding this peculiar character is still a challenge since there is no exact quantification of nutrient sinks and sources. Because nutrient in situ observations are generally infrequent and scattered in space and time, climatological mapping is often applied to sparse data in order to understand the biogeochemical state of the ocean. The dataset presented here partly addresses these issues.
Estrella Olmedo, Verónica González-Gambau, Antonio Turiel, Cristina González-Haro, Aina García-Espriu, Marilaure Gregoire, Aida Álvera-Azcárate, Luminita Buga, and Marie-Hélène Rio
Earth Syst. Sci. Data Discuss., https://doi.org/10.5194/essd-2021-364, https://doi.org/10.5194/essd-2021-364, 2021
Revised manuscript not accepted
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We present the first dedicated satellite salinity product in the Black Sea. We use the measurements provided by the European Soil Moisture and Ocean Salinity mission. We introduce enhanced algorithms for dealing with the contamination produced by the Radio Frequency Interferences that strongly affect this basin. We also provide a complete quality assessment of the new product and give an estimated accuracy of it.
Sylvain Watelet, Øystein Skagseth, Vidar S. Lien, Helge Sagen, Øivind Østensen, Viktor Ivshin, and Jean-Marie Beckers
Earth Syst. Sci. Data, 12, 2447–2457, https://doi.org/10.5194/essd-12-2447-2020, https://doi.org/10.5194/essd-12-2447-2020, 2020
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We present here a seasonal atlas of the Barents Sea including both temperature and salinity for the period 1965–2016. This atlas is curated using several in situ data sources interpolated thanks to the tool DIVA minimizing the expected errors. The results show a recent "Atlantification" of the Barents Sea, i.e., a general increase in both temperature and salinity, while its density remains stable. The atlas is made freely accessible (https://doi.org/10.21335/NMDC-2058021735).
Cited articles
Alvera-Azcárate, A., Barth, A., Parard, G., and Beckers, J.-M.: Analysis of SMOS sea surface salinity data using DINEOF, Remote Sens. Environ., 180, 137–145, https://doi.org/10.1016/j.rse.2016.02.044, special Issue: ESA's Soil Moisture and Ocean Salinity Mission – Achievements and Applications, 2016. a
Alvera-Azcárate, A., Van der Zande, D., Barth, A., Troupin, C., Martin, S., and Beckers, J.-M.: Analysis of 23 years of daily cloud-free chlorophyll and suspended particulate matter in the Greater North Sea, Frontiers in Marine Science, 8, 707632, https://doi.org/10.3389/fmars.2021.707632, 2021. a, b
Barth, A.: gher-uliege/DINDiff.jl: 0.1.0 (v0.1.0), Zenodo [data set], https://doi.org/10.5281/zenodo.13165363, 2024. a
Barth, A., Alvera-Azcárate, A., Licer, M., and Beckers, J.-M.: DINCAE 1.0: a convolutional neural network with error estimates to reconstruct sea surface temperature satellite observations, Geosci. Model Dev., 13, 1609–1622, https://doi.org/10.5194/gmd-13-1609-2020, 2020. a, b, c, d
Barth, A., Alvera-Azcárate, A., Troupin, C., and Beckers, J.-M.: DINCAE 2.0: multivariate convolutional neural network with error estimates to reconstruct sea surface temperature satellite and altimetry observations, Geosci. Model Dev., 15, 2183–2196, https://doi.org/10.5194/gmd-15-2183-2022, 2022. a, b, c, d
Bergstra, J. and Bengio, Y.: Random Search for Hyper-Parameter Optimization, J. Mach. Lear. Res., 13, 281–305, http://www.jmlr.org/papers/v13/bergstra12a.html (last access: 2 February 2024), 2012. a
Besard, T., Foket, C., and De Sutter, B.: Effective Extensible Programming: Unleashing Julia on GPUs, in: IEEE Transactions on Parallel and Distributed Systems, Vol. 30, 827–841, https://doi.org/10.1109/TPDS.2018.2872064, 2018. a
Besard, T., Churavy, V., Edelman, A., and De Sutter, B.: Rapid software prototyping for heterogeneous and distributed platforms, Adv. Eng. Softw., 132, 29–46, 2019. a
Bezanson, J., Edelman, A., Karpinski, S., and Shah, V. B.: Julia: A fresh approach to numerical computing, SIAM Rev., 59, 65–98, https://doi.org/10.1137/141000671, 2017. a
Buizza, R., Leutbecher, M., and Isaksen, L.: Potential use of an ensemble of analyses in the ECMWF Ensemble Prediction System, Q. J. Roy. Meteor. Soc., 134, 2051–2066, https://doi.org/10.1002/qj.346, 2008. a
Candille, G., Côté, C., Houtekamer, P. L., and Pellerin, G.: Verification of an Ensemble Prediction System against Observations, Mon. Weather Rev., 135, 2688–2699, https://doi.org/10.1175/MWR3414.1, 2007. a
Cressie, N.: Statistics for Spatial Data, A Wiley-interscience publication, J. Wiley, ISBN 9780471843368, 1991. a
Dhariwal, P. and Nichol, A.: Diffusion Models Beat GANs on Image Synthesis, in: Advances in Neural Information Processing Systems, Vol. 34, edited by: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P., and Vaughan, J. W., Curran Associates, Inc., 8780–8794, https://proceedings.neurips.cc/paper_files/paper/2021/file/49ad23d1ec9fa4bd8d77d02681df5cfa-Paper.pdf (last access: 28 March 2024), 2021. a, b
European Union-Copernicus Marine Service: Black Sea, Bio-Geo-Chemical, L3, daily Satellite Observations (1997–ongoing), https://doi.org/10.48670/moi-00303, dataset ID
cmems_obs-oc_blk_bgc-plankton_my_l3-olci-300m_P1D, dataset accessed: 26 September 2023, 2022. a, b
Evensen, G.: Data assimilation: the Ensemble Kalman Filter, 2nd edition, Springer, https://doi.org/10.1007/978-3-642-03711-5, 2009. a
Feller, W.: On the Theory of Stochastic Processes, with Particular Reference to Applications, in: Berkeley Symp. on Math. Statist. and Prob., 27–29 January 1946, Berkeley, California, USA, University of California Press, 403–432, 1949. a
Feng, L. and Hu, C.: Comparison of Valid Ocean Observations Between MODIS Terra and Aqua Over the Global Oceans, IEEE T. Geosci. Remote, 54, 1575–1585, https://doi.org/10.1109/tgrs.2015.2483500, 2016. a
Goh, E., Yepremyan, A. R., Wang, J., and Wilson, B.: MAESSTRO: Masked Autoencoders for Sea Surface Temperature Reconstruction under Occlusion, EGUsphere [preprint], https://doi.org/10.5194/egusphere-2023-1385, 2023. a
Goodfellow, I., Bengio, Y., and Courville, A.: Deep Learning, MIT Press, ISBN 978-0262035613, http://www.deeplearningbook.org (last access: 28 March 2024), 2016. a
Hamill, T. M.: Interpretation of Rank Histograms for Verifying Ensemble Forecasts, Mon. Weather Rev., 129, 550–560, https://doi.org/10.1175/1520-0493(2001)129<0550:IORHFV>2.0.CO;2, 2001. a
Han, Z., He, Y., Liu, G., and Perrie, W.: Application of DINCAE to Reconstruct the Gaps in Chlorophyll-a Satellite Observations in the South China Sea and West Philippine Sea, Remote Sens.-Basel, 12, 480, https://doi.org/10.3390/rs12030480, 2020. a
Hersbach, H.: Decomposition of the Continuous Ranked Probability Score for Ensemble Prediction Systems, Weather Forecast., 15, 559–570, https://doi.org/10.1175/1520-0434(2000)015<0559:DOTCRP>2.0.CO;2, 2000. a, b
Ho, J. and Salimans, T.: Classifier-Free Diffusion Guidance, NeurIPS 2021 Workshop on Deep Generative Models and Downstream Applications, arXiv, https://doi.org/10.48550/arXiv.2207.12598, 2022. a
Hong, Z., Long, D., Li, X., Wang, Y., Zhang, J., Hamouda, M. A., and Mohamed, M. M.: A global daily gap-filled chlorophyll-a dataset in open oceans during 2001–2021 from multisource information using convolutional neural networks, Earth Syst. Sci. Data, 15, 5281–5300, https://doi.org/10.5194/essd-15-5281-2023, 2023. a
Innes, M.: Flux: Elegant Machine Learning with Julia, Journal of Open Source Software, 3, 602, https://doi.org/10.21105/joss.00602, 2018. a
Innes, M., Saba, E., Fischer, K., Gandhi, D., Rudilosso, M. C., Joy, N. M., Karmali, T., Pal, A., and Shah, V.: Fashionable Modelling with Flux, CoRR, arXiv, arXiv:abs/1811.01457, 2018. a
Jensen, J. L. W. V.: Sur les fonctions convexes et les inégalités entre les valeurs moyennes, Acta Math., 30, 175–193, https://doi.org/10.1007/bf02418571, 1906. a
Ji, C., Zhang, Y., Cheng, Q., and Tsou, J. Y.: Investigating ocean surface responses to typhoons using reconstructed satellite data, Int. J. Appl. Earth Obs., 103, 102 474, https://doi.org/10.1016/j.jag.2021.102474, 2021. a
Jung, S., Yoo, C., and Im, J.: High-Resolution Seamless Daily Sea Surface Temperature Based on Satellite Data Fusion and Machine Learning over Kuroshio Extension, Remote Sens.-Basel, 14, 575, https://doi.org/10.3390/rs14030575, 2022. a
Kajiyama, T., D'Alimonte, D., and Zibordi, G.: Algorithms Merging for the Determination of Chlorophyll-a Concentration in the Black Sea, IEEE Geosci. Remote S., 16, 677–681, https://doi.org/10.1109/lgrs.2018.2883539, 2019. a
Kingma, D. P. and Ba, J.: Adam: A Method for Stochastic Optimization, CoRR, arXiv, arXiv:abs/1412.6980, 2014. a
Lee, Z., Carder, K. L., and Arnone, R. A.: Deriving inherent optical properties from water color: a multiband quasi-analytical algorithm for optically deep waters, Appl. Optics, 41, 5755, https://doi.org/10.1364/ao.41.005755, 2002. a
Lugmayr, A., Danelljan, M., Romero, A., Yu, F., Timofte, R., and Gool, L. V.: RePaint: Inpainting using Denoising Diffusion Probabilistic Models, in 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), New Orleans, LA, USA, 11451–11461, https://doi.org/10.1109/CVPR52688.2022.01117, 2022. a
Luo, X., Song, J., Guo, J., Fu, Y., Wang, L., and Cai, Y.: Reconstruction of chlorophyll-a satellite data in Bohai and Yellow sea based on DINCAE method, Int. J. Remote Sens., 43, 3336–3358, https://doi.org/10.1080/01431161.2022.2090872, 2022. a
Matheron, G.: Traité de géostatistique appliquée, no. v. 1 in Memoires, Éditions Technip, OCLC Number 491866302, 1962. a
Mikelsons, K. and Wang, M.: Optimal satellite orbit configuration for global ocean color product coverage, Opt. Express, 27, A445–A457, https://doi.org/10.1364/OE.27.00A445, 2019. a
Pujol, C., Pérez-Santos, I., Barth, A., and Alvera-Azcárate, A.: Marine Heatwaves Offshore Central and South Chile: Understanding Forcing Mechanisms During the Years 2016–2017, Frontiers in Marine Science, 9, https://doi.org/10.3389/fmars.2022.800325, 2022. 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
Ronneberger, O., Fischer, P., and Brox, T.: U-Net: Convolutional Networks for Biomedical Image Segmentation, in: Medical Image Computing and Computer-Assisted Intervention – MICCAI 2015, edited by Navab, N., Hornegger, J., Wells, W. M., and Frangi, A. F., Springer International Publishing, Cham, ISBN 978-3-319-24574-4, https://doi.org/10.1007/978-3-319-24574-4_28, 234–241, 2015. a, b
Saharia, C., Ho, J., Chan, W., Salimans, T., Fleet, D. J., and Norouzi, M.: Image Super-Resolution via Iterative Refinement, IEEE Transactions on Pattern Analysis and Machine Intelligence, 45, 4713–4726, https://doi.org/10.1109/TPAMI.2022.3204461, 2023. a
Saulquin, B., Gohin, F., and Garrello, R.: Regional Objective Analysis for Merging High-Resolution MERIS, MODIS/Aqua, and SeaWiFS Chlorophyll-a Data From 1998 to 2008 on the European Atlantic Shelf, IEEE T. Geosci. Remote, 49, 143–154, https://doi.org/10.1109/TGRS.2010.2052813, 2011. a
Sohl-Dickstein, J., Weiss, E., Maheswaranathan, N., and Ganguli, S.: Deep Unsupervised Learning using Nonequilibrium Thermodynamics, in: Proceedings of the 32nd International Conference on Machine Learning, edited by Bach, F. and Blei, D., vol. 37 of Proceedings of Machine Learning Research, 2256–2265, PMLR, Lille, France, arXiv, https://doi.org/10.48550/arXiv.1503.03585, 2015. a, b
Talagrand, O., Vautard, R., and Strauss, B.: Evaluation of probabilistic prediction systems, in: Proceedings, ECMWF Workshop on Predictability, ECMWF, 20–22 October 1997, Shinfield Park, Reading, UK, 1–25, https://www.ecmwf.int/sites/default/files/elibrary/1997/76596-evaluation-probabilistic-prediction-systems_0.pdf (last access: 5 February 2024), 1997. a
Wackernagel, H.: Multivariate Geostatistics: an introduction with applications, 3rd edn., Springer-Verlag, https://doi.org/10.1007/978-3-662-05294-5, 2003. a
Wylie, D., Jackson, D. L., Menzel, W. P., and Bates, J. J.: Trends in Global Cloud Cover in Two Decades of HIRS Observations, J. Climate, 18, 3021–3031, https://doi.org/10.1175/JCLI3461.1, 2005. a
Zibordi, G., Mélin, F., Berthon, J.-F., and Talone, M.: In situ autonomous optical radiometry measurements for satellite ocean color validation in the Western Black Sea, Ocean Sci., 11, 275–286, https://doi.org/10.5194/os-11-275-2015, 2015. a
Short summary
Most satellite observations have gaps, for example, due to clouds. This paper presents a method to reconstruct missing data in satellite observations of the chlorophyll a concentration in the Black Sea. Rather than giving a single possible reconstructed field, the discussed method provides an ensemble of possible reconstructions using a generative neural network. The resulting ensemble is validated using techniques from numerical weather prediction and ocean modelling.
Most satellite observations have gaps, for example, due to clouds. This paper presents a method...
