Articles | Volume 18, issue 14
https://doi.org/10.5194/gmd-18-4685-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-18-4685-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Model description paper
| 
30 Jul 2025
Model description paper |
| 30 Jul 2025
| 30 Jul 2025
Comparing an idealized deterministic–stochastic model (SUP model, version 1) of the tide- and wind-driven sea surface currents in the Gulf of Trieste to high-frequency radar observations
Sofia Flora
CORRESPONDING AUTHOR
Department of Mathematics, Informatics and Geosciences, University of Trieste, Trieste, Italy
National Institute of Oceanography and Applied Geophysics – OGS, Trieste, Italy
Laura Ursella
National Institute of Oceanography and Applied Geophysics – OGS, Trieste, Italy
Achim Wirth
Univ. Grenoble Alpes, CNRS, Grenoble INP, LEGI, 38000 Grenoble, France
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This study analyses the extreme meteo-marine event of October–November 2023 in the Gulf of Trieste, characterised by southerly strong winds, heavy rainfall, and high river discharge. Using high-frequency radar data, wind records, and numerical models, we analysed the interactions between river discharge and wind-driven currents. Results show that strong river discharge can dominate coastal circulation and overlay the wind effects. This multi-platform approach provides valuable insights into ocean dynamics.
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An increasing amount of data allows us to move from low-order moments of fluctuating observations to their PDFs. We found the analytical fat-tailed PDF form (a combination of Gaussian and two-exponential convolutions) for 2 years of sea surface current increments in the Gulf of Trieste, using superstatistics and the maximum-entropy principle twice: on short and longer timescales. The data from different wind regimes follow the same analytical PDF, pointing towards a universal behaviour.
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This study analyses the extreme meteo-marine event of October–November 2023 in the Gulf of Trieste, characterised by southerly strong winds, heavy rainfall, and high river discharge. Using high-frequency radar data, wind records, and numerical models, we analysed the interactions between river discharge and wind-driven currents. Results show that strong river discharge can dominate coastal circulation and overlay the wind effects. This multi-platform approach provides valuable insights into ocean dynamics.
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The hydrostatic approximation is the basis of most simulations of ocean and climate dynamics. It is evaluated here by using a projection method in the 4D Fourier space. The evaluation is analytic.
Felipe L. L. Amorim, Julien Le Meur, Achim Wirth, and Vanessa Cardin
Ocean Sci., 20, 463–474, https://doi.org/10.5194/os-20-463-2024, https://doi.org/10.5194/os-20-463-2024, 2024
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Analysis of a high-frequency time series of thermohaline data measured at the EMSO-E2M3A regional facility in the southern Adriatic Pit (SAP) reveals a significant change in the double-diffusive regime in 2017 associated with the intrusion of extremely salty waters into the area, suggesting salt fingering as the dominant regime. The strong heat loss at the surface during this winter allowed deep convection to transport this high-salinity water from the intermediate to deep layers of the pit.
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An increasing amount of data allows us to move from low-order moments of fluctuating observations to their PDFs. We found the analytical fat-tailed PDF form (a combination of Gaussian and two-exponential convolutions) for 2 years of sea surface current increments in the Gulf of Trieste, using superstatistics and the maximum-entropy principle twice: on short and longer timescales. The data from different wind regimes follow the same analytical PDF, pointing towards a universal behaviour.
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Ocean Sci., 18, 1321–1337, https://doi.org/10.5194/os-18-1321-2022, https://doi.org/10.5194/os-18-1321-2022, 2022
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Explaining the dynamics of jellyfish blooms is a challenge for scientists. Biological and meteo-oceanographic data were combined on different timescales to explain the exceptional bloom of the jellyfish Rhizostoma pulmo in the Gulf of Trieste (Adriatic Sea) in April 2021. The bloom was associated with anomalously warm seasonal sea conditions. Then, a strong bora wind event enhanced upwelling and mixing of the water column, causing jellyfish to rise to the surface and accumulate along the coast.
Pablo Lorente, Eva Aguiar, Michele Bendoni, Maristella Berta, Carlo Brandini, Alejandro Cáceres-Euse, Fulvio Capodici, Daniela Cianelli, Giuseppe Ciraolo, Lorenzo Corgnati, Vlado Dadić, Bartolomeo Doronzo, Aldo Drago, Dylan Dumas, Pierpaolo Falco, Maria Fattorini, Adam Gauci, Roberto Gómez, Annalisa Griffa, Charles-Antoine Guérin, Ismael Hernández-Carrasco, Jaime Hernández-Lasheras, Matjaž Ličer, Marcello G. Magaldi, Carlo Mantovani, Hrvoje Mihanović, Anne Molcard, Baptiste Mourre, Alejandro Orfila, Adèle Révelard, Emma Reyes, Jorge Sánchez, Simona Saviano, Roberta Sciascia, Stefano Taddei, Joaquín Tintoré, Yaron Toledo, Laura Ursella, Marco Uttieri, Ivica Vilibić, Enrico Zambianchi, and Vanessa Cardin
Ocean Sci., 18, 761–795, https://doi.org/10.5194/os-18-761-2022, https://doi.org/10.5194/os-18-761-2022, 2022
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High-frequency radar (HFR) is a land-based remote sensing technology that can provide maps of the surface circulation over broad coastal areas, along with wave and wind information. The main goal of this work is to showcase the current status of the Mediterranean HFR network as well as present and future applications of this sensor for societal benefit such as search and rescue operations, safe vessel navigation, tracking of marine pollutants, and the monitoring of extreme events.
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In non-equilibrium statistical mechanics, which describes forced-dissipative systems such as air–sea interaction, there is no universal probability density function (pdf). Some such systems have recently been demonstrated to exhibit a symmetry called a fluctuation theorem (FT), which strongly constrains the shape of the pdf. Using satellite data, the mechanical power input to the ocean by air–sea interaction following or not a FT is questioned. A FT is found to apply over specific ocean regions.
Miroslav Gačić, Laura Ursella, Vedrana Kovačević, Milena Menna, Vlado Malačič, Manuel Bensi, Maria-Eletta Negretti, Vanessa Cardin, Mirko Orlić, Joël Sommeria, Ricardo Viana Barreto, Samuel Viboud, Thomas Valran, Boris Petelin, Giuseppe Siena, and Angelo Rubino
Ocean Sci., 17, 975–996, https://doi.org/10.5194/os-17-975-2021, https://doi.org/10.5194/os-17-975-2021, 2021
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Experiments in rotating tanks can simulate the Earth system and help to represent the real ocean, where rotation plays an important role. We wanted to show the minor importance of the wind in driving the flow in the Ionian Sea. We did this by observing changes in the water current in a rotating tank affected only by the pumping of dense water into the system. The flow variations were similar to those in the real sea, confirming the scarce importance of the wind for the flow in the Ionian Sea.
Achim Wirth and Florian Lemarié
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We show that modern concepts of non-equilibrium statistical mechanics can be applied to large-scale environmental fluid dynamics, where fluctuations are not thermal but come from turbulence. The work theorems developed by Jarzynski and Crooks are applied to air–sea interaction. Rather than looking at the average values of thermodynamic variables, their probability density functions are considered, which allows us to replace the inequalities of equilibrium statistical mechanics with equalities.
Cited articles
Alberti, T., Consolini, G., De Michelis, P., Laurenza, M., and Marcucci, M. F.: On fast and slow Earth’s magnetospheric dynamics during geomagnetic storms: a stochastic Langevin approach, J. Space Weather Space Clim., 8, A56, https://doi.org/10.1051/swsc/2018039, 2018. a
ARPA FVG (Agenzia regionale per la protezione dell'ambiente del Friuli Venezia Giulia), Landing page, https://www.arpa.fvg.it, last access: 29 October 2024 a
Baldovin, M., Puglisi, A., and Vulpiani, A.: Langevin equation in systems with also negative temperatures, J. Stat. Mech. Theor. Exp., 2018, 043207, https://doi.org/10.1088/1742-5468/aab687, 2018. a
Beck, C. and Cohen, E. G.: Superstatistics, Physica A, 322, 267–275, 2003. a
Beck, C., Cohen, E. G. D., and Swinney, H. L.: From time series to superstatistics, Phys. Rev. E, 72, 056133, https://doi.org/10.1103/PhysRevE.72.056133, 2005. a
Berglund, N. and Gentz, B.: Metastability in simple climate models: pathwise analysis of slowly driven Langevin equations, Stoch. Dynam., 2, 327–356, 2002. a
Brillinger, D. R. and Stewart, B. S.: Stochastic modeling of particle movement with application to marine biology and oceanography, J. Stat. Plan. Infer., 140, 3597–3607, https://doi.org/10.1016/j.jspi.2010.04.026, 2010. a
Corgnati, L., Mantovani, C., Novellino, A., Rubio, A., and Mader, J.: Recommendation Report 2 on improved common procedures for HFR QC analysis. JERICO-NEXT WP5-Data Management, Deliverable 5.14, Version 1.0., https://doi.org/10.25607/OBP-944, 2018. a
Cosoli, S., Ličer, M., Vodopivec, M., and Malačič, V.: Surface circulation in the Gulf of Trieste (northern Adriatic Sea) from radar, model, and ADCP comparisons, J. Geophys. Res.-Oceans, 118, 6183–6200, 2013. a
Einstein, A.: Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen, Ann. Phys., 4, 549–560, 1905. a
Einstein, A.: Investigations on the Theory of the Brownian Movement, Courier Corporation, ISBN-13 978-0-486-60304-9, ISBN-10 0-486-60304-0, 1956. a
Flora, S., Ursella, L., and Wirth, A.: Superstatistical analysis of sea surface currents in the Gulf of Trieste, measured by high-frequency radar, and its relation to wind regimes using the maximum-entropy principle, Nonlin. Processes Geophys., 30, 515–525, https://doi.org/10.5194/npg-30-515-2023, 2023. a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p
Flora, S., Wirth, A., and Ursella, L.: Codes: Comparing an idealized deterministic-stochastic model (SUP model, version 1) of the tide-and-wind driven sea surface currents in the Gulf of Trieste to HF Radar observations, Zenodo [code], https://doi.org/10.5281/zenodo.14562025, 2024. a
Foreman, M.: Manual for Tidal Currents Analysis and Prediction, Pacific Marine Science Report 78-6, Institute of Ocean Sciences, Patricia Bay, Sidney, British Columbia, 70, 1978. a
Franzke, C., Majda, A. J., and Vanden-Eijnden, E.: Low-order stochastic mode reduction for a realistic barotropic model climate, J. Atmos. Sci., 62, 1722–1745, 2005. a
Franzke, C. L., O'Kane, T. J., Berner, J., Williams, P. D., and Lucarini, V.: Stochastic climate theory and modeling, Wires Clim. Change, 6, 63–78, 2015. a
Goglio, A. C.: Progetto NAUSICA, https://www.arpa.fvg.it/export/sites/default/tema/crma/pubblicazioni/docs_pubblicazioni/2018gen01_arpafvg_crma_nausica_rap2018_001.pdf (last access: 29 October 2024), 2018. a
Ham, L., Coomer, M. A., and Stumpf, M. P.: The chemical Langevin equation for biochemical systems in dynamic environments, J. Chem. Phys., 157, 9, https://doi.org/10.1063/5.0095840 2022. a
Hasselmann, K.: Stochastic climate models part I. Theory, Tellus, 28, 473–485, 1976. a
Kloeden, P. E. and Platen, E.: Numerical Solution of Stochastic Differential Equations, Springer, ISBN 978-3-642-08107-1, https://doi.org/10.1007/978-3-662-12616-5, 1999. a
Lacorata, G. and Vulpiani, A.: Fluctuation-Response Relation and modeling in systems with fast and slow dynamics, Nonlin. Processes Geophys., 14, 681–694, https://doi.org/10.5194/npg-14-681-2007, 2007. a, b, c
Langevin, P.: Sur la théorie du mouvement brownien, CR Acad. Sci. Paris, 146, 530, 1908. a
Lemons, D. S. and Gythiel, A.: Paul Langevin's 1908 paper “On the Theory of Brownian Motion” [Sur la thiorie du mouvement brownien, CR Acad. Sci. (Paris) 146, 530–533 (1908)], Am. J. Phys., 65, 1079–1081, https://doi.org/10.1119/1.18725, 1997. a
Lorente, P., Aguiar, E., Bendoni, M., Berta, M., Brandini, C., Cáceres-Euse, A., Capodici, F., Cianelli, D., Ciraolo, G., Corgnati, L., Dadić, V., Doronzo, B., Drago, A., Dumas, D., Falco, P., Fattorini, M., Gauci, A., Gómez, R., Griffa, A., Guérin, C.-A., Hernández-Carrasco, I., Hernández-Lasheras, J., Ličer, M., Magaldi, M. G., Mantovani, C., Mihanović, H., Molcard, A., Mourre, B., Orfila, A., Révelard, A., Reyes, E., Sánchez, J., Saviano, S., Sciascia, R., Taddei, S., Tintoré, J., Toledo, Y., Ursella, L., Uttieri, M., Vilibić, I., Zambianchi, E., and Cardin, V.: Coastal high-frequency radars in the Mediterranean – Part 1: Status of operations and a framework for future development, Ocean Sci., 18, 761–795, https://doi.org/10.5194/os-18-761-2022, 2022. a
Lorenz, E. N.: Predictability: A problem partly solved, in: Proc. Seminar on predictability, vol. 1, Reading, https://doi.org/10.1017/CBO9780511617652.004, 1996. a
Malačič, V., Petelin, B., Gačić, M., Artegiani, A., and Orlić, M.: Regional Studies, Springer Netherlands, Dordrecht, 167–216, ISBN 978-94-015-9819-4, https://doi.org/10.1007/978-94-015-9819-4_6, 2001. a
OGS, NIB, ARSO, and ARPAFVG: HFR-NAdr (High Frequency Radar NAdr network), European HFR-Node [data set], https://doi.org/10.57762/8RRE-0Z07, 2023. a, b
Palmer, T.: Stochastic weather and climate models, Nat. Rev. Phys., 1, 463–471, 2019. a
Pawlowicz, R., Beardsley, B., and Lentz, S.: Classical tidal harmonic analysis including error estimates in MATLAB using T_TIDE, Comput. Geosci.s, 28, 929–937, 2002. a
Poulain, P.-M. and Raicich, F.: Forcings, Springer Netherlands, Dordrecht, 45–65, ISBN 978-94-015-9819-4, https://doi.org/10.1007/978-94-015-9819-4_2, 2001. a
Querin, S., Crise, A., Deponte, D., and Solidoro, C.: Numerical study of the role of wind forcing and freshwater buoyancy input on the circulation in a shallow embayment (Gulf of Trieste, Northern Adriatic Sea), J. Geophys. Res.-Oceans, 111, C03S16, https://doi.org/10.1029/2006JC003611, 2006. a, b
Querin, S., Cosoli, S., Gerin, R., Laurent, C., Malačič, V., Pristov, N., and Poulain, P.-M.: Multi-platform, high-resolution study of a complex coastal system: The TOSCA experiment in the Gulf of Trieste, J. Mar. Sci. Eng., 9, 469, https://doi.org/10.3390/jmse9050469, 2021. a, b
Reyes Suárez, N. C., Tirelli, V., Ursella, L., Ličer, M., Celio, M., and Cardin, V.: Multi-platform study of the extreme bloom of the barrel jellyfish Rhizostoma pulmo (Cnidaria: Scyphozoa) in the northernmost gulf of the Mediterranean Sea (Gulf of Trieste) in April 2021, Ocean Sci., 18, 1321–1337, https://doi.org/10.5194/os-18-1321-2022, 2022. a
Silveira, F. A. and Aarão Reis, F. D. A.: Langevin equations for competitive growth models, Phys. Rev. E, 85, 011601, https://doi.org/10.1103/PhysRevE.85.011601, 2012. a
Sura, P.: Stochastic Models of Climate Extremes: Theory and Observations, Springer Netherlands, Dordrecht, 181–222, ISBN 978-94-007-4479-0, https://doi.org/10.1007/978-94-007-4479-0_7, 2013. a
van den Berk, J., Drijfhout, S., and Hazeleger, W.: Characterisation of Atlantic meridional overturning hysteresis using Langevin dynamics, Earth Syst. Dynam., 12, 69–81, https://doi.org/10.5194/esd-12-69-2021, 2021. a
Wand, T., Wiedemann, T., Harren, J., and Kamps, O.: Estimating stable fixed points and Langevin potentials for financial dynamics, Phys. Rev. E, 109, 024226, https://doi.org/10.1103/PhysRevE.109.024226, 2024. a
Wirth, A.: A fluctuation-dissipation relation for the ocean subject to turbulent atmospheric forcing, J. Phys. Oceanogr., 48, 831–843, 2018. a
Wirth, A.: On fluctuating momentum exchange in idealised models of air–sea interaction, Nonlinear Processes in Geophysics, 26, 457–477, https://doi.org/10.5194/npg-26-457-2019, 2019. a, b, c
Zhai, X., Johnson, H. L., Marshall, D. P., and Wunsch, C.: On the Wind Power Input to the Ocean General Circulation, J. Phys. Oceanogr., 42, 1357–1365, https://doi.org/10.1175/JPO-D-12-09.1, 2012. a
Short summary
We developed a hierarchy of idealized deterministic–stochastic models to simulate sea surface currents in the Gulf of Trieste. They include tide- and wind-driven sea surface current components, resolving the slowly varying part of the flow, and a stochastic signal, representing the fast-varying small-scale dynamics. The comparison with high-frequency radar observations shows that the non-Gaussian stochastic model captures key dynamics and mimics the observed fat-tailed probability distribution.
We developed a hierarchy of idealized deterministic–stochastic models to simulate sea surface...
