Articles | Volume 22, issue 1
https://doi.org/10.5194/os-22-427-2026
© Author(s) 2026. 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-22-427-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
09 Feb 2026
Research article |
| 09 Feb 2026
| 09 Feb 2026
Revisited heat budget and probability distributions of turbulent heat fluxes in the Mediterranean Sea
Mahmud Hasan Ghani
CORRESPONDING AUTHOR
Department of Physics and Astronomy, University of Bologna, Bologna, Italy
Nadia Pinardi
Department of Physics and Astronomy, University of Bologna, Bologna, Italy
CMCC Foundation – Euro-Mediterranean Center on Climate Change, Bologna, Italy
Antonio Navarra
CMCC Foundation – Euro-Mediterranean Center on Climate Change, Bologna, Italy
Department of Biological, Geological and Environmental Sciences, University of Bologna, Bologna, Italy
Lorenzo Mentaschi
Department of Physics and Astronomy, University of Bologna, Bologna, Italy
CMCC Foundation – Euro-Mediterranean Center on Climate Change, Bologna, Italy
Silvia Bianconcini
Department of Statistics, University of Bologna, Bologna, Italy
Francesco Maicu
CMCC Foundation – Euro-Mediterranean Center on Climate Change, Bologna, Italy
Francesco Trotta
CMCC Foundation – Euro-Mediterranean Center on Climate Change, Bologna, Italy
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Italo dos Reis Lopes, Ivan Federico, Michalis Vousdoukas, Luisa Perini, Salvatore Causio, Giovanni Coppini, Maurilio Milella, Nadia Pinardi, and Lorenzo Mentaschi
Nat. Hazards Earth Syst. Sci., 26, 811–825, https://doi.org/10.5194/nhess-26-811-2026, https://doi.org/10.5194/nhess-26-811-2026, 2026
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We improved a computer model to simulate coastal flooding by including temporary barriers like sand dunes. We tested it where sand dunes are built seasonally to protect the shoreline for two real storms: one that broke through the dunes and another where dunes held strong. Our model showed how important it is to design these defenses carefully since even if a small part of a dune fails, a major flooding can happen. Overall, our work helps create better tools to manage and protect coastal areas.
Paolo Oddo, Mario Adani, Francesco Carere, Andrea Cipollone, Anna Chiara Goglio, Eric Jansen, Ali Aydogdu, Francesca Mele, Italo Epicoco, Jenny Pistoia, Emanuela Clementi, Nadia Pinardi, and Simona Masina
Geosci. Model Dev., 19, 423–445, https://doi.org/10.5194/gmd-19-423-2026, https://doi.org/10.5194/gmd-19-423-2026, 2026
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This study present a data assimilation system that combines ocean observational data with ocean model results to better understand the ocean and predict its future state. The method uses a three dimensional incremental variational approach focusing on the physical relationships between all the state vector variables errors. Testing in the Mediterranean Sea showed that a complex sea level operator based on a barotropic model works best.
Lucia Gualtieri, Paolo Oddo, Hans Burchard, Federica Borile, Aimie Moulin, Pietro Miraglio, Francesco Maicu, and Emanuela Clementi
EGUsphere, https://doi.org/10.5194/egusphere-2025-5327, https://doi.org/10.5194/egusphere-2025-5327, 2025
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This study addresses a gap in understanding how turbulent mixing closure schemes and convective adjustments interplay in the Mediterranean Sea. Coupled ocean-wave simulations were performed with different mixing parameterizations and model results were compared against Argo float observations across different space and time scales. Results show that the Generalised Length Scale closure scheme best reproduces observed mixed layer properties and variability, without needing convective adjustment.
Rodrigo Campos-Caba, Paula Camus, Andrea Mazzino, Michalis Vousdoukas, Massimo Tondello, Ivan Federico, Salvatore Causio, and Lorenzo Mentaschi
EGUsphere, https://doi.org/10.5194/egusphere-2025-5313, https://doi.org/10.5194/egusphere-2025-5313, 2025
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We assess the ability of machine learning emulators, from Multivariate Linear Regression to Long Short-Term Memory (LSTM) networks, to reproduce storm surge dynamics in the northern Adriatic Sea. Using the corrected Mean Absolute Deviation squared (MADc²) loss function, we demonstrate that data-driven models can match high-resolution hydrodynamic simulations in representing extreme surge events with greatly reduced computational cost.
Seimur Shirinov, Ivan Federico, Simone Bonamano, Salvatore Causio, Nicolás Biocca, Viviana Piermattei, Daniele Piazzolla, Jacopo Alessandri, Lorenzo Mentaschi, Giovanni Coppini, Marco Marcelli, and Nadia Pinardi
Nat. Hazards Earth Syst. Sci., 25, 3737–3758, https://doi.org/10.5194/nhess-25-3737-2025, https://doi.org/10.5194/nhess-25-3737-2025, 2025
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This research investigates how seagrass meadows attenuate coastal waves. Our methodology integrates site measurements with numerical simulations, revealing that plant flexibility and seasonal growth cycles are crucial factors that enhance model fidelity for predicting wave damping. These insights aid ecosystem-based coastal protection and conservation of these vital habitats. Future work should address current–sediment–vegetation interactions for a more complete hydrodynamic understanding.
Leonardo Lima, Rafael Menezes, Ehsan Sadighrad, Ronan McAdam, Filipe Costa, Pietro Miraglio, Mehmet Ilicak, Eric Jansen, Ali Aydogdu, Francesco Maicu, and Emanuela Clementi
State Planet Discuss., https://doi.org/10.5194/sp-2025-6, https://doi.org/10.5194/sp-2025-6, 2025
Revised manuscript accepted for SP
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As climate change intensifies, marine heatwaves (MHWs), periods of unusually high ocean temperatures, threaten ecosystems and communities. This study analyzes MHWs in the Mediterranean and Black Seas, examining surface temperatures and ocean heat content in the upper 0–40 meters to capture subsurface warming. Findings highlight the need to monitor both surface and subsurface conditions for a comprehensive understanding and better management considering ongoing warming trends in both seas.
Skyler Kern, Mary E. McGuinn, Katherine M. Smith, Nadia Pinardi, Kyle E. Niemeyer, Nicole S. Lovenduski, and Peter E. Hamlington
EGUsphere, https://doi.org/10.5194/egusphere-2025-3795, https://doi.org/10.5194/egusphere-2025-3795, 2025
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The parameters that control a model's behavior determine its ability to represent a system. In this work, multiple cases test how to estimate the parameters of a model with components corresponding to both the physics and the chemical and biological processes (i.e. the biogeochemistry) of the ocean. While demonstrating how to approach this problem type, the results show estimating both sets of parameters simultaneously is better than estimating the physics then the biogeochemistry separately.
Salvatore Causio, Seimur Shirinov, Ivan Federico, Giovanni De Cillis, Emanuela Clementi, Lorenzo Mentaschi, and Giovanni Coppini
Ocean Sci., 21, 1105–1123, https://doi.org/10.5194/os-21-1105-2025, https://doi.org/10.5194/os-21-1105-2025, 2025
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This study examines how waves and ocean currents interact during severe weather, focusing on Medicane Ianos, one of the strongest storms in the Mediterranean. Using advanced modeling, we created a unique system to simulate these interactions, capturing effects like wave-induced water levels and wave-induced effects on the vertical structure of the ocean. We validated our approach with ideal tests and real data from the storm.
Rita Lecci, Robyn Gwee, Kun Yan, Sanne Muis, Nadia Pinardi, Jun She, Martin Verlaan, Simona Masina, Wenshan Li, Hui Wang, Salvatore Causio, Antonio Novellino, Marco Alba, Etiënne Kras, Sandra Gaytan Aguilar, and Jan-Bart Calewaert
EGUsphere, https://doi.org/10.5194/egusphere-2025-1763, https://doi.org/10.5194/egusphere-2025-1763, 2025
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This study explored how sea level is changing along the China-Europe Sea Route. By combining satellite and in-situ observations with advanced modeling, the research identified ongoing sea level rise and an increasing frequency of extreme water level events in some regions. These findings underscore the importance of continued monitoring and provide useful knowledge to support long-term planning, coastal resilience, and informed decision-making.
Mohammad Hadi Bahmanpour, Alois Tilloy, Michalis Vousdoukas, Ivan Federico, Giovanni Coppini, Luc Feyen, and Lorenzo Mentaschi
EGUsphere, https://doi.org/10.5194/egusphere-2025-843, https://doi.org/10.5194/egusphere-2025-843, 2025
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As natural hazards evolve, understanding how extreme events interact over time is crucial. While single extremes have been widely studied, joint extremes remain challenging to analyze. We present a framework that combines advanced statistical modeling with copula theory to capture changing dependencies. Applying it to historical data reveals dynamic patterns in extreme events. To support broader use, we provide an open-source tool for improved hazard assessment.
Rodrigo Campos-Caba, Jacopo Alessandri, Paula Camus, Andrea Mazzino, Francesco Ferrari, Ivan Federico, Michalis Vousdoukas, Massimo Tondello, and Lorenzo Mentaschi
Ocean Sci., 20, 1513–1526, https://doi.org/10.5194/os-20-1513-2024, https://doi.org/10.5194/os-20-1513-2024, 2024
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Here we show the development of high-resolution simulations of storm surge in the northern Adriatic Sea employing different atmospheric forcing data and physical configurations. Traditional metrics favor a simulation forced by a coarser database and employing a less sophisticated setup. Closer examination allows us to identify a baroclinic model forced by a high-resolution dataset as being better able to capture the variability and peak values of the storm surge.
José A. Jiménez, Gundula Winter, Antonio Bonaduce, Michael Depuydt, Giulia Galluccio, Bart van den Hurk, H. E. Markus Meier, Nadia Pinardi, Lavinia G. Pomarico, and Natalia Vazquez Riveiros
State Planet, 3-slre1, 3, https://doi.org/10.5194/sp-3-slre1-3-2024, https://doi.org/10.5194/sp-3-slre1-3-2024, 2024
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The Knowledge Hub on Sea Level Rise (SLR) has done a scoping study involving stakeholders from government and academia to identify gaps and needs in SLR information, impacts, and policies across Europe. Gaps in regional SLR projections and uncertainties were found, while concerns were raised about shoreline erosion and emerging problems like saltwater intrusion and ineffective adaptation plans. The need for improved communication to make better decisions on SLR adaptation was highlighted.
Nadia Pinardi, Bart van den Hurk, Michael Depuydt, Thorsten Kiefer, Petra Manderscheid, Lavinia Giulia Pomarico, and Kanika Singh
State Planet, 3-slre1, 2, https://doi.org/10.5194/sp-3-slre1-2-2024, https://doi.org/10.5194/sp-3-slre1-2-2024, 2024
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The Knowledge Hub on Sea Level Rise (KH-SLR), a joint effort between JPI Climate and JPI Oceans, addresses the critical need for science-based information on sea level changes in Europe. The KH-SLR actively involves stakeholders through a co-design process discussing the impacts, adaptation planning, and policy requirements related to SLR in Europe. Its primary output is the KH Assessment Report (KH-AR), which is described in this volume.
Bart van den Hurk, Nadia Pinardi, Alexander Bisaro, Giulia Galluccio, José A. Jiménez, Kate Larkin, Angélique Melet, Lavinia Giulia Pomarico, Kristin Richter, Kanika Singh, Roderik van de Wal, and Gundula Winter
State Planet, 3-slre1, 1, https://doi.org/10.5194/sp-3-slre1-1-2024, https://doi.org/10.5194/sp-3-slre1-1-2024, 2024
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The Summary for Policymakers compiles findings from “Sea Level Rise in Europe: 1st Assessment Report of the Knowledge Hub on Sea Level Rise”. It covers knowledge gaps, observations, projections, impacts, adaptation measures, decision-making principles, and governance challenges. It provides information for each European basin (Mediterranean, Black Sea, North Sea, Baltic Sea, Atlantic, and Arctic) and aims to assist policymakers in enhancing the preparedness of European coasts for sea level rise.
Bethany McDonagh, Emanuela Clementi, Anna Chiara Goglio, and Nadia Pinardi
Ocean Sci., 20, 1051–1066, https://doi.org/10.5194/os-20-1051-2024, https://doi.org/10.5194/os-20-1051-2024, 2024
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Tides in the Mediterranean Sea are typically of low amplitude, but twin experiments with and without tides demonstrate that tides affect the circulation directly at scales away from those of the tides. Analysis of the energy changes due to tides shows that they enhance existing oscillations, and internal tides interact with other internal waves. Tides also increase the mixed layer depth and enhance deep water formation in key regions. Internal tides are widespread in the Mediterranean Sea.
Roberta Benincasa, Giovanni Liguori, Nadia Pinardi, and Hans von Storch
Ocean Sci., 20, 1003–1012, https://doi.org/10.5194/os-20-1003-2024, https://doi.org/10.5194/os-20-1003-2024, 2024
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Ocean dynamics result from the interplay of internal processes and external inputs, primarily from the atmosphere. It is crucial to discern between these factors to gauge the ocean's intrinsic predictability and to be able to attribute a signal under study to either external factors or internal variability. Employing a simple analysis, we successfully characterized this variability in the Mediterranean Sea and compared it with the oceanic response induced by atmospheric conditions.
Skyler Kern, Mary E. McGuinn, Katherine M. Smith, Nadia Pinardi, Kyle E. Niemeyer, Nicole S. Lovenduski, and Peter E. Hamlington
Geosci. Model Dev., 17, 621–649, https://doi.org/10.5194/gmd-17-621-2024, https://doi.org/10.5194/gmd-17-621-2024, 2024
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Computational models are used to simulate the behavior of marine ecosystems. The models often have unknown parameters that need to be calibrated to accurately represent observational data. Here, we propose a novel approach to simultaneously determine a large set of parameters for a one-dimensional model of a marine ecosystem in the surface ocean at two contrasting sites. By utilizing global and local optimization techniques, we estimate many parameters in a computationally efficient manner.
Giovanni Coppini, Emanuela Clementi, Gianpiero Cossarini, Stefano Salon, Gerasimos Korres, Michalis Ravdas, Rita Lecci, Jenny Pistoia, Anna Chiara Goglio, Massimiliano Drudi, Alessandro Grandi, Ali Aydogdu, Romain Escudier, Andrea Cipollone, Vladyslav Lyubartsev, Antonio Mariani, Sergio Cretì, Francesco Palermo, Matteo Scuro, Simona Masina, Nadia Pinardi, Antonio Navarra, Damiano Delrosso, Anna Teruzzi, Valeria Di Biagio, Giorgio Bolzon, Laura Feudale, Gianluca Coidessa, Carolina Amadio, Alberto Brosich, Arnau Miró, Eva Alvarez, Paolo Lazzari, Cosimo Solidoro, Charikleia Oikonomou, and Anna Zacharioudaki
Ocean Sci., 19, 1483–1516, https://doi.org/10.5194/os-19-1483-2023, https://doi.org/10.5194/os-19-1483-2023, 2023
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The paper presents the Mediterranean Forecasting System evolution and performance developed in the framework of the Copernicus Marine Service.
Umesh Pranavam Ayyappan Pillai, Nadia Pinardi, Ivan Federico, Salvatore Causio, Francesco Trotta, Silvia Unguendoli, and Andrea Valentini
Nat. Hazards Earth Syst. Sci., 22, 3413–3433, https://doi.org/10.5194/nhess-22-3413-2022, https://doi.org/10.5194/nhess-22-3413-2022, 2022
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The study presents the application of high-resolution coastal modelling for wave hindcasting on the Emilia-Romagna coastal belt. The generated coastal databases which provide an understanding of the prevailing wind-wave characteristics can aid in predicting coastal impacts.
Giorgio Micaletto, Ivano Barletta, Silvia Mocavero, Ivan Federico, Italo Epicoco, Giorgia Verri, Giovanni Coppini, Pasquale Schiano, Giovanni Aloisio, and Nadia Pinardi
Geosci. Model Dev., 15, 6025–6046, https://doi.org/10.5194/gmd-15-6025-2022, https://doi.org/10.5194/gmd-15-6025-2022, 2022
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The full exploitation of supercomputing architectures requires a deep revision of the current climate models. This paper presents the parallelization of the three-dimensional hydrodynamic model SHYFEM (System of HydrodYnamic Finite Element Modules). Optimized numerical libraries were used to partition the model domain and solve the sparse linear system of equations in parallel. The performance assessment demonstrates a good level of scalability with a realistic configuration used as a benchmark.
Enrico Scoccimarro, Daniele Peano, Silvio Gualdi, Alessio Bellucci, Tomas Lovato, Pier Giuseppe Fogli, and Antonio Navarra
Geosci. Model Dev., 15, 1841–1854, https://doi.org/10.5194/gmd-15-1841-2022, https://doi.org/10.5194/gmd-15-1841-2022, 2022
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This study evaluated the ability of the CMCC-CM2 climate model participating to the last CMIP6 effort, in representing extreme events of precipitation and temperature at the daily and 6-hourly frequencies. The 1/4° resolution version of the atmospheric model provides better results than the version at 1° resolution for temperature extremes, at both time frequencies. For precipitation extremes, especially at the daily time frequency, the higher resolution does not improve model results.
Katherine M. Smith, Skyler Kern, Peter E. Hamlington, Marco Zavatarelli, Nadia Pinardi, Emily F. Klee, and Kyle E. Niemeyer
Geosci. Model Dev., 14, 2419–2442, https://doi.org/10.5194/gmd-14-2419-2021, https://doi.org/10.5194/gmd-14-2419-2021, 2021
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We present a newly developed reduced-order biogeochemical flux model that is complex and flexible enough to capture open-ocean ecosystem dynamics but reduced enough to incorporate into highly resolved numerical simulations with limited additional computational cost. The model provides improved correlations between model output and field data, indicating that significant improvements in the reproduction of real-world data can be achieved with a small number of variables.
Cited articles
Azzalini, A.: A class of distributions which includes the normal ones, Scandinav. J. Stat., 171–178, 1985.
Béthoux, J. P.: Budgets of the Mediterranean Sea-Their dependance on the local climate and on the characteristics of the Atlantic waters, Oceanolog. Acta, 2, 157–163, 1979.
Béthoux, J. P., Gentili, B., and Tailliez, D.: Warming and freshwater budget change in the Mediterranean since the 1940s, their possible relation to the greenhouse effect, Geophys. Res. Lett., 25, 1023–1026, https://doi.org/10.1029/98GL00724, 1998.
Bignami, F., Marullo, S., Santoleri, R., and Schiano, M. E.: Long wave radiation budget on the Mediterranean Sea, J. Geophys. Res., 100, 2501–2514, https://doi.org/10.1029/94JC02496, 1995.
Bunker, A. F., Charnock, H., and Goldsmith, R. A.: A note on the heat balance of the Mediterranean and Red Seas, J. Mar. Res., 40, 73–84, 1982.
Castellari, S., Pinardi, N., and Leaman, K.: A model study of air–sea interactions in the Mediterranean Sea, J. Mar. Syst., 18, 89–114, https://doi.org/10.1016/S0924-7963(98)90007-0, 1998.
Cessi, P., Pinardi, N., and Lyubartsev, V.: Energetics of semi enclosed basins with two-layer flows at the strait, J. Phys. Oceanogr., 44, 967–979, https://doi.org/10.1175/JPO-D-13-0129.1, 2014.
Copernicus Climate Change Service, Climate Data Store: ERA5 hourly 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.adbb2d47, 2023.
Criado-Aldeanueva, F., Soto-Navarro, F. J., and García-Lafuente, J.: Seasonal and interannual variability of surface heat and freshwater fluxes in the Mediterranean Sea: Budgets and exchange through the Strait of Gibraltar, Int. J. Climatol., 32, 286–302, https://doi.org/10.1002/joc.2268, 2012.
Cronin, M. F., Gentemann, C. L., Edson, J., Ueki, I., Bourassa, M., Brown, S., Clayson, C. A., Fairall, C. W., Farrar, J. T., Gille, S. T., Gulev, S., and Zhang, D.: Air–sea fluxes with a focus on heat and momentum, Front. Mar. Sci., 6, 430, https://doi.org/10.3389/fmars.2019.00430, 2019.
De Dominicis, M., Pinardi, N., Zodiatis, G., and Lardner, R.: MEDSLIK-II, a Lagrangian marine surface oil spill model for short-term forecasting – Part 1: Theory, Geosci. Model Dev., 6, 1851–1869, https://doi.org/10.5194/gmd-6-1851-2013, 2013.
Elderton, W. P.: Tables for Testing the Goodness of Fit of Theory to Observation, Biometrika, 1, 155–163, 1902.
Escudier, R., Clementi, E., Cipollone, A., Pistoia, J., Drudi, M., Grandi, A., Lyubartsev, V., Lecci, R., Aydogdu, A., Delrosso, D., Omar, M., Masina, S., Coppini, G., and Pinardi, N.: A high-resolution reanalysis for the Mediterranean Sea, Front. Earth Sci., 9, 702285, https://doi.org/10.3389/feart.2021.702285, 2021.
Fairall, C. W., Bradley, E. F., Hare, J. E., Grachev, A. A., and Edson, J. B.: Bulk parameterization of air–sea fluxes: Updates and verification for the COARE algorithm, J, Climate, 16, 571–591, https://doi.org/10.1175/1520-0442(2003)016<0571:BPOASF>2.0.CO;2, 2003.
Flecher, C., Naveau, P., Allard, D., and Brisson, N.: A stochastic daily weather generator for skewed data, Water Resour. Res., 46, https://doi.org/10.1029/2009WR008098, 2010.
Garrett, C., Outerbridge, R., and Thompson, K.: Interannual variability in Mediterranean heat and buoyancy fluxes, J. Climate, 6, 900–910, 1993.
Ghani, M. H.: Air-Sea_HeatFluxes-V1.0, Zenodo [code], https://doi.org/10.5281/zenodo.18432708, 2026.
Gulev, S. K. and Belyaev, K.: Probability distribution characteristics for surface air–sea turbulent heat fluxes over the global ocean, J. Climate, 25, 184–206, https://doi.org/10.1175/2011JCLI4211.1, 2012.
Hersbach, H., Bell, B., Berrisford, P., Hirahara, S., Horányi, A., Muñoz‐Sabater, J., Nicolas, J., Peubey, C., Radu, R., Schepers, D., and Simmons, A.: The ERA5 global reanalysis, Q. J. Roy. Meteorol. Soc., 146, 1999–2049, 2020.
Jordá, G., Von Schuckmann, K., Josey, S. A., Caniaux, G., García-Lafuente, J., Sammartino, S., Özsoy, E., Polcher, J., Notarstefano, G., Poulain, P. M., Adloff, F., and Macías, D.: The Mediterranean Sea heat and mass budgets: Estimates, uncertainties and perspectives, Prog. Oceanogr., 156, 174–208, https://doi.org/10.1016/j.pocean.2017.07.001, 2017.
Kara, A. B., Rochford, P. A., and Hurlburt, H. E.: Efficient and accurate bulk parameterizations of air–sea fluxes for use in general circulation models, J. Atmos. Ocean. Tech., 17, 1421–1438, https://doi.org/10.1175/1520-0426(2000)017<1421:EAABPO>2.0.CO;2, 2000.
Korolev, V., Gorshenin, A., Gulev, S., and Belyaev, K.: Statistical modeling of air–sea turbulent heat fluxes by finite mixtures of Gaussian distributions, in: International Conference on Information Technologies and Mathematical Modelling, Springer, Cham, 152–162, https://doi.org/10.1007/978-3-319-25861-4_13, 2015.
Large, W. and Yeager, S. G.: The global climatology of an interannually varying air–sea flux data set, Clim. Dynam., 33, 341–364, https://doi.org/10.1007/s00382-008-0441-3, 2009.
Marullo, S., Pitarch, J., Bellacicco, M., Sarra, A. G. D., Meloni, D., Monteleone, F., Sferlazzo, D., Artale, V., and Santoleri, R.: Air–sea interaction in the central Mediterranean Sea: assessment of reanalysis and satellite observations, Remote Sens., 13, 2188, https://doi.org/10.3390/rs13112188, 2021.
Matsoukas, C., Banks, A. C., Hatzianastassiou, N., Pavlakis, K. G., Hatzidimitriou, D., Drakakis, E., Stackhouse, P. W., and Vardavas, I.: Seasonal heat budget of the Mediterranean Sea J. Geophys. Res.-Oceans, 110, https://doi.org/10.1029/2004JC002566, 2005.
May, P.: A Brief Explanation of Mediterranean Heat and Momentum Flux Calculations, Naval Oceanography Atmospheric Research Laboratory, Washington, DC, USA, 1986.
Papoulis, A. and Pillai, S. U.: Probability, Random Variables, and Stochastic Processes, in: 4th Edn., McGraw Hill, New York, 2002.
Payne, R. E.: Albedo of the sea surface, J. Atmos. Sci., 29, 959–970, https://doi.org/10.1175/1520-0469(1972)029<0959:AOTSS>2.0.CO;2, 1972.
Pettenuzzo, D., Large, W. G., and Pinardi, N.: On the corrections of ERA-40 surface flux products consistent with the Mediterranean heat and water budgets and the connection between basin surface total heat flux and NAO, J. Geophys. Res.-Oceans, 115, https://doi.org/10.1029/2009JC005631, 2010.
Pinardi, N., Bonaduce, A., Navarra, A., Dobricic, S., and Oddo, P.: The mean sea level equation and its application to the mediterranean sea, J. Climate, 27, 442–447, https://doi.org/10.1175/JCLI-D-13-00139.1, 2014.
Pinardi, N., Cessi, P., Borile, F., and Wolfe, C. L.: The Mediterranean Sea Overturning Circulation, J. Phys. Oceanogr., 49, 1699–1721, https://doi.org/10.1175/JPO-D-18-0254.1, 2019.
Rabier, F., Järvinen, H., Klinker, E., Mahfouf, J. F., and Simmons, A.: The ECMWF operational implementation of four-dimensional variational assimilation. I: Experimental results with simplified physics, Q. J. Roy. Meteorol. Soc., 126, 1143–1170, https://doi.org/10.1002/qj.49712656415, 2000.
Reed, R. K.: On estimating insolation over the ocean, J. Phys. Oceanogr., 7, 482–485, https://doi.org/10.1175/1520-0485(1977)007<0482:OEIOTO>2.0.CO;2, 1977.
Rosati, A. and Miyakoda, K.: A general circulation model for upper ocean simulation, J. Phys. Oceanogr., 18, 1601–1626, https://doi.org/10.1175/1520-0485(1988)018<1601:AGCMFU>2.0.CO;2, 1988.
Ruiz, S., Gomis, D., Sotillo, M. G., and Josey, S. A.: Characterization of surface heat fluxes in the Mediterranean Sea from a 44-year high-resolution atmospheric data set, Global Planet. Change, 63, 258–274, https://doi.org/10.1016/j.gloplacha.2007.12.002, 2008.
Sanchez-Gomez, E., Somot, S., Josey, S. A., Dubois, C., Elguindi, N., and Déqué, M.: Evaluation of Mediterranean Sea water and heat budgets simulated by an ensemble of high-resolution regional climate models, Clim. Dynam., 37, 2067–2086, https://doi.org/10.1007/s00382-011-1012-6, 2011.
Sardeshmukh, P. D. and Penland, C.: Understanding the distinctively skewed and heavy-tailed character of atmospheric and oceanic probability distributions, Chaos, 25, https://doi.org/10.1063/1.4914169, 2015.
Small, R. J., Bryan, F. O., Bishop, S. P., and Tomas, R. A.: Air–sea turbulent heat fluxes in climate models and observational analyses: What drives their variability?, J. Climate, 32, 2397–2421, https://doi.org/10.1175/JCLI-D-18-0576.1, 2019.
Song, X. and Yu, L.: Air–sea heat flux climatologies in the Mediterranean Sea: Surface energy balance and its consistency with ocean heat storage, J. Geophys. Res.-Oceans, 122, 4068–4087, https://doi.org/10.1002/2016JC012254, 2017.
Sverdrup, H. U., Johnson, M. W., and Fleming, R. H.: The Oceans, Their Physics, Chemistry, and General Biology, Prentice-Hall, New York, http://ark.cdlib.org/ark:/13030/kt167nb66r/ (last access: 20 October 2025), 1942.
Tian, F., von Storch, J. S., and Hertwig, E.: Air–sea fluxes in a climate model using hourly coupling between the atmospheric and the oceanic components, Clim. Dynam., 48, 2819–2836, https://doi.org/10.1007/s00382-016-3228-y, 2017.
Tibshirani, R. J. and Efron, B.: An introduction to the bootstrap, Monogr. on Stat. Appl. Probabil., 57, 1–436, 1993.
Wallace, J. M. and Hobbs, P. V.: Atmospheric science: an introductory survey, in: Vol. 92, Elsevier, ISBN 978-0127329512, 2006.
Yu, K. and Zhang, J.: A three-parameter asymmetric Laplace distribution and its extension, Commun. Stat., 34, 1867–1879, https://doi.org/10.1080/03610920500199018, 2005.
Short summary
Using the same sea surface temperature and the same bulk formula but different atmospheric reanalysis and analysis surface-variable datasets, we show that a higher-resolution dataset is crucial for evaluating the heat-budget closure hypothesis in the Mediterranean Sea. For the first time, we investigate the impact of extreme heat-loss events in the Mediterranean Sea by computing the long-term, basin-averaged mean heat budget.
Using the same sea surface temperature and the same bulk formula but different atmospheric...
