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2. The Fourier analysis in inhomogeneous media

Author

Gnevyshev Vladimir and Belonenko Tatyana

Subjects
fourier analysis, laplace transform, cauchy problem, waves, inhomogeneous medium, Mathematics, QA1-939, Physics, QC1-999
Abstract

In the paper, the definition and basic properties of the Fourier transform (FT) are discussed. It has been shown with specific examples that integral solutions of the model inhomogeneous equation, the nonstationary Cauchy problem on an inhomogeneous shear flow, and the boundary value problem on the transformation of internal waves in the vicinity of the focus in the inhomogeneous medium can be found by FT and using its properties. The constructed Fourier integrals refuted the widely held claim that the Fourier analysis is unusable for the study of inhomogeneous media.

Published
2023
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3. Altimetry for the future: Building on 25 years of progress

Author

Team, International Altimetry, Abdalla, Saleh, Kolahchi, Abdolnabi Abdeh, Ablain, Michaël, Adusumilli, Susheel, Bhowmick, Suchandra Aich, Alou-Font, Eva, Amarouche, Laiba, Andersen, Ole Baltazar, Antich, Helena, Aouf, Lotfi, Arbic, Brian, Armitage, Thomas, Arnault, Sabine, Artana, Camila, Aulicino, Giuseppe, Ayoub, Nadia, Badulin, Sergei, Baker, Steven, Banks, Chris, Bao, Lifeng, Barbetta, Silvia, Barceló-Llull, Bàrbara, Barlier, François, Basu, Sujit, Bauer-Gottwein, Peter, Becker, Matthias, Beckley, Brian, Bellefond, Nicole, Belonenko, Tatyana, Benkiran, Mounir, Benkouider, Touati, Bennartz, Ralf, Benveniste, Jérôme, Bercher, Nicolas, Berge-Nguyen, Muriel, Bettencourt, Joao, Blarel, Fabien, Blazquez, Alejandro, Blumstein, Denis, Bonnefond, Pascal, Borde, Franck, Bouffard, Jérôme, Boy, François, Boy, Jean-Paul, Brachet, Cédric, Brasseur, Pierre, Braun, Alexander, Brocca, Luca, Brockley, David, Brodeau, Laurent, Brown, Shannon, Bruinsma, Sean, Bulczak, Anna, Buzzard, Sammie, Cahill, Madeleine, Calmant, Stéphane, Calzas, Michel, Camici, Stefania, Cancet, Mathilde, Capdeville, Hugues, Carabajal, Claudia Cristina, Carrere, Loren, Cazenave, Anny, Chassignet, Eric P, Chauhan, Prakash, Cherchali, Selma, Chereskin, Teresa, Cheymol, Cecile, Ciani, Daniele, Cipollini, Paolo, Cirillo, Francesca, Cosme, Emmanuel, Coss, Steve, Cotroneo, Yuri, Cotton, David, Couhert, Alexandre, Coutin-Faye, Sophie, Crétaux, Jean-François, Cyr, Frederic, d’Ovidio, Francesco, Darrozes, José, David, Cedric, Dayoub, Nadim, De Staerke, Danielle, Deng, Xiaoli, Desai, Shailen, Desjonqueres, Jean-Damien, Dettmering, Denise, Di Bella, Alessandro, Díaz-Barroso, Lara, Dibarboure, Gerald, Dieng, Habib Boubacar, Dinardo, Salvatore, Dobslaw, Henryk, Dodet, Guillaume, Doglioli, Andrea, Domeneghetti, Alessio, Donahue, David, and Dong, Shenfu

Subjects
Life Below Water, Climate Action, Satellite altimetry, Oceanography, Sea level, Coastal oceanography, Cryospheric sciences, Hydrology, Astronomical and Space Sciences, Aerospace Engineering, Mechanical Engineering, Aerospace & Aeronautics
Abstract

In 2018 we celebrated 25 years of development of radar altimetry, and the progress achieved by this methodology in the fields of global and coastal oceanography, hydrology, geodesy and cryospheric sciences. Many symbolic major events have celebrated these developments, e.g., in Venice, Italy, the 15th (2006) and 20th (2012) years of progress and more recently, in 2018, in Ponta Delgada, Portugal, 25 Years of Progress in Radar Altimetry. On this latter occasion it was decided to collect contributions of scientists, engineers and managers involved in the worldwide altimetry community to depict the state of altimetry and propose recommendations for the altimetry of the future. This paper summarizes contributions and recommendations that were collected and provides guidance for future mission design, research activities, and sustainable operational radar altimetry data exploitation. Recommendations provided are fundamental for optimizing further scientific and operational advances of oceanographic observations by altimetry, including requirements for spatial and temporal resolution of altimetric measurements, their accuracy and continuity. There are also new challenges and new openings mentioned in the paper that are particularly crucial for observations at higher latitudes, for coastal oceanography, for cryospheric studies and for hydrology. The paper starts with a general introduction followed by a section on Earth System Science including Ocean Dynamics, Sea Level, the Coastal Ocean, Hydrology, the Cryosphere and Polar Oceans and the “Green” Ocean, extending the frontier from biogeochemistry to marine ecology. Applications are described in a subsequent section, which covers Operational Oceanography, Weather, Hurricane Wave and Wind Forecasting, Climate projection. Instruments’ development and satellite missions’ evolutions are described in a fourth section. A fifth section covers the key observations that altimeters provide and their potential complements, from other Earth observation measurements to in situ data. Section 6 identifies the data and methods and provides some accuracy and resolution requirements for the wet tropospheric correction, the orbit and other geodetic requirements, the Mean Sea Surface, Geoid and Mean Dynamic Topography, Calibration and Validation, data accuracy, data access and handling (including the DUACS system). Section 7 brings a transversal view on scales, integration, artificial intelligence, and capacity building (education and training). Section 8 reviews the programmatic issues followed by a conclusion.

Published
2021

7. Altimetry for the future: Building on 25 years of progress

Author

Abdalla, Saleh, Abdeh Kolahchi, Abdolnabi, Ablain, Michaël, Adusumilli, Susheel, Aich Bhowmick, Suchandra, Alou-Font, Eva, Amarouche, Laiba, Andersen, Ole Baltazar, Antich, Helena, Aouf, Lotfi, Arbic, Brian, Armitage, Thomas, Arnault, Sabine, Artana, Camila, Aulicino, Giuseppe, Ayoub, Nadia, Badulin, Sergei, Baker, Steven, Banks, Chris, Bao, Lifeng, Barbetta, Silvia, Barceló-Llull, Bàrbara, Barlier, François, Basu, Sujit, Bauer-Gottwein, Peter, Becker, Matthias, Beckley, Brian, Bellefond, Nicole, Belonenko, Tatyana, Benkiran, Mounir, Benkouider, Touati, Bennartz, Ralf, Benveniste, Jérôme, Bercher, Nicolas, Berge-Nguyen, Muriel, Bettencourt, Joao, Blarel, Fabien, Blazquez, Alejandro, Blumstein, Denis, Bonnefond, Pascal, Borde, Franck, Bouffard, Jérôme, Boy, François, Boy, Jean-Paul, Brachet, Cédric, Brasseur, Pierre, Braun, Alexander, Brocca, Luca, Brockley, David, Brodeau, Laurent, Brown, Shannon, Bruinsma, Sean, Bulczak, Anna, Buzzard, Sammie, Cahill, Madeleine, Calmant, Stéphane, Calzas, Michel, Camici, Stefania, Cancet, Mathilde, Capdeville, Hugues, Carabajal, Claudia Cristina, Carrere, Loren, Cazenave, Anny, Chassignet, Eric P., Chauhan, Prakash, Cherchali, Selma, Chereskin, Teresa, Cheymol, Cecile, Ciani, Daniele, Cipollini, Paolo, Cirillo, Francesca, Cosme, Emmanuel, Coss, Steve, Cotroneo, Yuri, Cotton, David, Couhert, Alexandre, Coutin-Faye, Sophie, Crétaux, Jean-François, Cyr, Frederic, d’Ovidio, Francesco, Darrozes, José, David, Cedric, Dayoub, Nadim, De Staerke, Danielle, Deng, Xiaoli, Desai, Shailen, Desjonqueres, Jean-Damien, Dettmering, Denise, Di Bella, Alessandro, Díaz-Barroso, Lara, Dibarboure, Gerald, Dieng, Habib Boubacar, Dinardo, Salvatore, Dobslaw, Henryk, Dodet, Guillaume, Doglioli, Andrea, Domeneghetti, Alessio, Donahue, David, Dong, Shenfu, Donlon, Craig, Dorandeu, Joël, Drezen, Christine, Drinkwater, Mark, Du Penhoat, Yves, Dushaw, Brian, Egido, Alejandro, Erofeeva, Svetlana, Escudier, Philippe, Esselborn, Saskia, Exertier, Pierre, Fablet, Ronan, Falco, Cédric, Farrell, Sinead Louise, Faugere, Yannice, Femenias, Pierre, Fenoglio, Luciana, Fernandes, Joana, Fernández, Juan Gabriel, Ferrage, Pascale, Ferrari, Ramiro, Fichen, Lionel, Filippucci, Paolo, Flampouris, Stylianos, Fleury, Sara, Fornari, Marco, Forsberg, Rene, Frappart, Frédéric, Frery, Marie-laure, Garcia, Pablo, Garcia-Mondejar, Albert, Gaudelli, Julia, Gaultier, Lucile, Getirana, Augusto, Gibert, Ferran, Gil, Artur, Gilbert, Lin, Gille, Sarah, Giulicchi, Luisella, Gómez-Enri, Jesús, Gómez-Navarro, Laura, Gommenginger, Christine, Gourdeau, Lionel, Griffin, David, Groh, Andreas, Guerin, Alexandre, Guerrero, Raul, Guinle, Thierry, Gupta, Praveen, Gutknecht, Benjamin D., Hamon, Mathieu, Han, Guoqi, Hauser, Danièle, Helm, Veit, Hendricks, Stefan, Hernandez, Fabrice, Hogg, Anna, Horwath, Martin, Idžanović, Martina, Janssen, Peter, Jeansou, Eric, Jia, Yongjun, Jia, Yuanyuan, Jiang, Liguang, Johannessen, Johnny A., Kamachi, Masafumi, Karimova, Svetlana, Kelly, Kathryn, Kim, Sung Yong, King, Robert, Kittel, Cecile M.M., Klein, Patrice, Klos, Anna, Knudsen, Per, Koenig, Rolf, Kostianoy, Andrey, Kouraev, Alexei, Kumar, Raj, Labroue, Sylvie, Lago, Loreley Selene, Lambin, Juliette, Lasson, Léa, Laurain, Olivier, Laxenaire, Rémi, Lázaro, Clara, Le Gac, Sophie, Le Sommer, Julien, Le Traon, Pierre-Yves, Lebedev, Sergey, Léger, Fabien, Legresy, Benoı̂t, Lemoine, Frank, Lenain, Luc, Leuliette, Eric, Levy, Marina, Lillibridge, John, Liu, Jianqiang, Llovel, William, Lyard, Florent, Macintosh, Claire, Makhoul Varona, Eduard, Manfredi, Cécile, Marin, Frédéric, Mason, Evan, Massari, Christian, Mavrocordatos, Constantin, Maximenko, Nikolai, McMillan, Malcolm, Medina, Thierry, Melet, Angelique, Meloni, Marco, Mertikas, Stelios, Metref, Sammy, Meyssignac, Benoit, Minster, Jean-François, Moreau, Thomas, Moreira, Daniel, Morel, Yves, Morrow, Rosemary, Moyard, John, Mulet, Sandrine, Naeije, Marc, Nerem, Robert Steven, Ngodock, Hans, Nielsen, Karina, Nilsen, Jan Even Øie, Niño, Fernando, Nogueira Loddo, Carolina, Noûs, Camille, Obligis, Estelle, Otosaka, Inès, Otten, Michiel, Oztunali Ozbahceci, Berguzar, P. Raj, Roshin, Paiva, Rodrigo, Paniagua, Guillermina, Paolo, Fernando, Paris, Adrien, Pascual, Ananda, Passaro, Marcello, Paul, Stephan, Pavelsky, Tamlin, Pearson, Christopher, Penduff, Thierry, Peng, Fukai, Perosanz, Felix, Picot, Nicolas, Piras, Fanny, Poggiali, Valerio, Poirier, Étienne, Ponce de León, Sonia, Prants, Sergey, Prigent, Catherine, Provost, Christine, Pujol, M-Isabelle, Qiu, Bo, Quilfen, Yves, Rami, Ali, Raney, R. Keith, Raynal, Matthias, Remy, Elisabeth, Rémy, Frédérique, Restano, Marco, Richardson, Annie, Richardson, Donald, Ricker, Robert, Ricko, Martina, Rinne, Eero, Rose, Stine Kildegaard, Rosmorduc, Vinca, Rudenko, Sergei, Ruiz, Simón, Ryan, Barbara J., Salaün, Corinne, Sanchez-Roman, Antonio, Sandberg Sørensen, Louise, Sandwell, David, Saraceno, Martin, Scagliola, Michele, Schaeffer, Philippe, Scharffenberg, Martin G., Scharroo, Remko, Schiller, Andreas, Schneider, Raphael, Schwatke, Christian, Scozzari, Andrea, Ser-giacomi, Enrico, Seyler, Frederique, Shah, Rashmi, Sharma, Rashmi, Shaw, Andrew, Shepherd, Andrew, Shriver, Jay, Shum, C.K., Simons, Wim, Simonsen, Sebatian B., Slater, Thomas, Smith, Walter, Soares, Saulo, Sokolovskiy, Mikhail, Soudarin, Laurent, Spatar, Ciprian, Speich, Sabrina, Srinivasan, Margaret, Srokosz, Meric, Stanev, Emil, Staneva, Joanna, Steunou, Nathalie, Stroeve, Julienne, Su, Bob, Sulistioadi, Yohanes Budi, Swain, Debadatta, Sylvestre-baron, Annick, Taburet, Nicolas, Tailleux, Rémi, Takayama, Katsumi, Tapley, Byron, Tarpanelli, Angelica, Tavernier, Gilles, Testut, Laurent, Thakur, Praveen K., Thibaut, Pierre, Thompson, LuAnne, Tintoré, Joaquín, Tison, Céline, Tourain, Cédric, Tournadre, Jean, Townsend, Bill, Tran, Ngan, Trilles, Sébastien, Tsamados, Michel, Tseng, Kuo-Hsin, Ubelmann, Clément, Uebbing, Bernd, Vergara, Oscar, Verron, Jacques, Vieira, Telmo, Vignudelli, Stefano, Vinogradova Shiffer, Nadya, Visser, Pieter, Vivier, Frederic, Volkov, Denis, von Schuckmann, Karina, Vuglinskii, Valerii, Vuilleumier, Pierrik, Walter, Blake, Wang, Jida, Wang, Chao, Watson, Christopher, Wilkin, John, Willis, Josh, Wilson, Hilary, Woodworth, Philip, Yang, Kehan, Yao, Fangfang, Zaharia, Raymond, Zakharova, Elena, Zaron, Edward D., Zhang, Yongsheng, Zhao, Zhongxiang, Zinchenko, Vadim, and Zlotnicki, Victor

Published
2021
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21. Deep convection in the Lofoten Basin: ARGO vs MITgcm

Author

Aleksandr Fedorov and Belonenko Tatyana

Abstract

The Lofoten basin (the LB) contains relatively warm and salty waters regarding border basins such as Greenland and Barents Seas. Variability of the processes inside occurring in the basin reflects on the climate as on the mesoscales as on the interannual scales. We use a term mixed layer depth (MLD) as a border of the pycnocline in the water column, this parameter lets us evaluate the intensity of the convection in the region. Several methods of MLD calculations are tested in the current study: Kara, Montegut, and Dukhovskoy. The convection in the basin destructs stratification and forms massive intermediate water mass. The MITgcm data for 1993-2012 and over 5000 in-situ Argo T, S profiles for 2001-2017 were used in the calculations of the MLD.We consider the maximum MLD (mMLD) in the region and its spatial distribution. The mMLD is higher in the central part of the LB and corresponds to the location of the Lofoten basin eddy (the LBE). Here the mMLD reaches 1000 meters, the medium maximum is 400 meters based both on the in-situ and model data. The maximum mixed layer depth ​​varies in the range of 400-1000 meters according to both datasets were used. The MLD over 400 meters is observed from January to May every year.Acknowledgments: The authors acknowledge the support of the Russian Science Foundation (project No. 18-17-00027). The results of the MITgcm were provided by D.L. Volkov, Cooperative Institute for Marine and Atmospheric Studies, University of Miami, USA.

Published
2020

29. Analytical solution of the ray equations of Hamilton for Rossby waves on stationary shear flows.

Author

Gnevyshev, Vladimir and Belonenko, Tatyana

Subjects
STANDING waves, ROSSBY waves, HAMILTON'S equations, SHEAR flow, HAMILTON-Jacobi equations, ANALYTICAL solutions, OCEAN waves
Abstract

The asymptotic behavior of Rossby waves in the ocean interacting with a shear stationary flow is considered. It is shown that there is a qualitative difference between the problems for the zonal and non-zonal background flow. Whereas only one critical layer arises for a zonal flow, then several critical layers can exist for a non-zonal flow. It is established that the integrated ray equations of Hamilton are equivalent to the asymptotic behavior of the Cauchy problem solution. Explicit analytical solutions are obtained for the tracks of Rossby waves as a function of time and initial parameters of the wave disturbance, as well as the magnitude of the shear and angle of inclination of the flow to the zonal direction. On the example of Rossby waves on a shear flow, the ray equations of Hamilton are analytically integrated. The obtained explicit expressions make it possible to calculate in real-time the Rossby wave tracks for any initial wave direction and any shear current inclination angle. It is shown qualitatively that these tracks for a non-zonal flow are strongly anisotropic. [ABSTRACT FROM AUTHOR]

Published
2022
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41. WHAT ARE THEY: EDDIES OR WAVES?

Author

Belonenko, Tatyana and Foux, Victor

Subjects
*EDDIES, *WAVES (Physics), *OCEAN, *WATER currents, *ROSSBY waves
Abstract

The problem of seasonal variability of oceanic fields still retains debatable question about distinction between, and, if any, the relative energetic contributions from synoptic eddies and different kinds of low-frequency waves. An essential difference between synoptic eddies and low-frequency waves seems to be that eddies transfer the water mass and have almost circular currents, while in waves only their shapes are moving, as fluid particles perform motions along very meridionally stretched, ellipse-like orbits. Occasionally, synoptic eddies have some signs of Rossby waves: they travel with a westward component of the phase speed, with space-time scales coincide quantitatively with dispersion relations of Rossby waves. Why it is so, is not uniquely answered yet. Some investigators assume that this may be explained from views of static dynamics, in which synoptic eddies are considered as a peculiar large-scale turbulence whose equation contains, both eddies that transfer the water with them and Rossby waves that run over the sea surface. Thus, both the phenomena can co-exist. Other investigators associate these with essential non-linearity and dispersivity of wave motions, so that synoptic eddies are interpreted as Rossby solitons. Also, another interpretation of the synoptic ocean motions exist as if they are a system of moving energetic eddies of non-solitonic type, radiating Rossby waves. If so, the most typical way of evolution of the ocean eddy field is as follows: baroclinic eddies which are small compared to the Rossby inertial radius interact and become larger and larger by the two-dimensional turbulence law. The process proceed with decreasing frequencies and wave numbers, causing eddy parameters enter the dispersion surface of Rossby waves. Another explanation of the phenomenon progress is also possible: eddies, in the process of their evolution become barotropic and eventually take on Rossby parameters. [ABSTRACT FROM AUTHOR]

Published
2012
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