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Fifty years of numerical modeling of baroclinic ocean

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This paper presents a brief critical analysis of the main historical stages of numerical modeling for the last fifty years. It was a half a century ago that the numerical simulation of an actual baroclinic ocean was initiated by the author and his students [1, 2]. In meteorology, studies on the numerical modeling of a baroclinic atmosphere existed much earlier [21, 22]. Despite this, a similar move in oceanography was met with strong resistance. At that time, there were many studies on the calculation of the total mass transport. The founders of this field, V.B. Shtokman, H. Sverdrup, and W. Munk, were mistaken in believing that they addressed baroclinic models of the ocean. The author preferred works by V. Ekman [12] and I. Sandström and B. Helland-Hansen [19]. A generalization of recent studies made it possible to come to some conclusions on the need to use the level of the free oceanic surface as a basis rather than the function of total mass transport, on the role of the baroclinic β effect (BARBE), on the joint effect of baroclinicity and bottom relief (JEBAR), etc. The author conditionally divides these fifty years into the following three stages. (1) The first stage was 1961–1969, when the author and his students performed almost exclusively diagnostic and adaptation calculations of climatic characteristics. (2) The second stage began with papers by K. Bryan [23] and his students. This is an important and promising stage involving mainly prognostic studies and four-dimensional analysis. The major advances in modeling at this stage (the Gulf Stream separation point [61], the Kuroshio seasonal evolution [63], the formation of the cold intermediate layer in the Black Sea [80], the subsurface countercurrent in the Caspian Sea [25], the realistic four-dimensional analysis of the Kara Sea [60], etc.) were due to high-resolution and/or data assimilation with an adequate period of integration. (3) The third stage began with the activities of international intercalibration programs such as the Arctic Ocean Model Intercomparison Project (AOMIP), the Global Ocean Data Assimilation Experiment (GODAE), Coordinated Ocean-Ice Reference Experiments (COREs), etc. Despite some defects initially, this is the most significant stage. For example, there is still very little data on GODAE, and COREs data are often used for a comparison of integral characteristics, the reliability of which cannot be established by direct measurements.

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References

  1. A. S. Sarkisyan, “The Role of the Pure Drift Advection of Density in the Dynamics of the Wind-Driven Currents of a Baroclinic Ocean,” Izv. Akad. Nauk SSSR, Ser. Geofiz., no. 9, 1396–1407 (1961).

    Google Scholar 

  2. A. S. Sarkisyan, “On the Dynamics of Occurrence of Wind-Driven Currents in a Baroclinic Ocean,” Okeanologiya 2(3), 393–409 (1962).

    Google Scholar 

  3. P. S. Lineikin, The Main Issues of the Dynamic Theory of the Baroclinic Layer of the Sea (Gidrometeoizdat, Leningrad, 1957) [in Russian].

    Google Scholar 

  4. Yu. K. Gormatyuk and A. S. Sarkisyan, “The Results of Calculations of Currents in the North Atlantic according to the Four-Level Model,” Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 1(3), 313–326 (1965).

    Google Scholar 

  5. V. F. Kozlov, “The Use of One-Parameter Density Models to Study of the Thermohaline Circulation in an Ocean of a Finite Depth,” Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 4(6), 622–632 (1968).

    Google Scholar 

  6. V. V. Knysh, “The Results of Numerical Calculation of Unsteady Fields of Flow Velocity and Density in the Ocean Basin of a Constant Depth,” Morskie Gidrofiz. Issled., no. 2 (52) (1971).

  7. V. B. Shtokman, “The Equation of the Total Transport Excited by the Wind in an Inhomogeneous Sea,” Dokl. Akad. Nauk SSSR 54(5), 407–410 (1946).

    Google Scholar 

  8. V. B. Shtokman, “Using the Analogy between the Total Transport in the Sea and Bending of the Fixed Plate for Characterizing Flows in Some Specific Cases,” Dokl. Akad. Nauk SSSR. Nov. Ser. 54(8), 689–692 (1946).

    Google Scholar 

  9. H. U. Sverdrup, “Wind-Driven Currents in a Baroclinic Ocean with Application to the Equatorial Currents of the Eastern Pacific,” Proc. Nat. Acad. Sci. U.S.A. 33, 318–326 (1947).

    Article  Google Scholar 

  10. W. H. Munk, “On the Wind-Driven Ocean Circulation,” J. Meteorol. 7(2), 79–93 (1950).

    Article  Google Scholar 

  11. Lord Rayleigh, “On the Flow of Viscous Liquids, Especially in Two Dimensions,” Philos. Magaz. J. Sci. XXXVIII, 354–372 (London, 1893).

    Article  Google Scholar 

  12. V. W. Ekman, “On the Influence of the Earth Rotation on Ocean Currents,” Arkiv Mat., Astron., Fysik 2(11), 1–52 (1905).

    Google Scholar 

  13. H. Stommel, The Gulf Stream (Univ. of California and Cambridge Univ. Press, 1958).

  14. A. S. Sarkisyan, “On the Determination of Steady Wind-Driven Currents in a Baroclinic Ocean Layer,” Trudy Geofiz. Inst. AN SSSR 164(37), 50–61 (1956).

    Google Scholar 

  15. A. S. Sarkisyan, Numerical Analysis and Forecast of Sea Currents (Gidrometeoizdat, Leningrad, 1977) [in Russian].

    Google Scholar 

  16. A. S. Sarkisyan, “Forty Years of JEBAR—the Finding of the Joint Effect of Baroclinicity and Bottom Relief for the Modeling of Ocean Climatic Characteristics,” Izv. Atmos. Ocean. Phys. 42(5), 534–554 (2006).

    Article  Google Scholar 

  17. G. Neumann, “On the Mass Transport of Wind-Driven Currents in a Baroclinic Ocean with Applications to the North Atlantic,” Z. Fur Meteorol. 12(4–6), 138–147 (1958).

    Google Scholar 

  18. G. F. Carrier and A. R. Robinson, “On the Theory of the Wind-Driven Ocean Circulation,” J. Fluid Mech. 12Part I, 49–80 (1962).

    Article  Google Scholar 

  19. I. W. Sandstrom and B. Helland-Hansen, “Uber die Berechnung von Meeresstromungen,” Res. Norw. Fish Mar. Inst. B (1903).

  20. A. S. Sarkisyan, Fundamentals of the Theory and Calculation of Ocean Currents (Gidrometeoizdat, Leningrad, 1966) [in Russian].

    Google Scholar 

  21. L. F. Richardson, Weather Prediction by Numerical Process. London, Cambridge Univ. Press.. B (1922).

    Google Scholar 

  22. P. D. Thompson, Numerical Weather Analysis and Prediction (The Macmillan Company, New York, 1961).

    Google Scholar 

  23. K. Bryan, “A Numerical Method for the Study of the Circulation of the World Ocean,” J. Comp. Phys. 4, 347–376 (1969).

    Article  Google Scholar 

  24. A. S. Sarkisyan and J. E. Sundermann, Modelling Ocean Climate Variability (Springer, Heidelberg, 2009).

    Book  Google Scholar 

  25. R. A. Ibrayev, Mathematical Modeling of Thermo-Hydrodynamic Processes in the Caspian Sea (GEOS, Moscow, 2008) [in Russian].

    Google Scholar 

  26. E. V. Semenov, “Numerical Modeling of White Sea Dynamics and Monitoring Problem,” Izv. Atmos. Ocean. Phys. 40(1), 114–126 (2004).

    Google Scholar 

  27. A. S. Sarkisyan, “On Some Achievements and Major Problems in Mathematical Modeling of Climatic Characteristics of the Ocean (Critical Analysis),” Izv. Atmos. Ocean. Phys. 46(6), 668–676 (2010).

    Article  Google Scholar 

  28. A. S. Sarkisyan, R. A. Ibrayev, and N. G. Yakovlev, “High Resolution and Four-Dimensional Analysis As a Prospect for Ocean Modelling,” Russ. J. Numer. Anal. Math. Modelling 25(5), 477–496 (2010).

    Article  Google Scholar 

  29. M. Cox, “A Primitive Equation, 3-Dimensional Model of the Ocean,” GFDL Ocean Group Technical Report, No. 1 (1984).

  30. S. Griffies, M. J. Harrison, R. C. Pacanowski, et al., A Technical Guide to MOM4, GFDL Ocean Group Technical Report No. 5 (NOAA/Geophysical Fluid Dynamics Laboratory, Princeton, NJ, 2004).

    Google Scholar 

  31. Yu. L. Demin and A. S. Sarkisyan, “Calculation of Equatorial Currents,” J. Mar. Res. 35, 339–356 (1977).

    Google Scholar 

  32. R. A. Ibraev, “Reconstruction of the Climatic Characteristics of the Gulf Stream,” Izv. Akad. Nauk, Fiz. Atm. Okeana 29(6), 803–814 (1993).

    Google Scholar 

  33. R. A. Ibrayev, “Model of Enclosed and Semi-Enclosed Sea Hydrodynamics,” Russ. J. Numer. Anal. Math. Modelling 16(4), 291–304 (2001).

    Google Scholar 

  34. P. D. Killworth, D. Stainforth, D. J. Webb, et al., “The Development of a Free Surface Bryan-Cox-Semtner Model,” J. Phys. Oceanogr. 21(5), 1333–1348 (1991).

    Article  Google Scholar 

  35. K. Bryan, S. Manabe, and R. C. Pacanowski, “A Global Ocean-Atmosphere Climate Model, II: The Oceanic Circulation,” J. Comput. Phys. 5(1), 30–46 (1975).

    Google Scholar 

  36. A. S. Sarkisyan and Ju. L. Demin, “A Semidiagnostic Method of Sea Currents Calculation,” Large-Scale Oceanographic Experiments in the WCRP 2(1), 210–214 (1983).

    Google Scholar 

  37. A. S. Sarkisyan, Yu. L. Demin, A. L. Brekhovskikh, and T. V. Shakhanova, The Methods and Results of Calculation of Water Circulation in the World Ocean (Gidrometeoizdat, Leningrad, 1986) [in Russian].

    Google Scholar 

  38. T. Ezer and G. L. Mellor, “Diagnostic and Prognostic Calculations of the North Atlantic and Sea Level Using a Sigma Coordinate Ocean Model,” J. Geophys. Res. 99 (1994).

  39. Yu. L. Demin and R. A. Ibraev, “Ocean Dynamics Model,” in Numerical Models and Results of Calibration Calculations for Currents in the Atlantic Ocean, Ed. by A. S. Sarkisyan and Yu. L. Demin (IVM RAN, Moscow, 1992) [in Russian].

    Google Scholar 

  40. G. I. Marchuk and A. S. Sarkisyan, Mathematical Modelling of Ocean Circulation (Springer-Verlag, Berlin, 1988).

    Book  Google Scholar 

  41. Yu. L. Demin, R. A. Ibraev, and A. S. Sarkisyan, “Calibration Models of Circulation and Reproduction of the World Ocean Climate,” Izv. AN SSSR. Fizika Atmosfery I Okena 27(10), 1054–1067 (1991).

    Google Scholar 

  42. A. S. Sarkisyan, Ocean Dynamics Modeling (Gidrometeoizdat, St. Petersburg, 1991) [in Russian].

    Google Scholar 

  43. Yu. L. Demin and R. A. Ibraev, “On a Boundary Problem for the Level of the Basin in the Models of Ocean Currents,” Izv. AN SSSR. Fiz. Atmos. Okeana 22(7), 757–764 (1986).

    Google Scholar 

  44. A. S. Sarkisyan, “On Some Milestones in Ocean Modeling History,” Rus. J. Numer. Anal. Math. Modelling 16(6), 497–518 (2001).

    Google Scholar 

  45. A. S. Sarkisyan and J. Sundermann, “The Direction of Mathematical Modeling of the Ocean Initiated by GI Marchuk,” Izv. Akad. Nauk, Fiz. Atmos. Okeana 31(3), 427–454 (1995).

    Google Scholar 

  46. S. Levitus and A. S. Sarkisyan, “Ocean Dynamic Characteristics Obtained by Synthesizing Climatic Data and the WOCE Program Information,” Izv. Atmos. Ocean. Phys. 37(4), 496–507 (2001).

    Google Scholar 

  47. N. A. Diansky, A. V. Bagno, and V. B. Zalesny, “Sigma Model of Global Ocean Circulation and Its Sensitivity to Variations in Wind Stress,” Izv. Atmos. Ocean. Phys. 38(4), 477–494 (2002).

    Google Scholar 

  48. IPCC. Climate Change: The Scientific Basis. Contribution of Working Group 1 to the Third Assessment Report of the IPCC (Cambridge Univ. Press, Cambridge, 2001).

  49. S. Hakkinen and G. L. Mellor, “Modelling the Seasonal Variability of the Coupled Ice-Ocean System,” J. Geophys. Res. 97(20), 285–304 (1992).

    Google Scholar 

  50. W. D. Hibler and K. Bryan, “A Diagnostic Ice-Ocean Model,” J. Phys. Oceanogr. 17(3), 987–1015 (1987).

    Article  Google Scholar 

  51. N. G. Iakovlev, “Numerical Model of the General Circulation of the Arctic Ocean. A New Version and Preliminary Calculation Results,” Russ. J. Numer. Anal. Math. Modelling 13(6), 465–478 (1998).

    Article  Google Scholar 

  52. M. J. Karcher and J. M. Oberhuber, “Pathways and Modification of the Upper and Intermediate Waters of the Arctic Ocean,” J. Geophys. Res. 107(C6), 3049 (2002). doi: 10.1029/2002JC000530

    Article  Google Scholar 

  53. V. I. Kuzin, E. N. Golubeva, and G. A. Platov, “Modeling of Hydrophysical Characteristics of the Arctic Ocean-North Atlantic,” in Fundamental Studies of the Oceans and Seas, Ed. by N. P. Laverov (Nauka, Moscow, 2006), Book 1, pp. 166–190 [in Russian].

    Google Scholar 

  54. W. Maslowski, D. Marble, W. Walczowski, et al., “On the Climatological Mass, Heat, and Salt Transports Through the Barents Sea and Fram Strait from a PanArctic Coupled Ice-Ocean Model Simulation,” J. Geophys. Res. 109, C03032. doi: 10.1029/2001JC001039

  55. I. V. Polyakov and L. A. Timokhov, “The Thermohaline Circulation of the Arctic Ocean,” Dokl. Akad. Nauk 342(2), 254–258 (1995).

    Google Scholar 

  56. A. Y. Proshutinsky and M. A. Johnson, “Two Circulation Regimes of the Wind-Driven Arctic Ocean,” J. Geophys. Res. 102(C6), 12493–12514 (1997).

    Article  Google Scholar 

  57. V. A. Ryabchenko, G. V. Alekseev, I. A. Neelov, et al., “Reproduction of Climatic Changes in the Arctic Basin Based on the Model of Ocean and Ice Circulation without Reference to the Climatic Salinity on the Surface of the Ocean,” Tr. Arkt. Antarkt. Nauch.-Issled. Inst. 446, 60–82 (2003).

    Google Scholar 

  58. T. Martin and R. Gerdes, “Sea Ice Drift Variability in Arctic Ocean Model Intercomparison Project Models and Observations,” J. Geophys. Res. 112, C04S10 (2007). doi: 10.1029/2006JC003617

    Article  Google Scholar 

  59. G. Holloway and A. Proshutinsky, “Role of Tides in Arctic Ocean/Ice Model,” J. Geophys. Res. 112, C04S06. doi: 10.1029/2006JC003643

  60. G. Panteleev, A. Proshutinsky, M. Kulakov, et al., “Investigation of the Summer Kara Sea Circulation Employing a Variational Data Assimilation Technique,” J. Geophys. Res. 112, C04S15 (2007). doi: 10.1029/2006JC003728

    Article  Google Scholar 

  61. E. P. Chassignet and D. P. Marshall, “Gulf Stream Separation in Numerical Ocean Models,” in Ocean Modeling in an Eddying Regime, Geophysical Monograph 177, Ed. by Hecht M.W., H. Hasumi (American Geophysical Union, Washington, DC, 2008).

    Chapter  Google Scholar 

  62. M. G. Bulushev and A. S. Sarkisyan, “Energetics at the Initial Stage of the Adjustment of Equatorial Currents,” Izv. Atmos. Ocean. Phys. 32(5), 552–563 (1996).

    Google Scholar 

  63. X. Guo, H. Hukuda, Y. Miyazawa, et al., “A Triply Nested Ocean Model for Simulating the Kuroshio-Roles of Horizontal Resolution on JEBAR,” J. Phys. Oceanogr. 33(1), 146–169 (2003).

    Article  Google Scholar 

  64. A. S. Sarkisyan, “Modeling the Gulf Stream Dynamics,” Izv. Akad. Nauk, Fiz. Atmos. Okeana 40(5), 556–568 (2004).

    Google Scholar 

  65. X. Chen, Analysis of the Circulation on the East-Chinese Shelf and the Adjacent Pacific Ocean. Dissertation Zur Erlangung Des Doktorgrades Der Naturwissenschaften Im (Hamburg, 2004).

  66. A. S. Sarkisyan, “Forty Years of JEBAR-the Finding of the Joint Effect of Baroclinicity and Bottom Relief for the Modeling of Ocean Climatic Characteristics,” Izv. Atmos. Ocean. Phys. 42(5), 534–554 (2006).

    Article  Google Scholar 

  67. E. P. Chassignet, Z. D. Garrafo, R. D. Smith, et al., High Resolution Gulf Stream Modelling (2001). http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.38. 1574

  68. R. D. Smith, M. E. Maltrud, F. O. Bryan, et al., “Numerical Simulation of the North Atlantic Ocean at 1/10°,” J. Phys. Oceanogr. 30(6), 1532–1561 (2000).

    Article  Google Scholar 

  69. G. I. Marchuk, “Basic and Adjoint Equations of Atmosphere and Ocean,” Meteorol. Gidrol., No. 2, 17–34 (1974).

  70. G. I. Marchuk and M. S. Yudin, “On the Use of a Priori Information Using the Conjugate Equations,” Dokl. Akad. Nauk SSSR 243(1), 66–69 (1978).

    Google Scholar 

  71. S. S. Efimov and E. V. Semenov, “The Dependence of the Results of Model Calculations for the Four-Dimension Analysis from the Initial State,” Okeanologiya 30(1), 21–26 (1990).

    Google Scholar 

  72. G. I. Marchuk, Methods of Computational Mathematics (Nauka, Moscow, 1980) [in Russian].

    Google Scholar 

  73. G. I. Marchuk, Splitting Methods (Nauka, Moscow, 1988).

    Google Scholar 

  74. G. I. Marchuk, Adjoint Equations and Analysis of Complex Systems (Kluwer Academic Publishers, Dordrecht, 1995).

    Google Scholar 

  75. G. I. Marchuk, J. Sundermann, and V. B. Zalesny, “Mathematical Modeling of Marine and Ocean Currents,” Russ. J. Numer. Anal. Math. Modelling 16(4), 331–362 (2001).

    Google Scholar 

  76. G. I. Marchuk, V. P. Shutyaev, and V. B. Zalesny, “Approaches to the Solution of Data Assimilation Problems,” in Optimal Control and Partial Differential Equations, Ed. by J. L. Menaldi et al. (IOS Press, Amsterdam, 2001), pp. 489–497.

    Google Scholar 

  77. A. S. Sarkisyan and V. B. Zalesny, “Splitting-Up Method and Adjoint Equation Method in the Ocean Dynamics Problem,” Russ. J. Numer. Anal. Math. Modelling 15(3–4), 333–347 (2000).

    Article  Google Scholar 

  78. V. V. Knysh, A. S. Nelepo, A. S. Sarkisyan, et al., “Dynamic-Stochastic Approach to the Analysis of Observations of the Density Field in Hydrophysical Test Areas,” Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 14(10), 1079–1093 (1978).

    Google Scholar 

  79. S. G. Demyshev, G. K. Korotaev, and A. S. Sarkisyan, “Numerical Experiments of Adjustment of Hydrological Field in the Equatorial Atlantic on the Basis of Conservative Model,” Russ. J. Numer. Anal. Math. Modelling 7(1), 1–24 (1992).

    Article  Google Scholar 

  80. V. V. Knysh and A. S. Sarkisyan, “Four-Dimensional Analysis of Hydrophysical Ocean and Sea Fields: Numerical Experiments and Reconstructions,” Izv. Atmos. Ocean. Phys. 39(6), 739–753 (2003).

    Google Scholar 

  81. G. K. Korotaev, O. A. Saenko, Ch. J. Koblinski, et al., “Evaluation of the Accuracy, Methodology and Some Results of the Assimilation of Altimetric Data TOPEX/POSEIDON in General Circulation Model of the Black Sea,” Issled. Zemli Kosmosa, No. 3, 3–17 (1998).

  82. R. E. Kalman, “A New Approach to Linear Filtering and Prediction Problems,” ASME. J. Basic Eng. 82, 127–139 (1960).

    Google Scholar 

  83. G. L. Mellor and T. Yamada, “Development of a Turbulence Closure Model for Geophysical Fluid Problems,” Rev. Geophys. Space Phys. 20(4), 851–875 (1982).

    Article  Google Scholar 

  84. S. M. Griffies, A. Biastoch, C. Boning, et al., “Coordinated Ocean-Ice Reference Experiments (COREs),” Ocean Model. 26(1), 1–46 (2009).

    Article  Google Scholar 

  85. E. Dombrowsky, L. Bertino, G. B. Brassington, et al., “GODAE Systems in Operation,” Oceanography 22(3), 80–95 (2009).

    Article  Google Scholar 

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  1. Institute of Numerical Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119333, Russia

    A. S. Sarkisyan

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Original Russian Text © A.S. Sarkisyan, 2012, published in Izvestiya AN. Fizika Atmosfery i Okeana, 2012, Vol. 48, No. 1, pp. 6–20.

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Sarkisyan, A.S. Fifty years of numerical modeling of baroclinic ocean. Izv. Atmos. Ocean. Phys. 48, 1–14 (2012). https://doi.org/10.1134/S0001433812010100

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