Numerical Eddy-Resolving Modeling of the Ocean: Mesoscale and Sub-Mesoscale Examples

E. V. Stanev1, ✉, M. Ricker1, 2, S. Grayek1, B. Jacob1, V. Haid1, 3, J. Staneva1

1 Helmholtz-Zentrum Geesthacht, Geesthacht, Germany

2 Institute for Chemistry and Biology of the Marine Environment, University of Oldenburg, Oldenburg, Germany

3 Alfred Wegener Institute Helmholtz Centre for Polar and Marine Research, Bremerhaven, Germany

e-mail: emil.stanev@hzg.de

Abstract

Purpose. The study addresses rotational motion of geophysical fluids in the horizontal and vertical planes. It is aimed mainly at tracing the development of high-resolution numerical modeling of the ocean, as well as at demonstrating new physical processes due to more correct consideration both of the tides in the eddy-resolving numerical models and sub-mesoscale dynamics in the models of the sea straits.

Methods and Results. The ocean eddies and their interaction with tides are studied using numerical simulations by four NEMO models for the European North-West shelf with the resolutions ranging from 7 to 1.5 km. The vertical characteristics of motion in the Bosporus Strait were studied using numerical simulations with SCHISM, the unstructured grid model with the ultra-fine model resolution (less than 100 m). The barotropic tidal forcing resulted in substantial flattening of the slopes of the spectral curves. The most important difference between the spectral features of four models occurs in the motion rotational component. In the model with the 1.5 km resolution, the magnitude of the vorticity power spectral density at the scales ~ 70 km is by an order of magnitude higher than in the other three models. Although most of the tidal flattening is associated with the internal tides, beyond a certain horizontal resolution, the eddy dynamics become affected by the barotropic tides. The shelf of the Biscay Bay and the shallows around the Faroe Islands are the most sensitive areas to adding of the barotropic tides to the model forcing. Due to the grid ultra-fine resolution, new elements of physical motion emerged in the Bosporus region. The lateral circulation is dominated by the systems of multiple circulation cells with the scales ~ 1 km. In some areas, the lateral flow magnitude exceeds 0.5 m/s, which is comparable with the magnitude of the axial flow. This reveals importance of the helical elements of the strait circulation for overturning of water masses in the Bosporus.

Conclusions. Without proper resolution, the models of tidal oceanic dynamics simulate the ocean general circulation, but do not describe correctly the energy cascades at the eddy scales including interaction between the tides and the mesoscale eddies. Absence of this sub-mesoscale dynamics in the models can largely affect their capability to simulate the two-layer inter-basin exchange.

Keywords

ocean eddies, numerical ocean models, horizontal resolution, inter-basin exchange

Acknowledgements

The study was carried out at support of the Initiative and Networking Fund of the Helmholtz Association within the framework of the project “Advanced Earth System Modelling Capacity”.

Original russian text

Original Russian Text © The Authors, 2020, published in MORSKOY GIDROFIZICHESKIY ZHURNAL, Vol. 36, Iss. 6, pp. 691-719 (2020)

For citation

Stanev, E.V., Ricker, M., Grayek, S., Jacob, B., Haid, V. and Staneva, J., 2020. Numerical eddy-resolving modeling of the ocean: Mesoscale and sub-mesoscale examples. Physical oceanography, 27(6), pp. 631-658. doi:10.22449/1573-160X-2020-6-631-658

DOI

10.22449/1573-160X-2020-6-631-658

References

  1. Mossa, M., 2021. The Recent 500th Anniversary of Leonardo da Vinci’s Death: a Reminder of his Contribution in the Field of Fluid Mechanics. Environmental Fluid Mechanics, 21, pp. 1-10. https://doi.org/10.1007/s10652-020-09748-4
  2. Helmholtz, H., 2009. Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen. Journal fur die Reine und Angewandte Mathematik, 1858(55), pp. 25-55. https://doi.org/10.1515/crll.1858.55.25
  3. Monin, A.S., Kamenkovich, V.M. and Kort, V.G., 1977. Variability of the Oceans. London: John Wiley & Sons Ltd, 241 p.
  4. Kamenkovich, V.M., Koshlyakov, M.N. and Monin, A.S., Eds., 1986. Synoptic Eddies in the Ocean. Dordrecht, Holland: D. Reidel Publishing Company, 433 p.
  5. The MODE Group, 1978. The Mid-Ocean Dynamics Experiment. Deep Sea Research, 25(10), pp. 859-910. https://doi.org/10.1016/0146-6291(78)90632-X
  6. McWilliams, J.C., Owens, W.B. and Hua, B.L., 1986. An Objective Analysis of the POLYMODE Local Dynamics Experiment. Part I: General Formalism and Statistical Model Parameters. Journal of Physical Oceanography, 16(3), pp. 483-504. doi:10.1175/1520- 0485(1986)016<0483:AOAOTP>2.0.CO;2
  7. Semtner, A.J. and Chervin, R.M., 1992. Ocean General Circulation from a Global Eddy- Resolving Model. Journal of Geophysical Research, 9(C4), pp. 5493-5550. https://doi.org/10.1029/92JC00095
  8. Malone, R.C., Smith, R.D., Maltrud, M.E. and Hecht, M.W., 2003. Eddy-Resolving Ocean Modeling. Los Alamos Science, 28, pp. 223-231.
  9. Maltrud, M.E. and McClean, J.L., 2005. An Eddy Resolving Global 1/10° Ocean Simulation. Ocean Modelling, 8(1-2), pp. 31-54. doi:10.1016/j.ocemod.2003.12.001
  10. Treguier, A.M., Deshayes, J., Le Sommer, J., Lique, C., Madec, G., Penduff, T., Molines, J.-M., Barnier, B., Bourdalle-Badie, R. and Talandier, C., 2014. Meridional Transport of Salt in the Global Ocean from an Eddy-Resolving Model. Ocean Science, 10, pp. 243-255. https://doi.org/10.5194/os-10-243-2014
  11. Iovino, D., Masina, S., Storto, A., Cipollone, A. and Stepanov, V.N., 2016. A 1/16° Eddying Simulation of the Global NEMO Sea-Ice–Ocean System. Geoscientific Model Development, 9(8), pp. 2665-2684. https://doi.org/10.5194/gmd-9-2665-2016
  12. Robinson, A.R., Harrison, D.E. and Haidvogel, D.B., 1979. Mesoscale Eddies and General Ocean Circulation Models. Dynamics of Atmospheres and Oceans, 3(2-4), pp. 143-180. https://doi.org/10.1016/0377-0265(79)90005-8
  13. McWilliams, J.C., 2016. Submesoscale Currents in the Ocean. Proceedings of the Royal Society A. Mathematical, Physical and Engineering Sciences, 472(2189), 20160117. http://doi.org/10.1098/rspa.2016.0117
  14. Haid, V., Stanev, E.V., Pein, J., Staneva, J. and Chen, W., 2020. Secondary Circulation in Shallow Ocean Straits: Observations and Numerical Modeling of the Danish Straits. Ocean Modelling, 148, 101585. https://doi.org/10.1016/j.ocemod.2020.101585
  15. Stanev, E.V. and Ricker, M., 2020. Interactions between Barotropic Tides and Mesoscale Processes in Deep Ocean and Shelf Regions. Ocean Dynamics, 70, pp. 713-728. https://doi.org/10.1007/s10236-020-01348-6
  16. Madec, G. and the NEMO team, 2008. NEMO Ocean Engine. Note du Pôle de modélisation. Technical Report. France: Institut Pierre-Simon Laplace, no. 27. Available at: https://www.nemo-ocean.eu/doc/node1.html [Accessed: 5 November 2020]. 386 p.
  17. Lerczak, J.A. and Geyer, W.R., 2004. Modeling the Lateral Circulation in Straight, Stratified Estuaries. Journal of Physical Oceanography, 34(6), pp. 1410-1428. https://doi.org/10.1175/1520-0485(2004)034&lt;1410:MTLCIS&gt;2.0.CO;2
  18. Zhang, Y.J., Ye, F., Stanev, E.V. and Grashorn, S., 2016. Seamless Cross-Scale Modeling with SCHISM. Ocean Modelling, 102, pp. 64-81. https://doi.org/10.1016/j.ocemod.2016.05.002
  19. Di Fidio, M. and Gandolfi, C., 2011. Flow Velocity Measurement in Italy between Renaissance and Risorgimento. Journal of Hydraulic Research, 49(5), pp. 578-585. doi:10.1080/00221686.2011.594599
  20. Lelong, M.-P. and Kunze, E., 2013. Can Barotropic Tide-Eddy Interactions Excite Internal Waves? Journal of Fluid Mechanics, 721, pp. 1-27. https://doi.org/10.1017/jfm.2013.1
  21. Rocha, C.B., Chereskin, T.K., Gille, S.T. and Menemenlis, D., 2016. Mesoscale to Submesoscale Wavenumber Spectra in Drake Passage. Journal of Physical Oceanography, 46(2), pp. 601-620. https://doi.org/10.1175/JPO-D-15-0087.1
  22. Morozov, E.G., 1995. Semidiurnal Internal Wave Global Field. Deep-Sea Research Part I: Oceanographic Research Papers, 42(1), pp. 135-148. https://doi.org/10.1016/0967- 0637(95)92886-C
  23. Ray, R.D. and Mitchum, G.T., 1997. Surface Manifestation of Internal Tides in the Deep Ocean: Observations from Altimetry and Island Gauges. Progress on Oceanography, 40(1-4), pp. 135-162. https://doi.org/10.1016/S0079-6611(97)00025-6
  24. Egbert, G.D. and Ray, R.D., 2001. Estimates of M2 Tidal Energy Dissipation from TOPEX/Poseidon Altimeter Data. Journal of Geophysical Research: Oceans, 106(C10), pp. 22475-22502. https://doi.org/10.1029/2000JC000699
  25. Vlasenko, V., Stashchuk, N. and Hutter, K., 2005. Baroclinic Tides: Theoretical Modeling and Observational Evidence. Cambridge: Cambridge University Press, 372 p.
  26. Garrett, C. and Kunze, E., 2007. Internal Tide Generation in the Deep Ocean. Annual Review of Fluid Mechanics, 39, pp. 57-87. https://doi.org/10.1146/annurev.fluid.39.050905.110227
  27. Richman, J.G., Arbic, B.K., Shriver, J.F., Metzger, E.J., and Wallcraft, A.J., 2012. Inferring Dynamics from the Wavenumber Spectra of an Eddying Global Ocean Model with Embedded Tides. Journal of Geophysical Research: Oceans, 117(C12), C12012. https://doi.org/10.1029/2012JC008364
  28. Savage, A.C., Arbic, B.K., Richman, J.G., Shriver, J.F., Alford, M.H., Buijsman, M.C., Farrar, J.T., Sharma, H., Voet, G., Wallcraft, A.J. and Zamudio, L., 2017. Frequency Content of Sea Surface Height Variability from Internal Gravity Waves to Mesoscale Eddies. Journal of Geophysical Research: Oceans, 122(3), pp. 2519-2538. https://doi.org/10.1002/2016JC012331
  29. Tchilibou, M., Gourdeau, L., Morrow, R., Serazin, G., Djath, B. and Lyard, F., 2018. Spectral Signatures of the Tropical Pacific Dynamics from Model and Altimetry: a Focus on the Meso-/Submesoscale Range. Ocean Science, 14(5), pp. 1283-1301. https://doi.org/10.5194/os-14- 1283-2018
  30. Huthnance, J.M., 1995. Circulation, Exchange and Water Masses at the Ocean Margin: the Role of Physical Processes at the Shelf Edge. Progress in Oceanography, 35(4), pp. 353-431. https://doi.org/10.1016/0079-6611(95)00012-6
  31. Huthnance, J.M., Holt, J.T. and Wakelin, S.L., 2009. Deep Ocean Exchange with West-European Shelf Seas. Ocean Science, 5(4), pp. 621-634. https://doi.org/10.5194/os-5-621-2009
  32. Buckingham, C.E., Naveira Garabato, A.C., Thompson, A.F., Brannigan, L., Lazar, A., Marshall, D.P., George Nurser, A.J., Damerell, G., Heywood, K.J. and Belcher, S.E., 2016. Seasonality of Submesoscale Flows in the Ocean Surface Boundary Layer. Geophysical Research Letters, 43(5), pp. 2118-2126. https://doi.org/10.1002/2016GL068009
  33. Hallberg, R., 2013. Using a Resolution Function to Regulate Parameterizations of Oceanic Mesoscale Eddy Effects. Ocean Modelling, 72, pp. 92-103. https://doi.org/10.1016/j.ocemod.2013.08.007
  34. Polton, J.A., 2015. Tidally Induced Mean Flow over Bathymetric Features: a Contemporary Challenge for High-Resolution Wide-Area Models. Geophysical & Astrophysical Fluid Dynamics, 109(3), pp. 207-215. https://doi.org/10.1080/03091929.2014.952726
  35. Holt, J., Hyder, P., Ashworth, M., Harle, J., Hewitt, H.T., Liu, H., New, A.L., Pickles, S., Porter, A. [et al.], 2017. Prospects for Improving the Representation of Coastal and Shelf Seas in Global Ocean Models. Geoscientific Model Development, 10(1), pp. 499-523. https://doi.org/10.5194/gmd-10-499-2017
  36. Guihou, K., Polton, J., Harle, J., Wakelin, S., O'Dea, E. and Holt, J., 2017. Kilometric Scale Modeling of the North West European Shelf Seas: Exploring the Spatial and Temporal Variability of Internal Tides. Journal of Geophysical Research: Oceans, 123(1), pp. 688-707. https://doi.org/10.1002/2017JC012960
  37. Graham, J.A., Rosser, J.P., O'Dea, E. and Hewitt, H.T., 2018. Resolving Shelf Break Exchange around the European Northwest Shelf. Geophysical Research Letters, 45(22), pp. 12386-12395. https://doi.org/10.1029/2018GL079399
  38. Tonani, M., Sykes, P., King, R.R., McConnell, N., Péquignet, A.-C., O'Dea, E., Graham, J.A., Polton, J. and Siddorn, J., 2019. The Impact of a New High-Resolution Ocean Model on the Met Office North-West European Shelf Forecasting System. Ocean Science, 15(4), pp. 1133- 1158. https://doi.org/ 10.5194/os-15-1133-2019
  39. O’Dea, E.J., Arnold, A.K., Edwards, K.P., Furner, R., Hyder, P., Martin, M.J., Siddorn, J.R., Storkey, D., While, J., Holt, J.T. and Liu, H., 2012. An Operational Ocean Forecast System Incorporating NEMO and SST Data Assimilation for the Tidally Driven European North-West Shelf. Journal of Operational Oceanography, 5(1), pp. 3-17. https://doi.org/10.1080/1755876X.2012.11020128
  40. Ho-Hagemann, Ha T.M., Hagemann, S., Grayek, S., Petrik, R., Rockel, B., Staneva, J., Feser, F. and Schrum, C., 2020. Internal Model Variability of the Regional Coupled System Model GCOAST- AHOI. Atmosphere, 11(3), 227. https://doi.org/10.3390/atmos11030227
  41. Egbert, G.D. and Erofeeva, S.Y., 2002. Efficient Inverse Modeling of Barotropic Ocean Tides. Journal of Atmospheric and Oceanic Technology, 19(2), pp. 183-204. doi:10.1175/1520-0426(2002)019<0183:EIMOBO>2.0.CO;2
  42. Stanev, E.V., Grashorn, S. and Zhang, Y.J., 2017. Cascading Ocean Basins: Numerical Simulations of the Circulation and Interbasin Exchange in the Azov-Black-Marmara- Mediterranean Seas System. Ocean Dynamics, 67(8), pp. 1003-1025. http://dx.doi.org/10.1007/s10236-017-1071-2
  43. Ünlüata, T., Oğuz, T., Latif, M.A. and Özsoy, E., 1990. On the Physical Oceanography of the Turkish Straits. In: L. J. Pratt, Ed., 1990. The Physical Oceanography of Sea Straits. Dordrecht: Springer, pp. 25-60. doi:10.1007/978-94-009-0677-8
  44. Stanev, E.V., Pein, J., Grashorn, S., Zhang, Y. and Schrum, C., 2018. Dynamics of the Baltic Sea Straits via Numerical Simulation of Exchange Flows. Ocean Modelling, 131, pp. 40-58. doi:10.1016/j.ocemod.2018.08.009
  45. Zhang, Y. and Baptista, A.M., 2008. SELFE: A Semi-Implicit Eulerian-Lagrangian Finite Element Model for Cross-Scale Ocean Circulation. Ocean Modelling, 21(3-4), pр. 71-96. https://doi.org/10.1016/j.ocemod.2007.11.005
  46. Zhang, Y.J., Ateljevich, E., Yu, H.-C., Wu, C.H. and Yu, J.C.S., 2015. A New Vertical Coordinate System for a 3D Unstructured-Grid Model. Ocean Modelling, 85, pp. 16-31. http://dx.doi.org/10.1016/j.ocemod.2014.10.003
  47. Codiga, D.L., 2011. Unified Tidal Analysis and Prediction Using the UTide Matlab Functions. Technical Report 2011–01. Narragansett, RI.: Graduate School of Oceanography, University of Rhode Island, 59 p. doi:10.13140/RG.2.1.3761.2008
  48. Meyerjürgens, J., Ricker, M., Schakau, V., Badewien, T.H. and Stanev, E.V., 2020. Relative Dispersion of Surface Drifters in the North Sea: The Effect of Tides on Mesoscale Diffusivity. Journal of Geophysical Research: Oceans, 125(8), e2019JC015925. https://doi.org/10.1029/2019JC015925
  49. Van Sebille, E., Griffies, S.M., Abernathey, R., Adams, T.P., Berloff, P., Biastoch, A., Blanke, B., Chassignet, E.P., Cheng, Y. [et al.], 2018. Ocean Modelling, 121, pp. 49-75. https://doi. org/10.1016/j.ocemod.2017.11.008
  50. Hua, B.L. and Haidvogel, D.B., 1986. Numerical Simulations of the Vertical Structure of Quasi-Geostrophic Turbulence. Journal of the Atmospheric Sciences, 43(23), pp. 2923-2936. https://doi.org/10.1175/1520-0469(1986)043%3C2923:NSOTVS%3E2.0.CO;2
  51. Le Traon, P.Y., Klein, P., Hua, B.L. and Dibarboure, G., 2008. Do Altimeter Wavenumber Spectra Agree with the Interior or Surface Quasigeostrophic Theory? Journal of Physical Oceanography, 38(5), pp. 1137-1142. https://doi.org/10.1175/2007JPO3806.1
  52. Xu, Y. and Fu, L.-L., 2012. The Effects of Altimeter Instrument Noise on the Estimation of the Wavenumber Spectrum of Sea Surface Height. Journal of Physical Oceanography, 42(12), pp. 2229-2233. https://doi.org/10.1175/JPOD-12-0106.1
  53. Dufau, C., Orsztynowicz, M., Dibarboure, G., Morrow, R. and Le Traon, P.-Y., 2016. Mesoscale Resolution Capability of Altimetry: Present and Future. Journal of Geophysical Research: Oceans, 121(7), pp. 4910-4927. https://doi.org/10.1002/2015JC010904
  54. Ray, R.D. and Zaron, E.D., 2016. M2 Internal Tides and Their Observed Wavenumber Spectra from Satellite Altimetry. Journal of Physical Oceanography, 46(1), pp. 3-22. https://doi.org/10.1175/JPO-D-15-0065.1
  55. Jarosz, E., Teague, W.J., Book, J.W. and Beşiktepe, Ş., 2011. On Flow Variability in the Bosporus Strait. Journal of Geophysical Research: Oceans, 116(C8), C08038. https://doi.org/10.1029/2010JC006861
  56. Simpson, J.H., Brown, J., Matthews, J. and Allen, G., 1990. Tidal Straining, Density Currents, and Stirring in the Control of Estuarine Stratification. Estuaries, 13(2), pp. 125-132. doi:10.2307/1351581
  57. Nidzieko, N.J., Hench, J.L. and Monismith, S.G., 2009. Lateral Circulation in Well-Mixed and Stratified Estuarine Flows with Curvature. Journal of Physical Oceanography, 39(4), pp. 831-851. doi:10.1175/2008JPO4017.1
  58. Li, M., Cheng, P., Chant, R., Valle-Levinson, A. and Arnott, K., 2014. Analysis of Vortex Dynamics of Lateral Circulation in a Straight Tidal Estuary. Journal of Physical Oceanography, 44(10), pp. 2779-2795. https://doi.org/10.1175/JPO-D-13-0212.1

Download the article (PDF)