Skip to main content

Isopycnic and Hybrid Ocean Modeling in the Context of GODAE

  • Chapter
  • First Online:
Book cover Operational Oceanography in the 21st Century

Abstract

An ocean forecasting system has three essential components (observations, data assimilation, numerical model). Observational data, via data assimilation, form the basis of an accurate model forecast; the quality of the ocean forecast will depend primarily on the ability of the ocean numerical model to faithfully represent the ocean physics and dynamics. Even the use of an infinite amount of data to constrain the initial conditions will not necessarily improve the forecast against persistence of a poorly performing ocean numerical model. In this chapter, some of the challenges associated with global ocean modeling are introduced and the current state of numerical models formulated in isopycnic and hybrid vertical coordinates is reviewed within the context of operational global ocean prediction systems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Adcroft A, Hallberg R (2006) On methods for solving the oceanic equations of motion in generalized vertical coordinates. Ocean Model 11:224–233

    Article  Google Scholar 

  • Arbic BK, Wallcraft AJ, Metzger EJ (2010) Concurrent simulation of the eddying general circulation and tides in a global ocean model. Ocean Model 32:175–187

    Google Scholar 

  • Barron CN, Martin PJ, Kara AB, Rhodes RC, Smedstad LF (2006) Formulation, implementation and examination of vertical coordinate choices in the Global Navy Coastal Ocean Model (NCOM). Ocean Model 11:347–375

    Article  Google Scholar 

  • Barth A, Alvera-Azcárate A, Weisberg RH (2008) Benefit of nesting a regional model into a large-scale ocean model instead of climatology. Application to the West Florida Shelf. Cont Shelf Res 28:561–573

    Article  Google Scholar 

  • Bleck R (1978) Finite difference equations in generalized vertical coordinates. Part I: Total energy conservation. Contrib Atmos Phys 51:360–372

    Google Scholar 

  • Bleck R (1998) Ocean modeling in isopycnic coordinates. In: Chassignet EP, Verron J (eds) Ocean Modeling and Paramterization. NATO Science Series. Kluwer Academic Publishers, Dordrecht, pp 423–448

    Chapter  Google Scholar 

  • Bleck R (2002) An oceanic general circulation model framed in hybrid isopycnic-cartesian coordinates. Ocean Model 4:55–88

    Article  Google Scholar 

  • Bleck R, Benjamin S (1993) Regional weather prediction with a model combining terrain-following and isentropic coordinates. Part I: Model description. Mon Wea Rev 121:1770–1785

    Article  Google Scholar 

  • Bleck R, Boudra D (1981) Initial testing of a numerical ocean circulation model using a hybrid (quasi-isopycnic) vertical coordinate. J Phys Oceanogr 11:755–770

    Article  Google Scholar 

  • Bleck R, Chassignet EP (1994) Simulating the oceanic circulation with isopycnic coordinate models. In: Majundar SK, Mill EW, Forbes GS, Schmalz RE, Panah AA (eds) The oceans: Physical-chemical dynamics and human impact. The Pennsylvania Academy of Science, Easton, pp 17–39

    Google Scholar 

  • Bleck R, Rooth C, Hu D, Smith LT (1992) Salinity-driven thermocline transients in a wind- and thermohaline-forced isopycnic coordinate model of the North Atlantic. J Phys Oceanogr 22:1486–1505

    Article  Google Scholar 

  • Burchard H, Beckers JM (2004) Non-uniform adaptive vertical grids in one-dimensional numerical ocean models. Ocean Model 6:51–81

    Google Scholar 

  • Carnes MR, Fox DN, Rhodes RC, Smedstad OM (1996) Data assimilation in a North Pacific Ocean monitoring and prediction system. In: Malanotte-Rizzoli P (ed) Modern approaches to data assimilation in ocean modeling. Elsevier, New York, pp 319–345

    Chapter  Google Scholar 

  • Chassignet EP, Garraffo ZD (2001) Viscosity parameterization and the Gulf Stream separation. In: Muller P, Henderson D (eds) From stirring to mixing in a stratified ocean. Proceedings ‘Aha Huliko’a Hawaiian Winter Workshop. University of Hawaii. 15–19 January 2001, pp 37–41

    Google Scholar 

  • Chassignet EP, Malanotte-Rizzoli P (2000) Ocean circulation model evaluation experiments for the North Atlantic basin. Dyn Atmos Oceans 32:155–432 (Elsevier Science Ltd., special issue)

    Article  Google Scholar 

  • Chassignet EP, Marshall DP (2008) Gulf Stream separation in numerical ocean models. In: Hecht M, Hasumi H (eds) Eddy-Resolving Ocean Modeling. AGU monograph series, American Geophysical Union, Washington, DC, pp 39–62

    Chapter  Google Scholar 

  • Chassignet EP, Verron J (1998) Ocean modeling and parameterization. Kluwer Academic Publishers, Dordrecht, p 451

    Book  Google Scholar 

  • Chassignet EP, Verron J (2006) Ocean weather forecasting: an integrated view of oceanography. Springer, Dordrecht, p 577

    Book  Google Scholar 

  • Chassignet EP, Smith LT, Bleck R, Bryan FO (1996) A model comparison: Numerical simulations of the North and Equatorial Atlantic Ocean circulation in depth and isopycnic coordinates. J Phys Oceanogr 26:1849–1867

    Article  Google Scholar 

  • Chassignet EP, Smith LT, Halliwell GR, Bleck R (2003) North Atlantic simulations with the HYbrid Coordinate Ocean Model (HYCOM): Impact of the vertical coordinate choice, reference density, and thermobaricity. J Phys Oceanogr 33:2504–2526

    Article  Google Scholar 

  • Chassignet EP, Hurlburt HE, Smedstad OM, Halliwell GR, Wallcraft AJ, Metzger EJ, Blanton BO, Lozano C, Rao DB, Hogan PJ, Srinivasan A (2006) Generalized vertical coordinates for eddy-resolving global and coastal ocean forecasts. Oceanography 19:20–31

    Article  Google Scholar 

  • Chassignet EP, Hurlburt HE, Smedstad OM, Halliwell GR, Hogan PJ, Wallcraft AJ, Baraille R, Bleck R (2007) The HYCOM (HYbrid Coordinate Ocean Model) data assimilative system. J Mar Sys 65:60–83

    Article  Google Scholar 

  • Chassignet EP, Hurlburt HE, Metzger EJ, Smedstad OM, Cummings J, Halliwell GR, Bleck R, Baraille R, Wallcraft AJ, Lozano C, Tolman HL, Srinivasan A, Hankin S, Cornillon P, Weisberg R, Barth A, He R, Werner F, Wilkin J (2009) U.S. GODAE: Global ocean prediction with the HYbrid Coordinate Ocean Model (HYCOM). Oceanography 22(2):64–75

    Article  Google Scholar 

  • Clarke AJ (2008) An introduction to the dynamics of El Niño & the Southern oscillation. Amsterdam, Elsevier, p 324

    Google Scholar 

  • Cooper M, Haines K (1996) Altimetric assimilation with water property conservation. J Geophys Res 101:1059–1078

    Article  Google Scholar 

  • Cornillon P, Adams J, Blumenthal MB, Chassignet EP, Davis E, Hankin S, Kinter J, Mendelssohm R, Potemra JT, Srinivasan A, Sirott J (2009) NVODS and the development of OPeNDAP—an integrative tool for oceanographic data systems. Oceanography 22(2):116–127

    Article  Google Scholar 

  • Cox MD (1987) Isopycnal diffusion in a z-coordinate ocean model. Ocean Modelling (unpublished manuscripts) 74:1–5

    Google Scholar 

  • Cummings JA (2005) Operational multivariate ocean data assimilation. Quart J Royal Met Soc 131:3583–3604

    Article  Google Scholar 

  • Ezer T, Mellor G (2004) A generalized coordinate ocean model and a comparison of the bottom boundary layer dynamics in terrainfollowing and z-level grids. Ocean Model 6:379–403

    Google Scholar 

  • Fox DN, Teague WJ, Barron CN, Carnes MR, Lee CM (2002) The modular ocean data analysis system (MODAS). J Atmos Ocean Technol 19:240–252

    Article  Google Scholar 

  • Fratantoni DM (2001) North Atlantic surface circulation during the 1990’s observed with satellite-tracked drifters. J Geophys Res 106:22,067–22,093

    Google Scholar 

  • Gent PR, McWilliams JC (1990) Isopycnic mixing in ocean circulation models. J Phys Oceanogr 20:150–155

    Article  Google Scholar 

  • Gent PR, Willebrand J, McDougall TJ, McWilliams JC (1995) Parameterizing eddy-induced tracer transports in ocean circulation models. J Phys Oceanogr 25:463–474

    Article  Google Scholar 

  • Goff JA, Arbic BK (2010) Global prediction of abyssal hill roughness statistics for use in ocean models from digital maps of paleo-spreading rate, paleoridge orientation, and sediment thickness. Ocean Model 32:36–43. doi:10.1016/j.ocemod.2009.10.001

    Article  Google Scholar 

  • Greatbatch RJ, Mellor GL (1999) An overview of coastal ocean models. In: Mooers CNK (eds) Coastal ocean prediction. American Geophysical Union, Washington, pp 31–57, 526 pages total

    Chapter  Google Scholar 

  • Griffies SM, Adcroft AJ (2008) Formulating the equations of ocean models. In: Hecht M, Hasumi H (eds) Eddy resolving ocean modeling. Geophysical Monograph Series. American Geophysical Union, Washington, pp 281–318

    Google Scholar 

  • Griffies SM, Hallberg RW (2000) Biharmonic friction with a Smagorinsky viscosity for use in large-scale eddy-permitting ocean models. Mon Weather Rev 128:2935–2946

    Article  Google Scholar 

  • Griffies SM, Böning C, Bryan FO, Chassignet EP, Gerdes R, Hasumi H, Hirst A, Treguier A-M, Webb D (2000a) Developments in ocean climate modelling. Ocean Model 2:123–192

    Article  Google Scholar 

  • Griffies SM, Pacanowski RC, Hallberg RW (2000b) Spurious diapycnal mixing associated with advection in a z-coordinate ocean model. Monthly Weather Rev 128:538–564

    Article  Google Scholar 

  • Hallberg RW (1995) Some aspects of the circulation in ocean basins with isopycnals intersecting the sloping boundaries, Ph.D. thesis, University of Washington, Seattle, p 244

    Google Scholar 

  • Hallberg RW (1997) Stable split time stepping schemes for large-scale ocean modelling. J Comput Phys 135:54–65

    Article  Google Scholar 

  • Hallberg RW (2005) A thermobaric instability of Lagrangian vertical coordinate ocean models. Ocean Model 8:279–300

    Article  Google Scholar 

  • Hallberg RW, Adcroft A (2009) Reconciling estimates of the free surface height in Lagrangian vertical coordinate ocean models with mode-split time stepping. Ocean Model 29:15–26

    Google Scholar 

  • Halliwell G (2004) Evaluation of vertical coordinate and vertical mixing algorithms in the HYbrid Coordinate Ocean Model (HYCOM). Ocean Model 7:285–322

    Article  Google Scholar 

  • Halliwell GR Jr, Barth A, Weisberg RH, Hogan P, Smedstad OM, Cummings J (2009) Impact of GODAE products on nested HYCOM simulations of the West Florida Shelf. Ocean Dyn 59:139–155

    Article  Google Scholar 

  • Hecht MW, Hasumi H (2008) Ocean modeling in an eddying regime. Geophysical monograph series, vol 7. American Geophysical Union, Washington, p 409

    Book  Google Scholar 

  • Hecht MW, Hunke E, Maltrud ME, Petersen MR, Wingate BA (2008) Lateral mixing in the eddying regime and a new broad-ranging formulation. In: Hecht, Hasumi (eds) Ocean modeling in an eddying regime. AGU Monograph Series. AGU, Washington, pp. 339–352

    Chapter  Google Scholar 

  • Hurlburt HE, Chassignet EP, Cummings JA, Kara AB, Metzger EJ, Shriver JF, Smedstad OM, Wallcraft AJ, Barron CN (2008) Eddy-resolving global ocean prediction. In: Hecht M, Hasumi H (ed) “Ocean Modeling in an Eddying Regime”. Geophysical monograph 177. American Geophysical Union, Washington, pp 353–381

    Chapter  Google Scholar 

  • Hurlburt HE, Brassington GB, Drillet Y, Kamachi M, Benkiran M, Bourdalle-Badie R, Chassignet EP, LeGalloudec O, Lellouche JM, Metzger EJ, Oke PR, Pugh T, Schiller A, Smedstad OM, Tranchant B, Tsujino H, Usui N, Wallcraft AJ (2009) High resolution global and basin-scale ocean analyses and forecasts. Oceanography 22(3):110–127

    Article  Google Scholar 

  • Iselin CO (1939) The influence of vertical and lateral turbulence on the characteristics of the waters at mid-depths. Eos Trans Am Geophys Union 20:414–417

    Article  Google Scholar 

  • Jakobsson M, Cherkis N, Woodward J, Coakley B, Macnab R (2000) A new grid of Arctic bathymetry: A significant resource for scientists and mapmakers, EOS Transactions. Am Geophys Union 81(9):89, 93, 96

    Google Scholar 

  • Ledwell JR, Watson AJ, Law CS (1993) Evidence for slow mixing across the pycnocline from an open-ocean tracer-release experiment. Nature 364:701–703

    Article  Google Scholar 

  • Lee MM, Coward AC, Nurser AJ (2002) Spurious diapycnal mixing of the deep waters in an eddy-permitting global ocean model. J Phys Oceanogr 32:1522–1535

    Article  Google Scholar 

  • Legg S, Chang Y, Chassignet EP, Danabasoglu G, Ezer T, Gordon AL, Griffes S, Hallberg R, Jackson L, Large W, Özgökmen T, Peters H, Price J, Riemenschneider U, Wu W, Xu X, Yang J (2009) Improving oceanic overflow representation in climate models: the Gravity Current Entrainment Climate Process Team. Bull Am Met Soc 90(4):657–670. doi:10.1175/2008BAMS2667.1

    Article  Google Scholar 

  • Leveque, R.J. (2002) Finite volume methods for hyperbolic problems. Cambridge University Press, Cambridge, p 578

    Book  Google Scholar 

  • Maltrud ME, McClean JL (2005) An eddy resolving global 1/10_ ocean simulation. Ocean Model 8:31–54

    Article  Google Scholar 

  • Maximenko NA, Niiler PP (2005). Hybrid decade-mean sea level with mesoscale resolution. In: Saxena N (ed) “Recent Advances in Marine Science and Technology”. PACON International, Honolulu, pp. 55–59

    Google Scholar 

  • McDougall TJ, Church JA (1986) Pitfalls with the numerical representation of isopycnal and diapycnal mixing. J Phys Oceanogr 16:196–199

    Article  Google Scholar 

  • Meincke JC, Le Provost, Willebrand J (2001) Dynamics of the North Atlantic Circulation (DYNAMO). Prog Oceanogr 48:N°2–3

    Article  Google Scholar 

  • Metzger EJ, Smedstad OM, Thoppil P, Hurlburt HE, Wallcraft AJ, Franklin DS, Shriver JF, Smedstad LF (2008) Validation Test Report for Global Ocean Prediction System V3.0—1/12°HYCOM/NCODA: Phase I, NRL Memo. Report, NRL/MR/7320—08-9148

    Google Scholar 

  • Montgomery RB (1940) The present evidence on the importance of lateral mixing processes in the ocean. Bull Am Meteor Soc 21:87–94

    Google Scholar 

  • Oberhuber JM (1993) Simulation of the atlantic circulation with a coupled sea ice-mixed layer-isopycnal general circulation model. Part I: model description. J Phys Oceanogr 23:808–829

    Article  Google Scholar 

  • Papadakis MP, Chassignet EP, Hallberg RW (2003) Numerical simulations of the Mediterranean Sea outflow: Impact of the entrainment parameterization in an isopycnic coordinate ocean model. Ocean Model 5:325–356

    Article  Google Scholar 

  • Philander SGH (1990) El Niño, La Niña, and the Southern Oscillation. Academic Press, New York, p 293

    Google Scholar 

  • Redi MH (1982) Oceanic mixing by coordinate rotation. J Phys Oceanogr 12:87–94

    Article  Google Scholar 

  • Schmitz WJ (1996) On the World Ocean Circulation. Vol. 1: Some global features/North Atlantic circulation. Woods Hole Oceanographic Institute Tech. Rep. WHOI-96–03. p 141

    Google Scholar 

  • Schopf PS, Loughe A (1995) A reduced-gravity isopycnal ocean model: Hindcasts of El Niño. Mon Wea Rev 123:2839–2863

    Google Scholar 

  • Shchepetkin AF, McWilliams JC (2005) The Regional Ocean Modeling System (ROMS): A split-explicit, free-surface, topography-following coordinates ocean model. Ocean Model 9:347–404

    Article  Google Scholar 

  • Shriver JF, Hurlburt HE (2000) The effect of upper ocean eddies on the non-steric contribution to the barotropic mode. Geophys Res Lett 27:2713–2716

    Article  Google Scholar 

  • Shriver JF, Hurlburt HE, Smedstad OM, Wallcraft AJ, Rhodes RC (2007) 1/32°real-time global ocean prediction and value-added over 1/16 resolution. J Mar Sys 65:3–26

    Article  Google Scholar 

  • Smith WHF, Sandwell DT (1997) Global seafloor topography from satellite altimetry and ship depth soundings: evidence for stochastic reheating of the oceanic lithosphere. Science 277:1956–1962

    Article  Google Scholar 

  • Smith WHF, Sandwell DT (2004) Conventional bathymetry, bathymetry from space, and geodetic altimetry. Oceanography 17:8–23

    Article  Google Scholar 

  • Song YT, Haidvogel DB (1994) A semi-implicit ocean circulation model using topography-following coordinate. Journal of Computational Physics 115:228–244

    Google Scholar 

  • Song, YT, Hou TY (2006) Parametric vertical coordinate formulation for multiscale, Boussinesq, and non-Boussinesq ocean modeling. Ocean Model 11:298–332

    Google Scholar 

  • Stammer D, Wunsch C, Ponte RM (2000) De-aliasing of global high frequency barotropic motions in altimeter observations. Geophys Res Lett 27:1175–1178

    Article  Google Scholar 

  • Sun S, Bleck R, Rooth CG, Dukowicz J, Chassignet EP, Killworth P (1999) Inclusion of thermobaricity in isopycnic-coordinate ocean models. J Phys Oceanogr 29:2719–2729

    Article  Google Scholar 

  • van Leer B (1977) Towards the ultimate conservative difference scheme IV: a new approach to numerical numerical convection. J Comput Phys 23:276–299

    Article  Google Scholar 

  • Veronis G (1975) The role of models in tracer studies. In: Numerical models of ocean circulation. National Academy of Sciences, Washington, pp. 133–146

    Google Scholar 

  • Wallcraft AJ, Kara AB, Hurlburt HE, Rochford PA (2003) NRL Layered Ocean Model (NLOM) with an embedded mixed layer sub-model: formulation and tuning. J Atmos Oceanic Technol 20:1601–1615

    Article  Google Scholar 

  • Willebrand J, Barnier B, Böning C, Dieterich C, Killworth PD, Le Provost C, Jia Y, Molines JM, New AL (2001) Circulation characteristics in three eddy-permitting models of the North Atlantic. Prog Oceanogr 48:123–161

    Article  Google Scholar 

  • Xu X, ChangYS, Peters H, Özgökmen TM, Chassignet EP (2006). Parameterization of gravity current entrainment for ocean circulation models using a high-order 3D nonhydrostatic spectral element model. Ocean Model 14:19–44

    Article  Google Scholar 

  • Xu X, Chassignet EP, Price JF, Özgökmen TM, Peters H (2007) A regional modeling study of the entraining Mediterranean outflow. J Geophys Res 112:C12005. doi:10.1029/2007JC004145

    Article  Google Scholar 

Download references

Acknowledgements

As stated in the introduction, a lot of material presented in this chapter relies heavily on articles, notes, and review papers by R. Bleck, S. Griffies, A. Adcroft, and R. Hallberg. I also would like to acknowledge contributions by H. Hurlburt and B. Arbic. The development of the HYCOM ocean prediction system was sponsored by the National Oceanographic Partnership Program (NOPP) and the Office of Naval Research (ONR).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Eric P. Chassignet .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Chassignet, E.P. (2011). Isopycnic and Hybrid Ocean Modeling in the Context of GODAE. In: Schiller, A., Brassington, G. (eds) Operational Oceanography in the 21st Century. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0332-2_11

Download citation

Publish with us

Policies and ethics