6. References

References

[Adc95]

A. Adcroft. Numerical Algorithms for use in a Dynamical Model of the Ocean. PhD thesis, Imperial College, London, 1995.

[AC04]

A. Adcroft and J.-M. Campin. Re-scaled height coordinates for accurate representation of free-surface flows in ocean circulation models. Ocean Modelling, 7:269–284, 2004. doi:10.1016/j.ocemod.2003.09.003.

[ACHM04]

A. Adcroft, J.-M. Campin, C. Hill, and J. Marshall. Implementation of an atmosphere-ocean general circulation model on the expanded spherical cube. Mon.~Wea.~Rev., 132:2845–2863, 2004. URL: http://mitgcm.org/pdfs/mwr_2004.pdf, doi:10.1175/MWR2823.1.

[AHC+04]

A. Adcroft, C. Hill, J.-M. Campin, J. Marshall, and P. Heimbach. Overview of the formulation and numerics of the MITgcm. In Proceedings of the ECMWF seminar series on Numerical Methods, Recent developments in numerical methods for atmosphere and ocean modelling, 139–149. ECMWF, 2004. URL: http://mitgcm.org/pdfs/ECMWF2004-Adcroft.pdf.

[AHM97]

A.J. Adcroft, C.N. Hill, and J. Marshall. Representation of topography by shaved cells in a height coordinate ocean model. Mon.~Wea.~Rev., 125:2293–2315, 1997. URL: http://mitgcm.org/pdfs/mwr_1997.pdf, doi:10.1175/1520-0493%281997%29125<2293:ROTBSC>2.0.CO;2.

[AM99]

Hill C. Adcroft, A. and J. Marshall. A new treatment of the coriolis terms in c-grid models at both high and low resolutions. Mon.~Wea.~Rev., 127:1928–1936, 1999. URL: http://mitgcm.org/pdfs/mwr_1999.pdf, doi:10.1175/1520-0493%281999%29127<1928:ANTOTC>2.0.CO;2.

[BFLM13]

Sylvain Bouillon, Thierry Fichefet, Vincent Legat, and Gurvan Madec. The elastic-viscous-plastic method revisited. Ocean Modelling, 71(0):2–12, 2013. Arctic Ocean. URL: http://dx.doi.org/10.1016/j.ocemod.2013.05.013, doi:10.1016/j.ocemod.2013.05.013.

[CMF08]

Jean-Michel Campin, John Marshall, and David Ferreira. Sea-ice ocean coupling using a rescaled vertical coordinate z$^\ast $. Ocean Modelling, 24(1–2):1–14, 2008. doi:10.1016/j.ocemod.2008.05.005.

[CMKL+14]

Karel Castro-Morales, Frank Kauker, Martin Losch, Stefan Hendricks, Kathrin Riemann-Campe, and Rüdiger Gerdes. Sensitivity of simulated Arctic sea ice to realistic ice thickness distributions and snow parameterizations. J.~Geophys.~Res., 119(1):559–571, 2014. URL: http://dx.doi.org/10.1002/2013JC009342, doi:10.1002/2013JC009342.

[Cho90]

M-D. Chou. Parameterizations for the absorption of solar radiation by o$_2$ and co$_2$ with applications to climate studies. J.~Clim., 3:209–217, 1990.

[Cho92]

M-D. Chou. A solar radiation model for use in climate studies. J.~Atmos.~Sci., 49:762–772, 1992.

[CMJSuarez94]

M.-D. Chou and M.J.Suarez. An efficient thermal infrared radiation parameterization for use in general circulation models. NASA Technical Memorandum 104606-Vol 3, National Aeronautics and Space Administration, NASA; Goddard Space Flight Center; Greenbelt (MD), 20771; USA, 1994. http://www.gmao.nasa.gov/.

[CHM99]

Daniel Jamous Chris Hill, Alistair Adcroft and John Marshall. A strategy for terascale climate modeling. In In Proceedings of the Eighth ECMWF Workshop on the Use of Parallel Processors in Meteorology, 406–425. World Scientific, 1999.

[Cla70]

R. H. Clarke. Observational studies in the atmospheric boundary layer. Q.~J.~R.~Meteorol.~Soc., 96:91–114, 1970.

[Cox87]

M. D. Cox. An isopycnal diffusion in a z-coordinate ocean model. Ocean modelling, 74:1–5 (Unpublished manuscript), 1987.

[DT94]

R. S. Defries and J. R. G. Townshend. Ndvi-derived land cover classification at global scales. Int’l J. Rem. Sens., 15:3567–3586, 1994.

[DS89]

J. L. Dorman and P. J. Sellers. A global climatology of albedo, roughness length and stomatal resistance for atmospheric general circulation models as represented by the simple biosphere model (sib). J.~Appl.~Meteor., 28:833–855, 1989.

[FH92]

G. M. Flato and W. D. Hibler, III. Modeling pack ice as a cavitating fluid. J.~Phys.~Oceanogr., 22:626–651, 1992.

[GGL90]

P. Gaspar, Y. Grégoris, and J.-M. Lefevre. A simple eddy kinetic energy model for simulations of the oceanic vertical mixing: tests at station papa and long-term upper ocean study site. J.~Geophys.~Res., 95 (C9):16,179–16,193, 1990.

[GM90]

P. R. Gent and J. C. McWilliams. Isopycnal mixing in ocean circulation models. J.~Phys.~Oceanogr., 20:150–155, 1990.

[GWMM95]

P. R. Gent, J. Willebrand, T. J. McDougall, and J. C. McWilliams. Parameterizing eddy-induced tracer transports in ocean circulation models. J.~Phys.~Oceanogr., 25:463–474, 1995.

[GKW91]

R. Gerdes, C. Koberle, and J. Willebrand. The influence of numerical advection schemes on the results of ocean general circulation models. Clim.~Dynamics, 5(4):211–226, 1991. doi:10.1007/BF00210006.

[Gri98]

S. M. Griffies. The Gent-McWilliams skew flux. J.~Phys.~Oceanogr., 28:831–841, 1998.

[GGP+98]

S. M. Griffies, A. Gnanadesikan, R. C. Pacanowski, V. Larichev, J. K. Dukowicz, and R. D. Smith. Isoneutral diffusion in a z-coordinate ocean model. J.~Phys.~Oceanogr., 28:805–830, 1998.

[HL88]

H. M. Helfand and J. C. Labraga. Design of a non-singular level 2.5 second-order closure model for the prediction of atmospheric turbulence. J.~Atmos.~Sci., 45:113–132, 1988.

[HS95]

H. M. Helfand and S. D. Schubert. Climatology of the simulated great plains low-level jet and its contribution to the continental moisture budget of the united states. J.~Clim., 8:784–806, 1995.

[Hib79]

W. D. Hibler, III. A dynamic thermodynamic sea ice model. J.~Phys.~Oceanogr., 9:815–846, 1979.

[Hib80]

William D. Hibler, III. Modeling a variable thickness sea ice cover. Mon.~Wea.~Rev., 1:1943–1973, 1980.

[Hib84]

William D. Hibler, III. The role of sea ice dynamics in modeling co$_2$ increases. In J. E. Hansen and T. Takahashi, editors, Climate processes and climate sensitivity, volume 29 of Geophysical Monograph, pages 238–253. AGU, Washington, D.C., 1984.

[HB87]

William D. Hibler, III and Kirk Bryan. A diagnostic ice-ocean model. J.~Phys.~Oceanogr., 17(7):987–1015, 1987.

[HM95]

C. Hill and J. Marshall. Application of a parallel navier-stokes model to ocean circulation in parallel computational fluid dynamics. In N. Satofuka A. Ecer, J. Periaux and S. Taylor, editors, Implementations and Results Using Parallel Computers, pages 545–552. Elsevier Science B.V.: New York, 1995.

[HL5a]

W.R. Holland and L. B. Lin. On the origin of mesoscale eddies and their contribution to the general circulation of the ocean. i. a preliminary numerical experiment. J.~Phys.~Oceanogr., 5:642–657, 1975a.

[HD97]

E. C. Hunke and J. K. Dukowicz. An elastic-viscous-plastic model for sea ice dynamics. J.~Phys.~Oceanogr., 27:1849–1867, 1997.

[Hun01]

Elizabeth C. Hunke. Viscous-plastic sea ice dynamics with the EVP model: linearization issues. J.~Comput.~Phys., 170:18–38, 2001. doi:10.1006/jcph.2001.6710.

[HJL04]

Jennifer K. Hutchings, Hrvoje Jasak, and Seymour W. Laxon. A strength implicit correction scheme for the viscous-plastic sea ice model. Ocean Modelling, 7(1–2):111–133, 2004. doi:10.1016/S1463-5003(03)00040-4.

[KDL15]

Madlen Kimmritz, Sergey Danilov, and Martin Losch. On the convergence of the modified elastic-viscous-plastic method of solving for sea-ice dynamics. J.~Comput.~Phys., 296:90–100, 2015. doi:10.1016/j.jcp.2015.04.051.

[KDL16]

Madlen Kimmritz, Sergey Danilov, and Martin Losch. The adaptive EVP method for solving the sea ice momentum equation. Ocean Modelling, 101:59–67, 2016. doi:10.1016/j.ocemod.2016.03.004.

[KL10]

Jody M. Klymak and Sonya M. Legg. A simple mixing scheme for models that resolve breaking internal waves. Ocean Modelling, 33:224–234, 2010. doi:10.1016/j.ocemod.2010.02.005.

[Kon75]

J. Kondo. Air-sea bulk transfer coefficients in diabatic conditions. Bound.~Layer~Meteorol., 9:91–112, 1975.

[KS91]

Randal D. Koster and Max J. Suarez. A simplified treatment of sib’s land surface albedo parameterization. NASA Technical Memorandum 104538, National Aeronautics and Space Administration, NASA; Goddard Space Flight Center; Greenbelt (MD), 20771; USA, 1991. http://www.gmao.nasa.gov/.

[KS92]

Randal D. Koster and Max J. Suarez. Modeling the land surface boundary in climate models as a composite of independent vegetation stands. J.~Geophys.~Res., 97:2697–2715, 1992.

[LH74]

A. A. Lacis and J. E. Hansen. A parameterization for the absorption of solar radiation in the earth’s atmosphere. J.~Atmos.~Sci., 31:118–133, 1974.

[LDDM97]

W. G. Large, G. Danabasoglu, S. C. Doney, and J. C. McWilliams. Sensitivity to surface forcing and boundary layer mixing in a global ocean model: annual-mean climatology. J.~Phys.~Oceanogr., 27(11):2418–2447, 1997.

[LP81]

W. G. Large and S. Pond. Open ocean momentum flux measurements in moderate to strong winds. J.~Phys.~Oceanogr., 11:324–336, 1981.

[LMD94]

W.G. Large, J.C. McWilliams, and S.C. Doney. Oceanic vertical mixing: a review and a model with nonlocal boundary layer parameterization. Rev.~Geophys., 32:363–403, 1994.

[LKT+12]

Jean-François Lemieux, Dana Knoll, Bruno Tremblay, David M. Holland, and Martin Losch. A comparison of the Jacobian-free Newton-Krylov method and the EVP model for solving the sea ice momentum equation with a viscous-plastic formulation: a serial algorithm study. J.~Comput.~Phys., 231(17):5926–5944, 2012. doi:10.1016/j.jcp.2012.05.024.

[LTSedlacek+10]

Jean-François Lemieux, Bruno Tremblay, Jan Sedláček, Paul Tupper, Stephen Thomas, David Huard, and Jean-Pierre Auclair. Improving the numerical convergence of viscous-plastic sea ice models with the Jacobian-free Newton-Krylov method. J.~Comput.~Phys., 229:2840–2852, 2010. doi:10.1016/j.jcp.2009.12.011c.

[Lepparanta83]

Matti Leppäranta. A growth model for black ice, snow ican and snow thickness in subarctic basins. Nordic Hydrology, 14:59–70, 1983.

[LFLV14]

Martin Losch, Annika Fuchs, Jean-François Lemieux, and Anna Vanselow. A parallel Jacobian-free Newton-Krylov solver for a coupled sea ice-ocean model. J.~Comput.~Phys., 257(A):901–910, 2014. doi:10.1016/j.jcp.2013.09.026.

[LMC+10]

Martin Losch, Dimitris Menemenlis, Jean-Michel Campin, Patrick Heimbach, and Chris Hill. On the formulation of sea-ice models. Part 1: effects of different solver implementations and parameterizations. Ocean Modelling, 33(1–2):129–144, 2010. doi:10.1016/j.ocemod.2009.12.008.

[MGZ+99]

J. Marotzke, R. Giering, K.Q. Zhang, D. Stammer, C. Hill, and T. Lee. Construction of the adjoint mit ocean general circulation model and application to atlantic heat transport variability. J.~Geophys.~Res., 104, C12:29,529–29,547, 1999.

[MAC+04]

J. Marshall, A. Adcroft, J.-M. Campin, C. Hill, and A. White. Atmosphere-ocean modeling exploiting fluid isomorphisms. Mon.~Wea.~Rev., 132:2882–2894, 2004. URL: http://mitgcm.org/pdfs/a_o_iso.pdf, doi:10.1175/MWR2835.1.

[MAH+97]

J. Marshall, A. Adcroft, C. Hill, L. Perelman, and C. Heisey. A finite-volume, incompressible navier stokes model for studies of the ocean on parallel computers. J.~Geophys.~Res., 102(C3):5753–5766, 1997. URL: http://mitgcm.org/pdfs/96JC02776.pdf.

[MHPA97]

J. Marshall, C. Hill, L. Perelman, and A. Adcroft. Hydrostatic, quasi-hydrostatic, and nonhydrostatic ocean modeling. J.~Geophys.~Res., 102(C3):5733–5752, 1997. URL: http://mitgcm.org/pdfs/96JC02775.pdf.

[MJH98]

J. Marshall, H. Jones, and C. Hill. Efficient ocean modeling using non-hydrostatic algorithms. J.~Mar.~Sys., 18:115–134, 1998. URL: http://mitgcm.org/pdfs/journal_of_marine_systems_1998.pdf, doi:10.1016/S0924-7963%2898%2900008-6.

[Mol09]

Andrea Molod. Running GCM physics and dynamics on different grids: algorithm and tests. Tellus, 61A:381–393, 2009.

[MS92]

S. Moorthi and M. J. Suarez. Relaxed arakawa schubert: a parameterization of moist convection for general circulation models. Mon.~Wea.~Rev., 120:978–1002, 1992.

[Mou96]

J.N. Moum. Energy-containing scales of turbulence in the ocean thermocline. J.~Geophys.~Res., 101 (C3):14095–14109, 1996.

[Orl76]

I. Orlanski. A simple boundary condition for unbounded hyperbolic flows. J.~Comput.~Phys., 21:251–269, 1976.

[PR97]

T. Paluszkiewicz and R.D. Romea. A one-dimensional model for the parameterization of deep convection in the ocean. Dyn.~Atmos.~Oceans, 26:95–130, 1997.

[Pan73]

H. A. Panofsky. Tower micrometeorology. In D. A. Haugen, editor, Workshop on Micrometeorology. American Meteorological Society, 1973.

[Red82]

Martha H. Redi. Oceanic Isopycnal Mixing by Coordinate Rotation. J.~Phys.~Oceanogr., 12(10):1154–1158, oct 1982. doi:10.1175/1520-0485(1982)012<1154:OIMBCR>2.0.CO;2.

[Roe85]

P.L. Roe. Some contributions to the modelling of discontinuous flows. In B.E. Engquist, S. Osher, and R.C.J. Somerville, editors, Large-Scale Computations in Fluid Mechanics, volume 22 of Lectures in Applied Mathematics, pages 163–193. American Mathematical Society, Providence, RI, 1985.

[RSG87]

J. E. Rosenfield, M. R. Schoeberl, and M. A. Geller. A computation of the stratospheric diabatic circulation using an accurate radiative transfer model. J.~Atmos.~Sci., 44:859–876, 1987.

[SG94]

Harvey E. Seim and Michael C. Gregg. Detailed observations of a naturally occurring shear instability. J.~Geophys.~Res., 99 (C5):10049–10073, 1994.

[Sem76]

Albert J. Semtner, Jr. A model for the thermodynamic growth of sea ice in numerical investigations of climate. J.~Phys.~Oceanogr., 6:379–389, 1976.

[Ste90]

D. P. Stevens. On open boundary conditions for three dimensional primitive equation ocean circulation models. Geophys. Astrophys. Fl. Dyn., 51:103–133, 1990.

[Sto48]

H. Stommel. The western intensification of wind-driven ocean currents. Trans. Am. Geophys. Union, 29:206, 1948.

[SM88]

Y. C. Sud and A. Molod. The roles of dry convection, cloud-radiation feedback processes and the influence of recent improvements in the parameterization of convection in the gla gcm. Mon.~Wea.~Rev., 116:2366–2387, 1988.

[TS96]

L. L. Takacs and M.J. Suarez. Dynamical aspects of climate simulations using the geos general circulation model. NASA Technical Memorandum 104606 Volume 10, National Aeronautics and Space Administration, NASA; Goddard Space Flight Center; Greenbelt (MD), 20771; USA, 1996. http://www.gmao.nasa.gov/.

[Tho77]

S.A. Thorpe. Turbulence and mixing in a scottish loch. Phil.~Trans.~R.~Soc.~Lond., 286:125–181, 1977.

[VMHS97]

M. Visbeck, J. Marshall, T. Haine, and M. Spall. Specification of eddy transfer coefficients in coarse-resolution ocean circulation models. J.~Phys.~Oceanogr., 27(3):381–402, 1997.

[WG94]

J. C. Wesson and Michael C. Gregg. Mixing at camarinal sill in the strait of gibraltar. J.~Geophys.~Res., 99 (C5):9847–9878, 1994.

[Win00]

Michael Winton. A reformulated three-layer sea ice model. J.~Atmos.~Ocean.~Technol., 17:525–531, 2000.

[YK74]

A. M. Yaglom and B. A. Kader. Heat and mass transfer between a rough wall and turbulent fluid flow at high reynolds and peclet numbers. J.~Fluid Mech., 62:601–623, 1974.

[Yam77]

T. Yamada. A numerical experiment on pollutant dispersion in a horizontally-homogenious atmospheric boundary layer. Atmos. Environ., 11:1015–1024, 1977.

[ZHSR98]

J. Zhang, W. D. Hibler, III, M. Steele, and D. A. Rothrock. Arctic ice-ocean modeling with and without climate restoring. J.~Phys.~Oceanogr., 28:191–217, 1998.

[ZH97]

Jinlun Zhang and William D. Hibler, III. On an efficient numerical method for modeling sea ice dynamics. J.~Geophys.~Res., 102(C4):8691–8702, 1997.

[ZSL95]

J. Zhou, Y.C. Sud, and K.-M. Lau. Impact of orographically induced gravity wave drag in the gla gcm. Q.~J.~R.~Meteorol.~Soc., 122:903–927, 1995.