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\item[\label{_CITEREF_adcroft2006}%
\mbox{[}1\mbox{]}]Alistair Adcroft and Robert Hallberg. \href{http://www.sciencedirect.com/science/article/pii/S1463500305000090}{\tt On methods for solving the oceanic equations of motion in generalized vertical coordinates}. {\itshape Ocean Modelling}, 11(1-\/2)\+:224--233, January 2006. 


\item[\label{_CITEREF_adcroft2008}%
\mbox{[}2\mbox{]}]Alistair Adcroft, Robert Hallberg, and Matthew Harrison. \href{http://www.sciencedirect.com/science/article/pii/S1463500308000243}{\tt A finite volume discretization of the pressure gradient force using analytic integration}. {\itshape Ocean Modelling}, 22(3-\/4)\+:106--113, January 2008. 


\item[\label{_CITEREF_arakawa1990}%
\mbox{[}3\mbox{]}]Akio Arakawa and Yueh-\/\+Jiuan~G. Hsu. Energy conserving and potential-\/enstrophy dissipating schemes for the shallow water equations. {\itshape Monthly Weather Review}, 118\+:1960--1969, 1990. 


\item[\label{_CITEREF_arakawa1981}%
\mbox{[}4\mbox{]}]Akio Arakawa and Vivian~R. Lamb. \href{https://journals.ametsoc.org/doi/abs/10.1175/1520-0493(1981)109%3C0018:APEAEC%3E2.0.CO%3B2}{\tt A Potential Enstrophy and Energy Conserving Scheme for the Shallow Water Equations}. {\itshape Monthly Weather Review}, 109(1)\+:18--36, January 1981. 


\item[\label{_CITEREF_bleck1990}%
\mbox{[}5\mbox{]}]Rainer Bleck and Linda~T. Smith. A wind‐driven isopycnic coordinate model of the north and equatorial atlantic ocean\+: 1. model development and supporting experiments. {\itshape J\+GR Oceans}, 95\+:3273--3285, 1990. 


\item[\label{_CITEREF_bleck2002}%
\mbox{[}6\mbox{]}]Rainer Bleck. \href{http://www.sciencedirect.com/science/article/pii/S1463500301000129}{\tt An oceanic general circulation model framed in hybrid isopycnic-\/\+Cartesian coordinates}. {\itshape Ocean Modelling}, 4(1)\+:55--88, 2002. 


\item[\label{_CITEREF_carpenter1990}%
\mbox{[}7\mbox{]}]Jr. Carpenter, Richard~L., Kelvin~K. Droegemeier, Paul~R. Woodward, and Carl~E. Hane. Application of the piecewise parabolic method (ppm) to meteorological modeling. {\itshape Monthly Weather Review}, 118\+:586--–612, 1990. 


\item[\label{_CITEREF_colella1984}%
\mbox{[}8\mbox{]}]Phillip Colella and Paul~R Woodward. \href{https://www.sciencedirect.com/science/article/pii/0021999184901438}{\tt The Piecewise Parabolic Method (P\+PM) for gas-\/dynamical simulations}. {\itshape Journal of Computational Physics}, 54(1)\+:174--201, April 1984. 


\item[\label{_CITEREF_dukowicz2000}%
\mbox{[}9\mbox{]}]John~K. Dukowicz and John~R. Baumgardner. \href{http://www.sciencedirect.com/science/article/pii/S0021999100964659}{\tt Incremental Remapping as a Transport/\+Advection Algorithm}. {\itshape Journal of Computational Physics}, 160(1)\+:318--335, May 2000. 


\item[\label{_CITEREF_durran2010}%
\mbox{[}10\mbox{]}]Dale~R. Durran. {\itshape Numerical Methods for Fluid Dynamics With Applications to Geophysics}. Springer-\/\+Verlag New York, 2010. 


\item[\label{_CITEREF_easter1993}%
\mbox{[}11\mbox{]}]Richard~C. Easter. Two modified versions of bott\textquotesingle{}s positive-\/definite numerical advection scheme. {\itshape Monthly Weather Review}, 121\+:297--304, 1993. 


\item[\label{_CITEREF_fox-kemper2011}%
\mbox{[}12\mbox{]}]B.~Fox-\/\+Kemper, G.~Danabasoglu, R.~Ferrari, S.~M. Griffies, R.~W. Hallberg, M.~M. Holland, M.~E. Maltrud, S.~Peacock, and B.~L. Samuels. \href{http://www.sciencedirect.com/science/article/pii/S1463500310001290}{\tt Parameterization of mixed layer eddies. I\+I\+I\+: Implementation and impact in global ocean climate simulations}. {\itshape Ocean Modelling}, 39(1)\+:61--78, January 2011. 


\item[\label{_CITEREF_gent1995}%
\mbox{[}13\mbox{]}]Peter~R. Gent, Jurgen Willebrand, Trevor~J. Mc\+Dougall, and James~C. Mc\+Williams. \href{https://journals.ametsoc.org/doi/10.1175/1520-0485%281995%29025%3C0463%3APEITTI%3E2.0.CO%3B2}{\tt Parameterizing Eddy-\/\+Induced Tracer Transports in Ocean Circulation Models}. {\itshape Journal of Physical Oceanography}, 25(4)\+:463--474, April 1995. 


\item[\label{_CITEREF_griffies2000}%
\mbox{[}14\mbox{]}]Stephen~M. Griffies and Robert~W. Hallberg. \href{https://journals.ametsoc.org/doi/full/10.1175/1520-0493%282000%29128%3C2935%3ABFWASL%3E2.0.CO%3B2}{\tt Biharmonic Friction with a Smagorinsky-\/\+Like Viscosity for Use in Large-\/\+Scale Eddy-\/\+Permitting Ocean Models}. {\itshape Monthly Weather Review}, 128(8)\+:2935--2946, August 2000. 


\item[\label{_CITEREF_griffies2000-2}%
\mbox{[}15\mbox{]}]Stephen~M. Griffies, Claus B\"{o}ning, Frank~O. Bryan, Eric~P. Chassignet, Rüdiger Gerdes, Hiroyasu Hasumi, Anthony Hirst, Anne-\/\+Marie Treguier, and David Webb. \href{http://www.sciencedirect.com/science/article/pii/S1463500300000147}{\tt Developments in ocean climate modelling}. {\itshape Ocean Modelling}, 2(3)\+:123--192, January 2000. 


\item[\label{_CITEREF_SMGbook}%
\mbox{[}16\mbox{]}]Stephen~M. Griffies. {\itshape Fundamentals of Ocean Climate Models}. Princeton University Press, Princeton, U\+SA, 2004. 518+xxxiv pages.


\item[\label{_CITEREF_hallberg2009}%
\mbox{[}17\mbox{]}]Robert Hallberg and Alistair Adcroft. \href{http://www.sciencedirect.com/science/article/pii/S1463500309000298}{\tt Reconciling estimates of the free surface height in Lagrangian vertical coordinate ocean models with mode-\/split time stepping}. {\itshape Ocean Modelling}, 29(1)\+:15--26, January 2009. 


\item[\label{_CITEREF_hallberg1997}%
\mbox{[}18\mbox{]}]Robert Hallberg. \href{http://journals.ametsoc.org/doi/abs/10.1175/1520-0485(1997)027%3C0977%3ALCBSAB%3E2.0.CO%3B2}{\tt Localized Coupling between Surface and Bottom-\/\+Intensified Flow over Topography}. {\itshape Journal of Physical Oceanography}, 27(6)\+:977--998, June 1997. 


\item[\label{_CITEREF_hallberg1997a}%
\mbox{[}19\mbox{]}]Robert Hallberg. Stable split time stepping schemes for large-\/scale ocean modeling. {\itshape Journal of Computational Physics}, 135\+:54--65, 1997. 


\item[\label{_CITEREF_hallberg2005}%
\mbox{[}20\mbox{]}]Robert Hallberg. A thermobaric instability of lagrangian vertical coordinate ocean models. {\itshape Ocean Modelling}, 8, 2005. 


\item[\label{_CITEREF_hirt1997}%
\mbox{[}21\mbox{]}]C.~W. Hirt, A.~A. Amsden, and J.~L. Cook. \href{http://www.sciencedirect.com/science/article/pii/S0021999197957028}{\tt An Arbitrary Lagrangian-\/\+Eulerian Computing Method for All Flow Speeds}. {\itshape Journal of Computational Physics}, 135(2)\+:203--216, August 1997. 


\item[\label{_CITEREF_huynh1997}%
\mbox{[}22\mbox{]}]H.~T. Huynh. Schemes and constraints for advection. In P.~Kutler, J.~Flores, and J.\+J. Chattot, editors, {\itshape Fifteenth International Conference on Numerical Methods in Fluid Dynamics}, volume 490. Springer, Berlin, Heidelberg,
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\item[\label{_CITEREF_TEOS2010}%
\mbox{[}23\mbox{]}]I\+OC, S\+C\+OR, and I\+A\+P\+SO. {\itshape The international thermodynamic equation of seawater-\/2010\+: calculation and use of thermodynamic properties}. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, U\+N\+E\+S\+CO,
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\item[\label{_CITEREF_jackett1995}%
\mbox{[}24\mbox{]}]David~R. Jackett and Trevor~J. Mc\+Dougall. Minimal adjustment of hydrographic profiles to achieve static stability. {\itshape J. Atmos. Ocean. Tech.}, 12\+:381--389, 1995. 


\item[\label{_CITEREF_large1994}%
\mbox{[}25\mbox{]}]W.~G. Large, J.~C. Mc\+Williams, and S.~C. Doney. \href{https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/94RG01872}{\tt Oceanic vertical mixing\+: A review and a model with a nonlocal boundary layer parameterization}. {\itshape Reviews of Geophysics}, 32(4)\+:363--403, 1994. 


\item[\label{_CITEREF_lin1994}%
\mbox{[}26\mbox{]}]Shian-\/\+Jiann Lin, Winston~C. Chao, Y.~C. Sud, and G.~K. Walker. A class of the van leer-\/type transport schemes and its application to the moisture transport in a general circulation model. {\itshape Mon. Wea. Rev.}, 122\+:1575--1593, 1994. 


\item[\label{_CITEREF_mcdougall2001}%
\mbox{[}27\mbox{]}]Trevor~J. Mc\+Dougall and Peter~C. Mc\+Intosh. \href{https://journals.ametsoc.org/doi/10.1175/1520-0485%282001%29031%3C1222%3ATTRMVP%3E2.0.CO%3B2}{\tt The Temporal-\/\+Residual-\/\+Mean Velocity. Part I\+I\+: Isopycnal Interpretation and the Tracer and Momentum Equations}. {\itshape Journal of Physical Oceanography}, 31(5)\+:1222--1246, May 2001. 


\item[\label{_CITEREF_millero1978}%
\mbox{[}28\mbox{]}]F.\+J. Millero. \href{https://www.researchgate.net/publication/292574579_Freezing_point_of_seawater}{\tt Freezing point of seawater}. In {\itshape Eight report of the Joint Panel on Oceanographic Tables and Standards (J\+P\+O\+TS)}, number~28, pages 29--35. U\+N\+E\+S\+CO technical papers in marine sciences, 1978. Annex 6.


\item[\label{_CITEREF_roquet2015}%
\mbox{[}29\mbox{]}]F.~Roquet, G.~Madec, T.~J. Mc\+Dougall, and P.~M. Barker. Accurate polynomial expressions for the density and specific volume of seawater using the teos-\/10 standard. {\itshape Ocean Modelling}, 90\+:29--43, 2015.


\item[\label{_CITEREF_russell1981}%
\mbox{[}30\mbox{]}]Gary~L. Russell and Jean~A. Lerner. A new finite-\/differencing scheme for the tracer transport equation. {\itshape Journal of Applied Meteorology}, 20\+:1483--1498, 1981. 


\item[\label{_CITEREF_sadourny1975}%
\mbox{[}31\mbox{]}]Robert Sadourny. \href{https://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281975%29032%3C0680%3ATDOFDM%3E2.0.CO%3B2}{\tt The Dynamics of Finite-\/\+Difference Models of the Shallow-\/\+Water Equations}. {\itshape Journal of the Atmospheric Sciences}, 32(4)\+:680--689, April 1975. 


\item[\label{_CITEREF_shao2019-in-review}%
\mbox{[}32\mbox{]}]Andrew Shao, Alistair Adcroft, Robert Hallberg, and Stephen Griffies. A new, general-\/coordinate, non-\/local neutral diffusion operator, 2019.


\item[\label{_CITEREF_shchepetkin2005}%
\mbox{[}33\mbox{]}]A.~F. Shchepetkin and J.~C. Mc\+Williams. The regional ocean modeling system (roms)\+: A split-\/explicit, free-\/surface, topography-\/following coordinates oceanic model. {\itshape Ocean Modeling}, 9\+:347--404, 2005.


\item[\label{_CITEREF_sun1999}%
\mbox{[}34\mbox{]}]Shan Sun, Rainer Bleck, Claes Rooth, John Dukowicz, Eric Chassignet, and Peter Killworth. Inclusion of thermobaricity in isopycnic-\/coordinate ocean models. {\itshape Journal of Physical Oceanography}, 29\+:2719--2729, 1999.


\item[\label{_CITEREF_GVbook}%
\mbox{[}35\mbox{]}]Geoffrey~K. Vallis. {\itshape Atmospheric and Oceanic Fluid Dynamics\+: Fundamentals and Large-\/scale Circulation}. Cambridge University Press, Cambridge, 2nd edition, 2017. 946 + xxv pp.


\item[\label{_CITEREF_white2008}%
\mbox{[}36\mbox{]}]Laurent White and Alistair Adcroft. \href{http://www.sciencedirect.com/science/article/pii/S0021999108002593}{\tt A high-\/order finite volume remapping scheme for nonuniform grids\+: The piecewise quartic method (P\+QM)}. {\itshape Journal of Computational Physics}, 227(15)\+:7394--7422, July 2008. 


\item[\label{_CITEREF_white2009}%
\mbox{[}37\mbox{]}]Laurent White, Alistair Adcroft, and Robert Hallberg. \href{http://www.sciencedirect.com/science/article/pii/S0021999109004628}{\tt High-\/order regridding-\/remapping schemes for continuous isopycnal and generalized coordinates in ocean models}. {\itshape Journal of Computational Physics}, 228(23)\+:8665--8692, December 2009. 


\item[\label{_CITEREF_wright1997}%
\mbox{[}38\mbox{]}]Daniel~G. Wright. \href{https://journals.ametsoc.org/doi/abs/10.1175/1520-0426%281997%29014%3C0735%3AAEOSFU%3E2.0.CO%3B2}{\tt An Equation of State for Use in Ocean Models\+: Eckart\textquotesingle{}s Formula Revisited}. {\itshape Journal of Atmospheric and Oceanic Technology}, 14(3)\+:735--740, June
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