@article{lemarie_are_2012,
	title = {Are there inescapable issues prohibiting the use of terrain-following coordinates in climate models?},
	volume = {42},
	issn = {1463-5003},
	url = {https://www.sciencedirect.com/science/article/pii/S1463500311001831},
	doi = {10.1016/j.ocemod.2011.11.007},
	abstract = {The use of σ-coordinate ocean models has historically been considered a disadvantage for large-scale climate studies. The main reason resides in the non-alignment of the vertical coordinate isosurfaces with either geopotential surfaces or isopycnals making it harder to accurately compute the horizontal pressure gradient, advection, and isoneutral tracer diffusion. Moreover, this class of model requires a vertical mixing parameterization robust to large changes in the vertical resolution between shallow and deep areas. In this paper we show that, with some adjustments of the tracer advection, the surface boundary layer parameterization and the vertical grid, a σ-coordinate model can achieve an accurate representation of the oceanic interior and mixed-layer dynamics. To do so, a new way of handling the temporal discretization of the rotated biharmonic operator is used to achieve tracer variance dissipation in an adiabatic and computationally efficient way. Furthermore, a redesign of the K-Profile surface layer Parameterization (KPP) to improve the regularity of the solution and the overall numerical efficiency of the scheme is introduced. To validate the new algorithmic developments, we perform a set of coarse-resolution realistic basin-scale Pacific simulations. Besides improving the conservation of water mass properties, the use of an isoneutral tracer hyperdiffusion is shown to have a negative feedback on the circulation error growth rate, thus significantly reducing the sensitivity of the model solution to the degree of topographic smoothing. The overall validation of our simulations, focusing on the key characteristics of the circulation in the Pacific Ocean, provides some evidence of the efficacy of a terrain-following coordinate for large scale applications.},
	urldate = {2024-05-13},
	journal = {Ocean Modelling},
	author = {Lemarié, Florian and Kurian, Jaison and Shchepetkin, Alexander F. and Jeroen Molemaker, M. and Colas, François and McWilliams, James C.},
	month = jan,
	year = {2012},
	keywords = {Ocean modeling, Pacific Ocean, Advection, Diapycnal mixing, K-Profile Parameterization, Sigma coordinates},
	pages = {57--79},
	file = {Lemarie et al_2012_Are there inescapable issues prohibiting the use of terrain-following.pdf:/Users/noraloose/My Drive/Refs_Zotero/Lemarie et al_2012_Are there inescapable issues prohibiting the use of terrain-following2.pdf:application/pdf;ScienceDirect Snapshot:/Users/noraloose/Zotero/storage/7YFUJCGJ/S1463500311001831.html:text/html},
}

@article{lemarie_stability_2012,
	title = {On the stability and accuracy of the harmonic and biharmonic isoneutral mixing operators in ocean models},
	volume = {52-53},
	issn = {1463-5003},
	url = {https://www.sciencedirect.com/science/article/pii/S1463500312000674},
	doi = {10.1016/j.ocemod.2012.04.007},
	abstract = {Ocean models usually rely on a tracer mixing operator which diffuses along isoneutral directions. This requirement is imposed by the highly adiabatic nature of the oceanic interior, and a numerical simulation needs to respect these small levels of dianeutral mixing to maintain physically realistic results. For non-isopycnic models this is however non-trivial due to the non-alignment of the vertical coordinate isosurfaces with local isoneutral directions, rotated mixing operators must therefore be used. This paper considers the numerical solution of initial boundary value problems for the harmonic (Laplacian) and biharmonic rotated diffusion operators. We provide stability criteria associated with the conventional space–time discretizations of the isoneutral Laplacian operator currently in use in general circulation models. Furthermore, we propose and study possible alternatives to those schemes. A new way to handle the temporal discretization of the rotated biharmonic operator is also introduced. This scheme requires only the resolution of a simple one-dimensional tridiagonal system in the vertical direction to provide the same stability limit of the non-rotated operator. The performance of the various schemes in terms of stability and accuracy is illustrated by idealized numerical experiments of the diffusion of a passive tracer along isoneutral directions.},
	urldate = {2024-05-13},
	journal = {Ocean Modelling},
	author = {Lemarié, F. and Debreu, L. and Shchepetkin, A. F. and McWilliams, J. C.},
	month = aug,
	year = {2012},
	keywords = {Diffusion equations, Initial-boundary value problems, Isoneutral mixing, Time schemes, Von-Neumann stability analysis},
	pages = {9--35},
	file = {Lemarie et al_2012_On the stability and accuracy of the harmonic and biharmonic isoneutral mixing.pdf:/Users/noraloose/My Drive/Refs_Zotero/Lemarie et al_2012_On the stability and accuracy of the harmonic and biharmonic isoneutral mixing2.pdf:application/pdf;ScienceDirect Snapshot:/Users/noraloose/Zotero/storage/D96R2CS9/S1463500312000674.html:text/html},
}
