A multi-envelope vertical coordinate system for numerical ocean modelling
A multi-envelope generalised coordinate system for numerical ocean modelling is introduced. In this system, computational levels are curved and adjusted to multiple ‘virtual bottoms’ (aka envelopes) rather than following geopotential levels or the actual bathymetry. This allows defining computational levels which are optimised to best represent different physical processes in different sub-domains of the model. In particular, we show how it can be used to improve the representation of tracer advection in the ocean interior. The new vertical system is compared with a widely used z-partial step scheme. The modelling skill of the models is assessed by comparison with the analytical solutions or results produced by a model with a very high-resolution z-level grid. Three idealised process-oriented numerical experiments are carried out. Experiments show that numerical errors produced by the new scheme are much smaller than those produced by the standard z-partial step scheme at a comparable vertical resolution. In particular, the new scheme shows superiority in simulating the formation of a cold intermediate layer in the ocean interior and in representing dense water cascading down a steep topography.
KeywordsOcean modelling Vertical coordinate Oceanic transport
The authors are grateful to the valuable comments and suggestions of the two anonymous reviewers which have greatly contributed to improving the manuscript.
This work was funded by the EASME/EMFF/2014/ 188.8.131.52/LOT4/SI2.709436 - Seabasin Checkpoints - Lot 4 - ‘BLACK SEA’ project.
- Barnier B, Madec G, Penduff T, Molines J-M, Treguier A-M, Le Sommer J, Beckmann A, Biastoch A, Böning C, Dengg J, Derval C, Durand E, Gulev S, Remy E, Talandier C, Theetten S, Maltrud M, McClean J, De Cuevas B (2006) Impact of partial steps and momentum advection schemes in a global ocean circulation model at eddy-permitting resolution. Ocean Dyn 56(5-6):543– 567CrossRefGoogle Scholar
- Bleck R (1998) Ocean modeling in isopycnic coordinates. In: Chassignet EP, Verron J (eds) Ocean modeling and parameterization, NATO ASI mathematical and physical sciences series, vol 516. Kluwer Academic Publishers, Dordrecht, pp 423–448Google Scholar
- Blumberg AF, Mellor GL (1987) A description of a three-dimensional coastal ocean circulation model. In: Three-dimensional coastal ocean models, pp 1–16Google Scholar
- Chassignet EP, Hurlburt HE, Smedstad OM, Halliwell GR, Hogan PJ, Wallcraft AJ, Bleck R (2006) Ocean prediction with the hybrid coordinate ocean model (HYCOM). In: Chassignet EP, Verron J (eds) Ocean weather forecasting. Springer-Verlag, Berlin/Heidelberg, pp 413–426Google Scholar
- Furner R (2012) A review of lateral diffusion for Met Office ocean shelf modelling. Technical report, Met OfficeGoogle Scholar
- Griffies S, Böning C, Bryan FO, Chassignet EP, Gerdes R, Hasumi H, Hirst A, Treguier A-M, Webb D (2000a) Developments in ocean climate modelling. J Comput Phys 2(3-4):123–192Google Scholar
- Griffies S (2004) Fundamentals of ocean climate models. Princeton University Press, PrincetonGoogle Scholar
- Kantha LH, Clayson CA (2000) Numerical models of oceans and oceanic processes. Academic Press, CambridgeGoogle Scholar
- Legg S, Briegleb B, Chang Y, Chassignet EP, Danabasoglu G, Ezer T, Gordon AL, Griffies S, Hallberg R, Jackson L, Large W, Özgökmen TM, 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 Meteorol Soc 90(5):657–670CrossRefGoogle Scholar
- Madec G, The NEMO Team (2008) NEMO ocean engine. Note du Pôle de modélisation, Institut Pierre-Simon Laplace (IPSL), France, No 27, ISSN 1288-1619Google Scholar
- Mellor GL, Häkkinen SM, Ezer T, Patchen RC (2002) A generalization of a sigma coordinate ocean model and an intercomparison of model vertical grids. In: Pinardi N, Woods J (eds) Ocean forecasting: conceptual basis and applications. Springer, Berlin, pp 55–72Google Scholar
- MyOcean2 (2014) MyOcean catalogue of PRODUCTS, V4.0Google Scholar
- Valeport (2017) Model 106 Current Meter. http://www.valeport.co.uk/Portals/0/Docs/Datasheets/Valeport-Model-106.pdf. Accessed 12 November 2017