Skip to main content
SpringerLink
Log in

Some mathematical problems associated with the development and use of marine models

  • Conference paper
The Mathematics of Models for Climatology and Environment

Part of the book series: NATO ASI Series ((ASII,volume 48))

Abstract

“Science is now a tripartite endeavour with simulation added to the two classical components, experiment and theory (Robinson, 1987). The routine use of numerical “simulation in scientific research (numerical experimentation, sensitivity and process studies, etc.) is thought by many to represent the first major step forward in the basic scientific method since the seventeenth century”(Robinson, 1987).

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Adam, P. (1990) Modélisation Mathématique Tridimensionnelle d’un Ecosystème Marin — Application à la Région du Détroit de Bering, Mémoire de Fin d’Etudes, Faculté des Sciences Appliquées, Université de Liège, 159 pp.

    Google Scholar 

  • Arakawa, A. and Lamb, V.R. (1977) Computational design of the basic dynamical processes of the UCLA general circulation model, Methods in Computational Physics, Vol. 17, Academic Press, 337 pp.

    Google Scholar 

  • Batteen, M.L. and Han, Y.-J. (1981) On the computational noise of finite-difference schemes used in ocean models, Tellus, 33, 387–396.

    Article  Google Scholar 

  • Beckers, J.-M. (1991) Application of the GHER 3D general circulation model to the Western Mediterranean, J. Mar. Syst., 1, 315–332.

    Article  Google Scholar 

  • Beckers, J.-M. (1992) Analytical linear numerical stability conditions for an anisotropic 3D advection-diffusion equation, SIAM J. Numer. Anal., 29, 701–713.

    Article  Google Scholar 

  • Beckers, J.-M. and Deleersnijder, E. (1993) Stability of a FBTCS scheme applied to the propagation of shallow-water inertia-gravity waves on various space grids, J. Comput. Phys., 108, 95–104.

    Article  Google Scholar 

  • Bedford, K.W. Dingman, J.S. and Yeo, W.K. (1987) Preparation of estuary and marine model equations by generalized filtering methods, Three-Dimensional Models of Marine and Estuarine Dynamics (J.C.J. Nihoul and B.M. Jamart, Editors), Elsevier, pp. 113–125.

    Chapter  Google Scholar 

  • Bennett, A.F. (1992) Inverse Methods in Physical Oceanography, Cambridge Univ. Press, 346 pp.83

    Book  Google Scholar 

  • Blumberg, A.F. and Mellor, G.L. (1987) A description of a three-dimensional coastal ocean circulation model, Three-Dimensional Coastal Ocean Models (N.S. Heaps, Editor), American Geophysical Union, pp. 1–16.

    Google Scholar 

  • Blumen, W. (1972) Geostrophic adjustment, Rev. Geophys. and Space Phys., 10, 485–528.

    Article  Google Scholar 

  • Boussinesq, J. (1877) Essai sur la théorie des eaux courantes, Mém. Acad. Sci. Paris, 23, 1–680.

    Google Scholar 

  • Brasseur, P.P. (1991) A variational inverse method for the reconstruction of general circulation fields in the Northern Bering Sea, J. Geophys. Res., 96, 4891–4907.

    Article  Google Scholar 

  • Brasseur, P.P. and Haus, J. (1991) Application of a 3-D variational inverse model to the analysis of ecohydrodynamic data in the Northern Bering and Southern Chukchi seas, J. Mar. Syst., 1, 383–401.

    Article  Google Scholar 

  • Broecker, W.S. (1991) The great ocean conveyor, Oceanogr., 4, 79–89.

    Google Scholar 

  • Bryan, K. (1969) A numerical method for the study of the circulation of the World Ocean, J.Comput. Phys., 4, 347–376.

    Article  Google Scholar 

  • Bryan, K. (1982) Seasonal variation in meridional overturning and poleward heat transport in the Atlantic and Pacific oceans, J. Mar. Res., 40, 39–53.

    Google Scholar 

  • Bryan, K. (1987) Parameter sensitivity of primitive equations ocean general circulation models, J. Phys. Oceanogr., 17, 970–985.

    Article  Google Scholar 

  • Casulli, V. and Cattani, E. (1994) Stability, accuracy and efficiency of a semi-implicit method for three-dimensional shallow water flow, Computers Math. Applic, 27, 99–112

    Article  Google Scholar 

  • Casulli, V. and Cheng, R.T. (1992) Semi-implicit finite difference methods for ree-dimensional shallow water flow, Int. J. Numer. Methods Fluids, 15, 629–648.

    Article  Google Scholar 

  • Coachman, L.K. and Aagaard, K (1966) On the water exchange through Bering Strait, Limnol. Oceanogr., 11, 44–59.

    Article  Google Scholar 

  • Coachman, L.K. and Aagaard, K (1988) Transports through Bering Strait: annual and interannual variability, J. Geophys. Res., 93, 15535–15539.

    Article  Google Scholar 

  • Coachman, L.K., Aagaard, K. and Tripp, R.B. (1975) Bering Strait — The Regional Physical Oceanography, Univ. of Washington Press, 172 pp.

    Google Scholar 

  • Coward, A.C., Killworth, P.D. and Blundell, J.R. (1995) Tests of a two-grid world ocean model, J. Geophys. Res. (in press).

    Google Scholar 

  • Cox, M. (1984) A Primitive Equation, Three-Dimensional Model of the Ocean, GFDL Ocean Group, Tech. Rep. No. 1, GFDL/NOAA, Princeton.

    Google Scholar 

  • Cushman-Roisin, B. (1984) Analytical, linear stability criteria for the leap-frog, Dufort-Frankel method, J. Comput. Phys., 53, 227–239.

    Article  Google Scholar 

  • Cushman-Roisin, B. (1994) Introduction to Geophysical Fluid Dynamics, Prentice Hall, 320 pp.

    Google Scholar 

  • Deleersnijder, E. (1989) Upwelling and upsloping in three-dimensional marine models, Appl. Math. Model., 13, 462–467.

    Article  Google Scholar 

  • Deleersnijder, E. (1992) Modélisation Hydrodynamique Tridimensionnelle de la Circulation Générale Estivale de la Région du Détroit de Bering, Thèse de Doctorat, Faculté des Sciences Appliquées, Université Catholique de Louvain, 189 pp.

    Google Scholar 

  • Deleersnijder, E. (1994a) An analysis of the vertical velocity field computed by a three-dimensional model in the region of the Bering Strait, Tellus, 46A, 134–148.

    Google Scholar 

  • Deleersnijder, E. (1994b) The assimilation of altimetric data into the barotropic mode of a rigid lid ocean model, Mathl. Comput. Modelling, 20, 85–94.

    Article  Google Scholar 

  • Deleersnijder, E. and Campin, J.-M. (1993) Du Calcul de la Position de la Surface de l’Océan dans un Modèle de Circulation Générale, Contribution no. 70, Institut d’Astronomie et de Géophysique G. Lemaître, Université Catholique de Louvain, Louvain-la-Neuve.

    Google Scholar 

  • Deleersnijder, E. and Campin, J.-M. (1995) On the computation of the barotropic mode of a free-surface World Ocean model, Ann. Geophys. (in press).

    Google Scholar 

  • Deleersnijder, E. and Luyten, P. (1994) On the practical advantages of the quasi-equilibrium version of the Mellor and Yamada level 2.5 turbulence closure applied to marine modelling, Appl. Math. Model., 18, 281–287.

    Article  Google Scholar 

  • Deleersnijder, E. and Wolanski, E. (1990) Du rôle de la dispersion horizontale de quantité de mouvement dans les modèles marins tridimensionnels, Journées Numériques de Besançon 1990 — Courants Marins (J.-M. Crolet and P. Lesaint, Editors), Publications Mathématiques de Besançon, pp. 39–50.

    Google Scholar 

  • Deleersnijder, E., van Ypersele, J.-P., and Campin, J.-M. (1993) An orthogonal curvilinear coordinate system for a World Ocean model, Ocean Modelling, 100, 7–10 (+ figs.).

    Google Scholar 

  • Doos, K. (1994) Inter-ocean exchange of water masses (submitted).

    Google Scholar 

  • Dukowicz, J.K. and Smith, R.D. (1994) Impicit free-surface method for the Bryan-Cox-Semtner ocean model, J. Geophys. Res., 99, 7991–8014.

    Article  Google Scholar 

  • Dukowicz, J.K., Smith, R.D. and Malone, R.C. (1993) A reformulation and implementation of the Bryan-Cox-Semtner ocean model on the Connection Machine, J. Atmos. Ocean. Technol., 10, 195–208.

    Article  Google Scholar 

  • Eby M. and Holloway, G. (1994) Grid transformation for incorporating the Arctic in a global ocean model, Clim. Dyn., 10, 241–247.

    Article  Google Scholar 

  • England, M.H. (1992) On the formation of Antarctic Intermediate and Bottom Water in ocean general circulation models, J. Phys. Oceanogr., 22, 918–926.

    Article  Google Scholar 

  • England, M.H. (1993) Representing the global-scale water masses in ocean general circulation models, J. Phys. Oceanogr., 23, 1523–1552.

    Article  Google Scholar 

  • Gadd, A.J. (1978) A split-explicit integration scheme for numerical weather prediction, Q. J. R. Meteorol. Soc., 104, 569–582.

    Article  Google Scholar 

  • Galperin, B., Kantha, L.H., Hassid, S. and Rosati, A. (1988) A quasi-equilibrium turbulent energy model for geophysical flows, J. Atmos. Sci., 45, 55–62.

    Article  Google Scholar 

  • Godfrey, A.L. (1989) A Sverdrup model of the depth-integrated flow for the World Ocean allowing for island circulations, Geophys. Astrophys. Fluid Dyn., 45, 89–112.

    Article  Google Scholar 

  • Gordon, A.L. (1986) Interocean exchange of thermocline water, J. Geophys. Res., 91, 5037– 5046.

    Article  Google Scholar 

  • Gresho, P.M. and Sani, R.L. (1987) On pressure boundary conditions for the incompressible Navier-Stokes equations, Int. J. Numer. Methods Fluids, 7,1111–1145.

    Article  Google Scholar 

  • Haidvogel, D.B. and Bryan, F.O. (1992) Ocean general circulation modeling, Climate System Modeling (K.E. Trenberth, Editor), Cambridge University Press, pp. 371–412.

    Google Scholar 

  • Hall M.M. and Bryden, H.L. (1982) Direct estimates and mechanisms of ocean heat transport, Deep-Sea Res., 29, 339–359.

    Article  Google Scholar 

  • Hastenrath, S. (1982) On meridional heat transports in the World Ocean, J. Phys. Oceanogr., 12, 922–927.

    Article  Google Scholar 

  • Helfand, H.M. and Labraga, J.C. (1988) Design of a nonsingular level 2.5 second-order closure scheme for the prediction of atmospheric turbulence, J. Atmos. Sci., 45, 113–132.

    Article  Google Scholar 

  • Hellerman, S. and Rosenstein, M. (1983) Normal monthly wind stress over the world ocean with error estimates, J. Phys. Oceanogr., 13, 1093–1104.

    Article  Google Scholar 

  • Hirsch, C. (1988) Numerical Computation of Internal and External Flows. Vol. 1: Fundamentals of Numerical Discretization, Wiley, 515 pp.

    Google Scholar 

  • Hirst, A.C. and Cai, W. (1994) Sensitivity of a World Ocean GCM to changes in subsurface mixing parameterization, J. Phys. Oceanogr., 24, 1256–1279.

    Article  Google Scholar 

  • Houghton, J.T., Callander, B.A. and Varney, S.K. (Editors) (1992) Climate Change 1992: The Supplement Report to the IPCC Scientific Assessment, Cambridge University Press, 200 pp.

    Google Scholar 

  • Houghton, J.T., Jenkins, G.J. and Ephraums, J. (Editors) (1990) Climate Change: The IPCC Scientific Assessment, Cambridge University Press, 364 pp.

    Google Scholar 

  • Hsiung, J. (1985) Estimates of global oceanic meridional heat transport, J. Phys. Oceanogr., 15, 1405–1413.

    Article  Google Scholar 

  • Kato, H. and Phillips, O.M. (1969) On the penetration of a turbulent layer into stratified fluid, J. Fluid Mech., 37, 643–655.

    Article  Google Scholar 

  • Killworth, P.D. (1983) Deep convection in the worl ocean, Rev. Geophys., 21, 1–26.

    Article  Google Scholar 

  • Killworth, P.D. and Smith, J.M. (1984) Gradual instability of relaxation-extrapolation scheme, Dyn. Atmos. Oceans, 8, 185–213.

    Article  Google Scholar 

  • Killworth, P.D., Stainforth, D., Webb, D.J. and Paterson, S.M. (1991) The development of a free-surface Bryan-Cox-Semtner ocean model, J. Phys. Oceanogr., 21, 1333–1348.

    Article  Google Scholar 

  • LeBlond, P.H. and Mysak, L.A. (1978) Waves in the Ocean, Elsevier, 602 pp.

    Google Scholar 

  • Levitus, S. (1982) Climatological Atlas of the World Oceans, NOAA Prof. Paper 13, U.S. Gov. Print. Office, Washington, D.C.

    Google Scholar 

  • Longuet-Higgins, M.S. (1965) Planetary waves on a rotating sphere, II, Proc. R. Soc. London, 284A, 40–68.

    Google Scholar 

  • Luyten, P., Deleersnijder, E., Ozer, J. and Ruddick, K. (1994) Presentation of a family of turbulence closure models for stratified shallow water flows and preliminary application to the Rhine outflow region, Cont. Shelf Res. (in press).

    Google Scholar 

  • Madala, R.V. (1981) Efficient time integration schemes for atmosphere and ocean models, Finite-Difference Techniques for Vectorized Fluid Dynamics Calculations (D.L. Book, Editor), Springer-Verlag, pp. 56–74.

    Google Scholar 

  • Maier-Reimer, E., Mikolajewicz, U. and Hasselmann, K. (1993) Mean circulation of the Hamburg LSG OGCM and its sensitivity to the thermohaline surface forcing, J. Phys. Oceanogr., 23, 731–757.

    Article  Google Scholar 

  • Marotzke, J. and Willebrand, J. (1991) Multiple equilibria of the global thermohaline circulation, J. Phys. Oceanogr., 21, 1372–1385.

    Article  Google Scholar 

  • Marti, O., Chartier, M. and Delecluse, P. (1990) A World Ocean model in curvilinear coordinates, Journées Numériques de Besançon 1990 — Courants Marins (J.-M. Crolet and P. Lesaint, Editors), Publications Mathématiques de Besançon, pp. 17–25.

    Google Scholar 

  • Marti, O., Madec, G. and Delecluse, P. (1992) Comments on “Net diffusivity in ocean general circulation models with nonuniform grids” by F.L. Yin and I.Y. Fung, J. Geophys. Res., 97, 2763–12766.

    Article  Google Scholar 

  • Mellor, G.L. and Blumberg, A.F. (1985) Modeling vertical and horizontal diffusivities with the sigma coordinate system, Mon. Weather Rev., 113, 1379–1383.

    Article  Google Scholar 

  • Mellor, G.L. and Strub, P.T. (1980) Similarity solutions for the stratified turbulent Rayleigh problem, J. Phys. Oceanogr., 10, 455–60.

    Article  Google Scholar 

  • Mellor, G.L. and Yamada, T. (1982) Development of a turbulence closure model for geophysical fluid problems, Rev. Geophys. and Space Phys., 20, 851–875.

    Article  Google Scholar 

  • Mesinger, F. and Arakawa, A. (1976) Numerical Methods Used in Atmospheric Models, GARP Publications Series (no. 17, vol. 1), WMO-ICSU Joint Organizing Committee, 64 pp.

    Google Scholar 

  • Monin, A.S. (1975) The role of the oceans in climate models, The Physical Basis of Climate and Climate Modelling (no. 16, Appendix 6), WMO-ICSU Joint Organizing Committee, pp. 201–205.

    Google Scholar 

  • Nihoul, J.C.J. (1994) Do not use a simple model when a complex one will do, J. Mar. Syst., 5, 401–406.

    Google Scholar 

  • Nihoul, J.C.J., Adam, P., Brasseur, P., Deleersnijder, E., Djenidi, S. and Haus, J. (1993a) Three-dimensional general circulation model of the northern Bering Sea’s summer ecohydrodynamics, Cont. Shelf Res., 13, 509–542.

    Article  Google Scholar 

  • Nihoul, J.C.J., Adam, P., Djenidi, S. and Deleersnijder, E. (1993b) Modelling the coastal ocean’s complex ecohydrodynamics - A case study: the Northern Bering Sea, Progress in Belgian Océanographie Research, Royal Academy of Belgium, pp. 203–216.

    Google Scholar 

  • Nihoul, J.C.J, and Djenidi, S. (1987) Perspective in three-dimensional modelling of the marine system, Three-Dimensional Models of Marine and Estuarine Dynamics (J.C.J. Nihoul and B.M. Jamart, Editors), Elsevier, pp. 1–33.

    Chapter  Google Scholar 

  • Niiler, P.P. (1992) The ocean circulation, Climate System Modeling (K.E. Trenberth, Editor), Cambridge University Press, pp. 117–148.

    Google Scholar 

  • Nowlin, W.D. and Klinck, J.M. (1986) The physics of the Antarctic circumpolar current, Rev. Geophys., 24, 469–491.

    Article  Google Scholar 

  • Overland, J.E. and Roach, A.T. (1987) Northward flow in the Bering and Chukchi Seas, J. Geophys. Res., 92, 7097–7105.

    Article  Google Scholar 

  • Pacanowski, R.C. and Philander, S.G.H. (1981) Parameterization of vertical mixing in numerical models of tropical oceans, J. Phys. Oceanogr., 11, 1443–1451.

    Article  Google Scholar 

  • Patankar, S.V. (1980) Numerical Heat Transfer and Fluid Flow, Hemisphere, 197 pp.

    Google Scholar 

  • Peyret, R. and Taylor, T.D. (1983) Computational Methods for Fluid Flow, Springer-Verlag, 358 pp.

    Google Scholar 

  • Phillips, N.A. (1957) A coordinate system having some special advantages for numerical

    Google Scholar 

  • forecasting, J. Meteorol., 14, 184–185.

    Google Scholar 

  • Pinardi, N., Rosati, A. and Pacanowski, R.C. (1995) The sea surface pressure formulation of rigid lid models. Implications for altimetric data assimilation studies, J. Mar. Syst., 6, 109–119.

    Article  Google Scholar 

  • Ponte, R.M. (1993) Variability in a homogeneous global ocean forced by barometric pressure, Dyn. Atmos. Oceans., 18, 209–234.

    Article  Google Scholar 

  • Price, J.F. (1979) On the scaling of stress driven entrainment experiments, J. Fluid Mech., 90,

    Google Scholar 

  • 509–529.

    Google Scholar 

  • Reason, C.J.C. and Power, S.B. (1994) The influence of the Bering Strait on the circulation in a coarse resolution global ocean model, Clim. Dyn., 9, 363-369.

    Article  Google Scholar 

  • Reynolds, O. (1883) An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels, Philos. Trans. R. Soc. London, 174, 935–982.

    Article  Google Scholar 

  • Reynolds, O. (1894) On the dynamical theory of incompressible viscous fluids and the determination of the criterion, Philos. Trans. R. Soc. London, 186, 123–161.

    Article  Google Scholar 

  • Robinson, A.R. (1987) Predicting open ocean currents, fronts and eddies, Three-Dimensional Models of Marine and Estuarine Dynamics (J.C.J. Nihoul and B.M. Jamart, Editors), Elsevier, pp. 89–111.

    Chapter  Google Scholar 

  • Rodi, W. (1993, 3rd edition) Turbulence Models and their Application in Hydraulics. A State-of-the-Art Review, IAHR-AIRH Monograph, A.A. Balkema, 104 pp.

    Google Scholar 

  • Sambrotto, R.N., Goering, J.J. and McRoy, C.P. (1984) Large yearly production of phytoplankton in the Western Bering Strait, Science, 225, 1147–1150.

    Article  Google Scholar 

  • Sarmiento, J.L. (1992) Biogeochemical ocean models, Climate System Modeling (K.E. Trenberth, Editor), Cambridge University Press, pp. 519–551.

    Google Scholar 

  • Semtner, A.J. and Chervin, R.M. (1992) Ocean general circulation from a global eddy resolving model, J. Geophys. Res., 97, 5493–5550.

    Article  Google Scholar 

  • Sielecki, A. (1968) An energy-conserving difference scheme for the storm surge equations, Mon.Weather Rev., 96, 150–156.

    Article  Google Scholar 

  • Toggweiler, J.R., Dixon, K. and Bryan, K. (1989) Simulation of radiocarbon in a coarse-resolution world ocean model, 2. Distributions of bomb-produced carbon 14, J. Geophys. Res., 94, 8243–8264.

    Article  Google Scholar 

  • Waleffe, F. (1985) Modèle Mathématique 3D de la Mer de Bering, Mémoire de Fin d’Etudes, Faculté des Sciences Appliquées, Université de Liège, 126 pp.

    Google Scholar 

  • Walsh, J.J., McRoy, C.P., Coachman, L.K., Goering, J.J., Nihoul, J.C.J., Whitledge, T.E., Blackburn, T.H., Parker, P.L., Wirck, CD., Shuert, P.G., Grebmeier, J.M., Springer, A.M., Tripp, R.B., Hanseil, D.A., Djenidi, S., Deleersnijder, E., Henriksen, K., Lund, B.A., Andersen, P., Müller-Karger, F.E. and Dean, K. (1989) Carbon and nitrogen cycling within theering/Chukchi Seas: source regions for organic matter affecting AOU demands of the Arctic Ocean, Progr. Oceanogr., 22,279–361.

    Article  Google Scholar 

  • Williamson, D.L. (1979) Difference approximations for fluid flow on a sphere, Numerical Methods Used in Atmospheric Models, GARP Publications Series (no. 17, vol. 2), WMO-ICSU Joint Organizing Committee, pp. 51–120.

    Google Scholar 

  • Wimbush, M. and Munk, W. (1971) The benthic boundary layer, The Sea (Vol. 4) (A.E. Maxwell, Editor), Wiley, pp. 731–758.

    Google Scholar 

  • Zhang, R.H. and Endoh, M. (1992) A free-surface general circulation model for the tropical Pacific Ocean, J. Geophys. Res., 97, 11237–11255.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut d’Astronomie et de Géophysique G. Lemaître, Université Catholique de Louvain, 2 Chemin du Cyclotron, B-1348, Louvain-la-Neuve, Belgium

    Eric Deleersnijder (Research Associate, National Fund for Scientific Research (Belgium), Jean-Marie Beckers (Senior Research Assistant, National Fund for Scientific Research (Belgium), Jean-Michel Campin, Mohammed El Mohajir, Thierry Fichefet (Research Associate, National Fund for Scientific Research (Belgium) & Patrick Luyten

  2. GHER, University of Liège, Sart Tilman B5, B-4000, Liège, Belgium

    Jean-Marie Beckers (Senior Research Assistant, National Fund for Scientific Research (Belgium)

  3. MUMM, Gulledelle 100, B-1200, Brussels, Belgium

    Patrick Luyten

Authors
  1. Eric Deleersnijder
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jean-Marie Beckers
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jean-Michel Campin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mohammed El Mohajir
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Thierry Fichefet
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Patrick Luyten
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dpto. de Matemática Aplicada, Fac. Matemáticas, Universidad Complutense de Madrid, 28040, Avd. Complutense, s/n, Madrid, Spain

    Jesús Ildefonso Díaz

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Deleersnijder, E., Beckers, JM., Campin, JM., El Mohajir, M., Fichefet, T., Luyten, P. (1997). Some mathematical problems associated with the development and use of marine models. In: Díaz, J.I. (eds) The Mathematics of Models for Climatology and Environment. NATO ASI Series, vol 48. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60603-8_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-60603-8_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64472-6

  • Online ISBN: 978-3-642-60603-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation