An applied mathematical view of meteorological modelling

Applied Mathematics Entering the 21st Century: Invited Talks from the ICIAM 2003 Congress

Volumn , Issue , 2004, Pages 226-269+xi

  Klein, Rupert ^a,b  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

^b POTSDAM INSTITUTE FOR CLIMATE IMPACT RESEARCH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; COMPUTER SIMULATION; EARTH ATMOSPHERE; FLUID MECHANICS; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; SET THEORY; SPECIFIC HEAT;

ASYMPTOTIC LIMITS; METEOROLOGICAL MODELING; METEOROLOGICAL SCALES; SPACE-TIME COORDINATES;

METEOROLOGY;

EID: 3042801110     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Conference Paper

References (53)

1. Achatz U., and G. Branstator, 1999: A two-layer model with empirical linear corrections and reduced order for studies of internal climate variability, J. Atmos. Sci., 56, 3140-3160
2. Botta N., R. Klein, A. Almgren, 1999: Asymptotic Analysis of a Dry Atmosphere. ENUMATH, Jyväskylä, Finnland,
3. Botta N., R. Klein, S. Langenberg, S. Lützenkirchen, 2002: Well-Balanced Finite Volume Methods for Near-Hydrostatic Flows, under revision for J. Comp. Phys. (Preprint: PIK-Report No. 84, Potsdam Institute for Climate Impact Research.)
4. Botta N., R. Klein, S. Langenberg, S. Lützenkirchen, 2002: Well-Balanced Finite Volume Methods for Near-Hydrostatic Flows, under revision for J. Comp. Phys. (Preprint: PIK-Report No. 84, Potsdam Institute for Climate Impact Research.)
5. Benoit R., M. Desgagne, P. Pellerin, S. Pellerin, Y. Chartier, and S. Desjardin, 1997: The Canadian MC2: A semi-Lagrangian, semi-implicit wide-band atmospheric model suited for finescale process studies and simulation. Mon. Wea. Rev., 125, 2382-2415.
6. Bretherton C., and A. Sobel, 2001: The Gill model and the weak temperature gradient (WTG) approximation, submitted to J. Atmos. Sci. on 3/7/01.
7. Browning G. L., H. O. Kreiss, and W. H. Schubert, 2000: The Role of Gravity Waves in Slowly Varying in Time Tropospheric Motions near the Equator. J. Atmos. Sci., 57, 4008-4019.
8. Buckingham E., 1915: Model experiments and the forms of empirical equations. Trans. Am. Soc. Mech. Eng., 37, 263-296.
9. Cargo P., and A. Y. Le Roux, 1994: Un schéma équilibre adapté au modéle d' atmosphère avec termes de gravité. C. R. Acad. Sci. Paris, 318 Série 1, 73-76.
10. Charney J. G., 1963: A note on large-scale motions in the tropics. J. Atmos. Sci., 20, 607-609.
11. Conaty A., J. Jusem, L. Takacs, D. Keyser, and R. Atlas, 2001: The structure and evolution of extratropical cyclones, fronts, jet streams, and the tropopause in the geos general circulation model. Bull. Amer. Meteorol. Soc., 82, 1853-1867.
12. Cullen M. J. P., J. Norbury, R. J. Purser, 1991: Generalized Lagrangian solutions for atmospheric and oceanic flows. SIAM J. Appl. Math., 51, 20-31.
13. Durran D. R., 1989: Improving the anelastic approximation. J. Atmos. Sci., 46, 1453-1461.
14. Ebin D. G., 1982: Motion of slightly compressible fluids in a bounded domain. Comm. Pure Appl. Math., 35, 451-485.
15. Eliassen A., 1962: On the vertical circulatin in frontal zones. Geophys. Publ., 24, 147-160.
16. Embid P., and A. Majda, 1996: Averaging over fast gravity waves for geophysical flows with arbitrary potential vorticity. Comm. Partial Diff. Eqns., 21, 619-658.
17. Embid P., and A. Majda, 1998: Low Froude number limiting Dynamics for stably stratified flow with small or finite Rossby numbers. Geophys. Astrophys. Fluid Dynamics 87, 1-50.
18. Gill A. E., 1980: Some simple solutions for heat-induced tropical circulation. Quart. J. Roy. Meteor. Soc., 106, 447-462.
19. Gill A. E., 1982: Atmosphere-Ocean Dynamics Intl. Geophysics Series 30, Academic Press, San Diego.
20. Heckley W. A., and A. E. Gill, 1984: Some simple analytical solutions to the problem of forced equatorial long waves. Quart. J. Roy. Meteor. Soc., 110, 203-217.
21. Held I. M., and B. J. Hoskins, 1985: Large-scale eddies and the general circulation of the troposphere. Advances in Geophysics, 28, Academic Press, 3-31.
22. Hoskins B. J., and F. P. Bretherton, 1972: Atmospheric frontogenesis models: mathematical formulation and solution. J. Atmos. Sci., 29, 11-37.
23. Hoskins B. J., 1975: The geostrophic momentum approximation and the semi-geostrophic equations. J. Atmos. Sci., 32, 233-242.
24. Hunt J. C. R., K. J. Richards and P. W. M. Brighton, 1988: Stably Stratified Shear Flow over Low Hills. Q.J.R. Met. Soc., 114, 859-886.
25. Kevorkian J., and J. D. Cole, 1981: Perturbation methods in Applied Mathematics, Applied Mathematics Sciences 34, Springer-Verlag, New York.
26. Klainerman S. and A. J. Majda, 1982: Compressible and incompressible fluids. Comm. Pure Appl. Math., 35, 629-656.
27. Klein R., 2000: Asymptotic analyses for atmospherics flows and the construction of asymptotically adaptive numerical methods. Zeitschr. Angew. Math. Mech., 80, 765-777.
28. McIntyre M. E., and I. Roulstone, 2002: Are there higher-accuracy analogues of semi-geostrophic theory? in: Large-scale Atmospere-Ocean Dynamics II: Geometric Methods and Models Cambridge Univ. Press.
29. Majda A., 2001: Introduction to PDE's and Waves for the Atmosphere and Ocean. Lecture Notes from Courant Institute 2000-2001, published by American Mathematical Society Spring 2003, 189 pages.
30. Majda A., and P. Embid, 1998: Averaging over fast gravity waves for geophysical flows with unbalanced initial data. Theoret. Comput. Fluid Dynamics, 11, 155-169.
31. Majda A., and R. Klein, 2003: Systematic multi-scale models for the tropics. J. Atmos. Sci., 60, 393-408.
32. Majda A. and J. Sethian, (1985): The derivation and numerical solution of the equations for zero Mach number combustion. Combustion Science and Technology, 42, 185-205.
33. Majda A., and M. Shefter, 2001: Models for stratiform instability and convectively coupled waves. J. Atmos. Sci., 58, 1567-1584.
34. Majda A., I. Timofeyev, and E. Vanden-Eijnden, 2003: Systematic Strategies for Stochastic Mode Reduction in Climate, J. Atmos. Sci., 60, 1705-1722.
35. Matsuno T., 1966: Quasi-geostrophic motions in the equatorial area. J. Meteor. Soc. Japan, Ser II, 44, 25-43.
36. Neelin J. D., 1989: On the integration of the Gill model. J. Atmos. 3d., 46, 2466-2468.
37. Neelin J. D., and N. Zheng, 2000: A quasi-equilibrium tropical circulation model-Formulation. J. Atmos. Sci., 57, 1741-1766.
38. Newley T. M. J., H. J. Pearson and J. C. R. Hunt, 1991: Stably Stratified Rotating Flow through a Group of Obstacles. Geophys. Astrophys. Fluid Dynamics, 58, 147-171.
39. Ogura Y. and N. A. Phillips, 1962: Scale analysis of deep moist convection and some related numerical calculations. J. Atmos. Sci., 19, 173-179.
40. Pedlosky J., 1987: Geophysical Fluid Dynamics, Springer-Verlag, New York, Second edition.
41. Petoukhov V., A. Ganopolski, V. Brovkin, M. Claussen, A. Eliseev, C. Kubatzki, S. Rahmstorf, 2000: CLIMBER-2: A climatge system model of intermediate complexity. Part I: Model description and performance for the present climate. Climate Dynamics, 16, 1-17.
42. Ganopolski A., and S. Rahmstorf, 1999: Long-term global warming scenarios computed with an efficient coupled climate model. Climatic Change, 43, 353-367.
43. Roulstone I., and M. J. Sewell, 1997: The mathematical structure of theories of semi-geostrophic type. Phil. Trans. R. Soc. London, A 355, 2489-2517.
44. Saltzmann B., 1978: A survey of statistical-dynamical models of the terrestrial climate. Adv. Geophysics, 20, 183-304.
45. Schär C., D. Leuenberger, O. Fuhrer, D. Lüthi, and C. Girard, 2002: A new terrain-following vertical coordinate formulation for atmospheric prediction models. Mon. Wea. Rev., 130, 2459-2480.
46. Schneider W., 1978: Mathematische Methoden in der Strömungsmechanik. Vieweg.
47. Schochet S, 1994: Fast singular limits of hyperbolic pdes. Journal of Differential Equations, 114, 476-512.
48. Schroeder, W., 1997: Ertel's potential vorticity. (Ertel's collected papers Vol. III) Interdivisional Commission on History of IAGA / History Commission of the German Geophyical Society, Mitteilungen 16
49. Sobel A., J. Nilsson, and L. Polvani, 2001: The weak temperature gradient approximation and balanced tropical moisture waves. J. Atmos. Sci., 58, 3650-3665.
50. Stone P., and M.-S. Yao, 1990: Development of a two-dimensional zonally averaged statistical-dynamical model. Part III: The parameterization of the eddy fluxes of heat and moisture. J. Climate, 3, 726-740.
51. Wang B., and T. Li, 1993: A simple tropical atmosphere model of relevance to short-term climate variations. J. Atmos. Sci., 50, 260-284.
52. Webster P. J., 1972: Response of the tropical atmosphere to local steady forcing. Mon. Wea. Rev., 100, 518-541.
53. Zeytounian R. K., 1991: Meteorological Fluid Dynamics. Lecture Notes in Physics, m5, Springer, 1991.