Bibliography

The bibliography printed below represents a somewhat modified (mostly extended) version of the book's bibliography.

REFERENCES

Abramowitz, M. and I. A. Stegun, 1965: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, 1046 pp. 

Acheson, D. J., 1990: Elementary Fluid Dynamics. Oxford Applied Mathematics and Computing Science Series, Oxford University Press, 397 pp.

Adams, J. C. and P. N. Swarztrauber, 1999: SPHEREPACK 3.0: A Model Development Facility. Mon. Wea. Rev., 127, 1872–1878.

Adamson, D. S., S. E. Belcher, B. J. Hoskins, and R. S. Plant, 2006: Boundary–layer friction in midlatitude cyclones. Quart. J. Roy. Meteor. Soc., 132, 

        101–124.

Ahrens, C. D., 2009: Meteorology Today: An Introduction to Weather, Climate, and the Environment. ninth ed., Brooks/Cole, 549 pp.

Allen, J. S., J. A. Barth, and P. A. Newberger, 1990: On Intermediate Models for Barotropic Continental Shelf and Slope Flow Fields. Part I: Formulation

        and Comparison of Exact Solutions. J. Phys. Oceanogr., 20, 1017–1042.

Ambaum, M. H. P., 2010: Thermal Physics of the Atmosphere. Wiley–Blackwell, 239 pp. 

Ambrizzi, T., B. J. Hoskins, and H.-H. Hsu, 1995: Rossby Wave Propagation and Teleconnection Patterns in the Austral Winter. J. Atmos. Sci., 52 (21), 

        3661–3672. 

Ames, W. F., 1977: Numerical Methods for Partial Differential Equations (Second Edition). Computer Science and Applied Mathematics, Academic Press,

        365 pp. 

Andrews, D. G., 1983: A Conservation Law for Small–Amplitude Quasi–Geostrophic Disturbances on a Zonally Asymmetric Basic Flow. J. Atmos. Sci., 40,

        85–90.

Arakawa, A., 1997: Adjustment Mechanisms in Atmospheric Models. J. Meteor. Soc. Jap., 75(1B), 155–179.

Arakawa, A., 2000: A Personal Perspective on the Early Years of General Circulation Modeling at UCLA. General Circulation Model Development, 

        D. A. Randall, Ed., Academic Press, 807 pp., International Geophysics Series, Vol. 70, 1–65.

Arakawa, A. and V. R. Lamb, 1977: Computational Design of the Basic Dynamical Processes of the UCLA General Circulation Model. General Circulation

        Models of the Atmosphere, J. Chang, Ed., Academic Press, Methods in Com- putational Physics, Vol. 17, 173–265.

Arfken, G. B. and H. J. Weber, 2005: Mathematical Methods for Physicists (Sixth Edition). Elsevier – Academic Press, 1182 pp.

Aris, R., 1962: Vectors, Tensors, and the Basic Equations of Fluid Mechanics. Dover, 286 pp.

Ashford, O. M., 1985: Prophet – or Professor? The Life and Work of Lewis Fry Richardson. Adam Hilger, 304 pp.

Aspray, W., 1990: John von Neumann and the Origins of Modern Computing. The Massachusetts Institute of Technology Press, 376 pp.

Asselin, R. A., 1972: Frequency filter for time integrations. Mon. Wea. Rev., 100, 487–490. 

Baede, A. P. M., 1978: Documentation of the E.C.M.W.F. Spectral Model. Tech. rep., 157 pp., ECMWF Research Department Internal Report No. 19.

        [Available from ECMWF, Shinfield Park, Reading RG2 9AX, England].

Baede, A. P. M., M. Jarraud, and U. Cubasch, 1979: Adiabatic Formulation and Organization of ECMWF’s Spectral Model. Tech. rep., 40 pp., 

        ECMWF Technical Report No. 15, [Available from ECMWF, Shinfield Park, Reading RG2 9AX, England].

Baer, F. and G. W. Platzman, 1961: A Procedure for Numerical Integration of the Spectral Vorticity Equation. Journal of Meteorology, 18, 393–401.

Baer, F. and J. J. Tribbia, 1977: On Complete Filtering of Gravity Modes Through Nonlinear Initialization. Mon. Wea. Rev., 105, 1536–1539.

Baines, P. G., 1976: The stability of planetary waves on a sphere. J. Fluid Mech., 73, 193–213. Baldwin, M. P., P. B. Rhines, H.-P. Huang, 

        and M. E. McIntyre, 2007: The Jet–Stream Conundrum. Science, 315, 467–468. 

Banks, W. H. H., P. G. Drazin, and M. B. Zaturska, 1976: On the normal modes of parallel flow of inviscid stratified fluid. J. Fluid Mech., 75, 149–171.

Batchelor, G. K., 1988: An Introduction to Fluid Dynamics. Cambridge University Press, 615 pp.

Bates, C. C. and J. F. Fuller, 1986: America’s Weather Warriors, 1814–1985. Texas A&M University Press College Station, 360 pp.

Bates, J. R., 1985: Semi–Lagrangian Advective Schemes and their use in Meteorological Modeling. Large–Scale Compu- tations in Fluid Mechanics, 

        B. E. Engquist, S. Osher, and R. C. J. Somerville, Eds., American Mathematical Society, pp. xv + 370 & x + 409, Providence, 

        Rhode Island, Lectures in Applied Mathematics, Vol. 22 (Part 1 & 2), 1–29 (of Part 1).

Bates, J. R., S. Moorthi, and R. W. Higgins, 1993: A Global Multilevel Atmospheric Model Using a Vector Semi–Lagrangian Finite–Difference 

        Scheme. Part I: Adiabatic Formulation. Mon. Wea. Rev., 121, 244–263.

Bates, J. R., F. H. M. Semazzi, and S. R. M. Higgins, R. W. Barros, 1990: Integration of the Shallow Water Equations on the Sphere Using 

        a Vector Semi–Lagrangian Scheme with a Multigrid Solver. Mon. Wea. Rev., 118, 1615–1627.

Benedict, J. J. and D. A. Randall, 2009: Structure of the Madden–Julian Oscillation in the Superparameterized CAM. J. Atmos. Sci., 66, 3277–3296.

Bjerknes, V., 1904: Das Problem der Wettervorhersage, betrachtet vom Standpunkte der Mechanik und der Physik. Meteorol. Z., 21, 1–7.

Bolin, B., (Ed.) , 1959: The Atmosphere and Sea in Motion: Scientific Contributions to the Rossby Memorial Volume. 

        The Rockefeller Institute Press, 509 pp.

Bourke, W., 1972: An Efficient, One–Level, Primitive–Equation Spectral Model. Mon. Wea. Rev., 100, 683–689. Bourke, W., 1974: A Multi–Level 

        Spectral model. I. Formulation and Hemispheric Integrations. Mon. Wea. Rev., 102, 687–701.

Bourke, W., 1988: Spectral Methods in Global Climate and Weather Prediction Models. Physically–Based Modelling and Simulation of Climate and Climatic

         Change – Part 1, M. E. Schlesinger, Ed., Kluwer Academic Publishers, 624 pp., NATO ASI Series, Series C: Mathematical and Physical Sciences, 

         Vol. 243, 169–220.

Bourke, W., B. McAvaney, K. Puri, and R. Thurling, 1977: Global Modeling of Atmospheric Flow by Spectral Methods. General Circulation Models of the

        Atmosphere, J. Chang, Ed., Academic Press, Methods in Computational Physics, Vol. 17, 267–324.

Boyd, J. P., 1978a: Spectral and Pseudospectral Methods for Eigenvalue and Nonseparable Boundary Value Problems. Mon. Wea. Rev., 106, 1192–1203.

Boyd, J. P., 1978b: The Choice of Spectral Functions on a Sphere for Boundary and Eigenvalue Problems: A Comparison of Chebyshev, Fourier and 

         Associated Legendre Expansions. Mon. Wea. Rev., 106, 1184–1191.

Boyd, J. P., 2001: Chebyshev and Fourier Spectral Methods. 2d ed., Dover, 668 pp.

Briggs, W. L. and V. E. Henson, 1995: The DFT – An Owner’s Manual for the Discrete Fourier Transform. Society for Industrial and Applied Mathematics,

        434 pp.

Canuto, C., M. Y. Hussaini, A. Quarteroni, and T. A. Zang, 1988: Spectral Methods in Fluid Dynamics. Springer Series in Computational Physics, 

        Springer, 557 pp.

Canuto, C., M. Y. Hussaini, A. Quarteroni, and T. A. Zang, 2006: Spectral Methods: Fundamentals in Single Domains. Springer, 563 pp.

Canuto, C., M. Y. Hussaini, A. Quarteroni, and T. A. Zang, 2007: Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics.

        Springer, 596 pp.

Chandrasekhar, S., 1960: Radiative Transfer. Dover, 393 pp.

Charney, J. G., 1947: The dynamics of long waves in a baroclinic westerly current. Journal of Meteorology, 4, 135–162.

Charney, J. G., 1948: On the Scale of Atmospheric Motions. Geofysiske Publikasjoner, 17 (2), 1–17.

Charney, J. G. and A. Eliassen, 1949: A Numerical Method for Predicting the Perturbations of the Middle Latitude Westerlies. Tellus, 1 (2), 38–54.

Charney, J. G., R. Fj ̈ortoft, and J. von Neumann, 1950: Numerical Integration of the Barotropic Vorticity Equation. Tellus, 2, 237–254.

Charney, J. G. and N. A. Phillips, 1953: Numerical integration of the quasi–geostrophic equations for barotropic and simple baroclinic flows. 

        J. Meteorol., 10 (2), 71–99.

Charney, J. G. and M. E. Stern, 1962: On the Stability of Internal Baroclinic Jets in a Rotating Atmosphere. J. Atmos. Sci., 19, 159–172.

Chen, X.-S., 1997: Use of the Aliased Spectral Model in Numerical Weather Prediction. Mon. Wea. Rev., 125, 2998–3007.

Chung, T. J., 2006: Computational Fluid Dynamics. Cambridge University Press, 1012 pp.

Cipra, B. A., 2000: The Best of the 20th Century: Editors Name Top 10 Algorithms. SIAM News, 33 (4).

Corby, G. A., A. Gilchrist, and R. L. Newson, 1972: A general circulation model of the atmosphere suitable for long period integrations. 

        Quart. J. Roy.  Meteor. Soc., 98, 809–832.

Courant, R., K. Friedrichs, and H. Lewy, 1928: Über die partiellen Differenzengleichungen der mathematischen Physik. 

        Mathematische Annalen, 100, 32–74.

Courant, R., K. Friedrichs, and H. Lewy, 1967: On the Partial Difference Equations of Mathematical Physics. 

        IBM Journal, March, 215–234 (English translation of the 1928 German original).

Cullen, M., 2007: Modelling atmospheric flows. Acta Numerica, 16, 67–154. 

Curry, J. H., J. R. Herring, J. Loncaric, and S. A. Orszag, 1984: Order and disorder in two– and three–dimensional

        Bénard convection. J. Fluid Mech., 147, 1–38.

Daley, R., 1981: Normal Mode Initialization. Reviews of Geophysics and Space Physics, 19(3), 450–468.

Daley, R., 1991: Atmospheric Data Analysis. Cambridge Atmospheric and Space Science Series, Cambridge University Press, 457 pp.

Daley, R., 1997: Atmospheric data assimilation. J. Meteor. Soc. Jap., 75(1B), 319–329. 

Danaila, I., P. Joly, S. M. Kaber, and M. Postel, 2007: An Introduction to Scientific Computing: Twelve Computational Projects Solved with Matlab. 

        Springer, 294 pp.

Danielson, D. A., 2003: Vectors and Tensors in Engineering and Physics. Second Ed., Westview Press, 282 pp.

de Vries, H. and M. Ehrendorfer, 2008: Linear amplification of marginally neutral baroclinic waves. Tellus, 60A, 1079– 1088.

de Vries, H. and T. Opsteegh, 2007: Interpretation of discrete and continuum modes in a two–layer Eady model. Tellus, 59A, 182–197.

Dickinson, R. E., 1978: Rossby waves – long–period oscillations of oceans and atmospheres. Ann. Rev. Fluid Mech., 10, 159–195.

Dongarra, J. and F. Sullivan, 2000: Guest Editors’ Introduction: The Top 10 Algorithms. Computing in Science & Engineering, 2 (1), 22–23, 

        URL http://link.aip.org/link/?CSX/2/22/1.

Drazin, P. G., 2002: Introduction to Hydrodynamic Stability. Cambridge University Press, 258 pp.

Drazin, P. G. and W. H. Reid, 1981: Hydrodynamic Stability. Cambridge University Press, 527 pp.

Dritschel, D. G. and M. E. McIntyre, 2008: Multiple Jets as PV Staircases: The Phillips Effect and the Resilience of Eddy–Transport Barriers. 

        J. Atmos. Sci., 65, 855–874.

Dritschel, D. G., L. M. Polvani, and A. R. Mohebalhojeh, 1999: The Contour–Advective Semi–Lagrangian Algorithm for the Shallow Water Equations. 

        Mon. Wea. Rev., 127, 1551–1565.

Dugan, C. R. L. and S. S. R. Speer, 1945: Japan’s Invisible Ally. BRIEF (official publication of the Army Air Forces in the Pacific Ocean Areas) – April 10, 

        1945 (Vol. 2, No. 19), S. S. C. Howard, Ed., Army Air Forces in the Pacific Ocean Areas, produced under supervision of the 

        Information and Education Division of AAFPOA, 20 pp., 1–15.

Durran, D. R., 1999: Numerical Methods for Wave Equations in Geophysical Fluid Dynamics. Springer, 465 pp. 

Durran, D. R., 2010: Numerical Methods for Fluid Dynamics With Applications to Geophysics, Texts in Applied Mathematics, Vol. 32. 2d ed., 

        Springer, 516 pp.

Eady, E. T., 1949: Long waves and cyclone waves. Tellus, 1, 33–52.

Edwards, P. N., 2000: A brief history of atmospheric general circulation modeling. General Circulation Model Development, D. A. Randall, Ed., 

        Academic Press, 807 pp., International Geophysics Series, Vol. 70, 67–90.

Egger, J. and K. P. Hoinka, 2006: Austausch von atmosphärischem Drehimpuls an Gebirgen. Promet, 32, 48–53.

Ehrendorfer, M., 1998: Energy norms in the T21L3 Marshall/Molteni quasigeostrophic model. ECMWF Research Department Memorandum, R48.9/ME/70, 28 pp. [Available from ECMWF, Shinfield Park, Reading RG2 9AX, England; also available from author.].

Ehrendorfer, M., 2000: The Total Energy Norm in a Quasigeostrophic Model. J. Atmos. Sci., 57, 3443–3451. 

Ehrendorfer, M., 2004: A vector derivation of the semigeostrophic potential vorticity equation. J. Atmos. Sci., 61, 1461–1466.

Ehrendorfer, M., 2012: Spectral Numerical Weather Prediction Models. Society for Industrial and Applied Mathematics, xxv+498 pp., 

        ISBN 978-1-611971-98-9.

Ehrendorfer, M. and R. M. Errico, 1995: Mesoscale Predictability and the Spectrum of Optimal Perturbations. J. Atmos. Sci., 52, 3475–3500.

Ehrendorfer, M. and R. M. Errico, 2008: An Atmospheric Model of Intermediate Complexity for Data Assimilation Studies. Quart. J. Roy. Meteor. Soc., 

        134, 1717–1732.

Eliasen, E., B. Machenhauer, and E. Rasmussen, 1970: On a numerical method for integration of the hydrodynamical equations with a spectral 

        representation of the horizontal fields. Report No. 2, Institut for Teoretisk Meteorologi, Københavns Universitet, 37 pp.

Eliassen, A., 1949: The quasi–static equations of motion with pressure as independent variable. Geofysiske Publikasjoner, 17(3), 1–44.

Eliassen, A., 1984: Geostrophy. Quart. J. Roy. Meteor. Soc., 110, 1–12.

Engquist, B. E., S. Osher, and R. C. J. Somerville, (Eds.) , 1985: Large–Scale Computations in Fluid Mechanics, Lectures in Applied Mathematics, 

        Vol. 22 (Part 1 & 2). American Mathematical Society, pp. xv + 370 & x + 409, Providence, Rhode Island, pp. xv + 370 & x + 409 pp.

Errico, R. M., 1983: Convergence Properties of Machenhauer’s Initialization Scheme. Mon. Wea. Rev., 111, 2214–2223.

Errico, R. M., 1987: A Description of Software for Determination of Normal Modes of the NCAR Community Climate Model. NCAR Tech. Note 

        NCAR/TN-277+STR, 86 pp. [Available from the National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO, 80307].

Errico, R. M., 1997: What Is an Adjoint Model? Bull. Amer. Meteorol. Soc., 78, 2577–2591. 

Ertel, H., 1938: Methoden und Probleme der dynamischen Meteorologie, Ergebnisse der Mathematik und ihrer Grenzgebiete, Vol. 5. Verlag von Julius 

        Springer, 122 pp.

Ertel, H., 1942: Ein neuer hydrodynamischer Wirbelsatz. Meteorologische Zeitschrift, 59, 277–281.

Exner, F. M. and W. Trabert, 1912: Dynamische Meteorologie. Encyklopädie der Mathematischen Wissenschaften mit Einschluss ihrer Anwendungen – Des

        Sechsten Bandes Erster Teil – Geodäsie und Geophysik, P. Furtwängler and E. Wiechert, Eds., Verlag und Druck von B. G. Teubner, 

        pp. XVI + 372 + 580, 1906–1925; available at Goettingen State– and University Library, gdz@sub.uni-goettingen.de, Vol. 6, Part 1, 

        Chapter 8, 179–234 (of Part B. Geophysik).

Falk, G. and W. Ruppel, 1976: Energie und Entropie – Eine Einfu ̈hrung in die Thermodynamik. Springer, 408 pp.

Farrell, B., 1988: Optimal Excitation of Neutral Rossby Waves. J. Atmos. Sci., 45, 163–172.

Feller, W., 1968: An Introduction to Probability Theory and Its Applications, Vol. I. Revised Printing, Third ed., John Wiley & Sons, 509 pp.

Feynman, R. P., R. B. Leighton, and M. Sands, 1964: The Feynman Lectures on Physics. Addison–Wesley. 

Fleagle, R. G. and J. A. Businger, 1980: An Introduction to Atmospheric Physics, International Geophysics Series, Vol. 25. 2d ed., Academic Press, 

        New York, 432 pp.

Fornberg, B., 1996: A Practical Guide to Pseudospectral Methods, Cambridge Monographs on Applied and Computational Mathematics, Vol. 1. 

        Cambridge University Press, 231 pp.

Fornberg, B. and D. M. Sloan, 1994: A review of pseudospectral methods for solving partial differential equations. Acta Numerica, 203–267.

Fortak, H., 1960: Zur Verwendung Generalisierter Zeitabhängiger Koordinaten in den Hydrodynamischen Grundgleichungen der Theoretischen 

        Meteorologie [in German] (On the Use of Generalized Time–Dependent Coordinates in the Hydrodynamic Fundamental Equations of Theoretical

        Meteorology). [copy available from M. Ehrendorfer], Institut für Meteorologie der Freien Universität Berlin.

Fortak, H., 2004a: Hans Ertel’s life and his scientific work. Meteorol. Z., N.F., 13 (6), 453–464. 

Fortak, H., 2004b: Material derivatives of higher dimension in geophysical fluid dynamics. Meteorol. Z., N.F., 13 (6), 499–510. 

Fraedrich, K. and T. Frisius, 2001: Two–level primitive–equation baroclinic instability on an f–plane. Quart. J. Roy. Meteor. Soc., 127, 2053–2068. 

Fraedrich, K., E. Kirk, U. Luksch, and F. Lunkeit, 2005: The portable university model of the atmosphere (PUMA): 

        Storm track dynamics and low–frequency variability. Meteorologische Zeitschrift, 14 (6), 735–745. 

Fulton, S. R. and W. H. Schubert, 1987: Chebyshev Spectral Methods for Limited–Area Models. Part I: Model Problem Analysis. 

        Mon. Wea. Rev., 115 (9), 1940–1953.

Galewsky, J., R. K. Scott, and L. M. Polvani, 2004: An initial–value problem for testing numerical models of the global shallow–water equations. 

        Tellus, 56A, 429–440.

Galewsky, J., R. K. Scott, and L. M. Polvani, 2006: Corrigendum. Tellus, 58A, 520–522.

Gandin, L. S., 1969: Objective Analysis. Lectures on Numerical Short–Range Weather Prediction WMO Regional Training Seminar, 

        Moscow 17 November – 14 December, 1965, D. A. Davies, Ed., World Meteorological Organization, 706 pp., 633–677.

Gauthier, P., P. Courtier, and P. Moll, 1993: Assimilation of simulated wind lidar data with a Kalman filter. Mon. Wea. Rev., 121, 1803–1820.

Gill, A. E., 1982: Atmosphere–Ocean Dynamics, International Geophysics Series, Vol. 30. Academic Press, 662 pp. 

Gockenbach, M. S., 2006: Understanding and Implementing the Finite Element Method. Society for Industrial and Applied Mathematics, 363 pp.

Gordon, C. T. and W. F. Stern, 1982: A Description of the GFDL Global Spectral Model. Mon. Wea. Rev., 110 (7), 625–644.

Gottlieb, D., M. Y. Hussaini, and S. A. Orszag, 1984: Introduction: Theory and Applications of Spectral Methods. Spectral Methods for Partial Differential 

        Equations, R. G. Voigt, D. Gottlieb, and M. Y. Hussaini, Eds., Society for Industrial and Applied Mathematics, Philadelphia, 267 pp., 1–54.

Gottlieb, D. and S. A. Orszag, 1977: Numerical Analysis of Spectral Methods: Theory and Applications. CBMS–NSF Regional Conference Series in Applied 

        Mathematics, Society for Industrial and Applied Mathematics, 170 pp.

Guyon, E., J.-P. Hulin, L. Petit, and C. D. Mitescu, 2001: Physical Hydrodynamics. Oxford University Press, 505 pp.

Hack, J. J. and R. Jakob, 1992: Description of a Global Shallow Water Model Based on the Spectral Transform Method. NCAR Tech. Note 

        NCAR/TN-343+STR, 39 pp. [Available from the National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO, 80307].

Haltiner, G. J. and R. T. Williams, 1980: Numerical Prediction and Dynamic Meteorology. Wiley, 477 pp. 

Hann, J. v., 1915: Lehrbuch der Meteorologie. Verlag von Chr. Herm. Tauchnitz, 847 pp. 

Hardy, G. H., 1940: A Mathematician’s Apology. Cambridge University Press, Canto Edition 1992, 153 pp. 

Hart, J. E., 1979: Finite amplitude baroclinic instability. Ann. Rev. Fluid Mech., 11, 147–172.

Harten, U., 2009: Physik – Eine Einführung für Ingenieuere und Naturwissenschaftler. 4th ed., Springer, 441 pp.

Hartmann, D. L., 1983: Barotropic Instability of the Polar Night Jet Stream. J. Atmos. Sci., 40, 817–835.

Haurwitz, B., 1941: Dynamic Meteorology. McGraw–Hill Book Company, Inc., 365 pp.

Heifetz, E., C. H. Bishop, B. J. Hoskins, and J. Methven, 2004a: The counter–propagating Rossby–wave perspective on baroclinic instability. 

        I: Mathematical basis. Quart. J. Roy. Meteor. Soc., 130, 211–231.

Hesthaven, J. S., S. Gottlieb, and D. Gottlieb, 2007: Spectral Methods for Time–Dependent Problems, Cambridge Monographs on Applied and     

        Computational Mathematics, Vol. 21. Cambridge University Press, 273 pp.

Hinkelmann, K., 1951: Der Mechanismus des meteorologischen Lärmes. Tellus, 3, 285–296.

Hinkelmann, K., 1959: Ein numerisches Experiment mit den primitiven Gleichungen. The Atmosphere and Sea in Motion: Scientific Contributions 

        to the Rossby Memorial Volume, B. Bolin, Ed., The Rockefeller Institute Press, 509 pp., 486– 500.

Hinkelmann, K. H., 1969: Primitive Equations. Lectures on Numerical Short–Range Weather Prediction WMO Regional Training Seminar, 

        Moscow 17 November – 14 December, 1965, D. A. Davies, Ed., World Meteorological Organization, 706 pp., 306–375.

Holton, J. R., 2004: An Introduction to Dynamic Meteorology (Fourth Edition), International Geophysics Series, Vol. 88. Elsevier – Academic Press, 535pp.

Honerkamp, J. and H. Römer, 1989: Klassische Theoretische Physik. Springer, 323 pp.

Hortal, M. and A. J. Simmons, 1991: Use of reduced Gaussian grids in spectral models. Mon. Wea. Rev., 119, 1057–1074.

Hoskins, B. J., 1973: Stability of the Rossby–Haurwitz wave. Quart. J. Roy. Meteor. Soc., 99, 723–745.

Hoskins, B. J., 1975: The Geostrophic Momentum Approximation and the Semi–Geostrophic Equations. J. Atmos. Sci., 32, 233–242.

Hoskins, B. J., 1980: Representation of the Earth Topography Using Spherical Harmonics. Mon. Wea. Rev., 108 (1), 111–115.

Hoskins, B. J. and T. Ambrizzi, 1993: Rossby Wave Propagation on a Realistic Longitudinally Varying Flow. J. Atmos. Sci., 50 (12), 1661–1671.

Hoskins, B. J., I. Draghici, and H. C. Davies, 1978: A new look at the ω–equation. Quart. J. Roy. Meteor. Soc., 104, 31–38.

Hoskins, B. J. and A. Hollingsworth, 1973: On the Simplest Example of the Barotropic Instability of Rossby Wave Motion. J. Atmos. Sci., 30, 150–153.

Hoskins, B. J., M. E. McIntyre, and A. W. Robertson, 1985: On the use and significance of isentropic potential vorticity maps. 

        Quart. J. Roy. Meteor. Soc., 111, 877–946.

Hoskins, B. J. and A. J. Simmons, 1975: A multi–layer spectral model and the semi–implicit method. Quart. J. Roy. Meteor. Soc., 101, 637–655.

Hoskins, B. J. and A. J. Simmons, 1976: Spectral Methods Applied to the Integration of Meteorological Equations. Lecture Notes in Physics, Berlin 

        Springer Verlag, R. Glowinski and J. L. Lions, Eds., Lecture Notes in Physics, Berlin Springer Verlag, Vol. 58, 259–274, doi:10.1007/BFb0120594.

Houghton, J., 2005: The Physics of Atmospheres. 3d ed., Cambridge University Press, 320 pp.

Hussaini, M. Y. and T. A. Zang, 1987: Spectral Methods in Fluid Dynamics. Ann. Rev. Fluid Mech., 19, 339–367.

Jablonowski, C. and D. L. Williamson, 2006: A baroclinic instability test case for atmospheric model dynamical cores. 

        Quart. J. Roy. Meteor. Soc., 132, 2943–2975.

Jacobson, M. Z., 2005: Fundamentals of Atmospheric Modeling. Cambridge University Press, 813 pp.

Jakob, R., J. J. Hack, and D. L. Williamson, 1993: Solutions to the Shallow Water Test Set Using the Spectral Transform Method. NCAR Tech. 

        Note NCAR/TN-388+STR, 82 pp. [Available from the National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO, 80307].

Jakob-Chien, R., J. J. Hack, and D. L. Williamson, 1995: Spectral Transform Solutions to the Shallow Water Test Set. 

        Journal of Computational Physics, 119, 164–187.

Jarraud, M. and A. P. M. Baede, 1985: The Use of Spectral Techniques in Numerical Weather Prediction. Large–Scale Computations in Fluid 

        Mechanics, B. E. Engquist, S. Osher, and R. C. J. Somerville, Eds., American Mathematical Society, pp. xv + 370 & x + 409, Providence, 

        Rhode Island, Lectures in Applied Mathematics, Vol. 22 (Part 1 & 2), 1–41 (of Part 2).

Jarraud, M. and A. J. Simmons, 1983: The Spectral Technique. Proceedings ECMWF Seminar on Numerical Methods for Weather Prediction, 

        5–9 September 1983, Vol. 2, 1–59.

Jenkner, J. and M. Ehrendorfer, 2006: Resonant Continuum Modes in the Eady Model with Rigid Lid. J. Atmos. Sci., 63, 765–773.

Juang, H.-M. H., 2004: A Reduced Spectral Transform for the NCEP Seasonal Forecast Global Spectral Atmospheric Model. 

        Mon. Wea. Rev., 132, 1019–1035.

Kalnay, E., 2003: Atmospheric Modeling, Data Assimilation and Predictability. Cambridge University Press, 341 pp. 

Kantha, L. H. and C. A. Clayson, 2000: Numerical Models of Oceans and Oceanic Processes. Academic Press, 940 pp. 

Kasahara, A., 1982: Significance of Non–Elliptic Regions in Balanced Flows of the Tropical Atmosphere. Mon. Wea. Rev., 110, 1956–1967.

Kasahara, A. and M. Kanamitsu, 2001: Weather Prediction, Numerical. Encyclopedia of Physical Science and Technology, R. A. Meyers, Ed., 

        Academic Press, New York, 805–835, doi:10.1016/B0-12-227410-5/00824-3, 

        URL http://www. sciencedirect.com/science/article/B782V-4CKG1K4-YY/2/575e87e8ced3bd7bc654c56bca232f3a.

Kasahara, A. and K. Puri, 1981: Spectral Representation of Three–Dimensional Global Data by Expansion in Normal Mode Functions. 

        Mon. Wea. Rev., 109, 37–51.

Kiehl, J. T., J. J. Hack, G. B. Bonan, B. A. Boville, B. P. Briegleb, D. L. Williamson, and P. J. Rasch, 1996: Description of the NCAR 

        Community Climate Model (CCM3). NCAR Tech. Note NCAR/TN-420+STR, 152 pp. [Available from the National Center for Atmospheric 

        Research, P.O. Box 3000, Boulder, CO, 80307].

Koch, P., H. Wernli, and H. C. Davies, 2006: An event–based jet–stream climatology and typology. International Journal of Climatology, 26, 283–301.

Koren, B., 2006: Computational fluid dynamics: science and tool. Tech. rep., CWI. Modeling, Analysis and Simulation [MAS]; E 0602. 

        ISSN 1386-3703; http://www.cwi.nl/ftp/CWIreports/MAS/MAS-E0602.pdf, 

        on 16 dec 2011 available at: http://oai.cwi.nl/oai/asset/10816/10816D.pdf.

Krishnamurti, T. N., H. S. Bedi, and V. M. Hardiker, 1998: An Introduction to Global Spectral Modeling. Oxford University Press, 253 pp.

Krishnamurti, T. N., H. S. Bedi, V. M. Hardiker, and L. Ramaswamy, 2006: An Introduction to Global Spectral Modeling, Atmospheric and Oceanic 

        Sciences Library, Vol. 35. Second Revised and Enlarged ed., Springer, 317 pp.

Krishnamurti, T. N. and L. Bounoua, 1996: An Introduction to Numerical Weather Prediction Techniques. CRC Press, 293 pp.

Kuchling, H., 2011: Taschenbuch der Physik. 20th ed., Carl Hanser Verlag, 711 pp. 

Kurihara, Y., 1965: Numerical integration of the primitive equations on a spherical grid. Mon. Wea. Rev., 93 (7), 399–415. 

Kwizak, M. and A. J. Robert, 1971: A semi–implicit scheme for grid point atmospheric models of the primitive equations. Mon. Wea. Rev., 99, 32–36.

Leith, C. E., 1978: Objective Methods for Weather Prediction. Ann. Rev. Fluid Mech., 10, 107–128.

Leith, C. E., 1990: Stochastic backscatter in a subgrid–scale model: Plane shear mixing layer. Phys. Fluids A, 2, 297–299.

Lewis, J. M., 1998: Clarifying the Dynamics of the General Circulation: Phillips’s 1956 Experiment. Bull. Amer. Meteorol. Soc., 79, 39–60.

Lewis, J. M., 2003: Ooishi’s Observation Viewed in the Context of Jet Stream Discovery. Bull. Amer. Meteorol. Soc., 84, 357–369.

Lin, C. A., R. Laprise, and H. Ritchie, (Eds.) , 1997: Numerical Methods in Atmospheric and Oceanic Modelling: The André J. Robert Memorial Volume.

        Canadian Meteorological and Oceanographic Society and NRC Research Press, 581 + 52 pp.

Lin, C. C. and L. A. Segel, 1988: Mathematics Applied to Deterministic Problems in the Natural Sciences. 

        Society for Industrial and Applied Mathematics, 609 pp.

Lindzen, R. S., 1988: Instability of Plane Parallel Shear Flow (Towards a Mechanistic Picture of How it Works). PAGEOPH, 126 (1), 103–121.

Lindzen, R. S., 1990: Dynamics in Atmospheric Physics. Cambridge University Press, 310 pp.

Liou, K.-N., 1992: Radiation and Cloud Processes in the Atmosphere: Theory, Observation, and Modeling, Oxford Monographs on Geology 

        and Geophysics, Vol. 20. Oxford University Press, 487 pp.

Logan, D. J., 1987: Applied Mathematics – A Contemporary Approach. Wiley, 572 pp. 

Lordi, N. J., A. Kasahara, and S. K. Kao, 1980: Numerical Simulation of Stratospheric Sudden Warmings with a Primitive Equation Spectral Model. 

        J. Atmos. Sci., 37, 2746–2767.

Lorenz, E. N., 1955: Available Potential Energy and the Maintenance of the General Circulation. Tellus, 7, 157–167.

Lorenz, E. N., 1956: Empirical Orthogonal Functions and Statistical Weather Prediction. Scientific Report No. 1 Statistical Forecasting Project, 

        E. N. Lorenz, Ed., Massachusetts Institute of Technology, Department of Meteorology, Cambridge, Massachusetts, iii + 49 pp.

Lorenz, E. N., 1960a: Energy and Numerical Weather Prediction. Tellus, 12, 364–373.

Lorenz, E. N., 1960b: Maximum Simplification of the Dynamic Equations. Tellus, 12, 243–254.

Lorenz, E. N., 1963: Deterministic Nonperiodic Flow. J. Atmos. Sci., 20, 130–141.

Lorenz, E. N., 1966: The Circulation of the Atmosphere. American Scientist, 54, 402–420.

Lorenz, E. N., 1967: The Nature and Theory of the General Circulation of the Atmosphere. World Meteorological Organization, 161 pp. pp.

Lorenz, E. N., 1972: Barotropic Instability of Rossby Wave Motion. J. Atmos. Sci., 29, 258–264.

Lorenz, E. N., 1993: The Essence of Chaos. University of Washington Press, 227 pp.

Lorenz, E. N., 2006: Reflections on the Conception, Birth, and Childhood of Numerical Weather Prediction. Annu. Rev. Earth Planet. Sci., 34, 37–45.

Lynch, A. H. and J. J. Cassano, 2006: Applied Atmospheric Dynamics. Wiley, 280 pp.

Lynch, P., 1992: Richardson’s Barotropic Forecast: A Reappraisal. Bull. Amer. Meteorol. Soc., 73 (1), 35–47.

Lynch, P., 2002: Weather Forecasting – From Wolly Art to Solid Science. Meteorology at the Millennium, R. P. Pearce, Ed., Academic Press, 333 pp., 

        International Geophysics Series, Vol. 83, 106–119.

Lynch, P., 2006: The Emergence of Numerical Weather Prediction – Richardson’s Dream. Cambridge University Press, 279 pp.

Lynch, P., 2010: Weather and climate forecasting: chronicle of a revolution. WMO Bulletin 59 (2), 59 (2), 75–78. 

Machenhauer, B., 1977: On the dynamics of gravity oscillations in a shallow water model, with applications to normal mode initialization. 

        Contrib. Atmos. Phys., 50, 253–271. 

Machenhauer, B., 1979: The Spectral Method. Numerical Methods Used in Atmospheric Models Vol. II, World Meteorological Organization, 

        GARP Publications Series, Vol. No. 17, 121–275. 

Machenhauer, B. and E. Rasmussen, 1972: On the integration of the spectral hydrodynamical equations by a transform method. Report No. 3, 

        Institut for Teoretisk Meteorologi, Københavns Universitet, 44 pp. 

Macrae, N., 1999: John von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More.     

        American Mathematical Society, 405 pp.

Mak, M., 2011: Atmospheric Dynamics. Cambridge University Press, 486 pp.

Marshall, J. and F. Molteni, 1993: Toward a dynamical understanding of planetary-scale flow regimes. J. Atmos. Sci., 50, 1792–1818.

Marshall, J. and R. A. Plumb, 2008: Atmosphere, Ocean, and Climate Dynamics: An Introductory Text. Elsevier Academic Press, 319 pp.

McCartney, S., 2001: Eniac – The Triumphs and Tragedies of the World’s First Computer. Berkley Books, New York, 262 pp.

McDonald, A., 1991: Semi–Lagrangian Methods. Proceedings ECMWF Seminar on Numerical methods in atmospheric models, 9–13 September 1991, 

        Vol. 1, 257–271.

McIntyre, M. E. and W. A. Norton, 2000: Potential Vorticity Inversion on a Hemisphere. J. Atmos. Sci., 57, 1214–1235.

McWilliams, J. C., 2006: Fundamentals of Geophysical Fluid Dynamics. Cambridge University Press, 249 pp.

Merilees, P. E., 1973: An Alternative Scheme for the Summation of a Series of Spherical Harmonics. J. Appl. Meteor., 12, 224–227.

Merilees, P. E. and S. A. Orszag, 1979: The pseudospectral method. Numerical Methods Used in Atmospheric Models Vol. II, World Meteorological

        Organization, GARP Publications Series, Vol. No. 17, 276–299.

Mesinger, F. and A. Arakawa, 1976: Numerical Methods Used in Atmospheric Models. Numerical Methods Used in Atmospheric Models Vol. I, 

        World Meteorological Organization, GARP Publications Series, Vol. No. 17, 1–64.

Methven, J., B. J. Hoskins, E. Heifetz, and C. H. Bishop, 2005: The counter–propagating Rossby–wave perspective on baroclinic instability. 

        Part IV: Nonlinear life cycles. Quart. J. Roy. Meteor. Soc., 131, 1425–1440.

Miller, M., R. Buizza, J. Haseler, M. Hortal, P. Janssen, and A. Untch, 2010: Increased resolution in the ECMWF deterministic and ensemble 

        prediction systems. ECMWF Newsletter, No. 124, Summer 2010, Summer 2010 (124), 10–16.

Miller, R. N., 2007: Numerical Modeling of the Ocean Circulation. Cambridge University Press, 242 pp. 

Miyakoda, K., 2000: Weather and climate GCMs. Numerical Modeling of the Global Atmosphere in the Climate System, 

        P. Mote and A. O’Neill, Eds., Kluwer Academic Publishers, 517 pp., 1–27. 

Mohebalhojeh, A. R., 2009: On the momentum equation for the quasi–geostrophic model. Quart. J. Roy. Meteor. Soc., 135, 1638–1641. 

Mohebalhojeh, A. R. and M. E. McIntyre, 2007: Local Mass Conservation and Velocity Splitting in PV–Based Balanced Models. 

        Part I: The Hyperbalance Equations. J. Atmos. Sci., 64 (6), 1782–1793. 

Molteni, F., 2003: Atmospheric simulations using a GCM with simplified physical parameterizations. I: model climatology

        and variability in multi–decadal experiments. Climate Dyn., 20, 175–191. 

Morton, K. W. and D. F. Mayers, 2005: Numerical Solution of Partial Differential Equations. Cambridge University Press, 278 pp.

Müller, P., 1995: Ertel’s potential vorticity theorem in physical oceanography. Reviews of Geophysics, 33 (1), 67–97.

Nehrkorn, T., 1990: On the Computation of Legendre Functions in Spectral Models. Mon. Wea. Rev., 118, 2248–2251.

Neumaier, A., 2001: Introduction to Numerical Analysis. Cambridge University Press, 356 pp.

Olver, F. W. J., D. W. Lozier, R. F. Boisvert, and C. W. Clark, (Eds.), 2010: NIST Handbook of Mathematical Functions. 

        Cambridge University Press, 951 pp.

Orszag, S. A., 1970: Transform Method for the Calculation of Vector–Coupled Sums: Application to the Spectral Form of the Vorticity Equation. 

        J. Atmos. Sci., 27, 890–895.

Orszag, S. A., 1971: Accurate solution of the Orr–Sommerfeld stability equation. J. Fluid Mech., 50, 689–703.

Orszag, S. A., 1974: Fourier Series on Spheres. Mon. Wea. Rev., 102, 56–75.

Orszag, S. A. and M. Israeli, 1974: Numerical Simulation of Viscous Incompressible Flow. Ann. Rev. Fluid Mech., 6, 281–318.

Pedlosky, J., 1964a: An initial value problem in the theory of baroclinic instability. Tellus, 16, 12–17. 

Pedlosky, J., 1964b: The Stability of Currents in the Atmosphere and the Ocean: Part I. J. Atmos. Sci., 21, 201–219. 

Pedlosky, J., 1964c: The Stability of Currents in the Atmosphere and the Ocean: Part II. J. Atmos. Sci., 21, 342–353. 

Pedlosky, J., 1987: Geophysical Fluid Dynamics. Springer, 710 pp. 

Persson, A., 1998: How Do We Understand the Coriolis Force? Bull. Amer. Meteorol. Soc., 79 (7), 1373–1385.

Phillips, N., 2001: The Start of Numerical Weather Prediction in the United States. 50th Anniversary of Numerical Weather Prediction. 

        Commemorative Symposium. Potsdam 2000. Book of Lectures, A. Spekat, Ed., Deutsche Meteorologische Gesellschaft e.V., 255 pp., 13–28.

Phillips, N. A., 1954: Energy transformations and meridional circulations associated with simple baroclinic waves in a two–level, 

        quasi–geostrophic model. Tellus, 6, 273–286.

Phillips, N. A., 1956: The general circulation of the atmosphere: a numerical experiment. Quart. J. Roy. Meteor. Soc., 82, 123–164.

Phillips, N. A., 1957: A coordinate system having some special advantages for numerical forecasting. Journal of Meteo- rology, 14, 184–185.

Phillips, N. A., 1959: An Example of Non–Linear Computational Instability. The Atmosphere and Sea in Motion: Scientific Contributions to the Rossby     

        Memorial Volume, B. Bolin, Ed., The Rockefeller Institute Press, 509 pp., 501–504.

Phillips, N. A., 1963: Geostrophic motion. Rev. Geophys., 1, 123–176. 

Phillips, N. A., 1966: The Equations of Motion for a Shallow Rotating Atmosphere and the “Traditional Approximation”. J. Atmos. Sci., 23, 626–628.

Phillips, N. A., 1990: The Emergence of Quasi–Geostrophic Theory. The Atmosphere – A Challenge – The Science of Jule Gregory Charney, 

        R. S. Lindzen, E. N. Lorenz, and G. W. Platzman, Eds., American Meteorological Society, Boston, Massachusetts, 321 pp., 177–206.

Phillips, N. A., 1998: Carl–Gustav Rossby: His Times, Personality and Actions. Bull. Amer. Meteorol. Soc., 79, 1097– 1112.

Phillips, N. A., 2000: An Explication of the Coriolis Effect. Bull. Amer. Meteorol. Soc., 81 (2), 299–303.

Pichler, H., 1997: Dynamik der Atmosphäre. Spektrum Akademischer Verlag, 572 pp.

Platzman, G. W., 1960: The Spectral Form of the Vorticity Equation. Journal of Meteorology, 17, 635–644.

Platzman, G. W., 1979: The ENIAC Computations of 1950 – Gateway to Numerical Weather Prediction. Bull. Amer. Meteorol. Soc., 60 (4), 302–312.

Plumley, W. J., 1994: Winds over Japan. Bull. Amer. Meteorol. Soc., 75 (1), 63–68. 

Polvani, L. M., R. K. Scott, and S. J. Thomas, 2004: Numerically converged solutions of the global primitive equations for testing the 

        dynamical core of atmospheric GCMs. Mon. Wea. Rev., 132, 2539–2552. 

Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, 1992: Numerical Recipes in FORTRAN – The Art of Scientific Computing. 

        Cambridge University Press, 963 pp. 

Puri, K., 1983: Normal mode initialisation for the ANMRC spectral model. Australian Meteorological Magazine, 31 (2), 85–95. 

Randall, D. A., 1994: Geostrophic Adjustment and the Finite–Difference Shallow–Water Equations. Mon. Wea. Rev., 122 (6), 1371–1377. 

Randall, D. A., (Ed.) , 2000: General Circulation Model Development. Academic Press, 807 pp.

Reuter, H., 1976: Die Wettervorhersage: Einführung in die Theorie und Praxis. Springer–Verlag, Wien New York, 208 pp.

Richardson, L. F., 2007: Weather Prediction by Numerical Process. 2d ed., Cambridge University Press, 236 pp. 

Riley, K. F., M. P. Hobson, and S. J. Bence, 2006: Mathematical Methods for Physics and Engineering. Cambridge University Press, 1333 pp. 

Ritchie, H., 1988: Application of the Semi–Lagrangian Method to a Spectral Model of the Shallow Water Equations. Mon. Wea. Rev., 116, 1587–1598.

Ritchie, H. and A. Robert, 1997: A Historical Perspective on Numerical Weather Prediction: A 1987 Interview with André Robert. 

        Numerical Methods in Atmospheric and Oceanic Modelling: The André J. Robert Memorial Volume, C. A. Lin, R. Laprise, and 

        H. Ritchie, Eds., Canadian Meteorological and Oceanographic Society and NRC Research Press, 581 + 52 pp., 1–24.

Ritchie, H., C. Temperton, A. Simmons, M. Hortal, T. Davies, D. Dent, and M. Hamrud, 1995: Implementation of the Semi–Lagrangian Method 

        in a High–Resolution Version of the ECMWF Forecast Model. Mon. Wea. Rev., 123, 489–514.

Robert, A., 1969: The integration of a spectral model of the atmosphere by the implicit method. Proceedings WMO/IUGG Symposium on 

        Numerical Weather Prediction, Tokyo, Japan, Japan Meteorological Agency, VII.19–VII.24.

Robert, A., 1979: The semi–implicit method. Numerical Methods Used in Atmospheric Models Vol. II, World Meteorological Organization, 

        GARP Publications Series, Vol. No. 17, 417–437.

Robert, A., J. Henderson, and C. Turnball, 1972: An implicit time integration scheme for baroclinic models of the atmosphere. 

        Mon. Wea. Rev., 100, 329–335.

Robert, A. J., 1966: The Integration of a Low Order Spectral Form of the Primitive Meteorological Equations. 

        Journal of the Meteorological Society of Japan. Ser. II, 44 (5), 237–245.

Rosen, R. D., 1999: The global energy cycle. Global Energy and Water Cycles, K. A. Browning and R. J. Gurney, Eds., 

        Cambridge University Press, chap. 1.1, 1–9.

Rossow, W. B. and G. P. Williams, 1979: Large–Scale Motion in the Venus Stratosphere. J. Atmos. Sci., 36, 377–389.

Ruelle, D., 1989: Chaotic Evolution and Strange Attractors. Cambridge University Press, 96 pp.

Ruelle, D., 1991: Chance and Chaos. Princeton University Press, 195 pp.

Salby, M. L., 1996: Fundamentals of Atmospheric Physics, International Geophysics Series, Vol. 61. Academic Press, 627 pp.

Salmon, R., 1998: Lectures on Geophysical Fluid Dynamics. Oxford University Press, 378 pp. 

Sanders, F. and B. J. Hoskins, 1990: An Easy Method for Estimation of Q–Vectors from Weather Maps. Wea. Forecasting, 5, 346–353.

Satoh, M., 2004: Atmospheric Circulation Dynamics and General Circulation Models. Springer, 643 pp.

Satoh, M., T. Matsuno, H. Tomita, H. Miura, T. Nasuno, and S. Iga, 2008: Nonhydrostatic icosahedral atmospheric model (NICAM) for global 

        cloud resolving simulations. Journal of Computational Physics, 227 (7), 3486–3514, doi:DOI:10.1016/j.jcp.2007.02.006, 

        URL http://www.sciencedirect.com/science/article/B6WHY-4N2TS5M-3/2/ bd89a7afca08e3240616909565d91dbe.

Schubert, W., E. Ruprecht, R. Hertenstein, R. Nieto Ferreira, R. Taft, C. Rozoff, P. Ciesielski, and H.-C. Kuo, 2004: English translations 

        of twenty–one of Ertel’s papers on geophysical fluid dynamics. Meteorol. Z., N.F., 13 (6), 527–576.

Scott, R. K. and L. M. Polvani, 2007: Forced–Dissipative Shallow–Water Turbulence on the Sphere and the Atmospheric Circulation 

        of the Giant Planets. J. Atmos. Sci., 64, 3158–3176.

Shen, J. and L.-L. Wang, 2007: Analysis of a Spectral–Galerkin Approximation to the Helmholtz Equation in Exterior Domains. 

        SIAM J. Numer. Anal., 45, 1954–1978.

Shepherd, T. G., 1993: A Unified Theory of Available Potential Energy. Atmosphere–Ocean, 31, 1–26. 

Shuman, F. G., 1957: Numerical Methods in Weather Prediction: I. The Balance Equation. Mon. Wea. Rev., 85 (10), 329–332. 

Shutts, G. J., 1983: The propagation of eddies in diffluent jetstreams: eddy vorticity forcing of ‘blocking’ flow fields.

        Quart. J. Roy. Meteor. Soc., 109, 737–761.

Silberman, I., 1954: Planetary Waves in the Atmosphere. Journal of Meteorology, 11, 27–34.

Simmonds, J. G., 1994: A Brief on Tensor Analysis. Springer, 112 pp.

Simmons, A. J. and D. M. Burridge, 1981: An Energy and Angular–Momentum Conserving Vertical Finite-Difference Scheme and 

        Hybrid Vertical Coordinates. Mon. Wea. Rev., 109, 758–766.

Simmons, A. J. and A. Hollingsworth, 2002: Some aspects of the improvement in skill in numerical weather prediction. 

        Quart. J. Roy. Meteor. Soc., 128, 647–677.

Simmons, A. J., B. J. Hoskins, and D. M. Burridge, 1978: Stability of the Semi–Implicit Method of Time Integration. Mon. Wea. Rev., 106 (3), 405–412.

Smagorinsky, J., 1958: On the numerical integration of the primitive equations of motion for baroclinic flow in a closed region. 

        Mon. Wea. Rev., 86 (12), 457–466.

Smith, G. D., 1985: Numerical Solution of Partial Differential Equations: Finite Difference Methods. 3d ed., Oxford Applied Mathematics 

        and Computing Science Series, Oxford University Press, 337 pp.

Spekat, A., (Ed.) , 2001: 50th Anniversary of Numerical Weather Prediction. Commemorative Symposium. 

        Potsdam 2000. Book of Lectures. Deutsche Meteorologische Gesellschaft e.V., 255 pp.

Spiegel, M. R., 1959: Schaum’s Outline of Theory and Problems of Vector Analysis and an introduction to Tensor Analysis. McGraw–Hill, 225 pp.

Staniforth, A., 2001: Developing efficient unified nonhydrostatic models. 50th Anniversary of Numerical Weather Prediction. Commemorative 

        Symposium. Potsdam 2000. Book of Lectures, A. Spekat, Ed., Deutsche Meteorologische Gesellschaft e.V., 255 pp., 185–200.

Staniforth, A., A. A. White, and N. Wood, 2010: Treatment of vector equations in deep–atmosphere, semi–Lagrangian models. 

        I: Momentum equation. Quart. J. Roy. Meteor. Soc., 136, 497–506.

Stensrud, D. J., 2007: Parameterization Schemes – Keys to Understanding Numerical Weather Prediction Models. Cambridge University Press, 459 pp.

Strang, G., 1988: Linear Algebra and Its Applications. Harcourt Brace Jovanovich College Publishers, 505 pp.

Strang, G., 1993: Introduction to Linear Algebra. Wellesley–Cambridge Press, 472 pp.

Talagrand, O., 1997: Assimilation of observations, an introduction. J. Meteor. Soc. Jap., 75(1B), 191–209.

Tarantola, A., 2005: Inverse Problem Theory and Methods for Model Parameter Estimation. Society for Industrial and Applied Mathematics, 342 pp.

Taylor, M., J. Tribbia, and M. Iskandarani, 1997: The spectral element method for the shallow water equations on the sphere. 

        J. Comp. Phys., 130 (1), 92–108, doi:http://dx.doi.org/10.1006/jcph.1996.5554.

Taylor, T. D., 1984: Recent Advances in Pseudo–Spectral Methods. Spectral Methods for Partial Differential Equations, R. G. Voigt, D. Gottlieb, 

        and M. Y. Hussaini, Eds., Society for Industrial and Applied Mathematics, Philadelphia, 267 pp., 257–267.

Temperton, C., 1983: Self–sorting mixed–radix fast Fourier transforms. J. Comp. Phys., 52, 1–23.

Temperton, C., 1989: Implicit Normal Mode Initialization for Spectral Models. Mon. Wea. Rev., 117, 436–451.

Temperton, C., 1991: On Scalar and Vector Transform Methods for Global Spectral Models. Mon. Wea. Rev., 119, 1303–1307.

Thompson, P. D., 1961: Numerical Weather Analysis and Prediction. The Macmillan Company, New York, 170 pp. 

Thompson, P. D., 1983: Equilibrium statistics of two–dimensional viscous flows with arbitrary random forcing. Phys. Fluids, 26, 3461–3470.

Thompson, P. D., 1990: Charney and the Revival of Numerical Weather Prediction. The Atmosphere – A Challenge – The Science of Jule Gregory 

        Charney, R. S. Lindzen, E. N. Lorenz, and G. W. Platzman, Eds., American Meteorological Society, Boston, Massachusetts, 321 pp., 93–119.

Thompson, W. J., 1997: Atlas for Computing Mathematical Functions. Wiley, 888 pp. 

Trefethen, L. N., 2000: Spectral Methods in Matlab. Software – Environment – Tools, Society for Industrial and Applied Mathematics, 165 pp.

Trefethen, L. N. and M. Embree, 2005: Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators. 

        Princeton University Press, 606 pp.

Trefethen, L. N., A. E. Trefethen, S. C. Reddy, and T. A. Driscoll, 1993: Hydrodynamic stability without eigenvalues. Science, 261, 578–584.

Trenberth, K. E., J. T. Fasullo, and J. Kiehl, 2009: Earth’s Global Energy Budget. Bull. Amer. Meteorol. Soc., 90, 311–323.

Trenberth, K. E. and D. P. Stepaniak, 2004: The flow of energy through the earth’s climate system. Quart. J. Roy. Meteor. Soc., 130, 2677–2701.

Tribbia, J. J., 1981: Nonlinear Normal–Mode Balancing and the Ellipticity Condition. Mon. Wea. Rev., 109, 1751–1761.

Tribbia, J. J., 1982: On Variational Normal Mode Initialization. Mon. Wea. Rev., 110 (6), 455–470.

Ullrich, P. A., C. Jablonowski, and B. van Leer, 2010: High-order finite-volume methods for the shallow–water equations on the sphere. 

        J. Comp. Phys., 229 (17), 6104–6134, doi:http://dx.doi.org/10.1016/j.jcp.2010.04.044.

Vallis, G. K., 2006: Atmospheric and Oceanic Fluid Dynamics – Fundamentals and Large–scale Circulation. Cambridge University Press, 745 pp.

Verkley, W. T. M. and I. R. van der Velde, 2010: Balanced dynamics in the Tropics. Quart. J. Roy. Meteor. Soc., 136, 41–49.

Voigt, R. G., D. Gottlieb, and M. Y. Hussaini, (Eds.) , 1984: Spectral Methods for Partial Differential Equations. 

        Society for Industrial and Applied Mathematics, Philadelphia, 267 pp.

Vreugdenhil, C. B., 1994: Numerical Methods for Shallow–Water Flow, Water Science and Technology Library, Vol. 13. 

        Kluwer Academic Publishers, 261 pp.

Wang, W. and T. Lu, 2005: The alternating segment difference scheme for Burgers’ equation. International Journal 

        for Numerical Methods in Fluids,, 49, 1347–1358.

Warner, T. T., 2011: Numerical Weather and Climate Prediction. Cambridge University Press, 526 pp. 

Washington, W. M. and C. L. Parkinson, 2005: An Introduction to Three–Dimensional Climate Modeling. 2d ed., University Science Books, 353 pp. 

Wedi, N. P., 2010: Diagnostics of model numerical cores: a model hierarchy. Proceedings ECMWF Seminar on Diagnosis of Forecasting and Data

        Assimilation Systems, 7–10 September 2009, 191–203. 

Wedi, N. P. and S. Malardel, 2010: Non–hydrostatic modelling at ECMWF. ECMWF Newsletter, No. 125, Autumn 2010, Autumn 2010 (125), 17–21.

Wedi, N. P. and P. K. Smolarkiewicz, 2009: A framework for testing global non–hydrostatic models. Quart. J. Roy. Meteor. Soc., 135, 469–484.

White, A. A., B. J. Hoskins, I. Roulstone, and A. Staniforth, 2005: Consistent approximate models of the global atmosphere: shallow, deep, 

        hydrostatic, quasi–hydrostatic and non–hydrostatic. Quart. J. Roy. Meteor. Soc., 131, 2081– 2107.

Williamson, D. L., J. B. Drake, J. J. Hack, R. Jakob, and P. N. Swarztrauber, 1992: A standard test set for numerical approximations to the 

        shallow water equations in spherical geometry. Journal of Computational Physics, 102, 211–224.

Woods, A., 2006: Medium–Range Weather Prediction – The European Approach. Springer, 270 pp. 

Zagar, N., J. Tribbia, J. L. Anderson, K. Raeder, and D. T. Kleist, 2010: Diagnosis of systematic analysis increments by using normal modes. 

        Quart. J. Roy. Meteor. Soc., 136, 61–76.

Zang, T. A. and M. Y. Hussaini, 1985: Recent Applications of Spectral Methods in Fluid Dynamics. Large–Scale Computations in Fluid Mechanics, 

        B. E. Engquist, S. Osher, and R. C. J. Somerville, Eds., American Mathematical Society, pp. xv + 370 & x + 409, Providence, Rhode Island, 

        Lectures in Applied Mathematics, Vol. 22 (Part 1 & 2), 379–409 (of Part 2).

Zerroukat, M., N. Wood, A. Staniforth, A. A. White, and J. Thuburn, 2009: An inherently mass–conserving semi–implicit semi–Lagrangian 

        discretisation of the shallow–water equations on the sphere. Quart. J. Roy. Meteor. Soc., 135, 1104–1116.

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