435
Views
5
CrossRef citations to date
0
Altmetric
Original Articles

André Robert (1929–1993): His Pioneering Contributions to Numerical Modelling

Pages 25-54 | Received 16 Jan 1995, Published online: 26 Jul 2011

References

  • Asselin , R. 1972 . Frequency filter for time integrations . Mon. Weather Rev. , 100 : 487 – 490 .
  • Baer , F. 1964 . Integration with the spectral vorticity equation . J. Atmos. Sci. , 21 : 260 – 276 .
  • Baer , F. and Platzman , G. 1961 . A procedure for numerical integration of the spectral vorticity equation . J. Meteorol. , 18 : 393 – 401 .
  • Bates , J. R. and Mcdonald , A. 1982 . Multiply-upstream, semi-Lagrangian advective schemes: analysis and application to a multi-level primitive equation model . Mon. Weather Rev. , 112 : 1831 – 1842 .
  • Bates , J. R. , Mcdonald , A. , Semazzi , F. H.M. , Higgins , R. W. and Barros , S. R.M. 1990 . Integration of the shallow-water equations on the sphere using a vector semi-Lagrangian scheme with a multigrid solver . Mon. Weather Rev. , 118 : 1615 – 1627 .
  • Ben Had , J. and Tahar , N. 1993 . Introduction dune maille variable dans Ihorizontale dun modèle non-hydrostatique 100 Montréal, P.Q. : Université du Québec à Montréal . M.Sc. thesis
  • Bourke , W. 1988 . Physically-Based Modelling and Simulation of Climate and Climatic Change—Part 1 Edited by: Schlesinger , M. E. 169 – 220 . Kluwer Academic Publishers .
  • Bubnova , R. , Hello , G. , Bénard , P. and Geleyn , J.-F. 1995 . Integration of the fully elastic equations cast in hydrostatic pressure terrain-following coordinate in the framework of the ARPEGE/-Aladin NWP system . Mon. Weather Rev. , 129 : 515 – 535 .
  • Chouinard , C. , Mailhot , J. , Mitchell , H. L. , Staniforth , A. and Hocue , R. 1994 . The Canadian regional data assimilation system: operational and research applications . Mon. Weather Rev. , 122 : 1306 – 1325 .
  • Cohn , S. E. , Dee , D. , Isaacson , E. , Marchesin , D. and Zwas , G. 1985 . A fully implicit scheme for the barotropic primitive equations . Mon. Weather Rev. , 113 : 436 – 448 .
  • Coiffier , J. , Chapelet , P. and Marie , N. 1987 . “ Study of various quasi-Lagrangian techniques for numerical models. ” . In Proc. ECMWF Workshop on Techniques for Horizontal Discretization in Numerical Weather Prediction Models, 2–4 November 1987 19 – 46 . Shinfield Park, Reading, , U.K. : European Centre for Medium-range Weather Forecasts .
  • CÔTÉ , J. 1988 . A Lagrange multiplier approach for the metric terms of semi-Lagrangian models on the sphere . Q. J. R. Meterol. Soc. , 114 : 1347 – 1352 .
  • CÔTÉ , J. and Staniforth , A. 1988 . A two-time-level semi-Lagrangian semi-implicit scheme for spectral models . Mon. Weather Rev. , 116 : 2003 – 2012 .
  • Daley , R. W. 1988 . The normal modes of the spherical non-hydrostatic equations with applications to the filtering of acoustic modes . Tellus , 40A : 96 – 106 .
  • Davies , H. C. 1976 . A lateral boundary formulation for multi-level prediction models . Q. J. R. Meterol. Soc. , 102 : 405 – 418 .
  • Desharnais , F. and Robert , A. 1990 . Errors near the poles generated by a semi-Lagrangian integration scheme in a global spectral model . ATMOSPHERE-OCEAN , 28 : 162 – 176 .
  • Eliassen , E. , Machenhauer , B. and Rasmussen , E. 1970 . On a numerical method for integration of the hydrodynamical equations with a spectral representation of the horizontal fields. Rep. No. 2 Denmark : Institut for Teoretisk Meteorologi, Köbenhavns Iniversitet .
  • Jakimow , G. , Yakimiw , E. and Robert , A. 1992 . An implicit formulation for horizontal diffusion in grid point models . Mon. Weather Rev. , 120 : 124 – 130 .
  • Kaas , E. 1987 . The construction of and tests with a multi-level, semi-Lagrangian and semi-implicit limited area model 117 Copenhagen, , Denmark : Geophysics Institute, Copenhagen University . Diploma thesis
  • Krishnamurti , T. N. 1962 . Numerical integration of primitive equations by a quasi-Lagrangian advective scheme . J. Appl. Meterol. , 1 : 508 – 521 .
  • Kruger , H. B. 1964 . A statistical-dynamical objective analysis scheme , Canadian Meteorol. Memoirs, No. 18 39 Toronto, Ontario : Meteorological Branch, Dept. of Transport .
  • Kubota , S. 1960 . Surface Spherical harmonic representation of systems of equations for analysis. Papers in Meteorol. and Geophys. 145 – 166 . Tokyo : Meteorol. Res. Inst .
  • Kwizak , M. 1961 . A report on the solution of the barotropic geostrophic model on a medium-sized computer , Canadian Meteorol. Memoirs, No. 9 30 Toronto, Ontario : Meteorological Branch, Dept. of Transport .
  • Kwizak , M. and Robert , A. 1963 . An evaluation of simple non-geostrophic forecasts , Canadian Meteorol. Memoirs, No. 13 27 Toronto, Ontario : Meteorological Branch, Dept. of Transport .
  • Kwizak , M. 1971 . A semi-implicit scheme for grid point atmospheric models of the primitive equations . Mon. Weather Rev. , 99 : 32 – 36 .
  • Laprise , R. and Andrérobert , J. 1994 . 1929–1993: Original version (in French) . Le Climat , 12 : 81 – 94 . English translation: Can. Meteorol. Ocean. Soc. Bull. Vol. 22, 12–17.
  • Marchuk , G. I. 1965 . A new approach to the numerical solution of differential equations of atmospheric processes , World Meteorological Organisation Technical Note no. 66 286 – 294 . Geneva, , Switzerland
  • Mcdonald , A. and Bates , J. R. 1987 . Improving the estimate of the departure point position in a two time-level semi-Lagrangian and semi-implicit model . Mon. Weather Rev. , 115 : 737 – 739 .
  • Merilees , P. 1972 . Proceedings of the 9th Stanstead Seminar , Pub. in Meteorol. No. 103 136 Montreal : Dept. of Meteorology, McGill U .
  • Merilees , P. , Laprise , R. and Robert , J. 1994 . Necrology: André . Bull. Am Meteorol. Soc. , 75 : 456 1929–1993.
  • Oliger , J. and Sundströ , A. M. 1978 . Theoretical and practical aspects of some initial boundary value problems in fluid dynamics . SIAM J. Appl. Math. , 35 : 419 – 446 .
  • Orszag , S. A. 1970 . Transform method for calculation of vector-coupled sums: Application to the spectral form of the vorticity equation . J. Atmos. Sci. , 27 : 890 – 895 .
  • Perkey , D. J. and Kreitzberg , C. 1976 . A time-dependent lateral boundary scheme for limited-area primitive equation models . Mon. Wearher Rev. , 104 : 74 – 755 .
  • Phillips , N. A. 1959 . “ An example of non-linear computational instability. ” . In The Atmosphere in Motion 501 – 504 . N.Y. : Rockefeller Institute Press .
  • Platzman , G. W. 1960 . The Spectral form of the vorticity equation . J. Meteorol. , 17 : 635 – 644 .
  • Pudykiewicz , J. 1990 . A predictive atmospheric tracer model . J. Meteorol. Soc. Jpn. , 68 : 213 – 225 .
  • Pudykiewicz , J. and a , Staniforth . 1984 . Some properties and comparative performance of the semi-Lagrangian method of Robert in the solution of the advection-diffusion equation . ATMOSPHERE-OCEAN , 22 : 283 – 308 .
  • Ritchie , H. 1986 . Eliminating the interpolation associated with the semi-Lagrangian scheme . Mon. Weather Rev. , 114 : 135 – 146 .
  • Ritchie , H. 1987 . Semi-Lagrangian advection on a Gaussian grid . Mon. Weather Rev. , 115 : 608 – 619 .
  • Ritchie , H. 1988 . Application of the semi-Lagrangian method to a spectral model of the shallow-water equations . Mon. Weather Rev. , 116 : 1587 – 1598 .
  • Ritchie , H. 1991 . Application of the semi-Lagrangian method to a multi-level spectral primitive equations model . Q. J. R. Meteorol. Soc. , 117 : 91 – 106 .
  • Ritchie , H. , Temperton , C. , Simmons , A. , Hortal , M. , Davies , T. , Dent , D. and Hamrud , M. 1995 . Implementation of the semi-Lagrangian method in a high resolution version of the ECMWF forecast model . Mon. Weather Rev. , 123 : 489 – 514 .
  • Ritchmyer , R. D. 1963 . A survey of difference methods for non-steady fluid dynamics , NCAR Technical Notes 63–2 25 Boulder, Colorado : National Center for Atmospheric Research .
  • Rivest , C. , Staniforth , A. and Robert , A. 1994 . Spurious resonant response of semi-Lagrangian discretizations to orographic forcing: diagnosis and solution . Mon. Weather Rev. , 122 : 366 – 376 .
  • Robert , A. 1963a . Baroclinic prediction experiments with a four level statistical-dynamical model. Canadian Meteorol. Memoirs, No. 15 32 Toronto, Ontario : Meteorological Branch, Dept. of Transport .
  • Robert , A. 1963b . A baroclinic model for the Canadian numerical weather prediction program 83 – 88 . Montreal : Stanstead Seminars on the Stratosphere and Mesosphere and Polar Meteorology, Dept. of Meteorology, McGill U .
  • Robert , A. 1965 . The behaviour of planetary waves in an atmospheric model based on spherical harmonics , Pub. in Meteorol. No. 77 84 Montreal : Dept. of Meteorology, McGill U .
  • Robert , A. 1966 . The integration of a low order spectral form of the primitive meteorological equations . J. Meteorol. Soc. Jpn. , 44 : 237 – 245 .
  • Robert , A. 1968a . Integration of a spectral barotropic model from global 500-mb charts . Mon. Weather Rev. , 96 : 83 – 85 .
  • Robert , A. 1968b . Résultats de quelques applications récentes de la méthode spectrale . La météorologie , 2 : 453 – 469 .
  • Robert , A. 1968c . The treatment of moisture and precipitation in atmospheric models integrated by the spectral method . J. Appl. Meteorol. , 7 : 730 – 735 .
  • Robert , A. 1969a . “ The integration of a spectral model of the atmosphere by the implicit method. ” . In Proc. of WMO/IUGG Symposium on NWP in Tokyo VII. 19 – VII.24 . Tokyo, , Japan : Japan Meteorol. Agency .
  • Robert , A. 1969b . An unstable solution to the problem of advection by the finite difference Eulerian method , Office Note #30 3 Washington, D.C. : National Meteorological Center, U.S. Dept. of Commerce .
  • Robert , A. 1976 . “ Sensitivity experiments for the development of NWP models. ” . In Proc. of the 11th Stanstead Seminar , Pub. in Meteorology No. 114 68 – 81 . Montreal : McGill U .
  • Robert , A. 1979 . “ 8 ” . In The semi-implicit method. Numerical Methods used in Atnospheric Models , GARP Pub. Series no. 17 417 – 437 . Geneva, , Switzerland : World Meteorological Organisation . Chapter
  • Robert , A. 1981 . A stable numerical integration scheme for the primitive meteorological equations . ATMOSPHERE-OCEAN , 19 : 35 – 46 .
  • Robert , A. 1982 . A semi-Lagrangian and semi-implicit numerical integration scheme for the primitive meteorological equations . J. Meteorol. Soc. Jpn. , 60 : 319 – 325 .
  • Robert , A. 1993 . Bubble convection experiments with a semi-implicit formulation of the Euler equations . J. Atmos. Sci. , 50 : 1865 – 1873 .
  • Robert , A. , Shuman , F. G. and Gerrity , J. P. Jr . 1970 . On partial difference equations in mathematical physics . Mon. Weather Rev. , 98 : 1 – 6 .
  • Robert , A. , Henderson , J. and Turnbull , C. 1972 . An implicit time integration scheme for baroclinic models of the atmosphere . Mon. Weather Rev. , 100 : 329 – 335 .
  • Robert , A. , Yee , T. L. and Ritchie , H. 1985 . A semi-Lagrangian and semi-implicit numerical integration scheme for multilevel atmospheric models . Mon. Weather Rev. , 113 : 388 – 394 .
  • Robert , A. , Yee , T. L. , Ritchie , H. and Yakimiw , E. 1986 . Identification and elimination of an inflow boundary computational solution in limited area model integrations . ATMOSPHERE-OCEAN , 24 : 369 – 385 .
  • Sawyer , J. S. 1963 . A semi-Lagrangian method of solving the vorticity advection equation . Tellus , 15 : 336 – 342 .
  • Silberman , J. S. 1954 . Planetary waves in the atmosphere . J. Meteorol. , 11 : 27 – 34 .
  • Staniforth , A. and Temperton , C. 1986 . Semi-implicit semi-Lagrangian integration schemes for a barotropic finite-element regional model . Mon. Weather Rev. , 114 : 2078 – 2090 .
  • Staniforth , A. , Temperton , C. and CÔTÉ , J. 1991 . Semi-Lagrangian integration schemes for atmospheric models—a review . Mon. Weather Rev. , 119 : 2206 – 2223 .
  • Tanguay , M. and Robert , A. 1986 . Elimination of the Helmholtz equation associated with the semi-implicit scheme in a grid point model of the shallow water equations . Mon. Weather Rev. , 114 : 2154 – 2162 .
  • Tanguay , M. , Robert , A. , Simard , A. and Staniforth , A. 1989 . A three-dimensional semi-Lagrangian scheme for the Canadian regional finite-element forecast model . Mon. Weather Rev. , 117 : 1861 – 1871 .
  • Tanguay , M. , Robert , A. and Robert , A. 1990 . An efficient optimum interpolation analysis scheme . ATMOSPHERE-OCEAN , 28 : 365 – 371 .
  • Tanguay , M. , Robert , A. and Laprise , R. 1990 . A semi-implicit semi-Lagrangian fully compressible regional forecast model . Mon. Weather Rev. , 118 : 1970 – 1980 .
  • Tanguay , M. , Robert , A. , Yakimiw , B. , Ritchie , H. and Robert , A. 1992 . Advantages of spatial averaging in semi-implicit semi-Lagrangian schemes . Mon. Weather Rev. , 120 : 113 – 123 .
  • Temperton , C. and Staniforth , A. 1987 . An efficient two-time-level semi-Lagrangian semi-implicit integration scheme . Q. J. R. Meteorol. Soc. , 113 : 1025 – 1039 .
  • Wiin-nielsen , A. 1959 . On the application of trajectory methods in numerical forecasting . Tellus , 11 : 180 – 196 .
  • Williamson , D. L. and Browning , G. L. 1974 . Formulation of the lateral boundary conditions for the NCAR limited area model . J. Appl. Meteorol. , 13 : 8 – 16 .
  • Yakimiw , E. and Robert , A. 1986 . Accuracy and stability analysis of a fully implicit scheme for the shallow-water equations . Mon. Weather Rev. , 114 : 240 – 244 .
  • Yakimiw , E. and Robert , A. 1990 . Validation experiments for a nested grid-point regional forecast model . ATMOSPHERE-OCEAN , 28 : 466 – 472 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.