Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part I: numerical scheme

References

• Bates, J. R. and McDonald, A. 1982. Multiply upstream, semi-Lagrangian advective schemes: analysis and application to a multi-level primitive equation model. Mon. Wea. Re v. 110, 1831–1842.
   Google Scholar
• Bates, J. R., Moorthi, S. and Higgins, R. W. 1993. A global multilevel atmospheric model using a vector semi—Lagrangian finite—difference scheme. Part I: adiabatic formulation. Mon. Wea. Re v. 121, 244–263.
   Web of Science ®Google Scholar
• Benard, P., 2003. Stability of semi-implicit and iterative centered-implicit time discretization for various equation systems used in NVVP. Mon. Wea. Re v. 131, 2479–2491.
   Google Scholar
• Benard, R, 2004. On the use of a wider class of linear systems for the design of constant-coefficient semi-implicit time schemes in NVVP. Mon. Wea. Re v. 132, 1319–1324.
   Google Scholar
• Benoit, R., Desgagne, M., Pellerin, R, Chortler, Y. and Desjardins, S. 1997. The Canadian MC2: A Semi-Lagrangian, Semi-Implicit Wide-band Atmospheric Model Suited for Finescale Process Studies and Simulation. Mon. Wea. Re v. 125, 2382–2415.
   Web of Science ®Google Scholar
• Bubnova, R., Hello, G., Bernard, P. and Geleyn, J.-F. 1995. Integration of the fully elastic equations cast in the hydrostatic pressure terrain-following coordinate in the framework of APREGE/Aladin NWP system. Mon. Wea. Re v. 123, 515–535.
   Web of Science ®Google Scholar
• Côté, J. and Staniforth, A. 1988. A two-time-level semi-Lagrangian semi-implicit scheme for spectral models. Mon. Wea. Re v. 116, 2003–2012.
   Google Scholar
• Davies, H. C. 1976. A lateral boundary formulation for multilevel prediction models. Q. J. R. MeteoroL Soc. 102,405–418.
   Web of Science ®Google Scholar
• Girard, C., Benoit, R. and Desgagne, M. 2005. Finescale Topography and the MC2 Dynamics Kernel. Mon. Wea. Rev. 133, 1463-1477. Golding, B. W. 1992. An efficient non-hydrostatic forecast model. Meteorol. Atmos. Phys. 50, 89-103.
   Google Scholar
• Leslie, L. M. and Purser, R. J., 1991. High-order numerics in an unstaggered three-dimensional time-split semi-Lagrangian forecast model. Mon. Wea. Re v. 119, 1612–1623.
   Google Scholar
• Männik, A. 2003. Implementation and validation of the non-hydrostatic numerical weather prediction model HIRLAM. Dissertationes Geophysicales Tartu University Press. 86 p.
   Google Scholar
• Männik, A. and Room, R. 2001. Non-hydrostatic adiabatic kernel for HIRLAM. Part II. Anelastic, hybrid-coordinate, explicit-Eulerian model.HIRLAM Technical Report 49, 54 p. Available from http://hirlam.org/open/publications/TechReports/T’R49.pdf
   Google Scholar
• Männik, A., Room, R. and Luhamaa, A. 2003. Nonhydrostatic generalization of a pressure-coordinate-based hydrostatic model with implementation in HIRLAM: validation of adiabatic core. Tellus 55A, 219–231.
   Google Scholar
• McDonald, A. 1986. A semi-Lagrangian and semi-implicit two time level integration scheme. Mon. Wea. Re v. 114, 824–830.
   Google Scholar
• McDonald, A. 1995. The HIRLAM two time level, three dimensional semi-Lagrangian, semi-implicit, limited area, gridpoint model of the primitive equations. HIRLAIVI Technical Report 17, Norrkoping, 1995, 25 pp.
   Google Scholar
• McDonald, A. 1998. Alternative extrapolations to find the departure point in a ‘two time level’ semi-Lagrangian integration. HIRLAM Technical Report No 34. Publisher: HIRLAM 4 Project, do Met Eireann, Glasnevi Hill, Dublin 9, Ireland. 17 pp. Available from the HIRLAM member institutes.
   Google Scholar
• McDonald, A., 1999. An examination of alternative extrapolations to find the departure point position in a ‘two-time-level’ semi-Lagrangian integration. Mon. Wea. Re v. 127, 1985–1993.
   Google Scholar
• McDonald, A. and Bates, J. R. 1989. Semi-Lagrangian integration of a grid-point shallow-water model on the sphere. Mon. Wea. Re v. 117, 130–137.
   Google Scholar
• McDonald, A. and Haugen, J.-E. 1992. A two-time-level, three-dimensional, semi-Lagrangian, semi-implicit, limited-area gridpoint model of the primitive equations. Mon. Wea. Re v. 120, 2603–2621.
   Google Scholar
• McDonald, A. and Haugen, J.-E. 1993. A two-time-level, three-dimensional, semi-Lagrangian, semi-implicit, limited-area gridpoint model of the primitive equations. Part II: extension to hybrid vertical coordinates. Mon. Wea. Re v. 121, 2077–2087.
   Google Scholar
• Miller, M. J. 1974. On the use of pressure as vertical co-ordinate in modelling convection. Q. J. R. MeteoroL Soc. 100, 155–162.
   Web of Science ®Google Scholar
• Miller, M. J. and Pearce, R. P. 1974. A three-dimensional primitive equation model of cumulonimbus convection. Q. J. R. Meteorol. Soc. 100, 133–154.
   Web of Science ®Google Scholar
• Miller, M. J. and White, A. A. 1984. On the nonhydrostatic equations in pressure and sigma coordinates. Q. J. R. MeteoroL Soc. 110, 515–533.
   Web of Science ®Google Scholar
• Purser, R. J. and Leslie, L. M. 1988. A semi-implicit semi-Lagrangian finite-difference scheme using high-order spatial differencing on a nonstaggered grid. Mon. Wea. Re v. 116, 2069–2080.
   Google Scholar
• Ritchie, H. and Tanguay, M. 1996. A comparison of spatially averaged Eulerian and Semi-Lagrangian treatments of mountains. Mon. Wea. Re v. 124, 167–181.
   Google Scholar
• Ritchie, H., Temperton, C., Simmons, A., Hortal, M., Davies, T. and co-authors. 1995. Implementation of the Semi—Lagrangian method in a high—resolution version of the ECMWF forecast model.Mon. Wea. Rev. 123, 489-514.
   Google Scholar
• Robert, A. J. 1969. The integration of a spectral model of the atmosphere by the implicit method.Proc. WMO-IUGG Symposium on IVWP, Tokyo, Japan Meteorological Agency, VII, 19-24.
   Google Scholar
• Robert, A. 1981. A stable numerical integration scheme for the primitive meteorological equations. Atmos. Ocean 19, 35–46.
   Google Scholar
• Robert, A. 1982. A semi-Lagrangian and semi-implicit numerical integration scheme for the primitive meteorological equations. J. Meteor Soc. Japan 60, 319–325.
   Web of Science ®Google Scholar
• Robert, A., Henderson, J. and Thurnbull, C. 1972. An implicit time integration scheme for baroclinic models of the atmosphere. Mon. Wea. Re v. 100, 329–335.
   Google Scholar
• Robert, A., Yee, T. L. and H. Richie, H. 1985. A semi-Lagrangian and semi-implicit integration scheme for multi-level atmospheric models. Mon. Wea. Re v. 113, 388–394.
   Google Scholar
• Rõõm, R. 1990. General form of the equations of atmospheric dynamics in isobaric coordinates. Izvestiya, Atmospheric and Oceanic Physics 26, 9–14.
   Google Scholar
• Rõõm, R. 2001. Nonhydrostatic adiabatic kernel for HIRLAM. Part I: fundametals of nonhydrostatic dynamics in pressure-related co-ordinates.HIRLAIVI Technical Report 48, 26 p. Available fromhttp://hirlam.org/open/publications/TechReports/T’R48.pdf
   Google Scholar
• Rõõm, R. and Männilc, A. 1999. Response of different nonhydrostatic, pressure-coordinate models to orographic forcing. J. Atmos. Sc i. 56, 2553–2570.
   Google Scholar
• Rõõm, R. and Männilc, A. 2002. Nonhydrostatic adiabatic kernel for HIRLAM. Part BI: semi-implicit Eulerian scheme.HIRLAM Technical Report 55, 29 p. Available from http://hirlam.org/open/publications/TechReports/TR55.pdf
   Google Scholar
• Rõõm, R., Männilc, A. and Luhamaa, A. 2006. Nonhydrostatic adiabatic kernel for HIRLAM. Part IV: semi-implicit Semi-Lagrangian scheme.HIRLAIVI Technical Report 65,43 p. Available from http://hirlam.org/open/publications/TechReports/TR65.pdf
   Google Scholar
• Simmons, A. J. and Burridge, D. M. 1981. An energy and angular momentum conserving vertical finite difference scheme and hybrid vertical coordinates. Mon. Wea. Re v. 109, 758–766.
   Web of Science ®Google Scholar
• Tanguay, M., Simard, A. and Staniforth, A. 1989. A three-dimensional semi-Lagrangian scheme for the Canadian regional finite-element forecast model. Mon. Wea. Re v. 117, 1861–1871.
   Google Scholar
• Tanguay, M., Robert, A. and Laprise, R. 1990. A semi—implicit semi—Lagrangian fully compressible regional model. Mon. Wea. Re v. 118, 1970–1980.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Undén, P., Rontu, L., Järvinen, H., Lynch, P., Calvo, and co-authors. 2002. HIRLAM-5 Scientific Documentation, HIRLAM-5 Project, do Per Undén SMHI, S-60I 76 Norrkoping, SWEDEN, 144 p. Available from http://hirlam.org/open/publications/SciDoc_Dec2002.pdf
   Google Scholar
• White, A. A. 1989. An extended version of nonhydrostatic, pressure coordinate model. Q. J. R. MeteoroL Soc. 115, 1243–1251.
   Web of Science ®Google Scholar