On the convergence and error problems of the calculation of the pressure gradient force in sigma coordinate models

References

• Arakawa , A. 1972 . “ Design of the UCLA general circulation model ” . In Tech. Rept. No. 7 , 116 Los Angeles : Dept. of Meteorology, Univ. of California .
   Google Scholar
• Arakawa , A. and Lamb , V. R. 1977 . “ Computational design of the basic dynamical processes of the UCLA general circulation model ” . In Methods in Computational Physics. General Circulation Models of the Atmosphere , Edited by: Chang , J. Vol. 17 , 173 – 265 . Academic Press .
   Google Scholar
• Burridge , D. M. and Haseler , J. 1977 . “ A model for medium range weather forecasting; adiabatic formulation ” . 46 Reading, , U.K. : European Centre for Medium Range Weather Forecasts . Tech. Rept. No. 4
   Google Scholar
• Corby , G. A. , Gilchrist , A. and Newson , R. L. 1972 . A general circulation model of the atmosphere suitable for long period integrations . Quart. J. Roy. Meteor. Soc. , 98 : 809 – 832 .
   Web of Science ®Google Scholar
• Corby , G. A. , Gilchrist , A. and Rowntree , P. R. 1977 . “ United Kingdom Meterological Office five-level general circulation model ” . In Methods in Computational Physics. General Circulation Models of the Atmosphere , Edited by: Chang , J. Vol. 17 , 67 – 110 . Academic Press .
   Google Scholar
• Gilchrist , A. 1975 . “ The Meterological Office general circulation model ” . In Seminars on Scientific Foundations of Medium Range Weather Forecasts , 594 – 661 . Reading, , U.K. : European Centre for Medium Range Weather Forecasts .
   Google Scholar
• Janjić , Z. I. 1977 . Pressure gradient force and advection scheme used for forecasting with steep and small scale topography . Contrib. Atmos. Phys. , 50 : 186 – 199 .
   Google Scholar
• Janjić , Z. I. 1979 . “ Numerical problems related to steep mountains in sigma coordinates ” . In Workshop on Mountains and Numerical Weather Prediction , 48 – 88 . Reading, , U.K. : European Centre for Medium Weather Forecasts .
   Google Scholar
• Kasahara , A. 1980 . “ Influence of orography on the atmospheric general circulation ” . In GARP Publications Series, No. 23 , 1 – 49 . Geneva : World Meterological Organization .
   Google Scholar
• Mesinger , F. 1979 . “ Methods and problems of finite difference representation of mountains in numerical weather analysis and prediction ” . In Workshop on Mountains and Numerical Weather Prediction , 28 – 47 . Reading, , U.K. : European Centre for Medium Range Weather Forecasts .
   Google Scholar
• Nakamura , H. 1978 . Dynamical effects of mountains on the general circulation of the atmosphere: I. Development of finite-difference schemes suitable for incorporating mountains . J. Meteor. Soc. Japan , 56 : 317 – 340 .
   Google Scholar
• Phillips , N. A. 1974 . “ Application of Arakawa's energy conserving layer model to operational numerical weather prediction ” . 40 National Meteorological Center, NOAA/NWS, U.S. Dept. of Commerce . Office Note No. 104
   Google Scholar
• Rousseau , D. and Pham , H. L. 1971 . Premiers résultats d'un modèle deprévision numérique à courte échéance sur l'Europe . La Météorologie , 20 : 1 – 12 .
   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. Rev. , 109 : 758 – 766 .
   Web of Science ®Google Scholar
• Smagorinsky , J. , Strickler , R. F. , Sangster , W. E. , Manabe , S. , Holloway , J. L. Jr. and Hembree , G. D. Prediction experiments with a general circulation model . Proc. Intern. Symp. on Dynamics of Large Scale Atmospheric Processes . June 23–30 1965 , Moscow. pp. 70 – 134 . Moscow : Izdatel'stvo Nauka .
   Google Scholar
• Stackpole , J. D. , Vanderman , L. W. and Sela , J. G. 1980 . “ U.S.A. National Meteorological Center (NMC) numerical prediction models ” . In Catalogue of Numerical Atmospheric Models for the First GARP Global Experiment , 216 – 274 . Geneva : World Meteorological Organization .
   Google Scholar
• Sundqvist , H. 1975 . On truncation errors in sigma-system models . Atmosphere , 13 : 81 – 95 .
   Google Scholar
• Sundqvist , H. 1979 . “ Vertical coordinates and related discretization ” . In GARP Publications Series, No. 17 , Vol. II , 1 – 50 . Geneva : World Meteorological Organization .
   Google Scholar
• Tibaldi , S. 1979 . Lee cyclogenesis and its numerical simulation with special attention to the Alpine region: a review . Geoph. Astroph. Fluid Dyn. , 13 : 25 – 49 .
   Google Scholar
• Tokioka , T. 1978 . Some considerations on vertical differencing . J. Meteor. Soc. Japan , 56 : 98 – 111 .
   Google Scholar