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South African Journal of Science

On-line version ISSN 1996-7489
Print version ISSN 0038-2353

S. Afr. j. sci. vol.103 n.3-4 Pretoria Mar./Apr. 2007

 

RESEARCH ARTICLES

 

On the development of a new nonhydrostatic atmospheric model in South Africa

 

 

F.A. EngelbrechtI; J.L. McGregorII; C.J. deW. RautenbachI

IDepartment of Geography, Geoinformatics and Meteorology, University of Pretoria, Pretoria 0002, South Africa
IICSIRO Marine and Atmospheric Research, PB1 Aspendale, 3195, Victoria, Australia

 

 


ABSTRACT

With the advent of ever faster computers, the operational use of nonhydrostatic atmospheric models at resolutions beyond the hydrostatic limit has become a reality. A renewed global research effort is being made to formulate and improve nonhydrostatic models. In this paper, the status of numerical atmospheric modelling research in South Africa is briefly reviewed. We then report on the development of a new, nonhydrostatic atmospheric model at the University of Pretoria. The dynamic kernel of the model is based on a novel, split semi-Lagrangian formulation of a set of quasi-elastic equations in a terrain-following vertical coordinate based on the full pressure field. The main features of the model dynamics and numerics are discussed, and it is noted that the governing equation set presented here has not been applied in atmospheric modelling before. The model may be used to perform state-of-the-art research in numerical model development, for instance, for the derivation of new equation sets, numerical techniques and vertical coordinate systems. The model's ability to simulate highly nonlinear and nonhydrostatic flow is illustrated by means of a convective bubble experiment, where an updraft interacts with vertical shear of the horizontal wind. This experiment illustrates the potential of the new model to be used in the study of thunderstorm dynamics.


 

 

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REFERENCES

1. Holton J.R. (1992). An Introduction to Dynamic Meteorology, 3rd edn. Academic Press, San Diego.         [ Links ]

2. Ogura Y. and Charney J.C. (1962).A numerical model of thermal convection in the atmosphere. In Proc. Int. Symp. Numerical Weather Prediction, Tokyo, pp. 431-451. Meteorological Society of Japan, Tokyo.         [ Links ]

3. Dutton J.A. and Fichtl G.H. (1969). Approximate equations of motion for gases and liquids. J. Atmos. Sci. 26, 241-254.         [ Links ]

4. Miller M.J. and Pearce R.P. (1974). A three-dimensional primitive equation model of cumulonimbus convection. Q. J. R. Met. Soc. 100, 133-154.         [ Links ]

5. Tapp M.C. and White PW. (1976). A nonhydrostatic mesoscale model. Q. J. R. Met. Soc. 102, 277-296.         [ Links ]

6. Klemp J.B. and Wilhelmson R.B. (1978). Simulations of three-dimensional convective storm-dynamics. J. Atmos. Sci. 35, 1070-1096.         [ Links ]

7. Pielke R.A. (1984). Mesoscale Meteorological Modeling. Academic Press, San Diego.         [ Links ]

8. Bubnova R., Hello G., Benard P. and Geleyn J.F. (1995). Integration of the fully elastic equations cast in the hydrostatic pressure terrain-following coordinate in the framework of the ARPEGE/Aladin NWP system. Mon. Weath. Rev. 123, 515-535.         [ Links ]

9. Gallus W.A. Jr and Rancic M. (1996). A nonhydrostatic version of NMC's regional Eta model. Q. J. R. Met. Soc. 122, 495-513.         [ Links ]

10. Davies T., Cullen M.J.P., Malcolm A.J., Mawson M.H., Staniforth A.,White A.A. and Wood N. (2005). A new dynamical core for the Met Office's global and regional modelling of the atmosphere. Q. J. R. Met. Soc. 131, 1759-1782.         [ Links ]

11. Janjic Z.I., Gerrity J.P Jr. and Nickovic S. (2001). An alternative approach to nonhydrostatic modeling. Mon. Weath. Rev. 129, 1164-1178.         [ Links ]

12. Ohfuchi W., Sasaki H., Masumoto Y. and Nakamura H. (2005). Mesoscale resolving simulations of the global atmosphere and ocean on the Earth Simulator. EOS Trans. AGU 86, 45-46.         [ Links ]

13. Shen B-W., Atlas R., Chern J-D., Reale O., Lin S-J., Lee TandC hang J. (2006). The 0.125 degree finite-volume general circulation model on the NASA Columbia supercomputer: preliminary simulations of mesoscale vortices. Geophys. Res. Lett. 33, L05801, doi:10.1029/2005GL024594.         [ Links ]

14. Triegaardt D.O. (1965). The application of dynamic methods of weather prediction to the South African forecasting problem: a progress report. South African Weather Bureau News Letter, No. 201, 187-188.         [ Links ]

15. Triegaardt D.O. (1965). Experimental barotropic forecasting over subtropical regions. Notos 14, 3-15.         [ Links ]

16. Burger A.P. and Riphagen H.A. (1978). Analysis of energy-consistency of simple weather prediction models. CSIR Special Report, SWISK 1, Pretoria.         [ Links ]

17. Burger A.P. and Riphagen H.A. (1979). The lower boundary condition and energyconsistency in primitive and filtered models. J. Atmos. Sci. 36,1436-1449.         [ Links ]

18. Riphagen H.A. and Burger A.P. (1978). A non-integrated, adiabatic three-level filtered weather prediction model. CSIR Special Report, SWISK 7, Pretoria.         [ Links ]

19. RiphagenH.A. (1984). The implementation of asplit explicit weather prediction model for the Southern Hemisphere. M.Sc. dissertation, University of Pretoria, South Africa.         [ Links ]

20. Riphagen H.A. and Burger A.P. (1986). Comments on the computational stability of Gadd's adjustment and advection schemes for a split explicit model. Q. J. R. Met. Soc. 112, 276-282.         [ Links ]

21. Riphagen H.A. and Van Heerden J. (1986). Comparative trials of a semi-Lagrangian advection scheme in a numerical weather prediction model. In Proc. 12th South African Symposium on Numerical Mathematics, Umhlanga Rocks, pp. 139-153.         [ Links ]

22. Riphagen H.A. (1989). High latitude filtering for the global prediction model. In Proc. 6th Annual Conference of the South African Society for Atmospheric Sciences, Pretoria, p. 14.         [ Links ]

23. Riphagen H.A. (1999). The Eta model in South Africa. International Eta Model Newsletter, No. 2, February 1999.         [ Links ]

24. Riphagen H.A. (2000). Increased vertical resolution above elevated terrain in the Eta model through modification of the vertical coordinate. In Proc. 16th Conference of the South African Society for Atmospheric Sciences, Pretoria, p. P4.20.         [ Links ]

25. Riphagen H.A., Bruyere C.L., Jordaan W., Poolman E.R. and Gertenbach J.D. (2002). Experiments with the NCEP regional Eta model at the South African Weather Bureau, with emphasis on terrain presentation and its effect on precipitation predictions. Mon. Weath. Rev. 130, 1246-1263.         [ Links ]

26. Tennant W.J., Riphagen H.A., Gertenbach J.D., De Villiers M.P. and Rae K.J. (1997). The effect of radiosonde and buoy reduction on numerical prediction products at the South African Weather Bureau. In Proc. CGC/WMO Workshop on the Impact of Various Observing Systems on Numerical Weather Prediction, Geneva, ed. J. Pailleux, World Weather Watch Technical Report No. 18, WMO/TD No. 868, 165-183.         [ Links ]

27. Rautenbach C.J. deW. (1999). Introduction of a hybrid vertical co-ordinate to an atmospheric general circulation model. Ph.D. thesis, University of Pretoria, South Africa.         [ Links ]

28. Burger A.P. (1991). The potential vorticity equation: from planetary to small scale. Tellus 43A, 191-197.         [ Links ]

29. Burger A.P. and Riphagen H.A. (1990). The basic equations in meteorological dynamics - a reexamination of unsimplified forms for a general vertical coordinate. Beitr. Phys. Atmosph. 63, 151-164.         [ Links ]

30. Burger A.P. and Riphagen H.A. (1999). Energy conservation for a general vertical coordinate - a reexamination of unsimplified forms. Beitr. Phys. Atmosph. 72, 25-50.         [ Links ]

31. White A.A., Hoskins B.J., Roulstone I. and Staniforth A. (2005). Consistent approximate models of the global atmosphere: shallow, deep, hydrostatic, quasi-hydrostatic and non-hydrostatic. Q. J. R. Met. Soc. 131, 2081-2107.         [ Links ]

32. Eckart C. (1960). The Hydrodynamics of Oceans and Atmospheres. Pergamon Press, Oxford.         [ Links ]

33. White A.A. and Bromley R.A. (1995). Dynamically consistent, quasi-hydrostatic equations for global models with a complete representation of the Coriolis force. Q. J. R. Met. Soc. 121, 399-418.         [ Links ]

34. Dudhia J. and Bresch J.F. (2002). A global version of the PSU-NCAR mesoscale model. Mon. Weath. Rev. 130, 2989-3007.         [ Links ]

35. De Coning E. and Adam B.F. (2000). The tornadic thunderstorm events during the 1998-1999 South African summer. Water SA 26, 361-376.         [ Links ]

36. De Coning E., Adam B.F. and Banitz L. (2000). A severe weather event on 29 December 1997: synoptic and mesoscale perspectives. Water SA 26, 137-146.         [ Links ]

37. Landman W.A., Botes S., Goddard L. and Shongwe M.E. (2005). Assessing the predictability of extreme rainfall seasons over southern Africa. Geophys. Res. Lett. 32, L23818, doi: 10.1029/2005GL023965.         [ Links ]

38. Crimp S.J., Van den Heever S.C., D'Abreton P.C., Tyson P.D. and Mason S.J. (1997). Mesoscale modelling of tropical-temperate troughs and associated systems over southern Africa. WRC Report 595/1/97. Water Research Commission, Pretoria.         [ Links ]

39. Crimp S.J., Lutjeharms J.R.E. and Mason S.J. (1998). Sensitivity of a tropical-temperate trough to sea-surface temperature anomalies in the Agulhas retroflection region. Water SA 24, 93-100.         [ Links ]

40. Joubert A.M., Katzfey J.J., McGregor J.L. and Nguyen K.C. (1999). Simulating mid-summer climate over southern Africa using a nested regional climate model. J. Geophys. Res. 104, 19015-19025.         [ Links ]

41. Tadross M.A., Jack C. and Hewitson B.C. (2006). On RCM-based projections of change in southern African summer climate. Geophys. Res. Lett. 32, L23713, doi: 10.1029/2005GL024460.         [ Links ]

42. Hansingo K. and Reason C.J.C. (2006). Sensitivity of the atmospheric response        [ Links ]

to sea-surface temperature forcing in the South West lndian Ocean: a regional climate modelling study. S. Afr. J. Sci. 102, 137-143.         [ Links ]

43. Reason C.J.C. and Jagadheesha D. (2005). Relationships between South Atlantic SST variability and atmospheric circulation over the South African region during austral winter. J. Climate 18, 3059-3075.         [ Links ]

44. Singleton A.T. and Reason C.J.C. (2006). Numerical simulations of a severe rain-fall event over the Eastern Cape coast of South Africa: sensitivity to sea surface temperature and topography. Tellus 58A, 355-367.         [ Links ]

45. Van Heerden J., Rautenbach C.J. deW and Truter M.M. (1995). Techniques for seasonal and longer term rainfall prediction in South Africa. WRC Report 373/1/92. Water Research Commission, Pretoria.         [ Links ]

46. Jury M.R., Pathack B., Rautenbach C.J. deW. and Van Heerden J. (1996). Drought over South Africa and Indian Ocean SST: statistical and GCM results. Global Atmos. Ocean Syst 4, 47-63.         [ Links ]

47. Jury M.R., Mulenga H. and Rautenbach C.J. deW. (2000). Tropical Atlantic variability and Indo-Pacific ENSO: statistical analysis and numerical simulation. Global Atmos. Ocean Syst 7, 107-124.         [ Links ]

48. Rautenbach C.J. deW. (2003). Seasonal climate predictions with a coupled atmosphere-ocean general circulation model. WRC Report 904/1/03. Water Research Commission, Pretoria.         [ Links ]

49. Engelbrecht F.A., Rautenbach C.J. deW., McGregor J.L. and Katzfey J.J. (2002). January and July climate simulations over the SADC region using the limited-area model DARLAM. Water SA, 28, 361-374.         [ Links ]

50. Engelbrecht F.A. (2005). Simulations of climate and climate change over southern and tropical Africa with the conformal-cubic atmospheric model. In Climate Change and Water Resources in Southern Africa: Studies on scenarios, impacts, vulnerabilities and adaptation, ed. R.E. Schulze, chap. 4, pp. 57-74. WRC Report 1430/1/05. Water Research Commission, Pretoria.         [ Links ]

51. Rautenbach C.J. deW., Engelbrecht F.A., Engelbrecht C.J., Ndarana T. and McGregor J.L. (2005). Regional model development for simulating atmospheric behaviour and rainfall over southern Africa. WRC Report 1261/1/05. Water Research Commission, Pretoria.         [ Links ]

52. Engelbrecht F.A. (2006). Theory and application of quasi-elastic equations in terrain-following coordinates based on the full pressure field. Ph.D. thesis, University of Pretoria, South Africa.         [ Links ]

53. White A.A. (1989). An extended version of a nonhydrostatic, pressure coordinate model. Q. J. R. Met. Soc. 115, 1243-1251.         [ Links ]

54. Miller M.J. and White A.A. (1984). On the nonhydrostatic equations in pressure and sigma coordinates. Q. J. R. Met. Soc. 110, 515-533.         [ Links ]

55. Haltiner G.J. and Williams R.T. (1980). Numerical Prediction and Dynamic Meteorology, 2nd edn. Wiley, New York.         [ Links ]

56. Miller M.J. (1974). On the use of pressure as vertical coordinate in modelling convection. Q. J. R. Met. Soc. 100, 155-162.         [ Links ]

57. Laprise R. (1992). The Euler equations of motion with hydrostatic pressure as an independent variable. Mon. Weath. Rev. 122, 3-26.         [ Links ]

58. Juang H-M.H. (1992). A spectral fully compressible nonhydrostatic model in hydrostatic sigma coordinates: formulation and preliminary results. Meteorol. Atmos. Phys. 50, 75-88.         [ Links ]

59. Skamarock W.C., Klemp J.B., Dudhia J., Gill D.O., Barker D.M., Wang W. and Powers J.G. (2005). A description of the Advanced Research WRF Version 2. NCAR Technical Note, TN-468+STR.         [ Links ]

60. Mesinger F. and Arakawa A. (1976). Numerical Methods used in Atmospheric Models. Vol. 1. GARP Publications Series No. 17.         [ Links ]

61. McGregor J.L. (1993). Economical determination of departure points for semi-Lagrangian models. Mon. Weath. Rev. 121, 221-230.         [ Links ]

62. Shapiro R. (1975). Linear filtering. Math. Comp. 29, 1094-1097.         [ Links ]

63. Fischer G. (1965). On a finite difference scheme for solving the non-linear primitive equations for a barotropic fluid with application to the boundary current problem. Tellus 4, 405-412.         [ Links ]

64. Janjic Z.I. and Wiin-Nielsen A. (1977). On geostrophic adjustment and numerical procedures in a rotating fluid. J. Atmos. Sci. 34, 297-310.         [ Links ]

65. Straka J.M., Wilhelmson R.B., Wicker L.J., Anderson J.R. and Droegemeier K.K. (1993). Numerical solutions of a nonlinear density current: a benchmark solution and comparisons. Int. J. Num. Methods Fluids 17, 1-22.         [ Links ]

66. Wicker L.J. and Skamarock W.C. (2002). Time-splitting methods for elastic models using forward time schemes. Mon. Weath. Rev. 130, 2088-2097.         [ Links ]

67. Weisman M.L. and Klemp J.B. (1982). The dependence of numerically simulated convective storms on vertical wind shear and buoyancy. Mon. Weath. Rev. 110, 504-520.         [ Links ]

68. Thompson R.L., Edwards R., Hart J.A., Elmore K.L. and Markowski P. (2003). Close proximity soundings with supercell environments obtained from the Rapid Update Cycle. Weath. Forecasting 18, 1243-1261.         [ Links ]

69. Dupilka M.L. and Reuter G.W. (2006). Forecasting tornadic thunderstorm potential in Alberta using environmental sounding data. Part I: Wind shear and buoyancy. Weath. Forecasting 21, 325-335.         [ Links ]

70. Weisman M.L. and Klemp J.B. (1986). Characteristics of isolated storms. In Mesoscale Meteorology and Forecasting, ed. P.S. Ray, pp. 331-357. American Meteorological Society, Boston.         [ Links ]

71. Fujita T. and Grandoso H. (1968). Split of a thunderstorm into anticyclonic and cyclonic storms and their motion as determined from numerical model experiments. J. Atmos. Sci. 35, 1070-1096.         [ Links ]

72. Klemp J.B. (1987). Dynamics of tornadic thunderstorms. Annu. Rev. Fluid Mech. 19, 369-402.         [ Links ]

73. Rotunno R. (1981). On the evolution of thunderstorm rotation. Mon. Weath. Rev. 109, 171-180.         [ Links ]

74. Davies-Jones R.P. (1983). The onset of rotation in thunderstorms. In Preprints, 13th Conference of Severe Local Storms, Tulsa, Oklahoma, 215-218. American Meteorological Society, Boston.         [ Links ]

 

 

Received 11 August 2006
Accepted 25 January 2007.

 

 

We thank J.D. Gertenbach, H.A. Riphagen and C.J. Potgieter for insightful comments made during the course of the study. G.W. Reuter and M.J. Reeder helped to improve the paper. We also benefited from the comments of two reviewers. The research formed part of the Ph.D. studies of the first author, and contributed to a project on atmospheric model development sponsored by the Water Research Commission (WRC) in South Africa. The support and encouragement of G. Green from the WRC is gratefully acknowledged.
*
Author for correspondence. E-mail: francois.engelbrecht@up.ac.za

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