Abstract
In Chapters 20–23, numerical schemes of hydrostatic primitive equations using the spectral method have been described. As introduced in Chapter 20, however, the recent progress in computer resources has enabled us to drastically increase the horizontal resolution of global models, say, less than 10 km. For these highresolution simulations, we need to switch the governing equations from hydrostatic equations to nonhydrostatic equations. In the following three chapters (Chapters 24–26), numerical schemes of global nonhydrostatic models are described.
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References and suggested reading
Arakawa, A. and Lamb, V.R., 1977: Computational design of the basic dynamical processes of the UCLA general circulation model. Methods in Computational Physics, 17, 173–265.
Arakawa, A. and Suarez, M. J., 1983: Vertical differencing of the primitive equations in sigma coordinates. Mon. Wea. Rev., 111, 34–45.
Doms, G. and Schättler, U., 1997: The nonhydrostatic limited-area model LM (Lokal-Modell) of DWD. Part I: Scientific Documentation. Deutscher Wetterdienst, 174 pp.
Durran, D.R., 2010: Numerical Methods for Fluid Dynamics with Applications to Geophysics, 2nd ed. Springer, New York, 516 pp.
Durran, D.R. and Klemp, J., 1983: A compressible model for the simulation of moist mountain waves. Mon. Wea. Rev., 111, 2341–2361.
Gallus, W. Jr. and Ranˇci´c, M., 1996: A non-hydrostatic version of the NMC’s regional Eta model. Q. J. R. Meteorol. Soc., 122, 495–513.
Held, I.M., Hemler, R. S., and Ramaswamy, V., 1993: Radiative-convective equilibrium with explicit two-dimensional moist convection. J. Atmos. Sci., 50, 3909–3927.
Juang, H.-M.H., 1992: A spectral fully compressible nonhydrostatic mesoscale model in hydrostatic sigma coordinates: Formulation and preliminary results. Meteorol. Atmos. Phys., 50, 75–88.
Klemp, J. B. and Wilhelmson, R.B., 1978: The simulation of three-dimensional convective storm dynamics. J. Atmos. Sci., 35, 1070–1096.
Klemp, J.B., Skamarock, W. C., and Dudhia, J., 2007: Conservative split-explicit time integrationmethods for the compressible nonhydrostatic equations. Mon. Wea. Rev., 135, 2897–2913.
Laprise, R., 1992: The Euler equations of motion with hydrostatic pressure as independent variable. Mon. Wea. Rev., 120, 197–207.
Ogura, Y. and Phillips, A., 1962: Scale analysis of deep and shallow convection in the atmosphere. J. Atmos. Sci., 19, 173–179.
Ooyama, K.V., 1990: A thermodynamic foundation for modeling the moist atmosphere. J. Atmos. Sci., 47, 2580–2593.
Saito, K, Ishida, J., Aranami, K., Hara, T., Segawa, T., Narita, M., and Honda, Y., 2007: Nonhydrostatic atmospheric models and operational development at JMA. J. Meteor. Soc. Japan, 85B, 271–304.
Satoh, M., 2002: Conservative scheme for the compressible non-hydrostatic models with the horizontally explicit and vertically implicit time integration scheme. Mon. Wea. Rev., 130, 1227–1245.
Satoh, M., 2003: Conservative scheme for a compressible nonhydrostatic model with moist processes. Mon. Wea. Rev., 131, 1033–1050.
Skamarock, W. C. and Klemp, J.B., 1992: The stability of time-split numerical methods for the hydrostatic and the nonhydrostatic elastic equations. Mon. Wea. Rev., 120, 2109–2127.
Skamarock, W. C. and Klemp, J.B., 1994: Efficiency and accuracy of the Klemp- Wilhelmson time-splitting technique. Mon. Wea. Rev., 122, 2623–2630.
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.
Taylor, K.E., 1984: A vertical finite-difference scheme for hydrostatic and nonhydrostatic equations. Mon. Wea. Rev., 112, 1398–1402.
Tompkins, A.M. and Craig, G. C., 1998a: Time-scales of adjustment to radiativeconvective equilibrium in the troposphere. Q. J. Roy. Meteorol. Soc., 124, 2693–2713.
Tompkins, A. M. and Craig, G.C., 1998b: Radiative-convective equilibrium in a three-dimensional cloud ensemble model. Q. J. Roy. Meteorol. Soc., 124, 2073–2097.
Tompkins, A.M. and Craig, G. C., 1999: Sensitivity of tropical convection to sea surface temperature in the absence of large-scale flow. J. Clim., 12, 462–476.
Xue, M., Droegemeier, K.K., and Wong, V., 2000: The Advanced Regional Prediction System (ARPS) - A multi-scale nonhydrostatic atmospheric simulation and prediction model. Part I: Model dynamics and verification. Meteor.
Atmos. Physics, 75, 161–193.
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Satoh, M. (2014). Nonhydrostatic modeling. In: Atmospheric Circulation Dynamics and General Circulation Models. Springer Praxis Books(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13574-3_24
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DOI: https://doi.org/10.1007/978-3-642-13574-3_24
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