We would like to gratefully acknowledge that this effort would not have been possible without the ideas and many years of guidance provided by Gerald L. Browning.
Black, T. L., Z. I. Janjić, and J. H. Ward, 1990: Heavy precipitation forecasts from NMC’s Eta Model. Preprints, 16th Conf. on Severe Local Storms and Conf. on Atmospheric Electricity, Kananaskis Park, AB, Canada, Amer. Meteor. Soc., J1–J4.
Browning, G. L., and H.-O. Kreiss, 1985: Numerical problems connected with weather prediction. Progress in Scientific Computing, E. M. Murman and S. S. Abarbanel, Eds. Vol. 6, Birkhauser, 377–394.
——, and ——, 1986: Scaling and computation of smooth atmospheric motions. Tellus,38A, 295–313.
——, and A. E. MacDonald, 1993: Incorporating topography into the multiscale systems for the atmosphere and oceans. Dyn. Atmos. Oceans,18, 119–149.
——, and H.-O. Kreiss, 1994a: The impact of rough forcing on systems with multiple time scales. J. Atmos. Sci.,51, 369–383.
——, and ——, 1994b: Splitting methods for problems of different timescales. Mon. Wea. Rev.,122, 2614–2622.
——, and ——, 1997: The role of gravity waves in slowly varying in time mesoscale motions. J. Atmos. Sci.,54, 1166–1184.
——, A. Kasahara, and H.-O. Kreiss, 1980: Initialization of the primitive equations by the bounded derivative method. J. Atmos. Sci.,37, 1424–1436.
——, J. J. Hack, and P. N. Swartztrauber, 1989: A comparison of three numerical methods for solving differential equations on a sphere. Mon. Wea. Rev.,117, 1058–1075.
Gill, A. E., 1982: Atmosphere–Ocean Dynamics. Academic Press, 662 pp.
Klemp, J. B., and D. K. Lilly, 1978: Numerical simulation of hydrostatic mountain waves. J. Atmos. Sci.,35, 78–107.
Kreiss, H.-O., 1970: Initial boundary value problems for hyperbolic equations. Comm. Pure Appl. Math.,33, 277–298.
——, 1980: Problems with different time scales for partial differential equations. Comm. Pure Appl. Math.,33, 399–440.
——, and J. Lorenz, 1989: Initial-Boundary Value Problems and the Navier–Stokes Equations. Academic Press, 402 pp.
Lee, J. L., and A. E. MacDonald, 2000: QNH: Mesoscale bounded derivative initialization and winter storm test over complex terrain. Mon. Wea. Rev.,128, 1037–1051.
Long, R. R., 1953: Some aspects of the flow of stratified fluids. I. A theoretical investigation. Tellus,5, 42–58.
MacDonald, A. E., J. L. Lee, and S. Sun, 2000: QNH: Design and test of a quasi-nonhydrostatic model for mesoscle weather prediction. Mon. Wea. Rev.,128, 1016–1036.
Oliger, J., and A. Sundstrom, 1978: Theoretical and practical aspects of some initial value problems in fluid dynamics. SIAM, J. Appl. Math.,35, 419–446.
Orlanski, I., 1975: A rational subdivision of scales for atmospheric processes. Bull. Amer. Meteor. Soc.,56, 527–530.
——, 1981: The quasi-hydrostatic approximation. J. Atmos. Sci.,38, 572–582.
Pielke, R. A., 1984: Mesoscale Meteorological Modeling. Academic Press, 612 pp.
Skamarock, W. C., and J. B. Klemp, 1994: Efficiency and accuracy of the Klemp–Wilhelmson time-splitting technique. Mon. Wea. Rev.,122, 2623–2630.
Smith, R. B., 1980: Linear theory of stratified hydrostatic flow past an isolated mountain. Tellus,32, 348–364.