References
Amezcua, J.; Kalnay, E. and Williams, P. D. (2011). The effects of the RAW filter on the climatology and forecast skill of the SPEEDY model. Monthly Weather Review 139, 608–619.
Asselin, R. (1972). Frequency filter for time integrations. Monthly Weather Review 100, 487–490.
Barnes, E. A. and Hartmann, D. L. (2011). Rossby wave scales, propagation, and the variability of eddy-driven jets. Journal of the Atmospheric Sciences 68, 2893–2908.
Betts, A. K. (1986). A new convective adjustment scheme. Part I: Observational and theoretical basis. Quarterly Journal of the Royal Meteorological Society 112, 677–691.
Betts, A. K. and Miller, M. J. (1986). A new convective adjustment scheme. Part II: Single column tests using GATE wave, BOMEX, ATEX and arctic air-mass data sets. Quarterly Journal of the Royal Meteorological Society 112, 693–709.
Bluestein, L. I. (1970). A linear filtering approach to the computation of discrete Fourier transform. IEEE Transactions on Audio and Electroacoustics 18, 451–455.
Bourke, W. (1972). An efficient, one-level, primitive-equation spectral model. Monthly Weather Review 100, 683–689.
Cooley, J. W. and Tukey, J. W. (1965). An algorithm for the machine calculation of complex Fourier series. Mathematics of Computation 19, 297–301.
Daley, R. and Bourassa, Y. (1978). Rhomboidal versus triangular spherical harmonic truncation: Some verification statistics. Atmosphere-Ocean 16, 187–196.
Durran, D. R. (2010). Numerical methods for fluid dynamics: With applications to geophysics (Springer).
Frierson, D. M. (2007). The dynamics of idealized convection schemes and their effect on the zonally averaged tropical circulation. Journal of the Atmospheric Sciences 64, 1959–1976.
Frierson, D. M.; Held, I. M. and Zurita-Gotor, P. (2006). A gray-radiation aquaplanet moist GCM. Part I: Static stability and eddy scale. Journal of the Atmospheric Sciences 63, 2548–2566.
Frigo, M. and Johnson, S. G. (2005). The design and implementation of FFTW3. Proceedings of the IEEE 93, 216–231.
Galewsky, J.; Scott, R. K. and Polvani, L. M. (2004). An initial-value problem for testing numerical models of the global shallow-water equations. Tellus A 56, 429–440.
Górski, K. M.; Hivon, E.; Banday, A. J.; Wandelt, B. D.; Hansen, F. K.; Reinecke, M. and Bartelmann, M. (2005). HEALPix: A framework for high-resolution discretization and fast analysis of data distributed on the sphere. The Astrophysical Journal 622, 759–771.
Held, I. M. and Suarez, M. J. (1994). A proposal for the intercomparison of the dynamical cores of atmospheric general circulation models. Bulletin of the American Meteorological Society 75, 1825–1830.
Hoskins, B. J. and Simmons, A. J. (1975). A multi-layer spectral model and the semi-implicit method. Quarterly Journal of the Royal Meteorological Society 101, 637–655.
Hotta, D.; Kalnay, E. and Ullrich, P. A. (2016). A semi-implicit modification to the Lorenz N-cycle scheme and its application for integration of meteorological equations. Monthly Weather Review 144, 2215–2233.
Hotta, D. and Ujiie, M. (2018). A nestable, multigrid-friendly grid on a sphere for global spectral models based on Clenshaw–Curtis quadrature. Quarterly Journal of the Royal Meteorological Society.
Jablonowski, C. and Williamson, D. L. (2006). A baroclinic instability test case for atmospheric model dynamical cores. Quarterly Journal of the Royal Meteorological Society 132, 2943–2975.
Jeevanjee, N. and Zhou, L. (2022). On the resolution-dependence of anvil cloud fraction and precipitation efficiency in radiative-convective equilibrium. Journal of Advances in Modeling Earth Systems 14, e2021MS002759.
Kucharski, F.; Molteni, F. and Bracco, A. (2006). SPEEDY: A simplified atmospheric general circulation model. Appendix A: Model equations and parameters.
Malardel, S.; Wedi, N.; Deconinck, W.; Diamantakis, M.; Kühnlein, C.; Mozdzynski, G. and Hamrud, M. (2016). A new grid for the IFS. ECMWF Newsletter, 23–28.
Orszag, S. A. (1970). Transform method for the calculation of vector-coupled sums: Application to the spectral form of the vorticity equation. Journal of the Atmospheric Sciences 27, 890–895.
Pauluis, O. and Garner, S. T. (2006). Sensitivity of radiative-convective equilibrium simulations to the absorptivity of water vapor. Journal of the Atmospheric Sciences 63, 1912–1926.
Randall, D. A. (2021). An introduction to numerical modeling of the atmosphere (Colorado State University).
Robert, A. (1966). The integration of a low order spectral form of the primitive meteorological equations. Journal of the Meteorological Society of Japan. Ser. II 44, 237–245.
Seeley, J. T. and Wordsworth, R. D. (2023). Moist convection is most vigorous at intermediate atmospheric humidity. The Planetary Science Journal 4, 34.
Simmons, A. J. and Burridge, D. M. (1981). An energy and angular-momentum conserving vertical finite-difference scheme and hybrid vertical coordinates. Monthly Weather Review 109, 758–766.
Vallis, G. K. (2006). Atmospheric and oceanic fluid dynamics: Fundamentals and large-scale circulation (Cambridge University Press).
Vallis, G. K.; Gerber, E. P.; Kushner, P. J. and Cash, B. A. (2004). A mechanism and simple dynamical model of the North Atlantic Oscillation and annular modes. Journal of the Atmospheric Sciences 61, 264–280.
Viterbo, P. and Beljaars, A. C. (1995). An improved land surface parameterization scheme in the ECMWF model and its validation. Journal of Climate 8, 2716–2748.
Williams, P. D. (2009). A proposed modification to the Robert–Asselin time filter. Monthly Weather Review 137, 2538–2546.
Williams, P. D. (2011). The RAW filter: An improvement to the Robert–Asselin filter in semi-implicit integrations. Monthly Weather Review 139, 1996–2007.
Williamson, D. L.; Drake, J. B.; Hack, J. J.; Jakob, R. and Swarztrauber, P. N. (1992). A standard test set for numerical approximations to the shallow water equations in spherical geometry. Journal of Computational Physics 102, 211–224.
Willmert, J. (2020). Notes on calculating the spherical harmonics.
ECMWF (2024). IFS documentation CY49R1 – Part IV: Physical processes.
NOAA Geophysical Fluid Dynamics Laboratory (2013). Idealized models with spectral dynamics. Accessed on Aug 31, 2026.
NOAA Geophysical Fluid Dynamics Laboratory (2013). The barotropic vorticity equation. Accessed on Aug 31, 2026.
NOAA Geophysical Fluid Dynamics Laboratory (2013). The shallow water equations. Accessed on Aug 31, 2026.
NOAA Geophysical Fluid Dynamics Laboratory (2013). The spectral dynamical core. Accessed on Aug 31, 2026.