References for the dynamical core

[milankl]

This is an issue to discuss the implementation of the spectral dynamical core. There is

• Bourke 1974, Monthly Weather Review. A primitive equation spectral dynamical core on the sphere. Uses streamfunction and velocity potential instead of vorticity and divergence as prognostic variables, but probably doesn't make a difference given they are only a Laplacian away = easy in spherical harmonics.
• GFDL idealised global spectral models, part I: Barotropic vorticity equation. Derives the barotropic vorticity equation in spherical harmonics, explains the n=l-m-spectral packing, illustrates the calculation of some gradients in spectral space, outlines the algorithm and provides a simple test case.
• GFDL idealised global spectral models, part II: Shallow water model extends the barotropic equations with a Bernoulli-potential like term for the prognostic divergence and introduces the prognostic pressure/geopotential layer thickness.
• GFDL idealised global spectral models, part III: full spectral model. Furthermore introduces the thermodynamics, vertical aspects and the implicit handling of terms in the time stepping.
• Randall. An Introduction to Numerical Modeling of the Atmosphere, p. 409f. More on the spherical transform and truncations. Little about spherical dynamical cores.

[milankl]

@guidov also adds

• Orszag 1970, more on the calculation of gradients in the spectral space of spherical harmonics
• Canuto 2007, more general book on spectral methods.

[milankl]

Also very useful is (though not free)

• Dale Durran, 2010. Numerical Methods for Fluid Dynamics, Springer. In particular, section 6.2, 6.4

[milankl]

Adding a reference on some initial conditions for a test case

• Jablonowski and Williamson, 2006

and the Held-Suarez forcing

• Held and Suarez, 1994

[milankl]

And also initial conditions for the shallow water equations

• Galewsky, Scott and Palvani, 2004

[milankl]

For the vertical advection and the semi implicit scheme

• Hoskins and Simmons, 1975 (semi-implicit in sigma coordinates)
• Simmons and Burridge, 1981 (the hybrid vertical coordinate paper)
• Simmons, 1978 (stability tests of the semi-implicit scheme in sigma coordinates)
• Corby et al, 1972 (vertical differencing of the adiabatic term in a grid-point model though)

[milankl]

Given that the documentation is now in a much more mature state I feel this can be closed as an issue