Adcroft, A., Campin, J.-M., Hill, C., and Marshall, J.: Implementation of an
Atmosphere-Ocean General Circulation Model on the Expanded
Spherical Cube, Mon. Weather Rev., 132, 2845–2863,
https://doi.org/10.1175/mwr2823.1, 2004. a

Arakawa, A. and University of California, L. A. D. o. M.: Design of the UCLA
General Circulation Model, Numerical simulation of weather and climate:
Technical report, Department of Meteorology, University of California,
available at: https://books.google.com/books?id=nzEESwAACAAJ (last access: 15 November 2018), 1972. a

Coté, J.: A Lagrange multiplier approach for the metric terms of
semi-Lagrangian models on the sphere, Q. J. Roy.
Meteor. Soc., 114, 1347–1352, https://doi.org/10.1002/qj.49711448310, 1988. a, b

Du, Q., Gunzburger, M. D., and Ju, L.: Constrained Centroidal Voronoi
Tessellations for Surfaces, SIAM J. Sci. Comput., 24,
1488–1506, https://doi.org/10.1137/s1064827501391576, 2003. a

Hack, J. and Jakob, R.: Description of a Global Shallow Water Model Based on
the Spectral Transform Method, NCAR Technical Note NCAR/TN-343+STR, https://doi.org/10.5065/d64b2z73, 1992. a

Heikes, R. and Randall, D. A.: Numerical Integration of the Shallow-Water
Equations on a Twisted Icosahedral Grid. Part I: Basic Design and Results of
Tests, Mon. Weather Rev., 123, 1862–1880,
https://doi.org/10.1175/1520-0493(1995)123<1862:niotsw>2.0.co;2, 1995. a, b, c, d

Heikes, R. P., Randall, D. A., and Konor, C. S.: Optimized Icosahedral Grids:
Performance of Finite-Difference Operators and Multigrid Solver, Mon.
Weather Rev., 141, 4450–4469, https://doi.org/10.1175/mwr-d-12-00236.1, 2013. a, b

Läuter, M., Giraldo, F. X., Handorf, D., and Dethloff, K.: A discontinuous
Galerkin method for the shallow water equations in spherical triangular
coordinates, J. Comput. Phys., 227, 10226–10242,
https://doi.org/10.1016/j.jcp.2008.08.019, 2008. a

Lee, J.-L. and MacDonald, A. E.: A Finite-Volume Icosahedral Shallow-Water
Model on a Local Coordinate, Mon. Weather Rev., 137, 1422–1437,
https://doi.org/10.1175/2008mwr2639.1, 2009. a, b, c, d, e, f

Leer, B. V.: Towards the ultimate conservative difference scheme. IV. A new
approach to numerical convection, J. Comput. Phys., 23,
276–299, https://doi.org/10.1016/0021-9991(77)90095-x, 1977. a

Masuda, Y. and Ohnishi, H.: An Integration Scheme of the Primitive Equation
Model with an Icosahedral-Hexagonal Grid System and its Application to the
Shallow Water Equations, J. Meteorol. Soc. Japan. Ser.
II, 64A, 317–326, https://doi.org/10.2151/jmsj1965.64a.0_317, 1986. a

Miura, H. and Kimoto, M.: A Comparison of Grid Quality of Optimized Spherical
Hexagonal–Pentagonal Geodesic Grids, Mon. Weather Rev., 133,
2817–2833, https://doi.org/10.1175/mwr2991.1, 2005. a

Prather, M. J.: Numerical advection by conservation of second-order moments,
J. Geophys. Res., 91, 6671, https://doi.org/10.1029/jd091id06p06671, 1986. a

Putman, W. M. and Lin, S.-J.: Finite-volume transport on various cubed-sphere
grids, J. Comput. Phys., 227, 55–78,
https://doi.org/10.1016/j.jcp.2007.07.022, 2007. a, b

Qaddouri, A.: Nonlinear shallow-water equations on the Yin-Yang grid, Q.
J. Roy. Meteor. Soc., 137, 810–818,
https://doi.org/10.1002/qj.792, 2011. a

Ringler, T., Thuburn, J., Klemp, J., and Skamarock, W.: A unified approach to
energy conservation and potential vorticity dynamics for
arbitrarily-structured C-grids, J. Comput. Phys., 229,
3065–3090, https://doi.org/10.1016/j.jcp.2009.12.007, 2010. a, b, c, d, e, f

Russell, G. L.: Step-Mountain Technique Applied to an Atmospheric C-Grid Model,
or How to Improve Precipitation near Mountains, Mon. Weather Rev., 135,
4060–4076, https://doi.org/10.1175/2007mwr2048.1, 2007. a, b

Russell, G. L. and Lerner, J. A.: A New Finite-Differencing Scheme for the
Tracer Transport Equation, J. Appl. Meteorol., 20, 1483–1498,
https://doi.org/10.1175/1520-0450(1981)020<1483:anfdsf>2.0.co;2, 1981. a

Russell, G. L., Rind, D. H., and Jonas, J.:
Symmetric Equations on the Surface of a Sphere as Used by Model GISS:IB, Zenodo,
https://doi.org/10.5281/zenodo.1313736, 2018. a

Schmidt, G. A., Ruedy, R., Hansen, J. E., Aleinov, I., Bell, N., Bauer, M.,
Bauer, S., Cairns, B., Canuto, V., Cheng, Y., Genio, A. D., Faluvegi, G.,
Friend, A. D., Hall, T. M., Hu, Y., Kelley, M., Kiang, N. Y., Koch, D.,
Lacis, A. A., Lerner, J., Lo, K. K., Miller, R. L., Nazarenko, L., Oinas, V.,
Perlwitz, J., Perlwitz, J., Rind, D., Romanou, A., Russell, G. L., Sato, M.,
Shindell, D. T., Stone, P. H., Sun, S., Tausnev, N., Thresher, D., and Yao,
M.-S.: Present-Day Atmospheric Simulations Using GISS ModelE: Comparison
to In Situ, Satellite, and Reanalysis Data, J. Climate, 19, 153–192,
https://doi.org/10.1175/jcli3612.1, 2006. a, b

Stuhne, G. and Peltier, W.: New Icosahedral Grid-Point Discretizations of the
Shallow Water Equations on the Sphere, J. Comput. Phys., 148,
23–58, https://doi.org/10.1006/jcph.1998.6119, 1999. a, b, c, d, e

Sun, S. and Bleck, R.: Multi-century simulations with the coupled
GISS–HYCOM climate model: control experiments, Clim.
Dynam., 26, 407–428, https://doi.org/10.1007/s00382-005-0091-7, 2005. a

Swarztrauber, P. N.: The Vector Harmonic Transform Method for Solving Partial
Differential Equations in Spherical Geometry, Mon. Weather Rev., 121,
3415–3437, https://doi.org/10.1175/1520-0493(1993)121<3415:tvhtmf>2.0.co;2, 1993. a, b

Swarztrauber, P. N.: Spectral Transform Methods for Solving the Shallow-Water
Equations on the Sphere, Mon. Weather Rev., 124, 730–744,
https://doi.org/10.1175/1520-0493(1996)124<0730:stmfst>2.0.co;2, 1996.
a

Temperton, C.: On Scalar and Vector Transform Methods for Global Spectral
Models, Mon. Weather Rev., 119, 1303–1307,
https://doi.org/10.1175/1520-0493-119-5-1303.1, 1991. a

Weller, H., Thuburn, J., and Cotter, C. J.: Computational Modes and Grid
Imprinting on Five Quasi-Uniform Spherical C Grids, Mon. Weather Rev.,
140, 2734–2755, https://doi.org/10.1175/mwr-d-11-00193.1, 2012. a, b, c, d

Williamson, D. L., Drake, J. B., Hack, J. J., Jakob, R., and Swarztrauber,
P. N.: A standard test set for numerical approximations to the shallow water
equations in spherical geometry, J. Comput. Phys., 102,
211–224, https://doi.org/10.1016/s0021-9991(05)80016-6, 1992. a, b, c, d, e, f, g