# Welcome to the DYNAMICO website

The DYNAMICO project develops a new dynamical core for LMD-Z, the atmospheric general circulation model (GCM) part of IPSL-CM Earth System Model.

LMDZ4, the current version of LMD-Z, has a shallow-atmosphere, hydrostatic dynamical core. It is based on a latitude-longitude C-grid, a hybrid pressure-based terrain-following vertical coordinate, second-order enstrophy-conserving finite-difference discretization and positive-definite advection. Grid refinement is implemented as a continuous zoom via smooth grid stretching. An extensive package of physical paramererizations is coupled to the dynamical core. IPSL-CM is currently used to produce AR5 simulations. LMD-Z is also at the heart of GCMs of planetary atmospheres (Mars, Venus and Titan).

It is well-known that the latitude-longitude coordinates have a strong singularity at the poles which is undesirable in terms of both numerical stability and computational efficiency. Regular tesselations of the sphere such as a recursively subdivided icosahedron provide an almost-uniform grid and a path to highly parallel computations based on domain decomposition. LMD's logo is itself an icosahedron, evoking the pioneering work of Robert Sadourny on the use of icosahedral grids for solving the equations of atmospheric motion.

The primary goal of DYNAMICO is to re-formulate in LMD-Z the horizontal advection and dynamics on a icosahedral grid, while preserving or improving their qualities with respect to accuracy, conservation laws and wave dispersion. In turn, a new grid refinement strategy is required. A broader goal is to revisit all fundamental features of the dynamical core, especially the shallow-atmosphere/traditional approximation, the vertical coordinate and the coupling with physics. Efficient implementation on present and future supercomputing architectures is also a key issue addressed by DYNAMICO.

DYNAMICO is currently able to solve the hydrostatic primitive equations and participated to the DCMIP workshop held in August 2012 at NCAR. In the near future we will investigate its extension to deep-atmosphere and possibly non-hydrostatic equations following a variational approach that naturally conserves mass, energy and, in a somewhat restricted sense, potential vorticity. If you are not afraid of work-in-progress, you can browse our source code.

DYNAMICO is funded by the **Indo-French Centre for the Promotion of Advanced Research**, by **IPSL** and by the G8 Research Councils Initiative on Multilateral Research Funding, project **ICOMEX**.

## Get started

For a complete list of local wiki pages, see TitleIndex.

## Presentations

- An energy-conserving quasi-hydrostatic deep-atmosphere dynamical core PDEs on the Sphere workshop, NCAR, Boulder, Colorado, April 2014
- Conserving energy : from the continuuum to the discrete level Laboratoire Jean Kuntzmann, Grenoble, December 2013
- Modelling atmospheres : some barriers, and a few keys ORAP Forum, Saclay, October 2013
- Variational derivation of energy-conserving schemes for geophysical fluid equations. PDEs on the Sphere, Isaac Newton Institute, Cambridge, sept. 2012

## Publications

- T. Dubos and M. Tort (accepted)
*Equations of atmospheric motion in non-Eulerian vertical coordinates : vector-invariant form and Hamiltonian formulation*Mon. Wea. Rev.

- M. Tort, T. Dubos, V. Zeitlin and F. Bouchut (accepted)
*Consistent shallow-water equations on the rotating sphere with complete Coriolis force and topography*J. Fluid Mech.

- M. Tort and T. Dubos (accepted)
*Usual approximations to the equations of atmospheric motion : a variational perspective*J. Atmos. Sci. PDF

- M. Tort and T. Dubos (2014)
*Dynamically consistent shallow-atmosphere equations with a complete Coriolis force*Quart. J. Roy. Met. Soc. PDF

## Related publications

- M. Aechtner, N. Kevlahan, T. Dubos (accepted)
*A conservative adaptive wavelet method for the shallow water equations on the sphere.*Quart. J. Roy. Met. Soc.

- T. Dubos and F. Voitus (accepted)
*A semi-hydrostatic theory of gravity-dominated compressible flow*J. Atmos. Sci.

- J. Thuburn, C.J. Cotter, T. Dubos (accepted)
*A mimetic, semi-implicit, forward-in-time, finite volume shallow water model : comparison of hexagonal-icosahedral and cubed sphere grids*Geophys. Mod. Dev. - T. Dubos and N. Kevlahan, (2013)
*An adaptive wavelet method for the shallow-water equations on a staggered grid conserving mass and vorticity.*Quart. J. Roy. Met. Soc., 139: 1997-2020 PDF