# Peter Hjort Lauritzen - The Dynamical Core

In the heart of every weather, climate, and earth system model lies the *dynamical core, * which is the model component approximating a solution to the adiabatic frictionless equations of motion for the atmosphere. The next generation *dynamical cores * are expected to be, among other things, highly scalable. Parallel efficiency is important for fast execution on modern high-performance computers and thereby allows for higher resolution needed to resolve smaller scale dynamics. Providing modelers with *dynamical cores *that are accurate and efficient ultimately contributes to improving predictions of weather, climate, and other atmospheric phenomena. My research interests lie in developing numerical methods for *dynamical cores * and for their coupling to other model components. Here I will focus on a feasible computational grid for next generation *dynamical cores *, called the *cubed sphere * grid, and how to couple it with other model components.

Traditionally, global models have been formulated on regular latitude-longitude grids (dashed lines on Figure). A serious disadvantage of this grid is its anisotropy, that is, grid boxes decrease rapidly in size when approaching the poles. This has serious consequences for the model numerics and scalability on parallel computers. Some numerical methods only allow information to propagate one grid cell per time step and hence the time-step restrictions are excessive near the poles compared to the equatorial region. This undesired increased resolution in some parts of the domain is sought eliminated by constructing different and more isotropic grids on the sphere such as the *cubed sphere * grid (solid lines on Figure), and of course, accompanied by numerical methods that work on these grids. The cubed sphere grid is constructed by the decomposition of the sphere into six identical regions (black solid lines on Figure), obtained by projecting the sides of an inscribed cube onto the sphere. The cubed sphere grid lines on each panel are great circle arcs.

Having the *dynamical core * defined on the *cubed sphere * grid and other model components, such as the physics package or the land-surface and ocean modules, defined on different grids requires the development of methods to map independent variables from one grid to the other. For models intended for long runs it is important that such remapping is conservative and when remapping noisy variables such as humidity the remapping method must be monotone (a monotone remapping method is one that does not introduce unphysical spurious extrema in the remapped field). I have, in collaboration with Ram Nair (Image/NCAR), developed a high-order, conservative, and monotone remapping package between the cubed sphere and regular latitude-longitude grid called HOMCRES (High-order Monotone and Conservative Remapping algorithm on the Sphere). It is based on the cascade interpolation method where the two-dimensional integral problem is split into two one-dimensional problems. This allows for using high-order reconstruction methods without excessive increase in computational cost as well as the option of applying sophisticated monotone filters. HOMCRES is currently being incorporated into NCAR's HOMME project. For more information see http://www.cgd.ucar.edu/cms/pel/ .

ASP Spotlight February 2007

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