ICON mesh refinement

Currently, mesh refinement has been implemented and tested in the shallow-water version of ICON (ICOSWM). It follows the basic concepts of two-way nesting, which means that the time stepping starts with a large time step in the coarse (global) model domain, followed by interpolating the tendencies of the prognostic variables to the lateral boundaries of the nested domain. This is followed by conducting n time steps in the nested domain, where n is usually taken to be the same as the grid refinement ratio (2 in the case of ICON). The sequence is completed by a feedback of the prognostic variables (full fields or time increments) from the nested domain to the parent domain. Technically, the flow control is accomplished with the concept of recursive subroutine calls, which means that - in principle - an arbitrary number of refinement levels can be handled. The new feature of the mesh refinement in ICON is its realization on a triangular grid, which in some aspects is more challenging than on a regular quadrilateral grid. This is in particular true for the lateral boundary interpolation and the feedback, for which sufficiently accurate and numerically stable methods are more difficult to find than on a quadrilateral grid.

Generally spoken, the purpose of two-way mesh refinement is to allow for representing small-scale atmospheric features on a limited-area domain, having a horizontal resolution that is finer than what is computationally affordable on a global scale. Compared to the simpler one-way (off-line) nesting approach, in which stored and temporally interpolated data from a large-scale model provide the lateral boundary conditions for the nested model, two-way nesting allows for a dynamically more consistent treatment of atmospheric features with a short time scale (e.g. convection), and for a feedback from small scales to larger scales. The latter may be particularly important in the presence of steep topography with small horizontal scales, which cannot be appropriately resolved in a global-scale model.

Vorticity, day 7, global grid R2B5 (120km)

Vorticity, day 7, global grid R2B5 (120km) + regional R2B6 (60km)

Vorticity, day 7, global grid R2B6 (60km)

 

As an illustration, the figures show the vorticity field for a shallow-water test case with a circular mountain with small-scale corrugations, centred over the American Gulf coast (33N; 35W). The scale of the mountain is chosen such that it is reasonably well resolved at grid level 6 (average grid distance about 60 km) but not at grid level 5 (about 120 km). The figures show the result after 7 days of integration for (a) grid level 5 without mesh refinement, (b) grid level 5 with refinement to level 6 in the mountain area, and (c) grid level 6 globally. In all cases, the mountain triggers a downstream propagating Rossby wave with superimposed small-scale vorticity filaments, which mainly originate from the spin-up phase of the simulation. Comparing the results of the three experiments, one notices a fairly noisy vorticity field in case (a), which is originates from the forcing by the marginally resolved topography, whereas the high-resolution case (c) features a reasonably smooth vorticity field. The nested case (b) is in some sense intermediate, showing substantially less noise than case (a) but being still not as smooth as the high-resolution case (c). It is mentioned that the remaining noise could be removed by applying stronger filtering to the momentum field during the feedback process, which was kept at a relatively low level in the present experiment.

The next working step will be to extend the nesting capability to the hydrostatic model.

(gza, 27.10.2008)