cubed sphere in ROMS?

[rgoldman]

Hi,
I am fairly new to ROMS. I would like to run a few test cases on a barotropic ocean world (flat bottom, no land, homogeneous density). I have seen that mitGCM can be run on a cubed sphere grid and wondered if such a configuration was possible in ROMS and if anyone had tried it before.
Thank you in advance,
Ron Goldman

[kate]

I have not seen that coded up, though an adventurous sort could do so.

[shchepet]

I understand the feeling of excitement when one is about to embark on a new
adventure, but actually, while cubed-sphere was famously used for many years
in ECCO model (this is MITgcm global configuration), the most recent version,
ECCO v.4, has abandoned this approach in favor of conformal mapping design.

See Section 2 in a recent article for the discussion of pros and cons:

Forget, G., J.-M. Campin, P. Heimbach, C. N. Hill, R. M. Ponte, and C. Wunsch,
ECCO version 4: An integrated framework for non-linear inverse modeling
and global ocean state estimation. Geosci. Model Dev., 8, 3071–3104, 2015
http://www.geosci-model-dev.net/8/3071/2015/
doi:10.5194/gmd-8-3071-2015

So you may be asking to pursue a wrong target, because people who are known
to get the most use of cubed-sphere say no more.

Cubed-sphere is not an othtogonal coordinate system, so a modeling code must
have extra terms, which ROMS lacks.

[rgoldman]

Thank you for the answers and reference.
I see that the lon-lat-cap in ECCO has two "singularities" near the southern pole so I guess it is not optimal for waterworld problems.
Both lon-lat-cap and cubic sphere grids are similar at the north pole where three planes connect at each "corner" vertex. Can the existing nesting mechanism in ROMS handle such corners?

[shchepet]

Can the existing nesting mechanism in ROMS handle such corners?

No, because coordinates become strongly non-orthogonal there, so equation require
extra terms which ROMS lacks. ROMS generally follows Arakawa and Lamb, 1977 orthogonal
curvilinear coordinate framework and the associated discretizations keeping all the metric
terms in the momentum equations and packing them together with Coriolis terms. Note other
models, POM is a notable example, may drop the momentum curvilinear metric terms completely,
so velocities U and V are advected as they would be two independent scalars rather components
of a vector. The easiest way to understand why these terms are needed and what exactly they
do: imagine that coordinate line "xi" turns to the right, while water moves straight. Then,
as seen from the moving fluid parcel going straight, the coordinate system underneath tends
to turn to the right, so U-component in part becomes -V and V-component in part becomes U.
This leads to appearance of funny looking terms in the momentum equations.

MITgcm (at least ECCO version of it) apparently use so-called vector-invariant form of
momentum equations. The advection, pressure-gradient, and Coriolis terms are packaged
together and expressed in terms of Bernouli potential and absolute vorticity. This
leads to avoidance of the need for curvilinear metric terms. This helps, but still some
extra work is required.