Cubed-Sphere fvcore (Scientific Results)

The 2-dimensional shallow water equations have been implemented and thorough testing of the cubed-sphere results with the Williamson et al, 1992 standard test suite have shown the model to be performing beyond expectations. All results are comparable or better than those of the lat-lon core as reported in the Lin and Rood, 1996 and 1997 papers.

The cubed-sphere FV dycore has been run through a shallow water mass forcing experiment to generate a series of idealized barotropic vortices (representative of tropical cyclones.) The shallow water height field is relaxed to an idealized mass forcing where a mass source is located along the equator and a mass sink is placed along 12.5-N (2.5-degrees in width) and 170E to 160W. The solution is balanced such that the global mass is explicitly conserved and remains within machine precision, and the simulation continues stably beyond 200-days.

The two mass forcings are intended to represent typical lower tropospheric phenomenon. The mass source, along with the use of a scaled-down realistic topography as the surface of the shallow water fluid, generates a stationary subtropical flow similar in scale to that observed in the lower troposphere with westerlies along the equator and weak easterlies in the mid-latitudes. The mass sink acts as an inter-tropical convergence zone (ITCZ) generating a series of closed barotropic vortices which travel from their source at 12.5N and 170W north and westward across the Pacific Ocean basin in 10- to 15-days.

Forced Shallow Water Barotropic Vortices (+ View animation)

The full 3-dimensional baroclinic equations have been implemented and extensive testing through idealized test cases is nearing completion. The cubed-sphere finite-volume dynamical core has been run through the Jablonowski and Williamson baroclinic wave breaking experiment (Jablonowski, C. and D. L. Williamson, 2006). The baroclinic wave experiment is an idealized test which initializes the model with zonal flow in hydrostatic balance, and adds an initial perturbation to the wind field at all levels. In time, the perturbation organizes by day 4 and rapidly grows from day 6 onward. Explosive cyclogenesis occurs by day 7, and the baroclinic wave breaks by days 9 and 10. Results from this experiment are displayed showing the convergence of the solution at the breaking stage (day 10) with increasing resolution [The figures below display the surface pressure and 850 mb vorticity and temperature as the baroclinic wave breaks during the mature phase of the cyclone development at increasing horizontal resolution c44 (2-deg), c90 (1-deg) and c180 (0.5-deg).]

c-44 (2-degree)

 

c-90 (1-degree)

 

c180 (0.5-degree)

A conservative tracer transport module has been implemented to operate on the long time-step within the dynamics using accumulated mass fluxes and courant numbers. A simple tracer, constant in the vertical, has been tested within the idealized baroclinic wave test. The evolution of the vertically integrated tracer concentration (animation below) captures the impact of the zonal jet at 45N and the development of the baroclinic wave at lower levels of the atmosphere.

The cubed-sphere fvcore has also been run through the Held-Suarez idealized forcing test case. The c44 (2-degree) 32-level grid has been run for 1,200 simulated days on the Columbia SGI Altix supercomputer at NAS and the statistics have been computed over the final 1,000-days of the simulation. The total simulation time with 150 processors was 1 wall-clock hour. The zonal mean figures displayed below are in excellent agreement with the lat-lon core and those of the original Held-Suarez results. The zonal jet cores are located at about 250 mb and +/- 45-degrees latitude with a magnitude of 30 m/s. The tropopause is present at about 150 mb with a value of 190 K and a cold surface layer is also observed. The scale of the eddy transports of heat and momentum as well as the variance of the zonal wind and temperature are inline with results observed on the lat-lon grid. All results display an ideal symmetry about the equator. These results provide great confidence in the suitability of the cubed-sphere fvcore for real world climate/weather applications.

+ Computational Results

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