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Yuhe Song and Tao Tang

Abstract

The Turkel-Zwas-type schemes employ coarse grids to discretize the terms associated with the fast gravity-inertia waves and use fine grids to treat the terms associated with the slow Rossby waves. The ratio of the coarse and fine grids is an integer, p>1, and one can use time steps nearly p times larger than those allowed by the Courant-Friedrich-Lewy condition for the usual explicit leapfrog scheme. This paper investigates the Turkel-Zwas-type schemes with three spatial grids-namely, A (unstaggered), B, and C grids (staggered)-for two-dimensional shallow-water equations. A new method that uses the Laplace transform is introduced to solve the two-dimensional phase solutions. Comparisons of the three grids with coarse and fine-grid resolutions are made. One realistic model problem is tested to verify the linear analysis results. The test shows that the Turkel-Zwas-type schemes can be used for a larger time step in some practical simulations.

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Victor Zlotnicki, John Wahr, Ichiro Fukumori, and Yuhe T. Song

Abstract

Gravity Recovery and Climate Experiment (GRACE) gravity data spanning January 2003–November 2005 are used as proxies for ocean bottom pressure (BP) averaged over 1 month, spherical Gaussian caps 500 km in radius, and along paths bracketing the Antarctic Circumpolar Current’s various fronts. The GRACE BP signals are compared with those derived from the Estimating the Circulation and Climate of the Ocean (ECCO) ocean modeling–assimilation system, and to a non-Boussinesq version of the Regional Ocean Model System (ROMS). The discrepancy found between GRACE and the models is 1.7 cmH2O (1 cmH2O ∼ 1 hPa), slightly lower than the 1.9 cmH2O estimated by the authors independently from propagation of GRACE errors. The northern signals are weak and uncorrelated among basins. The southern signals are strong, with a common seasonality. The seasonal cycle GRACE data observed in the Pacific and Indian Ocean sectors of the ACC are consistent, with annual and semiannual amplitudes of 3.6 and 0.6 cmH2O (1.1 and 0.6 cmH2O with ECCO), the average over the full southern path peaks (stronger ACC) in the southern winter, on days of year 197 and 97 for the annual and semiannual components, respectively; the Atlantic Ocean annual peak is 20 days earlier. An approximate conversion factor of 3.1 Sv (Sv ≡ 106 m3 s−1) of barotropic transport variability per cmH2O of BP change is estimated. Wind stress data time series from the Quick Scatterometer (QuikSCAT), averaged monthly, zonally, and over the latitude band 40°–65°S, are also constructed and subsampled at the same months as with the GRACE data. The annual and semiannual harmonics of the wind stress peak on days 198 and 82, respectively. A decreasing trend over the 3 yr is observed in the three data types.

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