The Temporal Aliasing Formulas for the Tandem Mission of Jason-1 and TOPEX/Poseidon

Chang-Kou Tai NOAA/NESDIS, Camp Springs, Maryland

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Abstract

The temporal aliasing formulas are derived for the Tandem Mission of Jason-1 and the Ocean Topography Experiment (TOPEX)/Poseidon. Previously, aliasing formulas were derived for a single satellite or a constellation of coordinated satellites, wherein the coordination is such that the collective samplings appear as if they were carried out by a single satellite. In this vein, Jason-1 and TOPEX/Poseidon are coordinated spatially but not temporally. The problem is treated as a general problem about the temporal phasing between any two satellites that are coordinated spatially so that the Tandem Mission is just one special case, whereas the temporally coordinated case is another special case. The present results do agree with the formulas for a constellation of coordinated satellites when the temporal phasing yields temporal coordination, as they should. The benefit of temporal coordination shows itself as having a higher spatial resolution for temporally aliased features. The physical implication is twofold. First, a high-frequency and low-wavenumber feature (e.g., the barotropic Rossby waves) has a better chance of being aliased as a low-frequency and higher-wavenumber feature in a perfectly coordinated mission than it has in the Tandem Mission. Second, in a perfectly coordinated mission, a high-frequency and high-wavenumber feature could be aliased as a low-frequency and high-wavenumber feature rather than as a low-frequency and low-wavenumber feature in the Tandem Mission. Despite the extreme mathematical complexity, the physical case is rather intuitive. Namely, the two satellites need temporal coordination to work as one in fending off temporal aliasing. Without it, the two satellites behave as two independent satellites, thus each reverting to their original (i.e., lower) spatial resolution capability in dealing with temporal aliasing.

Corresponding author address: Chang-Kou Tai, E/RA3, NOAA/NESDIS, Camp Springs, MD 20746. Email: ck.tai@noaa.gov

Abstract

The temporal aliasing formulas are derived for the Tandem Mission of Jason-1 and the Ocean Topography Experiment (TOPEX)/Poseidon. Previously, aliasing formulas were derived for a single satellite or a constellation of coordinated satellites, wherein the coordination is such that the collective samplings appear as if they were carried out by a single satellite. In this vein, Jason-1 and TOPEX/Poseidon are coordinated spatially but not temporally. The problem is treated as a general problem about the temporal phasing between any two satellites that are coordinated spatially so that the Tandem Mission is just one special case, whereas the temporally coordinated case is another special case. The present results do agree with the formulas for a constellation of coordinated satellites when the temporal phasing yields temporal coordination, as they should. The benefit of temporal coordination shows itself as having a higher spatial resolution for temporally aliased features. The physical implication is twofold. First, a high-frequency and low-wavenumber feature (e.g., the barotropic Rossby waves) has a better chance of being aliased as a low-frequency and higher-wavenumber feature in a perfectly coordinated mission than it has in the Tandem Mission. Second, in a perfectly coordinated mission, a high-frequency and high-wavenumber feature could be aliased as a low-frequency and high-wavenumber feature rather than as a low-frequency and low-wavenumber feature in the Tandem Mission. Despite the extreme mathematical complexity, the physical case is rather intuitive. Namely, the two satellites need temporal coordination to work as one in fending off temporal aliasing. Without it, the two satellites behave as two independent satellites, thus each reverting to their original (i.e., lower) spatial resolution capability in dealing with temporal aliasing.

Corresponding author address: Chang-Kou Tai, E/RA3, NOAA/NESDIS, Camp Springs, MD 20746. Email: ck.tai@noaa.gov

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  • Bracewell, R. N., 1986: The Fourier Transform and Its Applications. McGraw-Hill, 474 pp.

  • Tai, C-K., 2004: The resolving power of a single exact-repeat altimetric satellite or a coordinated constellation of satellites. J. Atmos. Oceanic Technol., 21 , 810818.

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  • Tai, C-K., 2006: On the aliasing of sea level sampled by a single exact-repeat altimetric satellite or a coordinated constellation of satellites: Analytic aliasing formulas. J. Atmos. Oceanic Technol., 23 , 252267.

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  • Tai, C-K., and Fu L-L. , 2005: The 25-day-period large-scale oscillations in the Argentine Basin revisited. J. Phys. Oceanogr., 35 , 14731479.

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