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- Author or Editor: P. Gaspar x
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Abstract
Among the various sources of error on altimetric sea surface height variability, the orbit error has the largest amplitude. However, since orbit error is mostly at long wavelengths, it can theoretically be distinguished from the mesoscale signal, characterized by wavelengths of a few hundred kilometers. The most commonly used technique to subtract this long-wavelength error is polynomial adjustment (zero, first or second degree) over distances of a few thousand kilometers. This paper examines the error on estimating the polynomial, which directly impacts the mesoscale signal obtained after the adjustment. We demonstrate how it can be estimated in theory and how it varies according to the spatial and energetic mesoscale characteristics (variability level, nonhomogeneities). These results are checked against simulated data and validated using actual Geosat data. The error is far from negligible: for a first-degree fit over 1500 km or a second-degree fit over 2500 km, its amplitude is typically 30% to 50% of the total mesoscale signal amplitude at the profile center and ends, respectively. In certain cases, where nonhomogeneity is significant, it can be greater than the total signal amplitude. We show that in such cases, a polynomial adjustment that takes amount of the statistics of mesoscale signal is a considerably better method. However, in the longer term, more global techniques such as inverse methods should be used so that the mesoscale signal can be extracted with the fewest possible errors.
Abstract
Among the various sources of error on altimetric sea surface height variability, the orbit error has the largest amplitude. However, since orbit error is mostly at long wavelengths, it can theoretically be distinguished from the mesoscale signal, characterized by wavelengths of a few hundred kilometers. The most commonly used technique to subtract this long-wavelength error is polynomial adjustment (zero, first or second degree) over distances of a few thousand kilometers. This paper examines the error on estimating the polynomial, which directly impacts the mesoscale signal obtained after the adjustment. We demonstrate how it can be estimated in theory and how it varies according to the spatial and energetic mesoscale characteristics (variability level, nonhomogeneities). These results are checked against simulated data and validated using actual Geosat data. The error is far from negligible: for a first-degree fit over 1500 km or a second-degree fit over 2500 km, its amplitude is typically 30% to 50% of the total mesoscale signal amplitude at the profile center and ends, respectively. In certain cases, where nonhomogeneity is significant, it can be greater than the total signal amplitude. We show that in such cases, a polynomial adjustment that takes amount of the statistics of mesoscale signal is a considerably better method. However, in the longer term, more global techniques such as inverse methods should be used so that the mesoscale signal can be extracted with the fewest possible errors.
Abstract
This paper presents a relatively straightforward method for efficiently reducing the ERS-1 orbit error using Topex/Postidon data. The method is based on a global minimization of Topex/Poscidon-ERS-1 (TP-E) dual crossover differences. The TP-E crossover differences give an estimate of the ERS-1 radial orbit error almost directly, leading to a geometric estimation of orbit error. Smoothing cubic-spline functions are then used to obtain a continuous estimation of the orbit error over time. The splines can also be adjusted to minimize the ERS-1-ERS-1 (E-E) crossover differences. This allows a better estimation of the orbit error, especially poleward of 66° where no TP-E crossovers are available. The method was successfully applied to the final TP and ERS-1 datasets [i.e., the TP GDRs (geophysical data records) and the ERS-1 OPRs (ocean products)]. The authors used one full 35-day ERS-1 cycle and five TP cycles concurrent with ERS-1 data. Only crossovers with time differences lm than 5 days are used in the adjustment so that most of the large-scale oceanic signal is preserved. Just by using dual TP-E crossovers, E-E crossover differences are reduced from 18 to 10 cm. Also using the single E-E crossovers in the adjustment significantly improves the solution poleward of 66°. The E-E crossover differences are thus globally reduced to only 8 cm. The method was also shown to be almost insensitive to the initial ERS-1 orbit error. The results demonstrate that the orbit of ERS-1 can be determined with an accuracy similar to TP. The method also provides a precise, homogeneous ERS-1-TP dataset. This dataset can be used to map sea level variation or mean sea surface with high accuracy and excellent resolution. More generally, this study shows that when two satellites are flying simultaneously, the more precise one can be used as a reference. This is of great importance for future altimetric missions.
Abstract
This paper presents a relatively straightforward method for efficiently reducing the ERS-1 orbit error using Topex/Postidon data. The method is based on a global minimization of Topex/Poscidon-ERS-1 (TP-E) dual crossover differences. The TP-E crossover differences give an estimate of the ERS-1 radial orbit error almost directly, leading to a geometric estimation of orbit error. Smoothing cubic-spline functions are then used to obtain a continuous estimation of the orbit error over time. The splines can also be adjusted to minimize the ERS-1-ERS-1 (E-E) crossover differences. This allows a better estimation of the orbit error, especially poleward of 66° where no TP-E crossovers are available. The method was successfully applied to the final TP and ERS-1 datasets [i.e., the TP GDRs (geophysical data records) and the ERS-1 OPRs (ocean products)]. The authors used one full 35-day ERS-1 cycle and five TP cycles concurrent with ERS-1 data. Only crossovers with time differences lm than 5 days are used in the adjustment so that most of the large-scale oceanic signal is preserved. Just by using dual TP-E crossovers, E-E crossover differences are reduced from 18 to 10 cm. Also using the single E-E crossovers in the adjustment significantly improves the solution poleward of 66°. The E-E crossover differences are thus globally reduced to only 8 cm. The method was also shown to be almost insensitive to the initial ERS-1 orbit error. The results demonstrate that the orbit of ERS-1 can be determined with an accuracy similar to TP. The method also provides a precise, homogeneous ERS-1-TP dataset. This dataset can be used to map sea level variation or mean sea surface with high accuracy and excellent resolution. More generally, this study shows that when two satellites are flying simultaneously, the more precise one can be used as a reference. This is of great importance for future altimetric missions.
