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P. Y. Le Traon
and
G. Dibarboure

Abstract

The purpose of this paper is to quantify the contribution of merging multiple-satellite altimeter missions to the mesoscale mapping of sea level anomaly (H), and zonal (U) and meridional (V) geostrophic velocities. A space/time suboptimal interpolation method is used to estimate the mean and standard deviation of the H, U, and V mapping errors (as a percentage of signal variance) for different orbit configurations. Only existing or planned orbits [TOPEX/Poseidon (T/P), Jason-1, ERS-1/2–ENVISAT, Geosat–GFO] are analyzed. Jason-1 and T/P orbits are assumed to be interleaved. A large number of simulations are performed, including studies of sensitivity to a priori space scales and timescales, noise, and latitude. In all simulations, the Geosat orbit provides the best sea level and velocity mapping for the single-satellite case. In most simulations, the Jason-1–T/P orbit provides the best two-satellite mapping. However, the gain from an optimized two-satellite configuration (Jason-1 + T/P) compared to a nonoptimized configuration (T/P + ERS or T/P + Geosat) is small. There is a large improvement when going from one satellite to two satellites. Compared to T/P, the combination of T/P and ERS, for example, reduces the H mean mapping error by a factor of 4 and the standard deviation by a factor of 5. Compared to ERS or even Geosat, the reduction is smaller but still by a factor of more than 2. The H mapping improvement is not as significant when going from two to three or three to four satellites. Compared to the Geosat, ERS, and T/P mean mapping errors, the Jason-1 + T/P mean mapping error is, respectively, reduced by 5%, 9%, and 17% of the signal variance. The reduction in mean mapping error by going from two to three and from three to four satellites is, however, only 1.5% and 0.7% of the signal variance, respectively. These results differ from Greenslade et al. mainly because of the definition of resolution adopted in their study. The velocity field mapping is also more demanding in terms of sampling. The U and V mean mapping errors are two to four times larger than the H mapping error. Only a combination of three satellites can actually provide a velocity field mean mapping error below 10% of the signal variance. The mapping of V is also less accurate than the mapping of U but by only 10%–20%, even at low latitudes. These results are confirmed using model data from the Parallel Ocean Climate Model (POCM). POCM H, U, and V are thus very well reconstructed from along-track altimeter data when at least two satellites are used. The study also shows that the Jason-1–T/P orbit tandem scenario has to be optimized taking into account the other satellites (GFO and ENVISAT). It also confirms the usually agreed upon main requirement for future altimeter missions: at least two (and preferably three) missions (with one very precise long-term altimeter system to provide a reference for the other missions) are needed.

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P. Y. Le Traon
and
G. Dibarboure

Abstract

A detailed analysis of the velocity field mapping capabilities from existing and future multiple altimeter missions is carried out using the Los Alamos North Atlantic high-resolution model. The velocity mapping errors on the instantaneous fields and on 10-day averaged fields are systematically computed for all analyzed configurations. The T/P+ERS (Jason-1+ENVISAT) mapping error on the velocity remains acceptable (20%–30%) relative to the ocean signal. Mapping errors of 10-day averaged fields are twice as small, which shows that this configuration has a good potential for mapping lower frequencies of the velocity field. Compared to T/P+ERS, T/P+Jason-1 has a smaller error by about 20%–30% mainly because it is less sensitive to the aliasing of high-frequency signals. The mapping errors are twice as small with a three interleaved Jason-1 configuration. One of the main findings of this study is the role of high-frequency signals that strongly limit the velocity mapping accuracy. The high-wavenumber high-frequency signals contribute to the total velocity variance by up to 20% in high eddy energy regions. This explains why the velocity mapping errors remain larger than about 15%–20% of the signal variance even for the four satellite configurations. This also explains why they do not decrease with the number of satellites as rapidly as expected. The aliasing of high-frequency signals is also a very serious issue. The high-frequency signals can induce large erroneous or inconsistent gradients between neighboring or crossing tracks. This strongly impacts the velocity estimation and explains why the meridional velocity mapping errors are larger than the zonal velocity mapping errors for the T/P+ERS configuration. However, it is shown that these aliasing problems can be partly reduced if they are properly taken into account in the mapping procedure.

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P. Y. Le Traon
,
P. Gaspar
, and
C. Boissier

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.

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P. Y. Le Traon
,
P. Gaspar
,
F. Bouyssel
, and
H. Makhmara

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.

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J. Dorandeu
,
M. Ablain
, and
P-Y. Le Traon

Abstract

A new technique is developed and tested to correct for cross-track geoid gradients in altimeter data. The proposed method is based on direct estimations of geoid variations around nominal tracks and on knowledge of ocean signal variability. Apart from measurement errors, ocean variability is demonstrated to be the major source of error in cross-track geoid estimations using altimeter measurements. The method thus uses the outputs of multimission ocean signal mapping procedures to improve the estimation of geoid features. A detailed error analysis shows that such a technique allows reduction of the estimation error by a factor of 2. Therefore, the method is applied taking advantage of the unprecedented TOPEX/Poseidon mission length. It provides a gain of 50%, in terms of sea level anomaly (SLA) variance reduction, in the cross-track geoid gradient correction used in collocating the repeat-cycle data. It also improves the estimation of altimetric mean profiles. From this study, local mean sea surface estimates can be inferred and applied to present and future altimetric missions, since they can be easily updated using more data. New altimetric missions like Jason-1 and Envisat, with the same ground track as the former TOPEX/Poseidon and European Remote Sensing Satellite (ERS) missions, make the method even more relevant.

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M. Hamon
,
G. Reverdin
, and
P.-Y. Le Traon

Abstract

The authors use a collocation method between XBT and CTD/Ocean Station Data (OSD; including bottle cast and low-resolution CTD) from World Ocean Database 2005 (WOD2005) to statistically correct the XBT fall rate. An analysis of the annual median bias on depth shows that it is necessary to apply a thermal correction, a second-order correction on the depth, as well as a depth offset representing measurement errors during XBT deployment. Data were separated into several categories: shallow and deep XBTs and below or above 10°C of vertically averaged ocean temperatures (in the top 400 m). Also, XBT measurements in the western Pacific between 1968 and 1985 were processed separately because of large regional biases. The estimated corrections deviate from other published estimates with some large variations in time of both linear and curvature terms in the depth corrections, and less time variation of the temperature correction for the deep XBTs. This analysis of heat content derived from corrected XBTs provides at first order a similar variability to other estimates from corrected XBTs and mechanical bathythermographs (MBTs). It shows a fairly prominent trend in 0–700-m ocean heat content of 0.39 × 1022 J yr−1 between 1970 and 2008.

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F. Blanc
,
P. Y. Le Traon
, and
S. Houry

Abstract

The variable ocean dynamic topography is generally estimated from the satellite altimeter signal once the orbit error has been removed. To compute the orbit error, the most conventional technique is to fit a polynomial function (zeroth, first, or second degree) over lengths of several thousand kilometers to each altimetric profile. However, the method induces significant errors. To reduce them, one needs a more detailed representation of the orbit error spectrum and to take account of the spatial and temporal characteristics of the signal and noise. This can be achieved by the form of optimal analysis known as “inverse theory.” If a realistic statistical description of the altimeter signal components (i.e., oceanic variability and orbit error) is provided, the inverse formalism optimally separates the components. Although the whole set of altimeter data is reduced to the data at the intersections of ascending and descending ground tracks (crossover points), the method remains quasi-optimal.

The authors highlight the effectiveness of the method by applying it to the altimeter data for the Brazil-Malvinas confluence area, a few thousand kilometers wide. The authors compare the orbit error estimates to those of the most conventional method that is a method set to a similar environment (short-are analyses). With a homogeneous oceanic variability of 15 cm rms and a nominal orbit error of 30 cm rms, the error on the estimation is reduced to 2 cm all along the altimetric profiles. Taking into account the nonhomogeneous characteristics of the variability signal improves the estimation. It can he further improved simply by adding to the selected altimeter dataset the crossover points one orbital revolution away. For the Geosat satellite, they are at the same latitude but 25°25;prime; farther west or cast. The results encourage the use of the inverse method for orbit error reduction. The method is good at separating signals once the a priori parameters are well defined. Unlike polynomial fits, it does not remove other residual environmental terms.

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G. Dibarboure
,
P. Y. Le Traon
, and
N. Galin

Abstract

Sea surface height (SSH) measurements provided by pulse-limited radar altimeters are one-dimensional profiles along the satellite's nadir track, with no information whatsoever in the cross-track direction. The anisotropy of resulting SSH profiles is the most limiting factor of mesoscale SSH maps that merge the 1D profiles.

This paper explores the potential of the cross-track slope derived from the Cryosphere Satellite-2 (CryoSat-2)'s synthetic aperture radar interferometry (SARin) mode to increase the resolution of mesoscale fields in the cross-track direction. Through idealized 1D simulations, this study shows that it is possible to exploit the dual SARin measurement (cross-track slope and SSH profile) in order to constrain mesoscale mapping in the cross-track direction.

An error-free SSH slope allows a single SARin instrument to recover almost as much SSH variance as two coordinated altimeters. Noise-corrupted slopes can also be exploited to improve the mapping, and a breakthrough is observed for SARin errors ranging from 1 to 5 μrad for 150-km-radius features in strong currents, and 0.1–0.5 μrad for global mesoscale.

Although only limited experiments might be possible with the error level of current CryoSat-2 data, this paper shows the potential of the SAR interferometry technology to reduce the anisotropy of altimeter measurements if the SARin error is significantly reduced in the future, and in particular in the context of a prospective SARin demonstrator optimized for oceanography.

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P. Y. Le Traon
,
F. Nadal
, and
N. Ducet

Abstract

Objective analysis of altimetric data (sea level anomaly) usually assumes that measurement errors are well represented by a white noise, though there are long-wavelength errors that are correlated over thousands of kilometers along the satellite tracks. These errors are typically 3 cm rms for TOPEX/Poseidon (T/P), which is not negligible in low-energy regions. Analyzing maps produced by conventional objective analysis thus reveals residual long-wavelength errors in the form of tracks on the maps. These errors induce sea level gradients perpendicular to the track and, therefore, high geostrophic velocities that can obscure ocean features. To overcome this problem, an improved objective analysis method that takes into account along-track correlated errors is developed. A specific data selection is used to allow an efficient correction of long-wavelength errors while estimating the oceanic signal. The influence of data selection is analyzed, and the method is first tested with simulated data. The method is then applied to real T/P and ERS-1 data in the Canary Basin (a region typical of low eddy energy regions), and the results are compared to those of a conventional objective analysis method. The correction for the along-track long-wavelength error has a very significant effect. For T/P and ERS-1 separately, the mapping difference between the two methods is about 2 cm rms (20% of the signal variance). The variance of the difference in zonal and meridional velocities is roughly 30% and 60%, respectively, of the velocity signal variance. The effect is larger when T/P and ERS-1 are combined. Correcting the long-wavelength error also considerably improves the consistency between the T/P and ERS-1 datasets. The variance of the difference (T/P–ERS-1) is reduced by a factor of 1.7 for the sea level, 1.6 for zonal velocities, and 2.3 for meridional velocities. The method is finally applied globally to T/P data. It is shown that it is tractable at the global scale and that it provides an improved mapping.

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P. Y. Le Traon
,
Y. Faugère
,
F. Hernandez
,
J. Dorandeu
,
F. Mertz
, and
M. Ablain

Abstract

Merging Geosat Follow-On (GFO) with TOPEX/Poseidon (TP) and ERS-2 altimeter data has the potential to improve the mapping of sea level and ocean circulation variations. This can be achieved, however, only if measurement errors and inconsistencies between the different missions are sufficiently reduced. In this paper, it is shown how to get consistent sea surface heights from the three missions using the most precise mission (TP) as a reference. A new technique is then used to estimate a GFO mean profile. This allows consistent sea level anomalies (SLAs) to be extracted from GFO, TP, and ERS-2. SLA data are then merged with a mapping technique that takes into account noise and residual long wavelength errors. Thanks to these techniques, it is shown that GFO can be combined with TP and ERS-2 and that the combination provides a significant improvement in the description of the mesoscale circulation.

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