These along-track analyses on the global ocean have been completed for the different time periods mentioned above. Then the results have been high- and low-pass filtered, as described in section 2. All these results have been collected in bins of 1° × 1°, which allows us to visualize the results on color maps as presented in Figures 4 and 5, composed of 1° × 1° pixels.
4.1. Barotropic Signal and Its Temporal Stability
 First, to gain an overview of the results at a global scale, we have derived global maps of the semidiurnal M2 tide (amplitude and phase), after along-track 500-km filtering, for each of the periods analyzed (T0, T1, T2). These maps (not shown) are very similar to the standard solutions produced recently [Le Provost, 2001; Ray, 1999], at least qualitatively.
 The “complex difference” between these solutions (from periods T1 and T2) has been computed. We present on Figure 4a the mean over each 1° × 1° pixel of these complex differences. They are the two-dimensional equivalent of the lower curves displayed on Figure 2b. Differences are lower than 1 to 2 cm in most regions.
 1. Over the large oceanic current areas like the Gulf Stream, the Brazil Malvinas convergence, and the ACC, the differences range from 3 to 6 cm; this is the consequence of the high level of noise introduced in the altimeter signal by aliasing of the mesoscale variability, as pointed out by Desai et al. , Tierney et al. , and others.
 2. Differences of the order of 3 to 4 cm are also noticeable over the areas where the M2 tide is large over the three ocean basins: the Atlantic Ocean (the far north and northeast Atlantic, the western part of the equatorial Atlantic), the Pacific Ocean (the far northeastern part close to the coast of Alaska, around New Zealand, and over the antiamphidromes of the west, central, and east equatorial Pacific), and the Indian Ocean (over the central antiamphidrome of this basin, and west of Madagascar, in the Mozambique Channel). It is, however, important to note that over all these areas, the “complex difference-to-M2 amplitude” ratio is below 0.03.
 3. Finally, we should note that over the continental shelves these differences are of the order of 5 to 6 cm.
 Red spots in the Southern Ocean may correspond to ice-covered areas, which induce more scattered (in time and in space) altimeter time series. What is happening southeast of Africa is probably due to some errors during the processing of the T/P time series. The greater variability observed in the Gulf of Mexico and in the Indonesian Seas can be explained by the large number of small islands in these areas that make T/P measurements more uncertain and thus time series more scattered. Moreover, the baroclinic variability is apparently nonnegligible in this last region, which might bias the T/P data analysis; the Gulf of Mexico and the Indonesian Seas are characterized by a quite low signal-to-noise ratio, although their topographic configuration is favorable to internal wave generation (see section 4.3). Outside these limited areas, the effective stability of the barotropic signal is thus verified.
 Although these along-track estimates show a clear temporal stability, they remain a bit more noisy than expected for the barotropic tide; our findings corroborate previous ones [Tierney et al., 1998] that many different oceanographic signals may corrupt these barotropic estimations, ranging from nontidal signals with a period close to 60 days, the aliasing period of M2, to T/P instrumental noise, mesoscale variability, the existence of noncoherent baroclinic tides, and the possible temporal variability of the M2 harmonic tidal constituent itself. Note that all these sources of variability in the determination of the harmonic tidal constants have been partially canceled out in the more usual approach (not along-track analysis) applied to derive tidal solutions from and for satellite altimetry [Le Provost, 2001]. This has been done by combining neighboring data from neighboring tracks, by using the extra information available at crossovers, or by using dynamics models. The major advantage of these along-track estimates, although more noisy, is that they retain the short-wavelengths tidal features, which do not appear in the usual global models. Furthermore, along-track estimates must give results nearly as accurate in shallow waters as in the deep ocean, which is not true for the usual hydrodynamic and empirical models [Andersen, 1999; Tierney et al., 2000].
4.2. Similarities With the Standard Finite Elements (FES) and Global Ocean Tide (GOT) Solutions
 An interesting comparison is to compute the complex differences between these purely altimetric barotropic maps and maps derived from the FES 2002 (high-resolution version of FES 99 [Lefèvre et al., 2002]) and GOT 99.2 [Ray, 1999] tidal models. On Figure 4b, we present the amplitude of the vector difference between one of these solutions and FES 2002. Over the deep ocean, the difference remains below 5 cm, indeed closer to 1 cm on the global ocean. There are of course some areas where the difference can reach 10–20 cm: between Indonesia and Australia, in the Yellow Sea, in the English Channel and the North Sea, South of Brazil and beyond latitudes 60°N and 60°S. The problem of determining the boundary between ice and water in the Antarctic is also apparent in the red spots south of 60°S. The differences located southeast of Argentina, at the mouth of the Amazon, on the European Continental shelf, in the Yellow Sea, and in the Indonesian Seas, are certainly, in part, symptomatic of the fact that models are less efficient in shallow waters. The differences in the Indonesian Seas are also probably emphasized by the greater variability observed in T/P data analysis in this area.
4.3. Baroclinic Signal and Its Stability
 To investigate the baroclinic signal and its temporal stability, we have computed for the different time spans T0, Tx,… two sets of global maps, one for the ascending tracks and the other for the descending tracks, representing the along-track difference between the point-to-point M2 amplitudes and the 500-km smoothing. One such map (descending tracks) is shown on Figure 5a. These maps allow us to locate the areas where either the noise-to-signal ratio is high (the large ocean currents) or the areas where internal tides are significant. The major areas of intense baroclinic signal are easy to see: (1) the Mascaren ridge east of Madagascar, the Maldivian ridge, the Ninety East ridge and Carlesberg ridge in the northern Indian Ocean, (2) the Kusu-Palau ridge south of Japan, the Hawaiian island chain, the Tuamotu and the Society archipelagos, the Mendocino ridge off the west coast of the United States, (3) the Melanesian and the Micronesian island chains in the western equatorial Pacific, the Macquarien ridge south of New Zealand, (4) the Reykjanes ridge south of Iceland, the Great Meteor Banks in the North Atlantic, (5) the ridge off Trinidad east of Brazil, and the Walvis ridge in the South Atlantic Ocean.
 These maps display features very similar to those presented by Kantha and Tierney  and only computed with about 3 years of T/P data at that time. The results in the Hawaii region also show striking similarities with those obtained by Ray and Mitchum , although once again the analyses are computed on very different time spans. This confirms that the baroclinic signal is very stable there.
 Let us now focus on the results of the first 3 years (T1) of data and then the last 3 and a half years (T2), and compare them to the T0 time span. As explained above, this choice enables us to investigate distinct time periods covering in particular different climate conditions (El Niño period). The global map representing the amplitude of the “complex difference” between these computations is given on Figure 5b, interpolated on a 1° × 1° grid. The areas of high temporal variability are clearly visible (amplitude higher than 1.1 cm, in red on the maps) due to the large oceanic currents, such as the Gulf Stream, the Kuroshio Current, the Brazil Current, the West Australian Current, the CCA, and so on. In contrast, it is not possible to identify on Figure 5b the regions where we previously noticed the presence of potentially true baroclinic signals; they are located in the blue-green areas corresponding to an amplitude difference lower than 0.5 to 0.1 cm, for example, the areas around Hawaii and Papeete.
 To identify the areas where the coherent baroclinic signal is stable over time, we have thus computed everywhere along the tracks the signal-to-noise ratio previously mentioned. The result is displayed on Figure 5c. The main regions of intense baroclinic signatures are clearly shown on this map, and they are located around Tahiti, Hawaii, the Guinea Gulf, the northeast Atlantic, the Mascaren ridge, the mouth of the Amazon, and off the coast of Chile.
 This map contains important new information, since it identifies the areas over the global ocean where the coherent part of the baroclinic M2 tidal wave propagates from source points, where the barotropic tidal currents interact with particular topographic features.
 Our aim here is not to further investigate all these areas. We will focus on a few locations in order to illustrate their different characteristics.
4.3.1. Areas Already Well Studied From in Situ Data and Altimetry
 The baroclinic signal around Hawaii (23°N) is easy to notice on Figure 5; its amplitude reaches 6.8 cm “crest to trough” (see Figure 6a). The tide-coherent baroclinic signal has been extensively analyzed by Ray and Mitchum , who demonstrated that these oscillations are effectively the surface signature of the internal waves generated by the barotropic tide current flowing over the Hawaiian ridge. Let us point out the major characteristics that we similarly observe in our results and which appear to be temporally very stable. We focus on ascending track 223 (Figure 6a). The complex amplitude oscillates around 2 cm and grows to ∼4 cm toward Hawaii Island. There is an evident phase propagation, particularly south of the island, where one can estimate the wavelength to about 141 km. North of the island along track 223, the propagative signal is weaker (wavelength of 135 km), but it confirms previous in-situ studies results [Ray and Mitchum, 1997; Dushaw et al., 1995; Chiswell, 1994], which showed very clear internal tide records in this area. The M2 barotropic currents are coming from the north-northeast in this region [Le Provost et al., 1994], and the topography north of the ridge along track 223 is complex. The evanescent distance of these waves reaches nearly 2000 km southward and northward as already inferred by Dushaw et al. . Figure 5b reveals that these internal tide signatures are quite steady around the Hawaii chain. This area corresponds to a signal-to-noise ratio greater than 3.
Figure 6. Zoom on five areas where internal wave signatures appear in T/P measurements. Amplitude of the along-track M2 signal (barotropic plus baroclinic) is in centimeters. (a) Track 223 over the Hawaii chain. (b) Track 251 over the Java-Ontong plateau. (c) Track 3 over the west Indian Ocean. (d) Track 148 over the Gulf of Guinea. (e) Track 172 in the northeast Atlantic.
Download figure to PowerPoint
18.104.22.168. Java-Ontong Plateau
 Gourdeau  studied a region on the Java-Ontong plateau (at 2°S–156°E) where internal tides are easily spotted. Thanks to two pressure gauges at depths of 300 and 500 m, and an Autonomous Temperature Line Acquisition System (ATLAS) placed between 25 and 500 m, the COARE experiment, from September 1992 to February 1993, spotted semidiurnal internal waves propagating northeastward and with a high temporal variability. These waves are likely generated on the large sloping topography between the Kilinailau Trench and the Java-Ontong plateau. These experimental results were also validated by the analysis of a few cycles of T/P data (cycles 2 to 15, which cover the same temporal period) in this area, restricted to 0°S to 6°S. The characteristic wavelengths were then estimated to 100–150 km for a calculation along ascending track 251 and to 250 km for descending track 86. Our approach also reveals interesting baroclinic oscillations in this region, around 2.5°S–156°E, with a “crest to trough” amplitude of 4.7 cm for ascending track 251 (see Figure 6b). For descending track 86, which has a more tangential angle of incidence with respect to the relief, the signal is less obvious and the amplitude only reaches 2 cm. A power spectrum analysis of the M2 baroclinic elevation along these two tracks, taking into account cycles 11 to 255, gave wavelength characteristics similar to those suggested by Gourdeau : 200-km wavelength for track 86 and about 120 km for track 251. Our results, although computed over a longer time period of about 7 years, are very close to those of Gourdeau computed only over a 5-month period. The signal seems to be fairly stable. However, the rather low signal-to-noise ratio, about 2, suggests that we should be careful here, because although the altimeter detects internal waves signatures, the signal is often underestimated.
4.3.2. Areas of Complex Topography, Not Normal to T/P Tracks
22.214.171.124. Walvis Ridge
 Southwest of Africa, the baroclinic coherent signal reveals the existence of internal waves; the amplitude is 1.5 cm at about 40°S, where we know there is a submarine ridge expanding from southwest to northeast. However, probably owing to the fact that T/P tracks do not cross this relief at right angles, the signal remains rather weak in this area.
126.96.36.199. Gulf of Guinea
 In the Gulf of Guinea, the internal tide signature is clearly revealed by our altimetric approach. In this region, the exciting relief is the African coastline of the Ivory Coast. The signal is difficult to spot on the global maps: Satellite tracks do not cross the shelf break at right angles so the altimeter measurements probably underestimate the internal wave signal. The signal is stronger on the descending tracks. A close-up of track 148 (Figure 6d) shows the characteristics of the baroclinic signal in this area: short-wavelength oscillations of about 95 km and 5–6 cm “crest to trough,” which propagate until approximately 1400 km southward. This wavelength is coherent with the theoretical first baroclinic mode in the area, which is ∼90 km. The stability of the baroclinic signal detected here is really striking. The high values of the signal-to-noise ratio, reaching more than 4.6, also support the presence of a stable M2 coherent baroclinic signal in this region. Note, however, the long-wavelength differences between T0, T1, and T2 analysis, which correspond to the variability of the T/P barotropic M2 signal, as shown in Figure 4a.
188.8.131.52. West Indian Ocean
 In addition to the Mascaren ridge region where internal tides have already been studied [Morozov, 1995], some interesting internal wave signatures are noticeable northeast of Madagascar (latitudes 8°S to 20°S and longitudes around 50°E); the baroclinic signal has a crest to trough amplitude of 3.5 cm along track 131 and a wavelength of 157 km. The Seychelles' chain constitutes the major topographic feature of this area, which favors internal waves generation, particularly since this region is also characterized by a minimum of M2 amplitude and thus by high barotropic currents.
 Track 3 (Figure 6c), nearly perpendicular to the mid-Indian ridge, also shows very strong and stable oscillations with an amplitude of 2–3 cm, between latitudes 18°S and 25°S. The wavelength of these internal tides is 131 km. The signal-to-noise ratio is strong in this region of the western Indian Ocean, about 4, which corroborates the stability of these baroclinic waves.
4.3.3. Areas of More Complex Internal Tide Systems
184.108.40.206. Northeast Atlantic
 A region well known to be susceptible to generating internal waves is the European shelf break in the northeast Atlantic. We would thus expect to detect a quite large and coherent signal there. Yet this is not the case. In this area, our along-track analysis does not reveal any very clear oscillation (track 172 on Figure 6e). This signal's low temporal coherence is likely to explain the poor information given by T/P data in this region. This lack of temporal coherence is supported by the study of New  in the Bay of Biscay, which showed that baroclinic mode 3 dominates the displacements seaward of the shelf slope. These higher-order modes are very sensitive to stratification changes and thus they have a greater temporal variability. Consequently, the fact that their characteristics are not stable prevents them from being well detected by the altimetry. Moreover, the wavelengths are of the order of 50 km off the Bay of Biscay [Pingree and New, 1995]. We have filtered very high wavelength signals (cut off at 50 km) from our analysis, so the third-mode baroclinic signal that likely exists in this area has also probably been removed. However, an interesting feature on Figure 5b is the high signal-to-noise values on the European continental shelf, which suggests that a fairly strong and stable signal exists. At this stage, analysis of the noncoherent baroclinic signal would be worth expanding in this region of the European shelf break. However, this is not within the scope of this study.
220.127.116.11. Other Areas
 One also notices other interesting areas with fairly clear oscillations north of Brazil off the Amazon shelf, and weaker oscillations near the Cape Verde Islands, in the Atlantic Ocean, or off the Chilean coast in the Pacific. These patterns are less spatially coherent compared to the large propagating patterns found around Hawaii, Tahiti (see section 3.2 on track 221), or the Gulf of Guinea. A very complex ridge pattern in the region north of Brazil may explain this low spatial coherence. Off Chile, a strong barotropic tide arrives southward on the Nazca ridge, but satellite tracks are not at the right angle to the topography to let us see all the generated oscillations in all directions. Nevertheless, the signal-to-noise ratios of around 4 suggest that the internal tides in these regions are very stable.