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The Amazon shelf break is a key region for internal tide (IT) generation. It also shows a large seasonal variation in circulation and associated stratification. This study, based on a high-resolution model (1/36∘) explicitly forced by tide, aims to better characterize how the ITs vary between two contrasted seasons. During the season from March to July (MAMJJ) the currents and mesoscale eddies are weak while the pycnocline is shallower and stronger. From August to December (ASOND) mean currents and mesoscale eddies are strong, and the pycnocline is deeper and weaker than in MAMJJ. For both seasons, semi-diurnal M2 ITs are generated on the shelf break mainly between the 100 and 1000 m isobath in the model. South of 2∘ N, the conversion from barotropic to baroclinic tide is more efficient in MAMJJ than in ASOND. Local dissipation of the coherent M2 at the generation sites is higher in MAMJJ (30 %) than in ASOND (22 %), because higher modes are favourably generated (modes 2 and 3), making the internal wave packet more dispersive. The remaining fraction (70 %–80 %) propagates away from the generation sites and mainly dissipates locally every ∼ 100 km, which corresponds to the mode 1 reflection beams. About 13 %, 30 %, and 40 % of the M2 coherent IT dissipates at the first, second, and third beams. M2 coherent baroclinic flux propagates more northward during MAMJJ while it seems to be blocked at 6∘ N during ASOND. There is no intensified dissipation of the coherent M2 that could explain the disappearance of the coherent flux. In fact, the flux at this location becomes more incoherent because of strong interaction with the currents. This has been shown in the paper using 25 h mean snapshots of the baroclinic flux that shows branching and stronger eastward deviation of the IT when interacting with mesoscale eddies and stratification during ASOND. Finally, we evaluated sea surface height (SSH) frequency and wavenumber spectra for subtidal (f<1/28 h−1), tidal (1/28 h−1 < f<1/11 h−1), and supertidal (f>1/11 h−1) frequencies. Tidal frequencies explain most of the SSH variability for wavelengths between 250 and 70 km. Below 70 km, the SSH is mainly incoherent and supertidal. The length scale at which the SSH becomes dominated by unbalanced (non-geostrophic) IT was estimated to be around 250 km. Our results highlight the complexity of correctly predicting IT SSH in order to better observe mesoscale and sub-mesoscale eddies from existing and upcoming altimetric missions, notably the Surface Water Ocean Topography (SWOT) mission.

This study proposes an approach to estimate the ocean sea surface height signature of coherent internal tides from a 25-year along-track altimetry record, with a single inversion over time, resolving both internal tide contributions and mesoscale eddy variability. The inversion is performed on a reduced-order basis of topography and practically achieved with a conjugate gradient. The particularity of this approach is to mitigate the potential aliasing effects between mesoscales and internal tide estimation from the uneven altimetry sampling (observing the sum of these components) by accounting for their statistics simultaneously, while other methods generally use a prior mesoscale. The four major tidal components are considered (M2, K1, S2, O1) over the period 1992–2017 on a global configuration. From the solution, we use altimetry data after 2017 for independent validation in order to evaluate the performance of the simultaneous inversion and compare it with an existing model.

Ocean surface currents are critical not only to ocean dynamics, but also to marine ecosystems, maritime navigation and safety, search and rescue, monitoring and mitigation of marine pollution including oil spills, plastic, and debris. Wind-current coupling impacts both the ocean and the atmosphere, thereby influencing weather and climate. Recent modeling studies underscore the importance of submeoscale-to-mesoscale surface currents in ocean dynamics, marine ecosystems, and air-sea interactions. However, the present observing system is inadequate in observing these currents, posing major challenges in understanding their impacts. Moreover, many operational oceanography applications require measurements of these small-scale currents over the global ocean. To reduce these knowledge and capability gaps, here we present a satellite mission concept “Ocean Dynamics and Surface Exchange with the Atmosphere” (ODYSEA) that is being proposed as a NASA Earth System Explorers satellite through a strong partnership with CNES. The mission will provide the first-ever measurements of total (geostrophic+ageostrophic) surface currents in the global ocean along with simultaneous measurements of ocean-surface vector winds. ODYSEA is designed to have a 1700-km wide swath, providing approximately daily coverage of the global ocean with 5-km postings. These measurements will provide an unprecedented opportunity to unravel the physical processes underlying small-scale ocean dynamics and air-sea interactions. ODYSEA’s near real-time data will support key operational needs such as weather and ocean forecasting, search and rescue, and seafaring.

The Southwestern Tropical Pacific exhibits a complex bathymetry and represents a hot spot of internal tide generation. Based on a tailored high-resolution regional model, we investigate for the first time the internal tide field around the New Caledonia islands through energy budgets that quantify the internal tide generation, propagation, and dissipation. A total of 15.97 GW is converted from the barotropic to the baroclinic tide with the main conversion sites associated with the most prominent bathymetric structures such as continental slopes and narrow passages in the north (2.17 GW) and ridges and seamounts south of New Caledonia (3.92 GW). The bulk of baroclinic energy is generated in shallow waters around 500 m depth and on critical to supercritical slopes highlighting the limitations of linear semi-analytical models in those areas. Despite the strongly dominant mode-1 generation, more than 50 % of the locally generated energy dissipates in the near-field close to the generation sites. The remaining energy propagates within well-defined tidal beams with baroclinic energy fluxes of up to 30 kW m−1 toward the open ocean, strongly dominated by mode-1. The energetic mesoscale eddy activity in the region appears to be the main source of tidal incoherence. Locally, mesoscale eddy-driven stratification changes induce variations of the conversion term. In the far-field, incoherence of the energy flux arises through the interaction of the tidal beam with the eddying background flow. The New Caledonia site represents a challenge for SWOT (Surface Water Ocean Topography) observability of meso- and submesoscale dynamics in the presence of internal tides with sea surface height signatures > 6 cm. We show that a correction of the coherent baroclinic tide may improve the observability range by shifting the transition scale between balanced and unbalanced flow in winter from 180 km to 50–80 km. In contrast, in summer observability increases only marginally due to the seasonally amplified signature of the incoherent tide at scales below 100 km.

This study proposes new insights for the interpretation of GEOVIDE particle measurements. Potentiel resuspension sites due to internal tides (ITs) have been identified along the western Iberian shelf slope using a tidal regional model. Iberian shelf is mainly a source of lithogenic material whereas Galicia Bank is a source of biogenic matter. The potential pathways for particles from the resuspension sites toward the GEOVIDE stations are identified using IBIRYS reanalysis to infer their transport by the ocean circulation. It appears that each station is influenced by a specific pathway and mixed particles from several resuspension sites. This methodology reveals that the criticality of the bathymetry slope, commonly used to track resuspension sites from internal waves, is not sufficient to investigate ITs. An explicit resolution of ITs using a numerical tidal model is required for an exhaustive identification of the resuspension sites. Key Points Sites of high bottom tidal velocity along the Iberian continental slope were identified using a semi-realistic internal tides model Sediment resuspension was confirmed on five sites based on earlier sediment surveys and Shields criterion threshold Particle trajectories were proposed based on circulation modeling to improve the interpretation of geochemical tracers measurements Plain Language Summary Internal tides are waves with a tidal period generated when tides cross a steep slope of the sea floor. Internal tides then propagate in every stratified layer of the open ocean over hundreds to thousands of kilometers. The encounter of internal tides with underwater relief, either at the generation site or after propagation, results in high bottom friction that enhances sediment resuspension. Evidence of lithogenic particles was found at various depths during the GEOVIDE cruise, from the Iberian continental slope to thousands of kilometers away. The present study identifies the sites where internal tides are responsible for sediment resuspension. Additionally, the oceanic circulation is investigated to establish the trajectories of the resuspended sediment that could explain the GEOVIDE measurements.

Since the mid-1990s, a series of FES (finite element solution) global ocean tidal atlases has been produced and released with the primary objective to provide altimetry missions with tidal de-aliasing correction at the best possible accuracy. We describe the underlying hydrodynamic and data assimilation design and accuracy assessments for the latest FES2014 release (finalized in early 2016), especially for the altimetry de-aliasing purposes. The FES2014 atlas shows extremely significant improvements compared to the standard FES2004 and (intermediary) FES2012 atlases, in all ocean compartments, especially in shelf and coastal seas, thanks to the unstructured grid flexible resolution, recent progress in the (prior to assimilation) hydrodynamic tidal solutions, and use of ensemble data assimilation technique. Compared to earlier releases, the available tidal constituent's spectrum has been significantly extended, the overall resolution has been augmented, and additional scientific byproducts such as loading and self-attraction, energy diagnostics, or lowest astronomical tides have been derived from the atlas and are available. Compared to the other available global ocean tidal atlases, FES2014 clearly shows improved de-aliasing performance in most of the global ocean areas and has consequently been integrated in satellite altimetry geophysical data records (GDRs) and gravimetric data processing and adopted in recently renewed ITRF standards (International Terrestrial Reference System, 2020). It also provides very accurate open-boundary tidal conditions for regional and coastal modelling.

The forthcoming SWOT altimetric missions aim to resolve the mesoscale with an unprecedented spatial resolution and swath. However, high-frequency processes, such as tides, are undersampled in time and aliased onto lower frequencies, so they need to be corrected properly. Unlike barotropic tides, internal tides (ITs) are not completely stationary and have significant temporal variability due to their interactions with the ocean circulation and the stratification variability. Stratification changes impact both the generation and the propagation of ITs. The present study proposes a methodology to quantify the impacts of background stratification using a clustering method for the classification of a broad range of stratification and idealized modeling of ITs in the frequency domain. The methodology is successfully tested in the western equatorial Atlantic and in the Bay of Biscay. For the western equatorial Atlantic, a single pycnocline is observed and only the two first vertical modes of ITs have significant amplitudes. With no variation in the stratification intensity, the variation in the depth of this single pycnocline linearly impacts the elevation amplitude, energy fluxes and surface wavelength of the two modes. In the Bay of Biscay, there is a permanent deep pycnocline and secondary seasonal pycnoclines near the surface. No proxy have been found to describe the changes in ITs, so a seasonal climatology is explored. The seasonality of the stratification strongly affects the elevation amplitudes as well as the energy fluxes of modes 1, 2 and 3. The distribution of the modes vary with the background stratification, changing the horizontal scales of the ITs.

The forthcoming SWOT altimetric mission aims to access the smaller mesoscale oceanic circulation with an unprecedented spatial resolution and swath. The repetitivity of the mission orbit implies that high frequency processes, such as the internal tides (ITs), are under-sampled in time and their full temporal evolution is not observed. They are therefore aliased onto lower frequencies and possibly mixed into the mesoscale signals. As with the barotropic tides, the ITs must be corrected from the altimetric observations in order to access to the smaller mesoscales. But unlike barotropic tides, ITs are not completely stationary and have significant temporal variability due to their interactions with the ocean circulation and the stratification variability. ITs prediction, correction and error calculation requires a precise understanding of the ITs' surface elevation signature and its temporal variability. Stratification changes impact both on the generation and the propagation of ITs. This present study proposes to quantify the impacts of the background stratification variations alone with a classification of the observed stratification and an idealized modelling of the ITs. A single methodology is developed to handle a very broad range of stratification variability. The classification is made using clustering methods and the modelling uses the frequency domain model T-UGO. The methodology is successfully tested on the Amazon shelf and in the Bay of Biscay. For the Amazon shelf, the pycnocline depth linearly impacts on the amplitudes and wavelengths of the ITs first two modes. An increase of the pycnocline depth increases the total ITs' amplitude but also transfers the energy from the mode 2 to the mode 1. An increase of the pycnocline depth also increases the wavelengths of both modes 1 and 2. In the Bay of Biscay we found no such proxy to describe the changes in ITs' characteristics so a seasonal climatology is explored. The seasonality of the stratification strongly affects the amplitudes of modes 2 and 3 and significantly impacts on the surface elevation of ITs. Whereas the wavelengths of all modes and the amplitude of mode 1 are only weakly affected by the stratification seasonality. The amplitude variability of modes 2 and 3 also modifies the ratio between the modes in presence and makes the horizontal scales of ITs variable. The significance of the ITs wavelength modifications with stratification changes suggests that a more accurate ITs' surface elevation correction for SWOT measurements should take into account this stratification variability.

This study proposes a new methodology for implementing the barotropic tide in an ocean general circulation model (OGCM). The assumptions underlying this methodology are that the best barotropic tide solutions are computed by specialized models and that the fields that should be accurately reproduced by the OGCM are the transport fields from the specialized tide model. The target/reference solution for the OGCM is thus the projection of the tide model on the OGCM grid, for each tidal harmonic.The proposed methodology involves little change of the OGCM modeland yields almost exactly the reference solution, with a cost that is belowmost of the current methodologies. It relies on the modification of the tidepotential, or more accurately, on the replacement of all terms associatedwith the tide (tide potential, self attraction and loading, tide dissipation, ...) by a general tide forcing term in the barotropic momentum equationwhich is calculated from the –known- reference solution.The tide forcing terms can be tricky to calculate as they depend on details of the OGCM numerical schemes (for both temporal and spatial operators). A general procedure, automatically adapting the chosen schemes, is proposed for their calculation, so that the procedure is independent of the model. Tests with academic configurations are first proposed to validate the methodology and its implementation, and the OGCM is chosen to be the NEMO (Nucleus for European Modelling of the Ocean) model.A global ¼° configuration with realistic bathymetry and with FES tide solutions (Finite Element Solution) are then performed. Current tests show that when FES solutions are crudely interpolated on the NEMO grid, the methodology exactly reproduces the FES fluxes, but the associates NEMO SSH is very noisy in regions where FES has high resolution. This problem is currently addressed. To get rid of this problem, fluxes must be carefully integrated along each grid cell, so that the reproduced SSH is exactly an average of the FES SSH within the NEMO grid cell. Hopefully, we will be able to present final –clean- solutions at the conference.

Since the mid-1990’s, a series of Finite Element Solution (FES) global ocean tidal atlases has been produced and released with the primary objective to provide altimetry missions with tidal de-aliasing correction at the best possible accuracy. We describe the underlying hydrodynamic and data assimilation designs for the last FES2014 release (finalized in early 2016), and some accuracy assessments especially for the altimetry de-aliasing purposes. The FES2014 atlas shows extremely significant improvements compared to the FES2004 (Lyard et al. 2006) and (intermediary) FES2012 atlases, in all ocean regions, especially in shelf and coastal seas; these advances are due to the unstructured grid flexible resolution, recent progress in the (prior to assimilation) hydrodynamic tidal solutions and to the use of an ensemble data assimilation technique. Compared to earlier releases, the FES2014 available tidal constituents spectrum has been significantly extended, the overall resolution augmented; some new additional scientific by-products have been derived from the atlas and are available, including the loading and self-attraction effects, energy diagnostics or the lowest astronomical tides . Compared to the other available global ocean tidal atlases, FES2014 clearly shows improved de-aliasing performances in most of the global ocean areas. It has consequently been integrated in satellite altimetry and gravimetry data processing, and adopted in recently renewed ITRF standards. It also provides very accurate open boundary tidal conditions for regional and coastal modelling.

In order to access the targeted ocean signal, altimeter measurements are corrected for several geophysical parameters among which the ocean tide correction is one of the most critical, but the internal tide signature at the surface are not yet corrected globally. Internal tides can have a signature of several cm at the surface with wavelengths about 50–250 km for the first mode and even smaller scales for higher order modes. The goals of the upcoming Surface Water Ocean Topography (SWOT) mission and other high-resolution ocean measurements make the correction of these small scale signals a challenge, as the separation of all tidal variability from other oceanic signals becomes mandatory. In this context, several scientific teams are working on the development of new internal tide models, taking advantage of the very long altimeter time series now available, which represent an unprecedented and valuable global ocean database. The internal tide models presented here focus on the coherent internal tide signal and they are of three types: empirical models based upon analysis of existing altimeter missions, an assimilative model, and a three-dimensional hydrodynamic model. A detailed comparison and validation of these internal tide models is proposed using existing satellite altimeter databases. The analysis focuses on the four main tidal constituents M2, K1, O1 and S2. The validation process is based on a statistical analysis of multi-mission altimetry including Jason-2 and Cryosphere Satellite-2 data, taking advantage of the long-term altimeter databases available. The results show a significant altimeter variance reduction when using internal tide corrections on all ocean regions where internal tides are generating/propagating. A complementary spectral analysis also gives some estimation of the performance of each model as a function of wavelength, and some insight into the residual non-stationary part of internal tides in the different regions of interest.

Ocean tides play a major role in ocean mixing, and setting up water properties, both in the deep and the shallow ocean. Whether parameterized or explicitly simulated, tides can not be ignored in modern ocean prediction models. Representing them explicitly, the approach followed here to prepare the upcoming CMEMS (Copernicus Marine Environment Monitoring Service) global prediction system, allows for the generation of a large quantity of internal waves propagating at great distances. This is a useful information for future high resolution wide swath altimetry missions but also for forcing regional systems, enabling remotely generated internal waves to enter the user domain, providing in some places an important part of the high frequencyenergy.In the present work, we review numerical aspects in the NEMO ocean model influencing the explicit representation of both external and internal tidal waves in a global 1/12° configuration. The numerical core of NEMO has indeed largely evolved recently to simulate tides, by now including the lunisolar tidal potential, Self Attraction and Loading effects, a split-explicit barotropic solver but also Lagrangian vertical coordinates to limit the spurious numerical diffusion. We report here the effect of various parameters, using data assimilative tidal models and altimetry data as references. Semi-diurnal energy budgets are also computed. Throughout this work, a systematic comparison to HYCOM results (Ansong et al. 2015 and Buijsman et al. 2016) is performed.

The Arctic Ocean is a challenging region for tidal modelling. The accuracy of the global tidal models decreases by several centimeters in the Polar Regions, which has a large impact on the quality of the satellite altimeter sea surface heights and the altimetry-derived products. NOVELTIS, DTU Space and LEGOS have developed Arctide2017, a regional, high-resolution tidal atlas in the Arctic Ocean, in the framework of an extension of the CryoSat Plus for Ocean (CP4O) ESA STSE (Support to Science Element) project. In particular, this atlas benefits from the assimilation of the most complete satellite altimetry dataset ever used in this region, including Envisat data up to 82°N and CryoSat-2 data between 82°N and 88°N. The combination of these satellite altimetry missions gives the best possible coverage of altimetry-derived tidal constituents. The available tide gauge data were also used for data assimilation and validation. This paper presents the implementation methodology and the performance of this new regional tidal model in the Arctic Ocean, compared to the existing global and regional tidal models.

Since the beginning of the altimeter mission TOPEX/Poseidon (T/P), followed by Jason-1 and Jason-2 on similar orbits, and many other missions on different orbits (ERS, EnviSat, etc.), mean sea level (MSL) products became essential for the comprehension of global ocean circulation. Since early in the T/P mission, a suspicious signal, having a period of near 59 days and amplitude of roughly 5 mm, was apparent in the Global MSL record. Compared with the 4–5-mm amplitude of the annual signal, the 59-day signal has understandably attracted attention. Moreover, the same signal has been subsequently detected in Jason-1 and later in Jason-2 MSLs. In 2010, the Ocean Surface Topography Science Team (OSTST) concluded this signal as the aliasing of a higher frequency error inherited from the tide model correction: the semi-diurnal wave S2. The source of this error was mainly attributed to T/P measurements, which were assimilated in ocean tide models. When these models are used in the computation of T/P MSL, most of the error cancels. However, this error is communicated to Jason-1 and Jason-2 MSLs. In order to gather and publish the OSTST analyses on this matter, this paper first attempts to list the myriad possibilities for the puzzling 59-day error in MSL. Then, this paper goes deeper into the description of the main contributor to this list: the tide models error. Indeed, since 2010, considerable efforts have been undertaken within the ocean tide community in order to correct ocean tide S2-waves from this error, particularly in the Goddard Ocean Tide (GOT) and finite element solution (FES) latest versions. Comparing several GOT and FES versions and a pure hydrodynamic tide model, this paper assesses, quantifies, and describes a reduction of the MSL 59-day error thanks to the latest releases. These analyses also confirm that a large part of this error has its origins in the T/P mission and has contaminated ocean tide solutions and Jason-1 and Jason-2 MSLs. They also suggest that ocean tide is not the only possible vector. Jason-1 and Jason-2 MSLs contain additional 59-day error—though to a lesser extent—that may either come from the measurements themselves or from another vector.

Very intense internal tides take place in Indonesian seas. They dissipate and affect the vertical distribution of temperature and currents, which in turn influence the survival rates and transports of most planktonic organisms at the base of the whole marine ecosystem. This study uses the INDESO physical model to characterize the internal tides spatio-temporal patterns in the Indonesian Seas. The model reproduced internal tide dissipation in agreement with previous fine structure and microstructure observed in-situ in the sites of generation. The model also produced similar water mass transformation as the previous parameterization of Koch-Larrouy et al. (2007), and show good agreement with observations. The resulting cooling at the surface is 0.3 degrees C, with maxima of 0.8 degrees C at the location of internal tides energy, with stronger cooling in austral winter. The cycle of spring tides and neap tides modulates this impact by 0.1 degrees C to 0.3 degrees C. These results suggest that mixing due to internal tides might also upwell nutrients at the surface at a frequency similar to the tidal frequencies. Implications for biogeochemical modelling are important.

Consequences of tidal dynamics on hydro-sedimentary processes are a recurrent issue in estuarine and coastal processes studies, and accurate tidal solutions are a prerequisite for modeling sediment transport, especially in macro-tidal regions. The motivation for the study presented in this publication is to implement and optimize a model configuration that will satisfy this prerequisite in the frame of a larger objective in order to study the sediment dynamics and fate from the Red River Delta to the Gulf of Tonkin from a numerical hydrodynamical–sediment coupled model. Therefore, we focus on the main tidal constituents to conduct sensitivity experiments on the bathymetry and bottom friction parameterization. The frequency-domain solver available in the hydrodynamic unstructured grid model T-UGOm has been used to reduce the computational cost and allow for wider parameter explorations. Tidal solutions obtained from the optimal configuration were evaluated from tide measurements derived from satellite altimetry and tide gauges; the use of an improved bathymetry dataset and fine friction parameter adjustment significantly improved our tidal solutions. However, our experiments seem to indicate that the solution error budget is still dominated by bathymetry errors, which is the most common limitation for accurate tidal modeling.

Because of sparse in situ measurements, the use of altimeter and ocean models are currently the only options to understand the coastal variability of sea level anomalies (SLA) near the African coasts of the Eastern Tropical Atlantic Ocean (ETAO: 35°S–25°N; 25°W–African coasts). In this study, three SLA products derived from altimetry (X-TRACK and CMEMS) and from a regional ocean model (NEMO) are validated near the coast using the 14 tide gauges (TGs) available in the region. Statistical analysis (correlation, standard deviation and root mean square) are performed to compare our three products with the TG. We then analyze the sub-seasonal to inter-annual variability of SLAs (i.e. from 20 days up to 2 years) over the period January 2008–December 2014. We found a very good agreement between altimetry, model and TGs near the coasts of Senegal (10°N–25°N) and Gulf of Guinea (10°S–10°N). This is not the case near the coast of Benguela (south of 10°S) and is mainly explained by the combined effects of the position of TGs (located in semi-enclosed bays), the geophysical corrections used in the computations of the SLA derived from altimetry (i.e. tide, dynamical atmospheric correction -DAC- and sea state bias -SSB-). In addition, the low spatial resolution of the CMEMS and model data do not allow a good description of the small scale oceanic and atmospheric variability, which dominates in the Benguela upwelling system. We then show, with all products, that the temporal variability of SLA is mainly seasonal (annual and semi-annual) throughout the ETAO region. The altimetry data also show some inter-annual (15–24 months) variability in the equatorial band, which can be related to equatorial Kelvin waves. This is less pronounced with the NEMO model and does not appear over the whole equatorial band. We show that high spatial resolution and improved altimetric geophysical corrections near the coast can each reduce near-shore data errors by up to 10%. However, despite these improvements, agreements between SLA products are still unsatisfactory in the Benguela region, suggesting that efforts need to be intensified on geophysical corrections and in increasing the temporal and spatial resolution of data near the coast. Moreover, there exist gaps in TG measurements, along the West African coast, especially in the Benguela region. The TG network should thus be completed.

Intense equatorward western boundary currents transit the Solomon Sea, where active mesoscale structures exist with energetic internal tides. In this marginal sea, the mixing induced by these features can play a role in the observed water mass transformation. The objective of this paper is to document the M2 internal tides in the Solomon Sea and their impacts on the circulation and water masses, based on two regional simulations with and without tides. Since the Solomon Sea is under the influence of ENSO, the characteristics of the internal tides are also analyzed for two contrasted conditions: the January–March 1998 El Niño and the April–June 1999 La Niña. The generation, propagation, and dissipation of the internal tides are sensitive to changes in stratification and mesoscale activity, and these differ between these contrasted El Niño and La Niña case studies. Mode 1 is the dominant vertical mode to propagate baroclinic tidal energy within the Solomon Sea, but mode 2 becomes more energetic during the El Niño period when the stratification is closer to the surface. The La Niña period with a higher level of mesoscale activity exhibits more incoherent internal tides. These results illustrate the complexity of predicting internal tides in marginal seas in order to clearly observe meso- and submesoscale signatures from altimetric missions, including the future Surface Water Ocean Topography (SWOT) mission. Diapycnal mixing induced by tides contributes to a stronger erosion of the salinity maximum of the upper thermocline water and to cooling of the surface temperature interacting with the atmosphere. Such effects are particularly visible in quieter regions, where particles may experience the tidal effects over a longer time. However, when averaged over the Solomon Sea, the tidal effect on water mass transformation is an order of magnitude less than that observed at the entrance and exits of the Solomon Sea. These localized sites appear crucial for diapycnal mixing, since most of the baroclinic tidal energy is generated and dissipated locally here, and the different currents entering/exiting the Solomon Sea merge and mix. Finally, the extreme ENSO condition case studies suggest the strong role of local circulation changes, as well as stratification changes, in modifying the internal tides.

We investigate the impact of wave-dependent stress on surge modelling, from case studies in the North Sea, using a global ocean model forced with a wave-atmosphere coupled model. We select the storms with the largest surges and a range of sea state development from young to mature seas. The modelled surges are compared to tide gauges and altimeter data. The ocean model is able to accurately predict storm surges in coastal areas. The consistency of the model outputs, the altimeter, and the tide gauge data confirms the accuracy of altimeters for storm surge measurements. We show that using a wave-dependent rather than a wind-dependent only stress formulation gives more accurate surge simulations when the sea state is young and the sea rougher. Taking into account the waves in the stress formulation has a significant impact on the surges (up to 20 cm).

(IF 3.53 [2018]; Q1); International audience; The goal of the Surface Water and Ocean Topography (SWOT) mission, a future wide-swath radar altimeter, is to measure the elevations of ocean and continental water surfaces with unprecedented precision. A simulator of SWOT high-rate (HR) interferometric SAR images has been developed to provide SWOT-like data to scientists and as a tool to develop and test HR ground processing algorithms. In this letter, we evaluate the errors of the extracted water levels in different hydrodynamic and topographic contexts in the Seine estuary based on simulated SWOT HR data. The results confirm height errors generally below 10 cm after km-scale averaging for the majority of the observations. Higher errors mostly occur in areas where the surrounding topography causes layover. This letter also reveals the interactions between tide and streamflow and their impact on the spatial variability of the water levels in the estuary.

Mean sea level (MSL) is a prominent indicator of climatic change (Ablain et al., 2015; Cazenave et al., 2014; Leuliette and Willis, 2011), and is therefore of great scientific and societal interest. Since the beginning of the altimeter mission TOPEX/Poseidon, followed by Jason-1 and Jason-2 on similar orbits, and many other missions on different orbits (ERS, EnviSat, etc.), MSL products became essential to the comprehension of Global ocean circulation. Since early in the TOPEX/Poseidon mission (Nerem, 1995) a suspicious signal, having period near 59 days and amplitude of roughly 5 mm, was apparent in the GMSL record. Compared with the 4–5 mm amplitude of the annual signal (Minster et al., 1999), the suspicious 59-day signal has understandably attracted attention. Moreover, the same signal has been subsequently detected in Jason-1 and later Jason-2 MSLs. In 2010, it was the subject of a dedicated session at the Ocean Surface Topography Science Team (OSTST) meeting in Lisbon. The conclusions were this signal is the aliasing of a higher frequency error inherited from the tide model correction: the semi-diurnal wave S2. The source of this error was mainly attributed to TOPEX measurements which are assimilated in ocean tide models. When these models are used in the computation of TOPEX/Poseidon MSL, most of the error cancels. However, this error is communicated to Jason-1 and Jason-2 MSLs. Since 2010, considerable efforts have been undertaken within the ocean tide community in order to correct ocean tide S2-waves from this error, particularly in the Goddard Ocean Tide (GOT) and Finite Element Solution (FES) latest versions. The present paper aims at assessing, quantifying and characterizing the reduction of the 58.77-day error thanks to the latest releases.

International audience; Downscaling physical processes from a large scale to a regional scale 3D model is a recurrent issue in coastal processes studies. The choice of boundary conditions will often greatly influence the solution within the 3D circulation model. In some regions, tides play a key role in coastal dynamics and must be accurately represented. The Bay of Biscay is one of these regions, with highly energetic tides influencing coastal circulation and river plume dynamics. In this study, three strategies are tested to force with barotropic tides a 3D circulation model with a variable horizontal resolution. The tidal forcings, as well as the tidal elevations and currents resulting from the 3D simulations, are compared to tidal harmonics extracted from satellite altimetry and tidal gauges, and tidal currents harmonics obtained from ADCP data. The results show a strong improvement of the M2 solution within the 3D model with a "tailored" tidal forcing generated on the same grid and bathymetry as the 3D configuration, compared to a global tidal atlas forcing. Tidal harmonics obtained from satellite altimetry data are particularly valuable to assess the performance of each simulation. Comparisons between sea surface height time series, a sea surface salinity database, and daily averaged 2D currents also show a better agreement with this tailored forcing.

The Indonesian Mixing program (INDOMIX) was designed to quantify the very strong mixing that transforms Pacific waters into isohaline Indonesian Waters in the Indonesian archipelago. The turbulent dissipation rates and associated mixing were estimated and analyzed using a multidisciplinary approach that combines physical and geochemical in-situ observations: (1) direct measurements of the dissipation using a microstructure profiler, (2) use of density-based fine-scale methods applied to CTD and XCTD data, and (3) study of the vertical distribution of natural radionuclides (radium isotopes and actinium-227). Data were collected at five contrasting stations within the Indonesian archipelago, found above energetic straits or in relatively quiescent large basins. Strong instabilities, inversions of the density profiles and a very strong water mass transformation were observed. A wide range of dissipation values were obtained (between [10(-10), 10(-4)] W kg(-1)) with spots of higher dissipation in the ocean interior correlated with a strong internal tide signal. Both the fine-scale and micro-scale methods allow us to identify very strong energy dissipation levels above the straits, ranging between [10(-7), 10(-4)] W kg(-1), in contrast to lower values at stations further away from the generation sites. The dissipation for the station located in the center of the Halmahera Sea ([10(-9), 10(-8)] W kg(-1)) is stronger than for the Banda station ([10(-11), 10(-16)] W kg(-1)), which is even further away from the generation sites. The three approaches agree relatively well and provide vertical eddy diffusivities values ranging between 5 x 10(-4) and 5 x 10(-1) m(2) s(-1), except in the Banda Sea where values are similar to the ones found in the open ocean (10(-6) m(2) s). CTD and XCTD profilers (deployed between stations) give estimates of dissipation all along the transit. It is found that enhanced mixing occurs preferentially above rough topography, such as in the Ombai Strait, the Halmahera Sea's northern entrance, the Buru strait and Sumba strait. Finestructure parameters are very sensitive to depth and dissipation, which differs between stations. We recommend more systematic microstructure measurement in order to tune these parameters. Surface mixing, at the base of the mixed layer is found to be very strong with values between [10-4, 10(-3) m(2) s(-1)]. These results confirm the modeling studies that suggest the occurrence of intensified subsurface mixing which cools the sea surface temperatures and thus strongly affects the mean and variability of the tropical climate. We conclude, therefore, that climate models need to take into account this intensified ocean mixing to properly represent the mean state of the atmosphere and its climate variability.

International audience; The geodetic Corsica site was set up in 1998 in order to perform altimeter calibration of the TOPEX/Poseidon (T/P) mission and subsequently, Jason-1 and OSTM/Jason-2. The scope of the site was widened in 2005 in order to undertake the calibration of the Envisat mission and most recently of SARAL/AltiKa. Here we present the first results from the latter mission using both indirect and direct calibration/validation approaches. The indirect approach utilizes a coastal tide gauge and, as a consequence, the altimeter derived sea surface height (SSH) needs to be corrected for the geoid slope. The direct approach utilizes a novel GPS-based system deployed offshore under the satellite ground track that permits a direct comparison with the altimeter derived SSH. The advantages and disadvantages of both systems (GPS-based and tide gauges) and methods (direct or indirect) will be described and discussed. Our results for O/IGD-R data show a very good consistency for these three kinds of products: their derived absolute SSH biases are consistent within 17 mm and their associated standard deviation ranges from 31 to 35 mm. The AltiKa absolute SSH bias derived from GPS-zodiac measurement using the direct method is −54 ±10 mm based on the first 13 cycles.

The processes that contribute to the flat sea surface height (SSH) wavenumber spectral slopes observed in the tropics by satellite altimetry are examined in the tropical Pacific. The tropical dynamics are first investigated with a 1/12 degrees global model. The equatorial region from 10 degrees N to 10 degrees S is dominated by tropical instability waves with a peak of energy at 1000 km wavelength, strong anisotropy, and a cascade of energy from 600 km down to smaller scales. The off-equatorial regions from 10 to 20 degrees latitude are characterized by a narrower mesoscale range, typical of midlatitudes. In the tropics, the spectral taper window and segment lengths need to be adjusted to include these larger energetic scales. The equatorial and off-equatorial regions of the 1/12 degrees model have surface kinetic energy spectra consistent with quasi-geostrophic turbulence. The balanced component of the dynamics slightly flattens the EKE spectra, but modeled SSH wavenumber spectra maintain a steep slope that does not match the observed altimetric spectra. A second analysis is based on 1/36 degrees high-frequency regional simulations in the western tropical Pacific, with and without explicit tides, where we find a strong signature of internal waves and internal tides that act to increase the smaller-scale SSH spectral energy power and flatten the SSH wavenumber spectra, in agreement with the altimetric spectra. The coherent M2 baro-clinic tide is the dominant signal at similar to 140 km wavelength. At short scales, wavenumber SSH spectra are dominated by incoherent internal tides and internal waves which extend up to 200 km in wavelength. These incoherent internal waves impact space scales observed by today's along-track altimetric SSH, and also on the future Surface Water Ocean Topography (SWOT) mission 2-D swath observations, raising the question of altimetric observability of the shorter mesoscale structures in the tropics.

[1] In February 2010, the Mertz Glacier Tongue (MGT) calved, releasing an 80 × 40 km iceberg. We have developed a high-resolution barotropic ocean model of the region to simulate the local circulation in response to tides and atmospheric forcing. We improved the coastline, grounding line position and built a new bathymetry using satellite imagery and older bathymetry data to derive the best available tidal model for the region. We compared this and other available models to seven different sea level observations available in the area and significantly improved the tidal solutions reaching a root sum square of 2.3 cm. This model was then run in different bathymetric configurations, considering the ice draft of the major icebergs B9B and C28, to simulate the circulation before, during, and after the calving event. The currents changed substantially in the neighborhood of the MGT and icebergs. The barotropic model with tidal and atmospheric forcing and the atmospheric wind fields allow us to evaluate the forces acting on the MGT. The sea surface slope force dominates the budget. Calving occurred when high tide and strong nontidal currents (due to atmospheric forcing) combined to lead to the monthly maximum forces exerted on the MGT (i.e., between 10 and 13 February 2010). While the forces are not unusually large at the calving time, the currents are largely enhanced in the rifting area. Therefore, processes related to these currents, like melting the ice melange inside the rifts, should be investigated to fully explain the final stage of the calving.

In the coastal ocean zones, satellite altimetry data processing and interpretation poses specific difficulties, due to the interaction of the radar signal with land topography, inaccuracies in some of the geophysical corrections and to the fast changes in the sea level. In order to optimize the completeness and the accuracy of the sea surface height information derived from satellite altimetry in coastal ocean areas, a dedicated post-processing software, called X-TRACK, has been developed by the Center of Topography of the Ocean and Hydrosphere in Toulouse. It is tailored for extending the use of altimetry data to coastal ocean applications and provides freely available along-track Sea Level Anomaly time series that cover today all the coastal oceans. Here, we present the improvements made in version 2016 of X-TRACK and show the gain in near-coastal data accuracy using in situ tide gauge observations. The correlations between altimeter and tide gauge sea level anomalies are higher (by 15% in average) compared with the previous version of X-TRACK. Three examples of applications are shown. The recent evolutions done in the X-TRACK processing result in an improved observation of the seasonal variations of the boundary circulation in the Bay of Biscay. Along Western Africa, sea-level variations derived from X-TRACK data are observed closer to land (5 km) compared to AVISO (10 km), and the sea-level statistics are more robust due to the larger and more stable data availability. Along-track empirical tidal constants derived from X-TRACK Sea Level Anomaly time series are also used to validate tidal models. By improving the altimetric data accuracy in coastal areas, we extend the field of marine applications. Fil: Birol, F.. Universite de Toulouse; Francia. Centre National de la Recherche Scientifique; Francia Fil: Fuller, N.. Universite de Toulouse; Francia. Centre National de la Recherche Scientifique; Francia Fil: Lyard, F.. Universite de Toulouse; Francia. Centre National de la Recherche Scientifique; Francia Fil: Cancet, M.. Noveltis; Francia Fil: Niño, F.. Universite de Toulouse; Francia. Centre National de la Recherche Scientifique; Francia Fil: Delebecque, C.. Universite de Toulouse; Francia. Centre National de la Recherche Scientifique; Francia Fil: Fleury, S.. Universite de Toulouse; Francia. Centre National de la Recherche Scientifique; Francia Fil: Toublanc, F.. Universite de Toulouse; Francia. Centre National de la Recherche Scientifique; Francia Fil: Melet, A.. Universite de Toulouse; Francia. Centre National de la Recherche Scientifique; Francia Fil: Saraceno, Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Ciencias de la Atmósfera y los Océanos; Argentina Fil: Léger, F.. Universite de Toulouse; Francia. Centre National de la Recherche Scientifique; Francia

(IF 1.34; Q2); International audience; This work was supported by the National Center for Space Studies in the framework of the future mission surface water and ocean topography (SWOT). The estuarine zones with their complex hydrodynamics represent a great challenge for the future SWOT mission. The Seine estuary was selected by the SWOT Science Definition Team for the calibration/validation of the mission. Thus the aim of this study is to investigate the temporal hydrodynamic variability in the Seine estuary and the SWOT ability to reproduce this variability and hydrodynamic phenomena. For this, we used several statistical techniques and frequency analyses applied on the tide-gauge measurements of the Seine estuary and on SWOT simulated data. SWOT samples (SWOT simulated data) have been extracted synthetically from observations using the number of overpasses per repeat cycle [21 days (d)] in order to study the ability of SWOT to reproduce the time variability of the hydrodynamics. Results have demonstrated similar frequencies of multiyear, annual, and intraannual along the estuary from the Seine discharge to the Cherbourg sea level. The 11- to 22-d frequency has been only observed for estuarine and coastal time series suggesting the tide effect in these contexts. The distribution of levels has shown a high influence of tides and discharges at the downstream and the upstream, respectively. Low frequencies of water level are explained by the climate patterns of North Atlantic Oscillation with a mean range of 65%, whereas the high frequencies are associated to the periods of flooding and stormy events. Finally, simulated SWOT samples of water level show a better restitution of observations for high overpasses number. The results have shown a better restitution of hydrodynamic variability by SWOT in the river and upstream of estuary than in the downstream of estuary and coastal zone: in the estuary downstream and the coast, the annual mode is underexpressed while the 3-month (m) mode is overexpressed, which means the annual mode is underestimated and the 3-m mode is amplified by SWOT.

International audience; A regional baroclinic model forced with several tidal constituents at different frequencies is used to investigate the internal tide of the Bay of Biscay. The regional ocean model is free surface, sigma-coordinate and it is implemented in order to accurately take into account the barotropic forcing, the strong bathymetry gradients and the temperature and salinity stratifications. In a previous paper, the barotropic component of the tides was studied in details and the boundary conditions of the three-dimensional model were extracted from the atlases. In the present paper, we focus on the baroclinic component of the tides and the simulations are validated against observations from the MINT94 experiment. The observed currents and stratification are accurately reproduced by the model. The internal tide pattern is consistent with the descriptions found in the literature. Combining wavelet and principal component analysis we extract the patterns of generation and propagation of the internal tide at the semi-diurnal and quarter-diurnal frequencies. Secondary internal wave generation areas are identified over the plain. The vertical displacements of isopycnal surfaces for the M4 internal tide are found to be locally half those induced by the semi-diurnal internal tide. A sensitivity study shows the impact of using a three-dimensional initial stratification over the direction of propagation and wavelengths of the internal tides.

0278-4343; The baroclinic and barotropic properties of ocean processes vary on many scales. These scales are determined by various factors such as the variations in coastline and bottom topography, the forcing meteorology, the latitudinal dependence of the Coriolis force, and the Rossby radius of deformation among others. In this paper we attempt to qualify and quantify scales of these processes, with particular attention to the horizontal resolution necessary to accurately reproduce physical processes in numerical ocean models. We also discuss approaches taken in nesting or down-scaling from global /basin- scale models to regional-scale or shelf-scale models. Finally we offer comments on how vertical resolution affects the representation of stratification in these numerical models. (c) 2007 Elsevier Ltd. All rights reserved.

International audience; We have analyzed data from nine superconducting gravimeters in Western Europe and detected the contribution of non-linear ocean tides in the quarter-diurnal and sixth-diurnal frequency bands. Despite their small amplitudes, a few nanogals (10-11 m s-2), we have compared the tidal loading observations with the loading effects inferred from several non-linear ocean tide models over the North-West European continental shelf and found that they are coherent with the recent models. We also confirmed our results with tide gauge data and Topex/Poseidon altimetric data. We have also shown that the differences between the ocean tidal models are significantly larger than the accuracy of recent superconducting gravimeters. Therefore, we suggest that gravity measurements can be used as an independent validation tool for non-linear ocean tidal models, complementary to tide gauge and bottom pressure records.

Absolute calibration of sea level measurements collected from space-borne radar altimeters is usually performed with respect to collocated sea level in situ records from tide gauges or GPS buoys (Menard et al. 1994; Haines et al. 1996; Bonnefond et al. 2003; Haines et al. 2003; Schum et al. 2003; Watson et al. 2003; Watson et al. 2004). Such a method allows regular and long-term control of altimetric systems with independent records. However, this approach is based on a single, geographically dependent point. In order to obtain more significant and accurate bias and drift estimates, there is a strong interest in multiplying the number of calibration opportunities. This article describes a method, called the “offshore method” that was developed to extend the single-point approach to a wider regional scale. The principle is to compare altimeter and tide gauge sea level data not only at the point of closest approach of an overflying pass, but also at distant points along adjacent satellite passes. However, c...

Time series of sea level heights have been collected at different stations along the Cameroon coast. The dataset covers a period ranging from 2007 to 2012. Tide data measured by float type recorders have been digitalized and quality-controlled with tools developed at Laboratoire d’Etudes Geophysique et Oceanographie Spatiale (LEGOS). Short gaps in the data have been interpolated while large gaps were not. Tide constituents were retrieved through harmonic analysis using 123 waves having a period ranging from long ones to eighth-diurnal ones. The reconstructed signal is used to assess the quality of both the data and the analysis and the erroneous records were examined and corrected. The effect of the hourly averaging of the raw data on the quality of the analysis is also investigated. The tide constituents having the largest amplitudes are, as expected, the semi-diurnal, diurnal, fourth-diurnal and long term constituents. The major components of semi-diurnal waves are the M2 and S2 tides. The M2 tide height ranges between 0.5 and 0.85 m. The maximum height is found at Cameroon estuary and the minimum at the Kribi station located in the South coast. The S2 constituent varies similarly as the M2 constituent. Its amplitude ranges between 0.18 and 0.52 m. The lowest S2 amplitude occurs also at Kribi station. In the Dibamba estuary the spectrum shows a larger number of significant semi-diurnal and fourth-diurnal waves than other zones. Concerning diurnal waves, the dominant one is the K1 tide and its amplitude is homogeneous along the coast. The influence of the long-term components is the strongest in the Cameroon estuary due to important fluctuations of the rivers run-off.

International audience; An improved version of the global hydrodynamic tide solutions [finite element solutions (FESs) FES94, FES95.2.1, and FES98] has been developed, implemented, and validated. The new model is based on the resolution of the tidal barotropic equations on a global finite element grid without any open boundary condition, which leads to solutions independent of in situ data (no open boundary conditions and no assimilation). The accuracy of these "free" solutions is improved by assimilating tide gauge and TOPEX/Poseidon (T/P) altimeter information through a representer assimilation method. This leads to the FES99 version of this model. For the eight main constituents of the tidal spectrum (M2, S2, N2, K2, 2N2, K1, O1, and Q1), about 700 tide gauges and 687 T/P altimetric measurements are assimilated. An original algorithm is developed to calculate the tidal harmonic constituents at crossover points of the T/P altimeter database. Additional work is performed for the S2 wave by reconsidering the inverse barometer correction. To complete the spectrum, 19 minor constituents have been added by admittance. The accuracy of FES99 is evaluated against the former FESs. First, it is compared to two tide gauge datasets: ST95 (95 open-ocean measurements) and ST739 (739 coastal measurements). For ST95, the root-sum square of the differences between observations and solutions is reduced from 2.8 (FES95.2.1) to 2.4 cm (FES99), a gain of 17% in overall accuracy. Second, the variance of the sea surface variability is calculated and compared for FES95.2.1, FES98, and FES99 at the T/P and the European Remote Sensing Satellite (ERS-2) crossover data points. FES99 performed best, with a residual standard deviation for the independent ERS-2 dataset of 13.5 cm (15.2 cm for FES95.2.1). Third, tidal predictions are implemented for the FESs to provide along-track estimates of the sea surface variability for T/P and ERS-2. Compared to ERS-2, FES99 residuals are 11.8 cm (12.4 cm for FES95.2.1). All the accuracy tests show that FES99 is a significant improvement compared to former FESs both in the deep ocean and along coasts.

Rapid sea level signals are poorly resolved, or “aliased,” by the TOPEX/Poseidon altimeter, due to its ∼10-day repeat cycle (Nyquist period TN ∼ 20 days). To assess the potential for temporal aliasing in the altimeter data, the authors analyze hourly sea level records from a set of 110 island and coastal tide gauges. Time series are detided to focus on nontidal effects. Large variance is found at periods

A new sea level observation network initiated by the World Ocean Circulation Experiment (WOCE) program is delivering hourly data from about 150 ocean stations worldwide. A complete analysis of these data was performed using a least squares method allowing better accuracy over time series virtually unlimited in time (up to 13 yr in this case). In addition to the classical tidal harmonic constants, the power density spectrum of the detided signal was computed. The 95% confidence intervals of the results of the analysis have been systematically estimated. The numerical and statistical methods applied to produce these numbers are presented for three stations as an illustration. One example of application of this new dataset and its error bars is the selection of a tidal constant set, which is useful for validating and comparing the long-period tide models. This selection is performed by eliminating stations where the oceanic continuum spectrum magnitude (around a given tidal frequency) is more than 25% of the corresponding tidal peak amplitude. This study intends to lead to a better exploitation of sea level observations, which contain highly valuable information in the tidal and nontidal domains. The authors conclude that the WOCE Sea Level network must be maintained, in particular for a combined use with the present and future satellite altimetry missions. Thus, the aim of this paper is to present a new analysis of the in situ sea level observations acquired within the WOCE program with a particular emphasis given to the precise determination of the tidal harmonic constants.

For many years the ocean tide models of Schwiderski (1980) were the standards used by the Earth tide community to interpret deviations of observed Earth tides from predictions on the basis of earth models constructed by seismologists. Recently, the TOPEX/POSEIDON altimeter mission provided new and improved information on pelagic ocean tides, which led several research groups to generate new models of the major oceanic tides. This in turn renewed our own interest in the observations of long-period lunar tides at the geographic South Pole that were reported many years ago with an attempt to interpret the deviation from predictions using the Schwiderski models. We used four different models of the fortnightly (Mf) and monthly (Mm) ocean tides to calculate their attraction and loading effects at the South Pole and compared the results with the observed gravity tides. In our earlier interpretation we did not realize that for long-period ocean tides the so-called ‘Greenwich’ phase does not refer to the phase of these tides at the latitude of Greenwich, but to the phase at the equator. This resulted in a mistake in the relative phases of Earth tide and ocean effect at the South Pole. For Mf we now find that all models predict the phase lead of the observed versus theoretical tides within the formal uncertainties; however, the amplitude is still underpredicted by 1.5–2 per cent. This could be due to several reasons: instrument calibration, errors in the body and/or ocean tide models, relaxation of the Earth's elastic properties, and the huge ice sheet of Antarctica. These possibilities are discussed. For the Mm tide the observed amplitude is well predicted within error; however, the uncertainties in the measurements are rather large.