Comment on os-2022-8

Optimal interpolation method is applied to Geosat altimetry data both to remove orbit error and to separate temporal mean sea surface dynamic topography (SSDT) from temporal fluctuations around the mean. Loss of long-wavelength oceanic signals at orbit error reduction procedure is smaller in this method than that in conventional collinear methods, but the areal average height over the study domain is still removed as the orbit error. The fluctuation SSDT is quantitatively evaluated by sea level data from tide gauge stations at Japanese islands. The correlation coefficient of the two sea-level variations is 0.83 when the loss of the areal average is compensated by the seasonal variation of the areal average height determined from the climatological monthly-mean SSDT. In addition, the improvement of the geoid model by combined use of Seasat altimetry data and hydrographic data is validated through the estimated temporal mean SSDT. In a local area where hydrographic data contemporary with the Seasat mission exist, the geoid model has been significantly improved so that the absolute SSDT can be determined from combination of the altimetry data and geoid model; the absolute SSDT describes the onset event of a quasi-stationary large meander of the Kuroshio south of Japan very well. Outside this local area, however, errors of several tens of centimeters still remain in the improved geoid model.

<p>corresponding author: N.Flokos</p><p>flksnik@gmail.com</p><p>ABSTRACT</p><p>Sea level change is one of the key indicators of climate change with numerous effects such as flooding, erosion of beaches, salt intrusion.  The detailed global picture of sea level and the monitoring of its spatial-temporal changes is performed by Satellite Altimetry (SA). Nowadays, SA data compare well with measurements from the global tide gauge network, but the aim of 0.3 mm/year accuracy in the altimeter derived rate of global mean sea level rise is still not fully met. </p><p>Whilst the precise determination of global and regional sea level rise from SA data is promising, there is however an observational gap in our knowledge regarding the coastal zone. While Tide Gauges (TG) are usually located at the coast, therefore providing coastal sea level measurements, altimeters have difficulties there. Filling this gap becomes important when considering that the impact of sea level rise can be devastating on the coast with effects on society and ecosystems. This makes it even more significant knowing that there are many stretches of the world’s coast that still do not possess in situ level measuring devices.  </p><p>This work aims to discuss the available data and methods that link the SA measurements of sea level rise with TG measurements. Whilst there is rich literature on relevant applications, it is important to have a clear and concise methodology on this.</p><p>Tide gauge data</p><p>Several post processing steps need to be applied to the raw TG data to enrich the raw Sea Surface Heights (SSH) values and make them comparable with SA data. There are several geophysical corrections, such as pressure and wind effects, which can be applied to TG data in order to deduce  Sea Level (SL) and be consistent with altimeter data. High frequency atmospheric effects on TG data are corrected using the Dynamic Atmospheric Correction (DAC) provided by AVISO. One other large uncertainty is the vertical stability of the TG benchmark over time. TG data must be corrected for the Vertical Land Motion (VLM) to enable the comparison of two sea level measurements (TG and SA) and their later integration within the surfaces of the absolute sea heights. The main VLM dataset can be obtained from SONEL database (SONEL 2016) which provides crustal velocities from the continuous GNSS measurements at sites collocated to the TG.</p><p>Satellite altimetry data</p><p>Whilst Satellite Altimetry over the open ocean is a mature discipline, global altimetry data collected over the coastal ocean remain still largely unexploited. This is because of intrinsic difficulties in the corrections and issues of land contamination in the footprint that have so far resulted in systematic flagging and rejection of these data. In this work, the relevant methodology to overcome these problems and extend the capabilities of current and future altimeters to the coastal zone (coastal altimetry) will be discussed and a number of coastal altimetry data sets will be used (eg SARvatore, X-TRACK, RADS etc). Finally, a practical example using real data sets over the Aegean Sea will be presented. </p><p> </p><p> </p>

Abstract. Sea-level variations in coastal areas can differ significantly from those in the nearby open ocean. Monitoring coastal sea-level variations is therefore crucial to understand how climate variability can affect the densely populated coastal regions of the globe. In this paper, we study the sea-level variability along the coast of Norway by means of in situ records, satellite altimetry data, and a network of eight hydrographic stations over a period spanning 16 years (from 2003 to 2018). At first, we evaluate the performance of the ALES-reprocessed coastal altimetry dataset (1 Hz posting rate) by comparing it with the sea-level anomaly from tide gauges over a range of timescales, which include the long-term trend, the annual cycle, and the detrended and deseasoned sea-level anomaly. We find that coastal altimetry and conventional altimetry products perform similarly along the Norwegian coast. However, the agreement with tide gauges in terms of trends is on average 6 % better when we use the ALES coastal altimetry data. We later assess the steric contribution to the sea level along the Norwegian coast. While longer time series are necessary to evaluate the steric contribution to the sea-level trends, we find that the sea-level annual cycle is more affected by variations in temperature than in salinity and that both temperature and salinity give a comparable contribution to the detrended and deseasoned sea-level variability along the entire Norwegian coast. A conclusion from our study is that coastal regions poorly covered by tide gauges can benefit from our satellite-based approach to study and monitor sea-level change and variability.

Sea level and surface current variability in the Gulf of St Lawrence have been investigated primarily using seven years of TOPEX/Poseidon altimeter data. An orthogonal response analysis is used to derive an annual cycle from 1-s altimetric data along satellite ground tracks, while simultaneously removing aliased residual tides and dynamic signals at alias tide frequencies. An examination of tidal-frequency variability points to the need for a better tide model for detiding altimetric data in order to study shorter (than seasonal) period processes in the Gulf of St Lawrence. Annual sea level amplitudes and phase fields are constructed from the along-track analysis results using a linear interpolation procedure. The altimetric annual harmonic has a magnitude of 2-5 cm in amplitude and is highest in fall. The altimetric sea level results agree well with independent tide-gauge data at coastal stations and can be accounted for mainly by steric height. Geostrophic surface current anomalies derived from the altimetric annual sea level anomalies are then discussed in conjunction with numerical solutions from a regional hydrodynamic model. Interannual sea level change in the Gulf of St Lawrence is also investigated from both altimetry and tide-gauge data, indicating a prominent gulf-wide sea level drop around 1997, with exact timing dependent on location. The interannual sea level variability is thought to be primarily associated with the Labrador Current transport variability (via both the Strait of Belle Isle and Cabot Strait) and the south-north fluctuation of the Gulf Stream position (via Cabot Strait).

Internal waves generated by the interaction of the surface tides with topography are known to propagate long distances and lead to observable effects such as sea level variability, ocean currents, and mixing. In an effort to describe and predict these waves, the present work is concerned with using geographically distributed data from satellite altimeters and drifting buoys to estimate and map the baroclinic sea level associated with the M2, S2, N2, K1, and O1 tides. A new mapping methodology is developed, based on a mixed L1/L2-norm optimization, and compared with previously developed methods for tidal estimation from altimeter data. The altimeter and drifter data are considered separately in their roles for estimating tides and for cross-validating estimates obtained with independent data. Estimates obtained from altimetry and drifter data are found to agree remarkably well in regions where the drifter trajectories are spatially dense; however, heterogeneity of the drifter trajectories is a disadvantage when they are considered alone for tidal estimation. When the different data types are combined by using geodetic mission altimetry to cross validate estimates obtained with either exact-repeat altimetry or drifter data, and subsequently averaging the latter estimates, the estimates significantly improve on the previously published HRET8.1 model, as measured by their utility for predicting sea level and surface currents in the open ocean. The methodology has been applied to estimate the annual modulations of M2, which are found to have much smaller amplitudes compared to those reported in HRET8.1, and suggest that the latter estimates of these tides were not reliable. Significance Statement The mechanical and thermodynamic forcing of the ocean occurs primarily at very large scales associated with the gravitational perturbations of the sun and moon (tides), atmospheric wind stress, and solar insolation, but the frictional forces within the ocean act on very small scales. This research addresses the question of how the large-scale tidal forcing is transformed into the smaller-scale motion capable of being influenced by friction. The results show where internal waves are generated and how they transport energy across ocean basins to eventually be dissipated by friction. The results are useful to scientists interested in mapping the flows of mechanical energy in the ocean and predicting their influences on marine life, ocean temperature, and ocean currents.

This study assesses the variability of coastal extreme sea levels globally by utilizing nearly three decades of along-track, multi-mission satellite altimetry data. An altimetry-based global coastal database of the non-tidal residual sea level component has been produced. The climate variability of extremes is modeled through a parametric, non-stationary statistical model. This model captures intra-annual, inter-annual and long-term variations in non-tidal residual return levels. Comparisons with tide gauge data demonstrate the ability of altimetry data to capture the variability of coastal extreme sea levels. Our findings reveal a greater complexity in the monthly variability patterns of non-tidal residual extremes in tropical latitudes, often exhibiting multiple storm periods, contrasting with coasts in extratropical latitudes, which are mostly controlled by a winter–summer pattern. This study also highlights the significant influence of established climate circulation patterns on sea level extremes. The positive phase of the Arctic Oscillation pattern leads to increases of over 25% in non-tidal residual return levels in Northwestern Europe with respect to a neutral phase. Furthermore, return levels in the western coast of Central America could be 50% higher during El Niño compared to La Niña. Our results show a robust increasing trend in non-tidal residual return levels along most global coastlines. A comparative analysis shows that variations during the 1995–2020 period were primarily driven by intra-annual variations.

Sea-level variability in the South China Sea was investigated based on satellite altimetry, tide-gauge data, and temperature and salinity climatology. The altimetric sea-level results clearly reveal three distinct amphidromes associated with the annual cycle. The annual sea level is higher in fall/winter in the coast and shelf region and lower in summer/fall in the central sea, agreeing well with independent tide-gauge data. Averaged over the deep basin (bottom depth > 2,000 m), the annual cycle can be approximately accounted for by the steric height relative to 700 db. Significant interannual sea-level change is observed from altimetry and tide-gauge data. The interannual and longer-term sea-level variability in the altimetric data is negatively correlated (significant at the 95% confidence level) with the El Nino - Southern Oscillation (ENSO), attributed in part to the steric height change. The altimetric sea-level rise rate is 1.0 cm/year for the period from 1993 to 2001, which is consistent with the rate derived from coastal tide-gauge data and approximately accountable for by the steric height calculated relative to 700 db. The tide-gauge sea-level (steric height) rise rate of 1.05 (0.9) cm/year from 1993 to 2001 is much larger than that of 0.22 (0.12) cm/year for the period from 1979 to 2001, implying the sensitivity to the length of data as a result of the decadal variability. Potential roles of the ENSO in the interannual and longer-term sea-level variability are discussed in terms of regional manifestations such as the ocean temperature and salinity.

The global mean sea surface model WHU2013

Extensive validation of altimetry measurements is of fundamental importance prior to their scientific or commercial applications. In the present study, new CryoSat-2, HY-2A, SARAL/AltiKa, Jason-2 measured Sea Surface Height (SSH) obtained from RADS (Radar Altimeter Database System) and DUACS (Data Unification and Altimeter Combination System) are cross-validated and compared with tide gauge data in China Seas. The CryoSat-2 SAR (Synthetic Aperture Radar) and LRM (Low Repetition Mode) modes are available in the Bohai Sea/Yellow Sea and East China Sea, respectively, which enables the initial evaluation of the performance of the new satellite altimetry over the regions. The results demonstrate high consistency between the new altimetry missions with a root mean square difference of 3–5 cm in SSH. Coherent SSH time series are observed from the new satellite altimetry measurements and tide gauge data. The findings are important for continuous mapping the sea level variations based on 23 years of altimetry measurements in China Seas.

As a leading indicator of global climate change, contemporary global mean sea level (GMSL) change is mainly driven by thermosteric (thermal expansion) and barystatic (ocean mass increase) contributions. GMSL change has been continuously measured by satellite altimetry since 1993, while thermosteric sea level change can be inferred from in-situ hydrographic measurements dating back to the 1970s. However, direct observations of barystatic sea level change were generally lacking until the launch of the Gravity Recovery and Climate Experiment (GRACE) in 2002. In the absence of GRACE, barystatic sea level estimation relies primarily on the so-called mass budget approach by summing individual surface mass change estimates (e.g. ice sheets, glaciers, and terrestrial water storage) obtained from different remote sensing or geophysical modelling techniques, providing an indirect observation due to the lack of global constraints. In this study, we use low-degree gravity fields obtained from satellite laser ranging (SLR), a traditional space geodetic technique over decades, to directly estimate barystatic sea level changes since 1993. To this end, we effectively address the issues of signal leakage and missing geocenter motion for SLR gravity fields using the forward modelling technique. Our SLR-based barystatic sea level estimates allow the direct observation-based assessment of the GMSL budget over the satellite altimetry era, and also provide an independent dataset for cross-validation and gap-filling between GRACE and its successor GRACE-FO. Using reprocessed altimetry data from NASA's Goddard Space Flight Center and updated thermosteric sea level ensembles, we reconcile the GMSL rise budget from 1993 to 2022. Our results show that the sum of thermosteric and SLR-based barystatic contributions (3.16 ± 0.64 mm/yr) agrees well with the altimetry-observed GMSL rate (3.22 ± 0.28 mm/yr), suggesting that the GMSL budget can be closed within uncertainties over the last three decades. Nevertheless, we observe increased budget residuals when using different altimetry datasets, especially in recent years, highlighting the ongoing challenges in accurately observing GMSL change and robustly closing the GMSL budget.

The information of sea level rise was needed in the Indonesia as archipelago country to management risk and development coastal area. This research study took in West Sumatra waters, because the majority people have lived in coastal area and some areas is located below 100 m above Mean Sea Level (MSL). The sea level data was taken from multi-satellite altimetry, they are Topex/Poseidon, Jason-1, and Jason-2. The period of data started from 1993 until 2015.Preliminary data processing of satellite altimetry was done by global test and post-processing of satellite altimetry data. The sea level rise analysis done by linear regression methods. Linear regression formula of sea level rise in West Sumatra Waters during the period was y = 1.586 + 0.0000113x. The change of sea level during period 1993 until 2015 was 3.394 cm with mean sea level rise value was 1.35 mm/year

Regional sea level changes occur at different time scales. Global warming of the oceans, glacial and polar ice melting and meteorological or hydrological factors are major contributors to long-term sea level rise. In the recent years, a lot of attention has been paid to research concerning sea level change and seasonal fluctuations. The main objective of this paper was to determine the seasonal variability in the Baltic Sea level using satellite altimetry data for the period 1 January 2010 – 31 December 2014. The ANOVA analysis of variance was used in the research in order to estimate seasonal fluctuations. This study focused on investigate the monthly and annual amplitude in sea level anomalies over a given time period. The results from research showed that the amplitudes of fluctuations are the highest in winter and the smallest in summer in three analyzed points of the Baltic Sea. The results can bring valuable information about ongoing aspects in sea level changes, as a way of tracking climate change.

Sea level variability off East China has been investigated based primarily on 10 years of Ocean Topography Experiment (TOPEX)/Poseidon altimetry data. The altimetric annual harmonic has a magnitude of 10 to 30 cm in amplitude and is highest in summer, agreeing well with independent tide-gauge data. After the inverse barometer effect is removed, the annual sea level cycle can be approximately accounted for by the steric height variation. Significant interannual sea level change was also observed from altimetry and tide-gauge data, with a range of ∼10 cm. The interannual and longer-term sea level variability in the altimetric data are negatively correlated (significant at the 95% confidence level) with the Pacific decadal oscillation (PDO), attributed in part to steric height change. The altimetric sea level rise rate is 0.64 cm yr−1 for the period from 1992 to 2002, consistent with the tide-gauge rate of 0.6 cm yr−1. These values are much larger than the rate of 0.24 cm yr−1 observed at the same tide gauges but for the period from 1980 to 2002, implying the sensitivity to the length of data as a result of the decadal variability. The potential role of the PDO in the interannual and longer-term sea level variability is discussed in terms of regional manifestations such as the ocean temperature and salinity and the Kuroshio transport.

The increasing adoption of AI-based approaches in Earth system sciences has led to breakthroughs in modeling and forecasting, exemplified by state-of-the-art performance of neural weather forecasting systems [Bi et al., 2023, Lam et al., 2022]. In oceanography, Deep Learning techniques show significant promise for advancing ocean state modeling by combining both modeled and observational ocean datasets [Febvre et al., 2023, Martin et al., 2023, Wang et al., 2024]. However, in the context of ocean forecasting, the deployment of neural forecasting approaches faces challenges such as sparse observational data and uncertainties in existing datasets. Despite advances in ocean observation systems, the ocean remains under-sampled, complicating the training of robust forecasting models [Wang et al., 2024].This study presents the application of the 4DVarNet framework [Fablet et al., 2021, Fablet et al., 2023] in forecast mode, specifically for 7-day sea surface height (SSH) prediction. 4DVarNet employs an end-to-end Deep Learning strategy to forecast future SSH state from sparse satellite observational data. Using a variational data assimilation formulation, the framework combines a UNet with a convolutional LSTM to iteratively reconstruct future ocean state. The model was trained on synthetic altimetry observations sampled from the GLORYS12 operational reanalysis (2010–2019) and evaluated on independent Nadir altimetry tracks from 2023.The results demonstrate that 4DVarNet outperforms traditional state-of-the-art operational forecasting system GLO12 [Lellouche et al., 2013], achieving a normalized RMSE (nRMSE) score of 0.92 for lead time 0 compared to 0.86 for the baseline GLO12. The model shows superior accuracy across all forecast lead times, highlighting its potential advantage in operational oceanography. The framework improves the accuracy of the SSH forecast by effectively using gappy satellite altimetry data. This demonstrates a particular interest of applying the proposed method to other data sources, such as the SWOT altimetry mission, but also of implementing alternative learning strategies, including training on synthetic datasets and fine-tuning with real-world altimetry observations.In addition to the improved predictive performance compared to the state-of-the-art operational forecast system, this study establishes a standardized workflow for data processing, training, and evaluation, inspired by OceanBench framework [Johnson et al., 2023].This research highlights the potential of the 4DVarNet framework for short-term neural ocean forecasting. The proposed method efficiently handles sparse altimetry data and achieves significant performance in predicting 7-days gap-free SSH state at global scale, improving the accuracy by almost 65% in average compared to the baseline GLO12. Future studies should focus on improving the model by incorporating additional data sources, evaluating the impact of input and output resolutions and associated learning strategies (eg. patching), and exploring its applicability to additional variables describing ocean state other than the SSH.

The altimetric data from the first 2.5‐year Geosat Exact Repeat Mission were used to estimate the mean sea surface height (SSH) field in the region of the Gulf Stream and its recirculation gyres. Assuming the instantaneous surface velocity field is composed of an eastward flowing jet and two westward recirculating flows, we used the time‐varying surface data from the altimeter to determine the shape of the along‐track mean SSH profiles and the historical hydrographic data to constrain the net SSH difference across the Gulf Stream system. The two‐dimensional mean SSH field was determined by objectively mapping the mean height profiles along the ascending and descending tracks. The SSH jump across the mean Gulf Stream has a maximum of 1.15m around 65°W and drops to an almost constant 0.9m downstream of the New England Seamount Chain (NESC). While the SSH jump associated with the mean northern recirculating flow is mostly uniform, we found that the Gulf Stream's southern recirculation has two local gyres that are separated by the NESC. An attempt was then made to estimate the mean deep circulation in this region by comparing the mean SSH field derived from the altimetry data and the surface dynamic height field based on the historical hydrographic data. Despite the large uncertainties, the mean deep flow pattern thus estimated agrees favorably with the overall circulation pattern from the long‐term current meter observations. Like the well‐defined northern recirculation gyre, we found that a continuous southward flow exists along 57.5°W, which follows closely along the deep layer potential vorticity contours. To the south of the Gulf Stream, the deep circulation consists of two separated recirculation gyres; the recirculation gyre to the east of the NESC appears to be trapped around the Corner Rise.