Satellite Altimetry Research Articles

Differences among the total electron content derived by radio occultation, global ionospheric maps and satellite altimetry

In recent years, significant progress has been in ionospheric modeling research through data ingestion and data assimilation from a variety of sources, including ground-based global navigation satellite systems, space-based radio occultation and satellite altimetry (SA). Given the diverse observing geometries, vertical data coverages and intermission biases among different measurements, it is imperative to evaluate their absolute accuracies and estimate systematic biases to determine reasonable weights and error covariances when constructing ionospheric models. This study specifically investigates the disparities among the vertical total electron content (VTEC) derived from SA data of the Jason and Sentinel missions, the integrated VTEC from the Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) and global ionospheric maps (GIMs). To mitigate the systematic bias resulting from differences in satellite altitudes, the vertical ranges of various VTECs are mapped to a standardized height. The results indicate that the intermission bias of SA-derived VTEC remains relatively stable, with Jason-1 serving as a benchmark for mapping other datasets. The mean bias between COSMIC and SA-derived VTEC is minimal, suggesting good agreement between these two space-based techniques. However, COSMIC and GIM VTEC exhibit remarkable seasonal discrepancies, influenced by the solar activity variations. Moreover, GIMs demonstrate noticeable hemispheric asymmetry and a degradation in accuracy ranging from 0.7 to 1.7 TECU in the ocean-dominant Southern Hemisphere. While space-based observations effectively illustrate phenomena such as the Weddell Sea anomaly and longitudinal ionospheric characteristics, GIMs tend to exhibit a more pronounced mid-latitude electron density enhancement structure.

Evaluating D-InSAR performance to detect small water level fluctuations in two small lakes in Sweden

Monitoring lake water level fluctuations is critical for managing water resources, predicting the impacts of climatic change, and preserving ecosystem services lakes provide. However, traditional gauging stations are insufficient to monitor all lakes worldwide due to the large number of existing lakes, the challenges of installation and maintenance, and the remote locations of some. Although satellite altimetry is an alternative for measuring water levels, it cannot monitor small lakes effectively. This study evaluates the potential of Differential Interferometric Synthetic Aperture Radar (D-InSAR) for tracking minor water level changes in small lakes, a method more typically used in wetland studies. We investigate two Swedish lakes using Sentinel-1A and Sentinel-1B data from 2019, generating six-day interferograms and filtering out those with in situ water level changes exceeding one phase cycle. Our results show that D-InSAR can detect small water level changes with Lin’s correlations up to 0.63 and 0.89 and RMSE values of approximately 9 and 4 mm, respectively. These results evidence the potential of future L-band SAR missions with larger wavelengths, such as the NASA-ISRO SAR (NISAR) of the National Aeronautics and Space Administration (NASA) and the Indian Space Research Organisation (ISRO), to track water level changes in lakes and aid water tracking missions such as the SWOT (Surface Water and Ocean Topography).

The performance of Tiangong-2 InIRA in gravity anomaly recovery from fused conventional nadir-observing altimeter data

Satellite altimetry has emerged as the primary data source for deriving marine gravity, owing to advancements in satellite altimetry technologies. The Tiangong-2 interferometric imaging radar altimeter (TG2 InIRA) is a new generation wide-swath altimeter (WSA) launched by China on 15 September 2016. TG2 InIRA employs a short-baseline interferometry measurement method at a small incidence angle, thereby enabling the precise measurement of wide-swath sea surface heights (SSHs). The present study demonstrates the efficacy of utilizing data from the TG2 InIRA in conjunction with data from the CryoSat-2 (CS2) satellite to recover marine gravity anomalies. In the Northwest Pacific region (15°N ∼ 25°N, 140°E ∼ 150°E), the TG2 InIRA data were filtered to a 2 km × 2 km grid and any anomalous values were excluded using a mean sea surface model. Deflections of the vertical (DOVs) were calculated using the remove-restore technique, and the inverse Vening-Meinesz formula was applied to invert the gravity anomaly. A power spectral density analysis was conducted to assess variations in gravity anomalies at ship locations in the frequency domain. The results, based on the SIO V31.1 (DOV) model, indicate that the gridded vertical deflections derived from CS2 and TG2 InIRA data achieve more balanced accuracy in the east–west and north–south directions. The integration of TG2 InIRA and CS2 data yielded gravity results exhibiting a root mean square (RMS) of 0.519 mGal lower than those derived from TG2 InIRA data alone, and 0.034 mGal lower than those derived from CS2 data. These findings were derived from shipborne gravity data. Furthermore, the inversion of gravity anomalies from TG2 InIRA demonstrated an enhanced capability in the reduction of high-frequency gravity noise.

Seasonal Patterns, Inter‐Annual Variability, and Long‐Term Trends of Mean Sea Level Along the Western Iberian Coast and the North Atlantic Islands

AbstractSea level rise is challenging for coastal communities and land management decision makers. Understanding the patterns of regional variations at different temporal and spatial scales is key to implement adaptation plans that mitigate the local impacts of sea level rise. In this study, in situ observations from 14 tide gauges were complemented with satellite altimetry data to assess seasonality, multidecadal variability and long‐term trends in mean sea level around the Western Iberian Coast (WIC) and the Portuguese archipelagos (Azores and Madeira). Results show varying spatial seasonal patterns between regions, with minimum (maximum) sea level observed in April (September) at the islands and minimum (maximum) observed in July (November) at the WIC. The influence of coastal upwelling on the seasonal mean sea level variations was detected over mainland. Although the influence of atmospheric patterns was observed on sea level inter‐annual variability, the Atlantic Multidecadal Oscillation (AMO) showed a greater correlation with the sea level inter‐decadal patterns. Finally, the trend analysis confirmed widespread sea level rise along the mainland and around the islands, which has intensified in recent decades. The regions of La Coruña and Cascais showed trends that were similar to the global average sea level rise since 1993, but the mainland regional average pointed to lower rates of rise (2.00 ± 0.06 mm/year). This work reinforces the need for long‐term monitoring networks of sea level, ensuring the vertical stability of instruments and platforms. The implementation of regional adaptation plans to sea level rise is deeply dependent on high quality information.

Local Gravity and Geoid Improvements around the Gavdos Satellite Altimetry Cal/Val Site

The isle of Gavdos, and its wider area, is one of the few places worldwide where the calibration and validation of altimetric satellites has been carried out during the last, more than, two decades using dedicated techniques at sea and on land. The sea-surface calibration employed for the determination of the bias in the satellite altimeter’s sea-surface height relies on the use of a gravimetric geoid in collocation with data from tide gauges, permanent global navigation satellite system (GNSS) receivers, as well as meteorological and oceanographic sensors. Hence, a high-accuracy and high-resolution gravimetric geoid model in the vicinity of Gavdos and its surrounding area is of vital importance. The existence of such a geoid model resides in the availability of reliable, in terms of accuracy, and dense, in terms of spatial resolution, gravity data. The isle of Gavdos presents varying topographic characteristics with heights larger than 400 m within small spatial distances of ~7 km. The small size of the island and the significant bathymetric variations in its surrounding marine regions make the determination of the gravity field and the geoid a challenging task. Given the above, the objective of the present work was two-fold. First, to collect new land gravity data over the isle of Gavdos in order to complete the existing database and cover parts of the island where voids existed. Relative gravity campaigns have been designed to cover as homogenously as possible the entire island of Gavdos and especially areas where the topographic gradient is large. The second focus was on the determination of a high-resolution, 1′×1′, and high-accuracy gravimetric geoid for the wider Gavdos area, which will support activities on the determination of the absolute altimetric bias. The relative gravity campaigns have been designed and carried out employing a CG5 relative gravity meter along with geodetic grade GNSS receivers to determine the geodetic position of the acquired observations. Geoid determination has been based on the newly acquired and historical gravity data, GNSS/Leveling observations, and topography and bathymetry databases for the region. The modeling was based on the well-known remove–compute–restore (RCR) method, employing least-squares collocation (LSC) and fast Fourier transform (FFT) methods for the evaluation of the Stokes’ integral. Modeling of the long wavelength contribution has been based on EIGEN6c4 and XGM2019e global geopotential models (GGMs), while for the contribution of the topography, the residual terrain model correction has been employed using both the classical, space domain, and spectral approaches. From the results achieved, the final geoid model accuracy reached the ±1–3 cm level, while in terms of the absolute differences to the GNSS/Leveling data per baseline length, 28.4% of the differences were below the 1cmSij [km] level and 55.2% below the 2cmSij [km]. The latter improved drastically to 52.8% and 81.1%, respectively, after deterministic fit to GNSS/Leveling data, while in terms of the relative differences, the final geoid reaches relative uncertainties of 11.58 ppm (±1.2 cm) for baselines as short as 0–10 km, which improves to 10.63 ppm (±1.1 cm) after the fit.

“Gear-like” process between asymmetric dipole eddies from satellite altimetry

Mesoscale dipoles compose two counter-rotating mesoscale eddies. They are observed in oceans worldwide and significantly impact the biogeochemical cycle, marine ecosystems, and ocean water transport. This study investigates the evolution of asymmetric dipole eddies based on the satellite altimeter data for the period January 1993–December 2020. The coupling and decoupling of eddy dipoles impact various eddy properties. When the movement of eddies has a dipolar structure, a gentle convergence in parameters (rotational speed, amplitude, eddy kinetic energy, propagation speed, and advective nonlinearity) between the asymmetric dipole eddies is observed–this study refers to it as the “gear-like” process. Kinematic characteristics further indicate that the stronger dipole eddies generally drive the weaker ones to revolve during the “gear-like” process. The revolution direction remains consistent with the rotation direction of stronger dipole eddies. Additionally, eddy size remains relatively stable during the “gear-like” process. The composites of sea level anomaly (SLA) demonstrate that dipole eddies are compressed into a kidney-like shape along the line through their centers. This shape is confirmed by the composites of sea surface temperature anomalies, which closely correspond to the structure of SLA. These findings augment the knowledge regarding the evolution of asymmetric dipole eddies and provide a novel perspective for studying dipoles and eddy-eddy interactions.

Scalable interpolation of satellite altimetry data with probabilistic machine learning

We present GPSat; an open-source Python programming library for performing efficient interpolation of non-stationary satellite altimetry data, using scalable Gaussian process techniques. We use GPSat to generate complete maps of daily 50 km-gridded Arctic sea ice radar freeboard, and find that, relative to a previous interpolation scheme, GPSat offers a 504 × computational speedup, with less than 4 mm difference on the derived freeboards on average. We then demonstrate the scalability of GPSat through freeboard interpolation at 5 km resolution, and Sea-Level Anomalies (SLA) at the resolution of the altimeter footprint. Interpolated 5 km radar freeboards show strong agreement with airborne data (linear correlation of 0.66). Footprint-level SLA interpolation also shows improvements in predictive skill over linear regression. In this work, we suggest that GPSat could overcome the computational bottlenecks faced in many altimetry-based interpolation routines, and hence advance critical understanding of ocean and sea ice variability over short spatio-temporal scales.

Dense Water Formation Variability in the Aegean Sea from 1947 to 2023

The formation of dense water in the Aegean Sea is important as it affects the deep circulation and the hydrography of the Eastern Mediterranean Sea. In this study, the variability of dense water formation is investigated in relation to forcing mechanisms from 1947 to 2023 in the subbasins of the Aegean Sea, utilising in situ observations from various sources, which have been analysed in combination with satellite altimetry and reanalyses products. The analysis reveals that the Aegean Sea has been in a state of increased dense water formation since 2017 due to the combination of increased surface buoyancy loss and reduced Black Sea water inflow. Extremely high salinity has been recorded in the intermediate layers of the Aegean Sea since 2019. The anticyclonic circulation of the North Ionian gyre during 2017 and 2018 probably also contributed to the rapid transport of highly saline waters in the intermediate and, through dense water formation, the deep layers of the Aegean Sea in 2019. Until 2022, the dense waters formed during the peak of the Eastern Mediterranean Transient still occupied the bottom layers of some deep subbasins of the North and South Aegean; however, the 29.4 kg m−3 isopycnal in the North Aegean and the 29.3 kg m−3 isopycnal in the Southeastern Aegean have gradually deepened by 800 m, permitting the waters forming in the last ten years in the Aegean Sea to settle at ever greater depths. Temperature controls the density variability of the Cretan intermediate water up to the decadal time scale. Increased data availability since 2010 was sufficient to clarify that intrusions of dense water from the North–Central Aegean Sea contributed to the erosion of the Eastern Mediterranean transitional waters in the South Aegean Sea after 2017, as well as to raising the intermediate water masses of the South Aegean to shallower depths. The erosion of the transitional Mediterranean waters in the South Aegean Sea between 1947 and 1955 and 1973 and 1980 coincided with increased dense water formation in the North–Central Aegean Sea. During the peak of the Eastern Mediterranean Transient, the North Ionian circulation, the Black Sea water inflow, the Atlantic Multidecadal Oscillation, and the surface buoyancy fluxes favoured dense water formation in the Aegean Sea.

Modal Decomposition of Internal Tides in the Luzon Strait through Two-Dimensional Fourier Bandpass Filtering

Internal tides are pivotal dynamic processes enhancing the mixing of oceanic waters and facilitating energy transfer across various scales within the ocean. In recent years, the proliferation of satellite altimetry observations has enabled global predictions of the elevation and phase of internal tides. This study, leveraging the advanced global internal tide prediction model known as the Multivariate Inversion of Ocean Surface Topography-Internal Tide Model (MIOST-IT), employs a two-dimensional Fourier bandpass filtering approach to decompose the internal tides in the Luzon Strait, thereby addressing the east–west directional blind zones inherent in along-track satellite altimetry-based modal decomposition. To further elucidate the propagation trajectories of individual tidal modes in different directions, we introduce the directional Fourier filter method to characterize the spatial distribution features of each modal internal tide in the vicinity of the Luzon Strait. This work significantly enhances the accuracy and reliability of extracting parameters for distinct modal internal tides, furnishing a scientific basis for subsequent studies on internal tide dynamics and model refinement.

Lake gravity anomalies from ICESat-2 laser altimetry and geodetic radar altimetry

In the current most accepted global geopotential model, EGM2008, there are often data gaps in the source data used to compute the model over inland water. As a result, EGM2008 may be less reliable over lakes. Satellite altimetry has the potential to estimate gravity anomalies and update EGM2008 over lakes. Here, we evaluate the first attempt to extract gravity anomalies from ICESat-2 laser altimetry over several medium (100–1000 km2) and large (>1000 km2) lakes and compare them with conventional radar altimetry from CryoSat-2 and SARAL to investigate the performance of ICESat-2 for gravity determination over lakes. Aerial gravimetry from the GRAV-D project over the United States are utilized as the best estimate of the gravity field over the lakes. Gravity determination from altimetry is done using Fast Fourier Techniques (FFT) within a remove-restore geoid-to-gravity approach. The resulting altimetry derived gravity anomalies are then compared to the EGM2008 geoid over each lake with respect to GRAV-D. 18 lakes with area ranging from 108 km2 to 82,220 km2 across the United States were considered. Overall, gravity determination from ICESat-2 provides more reliable estimates than the other two radar altimetry missions. For all considered lakes, the performance of ICESat-2, measured in terms of standard deviation with GRAV-D, is comparable or better than the EGM2008 field over the same lake. Lake Pend Orielle is the best performing case, in which the standard deviation of the ICESat-2 derived gravity field is 2.14 mGal and the standard deviation of the EGM2008 gravity field is 2.66 mGal with respect to the GRAV-D measurements. Over Lake Tahoe, which is surrounded by mountainous terrain, ICESat-2 performs comparably to EGM2008 and captures clear gravity signal related to the lake’s bathymetry, whereas CryoSat-2 produces very unstable results. The method presented here for deriving gravity anomalies from altimetry applied to ICESat-2 laser altimetry data produces results that validate in supplement to the GRAV-D project over medium to large lakes in the United States.

Программный комплекс обработки данных спутниковой альтиметрии космической геодезической системы «ГЕО-ИК-2»

The Central Research Institute for Machine Building JSC has created a software package for processing primary satellite altimetry data of the “GEO-IK-2” space geodetic system, adapted for high-performance computing systems. The software package performs step-by-step multi-level processing of measuring and auxiliary information with sequential recording of intermediate and final results in a database. The technology of processing level 0 data received from the spacecraft up to and including level 2 has been implemented. The article provides information about the input data used at different levels of processing, about the algorithms and functionality of the software package. In the process of debugging the software package on high-performance computing systems all the valid data of the “GEO-IK-2” space geodetic system from 2018 to 2022 were processed for the first time. The developed software package should serve as a prototype of the satellite altimetry data processing subsystem of the ground-based special complex of the promising new generation space geodetic system

“Assessment of combined wind and wave energy in European coastal waters using satellite altimetry.”

In this study, the combined wind and wave energy potential assessment is presented for various locations in European coastal waters. The objective is to investigate the feasibility of satellite altimetry-based assessments of combined wind/wave renewable energy potential on the European shelf. The study is motivated by the potential reduction in energy supply variability by combining wind and wave. The method consists of using a homogenized multi-mission altimeter database available by the European Space Agency Sea State Climate Change Initiative (Sea_State_cci) that comprises 26 years of data, from January 1991 to December 2018, that allows extending the time range and spatial coverage to estimate site wind and wave power densities. An empirical model is used to estimate the wave energy period from the altimeter Ku band significant wave height and radar backscatter coefficient required to compute the wave power density. The results show that wind/wave energy is relatively correlated in the Mediterranean but not in the North Atlantic sites studied. Thus, the Western North Atlantic sites are the most adequate places for wind and wave farms, from the point of view of combined exploitation.The different characteristics of the studied sites show some correspondence between variability and mean wave power, which is an essential input to a marine renewable energy strategy in any jurisdiction. The level of overall variability decreases with an increase in mean wave power, related to the higher power swell waves are not highly correlated with the local wind.

Atmospheric-river-induced foehn events drain glaciers on Novaya Zemlya

Recently, climate extremes have been grabbing attention as important drivers of environmental change. Here, we assemble an observational inventory of energy and mass fluxes to quantify the ice loss from glaciers on the Russian High Arctic archipelago of Novaya Zemlya. Satellite altimetry reveals that 70 ± 19% of the 149 ± 29 Gt mass loss between 2011 and 2022 occurred in just four high-melt years. We find that 71 ± 3% of the melt, including the top melt cases, are driven by extreme energy imports from atmospheric rivers. The majority of ice loss occurs on leeward slopes due to foehn winds. 45 of the 54 high-melt days (>1 Gt d−1) in 1990 to 2022 show a combination of atmospheric rivers and foehn winds. Therefore, the frequency and intensity of atmospheric rivers demand accurate representation for reliable future glacier melt projections for the Russian High Arctic.

Synchronicity of the Gulf Stream path downstream of Cape Hatteras and the region of maximum wind stress curl

The Gulf Stream, a major ocean current in the North Atlantic ocean is a key component in the global redistribution of heat and is important for marine ecosystems. Based on 27 years (1993–2019) of wind reanalysis and satellite altimetry measurements, we present observational evidence that the path of this freely meandering jet after its separation from the continental slope at Cape Hatteras, aligns with the region of maximum cyclonic vorticity of the wind stress field known as the positive vorticity pool. This synchronicity between the wind stress curl maximum region and the Gulf Stream path is observed at multiple time-scales ranging from months to decades, spanning a distance of 1500 km between 70 and 55W. The wind stress curl in the positive vorticity pool is estimated to drive persistent upward vertical velocities ranging from 5 to 17 cm day−1 over its ~ 400,000 km2 area; this upwelling may supply a steady source of deep nutrients to the Slope Sea region, and can explain as much as a quarter of estimated primary productivity there.

Trends and Innovations in Surface Water Monitoring via Satellite Altimetry: A 34-Year Bibliometric Review

Trends and Innovations in Surface Water Monitoring via Satellite Altimetry: A 34-Year Bibliometric Review

Internal-tide vertical structure and steric sea surface height signature south of New Caledonia revealed by glider observations

Abstract. In this study, we exploit autonomous underwater glider data to infer internal-tide dynamics south of New Caledonia, an internal-tide-generation hot spot in the southwestern tropical Pacific. By fitting a sinusoidal function to vertical displacements at each depth using a least-squares method, we simultaneously estimate diurnal and semidiurnal tides. Our analysis reveals regions of enhanced tidal activity, strongly dominated by the semidiurnal tide. To validate our findings, we compare the glider observations to a regional numerical simulation that includes tidal forcing. This comparison assesses the simulation's realism in representing tidal dynamics and evaluates the glider's ability to infer internal-tide signals and their signature in sea surface height (SSH). The glider observations and a pseudo glider, simulated using hourly numerical model output with identical sampling, exhibit similar amplitude and phase characteristics along the glider track. Existing discrepancies are in large part explained by tidal incoherence induced by eddy–internal-tide interactions. We infer the semidiurnal internal-tide signature in steric SSH by the integration of vertical displacements. Within the upper 1000 m, the pseudo glider captures roughly 78 % of the steric SSH total variance explained by the full water column signal. This value increases to over 90 % when projecting the pseudo glider's vertical displacements onto climatological baroclinic modes and extrapolating to full depth. Notably, the steric SSH from glider observations aligns closely with empirical estimates derived from satellite altimetry, highlighting the internal tide's predominant coherent nature during the glider's sampling.

Optimized estimation of marine deflection of the vertical from multibeam laser altimeter data of ICESat-2

SUMMARY Satellite altimetry data, with its increasing density and quality, has become the primary source for marine deflection of the vertical (DOV) and gravity anomaly modelling. Limited by orbital inclinations, the precision of the meridian component of the gridded deflection of the vertical (GDOV) calculated by traditional altimetry satellites is significantly better than that of the prime vertical component, and the excessive precision difference between these two components restricts the inversion precision of marine gravity anomaly model. The study of cross-track deflection of the vertical (CTDOV) is enabled by the multibeam synchronous observation mode of the new laser altimetry satellite, Ice, Cloud and Land Elevation Satellite-2 (ICESat-2). Based on the remove-restore method, residual geoid gradients are first calculated in this paper using three approaches: along-track (A-T), cross-track (C-T) and an integration of along-track and cross-track. Vertical deflections are then computed on a 1′ × 1′ grid using the least squares collocation (LSC) method, and the precision is verified against the SIO V32.1_DOV model. An optimized combination is proposed to address the issue of precision differences between the meridian and prime vertical components, and to enhance the precision of DOV inversion. A new DOV combination is formed by combining the meridian component from along-track deflection of the vertical (ATDOV) with the prime vertical component from cross-track deflection of the vertical (CTDOV) based on the remove-restore method. The Philippine Sea (0°–35°N, 120°–150°E) is selected as the test area to verify the feasibility of the optimized combination. The results indicate that the optimized combination of the meridian and prime vertical components achieved test precision of 2.63 and 3.33 μrad, respectively, when compared against the SIO V32.1_DOV model. The precision gap between the components is effectively narrowed by this approach, which maintains the precision of the meridian component and enhances that of the prime vertical component, thereby achieving optimal inversion precision for gravity anomalies.

Enhanced lake elevation mapping using a zone-based method

Abstract Inland lakes play a crucial role in monitoring global climate change and managing responses to extreme weather events, with lake elevation being critical for assessing their regulatory capacities. However, due to the limited temporal resolution of current altimetry satellites, obtaining high-frequency, high-precision elevation data for water bodies remains challenging. Consequently, most studies utilize elevation-area (E-A) models constructed from historical elevation and area records, integrated with area observations from high-temporal resolution optical satellites to infer precise water levels. Yet, the construction of the E-A model often assumes a uniform water level across the lake, thus overlooking potential segmentation during dry periods. To address this, our study implemented a zone-based approach, utilizing hydrological connectivity principles to ensure that elevation data within E-A models are confined to appropriate zonal regions. This method effectively minimized uncertainties by preventing errors from zonal discrepancies, significantly improving accuracy compared to traditional methods. It reduced root mean square errors (RMSE) by 0.71–1.73 m during the dry season, achieving RMSEs of 0.35, 0.64, and 0.37 m across three segments. Furthermore, this method ensures water level data are confined to specific zones, preventing the inconsistencies typically caused by averaging data across multiple stations or selecting data from varying elevations. This consistent domain definition reduces extrapolation errors during the model prediction and inversion. Moreover, the method compensates for time information losses often incurred by relying on multi-year percentile charts, thereby enabling more precise aquatic boundary delineation than traditional regional boundaries.

Multidimensional Evaluation of Altimetry Marine Gravity Models with Shipborne Gravity Data from a New Platform Marine Gravimeter

With the development of satellite altimetry technology and the application of new altimetry satellites, the accuracy and resolution of altimeter-derived gravity field models have improved over the last decades. Nowadays, they are close enough to shipborne gravimetry. In this paper, multi-source shipborne gravity data in the South China Sea were taken to evaluate the accuracies of two high-precision altimeter-derived marine gravity field models (SS V30.1, DTU17). In these shipborne gravity data, there are dozens of routes’ ship gravimetry data, obtained from the National Geophysical Data Center (NGDC); data were tracked from a marine survey with a commercial marine gravimeter (type KSS31M), and data were tracked from a marine gravimetry campaign that was conducted with a newly developed platform gravimeter (type JMG) in the South China Sea in September 2020. After various data filtering, processing, and calibrations, the shipborne gravity data were validated with crossover points analysis. Then, the processed shipborne data were employed to evaluate the accuracy of the altimeter-derived marine gravity field models. During this procedure, the quality of JMG shipborne gravity data was compared with the results of KSS31M and NGDC data. Analysis and evaluation results show that the crossover points verification accuracies of KSS31M and JMG are 0.70 mGal and 1.61 mGal, which are much better than the accuracy of NGDC, which is larger than 8.0 mGal. In the area where the bathymetry changes slowly, the root mean square error values between altimetry gravity models and KSS31M data are respectively 3.28 mGal and 4.54 mGal, and those of the JMG data are respectively 2.94 mGal and 2.60 mGal. According to the above results, we can conclude that the JMG has the same 1–2 mGal accuracy level as KSS31M and can meet the measurement requirements of marine gravity.

Regional tidal modeling on the European coast using tide gauges and satellite altimetry

The study investigates sea-level measurements along the coastal area of Europe for the 60-year (1961–2020) time span. Linear and quadratic modeling of tide gauge measurements showed an almost positive rate of trend of sea-level rise (0.09 to 3.6 mm/yr) and low acceleration (−0.05 to 0.40 mm/yr2). A least-squares harmonic estimation tidal modeling was carried out to estimate frequency (cycles per day) for a certain period. The smaller and higher tidal frequencies of these stations indicate their stability in terms of their surface variation. We used the 1993–2020 satellite altimetry data from the nearest grid points of the tide gauge station. The correlation coefficient between observed and satellite altimetry (lowest 0.53 and highest 0.93) varies at each station. This happens because of many factors that can affect the large difference in the sea-level trend between the satellite-derived and tide gauge results. Finally, to implement a global reference system for physical heights, the offshore topographic slope direction and slope range with contour spacing from the sea to the associated coastline were analyzed using bathymetry data. The abrupt change in slope from the coastline toward the sea can be seen toward the east, west, and southeast on the European coast. This is also an important factor that affects the variation of sea level.