Tidal Model Research Articles

The effects of non-local observations on the adjoint estimation of local model parameters: An example of Manning’s n coefficient in a tidal model over the Bohai, Yellow, and East China Seas

Accurate parameter estimation is a key issue for enhancing the performance of hydrological models. With the rapid development of satellite technology, integrating satellite data and numerical modelling for parameter estimation has gained more prominence. The limited spatial coverage of altimeters necessitates areas without direct local observations to rely only on information from nearby non-local observations. However, the relation is far from clear between non-local observations and the estimation of local model parameters. In this study, a two-dimensional adjoint tidal model over the Bohai, Yellow, and East China Seas (BYECS) is developed, assimilating observations from TOPEX/Poseidon, Jason-1, and Jason-2 altimeters in conjunction with tide-gauge stations. In twin experiments, the feasibility and reliability of utilizing non-local observations are emphasized by varying synthetic observations. The experiments also reveal how the number and distance of non-local observations affect the ill-posedness of local parameter estimation. The estimation errors can be reduced by increasing observations within a ‘critical distance’, beyond which the accuracy does not improve further. Subsequently, the robustness of ‘critical distance’ is discussed under different prescribed parameter distributions, sizes of predefined optimized area, and random observational errors, indicating that the ‘critical distance’ is approximately 1.0°-2.0°. These results provide a positive reference for practical experiment. In BYECS, the order of Manning’s n coefficient ranges from 10-4 to 10-1, with an average value of 0.0246 in shallow waters. The spatial distribution reveals 9 high-value areas, primarily modulated by a concurrence of sandy sediment and weak tidal currents. This study offers valuable insights into refining the adjoint model for physical parameter estimation, particularly in anticipation of the expanded spatial coverage of SWOT. Compared to only assimilating T/P series altimeters, incorporating SWOT reduces discrepancies by over 38%. Additionally, the spatial Manning’s n coefficient provides guidance for enhancing tidal simulation in other models.

Tidal modeling based on satellite altimetry observations of TOPEX/Poseidon, Jason1, Jason2, and Jason3 with high prediction capability: A case study of the Baltic Sea

This research aims to optimize the utilization of long-term sea level data from the TOPEX/Poseidon, Jason1, Jason2, and Jason3 altimetry missions for tidal modeling. We generate a time series of along-track observations and apply a developed method to produce tidal models with specific tidal constituents for each location. Our tidal modeling methodology follows an iterative process: partitioning sea surface height (SSH) observations into analysis/training and prediction/validation parts and ultimately identifying the set of tidal constituents that provide the best predictions at each time series location. The study focuses on developing 1256 time series along the altimetry tracks over the Baltic Sea, each with its own set of tidal constituents. Verification of the developed tidal models against the SSH observations within the prediction/validation part reveals mean absolute error (MAE) values ranging from 0.0334 m to 0.1349 m, with an average MAE of 0.089 m. The same validation process is conducted on the FES2014 and EOT20 global tidal models, demonstrating that our tidal model, referred to as BT23 (short for Baltic Tide 2023), outperforms both models with an average MAE improvement of 0.0417 m and 0.0346 m, respectively. In addition to providing details on the development of the time series and the tidal modeling procedure, we offer the 1256 along-track time series and their associated tidal models as supplementary materials. We encourage the satellite altimetry community to utilize these resources for further research and applications.

Influence of wakes interaction and upstream turbulence on three tidal turbines behaviour

The current study presents numerical results on three tidal turbine models (two in front, one downstream) interacting in a turbulent upstream flow. The numerical results come from a lifting-line (LL) embedded in a Lagrangian vortex particle (VP) solver: Dorothy LL-VP. The objective is to assess the extent to which this numerical tool is suited to reproduce accurately wakes interaction as well as fluctuating loads perceived by the downstream turbine. To this aim, the numerical set-up reproduces an experimental campaign led at IFREMER’s wave and current flume tank. The downstream turbine is placed at different positions to change the wakes interaction. Two upstream turbulence intensities (TI) experimentally tested are reproduced numerically using the synthetic eddy method (SEM). Favourable comparisons are obtained between numerical and experimental wakes, including velocity profiles. Preliminary results suggest that the downstream turbine performance decrease is numerically well captured. More investigations are needed on the loads fluctuations with longer computation time, and adding an angular velocity controller as well as hub modelling to Dorothy LL-VP.

Quasi-Continuous Tidal Datum for Peninsular Malaysia using Tide Gauge, Satellite Altimetry, and Tide Model Driver (TMD) Data

Quasi-Continuous Tidal Datum for Peninsular Malaysia using Tide Gauge, Satellite Altimetry, and Tide Model Driver (TMD) Data

Effect of background wind and dissipation processes on the semidiurnal component of atmospheric solar tides

The equations governing the neutral wind velocities and temperature, which depict the oscillations of atmospheric tides, incorporate various elements of the atmosphere. These factors comprise background wind, temperature profiles, and the atmosphere’s composition, including ozone, oxygen, carbon dioxide, water, etc. The current work describes the method of solution of the atmospheric tidal model and investigates the effects of background wind and dissipation processes on the migrating semidiurnal tides during the March equinox. Thermal heating due to water vapour absorption in the troposphere, ozone in the stratosphere and oxygen absorption in the thermosphere is considered in this model. Furthermore, the model takes into account the various dissipation processes (i.e. ion drag and Hall coefficients, Newtonian cooling, divergence of momentum and heat fluxes due to molecular and eddy diffusion) and background wind. The semidiurnal tidal features obtained from the present model match well with the Global Scale Wave Model (GSWM-98). The bar charts are presented to quantify the effects of different parameters on horizontal winds for altitudes below 100 km and above 100 km, separately. It reveals that the background wind plays a vital role in deciding the semidiurnal tidal amplitudes of zonal and meridional winds. Momentum and heat flux coefficients also have a significant influence on semidiurnal tides. At higher altitudes (>100 km), the ion drag reduces the amplitude of semidiurnal tides considerably.

Improved tide level prediction model combined GA-BP neural networks and GNSS SNR data

High-precision tidal forecasting plays a crucial role in providing reliable tidal information to coastal communities, ship operators, fishermen, and government agencies. Existing tidal prediction models, such as backpropagation neural networks (BPNN) and genetic algorithm-optimized BPNN (GA-BPNN), frequently difficulty in in achieving high precision because they rely solely on past tidal variations for real-time predictions. Signal-to-Noise Ratio (SNR) data have emerged as a valuable indicator closely related to real-time sea level changes due to the widespread adoption of Global Navigation Satellite System Interferometric Reflectometry (GNSS-IR) technology. In this paper, we propose a nowcasting tide level prediction method by adding SNR data to BPNN, i.e., Improved BPNN and Improved GA-BPNN, which predicts the next momentary tide level value by using the previous 15 tidal values and real-time SNR as input factors to BPNN. The results of 100-day, 200-day and 1-year tide prediction based on Astoria and Friday Harbor tide gauge stations show that the improved model prediction accuracies are better than the traditional model. Meanwhile, among the two improved models, Improved GA-BPNN has the higher prediction accuracy and can adapt to different time lengths of tide level prediction.

Internal solitary waves in the central Andaman sea observed by combining mooring data and satellite remote sensing

The behavioral characteristics of internal solitary waves (ISWs) in the central Andaman Sea were revealed by analyzing multisource satellite remote sensing images combined with synchronous mooring data. The relationship between the generation time and tides of ISWs in the central Andaman Sea was analyzed and discussed. The ISWs in the central Andaman Sea exhibit a notable semidiurnal tidal cycle, primarily occurring during the spring tide. Additionally, it was observed that larger currents can generate ISWs with larger amplitudes. The propagation velocity of the ISWs initially increases and then decreases from the source, with no significant overall change in the deep areas. Based on the analysis of satellite remote sensing images that cover the source of ISWs in the central Andaman Sea, the generation time of ISWs was estimated. A comparison was made between the estimated generation time and the tidal flow predicted from the TPXO 9 global tidal model at the location of the ISW source. It was found that ISWs are generated when the westward tidal flow reaches its maximum. The ISWs in the central Andaman Sea are generated between the islands of Car Nicobar and Teresa Island. They propagate eastward into the Andaman Sea, grow in amplitude, split into multiple waves, dissipate, and vanish in the waters near the Danao Islands. The entire life cycle of these waves lasts for approximately 3∼4 days.

Assessing Tidal Models in the Ryukyu Islands Region Using the ENOPF Method

Abstract Satellite remote sensing can monitor sea level changes at temporal and spatial scales, plays an important role in the study of tides, and is widely used in numerical tidal models. However, these tidal models are usually computationally expensive. The equidistant nodes orthogonal polynomial fitting (ENOPF) method may overcome that drawback. This study evaluates the accuracy of the ENOPF method in fitting the major tidal constituents in the region near the Ryukyu Islands, where the water depth on either side of the islands varies significantly. The results show that the ENOPF method can accurately fit the major tidal constituents in the presence of complex topography. Furthermore, this approach can also be used to generate reasonable cotidal charts and provide valuable tidal information for hydrodynamic model simulations in the East China Sea. For the high-resolution hydrodynamic model of the East China Sea in particular, reasonable open boundary conditions can be provided by the ENOPF method.

Interpreting an Archaean paleoenvironment through 3D imagery of microbialites.

While stromatolites, and to a lesser extent thrombolites, have been extensively studied in order to unravel Precambrian (>539 Ma) biological evolution, studies of clastic-dominated microbially induced sedimentary structures (MISS) are relatively scarce. The lack of a consolidated record of clastic microbialites creates questions about how much (and what) information on depositional and taphonomic settings can be gleaned from these fossils. We used μCT scanning, a non-destructive X-ray-based 3D imaging method, to reconstruct morphologies of ancient MISS and mat textures in two previously described coastal Archaean samples from the ~3.48 Ga Dresser Formation, Pilbara, Western Australia. The aim of this study was to test the ability of μCT scanning to visualize and make 3D measurements that can be used to interpret the biotic-environmental interactions. Fossil MISS including mat laminae with carpet-like textures in one sample and mat rip-up chips in the second sample were investigated. Compiled δ13C and δ34S analyses of specimens from the Dresser Fm. are consistent with a taxonomically diverse community that could be capable of forming such MISS. 3D measurements of fossil microbial mat chips indicate significant biostabilization and suggest formation in flow velocities >25 cm s-1. Given the stratigraphic location of these chips in a low-flow lagoonal layer, we conclude that these chips formed due to tidal influence, as these assumed velocities are consistent with recent modeling of Archaean tides. The success of μCT scanning in documenting these microbialite features validates this technique both as a first step analysis for rare samples prior to the use of more destructive techniques and as a valuable tool for gaining insight into microbialite taphonomy.

Eccentric binaries: Periastron events and tidal heating

Context. Binary stars cannot be fully understood without assessing the interaction effects between the two components and the impact of these effects on observational diagnostics. Periastron brightening events, also known as the heartbeat phenomenon, are a clear manifestation of this type of interaction. Aims. We aim to explore the role of tidal shear energy dissipation in stars undergoing periastron brightening events. Methods. We performed a computation from first principles that uses a quasi-hydrodynamic Lagrangian scheme to simultaneously solve the orbital motion and the equations of motion of a 3D grid of volume elements covering the inner, rigidly rotating “core” of a tidally perturbed star. The equations of motion include the gravitational acceleration of both stars, the centrifugal, Coriolis, gas pressure accelerations, and viscous coupling between volume elements. The method is illustrated for a grid of model binary systems with a 10 M⊙ primary that is perturbed by a 6.97 M⊙ companion in eccentric orbits (e = 0 − 0.7). The model is then applied to the heartbeat star MACHO 80.7443.1718. Results. We find an increase by factors ∼10−6–10−3 in tidal shear energy dissipation at periastron, consistent with the majority of observed heartbeat stars. The magnitude of the periastron effect correlates with the degree of departure from synchronicity: stars rotating much faster or much slower than the synchronous rate at periastron present the strongest effect. We confirm that for eccentricities ≤0.3, pseudo-synchronization occurs for 0.8 < ω/Ωave < 1, where Ωave is the average orbital angular velocity. The minimum energy rotation rate (pseudo-synchronism) for e = 0.5 and 0.7 occurs for 1.0 < ω/Ωave < 1.15. The tidal shear energy dissipation model reproduces from first principles the ∼23% maximum brightness enhancement at periastron of MACHO 80.7443.1718. Conclusions. Our results suggest that the magnitude and shape of the heartbeat signal may serve as diagnostics for the internal stellar rotation and turbulent viscosity values.

Large‐Scale Wave‐Driven Interactions and Plasma‐Neutral Coupling in the Low‐Latitude Ionosphere‐Thermosphere

AbstractThe plasma and neutral density variations, interactions and coupling processes within ±30° latitudes are examined concurrently by the DMSP‐F18 and Swarm‐C satellite during geomagnetically quiet years in 2020–2021. The wavenumber (WN) patterns are computed in the form of neutral and electron density for two altitudes and their latitudinal profiles are analyzed. We observe that the WN1 structure of the electron density has a significant seasonal dependence in the topside ionosphere and dominates all other structures but WN2 neutral density amplitude dominates all other structures in the middle thermosphere (∼440 km). Additionally, we analyze vertical‐temporal‐latitudinal tidal structures from the Climatological Tidal Model of the Thermosphere (CTMT) to find evidence for the modulation of the large‐scale waves (LSWs) neutral density structures. Through the examination of the in situ observational and modeling approaches, we show that the tidal contributors of WN structures obtained from CTMT can capture the influence of terrestrial sources on the WN structures of plasma‐neutral density and imprint the corresponding vertical coupling in the IT system. Correlation analysis reveals that the amplitudes of the WN1 and WN3 structures of electron density in topside ionosphere and those of neutral density in the middle thermosphere show intermittent but significant correlations with each other, unlike the WN2 and WN4 structures. This study provides new insights into the topside ionospheric response to wave driving in the lower atmosphere, which ultimately improves our capability to understand the interaction and vertical coupling of large‐scale structures, thereby advancing our predictive capabilities of space weather critical for satellite operations.

PENGEMBANGAN ARDUINO DATA LOGGER MENGGUNAKAN TDR H3CR UNTUK SIMULATOR PASANG SURUT

Tides, crucial natural phenomena, significantly impact various aspects of life. Recognizing their importance, this study presents the development of a tidal simulator leveraging Arduino data logging and TDR H3CR technology. The simulator aims to mimic tidal processes, crucial for educational and research purposes. Traditional methods of acquiring tidal data are time-consuming and expensive. Thus, a simulator proves advantageous in reducing research time and costs. At Raja Ali Haji Maritime University, a tidal simulation model exists but with manual operation and limited data capture capabilities. To address these limitations, this study designed a new simulator utilizing H3CR, DC Water Pump, and DC Selenoid Valve for automated tidal circulation. The research method involved system design, component integration, and laboratory experiments. Calibration of components like the ultrasonic sensor HC-SR04 ensured accurate data collection. The overall system experiment validated the simulator's functionality, demonstrating its ability to replicate tidal processes effectively. Results indicated that the simulator produced tidal patterns resembling sinusoidal waves, with slight noise attributed to sensor limitations. The designed simulator serves as an efficient learning tool for understanding tidal phenomena, exhibiting comparable results to natural tidal data. This study contributes to the advancement of tidal simulation technology, offering a cost-effective and accessible solution for educational and research purposes.

On the selection of multi-satellite altimetry for empirical tide modelling over Indonesia

ABSTRACT Multi-satellite altimetry has been employed in tidal modelling as its accuracy has been proven acceptable in constructing good-quality models. However, the modelling process often fails to consider the varying temporal resolution and observation periods among satellites, which can affect the accuracy of the model due to aliasing and Rayleigh effects. In Indonesia, we investigate and propose a satellite selection procedure for tidal modelling utilizing the response method, validated with along-track data obtained from both older and newer generations of ERM (Exact Repeat Mission)-type altimetry satellites, including the TOPEX/Jason series (TOPEX, Jason-1, Jason-2, Jason-3, and SENTINEL-6A), ENVISAT, ERS-2, GFO, SENTINEL-3B, and SENTINEL3A. The most optimal satellite combination identified is the TOPEX/Jason series, GFO, and ENVISAT, as they contribute significantly less error compared to ERS-2, SENTINEL-3A, and SENTINEL-3B, with errors exceeding 50%, primarily due to aliasing and Rayleigh effects. This combination of three satellites with tide gauge stations achieves higher precision (11.31 cm) than the current global tidal model. This study provides empirical evidence that the accuracy of tidal models is not solely dependent on the number of altimetry satellites utilized, but implementing effective satellite selection procedures is also crucial to enhance the precision of a model.

Did atmospheric thermal tides cause a daylength locking in the Precambrian? A review on recent results

After the initial suggestion by Zahnle and Walker (1987) that the torque accelerating the spin rate of the Earth and produced by the heating of the atmosphere by the Sun could counteract the braking luni-solar gravitational torque in the Precambrian, several authors have recently revisited this hypothesis. In these studies, it is argued that the geological evidence of the past spin state of the Earth plays in favor of this atmospheric tidal locking of the length of the day (LOD). In the present review of the recent literature, we show that the drawn conclusions critically depend on LOD estimates based on stromatolite growth band data of Panella at 1.88 and 2.0 Ga which are subject to large uncertainties. When only the most robust cyclostatigraphic estimates of the LOD are retained, the LOD locking hypothesis is not supported. Moreover, our consideration of the published General Circulation Model numerical simulations and of a new analytical model for the thermal atmospheric tides suggest that the atmospheric tidal resonance, which is the crucial ingredient for the LOD locking in the Precambrian, was never of sufficiently large amplitude to allow for this tidal LOD lock.

Detecting Shoreline Changes on the Beaches of Hainan Island (China) for the Period 2013–2023 Using Multi-Source Data

This study presents an in-depth analysis of the dynamic beach landscapes of Hainan Island, which is located at the southernmost tip of China. Home to over a hundred natural and predominantly sandy beaches, Hainan Island confronts significant challenges posed by frequent marine natural disasters and human activities. Addressing the urgent need for long-term studies of beach dynamics, this research involved the use of CoastSat to extract and analyze shoreline data from 20 representative beaches and calculate the slopes of 119 sandy beaches around the island for the period from 2013 to 2023. The objective was to delineate the patterns of beach evolution that contribute to the prevention of sediment loss, the mitigation of coastal hazards, and the promotion of sustainable coastal zone management. By employing multi-source remote sensing imagery and the CoastSat tool, this investigation validated slope measurements across selected beaches, demonstrating consistency between the calculated and actual distances despite minor anomalies. The effective use of the finite element solution (FES) in the 2014 global tidal model for tidal corrections further aligned the coastlines with the mean shoreline, underscoring CoastSat’s utility in enabling precise coastal studies. The analysis revealed significant seasonal variations in shoreline positions, with approximately half of the monitored sites showing a seaward progression in summer and a retreat in winter, which were linked to variations in wave height. The southern beaches exhibited distinct seasonal variations, which contrasted with the general trend due to differing wave impacts. The western and southern shores showed erosion, while the northern and eastern shores displayed accretion. The calculated slopes across the island indicated that the southern beaches had steeper slopes, while the northern areas exhibited more pronounced slope variations due to wave and tidal impacts. These findings highlight the critical role of integrated coastal management and erosion control strategies in safeguarding Hainan Island’s beaches. By understanding the mechanisms driving seasonal and regional shoreline changes, effective measures can be developed to mitigate the impacts of erosion and enhance the resilience of coastal ecosystems amidst changing environmental conditions. This research provides a foundational basis for future efforts aimed at the sustainable development and utilization of coastal resources on Hainan Island.

Thermal tides in neutrally stratified atmospheres: Revisiting the Earth’s Precambrian rotational equilibrium

Rotational dynamics of the Earth, over geological timescales, have profoundly affected local and global climatic evolution, probably contributing to the evolution of life. To better retrieve the Earth’s rotational history, and motivated by the published hypothesis of a stabilized length of day during the Precambrian, we examined the effect of thermal tides on the evolution of planetary rotational motion. The hypothesized scenario is contingent upon encountering a resonance in atmospheric Lamb waves, whereby an amplified thermotidal torque cancels out the opposing torque generated by the oceans and solid interior, driving the Earth into rotational equilibrium. With this scenario in mind, we constructed an ab initio model of thermal tides on rocky planets describing a neutrally stratified atmosphere. The model takes into account dissipative processes with Newtonian cooling and diffusive processes in the planetary boundary layer. We retrieved, from this model, a closed-form solution for the frequency-dependent tidal torque, which captures the main spectral features previously computed using 3D general circulation models. In particular, under longwave heating, diffusive processes near the surface and the delayed thermal response of the ground prove to be responsible for attenuating, and possibly annihilating, the accelerating effect of the thermotidal torque at the resonance. When applied to the Earth, our model prediction suggests the occurrence of the Lamb resonance in the Phanerozoic, but with an amplitude that is insufficient for the rotational equilibrium. Interestingly, though our study was motivated by the Earth’s history, the generic tidal solution can be straightforwardly and efficiently applied in exoplanetary settings.

Tidal frequency dependence of the Saturnian k2 Love number

Context. Love numbers describe the fluid and elastic response of a body to the tidal force of another massive object. By quantifying these numbers, we can more accurately model the interiors of the celestial objects concerned. Aims. We determine Saturn’s degree-2 Love number, k2, at four different tidal forcing frequencies. Methods. To do this, we used astrometric data from the Cassini spacecraft and a dynamical model of the orbits of Saturn’s moons. Results. The values obtained for k2 are 0.384 ± 0.015, 0.370 ± 0.023, 0.388 ± 0.006, and 0.376 ± 0.007 (1σ error bar) for the tidal frequencies of Janus–Epimetheus, Mimas, Tethys, and Dione. Conclusions. We show that these values are compatible with a constant Love number formulation. In addition, we compared the observed values with models of dynamical tides excited in Saturn’s interior, also finding a good agreement. Future increases in the measurement precision of Love numbers will provide new constraints on the internal structure of Saturn.

Simulating emission line galaxies for the next generation of large-scale structure surveys

ABSTRACT We investigate emission line galaxies across cosmic time by combining the modified L-Galaxies semi-analytical galaxy formation model with the JiuTian cosmological simulation. We improve the tidal disruption model of satellite galaxies in L-Galaxies to address the time dependence problem. We utilize the public code cloudy to compute emission line ratios for a grid of H ii region models. The emission line models assume the same initial mass function as that used to generate the spectral energy distribution of semi-analytical galaxies, ensuring a coherent treatment for modelling the full galaxy spectrum. By incorporating these emission line ratios with galaxy properties, we reproduce observed luminosity functions for H α, H β, [O ii], and [O iii] in the local Universe and at high redshifts. We also find good agreement between model predictions and observations for autocorrelation and cross-correlation functions of [O ii]-selected galaxies, as well as their luminosity dependence. The bias of emission line galaxies depends on both luminosity and redshift. At lower redshifts, it remains constant with increasing luminosity up to around $\sim 10^{42.5}\, {\rm erg\, s^{-1}}$ and then rises steeply for higher luminosities. The transition luminosity increases with redshift and becomes insignificant above z = 1.5. Generally, galaxy bias shows an increasing trend with redshift. However, for luminous galaxies, the bias is higher at low redshifts, as the strong luminosity dependence observed at low redshifts diminishes at higher redshifts. We provide a fitting formula for the bias of emission line galaxies as a function of luminosity and redshift, which can be utilized for large-scale structure studies with future galaxy surveys.

Altimeter Calibrations in the Preliminary Four Years’ Operation of Wanshan Calibration Site

In order to accomplish the calibration and validation (Cal/Val) of altimeters, the Wanshan calibration site (WSCS) has been used as a calibration site for satellite altimeters since its completion in August 2019. In this paper, we introduced the WSCS and the dedicated equipment including permanent GNSS reference stations (PGSs), acoustic tide gauges (ATGs), and dedicated GNSS buoys (DGB), etc. placed on Zhi’wan, Wai’ling’ding, Dan’gan, and Miao’Wan islands of the WSCS. The PGSs data of Zhi’wan and Wai’ling’ding islands were processed and analyzed using the GAMIT/GLOBK (Version 10.7) and Hector (Version 1.9) software to define the datum for Cal/Val of altimeters in WSCS. The DGB was used to transfer the datum from the PGSs to the ATGs of Zhi’wan, Wai’ling’ding, and Dan’gan islands. Separately, the tidal and mean sea surface (MSS) corrections are needed in the Cal/Val of altimeters. We evaluated the global/regional tide models of FES2014, HAMTIDE12, DTU16, NAO99jb, GOT4.10, and EOT20 using the three in situ tide gauge data of WSCS and Hong Kong tide gauge data (No. B329) derived from the Global Sea Level Observing System. The HAMTIDE12 tide model was chosen to be the most accurate one to maintain the tidal difference between the locations of the ATGs and the altimeter footprints. To establish the sea surface connections between the ATGs and the altimeter footprints, a GPS towing body and a highly accurate ship-based SSH measurement system (HASMS) were used to measure the sea surface of this area in 2018 and 2022, respectively. The global/regional mean sea surface (MSS) models of DTU 2021, EGM 2008 (mean dynamic topography minus by CLS_MDT_2018), and CLS2015 were accurately evaluated using the in situ measured data and HY-2A altimeter, and the CLS2015 MSS model was used for Cal/Val of altimeters in WSCS. The data collected by the equipment of WSCS, related auxiliary models mentioned above, and the sea level data of the hydrological station placed on Dan’gan island were used to accomplish the Cal/Val of HY-2B, HY-2C, Jason-3, and Sentinel-3A (S3A) altimeters. The bias of HY-2B (Pass No. 375) was −16.7 ± 45.2 mm, with a drift of 0.5 mm/year. The HY-2C biases were −18.9 ± 48.0 mm with drifts of 0.0 mm/year and −5.6 ± 49.3 mm with −0.3 mm/year drifts for Pass No. 170 and 185, respectively. The Jason-3 bias was −4.1 ± 78.7 mm for Pass No. 153 and −25.8 ± 85.5 mm for Pass No. 012 after it has changed its orbits since April 2022, respectively. The biases of S3A were determined to be −16.5 ± 46.3 mm with a drift of −0.6 mm/year and −9.8 ± 30.1 mm with a drift of 0.5 mm/year for Pass No. 260 and 309, respectively. The calibration results show that the WSCS can commercialize the satellite altimeter calibration. We also discussed the calibration potential for a wide swath satellite altimeter of WSCS.

Gravity field recovery of inter-satellite links between Beidou navigation satellite system (BDS) and LEO based on geodesy and time reference in space (GETRIS)

The goal of this contribution is to construct the inter-satellite links (ISLs) between Global Navigation Satellite System (GNSS) and Low Earth Orbit (LEO) satellite to recover the Earth’s gravity field based on the concept of Geodesy and Time Reference in Space (GETRIS). Taking the constellation of the Beidou Navigation Satellite System (BDS) as an example, several types of high-low satellite-to-satellite tracking (H-L SST) modes combining BDS and GETRIS are used to research the tracking mode of high orbit satellites and the distribution of LEO satellite constellations to explore the optimal mode for gravity field recovery. The effects of multiple H-L SST modes on the accuracy of gravity field recovery are studied. In addition, the contribution of each error source is also analyzed. Finally, this study varies LEO satellite constellations to show reduced errors in the temporal gravity field solutions for the improved ISLs. The results showed that the Inclined GeoSynchronous Orbit (IGSO) satellite greatly improved the Geosynchronous orbit (GEO) satellite tracking LEO satellite mode in the high latitude regions. Compared with the Medium Earth Orbit (MEO) satellite tracking LEO satellite, the error of gravity field recovered by combining with GEO, IGSO and MEO can be reduced by 16 %. The largest error is the non-tidal signal, followed by the ocean tidal model difference, and the smallest is the instrument error. For a single LEO satellite, the combination model is more sensitive to the satellite orbital altitude, the cumulative error was decreased from 5.08 mm (550 km) to 0.33 mm (250 km). For LEO constellations, adding inclined orbit satellites can improve the accuracy of the solution to some extent. But the optimal solution can be obtained by the constellation composed of polar orbit satellites with different Right Ascension of Ascending Node (RAAN), the cumulative errors are 0.27 mm (two satellites), 0.19 mm (three satellites), and 0.19 mm (four satellites).