Determination of the mean dynamic ocean topography model through combining multi-source gravity data and DTU15 MSS around China's coast

Mean dynamic ocean topography (or MDT) is closely related to ocean circulation and global climate change. It has important scientific significance and application value for the development and utilization of marine resources in China's coastal areas. Based on the terrain gravity, marine gravity, and SRTM 3?s data, an algorithm to reduce the problem of gravity data gaps between land and sea is proposed. A consistent land-sea gravity model is established based on point-mass fusion method. Then geoid model, which accuracy was estimated to be 8.5?cm through the verification of 348 GNSS/level data from the coastal provinces, of China's coastal areas was calculated through remove-restore technique. Connecting the above geoid model with DTU15 MSS model to establish a MDT model in China's coastal areas using the direct method in space domain. The effect of gravity field model, dominant factors of sea surface topography, and low pass filter are analyzed. Taking Bohai Sea and Yellow Sea as an example, and comparing MDT with the two international models CNES_2013_MDT and DTU15_MDT. The results show that the MDT has the potential to construct a vertical datum of the ocean and carry out related scientific research and application.     

Comparative evaluation of five global gravity models over a part of the Bay of Bengal

Several global gravity models (GGMs) are freely available in the public domain, which can be utilised to study the earth's gravity field in almost every part of the globe. The present study compared the free-air gravity anomalies calculated from the five GGMs EGM2008, EIGEN6C4, GECO, XGM2019e_2159, and SGG-UGM-2 archived by the International Centre for Global Earth Models (ICGEM) with respect to shipborne gravity in the Bay of Bengal. The average correlation coefficient and covariance are ～ 96 % and ～ 450mGal². The mean difference between the shipborne and the modelled gravity is ? 5 mGal. Relatively higher amplitude gravity differences observed at the continental-oceanic transition, the 85°E and Ninetyeast ridges, and the western basin are possibly due to high gradient, dominant density contrasts, and rugged topography. The average standard deviation and root-mean-square-error (RMSE) of the differences are ～ 6.5 mGal and ～ 7.5 mGal. A significantly lower standard deviation and RMSE found for the models generated at higher degree/order compared to lower degree/order is due to diminishing omission error of the GGMs with increasing degrees of truncation. The spectral analysis and coherence estimation of the modelled gravity demonstrate excellent correspondence for anomalies wider than ～ 25 km. The agreement between anomaly amplitudes and shapes and calculated statistics indicates that the accuracy and resolution of the modelled gravity data are certainly good enough for regional-scale studies aiming to map Moho topography and mantle structures. However, the delineation of shorter wavelength features originating from the shallow-level basement/sedimentary might be uncertain and requires further validations. The present study confirms that all five models show promising results in terms of their accuracy and resolution. Moreover, the SGG-UGM-2 and XGM2019e_2159 models compare favourably with respect to the GECO, EIGEN6C4 and EGM2008 models in the Bay of Bengal.     

The X-TRACK/ALES multi-mission processing system: New advances in altimetry towards the coast

In the context of the ESA Climate Change Initiative project, a new coastal sea level altimetry product has been developed in order to support advances in coastal sea level variability studies. Measurements from Jason-1,2&3 missions have been retracked with the Adaptive Leading Edge Subwaveform (ALES) Retracker and then ingested in the X-TRACK software with the best possible set of altimetry corrections. These two coastal altimetry processing approaches, previously successfully validated and applied to coastal sea level research, are combined here for the first time in order to derive a 16-year-long (June 2002 to May 2018), high-resolution (20-Hz), along-track sea level dataset in six regions: Northeast Atlantic, Mediterranean Sea, West Africa, North Indian Ocean, Southeast Asia and Australia. The study demonstrates that this new coastal sea level product called X-TRACK/ALES is able to extend the spatial coverage of sea level altimetry data ~3.5 km in the land direction, when compared to the X-TRACK 1-Hz dataset. We also observe a large improvement in coastal sea level data availability from Jason-1 to Jason-3, with data at 3.6 km, 1.9 km and 0.9 km to the coast on average, for Jason-1, Jason-2 and Jason-3, respectively. When combining measurements from Jason-1 to Jason-3, we reach a distance of 1.2–4 km to the coast. When compared to tide gauge data, the accuracy of the new altimetry near-shore sea level estimations also improves. In terms of correlations with a large set of independent tide gauge observations selected in the six regions, we obtain an average value of 0.77. We also show that it is now possible to derive from the X-TRACK/ALES product an estimation of the ocean current variability up to 5 km to the coast. This new altimetry dataset, freely available, will provide a valuable contribution of altimetry in coastal marine research community.     

Autonomous navigation for lunar final approach based on gravity gradient measurements

Lunar final approach navigation is critical for pin-point lunar landing in future missions. This study investigates the use of lunar gravity gradient measurements for autonomous navigation of a lunar probe during the final approach phase. As the spacecraft approaches the Moon, the strength of gravity gradient signals improves. A spaceborne gravity gradiometer can precisely measure local gravity gradients, and the latest lunar gravity model GL1500E is used to provide reference values. The employed truncation degree and order of the gravity model are increased stepwise considering the decreasing altitude of the spacecraft in order to reach a compromise between computational costs and model accuracy. An iterative Kalman filter is developed for coupled orbit and attitude estimation using gravity gradient measurements and attitude quaternions obtained from star sensors. A simulated spacecraft with a gradiometer noise level of 0.01 E is considered. Simulation results show that the spacecraft’s position converges rapidly and achieves an accuracy of less than 100 m at the last epoch.     

基于神经网络的重力卸载系统控制器设计

吊挂系统是地面模拟空间机械臂重力卸载试验的重要方法之一。针对传统PID控制方式动作响应慢、鲁棒性差等缺点,提出了一种基于径向基函数（RBF）神经网络的智能控制方式。该方式有很强的非线性拟合能力,且学习规则简单,可映射任意复杂的非线性关系,便于计算机实现。利用该特性,设计了一种重力卸载精度较PID控制方式更高的控制器。该控制器应用正交最小二乘法辨识的控制模型,在带负荷的伺服电机数学模型条件下,使用基于梯度下降法更新权重的RBF神经网络,最后通过s 函数编写,得到Matlab仿真图像。仿真结果与PID控制方法相比响应迅速,鲁棒性强,重力卸载精度更高（98%）。     

Evaluation of using two-phase frictional pressure drop correlations for normal gravity to microgravity and reduced gravity

The calculation of two-phase frictional pressure drop (TPFPD) is required by two-phase systems operating under microgravity and reduced gravity. There are a large number of correlations for the TPFPD in tubes under normal gravity. However, it is hard to find out a TPFPD correlation obtained from microgravity and/or reduced gravity conditions, and thus people have to use TPFPD correlations for normal gravity to calculate TPFPD under microgravity and reduced gravity. It is necessary to evaluate the feasibility of such practice. This paper offers a comprehensive review of the TPFPD correlations for normal gravity and an up-to-data survey of the TPFPD experimental study under microgravity and reduced gravity. There are 23 TPFPD correlations for normal gravity reviewed and 135 experimental data under microgravity obtained from the literature. These experimental data are used to evaluate the reviewed TPFPD correlations. It is found that the smallest mean absolute relative deviation (MARD) of the correlations is greater than 34%. Using TPFPD correlations for normal gravity to reduced gravity and microgravity may be acceptable for the first approximation, but correlations intended for microgravity and reduced gravity are needed and more experiments are desired to obtain more data with high accuracy.     

The temporal variation of mean gravity of atmosphere

One of the precise widely used global Zenith Hydrostatic Delay (ZHD) model is based on the gravity value at the centroid of the atmospheric column at the station of observation and gravity value at the centroid is constant in this model for a specific location throughout the year. However, as the content and extent of atmosphere varies temporally, its centroid and consequently gravity value at the centroid also varies. Apart from this, the actual atmospheric condition of different region is not alike. Therefore, there is a need to develop a regional mean gravity model and development of such model has been discussed in this paper. To obtain the mean gravity model, first a regional model of centroid height of atmospheric column was developed as a function of the surface pressure and temperature. It was developed by multiple regressions between estimated centroid of the atmosphere and surface pressure, surface temperature using radiosonde data of five radiosonde stations spread over the Indian subcontinent. Three years radiosonde data from 2006 to 2008 was used for each station. The root mean square error in estimating centroid of the atmospheric column is about ±326 m, which is negligible considering the variability of the atmosphere and its content. The centroid height model has been used to formulate the mean gravity model, considering uniform lapse rate in gravity with height. It is found that proposed mean gravity model provides temporal variation of mean gravity values at the centroid and thus matches with the reality. The interesting advantage of the developed model is that the model shows diurnal variation of mean gravity. The accuracy of ZHD has shown of the order of about 0.3 mm using the developed regional mean gravity model. However, already developed ZHD model has shown a slight inferior result compared to the developed model. These models have shown accuracy of about 0.8 mm and 0.6 mm.     

Detection of surface temperature anomaly of the Sea of Marmara

Monitoring sea surface temperature (SST) over a long-term and detecting the anomalies highly contribute to understanding the prevailing water quality of the sea. Earth observation satellite images are the key data sources that offer the long-term SST detection in a cost and time effective way. Since the Sea of Marmara in Türkiye is surrounded by the highly populated provinces, the water quality of the sea has gained importance for scientific and public communities over the years. This article emphasizes on the significance of detecting SST trend and corresponding anomalies of the Sea of Marmara over the past 32 years. To address the SST variations of the Sea of Marmara in time, a comprehensive set of both field and satellite data regarding SSTs were obtained within the context of this study. The SST trend and its anomalies between the years 1990 and 2021 were detected by applying Seasonal-Trend decomposition procedure based on LOESS (STL) method to NOAA OISST V2 data. On the other hand, spatial SST distribution was detected with Landsat-8, Sentinel-3 and NOAA OISST V2 satellite data. SST results were verified with the in-situ data within the scope of accuracy assessment. The results showed that SST time-series data performed an increasing trend and had anomalies mostly during the spring months in the recent years.     

The effect of spatial truncation error on integral inversion of satellite gravity gradiometry data

The satellite gravity gradiometry (SGG) data can be used for local modelling of the Earth’s gravity field. In this study, the SGG data in the local north-oriented and orbital frames are inverted to the gravity anomaly at sea level using the second-order partial derivatives of the extended Stokes formula. The emphasis is on the spatial truncation error and the kernel behaviour of the integral formulas in the aforementioned frames. The paper will show that only the diagonal elements of gravitational tensor at satellite level are suitable for recovering the gravity anomaly at sea level. Numerical studies show that the gravity anomaly can be recovered in Fennoscandia with an accuracy of about 6 mGal directly from on-orbit SGG data.     

ASAR imaging for coastal upwelling in the Baltic Sea

Analysis of Envisat Advanced Synthetic Aperture Radar (ASAR) and Aqua/Terra Moderate Imaging Spectrometer (MODIS) infrared (IR) imagery of coastal upwelling in the southeastern Baltic Sea is presented. It is found that upwelling features are well distinct in the SAR images, and the leading imaging mechanism appears to be the change of the marine atmospheric boundary layer (MABL) stratification over the sea surface temperature (SST) front. This finding is supported by model calculations of the MABL transformation supplemented with the SAR backscatter calculations based on the CMOD4 model. In addition an empirical dependence of the SAR contrasts over the upwelling region on the wind speed and the SST drop is suggested. Finally, surface slicks accumulated in the sea surface current convergence zones generate additional distinct features in SAR imagery. This effect is interpreted within the framework of the coastal current circulation model based on analysis of the SST snapshot.     

Estimation of sediment settling velocity in estuarine and coastal waters using optical remote sensing data

A robust method has been developed for estimating sediment settling velocity (w_s) from high resolution optical remote sensing data in estuarine, coastal and harbor waters. This method estimates settling velocity as a function of the drag coefficient (C_d), Reynolds number (Re), grain size (D₅₀), specific gravity (Δ_SG) and grain shape (in terms of the Corey Shape Factor – CSF). These parameters were derived from the particulate inherent optical properties such as backscattering (b_bp), beam attenuation (c_p), suspended sediment concentration and turbidity using Landsat 8 OLI and HICO data. Preliminary results for the Gulf of Cambay in the eastern Arabian Sea and Yangtze river estuary in the East China Sea, showed that satellite-retrieved settling velocities (m?s^?1) varied from very low values in clear oceanic waters, intermediate values in coastal waters, to very high values in river plumes and sediment-laden coastal waters. The remote sensing retrievals of sediment properties and their settling velocities were generally consistent with the field and laboratory results, which indicate that the proposed methodology will have important implications in various coastal engineering, environmental and management studies.     

Simulation study for the determination of the lunar gravity field from PRARE-L tracking onboard the German LEO mission

A simulation study has been performed at GFZ Potsdam, which shows the anticipated improvement of the lunar gravity field model with respect to current (LP150Q model) or near-future (SELENE) knowledge in the framework of the planned German Lunar Explorations Orbiter (LEO) mission, based on PRARE-L (Precise Range And Range-rate Equipment – Lunar version) Satellite-to-Satellite (SST) and Satellite-Earth-Satellite (SEST) tracking observations. It is shown that the global mean error of the lunar gravity field can be reduced to less than 0.1 mGal at a spatial resolution of 50 km. In the spectral domain, this means a factor of 10 (long wavelengths) and some 100 (mid to short wavelengths) improvement as compared to predictions for SELENE or a factor of 1000 with respect to LP150Q. Furthermore, a higher spatial resolution of up to 28 km seems feasible and would correspond to a factor of 2–3 improvement of SELENE results. Moreover, PRARE-L is expected to derive the low-degree coefficients of the lunar gravity field with unprecedented accuracy. Considering long mission duration (at least 1 year is planned) this would allow for the first time a precise direct determination of the low-degree tidal Love numbers of the Moon and, in combination with high precision SEST, would provide an experimental basis to study relativistic effects such as the periselenium advance in the Earth–Moon system.     

Integrating Non-Tidal Sea Level data from altimetry and tide gauges for coastal sea level prediction

The main objective of this paper is to integrate Non-Tidal Sea Level (NSL) from the joint TOPEX, Jason-1 and Jason-2 satellite altimetry with tide gauge data at the west and north coast of the United Kingdom for coastal sea level prediction. The temporal correlation coefficient between altimetric NSLs and tide gauge data reaches a maximum higher than 90% for each gauge. The results show that the multivariate regression approach can efficiently integrate the two types of data in the coastal waters of the area. The Multivariate Regression Model is established by integrating the along-track NSL from the joint TOPEX/Jason-1/Jason-2 altimeters with that from eleven tide gauges. The model results give a maximum hindcast skill of 0.95, which means maximum 95% of NSL variance can be explained by the model. The minimum Root Mean Square Error (RMSe) between altimetric observations and model predictions is 4.99 cm in the area. The validation of the model using Envisat satellite altimetric data gives a maximum temporal correlation coefficient of 0.96 and a minimum RMSe of 4.39 cm between altimetric observations and model predictions, respectively. The model is furthermore used to predict high frequency NSL variation (i.e., every 15 min) during a storm surge event at an independent tide gauge station at the Northeast of the UK (Aberdeen).     

Satellite evidence of harmful algal blooms and related oceanographic features in the Bohai Sea during autumn 1998

Harmful algal blooms (HABs) are truly global marine phenomena of increasing significance. Some HAB occurrences are different to observe because of their high spatial and temporal variability and their advection, once formed, by surface currents. A serious HAB occurred in the Bohai Sea during autumn 1998, causing the largest fisheries economic loss. The present study analyzes the formation, distribution, and advection of HAB using satellite SeaWiFS ocean color data and other oceanographic data. The results show that the bloom originated in the western coastal waters of the Bohai Sea in early September, and developed southeastward when sea surface temperature (SST) increased to 25–26 °C. The bloom with a high Chl-a concentration (6.5 mg m⁻³) in center portion covered an area of 60 × 65 km². At the end of September, the bloom decayed when SST decreased to 22–23 °C. The HAB may have been initiated by a combination of the river discharge nutrients in the west coastal waters and the increase of SST; afterwards it may have been transported eastward by the local circulation that was enhanced by northwesterly winds in late September and early October.     

Long-wavelength lunar gravity field recovery from simulated orbit and inter-satellite tracking data

As has been demonstrated recently, inter-satellite Ka-band tracking data collected by the GRAIL (Gravity Recovery And Interior Laboratory) spacecraft have the potential to improve the resolution and accuracy of the lunar gravity field by several orders of magnitude compared to previous models. By means of a series of simulation studies, here we investigate the contribution of inter-satellite ranging for the recovery of the Moon’s gravitational features; the evaluation of results is made against findings from ground-based Doppler tracking. For this purpose we make use of classical dynamic orbit determination, supported by the analysis of satellite-to-satellite tracking observations. This study sheds particularly light on the influence of the angular distance between the two satellites, solar radiation modeling and the co-estimation of the lunar Love number k₂. The quality of the obtained results is assessed by gravity field power spectra, gravity anomalies and precision orbit determination. We expect our simulation results to be supportive for the processing of real GRAIL data.     

Analysis of coastal altimetry in the Mexican Caribbean

A reprocessing of sea-level anomalies (SLA) resulting from X-TRACK coastal altimetry was carried out for the ENVISAT (2002–2010) and TOPEX/POSEIDON-Jason (1992–2019) satellite missions in the coastal area of the Mexican Caribbean. This consisted of applying a tidal correction to coastal altimetry sea level observations. Harmonic analysis of five coastal tide gauge records was performed to estimate the most important tidal components of the area, resulting on M2, N2, O1, S2, K1, MF, and MM. The tidal signal was reconstructed with the seven tidal components using the TPXO9 model. The SLA signals corrected with the seven tidal components were validated with in situ data from coastal tide gauges. The validation showed that the TPXO9 tidal barotropic model (1/30° grid) used to reconstruct the tidal signal with the seven representative tidal components performed better than the FES2012 global model (1/16° grid) that uses 33 tidal components. The reprocessed SLAs showed clear seasonality with significant signals at 4, 6, and 12 months, with the annual signal being the dominant one. In the Mexican Caribbean coastal zone, oceanographic processes with different scales (from coastal to mesoscale) converge, showing their complexity in the different SLA signals observed. The aim of this work is to contribute to the analysis of coastal altimetry data and understanding the sea level variations in the Mexican Caribbean. This work is the first step in the implementation of methodologies that take advantage of coastal satellite altimetry in the Caribbean Sea.     

A simulation of Martian gravity field recovery by using a near equatorial orbiter

An improvement to the Martian gravity field may be achieved by means of future orbiting spacecraft with small eccentricity and low altitude exemplified through a newly proposed mission design that may be tested in upcoming reconnaissance of Mars. Here, the near equatorial orbital character (with an inclination approximating 10°, eccentricity as 0.01 and semi-major axis as 4000 km) is considered, and its contribution to Martian gravity field solution is analyzed by comparing it with a hypothetical polar circular orbiter. The solution models are evaluated in terms of the following viewpoints: power spectra of gravity field coefficients, correlations of low degree zonal coefficients, precise orbit determination, and error distribution of both Mars free air gravity anomaly and areoid. At the same time, the contributions of the near equatorial orbiters in low degree zonal coefficients time variations are also considered. The present results show that the near equatorial orbiter allows us to improve the accuracy of the Martian gravity field solution, decrease correlation of low degree zonal coefficients, retrieve much better time variable information of low degree zonal coefficients, improve precise orbit determination, and provide more accurate Mars free air gravity anomaly and areoid around the equatorial region.     

Lunar gravity field modeling critical analysis and challenges

This paper summarizes and provides a critical analysis of the historical developments of lunar gravitational models from the earliest use of ground based tracking systems of the Lunar Orbiter to the Lunar Prospector mission. This encompasses a comprehensive and critical analysis of the various methods used in the estimation of the gravity coefficients and the processing of large batches of diverse measurements and data types. It has been shown that weakness exists in the current models of the lunar gravity field, which is primarily due to the lack of far side lunar tracking data information, which makes the lunar potential modeling difficult but expected to be overcome as data from SELENE satellite-to-satellite tracking becomes available. Comparisons of various lunar models reveal an agreement in the low order coefficients of the spherical harmonics. However, substantial differences in the models exist in the higher-order harmonics. A numerical comparison has been presented showing the performance of all the contemporary lunar gravitational models used within the astrodynamics community and available in public domain. Improvements to the current models are part of a continuing process and the recent model improvements and future possibilities in lunar gravity modeling are discussed. A brief review of the recent missions has been presented. It is hoped that this critical review will benefit the researchers by presenting the historical as well as state of the art in this field.     

Proposal of application of same beam VLBI measurements in precision orbit determination of lunar orbiter and return capsule and lunar gravity field simulation in Chang’E-3 mission

High accuracy differenced phase delay can be obtained by observing multiple point frequencies of two spacecraft using the same beam Very Long Baseline Interferometry (VLBI) technology. Its contribution in lunar spacecraft precision orbit determination has been performed during the Japanese lunar exploration mission SELENE. In consideration that there will be an orbiter and a return capsule flying around the moon during the Chinese lunar exploration future mission Chang’E-3, the contributions of the same beam VLBI in spacecraft precision orbit determination and lunar gravity field solution have been investigated. Our results show that the accuracy of precision orbit determination can be improved more than one order of magnitude after including the same beam VLBI measurements. There are significant improvements in accuracy of low and medium degree coefficients of lunar gravity field model obtained from combination of two way range and Doppler and the same beam VLBI measurements than the one that only uses two way range and Doppler data, and the accuracy of precision orbit determination can reach meter level.     

Inversion of satellite gradiometry data using statistically modified integral formulas for local gravity field recovery

The satellite gravity gradiometric data can be used directly to recover the gravity anomaly at sea level using inversion of integral formulas. This approach suffers by the spatial truncation errors of the integrals, but these errors can be reduced by modifying the formulas. It allows us to consider smaller coverage of the satellite data over the region of recovery. In this study, we consider the second-order radial derivative (SORD) of disturbing potential (T_rr) and determine the gravity anomaly with a resolution of 1° × 1° at sea level by inverting the statistically modified version of SORD of extended Stokes’ formula. Also we investigate the effect of the spatial truncation error on the quality of inversion considering noise of T_rr. The numerical investigations show satisfactory results when the area of T_rr coverage is the same with that of the gravity anomaly and the integral formula is modified by the biased least-squares modification. The error of recovery will be about 6 mGal after removing the regularization bias in the presence of 1 mE noise in T_rr measured on the orbit.