Recovering Marine Gravity Over the Gulf of Guinea From Multi-Satellite Sea Surface Heights

A regional gravity field product, comprising vertical deflections and gravity anomalies, of the Gulf of Guinea (15°W to 5°E, 4°S to 4°N) has been developed from sea surface heights (SSH) of five altimetry missions. Though the remove-restore technique was adopted, the deflections of the vertical were computed directly from the SSH without the influence of a global geopotential model. The north-component of vertical deflections was more accurate than the east-component by almost three times. Analysis of results showed each satellite can contribute almost equally in resolving the north-component. This is attributable to the nearly northern inclinations of the various satellites. However, Cryosat-2, Jason-1/GM, and SARAL/AltiKa contributed the most in resolving the east-component. We attribute this to the superior spatial resolution of Cryosat-2, the lower inclination of Jason-1/GM, and the high range accuracy of the Ka-band of SARAL/AltiKa. Weights of 0.687 and 0.313 were, respectively, assigned to the north and east components in order to minimize their non-uniform accuracy effect on the resultant gravity anomaly model. Histogram of computed gravity anomalies compared well with those from renowned models: DTU13, SIOv28, and EGM2008. It averagely deviates from the reference models by −0.33 mGal. Further assessment was done by comparing it with a quadratically adjusted shipborne free-air gravity anomalies. After some data cleaning, observations in shallow waters, as well as some ship tracks were still unreliable. By excluding the observations in shallow waters, the derived gravity field model compares well in ocean depths deeper than 2,000 m.

Performance Assessment of PPP-AR Positioning and Zenith Total Delay Estimation with Modernized CSRS-PPP

The precise point positioning (PPP) method has become more popular due to powerful online global navigation satellite system (GNSS) data processing services, such as the Canadian Spatial Reference System-PPP (CSRS-PPP). At the end of 2020, the CSRS-PPP service launched the ambiguity resolution (AR) feature for global positioning system (GPS) satellites. More reliable results are obtained with AR compared to the results with traditional ambiguity-float PPP. In this study, the performance of the modernized CSRS-PPP was comparatively assessed in terms of static positioning and zenith total delay (ZTD) estimation. Data for 1 month in the year 2019 obtained from 47 international GNSS service (IGS) stations were processed before and after modernization of the CSRS-PPP. The processes were conducted for GPS and GPS + GLONASS (GLObalnaya NAvigatsionnaya Sputnikovaya Sistema) satellite combinations. Besides, the results were analyzed in terms of accuracy and convergence time. According to the solutions, the AR feature of the CSRS-PPP improved the accuracy by about 50% in the east component for GPS + GLONASS configuration. The root-mean-square error (RMSE) of the ZTD difference between modernized CSRS-PPP service and IGS final troposphere product is 5.8 mm for the GPS-only case.

The quality of velocities from GNSS campaign measurements when gaps in data exist

<p>In this study, we investigate the effect of gaps in data on the accuracy of deformation rates produced from GNSS campaign measurements. Our motivation in investigating gaps in data is that campaign GNSS time series might not be collected regularly due to various constraints in real life conditions. We used the baseline components produced from continuous GPS time series of JPL, NASA from a global network of the IGS to generate data gaps. The solutions of the IGS continuous GNSS time series were decimated to the solutions of the campaign data sampled one measurement per each month or three measurements per year. Furthermore, the effect of antenna set-up errors, which show Gaussian distribution, in campaign measurements was taken into account following the suggestions from the literature. The number of gaps in campaign GNSS time series was incremented plus one for each different trial until only one month is left within the specific year. Eventually, we tested whether the velocities obtained from GNSS campaign series containing data gaps differ significantly from the velocities derived from continuous data which is taken as to be the “truth”. The initial efforts using the samples from a restricted amount of data reveal that the deformation rate produced from the east component is more sensitive to the gaps in data than that of the components north and vertical.</p><p><strong>Keywords: </strong>GPS time series; GPS campaigns; Velocity estimation; Gaps in data; Deformation.</p>

Combining multi-GNSS phase bias products for improved undifferenced ambiguity resolution

<p>The rapid development of multi-GNSS constellations, e.g., Galileo and BeiDou, is catalyzing innovations in high-precision applications. Precise point positioning ambiguity resolution (PPP-AR) has been essential to achieving the highest positioning precision using multi-GNSS data in wide areas. In recent years, several International GNSS Service analysis centers (IGS ACs such as CNES, CODE, WHU) have been providing phase bias products to enable PPP-AR, but whether these AC-specific multi-GNSS (e.g., GPS/Galileo/BeiDou-2/3) products are compatible with each other and whether they can be reconciled for an IGS combination product are pending. In this study, we combined phase bias products from four organizations for GPS/Galileo/BeiDou-2/3 in 2020. All phase bias products are first converted to observable-specific representation and then reconciled with satellite clocks before the combination; their capability of recovering integer undifferenced ambiguities has been always kept after properly addressing inter-system biases and satellite attitude discrepancies. It is found that the RMS of clock alignment residuals are around 6.8, 7.1, 14.9 and 14.6 ps for GPS, Galileo BeiDou-2 and BeiDou-3, respectively. BeiDou products perform worse due largely to sparse tracking networks and deficient orbit models. In a kinematic PPP experiment with 151 global MGEX (Multi-GNSS Experiment) stations, the combined phase bias products provide better or at least equivalent positioning results as opposed to AC specific products. Compared with ambiguity-float solutions, ambiguity-fixed PPP solutions can improve the positioning precision by 29-50% in the east component. With combined phase bias products, the positioning precision of GPS/Galileo/BDS-2/3 PPP-AR solutions can achieve 0.62, 0.64 and 1.90 cm in the east, north and up components, respectively, in contrast to 0.87, 0.88 and 2.60 cm for GPS only PPP-AR solutions.</p>

Bathymetry Inversion Using Vertical Deflections: a Case Study in South China Sea

As an alternative method, an algorithm for bathymetry inversion using vertical deflections is proposed. Firstly, the formulas for the bathymetry inversion from north and east components of vertical deflections are derived and the data processing is introduced. Then a local area in the South China Sea is selected as an example to experiment the method. The bathymetry inversion based on gravity anomaly was also conducted for a comparison. The results show that the bathymetry derived from the north component of the vertical deflections have almost the same accuracy as that derived from gravity anomalies and the results derived from the east component have the poorest accuracy. The experiment’s results also show that accuracy of the derived bathymetry can be improved if the fitting parameters are adjusted according to the water depths. In summary, among the gravity field products used in this study, although the gravity anomaly yielded the best performance in the bathymetry inversion, the vertical defections can still be used as supplements, especially in areas where accurate vertical deflections exist. This is because deriving gravity anomaly from altimetry observations needs additional data and calculation efforts.

MIDDLE EAST POLICY COMPONENT OF THE USA, CHINA AND RUSSIAN FEDERATION: RUSSIAN POLICY

The paper considers the assessment of the influence of the Middle East component of the policy of the United States of America, the People's Republic of China and the Russian Federation on the national security of these countries. An approach to comparing this influence is proposed, which allows us to identify the priorities of Russia's policy in the Middle East and other regions of the world. Compare the middle East policy of the States strategic triangle Russia – China – US can be used to justify recommendations to the military-political leadership of our country.

An alternative integer recovery clock method for precise point positioning with ambiguity resolution

When using Global Navigation Satellite System (GNSS) measurements, Precise Point Positioning with Ambiguity Resolution (PPP-AR) has been a popular substitute for relative positioning in geoscience applications. Compared with the Fractional Cycle Biases (FCB) method, the processing of Integer Recovery Clocks (IRC) products estimate, especially for ambiguity datum fixing, is so complex that its application has been greatly limited. Based on the concept of “carrier range”, we introduce an efficient way to implement the IRC method, termed as the alternative IRC method in this paper. In this method, the fixed ambiguities derived from PPP-AR using the FCB method, and not a fixed-ambiguity datum, are fixed in the IRC products estimate. This greatly reduces the complexity of implementing the IRC method and does not influence the accuracy of positioning. The alternative IRC method outperforms the FCB method by corroborating the consistency of daily positions in nature with international GNSS service weekly solution. To confirm this improvement, global positioning system measurements acquired over a year (2016) from approximately 500 globally distributed stations were processed. The accuracy of IRC products is approximately 20 ps and is highly stable for this year. Moreover, comparing the positioning accuracy of the FCB method to the alternative IRC method, we find that the mean root mean square over the year falls evidently from 2.03 to 1.65 mm at the east component. Therefore, we suggest that the alternative IRC method should be implemented when estimate IRC products.

Assessment of HY-2A GM data by deriving the gravity field and bathymetry over the Gulf of Guinea

Nine cycles of Haiyang-2A (HY-2A) IGDR (Interim Geophysical Data Record) data are used to derive gravity products over the Gulf of Guinea (15° W–5° E, 4° S–4° N). Firstly, the sea surface heights (SSH) and vertical deflections are derived and their precisions are evaluated. The comparison results show that the east component of vertical deflections has a poorer precision than the north component by 4.15 times. A theoretical proof was given to explain this point according to the error propagation rule. Gravity anomalies are then derived from vertical deflections using the remove–restore method. The precision of the derived HY-2A gravity anomalies is evaluated with SIO, DTU13, EGM2008, EIGEN-6C4 products. The results showed that the differences between HY-2A-derived gravity anomalies and these models have mean values larger than 0.5 mGal and std values around 7.0–7.3 mGal. In order to improve the precision, an improved new version of gravity anomalies was derived by assigning a small weight to the east component of vertical deflections, since the precision of which is poorer than the north component. Comparison with the initial model showed that the precision of the new gravity anomalies is an improvement of the initial model by approximately two times. When compared with EGM2008, EIGEN-6C4, SIOv28 and DTU13, the mean values of the differences are close to zero and standard deviation of the differences are around 2.7–3.0 mGal. The improved gravity anomalies were used to invert the bathymetry of the region using the gravity-geologic method. The modeled bathymetry compared well with a previous bathymetric study by the authors that used DTU13 gravity anomalies. It also performed well against ETOPO1 and SRTM15+V2; with difference means, standard deviations and correlation coefficients of 26.67 m, 183.09 m, 0.9562; and 12.26 m, 174.55 m, 0.9590, respectively. This implies that SSH data from HY-2A are geophysically reliable; and hence, can be incorporated with SSH data from other satellite altimeters.

Vertical Deflections and Gravity Disturbances Derived from HY-2A Data

The first Chinese altimetry satellite, Haiyang-2A (HY-2A), which was launched in 2011, has provided a large amount of sea surface heights which can be used to derive marine gravity field. This paper derived the vertical deflections and gravity disturbances using HY-2A observations for the major area of the whole Earth’s ocean from 60°S and 60°N. The results showed that the standard deviations (STD) of vertical deflections differences were 1.1 s and 3.5 s for the north component and the east component between HY-2A’s observations and those from EGM2008 and EIGEN-6C4, respectively. This indicates the accuracy of the east component was poorer than that of the north component. In order to clearly demonstrate contribution of HY-2A’s observations to gravity disturbances, reference models and the commonly used remove-restore method were not adopted in this study. Therefore, the results can be seen as ‘pure’ signals from HY-2A. Assuming the values from EGM2008 were the true values, the accuracy of the gravity disturbances was about −1.1 mGal in terms of mean value of the errors and 8.0 mGal in terms of the STD. This shows systematic errors if only HY-2A observations were used. An index of STD showed that the accuracy of HY-2A was close to the theoretical accuracy according to the vertical deflection products. To verify whether the systematic errors of gravity field were from the long wavelengths, the long-wavelength parts of HY-2A’s gravity disturbance with wavelengths larger than 500 km were replaced by those from EGM2008. By comparing with ‘pure’ HY-2A version of gravity disturbance, the accuracy of the new version products was improved largely. The systematic errors no longer existed and the error STD was reduced to 6.1 mGal.

Effects of Interferometric Radar Altimeter Errors on Marine Gravity Field Inversion

The traditional altimetry satellite, which is based on pulse-limited radar altimeter, only measures ocean surface heights along tracks; hence, leads to poorer accuracy in the east component of the vertical deflections compared to the north component, which in turn limits the final accuracy of the marine gravity field inversion. Wide-swath altimetry using radar interferometry can measure ocean surface heights in two dimensions and, thus, can be used to compute vertical deflections in an arbitrary direction with the same accuracy. This paper aims to investigate the impact of Interferometric Radar Altimeter (InRA) errors on gravity field inversion. The error propagation between gravity anomalies and InRA measurements is analyzed, and formulas of their relationship are given. By giving a group of possible InRA parameters, numerical simulations are conducted to analyze the accuracy of gravity anomaly inversion. The results show that the accuracy of the gravity anomalies is mainly influenced by the phase errors of InRA; and the errors of gravity anomalies have a linear approximation relationship with the phase errors. The results also show that the east component of the vertical deflections has almost the same accuracy as the north component.