Altimetry-derived Gravity Anomalies Research Articles

High-resolution regional gravity field modeling in data-challenging regions for the realization of geopotential-based height systems

Modern height systems are based on the combination of satellite positioning and gravity field models of high resolution. However, in many regions, especially developing or newly industrializing countries, there is no (reliable) regional gravity model at all, due to challenges such as limited data availability, unknown/low data quality, and missing metadata. This paper addresses this issue in a case study of Colombia, where eight decades of historical terrestrial and airborne gravity measurements are available but widely contain systematic errors, outliers, and biases. Correspondingly, processing strategies and structures are proposed and applied to validate and improve the quality of old gravity datasets. A novel method is developed based on spherical radial basis functions (SRBFs) for estimating biases, which are found in different airborne surveys with values exceeding 40 mGal. The validity of this bias estimation method is demonstrated both by a simulation test and by the evaluation of the airborne data in comparison to the SATOP (SAtellite-TOPography) model, which merges the satellite-only global gravity model GOCO06s with the Earth2014 topography model. The terrestrial and airborne data are then combined with a global gravity model (GGM), ultra-high-resolution topography models, as well as altimetry-derived gravity anomalies from DTU21GRA for the offshore areas. The results are presented in terms of height anomalies (QGeoidCOL2023), and they are thoroughly validated using GPS/leveling data both in the absolute and relative manner. The standard deviation in comparison to the GPS/leveling data after applying a correction surface to account for the datum inconsistencies amounts to 15.76 cm, which is 27% smaller compared to the mean standard deviation value given by five recent high-resolution GGMs, and 36% smaller than the one delivered by the latest South American quasi-geoid model QGEOID2021. The relative validation results show that QGeoidCOL2023 performs better, i.e., delivers lower RMS errors than the GGMs and QGEOID2021 in all the baseline length groups. These results indicate the validity and benefits of the developed methods and procedures, which can be used for other data-challenging areas to facilitate the realization of geopotential-based height systems.Graphical

A VGGNet-based correction for satellite altimetry-derived gravity anomalies to improve the accuracy of bathymetry to depths of 6 500 m

A VGGNet-based correction for satellite altimetry-derived gravity anomalies to improve the accuracy of bathymetry to depths of 6 500 m

The optimization of marine geoid model from altimetry data using Least Squares Stokes modification approach with additive corrections across Malaysia

ABSTRACT Due to the high cost and time constraints, geoid and gravity surveys utilizing airborne and shipborne surveys can only be implemented in marine areas with limited coverage. Satellite altimeter has become an essential tool for global geoid and gravity field recovery. With approximately 60% observation coverage of the Earth’s surface for ocean height, researchers can replace conventional marine geoid models by conducting faster surveys over massive areas at a minimal cost. This study attempts to develop a marine geoid model from multi-mission satellite altimetry along-track data using the Least Squares Modification of Stokes with Additive Corrections. The gravity anomaly has been computed using Gravity Software, and the planar Fast Fourier Transformation method has been applied. The evaluation, selection, blunder detection, combination, and re-gridding of the altimetry-derived gravity anomalies and Global Geopotential Model data are demonstrated. The cross-validation approach has been employed in the cleaning and quality control the data using the Kriging interpolation method. The optimal condition modification parameters of the spherical cap, terrestrial gravity data error, and correlation length have also been applied. Then, the additive corrections based on Downward Continuation, Atmospheric Effects, and Ellipsoidal corrections were combined with the estimated geoid to provide a precise marine geoid over the Malaysian seas. The findings have been evaluated with the MyGeoid17 model from the Department of Survey and Mapping Malaysia. The validation yields satisfactory results with accuracy up to a centimetre level. Hence, the marine geoid model can be utilized for orthometric height determination in marine areas over the Malaysian seas.

Optimised gravity anomaly fields from along-track multi-mission satellite altimeter over Malaysian seas

Marine gravity anomalies are crucial parameters and elements for determining coastal and ocean geoid, tectonics and crustal structures, as well as offshore studies. This study aims to derive and develop a marine gravity anomaly model over Malaysian seas from multi-mission altimetry data. Universiti Teknologi Malaysia 2020 Mean Sea Surface Model is computed based on along-track data from nine satellite missions, incorporating TOPEX, Jason-1, Jason-2, ERS-2, Geosat Follow on (GFO), Envisat-1, CryoSat-2, SARAL/AltiKa, and Sentinel-3A. The data exploited are from 1993 to 2019 (27 years). Residual gravity anomaly is computed using Gravity Software, and two-dimensional planar Fast Fourier Transformation method is applied. The evaluation, selection, blunder detection, combination, and re-gridding of the altimetry-derived gravity anomalies and Global Geopotential Model data are demonstrated. Cross-validation procedure is employed for data cleaning and quality control using the Kriging interpolation method. Then, cross-validation procedure is applied to the tapering window width 200, which adopting the GECO model denotes the optimum gravity anomaly with root mean square errors in the range of ± 4.2472 mGal to ± 6.0202 mGal. The findings suggest that the estimated marine gravity anomaly is acceptable to be implemented in the marine geoid determination and bathymetry estimation over Malaysian seas. In addition, the results of this study are valuable for geodetic and geophysical applications in marine areas.

High-Resolution Bathymetry in Shallow Waters off the Southern Coast of Korea from Satellite Altimetry and Remote Sensed Imagery

Kim, K.B. and Yun, H.S., 2021. High-resolution bathymetry in shallow waters off the southern coast of Korea from satellite altimetry and remote sensed imagery. In: Lee, J.L.; Suh, K.-S.; Lee, B.; Shin, S.; and Lee, J. (eds.), Crisis and Integrated Management for Coastal and Marine Safety. Journal of Coastal Research, Special Issue No. 114, pp. 390–394. Coconut Creek (Florida), ISSN 0749-0208. Bathymetry in shallow waters off coastal areas has been measured using conventional methods such as with single-beam and multi-beam echo-sounders installed on the ship. However, shipborne depth data are spatially limited and unevenly distributed over shallow waters off coastal areas. In this study, various methods that use satellite altimetry-derived gravity anomalies and high-resolution remote sensed imagery were explored for the recovery of high-resolution bathymetry data over shallow waters off Gwangyang Bay between Yeosu Peninsula and Namhae Island on the South Sea of Korea. Estimated high-resolution bathymetry data from satellite altimetry-derived gravity anomalies and remote sensed imagery were compared with shipborne depth measurements to validate their accuracy in shallow waters. This study concluded that bathymetry data estimated with the gravity-geologic method (GGM) in shallow waters are better than those predicted by Sentinel-2 imagery.

Coastal gravity field refinement by combining airborne and ground-based data

Gravity field modelling in coastal region faces challenges due to the degradation of the quality of altimeter data and poor coverage of gravimetric measurements. Airborne gravimetry can provide seamless measurements both onshore and offshore with uniform accuracies, which may alleviate the coastal zone problem. We study the role of airborne data for gravity field recovery in a coastal region and the possibility to validate coastal gravity field model against recent altimetry data (CryoSat-2, Jason-1, and SARAL/Altika). Moreover, we combine airborne and ground-based gravity data for regional refinement and quantify and validate the contribution introduced by airborne data. Numerical experiments in the Gippsland Basin over the south-eastern coast of Australia show that the effects introduced by airborne gravity data appear as small-scale patterns on the centimetre scale in terms of quasi-geoid heights. Numerical results demonstrate that the combination of airborne data improves the coastal gravity field, and the recent altimetry data can be potentially used to validate the high-frequency signals introduced by airborne data. The validation against recent altimetry data demonstrates that the combination of airborne measurements improves the coastal quasi-geoid, by ~ 5 mm, compared with a model computed from terrestrial and altimetry-derived gravity anomalies alone. These results show that the recently released altimetry data with relatively denser spatial resolutions and higher accuracies than older altimeter data may be beneficial for gravity field model assessment in coastal areas.

Evaluation of the Accuracy of Bathymetry on the Nearshore Coastlines of Western Korea from Satellite Altimetry, Multi-Beam, and Airborne Bathymetric LiDAR.

Bathymetric mapping is traditionally implemented using shipborne single-beam, multi-beam, and side-scan sonar sensors. Procuring bathymetric data near coastlines using shipborne sensors is difficult, however, this type of data is important for maritime safety, marine territory management, climate change monitoring, and disaster preparedness. In recent years, the bathymetric light detection and ranging (LiDAR) technique has been tried to get seamless geospatial data from land to submarine topography. This paper evaluated the accuracy of bathymetry generated near coastlines from satellite altimetry-derived gravity anomalies and multi-beam bathymetry using a tuning density contrast of 5000 kg/m3 determined by the gravity-geologic method. Comparing with the predicted bathymetry of using only multi-beam depth data, 78% root mean square error from both multi-beam and airborne bathymetric LiDAR was improved in shallow waters of nearshore coastlines of the western Korea. As a result, the satellite-derived bathymetry estimated from the multi-beam and the airborne bathymetric LiDAR was enhanced to the accuracy of about 0.2 m.

Improved gravity anomaly fields from retracked multimission satellite radar altimetry observations over the Persian Gulf and the Caspian Sea

Satellite radar altimetry observations are used to derive short wavelength gravity anomaly fields over the Persian Gulf and the Caspian Sea, where in situ and ship-borne gravity measurements have limited spatial coverage. In this study the retracking algorithm ‘Extrema Retracking’ (ExtR) was employed to improve sea surface height (SSH) measurements that are highly biased in the study regions due to land contaminations in the footprints of the satellite altimetry observations. ExtR was applied to the waveforms sampled by the five satellite radar altimetry missions: TOPEX/POSEIDON, JASON-1, JASON-2, GFO and ERS-1. Along-track slopes have been estimated from the improved SSH measurements and used in an iterative process to estimate deflections of the vertical, and subsequently, the desired gravity anomalies. The main steps of the gravity anomaly computations involve estimating improved SSH using the ExtR technique, computing deflections of the vertical from interpolated SSHs on a regular grid using a biharmonic spline interpolation and finally estimating gridded gravity anomalies. A remove–compute–restore algorithm, based on the fast Fourier transform, has been applied to convert deflections of the vertical into gravity anomalies. Finally, spline interpolation has been used to estimate regular gravity anomaly grids over the two study regions. Results were evaluated by comparing the estimated altimetry-derived gravity anomalies (with and without implementing the ExtR algorithm) with ship-borne free air gravity anomaly observations, and free air gravity anomalies from the Earth Gravitational Model 2008 (EGM2008). The comparison indicates a range of 3–5 mGal in the residuals, which were computed by taking the differences between the retracked altimetry-derived gravity anomaly and the ship-borne data. The comparison of retracked data with ship-borne data indicates a range in the root-mean-square-error (RMSE) between approximately 1.8 and 4.4 mGal and a bias between 0.4062 and 2.1413 mGal over different areas. Also a maximum RMSE of 4.4069 mGal, with a mean value of 0.7615 mGal was obtained in the residuals. An average improvement of 5.2746 mGal in the RMSE of the altimetry-derived gravity anomalies corresponding to 89.9 per cent was obtained after applying the ExtR post-processing.

THE EVALUATION OF THE NEW ZEALAND'S GEOID MODEL USING THE KTH METHOD / NAUJOSIOS ZELANDIJOS GEOIDO MODELIO VERTINIMAS KTH METODU / ОЦЕНКА МОДЕЛИ ГЕОИДА НОВОЙ ЗЕЛАНДИИ С ПРИМЕНЕНИЕМ МЕТОДА КТН

We compile a new geoid model at the computation area of New Zealand and its continental shelf using the method developed at the Royal Institute of Technology (KTH) in Stockholm. This method utilizes the least-squares modification of the Stokes integral for the biased, unbiased, and optimum stochastic solutions. The modified Bruns-Stokes integral combines the regional terrestrial gravity data with a global geopotential model (GGM). Four additive corrections are calculated and applied to the approximate geoid heights in order to obtain the gravimetric geoid. These four additive corrections account for the combined direct and indirect effects of topography and atmosphere, the contribution of the downward continuation reduction, and the formulation of the Stokes problem in the spherical approximation. The gravimetric geoid model is computed using two heterogonous gravity data sets: the altimetry-derived gravity anomalies from the DNSC08 marine gravity database (offshore) and the ground gravity measurements from the GNS Science gravity database (onshore). The GGM coefficients are taken from EIGEN-GRACE02S complete to degree 65 of spherical harmonics. The topographic heights are generated from the 1×1 arc-sec detailed digital terrain model (DTM) of New Zealand and from the 30×30 arc-sec global elevation data of SRTM30_PLUS V5.0. The least-squares analysis is applied to combine the gravity and GPS-levelling data using a 7-parameter model. The fit of the KTH geoid model with GPS-levelling data in New Zealand is 7 cm in terms of the standard deviation (STD) of differences. This STD fit is the same as the STD fit of the NZGeoid2009, which is the currently adopted official quasigeoid model for New Zealand. Santrauka Stokholmo Karališkajame technologijos institute (KTH) sukurtu metodu apskaičiuotas naujas Naujosios Zelandijos ir kontinentinio šelfo geoido modelis. Taikoma Stokso integralo mažiausiųjų kvadratų modifikacija, įvertinant paklaidas ir jų nevertinant bei ieškant optimalių stochastinių sprendinių. Modifikuotas Bruno ir Stokso integralas sieja regioninius žemyninius gravimetrinius duomenis su globaliuoju geopotencialo modeliu (GGM). Gravimetriniam geoidui gauti skaičiuojamos keturios papildomos pataisos: topografinės situacijos ir atmosferos tiesioginės ir netiesioginės įtakos, redukcijos įtakos ir Stokso integralo taikymo sferiniam paviršiui. Gravimetrinis geoido modelis apskaičiuotas pagal du duomenų rinkinius: DNSC08 jūrinių gravimetrinių duomenų bazėje (šelfas) esančias altimetriniu metodu nustatytas sunkio pagreičio anomalijas ir žemyninės dalies gravimetrinių matavimų duomenis iš GNS gravimetrinės duomenų bazės (pakrantė). GGM koeficientai imti iš EIGEN-GRACE02S modelio sferinių iki 65 laipsnio harmonikų. Topografiniai aukščiai sugeneruoti iš Naujosios Zelandijos 1×1 sekundės detaliojo skaitmeninio reljefo modelio ir iš 30×30 sekundžių globaliojo aukščių modelio SRTM30_PLUS V5.0. Gravimetriniams ir GPS niveliacijos duomenims sujungti taikytas mažiausiųjų kvadratų 7 parametrų metodas. KTH metodu sudaryto geoido modelio vidutinė kvadratinė paklaida 7 cm. Tai sutampa su NZGeoid 2009 geoido modelio, taikomo Naujoje Zelandijoje, tikslumu. Резюме Модель геоида континентального шельфа Новой Зеландии построена с применением метода, созданного в Королевском технологическом институте Стокгольма. Данный метод основан на модификации решения интеграла Стокса методом наименьших квадратов с оценкой или без оценки погрешностей и поиском оптимальных статистических решений. Модифицированный интеграл БрунаСтокса объединяет региональные надземные гравиметрические данные с глобальной геопотенциальной моделью (GGM). Для определения гравиметрического геоида вычисляются дополнительные поправки прямого и косвенного влияния топографии и атмосферы, редукции и применения проблемы Стокса для сферической поверхности. Гравиметрическая модель геоида вычисляется на основе двух баз данных: альтиметрическим методом определенных аномалий силы тяжести в базе морских гравиметрических данных DNSC08 (шельф) и надземной части гравиметрических измерений из базы данных GNS. Коэффициенты GGM взяты из сферических гармоник до 65 степени модели EIGENGRACEO2S. Топографические высоты сгенерированы из детальной цифровой модели рельефа Новой Зеландии с сеткой 1×1 секунду и из глобальной модели высот SRTM30_PLUSv5.0 с сеткой 30×30 секунд. Для объединения гравиметрических и GPSнивелирных данных применялся метод наименьших квадратов с 7 параметрами. Среднеквадратическая погрешность модели геоида, созданной по методу КТН, равна 7 см. Точность аналогична точности применяемой в Новой Зеландии модели геоида NZGeoid2009.

Bathymetry Estimation Using the Gravity-Geologic Method: An Investigation of Density Contrast Predicted by the Downward Continuation Method

The downward continuation (DWC) method was used to determine the density contrast between the seawater and the ocean bottom topographic mass to estimate accurate bathymetry using the gravity-geologic method (GGM) in two study areas, which are located south of Greenland (Test Area #1: 40-50°W and 50-60°N) and south of Alaska (Test Area #2: 140-150°W and 45-55°N). The data used in this study include altimetry-derived gravity anomalies, shipborne depths and gravity anomalies. Density contrasts of 1.47 and 1.30 g cm^(-3) were estimated by DWC for the two test areas. The considerations of predicted density contrasts can enhance the accuracy of 3~4 m for GGM. The GGM model provided results closer to the NGDC (National Geophysical Data Center) model than the ETOPO1 (Earth topographical database 1) model. The differences along the shipborne tracks between the GGM and NGDC models for Test Areas #1 and #2 were 35.8 and 50.4 m in standard deviation, respectively. Furthermore, these differences were more strongly correlated with gravity anomalies than bathymetry in the test areas. It is shown that an accuracy of under 40 m can be obtained with comparisons to shipborne depths only in Test Area #1.

Bathymetry enhancement by altimetry-derived gravity anomalies in the East Sea (Sea of Japan)

The gravity-geologic method (GGM) was used to enhance the bathymetry of the East Sea (Sea of Japan) with satellite altimetry-derived free-air gravity anomalies and shipborne depth measurements. By comparison with the bathymetry model of Smith and Sandwell’s (SAS) approach (1994), GGM was found to have an advantage with short wavelength (≤12 km) components, while SAS better predicts longer wavelength (≥25 km) components, despite its dependency on density contrast. To mitigate this limitation, a tuning density contrast of 10.25 g/cm3 between seawater and the seafloor was primarily estimated by the downward continuation method and then validated by the check points method with GGM. Similarly, SAS is limited by the “A” value in low-pass part of the Wiener filter, which defines the effective range of the wavelength components on bathymetry. As a final result, we present an enhanced GGM bathymetry model by integrating all available data.

A comparison of recent Earth gravitational models with emphasis on their contribution in refining the gravity and geoid at continental or regional scale

Since the publication of the Earth gravitational model (EGM)96 considerable improvements in the observation techniques resulted in the development of new improved models. The improvements are due to the availability of data from dedicated gravity mapping missions (CHAMP, GRACE) and to the use of 5′ × 5′ terrestrial and altimetry derived gravity anomalies. It is expected that the use of new EGMs will further contribute to the improvement of the resolution and accuracy of the gravity and geoid modeling in continental and regional scale. To prove this numerically, three representative Earth gravitational models are used for the reduction of several kinds of data related to the gravity field in different places of the Earth. The results of the reduction are discussed regarding the corresponding covariance functions which might be used for modeling using the least squares collocation method. The contribution of the EIGEN-GL04C model in most cases is comparable to that of EGM96. However, the big difference is shown in the case of EGM2008, due not only to its quality but obviously to its high degree of expansion. Almost in all cases the variance and the correlation length of the covariance functions of data reduced to this model up to its maximum degree are only a few percentages of corresponding quantities of the same data reduced up to degree 360. Furthermore, the mean value and the standard deviation of the reduced gravity anomalies in extended areas of the Earth such as Australia, Arctic region, Scandinavia or the Canadian plains, vary between −1 and +1 and between 5 and 10 × 10−5 ms−2, respectively, reflecting the homogenization of the gravity field on a regional scale. This is very important in using least squares collocation for regional applications. However, the distance to the first zero-value was in several cases much longer than warranted by the high degree of the expansion. This is attributed to errors of medium wavelengths stemming from the lack of, e.g., high-quality data in some area.

The quasigeoid modelling in New Zealand using the boundary element method

We compile a quasigeoid model at the study area of New Zealand using theboundary element method (BEM). The direct BEM formulation for the Laplace equationis applied to obtain a numerical solution to the linearized fixed gravimetric boundaryvalueproblem in points at the Earth’s surface. The numerical scheme uses the collocationmethod with linear basis functions. It involves a discretisation of the Earth’s surfacewhich is considered as a fixed boundary. The surface gravity disturbances represent theoblique derivative boundary condition. The geocentric positions of the collocation pointsare determined combining the digital elevation data and the a priori quasigeoid model(onshore) and the mean sea surface topography (offshore). In our numerical realization,we use the global elevation data from SRTM30PLUS V5.0, the detailed DTM of NewZealand, the EGM2008 quasigeoid heights, and the mean sea surface topography fromthe DNSC08 marine database. The gravity disturbances are computed using two heterogeneousgravity data sets: the altimetry-derived gravity anomalies from the DNSC08gravity database (offshore) and the observed ground gravity anomalies from the GNSScience gravity database (onshore). The transformation of gravity anomalies to gravitydisturbances is realized using the quasigeoid heights calculated from the EGM2008 globalgeopotential model. The new experimental quasigeoid model NZQM2010 is compiled atthe study area of New Zealand bounded by the parallels of 34 and 47.5 arc-deg southernlatitude and the meridians of 166 and 179 arc-deg eastern longitude. The least-squaresanalysis is applied to combine the gravimetric solution with GPS-levelling data using a7-parameter model. NZQM2010 is validated using GPS-levelling data and compared withthe existing regional and global quasigeoid models NZGeoid2009 and EGM2008.&nbsp

Gravity Anomaly Map over The Black Sea Using Corrected Sea Surface Heights from ERS1, ERS2 and Topex/Poseidon Satellite Altimetry Missions

Approximately nine-year data from ERS1, ERS2 and TOPEX/POSEIDON (T/P) satellite altimetry missions have been used for the recovery of gravity anomalies over the Black Sea. The Corrected Sea Surface Height product of Aviso/Altimetry has been proven to be homogeneous after a cross-over adjustment. The Least Squares Collocation method was applied in a so-called “remove-restore” procedure. The residual geoid heights, obtained by subtracting EGM96 geoid heights from cross-over adjusted sea surface heights, were inverted to recover residual gravity anomalies in a grid structure over the Black Sea. Finally, EGM96 free air gravity anomalies were added to the predicted residual gravity anomalies to obtain the free air gravity anomalies. In order to check the consistency with respect to an external source, these computed free air gravity anomalies were compared to ship gravity observations, and to alternative satellite altimetry derived gravity anomalies. Comparisons with the observed gravity data yielded that external consistency of the gravity anomalies computed in this study is about 3 mGal for individual ship tracks. Overall external consistency in the test area is 4.8 mGal. Comparison with other satellite altimetry derived gravity anomalies presented a good agreement.