A Precise Geoid Model for Africa: AFRgeo2019

In the framework of the IAG African Geoid Project, an attempt towards a precise geoid model for Africa is presented in this investigation. The available gravity data set suffers from significantly large data gaps. These data gaps are filled using the EIGEN-6C4 model on a 15′× 15′ grid prior to the gravity reduction scheme. The window remove-restore technique (Abd-Elmotaal and Kühtreiber, Phys Chem Earth Pt A 24(1):53–59, 1999; J Geod 77(1–2):77–85, 2003) has been used to generate reduced anomalies having a minimum variance to minimize the interpolation errors, especially at the large data gaps. The EIGEN-6C4 global model, complete to degree and order 2190, has served as the reference model. The reduced anomalies are gridded on a 5′× 5′ grid employing an un-equal weight least-squares prediction technique. The reduced gravity anomalies are then used to compute their contribution to the geoid undulation employing Stokes’ integral with Meissl (Preparation for the numerical evaluation of second order Molodensky-type formulas. Ohio State University, Department of Geodetic Science and Surveying, Rep 163, 1971) modified kernel for better combination of the different wavelengths of the earth’s gravity field. Finally the restore step within the window remove-restore technique took place generating the full gravimetric geoid. In the last step, the computed geoid is fitted to the DIR_R5 GOCE satellite-only model by applying an offset and two tilt parameters. The DIR_R5 model is used because it turned out that it represents the best available global geopotential model approximating the African gravity field. A comparison between the geoid computed within the current investigation and the existing former geoid model AGP2003 (Merry et al., A window on the future of geodesy. International Association of Geodesy Symposia, vol 128, pp 374–379, 2005) for Africa has been carried out

Evaluation of the Recent African Gravity Databases V2.x

In the framework of the activities of the IAG Sub-Commission on the gravity and geoid in Africa, a recent set of gravity databases has been established. They are namely: AFRGDB_V2.0 and AFRGDB_V2.2. The AFRGDB_V2.0 has been created using the window remove-restore technique employing EGM2008 as geopotential Earth model complete to degree and order 1800. The AFRGDB_V2.2 has been established using the Residual Terrain Model (RTM) reduction technique employing GOCE DIR_R5 complete to degree and order 280, using the best RTM reference surface. The available gravity data set for Africa, used to establish the above mentioned two independently derived databases, consists of shipborne, altimetry derived gravity anomalies and of land point gravity data. In particular, the data set of point gravity values shows clear deficits with regard to a homogeneous data coverage over the completely African continent. The establishment of the gravity databases has been carried-out using the weighted least-squares prediction technique, in which the point gravity data on land has got the highest precision, while the shipborne and altimetry gravity data got a moderate precision. In this paper a new gravity data set on land and on sea, which became recently available for the IAG Sub-Commission on the gravity and geoid in Africa, located partly in the gap areas of the data set used for generating the gravity databases, has been employed to evaluate the accuracy of the previously created gravity databases. The results show reasonable accuracy of the established gravity databases considering the large data gaps in Africa

AFRgeo_v1.0: A Geoid Model for Africa

The paper presents an attempt to compute a geoid model for Africa in the framework of the IAG African Geoid Project. The available gravity data set consists of land point gravity data as well as shipborne and altimetry-derived gravity anomaly data, having a lot of significant gaps allover the continent. The reduced gravity anomalies are gridded on a 50´ x 50´ grid using an iterative process employing a tailored reference model, to fill in the data gaps, and a weighted least-squares prediction technique. The tailored reference model, up to degree and order 2160, has been used to compute a geoid model for Africa within the window remove-restore technique employing the Stokes integral in frequency domain by the 1-D FFT technique. For the sake of comparison, another geoid model for Africa has been computed using a different approach. This approach renounces the use of the topographic-isostatic reduction and uses the recent global combined geopotential model EIGEN-6C4, complete to degree and order 2190, serving as the reference model. The computed geoids are scaled using the GO_CONS_GCF_2_DIR_R5 GOCE satellite-only model, which represents the best available global geopotential model approximating the African gravity field. An extensive comparison between the geoids computed within the current investigation and the former geoid model for Africa has been carried out

Estimation of GRACE-like geopotential models

The availability of time-dependent global gravity field models like EIGEN-6C or EIGEN-6C2 allows the generation of GRACE-like geopotential Earth models. The paper introduces an approach to generate those GRACE-like models using time-dependent global gravity field models. Such GRACE-like models can then be used to estimate, for example, the Terrestrial Water Storage (TWS) for the months where GRACE data are not available. The paper gives the necessary derivation of such GRACE-like models from the time-dependent global gravity field models. GRACE-like models, created by using the time-dependent global gravity field models at the same months where GRACE data are available, are compared to the original GRACE models. The results proved that the GRACE-like models give comparable values to the original GRACE models and no loss of spectrum power occurs

Behaviour of earth’s crust due to topographic loads derived by inverse and direct isostasy

The behaviour of the earth’s crust due to topographic loads can be derived by either inverse or direct approach. As for the inverse approach, it is postulated that the density anomaly is proportional to the earth’s radius vector so that it is linearly related to topography by a convolution of the topography and an isotropic kernel function. Accordingly, one can prove that the attraction of the compensating masses is also a convolution of the topography and an isotropic isostatic response function. Such an isostatic response function can be determined by deconvolution. This paper gives the derivation of such a deconvolution by means of spherical harmonics. A practical determination of the isotropic isostatic response function needs the harmonic analysis of both the topography and the attraction of the compensating masses. Applying the principle of inverse isostasy, by which we aim to achieve zero isostatic anomalies, then the attraction of the compensating masses equals the Bouguer anomalies with an opposite sign. The harmonic analysis of the Bouguer anomalies is thus a combination of the harmonic analysis of the topographic potential and the already existing global reference models. As for the direct approach, consider that the earth’s crust is an infinite thin plate subject to topographic loads. The solution of such a bent plate represents the displacement of the earth’s crust due to topographic loads. The paper illustrates that the exact solution of the bent plate is given by the Kelvin function keix. A practical application has been carried out for both approaches using EGM96 and GPM98CR geopotential earth models as well as TUG87 and TBASE digital height models. The results show that the estimated isotropic isostatic response functions derived by the inverse approach behave similarly as that given by direct approach represented by the Kelvin function keix

Assessing Groundwater Sustainability in the Arabian Peninsula and Its Impact on Gravity Fields through Gravity Recovery and Climate Experiment Measurements

This study addresses the imperative to comprehend gravity shifts resulting from groundwater storage (GWS) variations in the Arabian Peninsula. Despite the critical importance of water resource sustainability and its relationship with gravity, limited research emphasizes the need for expanded exploration. The investigation explores the impact of GWS extraction on the gravity field, utilizing Gravity Recovery and Climate Experiment (GRACE) and Global Land Data Assimilation System (GLDAS) data in addition to validation using the WaterGAP Global Hydrology Model (WGHM). Spanning April 2002 to June 2023, this study predicts GWS trends over the next decade using the Seasonal Autoregressive Integrated Moving Average (SARIMA) model. The comprehensive time-series analysis reveals a significant GRACE-derived groundwater storage (GWS) trend of approximately −4.90 ± 0.32 mm/year during the study period. This trend has a notable impact on the gravity anomaly (GA) values, as observed through the decomposition analysis. The projected GWS indicates a depletion rate of 14.51 km3/year over the next decade. The correlation between GWS and GA is substantial at 0.80, while the GA and rainfall correlation is negligible due to low precipitation rates. Employing multiple linear regression explains 80.61% of the variance in gravity anomaly due to GWS, precipitation, and evapotranspiration. This study investigates climate change factors—precipitation, temperature, and evapotranspiration—providing a holistic understanding of the forces shaping GWS variations. Precipitation and evapotranspiration exhibit nearly equal values, limiting GWS replenishment opportunities. This research holds significance in studying extensive GWS withdrawal in the Arabian Peninsula, particularly concerning crust mass stability