Time-variable Gravity Research Articles

GRACE-FO precise orbit determination and gravity recovery

The gravity recovery and climate experiment follow-on (GRACE-FO) satellites, launched in May of 2018, are equipped with geodetic quality GPS receivers for precise orbit determination (POD) and gravity recovery. The primary objective of the GRACE-FO mission is to map the time-variable and mean gravity field of the Earth. To achieve this goal, both GRACE-FO satellites are additionally equipped with a K-band ranging (KBR) system, accelerometers and star trackers. Data processing strategies, data weighting approaches and impacts of observation types and rates are investigated in order to determine the most efficient approach for processing GRACE-FO multi-type data for precise orbit determination and gravity recovery. Two GPS observation types, un-differenced (UD) and double-differenced (DD) observations in general can be used for GPS-based POD and gravity recovery. The GRACE-FO KBR observations are mainly used for gravity recovery, but they can be also used for POD to improve the relative orbit accuracy. The main purpose of this paper is to study the impacts of the DD, UD and KBR observations on GRACE-FO POD and gravity recovery. The precise orbit accuracy is assessed using several tests, which include analysis of orbital fits, satellite laser ranging residuals, KBR range residuals and orbit comparisons. The gravity recovery is validated by comparing different gravity solutions through coefficient-wise comparison, degree difference variances and water height variations over the whole Earth and selected area and river basins.

Improved recovery of temporal variations of the Earth\u2019s gravity field from satellite kinematic orbits using an epoch-difference scheme

To monitor temporal variations of the Earth’s gravity field and mass transport in the Earth’s system, data from gravity recovery and climate experiment (GRACE) satellite mission and its successor GRACE Follow-On (GFO) are used. To fill in the temporal gap between these missions, other satellites’ kinematic orbits derived from GPS-based high-low satellite-to-satellite tracking data may be considered. However, it is well known that kinematic orbits are highly sensitive to various systematic errors. These errors are responsible for a non-stationary noise in the kinematic orbits, which is difficult to handle. As a result, the quality of the obtained gravity field solutions is reduced. In this research, we propose to apply an epoch-difference (ED) scheme in the context of the classical dynamic approach to gravity field recovery. Compared to the traditional undifferenced (UD) scheme, the ED scheme is able to mitigate constant or slowly varying systematic errors. To demonstrate the added value of the ED scheme, three sets of monthly gravity field solutions produced from 6 years of GRACE kinematic orbits are compared: two sets produced in-house (with the ED and UD scheme), and a set produced with the undifferenced scheme in the frame of the short-arc approach (Zehentner and Mayer-Gürr in J Geodesy 90(3):275–286, 2015. https://doi.org/10.1007/s00190-015-0872-7). As a reference, we use state-of-the-art ITSG-Grace2018 monthly gravity field solutions. A comparison in the spectral domain shows that the gravity field solutions suffer from a lower noise level when the ED scheme is applied, particularly at low-degree terms, with cumulative errors up to degree 20 being reduced by at least 20%. In the spatial domain, the ED scheme notably reduces noise levels in the mass anomalies recovered. In addition, the signals in terms of mean mass anomalies in selected regions become closer to those inferred from ITSG-Grace2018 solutions, while showing no evidence of any damping, when the ED scheme is used. We conclude that the proposed ED scheme is preferable for time-varying gravity field modeling, as compared to the traditional UD scheme. Our findings may facilitate, among others, bridging the gap between GRACE and GFO satellite mission.

Lithospheric stress, strain and displacement changes from GRACE-FO time-variable gravity: case study for Sar-e-Pol Zahab Earthquake 2018

SUMMARY Temporal variations in the Earth's gravity field can be used for monitoring of lithospheric deformations. The network of continuously operating gravity stations is required for this purpose but a global coverage by such network is currently extremely sparse. Temporal variations in long-wavelength part of the Earth's gravity field have been, however, observed by two satellite missions, namely the Gravity Recovery And Climate Experiment (GRACE) and the GRACE Follow-On (GRACE-FO). These satellite gravity observations can be used to study long-wavelength deformations of the lithosphere. Consequently, considering the lithosphere as a spherical elastic shell and solving the partial differential equation of elasticity for it, the stress, strain and displacement inside the lithosphere can be estimated. The lower boundary of this shell is assumed to be stressed by mantle convection, which has a direct relation to the Earth's gravity field according to Runcorn's theory. Changes in gravity field lead to changes in the sublithospheric stress and the stress propagated throughout the lithosphere. In this study, we develop mathematical models in spherical coordinates for describing the stress propagation from the sublithosphere through the lithosphere. We then organize a system of observation equations for finding a special solution to the boundary-value problem of elasticity in the way that provides a stable solution. In contrast, models presented in previously published studies are ill-posed. Furthermore, we use constants of the solution determined from the boundary stresses to determine the strain and displacements leading to these stresses, while in previous studies only the stress has been considered according to rheological properties of the lithosphere. We demonstrate a practical applicability of this theoretical model to estimate the stress–strain redistribution caused by the Sar-e-Pol Zahab 2018 earthquake in Iran by using the GRACE-FO monthly solutions.

Laser metrology concept consolidation for NGGM

The measurement of the static and temporal variation of Earth’s gravity field yields important information on water storage, seasonal and sub-seasonal water cycles, their impact on water levels and delivers key data to Earth’s climate models. The satellite missions GOCE (ESA), GRACE (US-GER) and just recently GRACE Follow-On (US-GER) resulted in a significant improvement on our understanding of the system Earth. To further improve the measurement accuracy of the time-variable gravity field, ESA is investigating the concept of a ‘Next Generation Gravity Mission’ (NGGM), consisting of two pairs of satellites and a heterodyne laser interferometer for inter-satellite ranging. Based on the heritage of the development of the laser ranging interferometer for GRACE Follow-On and the former and ongoing studies for NGGM, two schemes for the Laser Metrology Instrument (LMI) for NGGM, namely the transponder and the retroreflector scheme have been investigated and are presented in this paper. The results include the instrument ranging performance analyses, the laser link acquisition, an instrument reliability assessment and redundancy approach as well as the Technology Readiness Level assessment of the individual instrument units.

Description of the multi-approach gravity field models from Swarm GPS data

Abstract. Although the knowledge of the gravity of the Earth has improved considerably with CHAMP, GRACE, and GOCE (see appendices for a list of abbreviations) satellite missions, the geophysical community has identified the need for the continued monitoring of the time-variable component with the purpose of estimating the hydrological and glaciological yearly cycles and long-term trends. Currently, the GRACE-FO satellites are the sole dedicated provider of these data, while previously the GRACE mission fulfilled that role for 15 years. There is a data gap spanning from July 2017 to May 2018 between the end of the GRACE mission and start the of GRACE-FO, while the Swarm satellites have collected gravimetric data with their GPS receivers since December 2013. We present high-quality gravity field models (GFMs) from Swarm data that constitute an alternative and independent source of gravimetric data, which could help alleviate the consequences of the 10-month gap between GRACE and GRACE-FO, as well as the short gaps in the existing GRACE and GRACE-FO monthly time series. The geodetic community has realized that the combination of different gravity field solutions is superior to any individual model and set up the Combination Service of Time-variable Gravity Fields (COST-G) under the umbrella of the International Gravity Field Service (IGFS), part of the International Association of Geodesy (IAG). We exploit this fact and deliver the highest-quality monthly GFMs, resulting from the combination of four different gravity field estimation approaches. All solutions are unconstrained and estimated independently from month to month. We tested the added value of including kinematic baselines (KBs) in our estimation of GFMs and conclude that there is no significant improvement. The non-gravitational accelerations measured by the accelerometer on board Swarm C were also included in our processing to determine if this would improve the quality of the GFMs, but we observed that is only the case when the amplitude of the non-gravitational accelerations is higher than during the current quiet period in solar activity. Using GRACE data for comparison, we demonstrate that the geophysical signal in the Swarm GFMs is largely restricted to spherical harmonic degrees below 12. A 750 km smoothing radius is suitable to retrieve the temporal variations in Earth's gravity field over land areas since mid-2015 with roughly 4 cm equivalent water height (EWH) agreement with respect to GRACE. Over ocean areas, we illustrate that a more intense smoothing with 3000 km radius is necessary to resolve large-scale gravity variations, which agree with GRACE roughly at the level of 1 cm EWH, while at these spatial scales the GRACE observes variations with amplitudes between 0.3 and 1 cm EWH. The agreement with GRACE and GRACE-FO over nine selected large basins under analysis is 0.91 cm, 0.76 cm yr−1, and 0.79 in terms of temporal mean, trend, and correlation coefficient, respectively. The Swarm monthly models are distributed on a quarterly basis at ESA's Earth Swarm Data Access (at https://swarm-diss.eo.esa.int/, last access: 5 June 2020, follow Level2longterm and then EGF) and at the International Centre for Global Earth Models (http://icgem.gfz-potsdam.de/series/02_COST-G/Swarm, last access: 5 June 2020), as well as identified with the DOI https://doi.org/10.5880/ICGEM.2019.006 (Encarnacao et al., 2019).

Constrained Linear Deconvolution of GRACE Anomalies to Correct Spatial Leakage

Time-varying gravity observed by the Gravity Recovery and Climate Experiment (GRACE) satellites measures surface water and ice mass redistribution driven by weather and climate forcing and has emerged as one of the most important data types in measuring changes in Earth’s climate. However, spatial leakage of GRACE signals, especially in coastal areas, has been a recognized limitation in quantitatively assessing mass change. It is evident that larger terrestrial signals in coastal regions spread into the oceans and vice versa and various remedies have been developed to address this problem. An especially successful one has been Forward Modeling but it requires knowledge of geographical locations of mass change to be fully effective. In this study, we develop a new method to suppress leakage effects using a linear least squares operator applied to GRACE spherical harmonic data. The method is effectively a constrained deconvolution of smoothing inherent in GRACE data. It assumes that oceanic mass changes near the coast are negligible compared to terrestrial changes, with additional spatial regularization constraints. Some calibration of constraint weighting is required. We apply the method to estimate surface mass loads over Australia using both synthetic and real GRACE data. Leakage into the oceans is effectively suppressed and when compared with mascon solutions there is better performance over interior basins.

An Iterative ICA-Based Reconstruction Method to Produce Consistent Time-Variable Total Water Storage Fields Using GRACE and Swarm Satellite Data

Observing global terrestrial water storage changes (TWSCs) from (inter-)seasonal to (multi-)decade time-scales is very important to understand the Earth as a system under natural and anthropogenic climate change. The primary goal of the Gravity Recovery And Climate Experiment (GRACE) satellite mission (2002–2017) and its follow-on mission (GRACE-FO, 2018–onward) is to provide time-variable gravity fields, which can be converted to TWSCs with ∼ 300 km spatial resolution; however, the one year data gap between GRACE and GRACE-FO represents a critical discontinuity, which cannot be replaced by alternative data or model with the same quality. To fill this gap, we applied time-variable gravity fields (2013–onward) from the Swarm Earth explorer mission with low spatial resolution of ∼ 1500 km. A novel iterative reconstruction approach was formulated based on the independent component analysis (ICA) that combines the GRACE and Swarm fields. The reconstructed TWSC fields of 2003–2018 were compared with a commonly applied reconstruction technique and GRACE-FO TWSC fields, whose results indicate a considerable noise reduction and long-term consistency improvement of the iterative ICA reconstruction technique. They were applied to evaluate trends and seasonal mass changes (of 2003–2018) within the world’s 33 largest river basins.

Lake and reservoir volume variations in South America from radar altimetry, ICESat laser altimetry, and GRACE time-variable gravity

Thanks to 25-years of radar altimetry measurements from TOPEX/POSEIDON, Jason 1, 2 and 3, ENVISAT and others, water level changes of major lakes and rivers can be measured regularly, remotely, with unprecedented precision, facilitating monitoring of continental water storage variations. In addition, the 18 laser altimeter measurement campaigns over 6 years by the Ice, Cloud and Land Elevation Satellite (ICESat) satellite complement these radar altimetry measurements and also validate them, expanding our monitoring capabilities. We extract derived water height estimates for various lakes in South America from radar and laser altimetry measurements. Using available imagery from the Moderate Resolution Imaging Spectroradiometer (MODIS), we estimate time-variable surface extent of these water bodies, and together with the altimetry, we derive corresponding estimates of relative volume variations for a number of lakes and reservoirs in South America. We see good agreement between our water extent and available products, with some differences when snow covered area are present. We find good agreement between the temporal variations of lake water heights obtained from ICESat, radar altimetry, and in situ measurements, when available. Lake-dependent biases still exist, likely due to differences in reference datum, choice of geoid model, and differences in data processing schemes. The is a good agreement in volume changes obtained from imagery and the various altimetry techniques. Furthermore, using the latest one-degree global iterated mascon solutions from NASA Goddard Space Flight Center, we successfully compare them to independent volume changes assessments for these water bodies, derived from mass variations from time-variable gravity measurements from 15 years of Gravity Recovery And Climate Experiment (GRACE) observations. The agreement in water volume changes from GRACE with those from altimetry and imagery is higher for lakes in arid and semi-arid regions than on mountainous areas. GRACE volume estimates remain limited to the spatial resolution and the quality of the hydrology models used to correct for soil-moisture and snow contributions. Overall, studies like the one presented here further validate the power of leveraging these data synergies to monitor continental water storage changes from space, taking advantage of what each of the techniques has to offer. We show that water level measurements from laser and radar altimeters have similar precision, of a few centimeters over inland water bodies, and prove that GRACE global mascons allow to retrieve small lake relative volume changes, even for small bodies, thanks to their higher sensitivity to small wavelength mass variations.

Global Glacial Isostatic Adjustment Constrained by GPS Measurements: Spherical Harmonic Analyses of Uplifts and Geopotential Variations

In addition to studies of sea level change and mantle rheology, reliable Glacial Isostatic Adjustment (GIA) models are necessary as a background model to correct the widely used Gravity Recovery and Climate Experiment (GRACE) monthly gravity solutions to determine subsecular, nonviscous variations. Based on spherical harmonic analyses, we developed a method using degree-dependent weighting to assimilate the Global Positioning System (GPS) derived crustal uplift rates into GIA model predictions, in which the good global pattern of GIA model predictions and better local resolution of GPS solutions are both retained. Some systematic errors in global GPS uplift rates were also corrected during the spherical harmonic analyses. Further, we used the refined GIA uplift rates to infer the GIA-induced rates of Stokes coefficients (complete to degree/order 120) relying on the accurate relationship between GIA vertical surface deformation and gravitational potential changes. The results show notable improvements relative to GIA model outputs, and may serve as a GIA-correction model for GRACE time-variable gravity data.

Empirical Analysis on Foreign Economic Trade of Smart City under the Background of Free Trade Agreement

Taking the construction of smart city in Yantai as an opportunity, this paper analyzes the current situation of foreign trade under the background of free trade agreement, explores the main factors affecting the level of trade, and puts forward feasible Suggestions for the development of foreign trade in Yantai based on the construction of smart city. Through the analysis of the trade flow between Yantai and 13 major trading countries(regions), the time-varying attenuation stochastic frontier gravity model is constructed to explore the main factors affecting Yantai’s foreign trade, and the total trade efficiency of Yantai is analyzed. The research shows that the total trade efficiency presents an overall increasing trend, and the trade and population size of Yantai have a significant impact on the trade flow. In the process of building a smart city, the planning and integration of Yantai’s foreign trade should be carried out from various aspects to further improve the trade efficiency.

Studies on glacier mass balance in the High Asia retrieved by ICESat-GLAS data and GRACE time-varying gravity field

Studies on glacier mass balance in the High Asia retrieved by ICESat-GLAS data and GRACE time-varying gravity field

Ganymede's gravity, tides and rotational state from JUICE's 3GM experiment simulation

The JUpiter Icy Moons Explorer (JUICE) is a European Space Agency (ESA) mission that will launch in 2022 and arrive in the Jovian system in 2029 to investigate Jupiter's icy satellites. The mission will perform flybys of the icy moons Europa, Callisto and Ganymede before being inserted into a 280-day orbit around Ganymede: 150 days in Elliptical Orbit (GEO) followed by 130 days Circular Orbit at 500 km (GCO-500). During the orbital phase, JUICE will investigate the moon's surface, interior and exosphere, carrying out for the first time a complete characterization of an icy satellite. A suite of field and particle instruments will characterize the plasma and magnetic environment around the body. The 3GM experiment on board the spacecraft will exploit the GCO-500 phase to collect accurate Doppler and range measurements to determine the moon's orbit, gravity field and tide, therefore providing crucial information to accurately model its internal structure. The simulations carried out reveal that the moon's gravity field can be determined up to degree and order 40, depending on the magnitude of the gravity spectrum. The Love number k2, modelling the gravitational response to eccentricity-driven, time-variable gravity gradient from Jupiter, is determined with an accuracy of σk2∼10−4. The obliquity, φ, and the libration at orbital period, ϕ, can be retrieved with a level of uncertainty of 1 and 2 μrad, respectively. Because of the 97 m2 solar panels and the ensuing large area-to-mass ratio, JUICE will be affected by neutral particle drag. Here, we also assess the potential effect of spacecraft drag due to Ganymede's tenuous exosphere, which ranges between 10−17−10−16kg/m3 and generates an average drag of ∼4⋅10−12m/s2, in the GCO-500 phase.

The natural circulation flow characteristic of the core in floating nuclear power plant in rolling motion

In recent years, the FNPP (Floating Nuclear Power Plant) has got more and more attention and rapid development due to very wide prospect application on remote areas or islands. In general, the IPWR (Integral Pressurized Water Reactor) is adopted to meet the requirements of the limited space, the nuclear safety and the maneuverability in marine. The IPWR could depend on natural circulation operation to remove the residual heat of core under accident conditions or low load operation condition. Because the driving head is low, the natural circulation flow in many parallel channels is likely to be influenced by ocean motion and thermonuclear coupling effect. Among various kinds of ocean motions, the rolling motion will introduce the additional force pressure drop and change the gravity pressure drop with time, so the force acting on coolant in the assemblies will be more complex. In order to clarify the natural circulation flow characteristics of the core in FNPP in rolling motion, based on the modified RELAP5 code by adding the ocean motion module and spatial coordinate convert module, the neutron physics and thermal-hydraulic coupled model of IPWR was been established. The core three-dimensional distribution, the radial cross-section and axial distribution of main thermal-hydraulic parameters were obtained. The effect of the tangential force pressure drop, the centripetal force pressure drop and the gravity pressure drop on the coolant in the core in rolling motion were discussed. The results showed that the natural circulation flow rate fluctuates periodically with the rolling motion. And the time-varying gravity pressure drop is the main effect factor of fluctuation. Because of the structure of IPWR is compact, the rolling radius is relatively short, the effect of the general rolling motion on the natural circulation flow distribution of the core is not obvious. The coolant temperature and the fuel power distribution of the core periphery fluctuates slightly, and the reactivity feedback introduced by the coolant temperature and the fuel temperature fluctuation is relatively small. In consequence, the FNPP in the movable marine platform in natural circulation mode operation is safety in general rolling motion.

Hybrid modeling and analysis of multidirectional variable stiffness of the linear rolling guideway under combined loads

In the working process of high-speed multiaxis machine tools, inertial loads due to high feed acceleration and time-varying gravity loads due to changing configuration of multiaxis structure result in time-varying complex loads applied to linear rolling guideway. Existing models cannot efficiently represent the effect of complex loads on multidirectional stiffness variation of linear rolling guideway. In this paper, a hybrid model of multidirectional stiffness of linear rolling guideway and the solving algorithm are proposed. The complex loading conditions of linear rolling guideway in high-speed multiaxis machine tool structure are considered. And contact flexibilities between rolling balls and grooves are modeled with the effect of elastic deformations of runner block and rail. The proposed model can calculate the multidirectional stiffness with high accuracy. Meanwhile the differences between the stiffness characteristics in different directions are represented correctly. The variations of multidirectional stiffness of linear rolling guideway under time-varying combined loads are analyzed. This study provides an effective way to comprehensively evaluate the stiffness characteristics of linear rolling guideway which can contribute to the dynamic analysis and active design of high-speed machine tool structure.

Gravity and crustal dynamics in Italy

Mapping the static gravity field in the Italian area is fundamental to identify the main lithospheric structures, to delineate the main geological elements at regional level and to infer the regional geodynamic setting. The ongoing tectonic processes highlight nevertheless the need to measure and model the time-variable gravity field, namely the dynamic gravity field, which requires increased accuracy and long time series of observations to separate the secular from the short-term variable components. The first, with a minor impact in Italy, are due to variations of ice mass balance (the viscoelastic response of the Earth to past changes in ice mass loading, and the elastic response of the Earth to present-day deglaciation), and the sea-level rise; the second are due to space/time variations of underground mass distributions, such as those related to seismic deformations, volcanic dynamics/eruptions and water transfer. Local-scale gravity studies along seismogenic faults may provide useful hints to study the seismic cycle and to unravel those areas more prone to seismic release by studying if the crustal volume is undergoing dilatancy (gravity decrease) or overpressure (gravity increase) before earthquake occurrence. This process, however, is accompanied by possible fluid migration, which can be revealed by other geophysical measurements, for example, by magnetotelluric and geoelectrical surveys. In this short paper, we briefly summarize the main sources of gravity variation providing on the same time orders of magnitude, spatial and temporal scales of their effects.

Gravity gradient bias in the EPF experiment

The Eötvös Pekár and Fekete (EPF) equivalence test was aimed to check composition dependence of the gravitational force. It was designed to be free from any bias related to the possibly time-varying ambient gravity field. Interestingly in 1986 Fischbach and his colleagues found a systematic composition dependency in the EPF data. This discovery induced an intense debate, and even though the effect was unreproducible, the cause behind is still unknown. Now we found, however, that time-varying gravity gradients may have biased the results in spite of the experimenters’ protocol to avoid it. Moreover, even in a constant, but inhomogeneous gravity field the gravitational force was necessarily different on the EPF samples that had different shapes. These issues are serious: we demonstrate that time-varying ambient gravity alone can fully reproduce the EPF results. Hence, we propose a remeasurement with a careful control of gravity gradient bias. We also discuss other more precise equivalence tests in connection with the above bias.

Equivalent water height changes over Qinghai-Tibet Plateau determined from GRACE with an independent component analysis approach

We estimated the equivalent water height (EWH) over Qinghai-Tibet Plateau (QTP) from time-variable gravity field models derived from the Gravity Recovery and Climate Experiment (GRACE) data released by CSR, JPL, GFZ, and GRGS. EWHs calculated from CSR, GFZ, JPL, and GRGS models, respectively, were taken as the observed signals, and the corresponding 4 independent source signals of each observed signal were determined by independent component analysis to remove the north-south stripe errors and identify the fourth independent components as meaningful water storage change (WSC) signals. These interesting signals are highly correlated to those predicted by hydrological models such as CPC and GLDAS with the maximum and minimum correlation coefficients of 0.89 and − 0.5, respectively. The result shows that EWHs over QTP wholly have the rising trend with the mean rate of WSC of greater than 0.7 mm/year. The in situ precipitations on 140 meteorological stations are also analyzed to verify the water storage changes determined from GRACE data. The results indicate that precipitation is one important water source to replenish the groundwater in QTP.

Improved Arctic Ocean Mass Variability Inferred from Time-Variable Gravity with Constraints and Dual Leakage Correction

The ocean mass variability inferred from Gravity Recovery and Climate Experiment (GRACE) satellites mission is challenged by the stripes and the leakage across land-ocean boundary. The recently released GRACE mascons solutions are advanced by applying constraints that remove efficiently the stripes and dual leakage correction that restores the coastal ocean mass variability. Here we quantitatively evaluate the improvement in the Arctic Ocean mass variability by GRACE mascons. To do so, we compare the combination of GRACE solutions (including the mascons solutions and traditional spherical harmonic coefficients (SHCs) solutions) and the steric estimates against the altimeter observations. Our results suggest that mascons solutions produce stronger correlations compared to SHCs solutions, especially along the coastal zone, indicating the importance of the dual leakage correction. Stronger correlation is produced by the mascons over a small basin in the interior of the Arctic Ocean, suggesting that mascons solutions deliver better ocean mass variability than the SHCs solutions. Since the comparisons are carried out over two sub-basins, we conclude that mascons are able to provide better regional ocean mass variability that may have implications for regional sea level budget, in particular over the coastal zone.

Evaluation of Nile Delta-Mediterranean Sea Conjunction Using GPS, Satellite-Based Gravity and Altimetry Datasets

Sinking of the Nile Delta region of Egypt is one of urgent issues to be investigated due to its vital importance to numerous perspectives such as economic, environmental and social impact on the whole Egyptian territory. This contribution represents one of the project outcomes entitled “Evaluation of Nile Delta Sinking Hypothesis Using the Global Positioning System (GPS), Tide Gauge and Satellite Altimetry and Gravity Techniques” that has been funded by the Science & Technology Development FUND (STDF), Egypt in the period from 2013 till 2017. To detect the rates of the horizontal and vertical movements, three main geodetic techniques; Global Positioning System (GPS) measurements of Delta region, time-varying gravity models of the Gravity Recovery and Climate Experiment (GRACE) mission to monitor the temporal changes over the delta regions and satellite altimetry time series have been used. Our findings regarding the GPS technique show that the northern part of the Nile Delta region suffers from clear subsidence especially at the eastern and western side as represented by Port Said, Mansoura, Gamalyia, Alexandria and Edfena stations. The central part as well as the surrounding areas of Nile Delta suffers from clear uplift as represented by Tanta, Damnhour and Hamoul stations. Satellite gravity results show erosion rates of the conjunction part of Nile Delta and Mediterranean contact, especially at its eastern (Port Said surrounding areas) and western (Alexandria surrounding areas) parts. As we go inland to the southern part of the Nile Delta, the temporal gravity variations pattern decreases showing that the Delta subsidence follows the regular subsidence pattern, except that for the northern contact part of the Delta to the Mediterranean Sea. This is also supported by satellite altimetry missions which shows a continuously rising rate of the Mediterranean Sea level as detected from the Saral/AltiKa mission.

Identifying the footprints of global climate modes in time-variable gravity hydrological signals

Modelling continental freshwater dynamics is expected to be challenging in regions with considerable influence of multi-scale global climatic drivers. An assessment of the interplay between these climatic drivers (e.g. El-Nino Southern Oscillation-ENSO) that influence hydro-climatic conditions and hydrological processes is therefore required to optimize predictive frameworks. The main aim of this study is to assess the impacts of eleven key climate modes describing oceanic variability in the nearby oceans on the spatial and temporal distributions of terrestrial water storage (TWS) derived from Gravity Recovery and Climate Experiment (GRACE) (2002 − 2017) over South America (SA). Considering that SA accounts for nearly one-fifth of global continental freshwater discharge, this assessment is crucial because of the differences in the intrinsic response of freshwater availability in some regions to several important processes of inter-annual variability. The novel integration of independent component analysis with parameter estimation techniques in this study shows that climate variability drivers (ENSO; Southern Oscillation Index (SOI); Pacific Decadal Oscillation (PDO); Ninos 1 + 2, 3.0, 3.4 and 4.0; North Tropical Atlantic (NTA); and the Caribbean Sea Surface Temperature (SST) anomalies) have considerable association (α = 0.05) with GRACE-derived TWS over SA. The influence of Nino 4.0 (r = − 0.72), Nino 3.4 (− 0.68), Nino 3.0 (− 0.53), ENSO (r = − 0.71), PDO (r = − 0.69), SOI (r = 0.64), Caribbean SST (r = − 0.67) and NTA (r = − 0.51) on TWS are relatively stronger in tropical SA (Amazon basin/northern SA) and result in higher amplitudes of TWS (> 100 mm). Given the temporal and spatial relationships of TWS with PDO over SA, there is also evidence to suggest strong multi-decadal variability in TWS.