Earth’s crust deforms in various time and spatial resolutions. To estimate them, geodetic observations are widely employed and compared to geophysical models. In this research, we focus on the Earth’s crust deformations resulting from hydrology mass changes, as observed by GRACE (Gravity Recovery and Climate Experiment) gravity mission and modeled using WGHM (WaterGAP Global Hydrological Model) and GLDAS (Global Land Data Assimilation System), hydrological models. We use the newest release of GRACE Level-2 products, i. e. RL06, provided by the CSR (Center for Space Research, Austin) analysis center in the form of a mascon solution. The analysis is performed for the European area, divided into 29 river basins. For each basin, the average signal is estimated. Then, annual amplitudes and trends are calculated. We found that the eastern part of Europe is characterized by the largest annual amplitudes of hydrology-induced Earth’s crust deformations, which decrease with decreasing distance to the Atlantic coast. GLDAS largely overestimates annual amplitudes in comparison to GRACE and WGHM. Hydrology models underestimate trends, which are observed by GRACE. For the basin-related average signals, we also estimate the non-linear variations over time using the Singular Spectrum Analysis (SSA). For the river basins situated on the southern borderline of Europe and Asia, large inter-annual deformations between 2004 and 2009 reaching a few millimeters are found; they are related to high precipitation and unexpectedly large drying. They were observed by GRACE but mismodelled in the GLDAS and WGHM models. Few smaller inter-annual deformations were also observed by GRACE between 2002-2017 for central and eastern European river basins, but these have been also well-covered by the WGHM and GLDAS hydrological models.

We discuss the determination of gravity gradients from the orbital ceiling to the depth of the Mohorovičić discontinuity (Moho) for Central Europe. Components of the Eötvös tensor were derived from "Heterogeneous gravity data combination for Earth interior and geophysical exploration research" project ("GOCE+") by using the gridded data with a resolution of 0.2° per 0.2°. Gravity gradients to Moho boundary depth were modelled forward to the 255 km orbital height. We calculated gradient sensitivity using a 3D model divided into: sediments and consolidated crust including the precise location of the Moho boundary. To define tesseroids as mathematical model we need to set two parameters of the crust: density and thickness for each spherical layer separately. Altitudes for topography/bathymetry were derived from ETOPO1 model, sediments thickness from EuCRUST-07 model,

The inter-comparison of ground gravity measurements and vertical surface displacements enables to better understand the structure, dynamics and evolution of the Earth's system. Within this research we analyzed the Global Positioning System vertical position time series acquired in the vicinity of the superconducting gravimeters. We estimated of noise character of GPS and SG by comparison of the satellite and terrestrial measurements collected at 18 globally distributed neighboring sites. The comparable results were provided by applying the appropriate and corresponding models of geophysical phenomena to obtain residual time series, and by unifying the sampling rate since the noise characteristics may depend on it. The deterministic part of the series was assumed to follow the Polynomial Trend Model and was subtracted prior to noise analysis. Then, a combination of power-law and white noise was presumed and the Maximum Likelihood Estimation implemented in the Hector software to investigate the stochastic part was applied. Within the paper, we show that the spectral indices for all SG time series fall in the area of fractional Brownian motion (-2 \ j \ -1), while GPS data are best characterized by fractional Gaussian noises (-1 \ j \ 0). The estimated ratio between spectral indices of GPS and SG is stable worldwide with a global median value of about 0.5. Concerning the power-law amplitudes, these are very consistent worldwide for the GPS position time series and fluctuate around 15 mm/year -j/4 , while in the case of SG records they spread between 60 and 300 nm/ s 2 /year -j/4 . The fraction of power-law noise employed in the assumed combination is equal to 100% for almost all SG stations, while in case of GPS it varies between 26.1 and 99.9%. The main finding of this research is that the assumption of power-law noise is much more preferred for SG data than the assumption of a pure white noise being used until now.

For 15 years, the Gravity Recovery and Climate Experiment (GRACE) mission have monitored total water storage (TWS) changes. The GRACE mission ended in October 2017, and 11 months later, the GRACE Follow-On (GRACE-FO) mission was launched in May 2018. Bridging the gap between both missions is essential to obtain continuous mass changes. To fill the gap, we propose a new approach based on a remove–restore technique combined with an autoregressive (AR) prediction. We first make use of the Global Land Data Assimilation System (GLDAS) hydrological model to remove climatology from GRACE/GRACE-FO data. Since the GLDAS mis-models real TWS changes for many regions around the world, we further use least-squares estimation (LSE) to remove remaining residual trends and annual and semi-annual oscillations. The missing 11 months of TWS values are then predicted forward and backward with an AR model. For the forward approach, we use the GRACE TWS values before the gap; for the backward approach, we use the GRACE-FO TWS values after the gap. The efficiency of forward–backward AR prediction is examined for the artificial gap of 11 months that we create in the GRACE TWS changes for the July 2008 to May 2009 period. We obtain average differences between predicted and observed GRACE values of at maximum 5 cm for 80% of areas, with the extreme values observed for the Amazon, Alaska, and South and Northern Asia. We demonstrate that forward–backward AR prediction is better than the standalone GLDAS hydrological model for more than 75% of continental areas. For the natural gap (July 2017–May 2018), the misclosures in backward–forward prediction estimated between forward- and backward-predicted values are equal to 10 cm. This represents an amount of 10–20% of the total TWS signal for 60% of areas. The regional analysis shows that the presented method is able to capture the occurrence of droughts or floods, but does not reflect their magnitudes. Results indicate that the presented remove–restore technique combined with AR prediction can be utilized to reliably predict TWS changes for regional analysis, but the removed climatology must be properly matched to the selected region.

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