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.

The goal of this paper is to determine and analyze the common geocenter signal from the geocenter coordinates based on four independent techniques: Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), Global Navigation Satellite System (GNSS), Gravity Recovery And Climate Experiment with the ocean bottom pressure model, and Satellite Laser Ranging, and to analyze the residuals as the differences between these geocenter coordinates and their common signal. Another objective of this paper is to compute variable amplitudes and phases of the annual and semi-annual oscillations in the geocenter coordinates of these techniques by the combination of the Fourier Transform Band Pass Filter (FTBPF) with the Hilbert Transform (FTBPF + HT) and to compare their mean values with those obtained by other authors. It was assumed that the geocenter time series of individual techniques consist of the common signal of geocenter motion, systematic errors resulting from orbital modeling and noise. Generally, the annual oscillation amplitudes in these techniques computed by the FTBPF + HT vary in time and their mean values are of the order of 2 mm for the X coordinate, 2.4–3.6 mm for the Y coordinate and 2.8–5.6 mm for the Z coordinate and the semi-annual oscillation amplitude is variable and about two times smaller than the annual one. The phases of these two oscillations are also variable, there are differences in their mean values for different techniques and the semi-annual oscillation phases changes throughout the entire phase range. To detect the common geocenter signal the wavelet-based semblance filtering (WBSF) method was applied. The weighted mean model was computed from all geocenter coordinate pairs from individual techniques assuming weights as inversely proportional to the variances of differences between the geocenter coordinates and their corresponding WBSF outputs. The average and median models computed from these outputs show a good agreement with the weighted mean model and generally, the average amplitudes of the annual signal in these models are of the order of 2 mm in each geocenter coordinate. The FTBPF amplitude spectra of these models reveals the retrograde annual oscillation in the XY equatorial plane. The FTBPF and FTBPF + HT amplitude spectra of geocenter time series and their residuals show mainly the maxima of different heights in the annual frequency band. The annual oscillations left in all residuals and oscillations with period less than ~ 120 days in DORIS and GNSS amplitude spectra may be caused by systematic errors of techniques resulting from mis-modeling of satellite orbits.

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.

This paper employs time-frequency analysis on time series with a sampling interval of 10 s of the E, N, H components of a single permanent GNSS station in Krakow which uses three different Ground-Based Augmentation Systems (GBAS). Time-frequency analysis was conducted using the Fourier transform band-pass filter, which segments the time series into frequency components. Through the examination of these coordinates and their discrepancies, it was observed that the correlation between results from different GBAS solutions is negligible. Additionally, the analysis of power-law noise in the E, N and H components reveals that the spectrum index of these time series, computed through robust estimation and a linear regression model, ranges from α = 0.90 to 1.22. This suggests their resemblance to pink noise or flicker noise.