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Over the last 15 years, the Gravity Recovery and Climate Experiment (GRACE) mission has provided measurements of temporal changes in mass redistribution at and within the Earth that affect polar motion. The newest generation of GRACE temporal models, are evaluated by conversion into the equatorial components of hydrological polar motion excitation and compared with the residuals of observed polar motion excitation derived from geodetic measurements of the pole coordinates. We analyze temporal variations of hydrological excitation series and decompose them into linear trends and seasonal and non-seasonal changes, with a particular focus on the spectral bands with periods of 1000–3000, 450–1000, 100–450, and 60–100 days. Hydrological and reduced geodetic excitation series are also analyzed in four separated time periods which are characterized by different accuracy of GRACE measurements. The level of agreement between hydrological and reduced geodetic excitation depends on the frequency band considered and is highest for interannual changes with periods of 1000–3000 days. We find that the CSR RL06, ITSG 2018 and CNES RL04 GRACE solutions provide the best agreement with reduced geodetic excitation for most of the oscillations investigated.

To mitigate temporal aliasing effects in monthly mean global gravity fields from the GRACE and GRACE‐FO satellite tandem missions, both tidal and non‐tidal background models describing high‐frequency mass variability in atmosphere and oceans are needed. To quantify tides in the atmosphere, we exploit the higher spatial (31 km) and temporal (1 hr) resolution provided by the latest atmospheric ECMWF reanalysis, ERA5. The oceanic response to atmospheric tides is subsequently modeled with the general ocean circulation model MPIOM (in a recently revised TP10L40 configuration that includes the feedback of self‐attraction and loading to the momentum equations and has an improved bathymetry around Antarctica) as well as the shallow water model TiME (employing a much higher spatial resolution and more elaborate tidal dissipation than MPIOM). Both ocean models consider jointly the effects of atmospheric pressure variations and surface wind stress. We present the characteristics of 16 waves beating at frequencies in the 1–6 cpd band and find that TiME typically outperforms the corresponding results from MPIOM and also FES2014b as measured from comparisons with tide gauge data. Moreover, we note improvements in GRACE‐FO laser ranging interferometer range‐acceleration pre‐fit residuals when employing the ocean tide solutions from TiME, in particular, for the S1 spectral line with most notable improvements around Australia, India, and the northern part of South America. Plain Language Summary In addition to many rather slow processes such as the melting of glaciers, rapid mass redistribution related to the weather also measurably affect the Earth's gravity field. The ability of monitoring liquid freshwater changes within the Earth system from the satellite gravity missions GRACE (2002–2017) and GRACE‐FO (since 2018) relies on accurate background models of mass variability in atmosphere and oceans for both tidal and non‐tidal processes. Atmospheric tides are primarily excited in the middle atmosphere by solar energy absorption at periods of 24 hr and its overtones. We find additional tidal signatures in the atmosphere excited by periodic deformations of both crust and sea‐surface of the Earth. We thus introduce here a new data set for the atmospheric tides and their corresponding oceanic response that features both more waves and higher accuracy than other background models previously used for the processing of GRACE and GRACE‐FO satellite gravimetry data. Key Points Sixteen relevant tidal lines identified in hourly data from ERA5 atmospheric reanalysis Dedicated simulations with a high‐resolution global hydrodynamic model to simulate ocean tides with atmospheric influence New tidal models reduce pre‐fit residuals in GRACE‐FO Laser Ranging Interferometer data

We present ground deformations in response to water level variations at the Toktogul Reservoir, located in Kyrgyzstan, Central Asia. Ground deformations were measured by Envisat Advanced Synthetic Aperture Radar (ASAR) and Sentinel-1 Differential Interferometric Synthetic Aperture Radar (DInSAR) imagery covering the time periods 2004–2009 and 2014–2016, respectively. The net reservoir water level, as measured by satellite radar altimetry, decreased approximately 60 m (∼13.5 km3) from 2004–2009, whereas, for 2014–2016, the net water level increased by approximately 51 m (∼11.2 km3). The individual Small BAseline Subset (SBAS) interferograms were heavily influenced by atmospheric effects that needed to be minimized prior to the time-series analysis. We tested several approaches including corrections based on global numerical weather model data, such as the European Centre for Medium-RangeWeather Forecasts (ECMWF) operational forecast data, the ERA-5 reanalysis, and the ERA-Interim reanalysis, as well as phase-based methods, such as calculating a simple linear dependency on the elevation or the more sophisticated power-law approach. Our findings suggest that, for the high-mountain Toktogul area, the power-law correction performs the best. Envisat descending time series for the period of water recession reveal mean line-of-sight (LOS) uplift rates of 7.8 mm/yr on the northern shore of the Toktogul Reservoir close to the Toktogul city area. For the same area, Sentinel-1 ascending and descending time series consistently show a subsidence behaviour due to the replenishing of the water reservoir, which includes intra-annual LOS variations on the order of 30mm. A decomposition of the LOS deformation rates of both Sentinel-1 orbits revealed mean vertical subsidence rates of 25 mm/yr for the common time period of March 2015–November 2016, which is in very good agreement with the results derived from elastic modelling based on the TEA12 Earth model.

The Atmosphere and Ocean non-tidal De-aliasing Level-1B (AOD1B) product is widely used in precise orbit determination and satellite gravimetry to correct for transient effects of atmosphere–ocean mass variability that would otherwise alias into monthly mean global gravity fields. The most recent release is based on the global ERA5 reanalysis and ECMWF operational data together with simulations from the general ocean circulation model MPIOM consistently forced with fields from the corresponding atmospheric dataset. As background models are inevitably imperfect, residual errors will consequently propagate into the resulting geodetic products. Accounting for uncertainties of the background model data in a statistical sense, however, has been shown before to be a useful approach to mitigate the impact of residual errors leading to temporal aliasing artefacts. In light of the changes made in the new release RL07 of AOD1B, previous uncertainty assessments are deemed too pessimistic and thus need to be revisited. We here present an analysis of the residual errors in AOD1B RL07 based on ensemble statistics derived from different atmospheric reanalyses, including ERA5, MERRA2 and JRA55. For the oceans, we investigate the impact of both the forced and intrinsic variability through differences in MPIOM simulation experiments. The atmospheric and oceanic information is then combined to produce a new time-series of true errors, called AOe07, which is applicable in combination with AOD1B RL07. AOe07 is further complemented by a new spatial error variance–covariance matrix. Results from gravity field recovery simulation experiments for the planned Mass-Change and Geosciences International Constellation (MAGIC) based on GFZ’s EPOS software demonstrate improvements that can be expected from rigorously implementing the newly available stochastic information from AOD1B RL07 into the gravity field estimation process.

Since more than 10 years, the Earth system modeling group at GFZ (ESMGFZ) provides effective angular momentum (EAM) functions for Earth orientation parameter assessment on a routinely daily basis. In addition to EAM of the individual Earth’s subsystems atmosphere, ocean, and hydrology, the global mass balance is calculated as barystatic sea level variation by solving explicitly the sea-level equation. ESMGFZ provides also 6-day forecasts for all of these EAM products. EAM forecasts are naturally degraded by forecast errors that typically grow with increasing forecast length, but they also show recurring patterns with occasionally higher errors at very short forecast horizons. To characterize such errors which are not randomly distributed in time, we divided the errors into a systematic and a stochastic contribution. In an earlier study, we were able to detect and remove the large systematic fraction occurring in the atmospheric angular momentum (AAM) wind term forecast errors with a cascading forward neural network model, thereby reducing the total forecast error by about 50%. In contrast, we were not able to remove the random error component assed in this study. Nevertheless, we show that machine learning methods are able to predict quasi-daily variations in time variable EAM forecasts error levels. We plan to provide these forecast error estimates along with the deterministic EAM forecast products for subsequent use in, for example, EOP Kalman filter prediction schemes.

We examine the sensitivity of the Global Positioning System (GPS) to non-tidal loading for a set of continental Eurasia permanent stations. We utilized daily vertical displacements available from the Nevada Geodetic Laboratory (NGL) at stations located at least 100 km away from the coast. Loading-induced predictions of displacements of earth’s crust are provided by the Earth-System-Modeling Group of the GFZ (ESMGFZ). We demonstrate that the hydrological loading, supported by barystatic sea-level changes to close the global mass budget (HYDL + SLEL), contributes to GPS displacements only in the seasonal band. Non-tidal atmospheric loading, supported by non-tidal oceanic loading (NTAL + NTOL), correlates positively with GPS displacements for almost all time resolutions, including non-seasonal changes from 2 days to 5 months, which are often considered as noise, intra-seasonal and seasonal changes with periods between 4 months and 1.4 years, and, also, inter-annual signals between 1.1 and 3.0 years. Correcting the GPS vertical displacements by NTAL leads to a reduction in the time series variances, evoking a whitening of the GPS stochastic character and a decrease in the standard deviation of noise. Both lead, on average, to an improvement in the uncertainty of the GPS vertical velocity by a factor of 2. To reduce its impact on the GPS displacement time series, we recommend that NTAL is applied at the observation level during the processing of GPS observations. HYDL might be corrected at the observation level or remain in the data and be applied at the stage of time series analysis.

The Earth System Modelling Group of GeoForschungsZentrum Potsdam (ESMGFZ) provides geodetic products for gravity variations, Earth rotation excitations, and Earth surface deformations related to mass redistributions and mass loads in the atmosphere, ocean, and terrestrial water storage. Earth rotation excitation compiled as effective angular momentum (EAM) functions for each Earth subsystem (atmosphere, ocean, continental hydrology) are important for Earth rotation prediction. Especially the 6-day forecasts extending the model analysis runs offer essential information for the improvement of ultra-short-term Earth rotation predictions. In addition to the individual effective angular momentum function of each subsystem, ESMGFZ calculates a combined EAM prediction product. Adjusted to the official Earth orientation parameter (EOP) products IERS 14C04 and Bulletin A, this EAM prediction product allows to extrapolate the polar motion and Length-of-Day parameter time series for 90 days into the future via the Liouville equation. ESMGFZ submits such an EOP prediction to the 2nd EOPPCC campaign.

Time-dependent mass variations of the near-surface geophysical fluids in atmosphere, oceans and the continental hydrosphere lead to systematic and significant load-induced deformations of the Earth’s crust. The Earth System Modeling group of Deutsches GeoForschungsZentrum (ESMGFZ) provides vertical and horizontal surface deformations based on numerical models of the global geophysical fluids in atmosphere, oceans and the continental hydrosphere with a spatial resolution of 0.5∘ and a temporal sampling of down to 3 h (Dill and Dobslaw in J Geophys Res 118(9):5008–5017, 2013. https://doi.org/10.1002/jgrb.50353). The assessment of conventionally—i.e. without consideration of non-tidal loading models—processed global GNSS datasets reveals that large parts of the residual station coordinates are indeed related to surface loading effects. Residuals explained by the models often have a pronounced annual component, but variability at other periodicities also contributes to generally high correlations for 7-day averages. More than 10 years of observations from about 400 GNSS and 33 VLBI stations were specifically reprocessed for this study to incorporate non-tidal loading correction models at the observation level. Comparisons with the corresponding conventional processing schemes indicate that the coordinate repeatabilities and residual annual amplitudes decrease by up to 13 mm and 7 mm, respectively, when ESMGFZ’s loading models are applied. In addition, the standard deviation of the daily estimated vertical coordinate is reduced by up to 6.8 mm. The network solutions also allow for an assessment of surface loading effects on GNSS satellite orbits, resulting in radial translations of up to 4 mm and Earth orientation parameters (EOP). In particular, the VLBI-based EOP estimates are critically susceptible to surface loading effects, with root-mean-squared differences reaching of up to 0.2 mas for polar motion, and 10 µs for UT1-UTC.

A new synthetic model of the time-variable global gravity field is now available based on realistic mass variability in atmosphere, oceans, terrestrial water storage, continental ice-sheets, and the solid Earth. The updated ESA Earth System Model is provided in Stokes coefficients up to degree and order 180 with a temporal resolution of 6 h covering the time period 1995–2006, and can be readily applied as a source model in future gravity mission simulation studies. The model contains plausible variability and trends in both low-degree coefficients and the global mean eustatic sea level. It depicts reasonable mass variability all over the globe at a wide range of frequencies including multi-year trends, year-to-year variability, and seasonal variability even at very fine spatial scales, which is important for a realistic representation of spatial aliasing and leakage. In particular on these small spatial scales between 50 and 250 km, the model contains a range of signals that have not been reliably observed yet by satellite gravimetry. In addition, the updated Earth System Model provides substantial high-frequency variability at periods down to a few hours only, thereby allowing to critically test strategies for the minimization of temporal aliasing.

Estimates of terrestrial water storage (TWS) variations from the Gravity Recovery and Climate Experiment (GRACE) satellite mission are used to assess the accuracy of four global numerical model realizations that simulate the continental branch of the global water cycle. Based on four different validation metrics, we demonstrate that for the 31 largest discharge basins worldwide all model runs agree with the observations to a very limited degree only, together with large spreads among the models themselves. Since we apply a common atmospheric forcing data set to all hydrological models considered, we conclude that those discrepancies are not entirely related to uncertainties in meteorologic input, but instead to the model structure and parametrization, and in particular to the representation of individual storage components with different spatial characteristics in each of the models. TWS as monitored by the GRACE mission is therefore a valuable validation data set for global numerical simulations of the terrestrial water storage since it is sensitive to very different model physics in individual basins, which offers helpful insight to modellers for the future improvement of large-scale numerical models of the global terrestrial water cycle.