Description: Satellite radar altimetry observations are used to derive short wavelength gravity anomaly fields over the Persian Gulf and the Caspian Sea, where in situ and ship-borne gravity measurements have limited spatial coverage. In this study the retracking algorithm ‘Extrema Retracking’ (ExtR) was employed to improve sea surface height (SSH) measurements that are highly biased in the study regions due to land contaminations in the footprints of the satellite altimetry observations. ExtR was applied to the waveforms sampled by the five satellite radar altimetry missions: TOPEX/POSEIDON, JASON-1, JASON-2, GFO and ERS-1. Along-track slopes have been estimated from the improved SSH measurements and used in an iterative process to estimate deflections of the vertical, and subsequently, the desired gravity anomalies. The main steps of the gravity anomaly computations involve estimating improved SSH using the ExtR technique, computing deflections of the vertical from interpolated SSHs on a regular grid using a biharmonic spline interpolation and finally estimating gridded gravity anomalies. A remove–compute–restore algorithm, based on the fast Fourier transform, has been applied to convert deflections of the vertical into gravity anomalies. Finally, spline interpolation has been used to estimate regular gravity anomaly grids over the two study regions. Results were evaluated by comparing the estimated altimetry-derived gravity anomalies (with and without implementing the ExtR algorithm) with ship-borne free air gravity anomaly observations, and free air gravity anomalies from the Earth Gravitational Model 2008 (EGM2008). The comparison indicates a range of 3–5 mGal in the residuals, which were computed by taking the differences between the retracked altimetry-derived gravity anomaly and the ship-borne data. The comparison of retracked data with ship-borne data indicates a range in the root-mean-square-error (RMSE) between approximately 1.8 and 4.4 mGal and a bias between 0.4062 and 2.1413 mGal over different areas. Also a maximum RMSE of 4.4069 mGal, with a mean value of 0.7615 mGal was obtained in the residuals. An average improvement of 5.2746 mGal in the RMSE of the altimetry-derived gravity anomalies corresponding to 89.9 per cent was obtained after applying the ExtR post-processing.

Description: Satellite radar altimetry observations are used to derive short wavelength gravity anomaly fields over the Persian Gulf and the Caspian Sea, where in situ and ship-borne gravity measurements have limited spatial coverage. In this study the retracking algorithm ‘Extrema Retracking’ (ExtR) was employed to improve sea surface height (SSH) measurements that are highly biased in the study regions due to land contaminations in the footprints of the satellite altimetry observations. ExtR was applied to the waveforms sampled by the five satellite radar altimetry missions: TOPEX/POSEIDON, JASON-1, JASON-2, GFO and ERS-1. Along-track slopes have been estimated from the improved SSH measurements and used in an iterative process to estimate deflections of the vertical, and subsequently, the desired gravity anomalies. The main steps of the gravity anomaly computations involve estimating improved SSH using the ExtR technique, computing deflections of the vertical from interpolated SSHs on a regular grid using a biharmonic spline interpolation and finally estimating gridded gravity anomalies. A remove–compute–restore algorithm, based on the fast Fourier transform, has been applied to convert deflections of the vertical into gravity anomalies. Finally, spline interpolation has been used to estimate regular gravity anomaly grids over the two study regions. Results were evaluated by comparing the estimated altimetry-derived gravity anomalies (with and without implementing the ExtR algorithm) with ship-borne free air gravity anomaly observations, and free air gravity anomalies from the Earth Gravitational Model 2008 (EGM2008). The comparison indicates a range of 3–5 mGal in the residuals, which were computed by taking the differences between the retracked altimetry-derived gravity anomaly and the ship-borne data. The comparison of retracked data with ship-borne data indicates a range in the root-mean-square-error (RMSE) between approximately 1.8 and 4.4 mGal and a bias between 0.4062 and 2.1413 mGal over different areas. Also a maximum RMSE of 4.4069 mGal, with a mean value of 0.7615 mGal was obtained in the residuals. An average improvement of 5.2746 mGal in the RMSE of the altimetry-derived gravity anomalies corresponding to 89.9 per cent was obtained after applying the ExtR post-processing.

Description: The ability of any satellite gravity mission concept to monitor mass transport processes in the Earth system is typically tested well ahead of its implementation by means of various simulation studies. Those studies often extend from the simulation of realistic orbits and instrumental data all the way down to the retrieval of global gravity field solution time-series. Basic requirement for all these simulations are realistic representations of the spatio-temporal mass variability in the different sub-systems of the Earth, as a source model for the orbit computations. For such simulations, a suitable source model is required to represent (i) high-frequency (i.e., subdaily to weekly) mass variability in the atmosphere and oceans, in order to realistically include the effects of temporal aliasing due to non-tidal high-frequency mass variability into the retrieved gravity fields. In parallel, (ii) low-frequency (i.e., monthly to interannual) variability needs to be modelled with realistic amplitudes, particularly at small spatial scales, in order to assess to what extent a new mission concept might provide further insight into physical processes currently not observable. The new source model documented here attempts to fulfil both requirements: Based on ECMWF’s recent atmospheric reanalysis ERA-Interim and corresponding simulations from numerical models of the other Earth system components, it offers spherical harmonic coefficients of the time-variable global gravity field due to mass variability in atmosphere, oceans, the terrestrial hydrosphere including the ice-sheets and glaciers, as well as the solid Earth. Simulated features range from sub-daily to multiyear periods with a spatial resolution of spherical harmonics degree and order 180 over a period of 12 years. In addition to the source model, a de-aliasing model for atmospheric and oceanic high-frequency variability with augmented systematic and random noise is required for a realistic simulation of the gravity field retrieval process, whose necessary error characteristics are discussed. The documentation of the updated ESA Earth System Model (updated ESM) for gravity mission simulation studies is organized as follows: The characteristics of the updated ESM along with some basic validation is presented in Volume 1. A detailed comparison to the original ESA ESM (Gruber et al., 2011) is provided in Volume 2, while Volume 3 contains the description of a strategy to derive realistic errors for the de-aliasing model of high-frequency mass variability in atmosphere and ocean.

Description: For Brazil, a country frequented by droughts and whose rural inhabitants largely depend on groundwater, reliance on isotope for its monitoring, though accurate, is expensive and limited in spatial coverage. We exploit total water storage (TWS) derived from Gravity Recovery and Climate Experiment (GRACE) satellites to analyse spatial-temporal groundwater changes in relation to geological characteristics. Large-scale groundwater changes are estimated using GRACE-derived TWS and altimetry observations in addition to GLDAS and WGHM model outputs. Additionally, TRMM precipitation data are used to infer impacts of climate variability on groundwater fluctuations. The results indicate that climate variability mainly controls groundwater change trends while geological properties control change rates, spatial distribution, and storage capacity. Granular rocks in the Amazon and Guarani aquifers are found to influence larger storage capability, higher permeability ( 〉10-4 m/s) and faster response to rainfall (1 to 3 months' lag) compared to fractured rocks (permeability 〈10-7 m/s and lags 〉 3 months) found only in Bambui aquifer. Groundwater in the Amazon region is found to rely not only on precipitation but also on inflow from other regions. Areas beyond the northern and southern Amazon basin depict a ‘dam-like’ pattern, with high inflow and slow outflow rates (recharge slope 〉 0.75, discharge slope 〈 0.45). This is due to two impermeable rock layer-like ‘walls' (permeability 〈10-8 m/s) along the northern and southern Alter do Chão aquifer that help retain groundwater. The largest groundwater storage capacity in Brazil is the Amazon aquifer (with annual amplitudes of 〉 30 cm). Amazon's groundwater declined between 2002 and 2008 due to below normal precipitation (wet seasons lasted for about 36 to 47% of the time). The Guarani aquifer and adjacent coastline areas rank second in terms of storage capacity, while the northeast and southeast coastal regions indicate the smallest storage capacity due to lack of rainfall (annual average is rainfall 〈10 cm).

Description: Recently completed performance studies of future gravity mission concepts arrived at sometimes contradicting conclusions about the importance of non-tidal aliasing errors that remain in the finally retrieved gravity field time-series. In those studies, typically a fraction of the differences between two different models of atmosphere and ocean mass variability determined the magnitude of the aliasing errors. Since differences among arbitrary pairs of the numerical models available might lead to widely different aliasing errors and thus conclusions regarding limiting error contributors of a candidate mission, we present here for the first time a version of a realistically perturbed de-aliasing model that is consistent with the updated ESA Earth System Model for gravity mission simulation studies (Dobslaw et al., 2015). The error model is available over the whole 12-year period of the ESA ESM and consists of two parts: (i) a component containing signals from physical processes that are intentionally omitted from de-aliasing models, as for a example, variations in global eustatic sea-level; and (ii) a series of true errors that consist of in total five different components with realistically re-scaled variability at both small and large spatial scales for different frequency bands ranging from sub-daily to sub-monthly periods. Based on a multi-model ensemble of atmosphere and ocean mass variability available to us for the year 2006, we will demonstrate that our re-scaled true errors have plausible magnitudes and correlation characteristics in all frequency bands considered. The realism of the selected scaling coefficients for periods between 1 and 30 days is tested further by means of a variance component estimation based on the constrained daily GRACE solution series ITSG-GRACE2014. Initial full-scale simulation experiments are used to re-assess the relative importance of non-tidal de-aliasing errors for the GRACE-FO mission, which might be subsequently expanded to further mission candidates currently under consideration for a potential Next Generation Gravity Mission. Dobslaw, H. Bergmann-Wolf, I., Dill, R., Forootan, E., Klemann, V., Kusche, J., Sasgen, I. (2015), The updated ESA Earth System Model for future gravity mission simulation studies, J. Geodesy, doi:10.1007/s00190- 014-0787-8.

Description: The ability of any satellite gravity mission concept to monitor mass transport processes in the Earth system is typically tested well ahead of its implementation by means of various simulation studies. Those studies often extend from the simulation of realistic orbits and instrumental data all the way down to the retrieval of global gravity field solution time-series. Basic requirement for all these simulations are realistic representations of the spatio-temporal mass variability in the different sub-systems of the Earth, as a source model for the orbit computations. For such simulations, a suitable source model is required to represent (i) high-frequency (i.e., sub-daily to weekly) mass variability in the atmosphere and oceans, in order to realistically include the effects of temporal aliasing due to non-tidal high-frequency mass variability into the retrieved gravity fields. In parallel, (ii) low-frequency (i.e., monthly to interannual) variability needs to be modelled with realistic amplitudes, particularly at small spatial scales, in order to assess to what extent a new mission concept might provide further insight into physical processes currently not observable. The new source model documented here attempts to fulfil both requirements: Based on ECMWF’s recent atmospheric reanalysis ERA-Interim and corresponding simulations from numerical models of the other Earth system components, it offers spherical harmonic coefficients of the time-variable global gravity field due to mass variability in atmosphere, oceans, the terrestrial hydrosphere including the ice-sheets and glaciers, as well as the solid Earth. Simulated features range from sub-daily to multiyear periods with a spatial resolution of spherical harmonics degree and order 180 over a period of 12 years. In addition to the source model, a de-aliasing model for atmospheric and oceanic high-frequency variability with augmented systematic and random noise is required for a realistic simulation of the gravity field retrieval process, whose necessary error characteristics are discussed. The documentation is organized as follows: The characteristics of the updated ESM along with some basic validation are presented in Volume 1 of this report (Dobslaw et al., 2014). A detailed comparison to the original ESA ESM (Gruber et al., 2011) is provided in Volume 2 (Bergmann-Wolf et al., 2014), while Volume 3 (Forootan et al., 2014) contains a description of the strategy to derive a realistically noisy de-aliasing model for the high-frequency mass variability in atmosphere and oceans. The files of the updated ESA Earth System Model for gravity mission simulation studies are accessible at DOI:10.5880/GFZ.1.3.2014.001.

Description: The ability of any satellite gravity mission concept to monitor mass transport processes in the Earth system is typically tested well ahead of its implementation by means of various simulation studies. Those studies often extend from the simulation of realistic orbits and instrumental data all the way down to the retrieval of global gravity field solution time-series. Basic requirement for all these simulations are realistic representations of the spatio-temporal mass variability in the different sub-systems of the Earth, as a source model for the orbit computations. For such simulations, a suitable source model is required to represent (i) high-frequency (i.e., sub-daily to weekly) mass variability in the atmosphere and oceans, in order to realistically include the effects of temporal aliasing due to non-tidal high-frequency mass variability into the retrieved gravity fields. In parallel, (ii) low-frequency (i.e., monthly to interannual) variability needs to be modelled with realistic amplitudes, particularly at small spatial scales, in order to assess to what extent a new mission concept might provide further insight into physical processes currently not observable. The new source model documented here attempts to fulfil both requirements: Based on ECMWF’s recent atmospheric reanalysis ERA-Interim and corresponding simulations from numerical models of the other Earth system components, it offers spherical harmonic coefficients of the time-variable global gravity field due to mass variability in atmosphere, oceans, the terrestrial hydrosphere including the ice-sheets and glaciers, as well as the solid Earth. Simulated features range from sub-daily to multiyear periods with a spatial resolution of spherical harmonics degree and order 180 over a period of 12 years. In addition to the source model, a de-aliasing model for atmospheric and oceanic high-frequency variability with augmented systematic and random noise is required for a realistic simulation of the gravity field retrieval process, whose necessary error characteristics are discussed. The documentation is organized as follows: The characteristics of the updated ESM along with some basic validation are presented in Volume 1 of this report (Dobslaw et al., 2014). A detailed comparison to the original ESA ESM (Gruber et al., 2011) is provided in Volume 2 (Bergmann-Wolf et al., 2014), while Volume 3 (Forootan et al., 2014) contains a description of the strategy to derive a realistically noisy de-aliasing model for the high-frequency mass variability in atmosphere and oceans. The files of the updated ESA Earth System Model for gravity mission simulation studies are accessible at DOI:10.5880/GFZ.1.3.2014.001.

Description: 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.