Description: One decade of time-variable gravity field observations from the GRACE satellite mission reveals low-frequency ocean bottom pressure (OBP) variability of up to 2.5 hPa centered at the northern flank of the subtropical gyre in the North Pacific. From a 145 year-long simulation with a coupled chemistry climate model, OBP variability is found to be related to the prevailing atmospheric sea-level pressure and surface wind conditions in the larger North Pacific area. The dominating atmospheric pressure patterns obtained from the climate model run allow in combination with ERA-Interim sea-level pressure and surface winds a reconstruction of the OBP variability in the North Pacific from atmospheric model data only, which correlates favorably (r=0.7) with GRACE ocean bottom pressure observations. The regression results indicate that GRACE-based OBP observations are indeed sensitive to changes in the prevailing sea-level pressure and thus surface wind conditions in the North Pacific, thereby opening opportunities to constrain atmospheric models from satellite gravity observations over the oceans.

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: 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: We present a method for reconstructing a global, time-variable field of displacements of the Earth's crust caused by non-tidal ocean loading (NTOL) from a small number of local displacement measurements. This is achieved by the decomposition of the NTOL field into empirical orthogonal functions (EOFs), which we obtain from GRACE satellite data. With this method, we achieve the reproduction of a highly correlated displacement signal across 95% of the land surface and the reduction of residual continental displacement from up to 1 mm to mostly below 0.5 mm on monthly GRACE data. The extrapolation of the displacement signal into the time for which no global EOF patterns can be recovered is exemplarily shown. Further, the possibilities and limitations of applying the method on submonthly GRACE products are investigated. We conclude that the described method can be a useful complement to existing data sets of ocean mass-induced surface displacement, especially when in-situ measurement accuracy has improved.

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 global numerical weather prediction model routinely operated at the European Centre for Medium-Range Weather Forecasts (ECMWF) is typically updated about two times a year to incorporate the most recent improvements in the numerical scheme, the physical model or the data assimilation procedures into the system for steadily improving daily weather forecasting quality. Even though such changes frequently affect the long-term stability of meteorological quantities, data from the ECMWF deterministic model is often preferred over alternatively available atmospheric re-analyses due to both the availability of the data in near real-time and the substantially higher spatial resolution. However, global surface pressure time-series, which are crucial for the interpretation of geodetic observables, such as Earth rotation, surface deformation, and the Earth’s gravity field, are in particular affected by changes in the surface orography of the model associated with every major change in horizontal resolution happened, e.g., in February 2006, January 2010, and May 2015 in case of the ECMWF operational model. In this contribution, we present an algorithm to harmonize surface pressure time-series from the operational ECMWF model by projecting them onto a time-invariant reference topography under consideration of the time-variable atmospheric density structure. The effectiveness of the method will be assessed globally in terms of pressure anomalies. In addition, we will discuss the impact of the method on predictions of crustal deformations based on ECMWF input, which have been recently made available by GFZ Potsdam.

Description: Global degree-1 coefficients are derived by means of the method by Swenson et al. (2008) from a model of ocean mass variability and RL05 GRACE monthly mean gravity fields. Since an ocean model consistent with the GRACE GSM fields is required to solely include eustatic sea-level variability which can be safely assumed to be globally homogeneous, it can be empirically derived from GRACE aswell, thereby allowing to approximate geocenter motion entirely out of the GRACE monthly mean gravity fields. Numerical experiments with a decade-long model time-series reveal that the methodology is generally robust both with respect to potential errors in the atmospheric part of AOD1B and assumptions on global degree-1 coefficients for the eustatic sea-level model. Good correspondence of the GRACE RL05-based geocenter estimates with independent results let us conclude that this approximate method for the geocenter motion is well suited to be used for oceanographic and hydrological applications of regional mass variability from GRACE,where otherwise an important part of the signal would be omitted.

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.