Gravity

Scientific staff: Roland Klees (1.0 fte), Pavel Ditmar (1.0 fte), David Lavallee (1.0 fte until 2010), Brian Gunter (1.0 fte until 2012), Riccardo Riva (1.0 fte, since 2011), Cornelis Slobbe (1.0 fte, since 2014). 

Introduction. We develop novel methodologies for modelling the static and time-variable gravity field from satellite, airborne, and/or terrestrial data on global to local scales. We follow an operational approach in which observations are coupled to a set of model parameters that are estimated using statistically-optimal techniques. We contributed to novel applications of static and time-varying gravity in continental hydrology, glaciology, hydrography, hydrocarbon reservoir modelling, and solid Earth geophysics. During the review period, we published 176 peer-reviewed papers on this theme, among which one in Science (Bamber et al 2009) and one in Reports on Progress in Physics (Wouters et al 2014).

Satellite gravity modelling encompasses the estimation of a set of parameters describing the Earth’s gravity field using data from the dedicated satellite gravity missions CHAMP (2000-2010), GRACE (2002-now), and GOCE (2009-2013). The main developments during the review period concern refinements of functional models for GRACE and GOCE data, the development of data-driven weighting and regularization schemes based on statistical theory, and the validation of the estimated gravity models. In particular, a novel methodology for statistically-optimal filtering of temporal gravity field variations on the basis of full noise and signal covariance matrices was developed; the corresponding publication (Klees et al 2008) has 61 citations so far (Web of Science 31 August 2015). In combination with an accurate estimation of data noise, developed methodologies provided models of comparable or higher quality than those computed from the same data by other research teams. This concerns the Delft Mass Transport (DMT) models of temporal gravity variations, and the Delft Gravity Model (DGM-1S) of the static gravity field. A novel methodology for model validation was developed, which provided new insight into the p

erformance per region of state-of-the-art combined high-resolution global gravity field models such as EGM2008.
We studied future concepts of satellite gravity missions. A novel methodology was developed, which allows the use of kinematic satellite orbits in gravity modelling even if the satellite is not equipped with an accelerometer to measure non-gravitational forces acting on the satellite. In this way, we paved the way to the use of non-dedicated satellites to study temporal variations of the Earth’s gravity field. We were the first who applied this methodology to investigate the performance of satellite formations of opportunities, such as the IridiumNext constellation.  We investigated the capability of Satellite Gravity Gradiometry (SGG) to observe temporal gravity field variations and showed that SGG may become one of the primary future techniques if a technically feasible improvement by one-to-two orders of magnitude upon the accuracy of the GOCE gradiometer is achieved.

In the coming period, we intend to continue our efforts on static and time-varying gravity field modelling on the basis of gravity data from GRACE, GRACE Follow-On (to be launched in 2017), and other suitable satellites. One of the main challenges and focus of our research is on producing dedicated optimally-filtered products tailored for specific applications in terms of spatial parameterization, temporal parameterization, and expected stochastic properties of the signal, which will facilitate, in particular, accurate modelling of mass redistribution in the Earth’s system. We will put efforts in the further improvement of estimated low-degree spherical harmonic coefficients (i.e., those describing global gravity field features and geocentre motion), exploiting appropriate combinations of satellite gravity data and other information like ocean bottom pressure models. We will continue studying the optimal set-up of future satellite gravity missions to be launched in 10 to 20 years from now, keeping in mind a variety of different applications of those missions. We will continue the investigation of the noise budgets of satellite gravity data, which may facilitate both an improvement in processing of available data and a better design of future satellite gravity missions.

Figure 5 Linear trend of mass variations 2003-2011 in the Arctic. Superior spatial resolution of a Wiener linear-trend-filter developed at our unit (left) compared to a state-of-the-art official Level-2 data product (right). Results of our fundamental research on mass distribution and re-distribution from GRACE satellite gravity data.

Mass distribution and redistribution encompasses the exploitation of geodetic data to model the distribution and redistribution of mass inside the Earth and at the Earth’s surface. We used satellite gravity data to quantify hydrological processes in various river basins in Europe, Africa, and China in collaboration with hydrologists from TU Delft and Utrecht University. We developed a tailored retracking algorithm to extract lake level variations from high-resolution level-1b data provided by the Cryosat-2 satellite altimetry mission and applied this methodology successfully to monitor lake levels in the Tibetean Plateau and the Tian Shan. A novel technique was developed to process ICESat satellite laser altimeter data, and used to estimate volume variations of the Greenland Ice Sheet (GrIS). We combined these estimates with satellite gravity data and made for the first time estimates of individual contributors (snow and ice) to observed GrIS mass variations. This result was cited in the IPCC AR5 Assessment Report. We developed a novel filter technique for long-term mass trends of the GrIS, and demonstrated its superior spatial resolution compared to state-of-the-art processing techniques (cf. Fig 5).

We developed a new technique to monitor hydrocarbon reservoirs from a combination of time-lapse gravimetry, production data, and reservoir model data. This technique will be used by Shell for the future monitoring of the Groningen gas field.

Novel methodologies were developed for an estimation of the Moho geometry on the basis of gravity field data. This included: (i) efficient computational schemes to clean gravity anomalies and disturbances from nuisance signals related to terrain, bathymetry, and crust; (ii) validation of results by computing correlations between cleaned gravity field quantities on the one hand and geometry of Moho and other interfaces on the other hand; (iii) optimal weighting of gravity data and ancillary geophysical information. In this way, new Moho models were computed both for selected regions (Hellenic subduction zone, Red Sea area) and globally. We demonstrated that the new global Moho model improves upon existing models, particularly in areas poorly covered with seismic data, such as central Africa and northern South America.

We have used GRACE data to study mass redistribution inside the Earth due to (visco-)elastic deformation processes. In particular, we have done pioneering work on the determination of Glacial Isostatic Adjustment (GIA) over Antarctica through the combination of gravity and altimetry (ICESat) observations, which led to the first solution based on widespread observations of contemporary changes, cited 41 times in refereed journal articles (Web of Science, 31 August 2015) and in the IPCC AR5 Assessment Report (Riva et al 2009). We have also studied mass redistribution following large subduction earthquakes, including theoretical work on the effect on earthquake-driven ocean mass redistribution on satellite gravimetric observations.  

Figure 6 Cryosat-2 altimetry data processing over Lake Nasser, Egypt. Time series of lake levels obtained with the retracker developed at the Geodesy unit (blue triangles and error bars), and of the official Cryosat-2 level-2 data product (orange triangles and error bars). The length of the bars indicates the accuracy of individual lake level measurements. The proposed retracker delivers much more accurate results than the official level-2 data product, which is mostly explained by a more efficient handling of the waveforms that are polluted by reflections from surrounding land topography. Result of on-going research on mass distribution and redistribution.

In the coming period we will continue our research in this field with emphasis on the application of satellite gravity (in particular, GRACE and the GRACE-FO mission) and other remote sensing data (in particular, satellite altimeter data from Cryosat 2, ICESat 2, and Sentinel 3) to describe and analyse mass redistribution in various components of the Earth’s system (cf. Fig 6). The focus will be on ice sheets and glaciers, river-basin-scale hydrology, permafrost, and GIA. We aim at tailored mass redistribution estimates that are i) based on a combination of various observation techniques, ii) fine-tuned to the needs of a particular application community, and iii) constrained by additional information from models and/or ancillary data provided by the application community; we also aim at the assimilation of satellite gravity and altimetry data in geophysical models developed by the geophysical community in an attempt to improve their spatial and temporal resolution.

Vertical reference frames refer to the realization of surfaces to which heights/depths refer. We did pioneering work on the use of spherical radial base functions for regional quasi-geoid modelling. Using fundamental aspects of potential theory, we developed a new methodology combine a gravimetric quasi-geoid with geometric height anomalies from GNSS, terrestrial gravity, and spirit levelling data, and applied this methodology successfully to the computation of a new quasi-geoid for the Netherlands and Germany with significant improvements upon the state-of-the-art models. We developed, in close cooperation with Deltares, an Dutch institute for applied research in the field of water and subsurface, a conceptual framework to realize a set of vertical reference surfaces (land and sea) by combining gravity data, radar altimetry data, and water levels at on- and offshore tidal stations with a regional hydrodynamic model in a feedback loop. The overall methodology comprises a number of novel ideas: i) the realization of a coastal-waters-inclusive continuous separation model of chart datum without any spatial interpolation; ii) a methodology to vertically reference a regional hydrodynamic model to a particular quasi-geoid; iii) a reduction of altimeter-derived sea surface heights to geometric quasi-geoid heights using the properly referenced regional hydrodynamic model that includes astronomical tidal forcing, wind and pressure forcing, and baroclinic forcing, iv) a probabilistic design of chart datum, which is operational and much easier to implement and validate than all tidal vertical reference surfaces (cf. Fig 7). This new concept is currently being discussed within the International Hydrographic Society.  

Figure 7 Probability that the minimum instantaneous water level in periods of tidal minima drops below Lowest Astronomical Tide (LAT). Result of our research towards a probabilistic design of depth reference surfaces.

In the coming period, we want to operationalize the conceptual framework to bring to society a new set of vertical reference surfaces (land and sea) for the Dutch mainland, Wadden islands, and Continental Shelf. For this, we recently acquired a STW grant for 1 PhD student and one PostDoc and made agreements with the Hydrographic Service of the Royal Netherlands Navy, the Ministry of Infrastructure and Environment/Rijkswaterstaat, and a broad user community comprising govern-mental agencies, surveying companies (among others Fugro), companies offering positioning services (among others QPS), and the dredging industry (among others Boskalis, van Oord).

We consider the integrated realization of vertical reference surfaces (land and sea) in coastal regions as an emerging field with numerous benefits for accurate hydrographic surveys, coastal zone management, maritime vertical positioning, offshore dredging, and safety. For the coming period, we plan to apply the methodology to the coastal regions of Hong Kong and the South China Sea as part of the research activities of the TU Delft-Wuhan University Joint Research Centre. We also want to exploit the possibilities offered by proper vertically referenced hydrodynamic models for providing new services to the hydrographic community, including improved vertical positioning of underwater vehicles.
The developed methodology of quasi-geoid modeling in coastal areas will be improved by better models of noise in altimeter-derived sea surface heights, incorporating GRACE/GOCE data as noisy data type, and a more sophisticated design of the spherical radial base function network. For the first time, we will investigate the use of shipboard GNSS data to close the 5-10 km gap between the area covered by (re-tracked) radar altimetry data and land for coastal quasi-geoid modelling.

Sea level change refers to the quantification of global and regional changes in the reference sea surface at temporal scales from years to centuries.  We were the first to make use of GRACE data to determine trends in sea level driven by continental water mass redistribution (sea level fingerprints) and the resulting paper has been cited about 30 times (Riva et al 2010). We have modelled the effect on sea level of a collapse of the West Antarctic Ice Sheet in a study that was published in Science and cited about 150 times (Bamber et al 2009). We have also provided estimates of mass-induced sea level change to several international research groups, which resulted in 7 citations in the IPCC AR5 Assessment Report for (co-)authored papers about sea level (Bamber et al 2009, Bamber and Riva 2010, Riva et al 2010, Broerse et al 2011, King et al 2012, Slangen et al 2012, Perrette et al 2013).

Figure 8 Trend in sea level change driven by the redistribution of continental water, as estimated from GRACE data for the years 2003-2009. Mean sea level rise is equal to 1.0. Result of our research on regional sea level change.

In the coming period we will extend our research about sea level change by working on a data-driven multi-scale model that encompasses changes in both the sea surface and the solid earth, at global to regional spatial scales and at secular to annual temporal scales. This activity is financially supported by NWO through a Vidi grant received by Riccardo Riva (period 2014-2018, two PhD positions and one post-doctoral fellow position). We believe that studying processes that act at different spatial/temporal scales within a homogenous and self-consistent framework will allow us to greatly improve our understanding of the size and causes of recent sea level change. A key role will be played by satellite gravimetry observations provided by the GRACE and GRACE-FO missions, which will ensure enforcing of mass conservation at all scales of interest. In particular, we aim at providing time-series of sea level change in coastal areas (from tide gauges) that are consistent with regional estimates over the oceans (from satellite altimetry). In addition, we will produce a global model of present-day GIA tuned to sea level studies, which will be made available to the geophysical and geodetic community.