Gravity field solutions and errors

The raw data is collected from the satellite by the GRACE project Science Data System (SDS), which is distributed between the University of Texas Centre for Space Research (CSR), Jet Propulsion Laboratory (JPL) and the German Research Centre (GFZ). These data undergo extensive processing and are converted to edited and cleaned data products, labelled as Level-1B, before being further processed to produce monthly gravity field estimates as spherical harmonic coefficients (Level-2), which are then released to the public after validation. They can be obtained through the Physical Oceanography Distributed Active Archive Center (PO.DAAC) at JPL or via

the Information System & Data Center at the German Research Center (GFZ).

The solutions are generated by taking into account gravitational variations such as Earth tides, ocean tides, atmospheric pressure fields and barotropic ocean response. However, further effects from hydrology, baroclinic oceanic signals, snow cover and glacial isostatic adjustment (GIA) are not incorporated and need to be separated individually by the user [Biancale, 2012]. It is not possible to separate these un-modelled effects from the temporal gravity signal to determine whether a change in mass is caused by variations in the Earth’s crust, surface water, groundwater or atmospheric mass above the measured region, and the contributions need to be separated independently by the user [Wahr et al., 2006]. Wahr et al. [2006] distinguished two error categories: errors in the GRACE gravity field solutions including measurement and processing errors (i.e. accelerometer error, system-noise errors, orbital errors, remaining errors in forcing models) and the measured but unknown signals of surface mass balance and GIA. To remove atmospheric effects, the GRACE project uses ECWMF (European Centre for Medium-Range Weather Forecasts) meteorological fields in the reduction of the observations. This implies that the atmosphere contributes to both error sources, as there are errors in the ECWMF fields as well [Wahr et al., 2006]. Due to a roughly north-south ground track direction, the estimates of the east-west variations are less accurate, which leads to a north- south striping pattern of error, and requires the application of destriping filters to reduce north-south striping [Swenson and Wahr, 2006]. As previously mentioned, ocean tide effects are removed from the raw data, using global ocean tide models, as these affect mass variations around shorelines. However, in general not all of the signal is removed due to uncertainties in the tidal model, and the remaining tidal signals alias into longer period signals [Melachroinos et al, 2009]. The spatial accuracy of the GRACE data estimates is on a scale of a few hundred kilometres or greater, depending on the degree and order of the spherical harmonic model of the GRACE solutions. Hence, the surface mass variation is a spatial average, rather than a point measurement [Bruinsma et al., 2010]. Previously, the spatial resolution varied depending on the study and generally ranged from 400 to 600 km, using a maximum degree of around 50 [Ramillien et al., 2006; Velicogna and Wahr, 2006]. Since the release of the GRACE solutions the Stokes coefficients have been improved and are now available up to

degree 80 (GRGS) and 96 (CSR) [Lemoine et al., 2013; Bouman et al., 2014]. The GRACE solutions used for this thesis are provided by the Groupe de Reserches de Géodésie Spatiale (GRGS)

Release 02

In 2009, GRGS published the second series (RL02) of gravity fields in form of 10-day gravity field models as described by Bruinsma et al. [2010]. The processing strategy employed normalised spherical harmonic coefficients up to degree and order 50 at a 10-day interval, with a spatial resolution of ~400 km. The new time-variable mean gravity field EIGEN-GRGS.RL02.mean- field was used as the reference model, the background models IERS2003, FES2004 and MOG2D were used to correct for various tidal variations, such as the gravitational potential of the Earth and that of external bodies [McCarthy and Petit, 2003], ocean tides that affect solid Earth and ocean pole tide deformations [Desai, 2002], and the global barotropic response to atmospheric forced variability of the oceans [Carrère and Lyard, 2003], respectively [Bruinsma et al., 2010]. The ECWMF climate model was used to model atmospheric effects. Due to a stabilisation process during their generation by constraining the coefficients (degree 2 to 50) to the coefficients of the static field, noise in form of North-South striping in the GRGS solutions is already reduced and subsequent filtering is not necessary for the analysis [Lemoine et al., 2007, Bruinsma et al., 2010].

Release 03

After more than ten years of successful operation, reprocessed Level-1B data (“V2”) [Lemoine et al., 2013] of the GRACE mission have been released by JPL and new release 05 solutions have been made available by JPL, CSR and GFZ, recently followed by the release 03 (RL03) solutions from GRGS. The RL03 feature monthly as well as 10-day solutions [Biancale, 2012; Lemoine et al., 2013]. These solutions have been improved by using upgraded versions of data, models and inversion procedures [Lemoine et al., 2013]. In addition to using the new Level-1B V2 data, the gravity solutions feature an improved a priori gravity model, updated and improved versions of the tide model (FES2012 in place of FES2004), the atmospheric dealiasing fields (ECMWF ERA-Interim (every 3 hours) instead of ECMWF operational model (every 6 hours)) and the ocean dealiasing fields (TUGO (every 3 hours) in replacement of MOG2D (every 6 hours). Furthermore, some changes in the K-band ranging and accelerometer parameterisation have

been undertaken and the maximum degree has been extended from 50 to 80, improving the spatial resolution [Lemoine et al., 2013]. Additionally, a new “mean field” has been computed and the inversion process is now based on a truncated single value decomposition scheme [Biancale, 2012]. However, due to an error at high latitudes in the FES2012 tidal model, the GRGS RL03 solutions cannot be used in polar areas between 82 and 90 degrees at present [Biancale, 2012].

I chose to use the GRGS solutions for my research due to their stabilisation process that is applied to reduce noise in the form of North-South striping by regularising the inversion for spherical harmonic coefficients. Bruinsma et al. [2010] stated that regularising geopotential coefficients leads to “more accurate geoid difference/EWH anomaly maps than a-posteriori filtering of solutions, because the level of stabilisation of a solution depends on the sensitivity of a given spherical harmonic coefficient to the normal equation system”. Generally both signal and noise are attenuated randomly when filtering and smoothing geopotential solutions, as the data distribution and quality is not known [Lemoine et al., 2007; Bruinsma et al., 2010]. Due to their stabilisation process, the GRGS solutions are also less prone to signal contamination (leakage), which is enhanced by increasing the radius of the Gaussian smoother [Bruinsma et al., 2010; Velicogna and Wahr, 2006].