remote sensing

Article
The GFZ GRACE RL06 Monthly Gravity Field T ime
Series: Processing Details and Quality Assessment
Christoph Dahle 1, * , Michael Murböck 1,2 , Frank Flechtner 1,2 , Henryk Dobslaw 1 ,
Grzegorz Michalak 1 , Karl Hans Neumayer 1 , Oleh Abrykosov 1,† , Anton Reinhold 1 ,
Rolf König 1 , Roman Sulzbach 1,3 and Christoph Förste 1
1 Department 1: Geodesy , GFZ German Resear ch Centre for Geosciences, 14473 Potsdam, Germany;
[email protected] (M.M.); [email protected] (F .F .);
[email protected] (H.D.); [email protected] (G.M.);
[email protected] (K.H.N.); [email protected] (O.A.);
contact@antoncouper .com (A.R.); [email protected] (R.K.);
[email protected] (R.S.); [email protected] (C.F .)
2 Institute of Geodesy and Geoinformation Science, T echnische Universität Berlin, 10623 Berlin, Germany
3 Institute of Meteorology , Freie Universität Berlin, 12165 Berlin, Germany
* Correspondence: [email protected]
† Current addr ess: SpaceT ech GmbH Immenstaad, 88090 Immenstaad, Germany .
Received: 10 August 2019; Accepted: 6 September 2019; Published: 11 September 2019
       
  

Abstract:
T ime-variable gravity field models derived from observations of the Gravity Recovery and
Climate Experiment (GRACE) mission, whose science operations phase ended in June 2017 after more
than 15 years, enabled a multitude of studies of Earth’s surface mass transport pr ocesses and climate
change. The German Resear ch Centre for Geosciences (GFZ), r outinely processing such monthly
gravity fields as part of the GRACE Science Data System, has r epr ocessed the complete GRACE
mission and r eleased an improved GFZ GRACE RL06 monthly gravity field time series. This study
pr ovides an insight into the processing strategy of GFZ RL06 which has been considerably changed
with r espect to previous GFZ GRACE r eleases, and modifications r elative to the precursor GFZ RL05a
ar e described. The quality of the RL06 gravity field models is analyzed and discussed both in the
spectral and spatial domain in comparison to the RL05a time series. All r esults indicate significant
impr ovements of about 40% in terms of reduced noise. It is also shown that the GFZ RL06 time series
is a step forwar d in terms of consistency , and that err ors of the gravity field coefficients ar e more
r ealistic. These findings are confirmed as well by independent validation of the monthly GRACE
models, as done in this work by means of ocean bottom pr essure in situ observations and orbit tests
with the GOCE satellite. Thus, the GFZ GRACE RL06 time series allows for a better quantification of
mass changes in the Earth system.
Keywords:
satellite gravimetry; GRACE; Level-2 processing; time-variable gravity field; mass change
monitoring
1. Introduction
During mor e than 15 years (April 2002 through June 2017) of successful science operations phase,
the Gravity Recovery and Climate Experiment (GRACE) mission enabled br eakthroughs in monitoring
the terr estrial water cycle (e.g., [
1
,
2
]), ice sheet and glacier mass balances (e.g., [
3
,
4
]), sea-level change
(e.g., [
5
,
6
]) and ocean bottom pr essure variations (e.g., [
7
,
8
]). A comprehensive overview of numer ous
other GRACE-r elated studies and their contributions to understanding changes in the global climate
system is r eviewed by T apley et al. [
9
]. These results ar e based on time-variable, in general monthly ,
global gravity field models.
Remote Sens. 2019 , 11 , 2116; doi:10.3390/rs11182116 www .mdpi.com/journal/r emotesensing

Remote Sens. 2019 , 11 , 2116 2 of 22
Such models, so-called GRACE Level-2 pr oducts, ar e routinely generated by the joint US-German
GRACE Science Data System (SDS) consisting of the Center for Space Resear ch at the University of
T exas at Austin (CSR), NASA ’s Jet Pr opulsion Laboratory (JPL), and the German Research Centr e for
Geosciences (GFZ). T o provide consistent long-term gravity field time series of highest possible quality
to the user community the SDS has r ecently repr ocessed its gravity field solutions over the complete
GRACE mission duration. This latest repr ocessing, referr ed to as release 06 (RL06) [
10
–
12
], comprises
updated backgr ound models and processing standar ds which are also applied to consistently pr ocess
the first r elease of gravity field solutions based on data from the GRACE Follow-on (GRACE-FO)
mission [
13
]. The GRACE-FO satellites were successfully launched in May 2018 and ar e designed to
continue the unique GRACE data r ecord for at least five additional years.
Apart fr om the SDS, recent GRACE gravity field time series ar e provided by other pr ocessing
centers, e.g., ITSG-Grace2018 [
14
], CNES/GRGS RL04 [
15
], AIUB RL02 [
16
], or T ongji-Grace2018 [
17
].
The purpose of this work is to demonstrate the progr ess that has been achieved with the current
GFZ GRACE RL06 time series compar ed to its precursor GFZ RL05a [
18
]. First, an overview of
the GRACE gravity field pr ocessing procedur e at GFZ is given and modifications implemented
within the RL06 r eprocessing ar e described (Section 2 ). Ther eafter , r esults are discussed with focus
on the internal quality in the spectral and spatial domain comparing RL06 with RL05a (Section 3 ).
Additionally , both time series ar e validated by external data (Section 4 ). Finally , conclusions are drawn,
and the main findings of this work ar e summarized (Section 5 ). All r esults confirm that GFZ’s RL06
time series is a significant step forwar d in terms of accuracy , consistency and r eliability and thus
enables a better quantification of climate change r elated phenomena in the Earth system.
2. GRACE Level-2 Gravity Field Processing at GFZ
GRACE global monthly gravity field r ecovery at GFZ is based on the so-called “dynamical
appr oach” using GFZ’s Earth Parameter and Orbit System (EPOS) softwar e package
( https://www .gfz- potsdam.de/en/section/global- geomonitoring- and- gravity- field/topics/
earth- system- parameters- and- orbit- dynamics/earth- parameter - and- orbit- system- software- epos/ ).
Underlying satellite orbit perturbations rely on a pr ecise numerical orbit integration taking into
account all r eference system and for ce model related quantities [
19
]. The integrated orbit is then
fitted to the GRACE tracking observations, i.e., GPS code and carrier phase observations and K-band
inter -satellite ranging data between the two GRACE satellites. This step is done in a least-squares
adjustment pr ocess solving iteratively for both satellites’ state vector at the beginning of each arc,
observation-specific parameters, in particular GPS receiver clock of fsets, GPS carrier phase ambiguities
and calibration parameters for the acceler ometers, and other arc-specific parameters such as empirical
accelerations. The term “arc” r efers to the time length of the integrated orbit starting with one initial
state vector which is typically one day . After convergence of the initial orbit adjustment with the a
priori for ce models, the observation equations are extended by partial derivatives for the unknown
global parameters describing the gravitational potential, repr esented by spherical harmonic (SH)
gravity field coef ficients. Ar c-by-arc normal equation (NEQ) systems ar e generated in this way from
the observation equations and accumulated over nominally one month to one overall system which is
then solved by matrix inversion. For the complete GRACE mission 163 of these NEQ systems and
corr esponding Level-2 gravity field products have been derived.
In the following subsections, specific aspects relevant for GRACE gravity field pr ocessing are
discussed and modifications in GFZ’s RL06 pr ocessing relative to the pr ocessing of the previous r elease
GFZ RL05a ar e described.
2.1. GPS Constellation
Since GPS tracking data ar e processed, the precise orbits and sender clock of fsets of the GPS
constellation, nominally consisting of 32 satellites, must be known. Using GFZ’s EPOS software, it has
been demonstrated by König [
20
] that an integrated pr ocessing of both GPS satellites and the GRACE

Remote Sens. 2019 , 11 , 2116 3 of 22
satellites, i.e., simultaneous orbit determination and parameter adjustment at the observation level, is
beneficial for the determination of the terr estrial refer ence frame (TRF). However , the dynamic part
of the TRF in König [
20
] is limited to the SH gravity field coef ficients of degrees one and two and all
parameters have been estimated daily . When expanding the parameter space of the gravity field to a
maximum degr ee and order (d/o) of 90 or higher , typically for monthly GRACE gravity field solutions,
which r equir es that daily NEQs need to be stacked to obtain a monthly solution, such an integrated
appr oach becomes quite demanding in terms of computational efficiency and pr oper separation of
daily and monthly Earth system and other parameters. Thus, for GRACE gravity field r ecovery , it is
common practice to determine precise GPS orbits and clock of fsets beforehand using GPS tracking
data fr om a globally distributed ground station network, and then keep them fixed in the subsequent
GRACE orbit and gravity field adjustment pr ocess. At GFZ, the GPS constellation used for gravity
field determination is traditionally generated in-house allowing for best possible consistency .
For pr ocessing GRACE RL06, the GPS constellation has been repr ocessed as well. Compared to the
pr evious RL05 GPS constellation, the following changes have been implemented: (1) application of the
ITRF2014 r eference frame r ealized by the IGS14 ground station network ( https://mediatum.ub.tum.
de/doc/1341338/1341338.pdf ) instead of ITRF2008/IGS08; (2) incr ease in the number of GPS gr ound
stations fr om approx. 70 to approx. 120 to 140; (3) improved solar radiation pr essure parameterization;
and (4) adaption of the backgr ound models according to GRACE RL06 standar ds (see Section 2.3 ).
T o assess the level of accuracy of GFZ’s RL05 and RL06 GPS constellations, daily root mean squar e
(RMS) values of position dif ferences r egarding final orbits pr ovided by the International GNSS Service
(IGS) for all available GPS satellites ar e calculated. During the GRACE mission period, these 3D RMS
values ar e typically in the range of 3 to 5 cm in the first years until end of 2006 and ar ound 3 cm for all
years ther eafter for the RL06 constellation. The corresponding global 1D RMS over the whole 15 years
is 1.96 cm for RL06 and 2.28 cm for RL05 r evealing that the current RL06 constellation is closer to and
mor e consistent with the official IGS pr oducts compared to its pr edecessor .
2.2. GRACE Observations
Both GFZ RL05a and RL06 ar e based on of fi cial GRACE Level-1B (L1B) instrument data pr ocessed
and pr ovided by JPL [ 21 ]. In particular , the following L1B observations ar e used:
•
K-band range-rate (KRR) observations (KBR1B pr oduct) as primary observations to retrieve
monthly gravity field estimates.
•
GPS code and carrier phase observations (GPS1B pr oduct) used for precise orbit determination
of the GRACE satellites. Please note that inside GFZ’s EPOS softwar e, zer o-dif ference
ionospher e-free (L3) linear combinations of the measur ements are generated and pr ocessed.
•
Linear accelerations (ACC1B product) to model non-conservative for ces acting on the GRACE
satellites. Please note that these onboar d accelerometer (ACC) observations ar e not treated as
classical observations in a least-squar es sense, but only as part of the right-hand side force model.
•
Star camera observations (SCA1B pr oduct) describing the GRACE satellites’ attitude, requir ed for
the r otation from the satellite r eference frame (SRF) to the inertial frame.
For GFZ RL05a, L1B RL02 data were used. The same RL02 data ar e used for RL06 in case of
ACC1B and GPS1B. Regar ding KBR1B and SCA1B, an impr oved L1B RL03 dataset [
22
] has been made
available by JPL and is used for RL06. At the end of the mission, i.e., during the period November
2016 thr ough June 2017, the ACC instrument aboar d GRACE-B was turned off due to battery issues,
and thus transplanted ACC observations fr om GRACE-A have to be used (in the following, this period
is denoted by “GRACE single ACC”). For RL05a, a simple ACC data transplant was used, which had
only attitude and time corr ections applied. As part of JPL ’s L1B RL03 dataset, an impr oved transplant
version [
23
], additionally corr ected for thruster spikes, has been made available and is used for RL06.
Befor e orbit and gravity field determination with EPOS, the L1B data ar e prepr ocessed as follows
for RL05a: (1) KRR observations are modified by adding the light time corr ection and the antenna

Remote Sens. 2019 , 11 , 2116 4 of 22
of fset correction (both also taken fr om the KBR1B products); (2) GPS observations ar e cleaned, phase
cycle slips ar e detected, and the data are downsampled to 30 s; (3) ACC observations ar e downsampled
fr om 1 Hz to 0.2 Hz by simple decimating and data gaps < 100 s ar e interpolated; and (4) data gaps
< 500 s in the SCA1B data ar e interpolated. For RL06, the only modification concerns (4): SCA1B data
ar e downsampled from 1 Hz to 0.2 Hz, smoothed and data gaps ar e filled, all done simultaneously
using spherical quadrangle interpolation (SQUAD). After pr eprocessing, the L1B observations are
analyzed for data gaps caused by satellite-specific events such as, e.g., maneuvers and r eboots of the
Instrument Pr ocessing Unit (IPU). In case of larger gaps, the nominally one day long arcs ar e split
into two or mor e shorter arcs over partial days. The minimum length of an arc, however , is set to
thr ee hours. T o avoid any unwanted effects in the observations ar ound such events, a margin of ten
minutes is applied befor e and after data gaps when defining the final arcs.
2.3. Background Models
By definition, GRACE gravity field models r epresent geophysical signals caused by variations
in the terr estrial water storage, mass loss in polar ice sheets and inland glacier systems, ocean mass
variations, global isostatic adjustment and lar ge earthquakes. Consequently , gravity variations caused
by solid Earth and pole tides, atmospher e and ocean tides or short-term non-tidal atmospheric and
oceanic mass variations ar e not supposed to be included in the gravity field solutions and are ther efore
taken into account during the data pr ocessing via background models. On the other hand, any err or
contained in the backgr ound models degrades the quality of the gravity field solutions, especially at
low fr equencies [
24
]. Thus, some of these background models have been updated for pr ocessing the
GFZ RL06 time series (T able 1 ).
T able 1. Overview of background models used for GFZ RL05a and RL06 processing.
Background Model GFZ RL05a GFZ RL06
Static a priori gravity field EIGEN-6C [ 25 ] (up to d/o 200) EIGEN-6C4 [ 26 ] (up to d/o 200)
T ime-variable a priori gravity field
T r end, annual and semi-annual GFZ RL05a (DDK1 smoothed,
coefficients of EIGEN-6C up to d/o 50), only used
(up to d/o 50) during data editing
Ocean tides EOT11a [ 27 ] FES2014 [ 28 ]
Atmospheric tides Biancale & Bode [ 29 ] same as RL05a
Non-tidal atmospheric and AOD1B RL05 [ 30 ] AOD1B RL06 [ 31 ]
oceanic mass variations
Ocean pole tide Desai [ 32 ] same as RL05a
Solid Earth and pole tides IERS2010 [ 33 ] same as RL05a
3rd body ephemerides JPL DE421 JPL DE430
Among the backgr ound models listed in T able 1 , the choice of the Atmospher e and Ocean
De-aliasing (AOD) and the ocean tide model has the most impact on the quality of the monthly GRACE
solutions and hence their geophysical interpr etation [
24
]. The AOD1B model is an official GRACE L1B
pr oduct routinely generated at GFZ. Compar ed to its precursor AOD1B RL05, the most r ecent release
AOD1B RL06 has higher temporal (3-hourly vs. 6-hourly) and spatial (maximum SH d/o 180 vs. 100)
r esolution. Further details are described by Dobslaw et al. [
31
], wher e also improvements in
GRACE gravity field pr ocessing by means of variance reduction of K-band range-acceleration
r esiduals are alr eady reported when using AOD1B RL06 instead of RL05. Regar ding ocean tides,
similar impr ovements are observed when using FES2014 instead of EOT11a. Generally , the choice
of the ocean tide model does not significantly af fect the quality of individual monthly GRACE
solutions, but regional deficiencies, especially at high latitudes, can become visible in GRACE time
series analysis. In this context, Ray et al. [
34
] r eported that the FES2014 model, used for GFZ RL06,
shows impr ovements in most of the polar regions compar ed to its precursor and performs comparable
to other state-of-the-art ocean tide models.

Remote Sens. 2019 , 11 , 2116 5 of 22
2.4. Processing Strategy
The pr ocessing scheme of GRACE gravity field processing at GFZ consists of the following steps:
(1) GPS data editing; (2) KRR data editing; (3) generation of a priori orbits; (4) generation of
ar c-wise NEQs; and (5) accumulation to and solving of monthly NEQs. For all previous GFZ GRACE
r eleases from RL01 to RL05a, the strategy how these steps ar e performed is more or less identical and
has been described by Schmidt [
35
]. For the curr ent GFZ GRACE RL06 processing, the strategy has
been considerably changed and is described in this section. An overview of the GFZ RL05a and RL06
pr ocessing strategies is given in T able 2 .
T able 2. Overview of GFZ RL05a and RL06 processing strategies.
GFZ RL05a GFZ RL06
GPS data editing
Remarks GRACE-A & -B jointly processed GRACE-A & -B independently processed
T ime-variable a priori yes yes
gravity field
Observation weights
σ G P S p h a s e 0.7 cm 0.3 cm
σ G PScode 70.0 cm 40.0 cm
σ K R R 50 µ m/s no KRR observations
KRR data editing
Remarks
further GPS data editing no further GPS
still possible data editing
automated editing based no automated editing, instead
on 8-sigma elimination visual inspection of residuals
T ime-variable a priori yes yes
gravity field
Observation weights
σ G P S p h a s e 0.7 cm 0.3 cm
σ G PScode 70.0 cm 40.0 cm
σ K R R 0.1 µ m/s 0.3 µ m/s
Generation of a priori orbits / generation of arc-wise NEQs
T ime-variable a priori yes no
gravity field
Observation weights
σ G P S p h a s e 0.7 cm arc-wise based on r esiduals scaled by empirical factor of 7
σ G PScode 70.0 cm
σ K R R 0.1 µ m/s arc-wise based on r esiduals
Editing of GPS data is done by automated elimination during an iterative pr ecise orbit
determination (POD). The elimination is based both on an
n
-sigma criterion, with varying values for
n
in the dif fer ent iterations, and additionally an absolute thr eshold for the size of GPS residuals. The
main dif ference in the GPS data editing step is that for RL06 the POD for both GRACE satellites is
done completely independently fr om each other in contrast to RL05a, where down-weighted KRR
observations wer e included and a common POD for GRACE-A and -B was applied. The goal for RL06
is to obtain best possible absolute orbit accuracy for each of the two spacecraft and thus to avoid that the
elimination of GPS observations for one satellite is influenced by the other . Another differ ence concerns
the empirical corr ections for GPS phase center variations (PCV): For RL05a, a certain unvaried PCV
corr ection based on one month (April 2008) of GPS residuals has been applied for the whole time series,
wher eas for RL06, monthly PCV corrections ar e computed from the corr esponding monthly residuals.
A novelty of RL06 is that also GPS code residual variation maps per month ar e computed and applied.
In general, these empirical corrections ar e very stable over time, but they are significantly af fected
by systematic patterns whenever radio occultation measur ements are activated onboar d one of the
GRACE satellites (Figur e 1 ). Because activation and deactivation of these measurements has occurr ed
several times thr oughout the GRACE mission (mostly related to satellite swap maneuvers), a monthly
computation of these corr ections has been chosen as the preferable option. Finally , the a priori weights
for GPS phase and code observations have been changed from RL05a to RL06 to better r eflect the
actual level of the RMS of the corr esponding residuals (see T able 2 ).

Remote Sens. 2019 , 11 , 2116 6 of 22
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−200 −150 −100 −50 0 50 100 150 200
[cm]

Figure 1.
Code residual variation maps of GRACE-A (
top
) and GRACE-B (
bottom
) for June 2014 (
left
)
and August 2014 (
right
). Radio occultation measur ements on GRACE-A were activated in June 2014
and deactivated in August 2014 and vice versa on GRACE-B, after a satellite swap in July 2014.
For KRR data editing, a common POD for GRACE-A and -B is performed. In case of RL05a, where
down-weighted KRR observations wer e already included in the pr evious step, the KRR weight was
incr eased by setting the a priori standar d deviation to 0.1
µ
m/s, and elimination of KRR observations
was automatically done based on an 8-sigma criterion. Further editing of GPS observations during this
step was not explicitly turned of f. In contrast, now for RL06 KRR observations are only intr oduced in
this step with a slightly incr eased a priori standar d deviation of 0.3
µ
m/s which better matches—as
done similarly for GPS—the corr esponding orbit fit RMS. No automated elimination at all is applied;
instead, possible elimination of KRR observations-if needed-is based on visual inspection of the
KRR r esiduals. Usually , observations are edited if the r esiduals exceed a threshold of 3
µ
m/s, but this
thr eshold is not fixed and other editing criteria such a s anomalous behavior of the KRR r esiduals
over a certain period of time within one ar c might be applied. By modifying the KRR data editing
as described, inadvertent elimination of observations over areas with lar ge geophysical signals is
avoided and about 1% mor e KRR observations (approx. 0.3 days accumulated over one month) r emain
and ar e used for gravity field determination in the case of RL06.
The purpose of generating the a priori orbit is to assur e that convergence of a POD using the
edited GPS and KRR observations and iterated orbit parameter estimates is r eached after one iteration.
If this condition is fulfilled, arc-wise NEQs ar e set up starting with the observations and initial
parameters fr om the a priori orbit run. In case of RL05a, the observation weights from the pr evious
data editing steps r emained unchanged, wher eas for RL06 individual ar c-wise weighting for GPS
and KRR observations has been intr oduced. Ar c-wise a priori standard deviations ar e based on the
RMS of the corr esponding residuals after the KRR editing run: In case of KRR, they ar e equal to the
RMS values; for GPS, the RMS values ar e multiplied by an empirical factor of 7. This intentional
down-weighting of GPS observations r elative to the K-band observations is necessary to obtain better
gravity field solutions and is also done similarly by other pr ocessing centers (see, e.g., [ 10 , 16 ]).

Remote Sens. 2019 , 11 , 2116 7 of 22
Another modification fr om RL05a to RL06 regar ds the time-variable a priori gravity field which
in case of RL05a was used as backgr ound model also during these two last-mentioned processing
steps. This r equired r estoring of the monthly mean of these a priori fields to the estimated monthly
GRACE solution to pr ovide users a Level-2 gravity field product which contains the full time-variable
signal as expected per definition. For RL06, the time-variable gravity field background model is
only used during the data editing steps, where backgr ound modeling is desired to be as r ealistic as
possible, but not during the steps wher e gravity field determination takes place. Thus, any possible
bias that might be intr oduced by applying a r emove-restor e procedur e as described for RL05a is
avoided for RL06.
2.5. Parametrization
In conjunction with the pr ocessing strategy , the orbit and instrument parametrization has also
been significantly changed fr om GFZ RL05a to RL06 (see T able 3 ).
In RL05a pr ocessing, empirical accelerations were only set up and estimated during the GPS
data editing step. In the subsequent steps, these parameters were completely r emoved, and empirical
K-band parameters wer e introduced [
35
]. For RL06, empirical accelerations are set up mor e frequently
(once per orbital r evolution) and remain as parameters thr oughout all processing steps to assur e
a consistent parametrization fr om GPS editing until gravity field estimation. T o avoid that these
parameters absorb too much gravity field signal, an a priori standar d deviation of 1E-8 m/s
2
is applied
as constraint. In contrast to RL05a, no K-band parameters at all are set up in RL06. Internal tests have
shown that the additional estimation of K-band parameters does not significantly impact the estimated
gravity field solution, but leads to a degradation in orbit accuracy .
Further modifications fr om RL05a to RL06 affect the ACC instrument parameters. Regarding
the ACC biases, their number has been decreased. Now for RL06, usually three biases per ar c are
estimated in along-track and radial dir ection (at the beginning, middle, and end of the ar c), and nine
in cr oss-track direction (at the beginning and end, and equally spaced in between). The number of
biases can become less in case the ar c length is shorter than 24 h, as the minimum spacing between
two biases is set to thr ee hours. Between the epochs wher e biases are estimated, the bias is modeled
as a natural cubic spline function (RL05a: linear interpolation). Regarding ACC scale factors, one
per ar c and dir ection is estimated in case of RL06. This is a lesson learned fr om RL05a processing,
wher e for most of the time series the scales were fixed to one, which turned out to be not optimal
especially in the later years of the GRACE mission. Ther efor e, this was modified within RL05a to
estimating 3-hourly scales, which helped to improve the quality of the RL05a solutions, but on the
other hand tends to over -parameterize the gravity field estimation pr ocess. Another notable differ ence
between RL05a and RL06 is the parametrization during the “GRACE single ACC” period: Wher eas
for RL05a the parametrization was the same as for the r est of the GRACE mission, a fully populated
scale factor matrix is estimated per ar c in case of RL06. This has been proposed first by Klinger and
Mayer -Gürr [
36
] and is applied to the complete ITSG-Grace2016/2018 time series, as well as to other
r ecent releases such as the CSR RL06 [
10
] and JPL RL06 [
11
] time series. For GFZ RL06, the additional
six parameters, i.e., the off-diagonal elements of the scale factor matrix, ar e constrained with an a priori
standar d deviation of 1E-3 since otherwise, the inversion of the NEQ system becomes unstable and in
many cases would fail.
In summary , the total number of orbit and instrument parameters described above has decr eased
for RL06 compar ed to most of the RL05a solutions, and is nearly identical compared to the RL05a
solutions with modified ACC parametrization. Moreover , as already mentioned, the parametrization
is now consistent during all pr ocessing steps. It has to be mentioned as well that ther e are other
parameters not listed in T able 3 , namely GPS receiver clock of fsets (2880 per 1-day arc and satellite)
and GPS phase ambiguities (appr ox. 400 per 1-day ar c and satellite). However , these two parameter
gr oups are pr e-eliminated before gravity field estimation and ther e are no dif ferences in their tr eatment
between RL05a and RL06 pr ocessing.

Remote Sens. 2019 , 11 , 2116 8 of 22
Finally , regar ding the main parameters of inter est, i.e., the gravity field parameters, the maximum
SH d/o estimated was slightly increased fr om 90 (RL05a) to 96 (RL06). New with GFZ RL06,
an independently estimated GRACE time series only up to d/o 60 is pr ovided additionally . These two
decisions have been made jointly within the GRACE SDS to ensur e better consistency between the
thr ee SDS time series than it was the case with RL05. Furthermore, both KRR and GPS observations
contribute to the full spectrum of the monthly gravity field estimates in GFZ RL06, wher eas in GFZ
RL05a the contribution of GPS was limited to SH d/o 80.
T able 3.
Number and properties of GFZ RL05a and RL06 orbit and instr ument parameters (numbers
are per ar c repr esentative for the nominal arc length of 24 h).
GFZ RL05a GFZ RL06
GPS editing step subsequent steps GPS editing step subsequent steps
Orbital elements 6/6 (GRACE-A/GRACE-B)
Empirical accel. 20/20 none 64/64
Details
cos/sin coefficients of 1/r ev periodical model
every 4.8 h in TN - 1/rev in TN
no constraint - constraint: σ = 1E-8 m/s 2
K-band param. none 48 none
Details
- range-rate bias & -
drift every 90 min;
cos/sin coeff. of range
bias every 180 min
ACC param. 75/75 ( 1 ) 18/18 ( 3 )
54/54 ( 2 ) 18/18 ( 4 ) 24/24 ( 4 )
Details
1-hourly biases in R TN; 3 biases per arc in R T ; 9 in N
scale factors fixed to 1 ( 1 ) 1 scale factor per arc in R TN
3-hourly biases in R TN; 6 off-diagonal elements
3-hourly scale factors in R TN ( 2 ) of scale factor matrix;
constraint: σ = 1E-3 ( 4 )
R, T , N: radial, along-track and cross-track direction in SRF .
( 1 )
period from 2003/01 thr ough 2013/05;
( 2 )
period from 2002/04 thr ough 2002/12 and 2013/06 through 2017/06;
( 3 )
period from 2002/04
through 2016/08; ( 4 ) period fr om 2016/11 through 2017/06 (“GRACE single ACC”).
2.6. Orbit Quality
The quality of the GRACE orbits determined prior to gravity field estimation was not in the
focus during GFZ RL05a processing. For GFZ RL06, the modifications in processing strategy and
parametrization ar e motivated not only to obtain improved gravity fields, but also orbits of high quality .
A first indication that this goal is r eached is given by GPS phase and code r esiduals of the GPS
editing runs which ar e extremely stable during the whole mission with ar c-wise RMS values of about
3 mm and 40 cm, respectively (for the “GRACE single ACC” period, only a slight increase is observed).
In contrast to RL05a, the size of GPS r esiduals does not increase at all when adding KRR observations
in the subsequent pr ocessing steps which can be attributed to the consistent parametrization.
Another independent orbit validation during RL06 processing is r outinely done by means of
satellite laser ranging (SLR) observations fr om ground stations to the GRACE satellites, pr ovided by
the International Laser Ranging Service (ILRS). Coarse outliers in the SLR observations ar e eliminated
by a 20 cm thr eshold. Mean values and standar d deviations of GRACE-A and -B SLR residuals per
year ar e shown in Figure 2 for all available stations and a subset of high-quality stations. The definition
of such a subset has been outlined by Arnold et al. [
37
] and the same 12 stations ar e used here for
better comparability . These high-quality stations contribute between 50% and 75% of all available
observations. It can be seen that the standard deviations ar e in the range of 20 mm to 25 mm for all
stations and about 15 mm for the high-quality stations. For the year 2010, the standar d deviations

Remote Sens. 2019 , 11 , 2116 9 of 22
for GRACE-A ar e 24.5 mm and 13.7 mm, respectively , which agr ees very well with values of 24.4 mm
and 12.3 mm, r espectively , reported in [
37
]. As for the GPS residuals, the values ar e the same whether
only GPS observations ar e used or KRR observations are added, and ar e also very similar for both
GRACE satellites. Increased standar d deviations, in particular for recent years, ar e observed for the a
priori orbits which can be explained by the fact that these orbits ar e determined without a time-variable
gravity backgr ound model and GPS observations are down-weighted. The mean values of GRACE-A
and -B as ar e also very consistent, independent of the processing step or whether all or the high-quality
stations ar e evaluated. They are mostly in the range of
−
10 mm to
−
15 mm which is r elatively large.
However , this is not necessarily due to the orbit quality , but may also be caused by incorr ect values
for the GPS phase center offset (PCO) of the GRACE GPS navigation antennas. For GFZ RL06, PCOs
r elative to the antenna refer ence point provided by Montenbruck et al. [
38
] ar e used. A geometrical
of fset (distance between the satellites’ center of mass and the antenna refer ence point) of
−
444 mm is
added–only for the z-component in the SRF–r esulting in a total L3 PCO in z-dir ection of
−
391.7 mm.
This value is appr ox. 22 mm larger than the corr esponding value derived from the of ficial GRACE L1B
vector of fset product for the GPS main antenna (VGN1B, see [
21
]) which might at least partly explain
the r elatively large negative of fsets reported her e.
Overall, the quality of the GFZ GRACE RL06 orbits is satisfyingly well confirming that the
pr ocessing changes relative to GFZ RL05a have been a step into the right dir ection.
yea r
mea n [mm] standard deviation [mm]
2002 2004 2006 2008 2010 2012 2014 2016
-30
-20
-10
0
10
20
30
40
50
60
GPS editing step, all stati ons
GPS editing step, high -quality station s
KRR edit ing st ep, all station s
KRR edit ing st ep, high-qu ality st ations
a priori orbit step, all stations
a priori orbit step, hi gh-qualit y stati ons

Figure 2.
Mean and standar d deviation per year of GRACE-A (blue) and -B (r ed) SLR residuals during
the differ ent GRACE processing steps for all available stations and a subset of high-quality stations.
3. Results
GFZ GRACE RL06 gravity field r esults are analyzed and discussed in comparison to GFZ’s
RL05a GRACE time series in the following subsections. Most of the results shown are relative to a
climatology model (individually derived for each time series) which has been estimated as follows:
The dominating signal content of the time series is appr oximated by fitting a pr oper parameter model
coef ficient-wise to the monthly solutions. Here, eight parameters describing the constant and linear
part as well as periodic sine and cosine amplitudes for annual, semi-annual and 161-days (GRACE
aliasing period for the ocean tide S2) periods ar e used. Furthermor e, the formal err ors of the monthly
SH coef ficients are used as a priori information to weight each individual monthly coef ficient when
estimating the climatology . Months with short repeat cycles (i.e., solutions which wer e regularized in
RL05a) as well as the seven “GRACE single ACC” solutions ar e excluded.

Remote Sens. 2019 , 11 , 2116 10 of 22
3.1. Formal and Empirical Errors
In this subsection formal and empirical err ors of the GFZ RL06 time series are analyzed in
the spectral domain and compar ed to GFZ RL05a. The formal errors ar e the standard deviations
of the gravity field parameters estimated in the least-squar es adjustment process, i.e., the square
r oot of the diagonal of the gravity field parameter part of the variance-covariance matrices. In
principle, these errors should give a good indication of the r eal errors of the estimated parameters.
However , as variance-covariance information of all the input data is insuf ficiently (observations) or
not all (backgr ound models) applied, the formal errors ar e typically too optimistic.
Another quantification of the err ors of such a gravity field time series are empirically
derived values. Here, r esiduals regar ding the climatology described above are defined as empirical
err ors of the time series.
Figur e 3 shows the RMS over the whole time series of the empirical and formal err ors for RL05a
and RL06. The main dif ferences between empirical and formal err ors can be seen in the very low
SH degr ees and ar ound so-called r esonance or ders. Due to residual signals in the very low degr ees,
which ar e not covered by the eight parameters, the empirical err ors show much higher values than
the formal ones her e. Around the r esonance or ders, which are integer multiples of appr oximately 15,
it is well known that GRACE err ors are lar ger due to systematic effects fr om temporal aliasing caused
by backgr ound model errors. This effect is not very well r epresented in the formal err ors.
( a ) ( b )
( c ) ( d )
( e ) ( f )
Figure 3.
(
a
–
d
) SH spectra of empirical error RMS for RL05a (
a
) and RL06 (
b
); and of formal err or RMS
for RL05a (
c
) and RL06 (
d
); (
e
) Ratio of SH spectra of empirical err or RMS “RL05a/RL06”; (
f
) SH degree
amplitudes of the ratio of empirical err or RMS “RL05a/RL06” (blue), and the ratios “empirical/formal
error RMS” for RL05a (r ed), and RL06 (green).
Compar ed to RL05a (Figure 3 a,c), Figur e 3 b,d reveal smaller empirical err ors and more r ealistic
formal err ors for RL06. This becomes even more clear when looking at the ratio of the empirical error

Remote Sens. 2019 , 11 , 2116 11 of 22
RMS values between RL05a and RL06 (Figur e 3 e) which is > 1 for nearly all coefficients and also when
plotted as amplitudes per SH degr ee (Figure 3 f). Also, the degree amplitudes of the ratio between
empirical and formal err ors indicate that the GFZ RL06 formal errors ar e more r ealistic as smaller
variations than for GFZ RL05a ar e visible and the curve is closer to the value of one.
3.2. Degree Amplitudes
Dif ference degr ee amplitudes relative to climatology ar e shown in Figure 4 . The spread of monthly
degr ee amplitudes is less for RL06 than for RL05a which illustrates that RL06 is a mor e homogeneous
time series. Significant differ ences between the RL05a and RL06 median degree amplitudes ar e already
visible at appr ox. SH degr ee 15, and almost all monthly RL06 degree amplitude curves ar e well
below the median RL05a curve (or vice versa) for medium and high degrees indicating a notably
impr oved signal-to-noise ratio for RL06. When only looking at the “GRACE single ACC” period,
lar ge improvements fr om RL05a to RL06 are achieved accor ding to the corresponding median degr ee
amplitudes. These improvements ar e not only present for medium and high degrees, but also for the
very low degr ees. However , the quality of the “GRACE single ACC” solutions is still significantly
worse than for the r est of the GRACE mission also in case of RL06.
Figure 4.
Degree amplitudes relative to a climatology model for GFZ RL05a (
left
) and GFZ RL06 (
right
);
thin lines repr esent monthly solutions (without “GRACE single ACC” solutions and those regularized
in RL05a), and bold lines repr esent the median curves (the same curves are shown in both plots) for
RL05a (red), RL06 (96
×
96, green), RL06 (60
×
60, blue), and the “GRACE single ACC” months only
for RL05a (black) and RL06 (96 × 96, grey).
3.3. RMS of Residuals in the Spatial Domain
T o assess the quality of the GFZ RL06 time series in the spatial domain, monthly residual SH
coef ficients relative to climatology ar e converted to gridded mass anomalies in terms of equivalent
water height (EWH). T o reduce the impact of spatially correlated noise, the solutions ar e de-corr elated
and smoothed by applying the non-isotr opic DDK filter [
39
]. Then, RMS values of the time
series per grid point ar e calculated and shown in Figur e 5 . For the period until August 2016,
i.e., without the “GRACE single ACC” months, a clear reduction of RMS variability for RL06 has
been achieved (Figur e 5 a,b). Geophysical signals over continental areas, where they ar e much
lar ger than over the oceans, ar e less superimposed by the typical GRACE striping pattern and
thus better detectable. V ariability over the oceans is generally expected to be rather small and is
ther efore often interpr eted as upper error bound for monthly global GRACE gravity field models.
Latitude-dependent weighted RMS (wRMS) values over the oceans decrease fr om 6.8 cm (RL05a) to
4.0 cm (RL06, 41% relative impr ovement) when DDK5 filtered, and from 3.4 cm (RL05a) to 2.1 cm
(RL06, 38% relative impr ovement) when DDK3 filtered. For the “GRACE single ACC” period,

Remote Sens. 2019 , 11 , 2116 12 of 22
Figur e 5 c shows DDK3 filtered RMS variability to allow a dir ect comparison with the period before,
but it becomes obvious that much str onger decorrelation and smoothing would be r equired her e to
extract geophysical signals. Nevertheless, the corresponding wRMS values over ocean decr ease again
significantly fr om 9.5 cm (RL05a) to 6.1 cm (RL06, 36% relative impr ovement).
( a )
( b )
( c )
Figure 5.
RMS of the time series of residuals (cm EWH ) relative to a climatology model (without
months regularized in RL05a) for GFZ RL05a (left) and GFZ RL06 (right); the following differ ent
cases are shown: period from 2002/04 thr ough 2016/08, DDK5 filtered (
a
) and DDK3 filtered (
b
);
and “GRACE single ACC” period, DDK3 filtered ( c ).
Monthly wRMS values over the oceans for the complete GRACE time series (DDK5 filter ed) are
shown in Figur e 6 . Again, it becomes visible that GFZ RL06 is a clear impr ovement over RL05a in terms
of noise r eduction and homogeneity . Some months where RL06, particularly for the 96
×
96 time series,
exhibits lar ger wRMS values than RL05a can be attributed to short period repeat orbit cycles (the most
harmful r epeat orbits during the GRACE mission are: 61/4 around September 2004, 46/3 around
May 2012, 77/5 around December 2013, 31/2 around February 2015). RL05a solutions for these
months wer e regularized which is not the case anymor e for RL06 as the additionally provided RL06
60
×
60 time series, which is less sensitive to these short period repeat orbits, might be analyzed instead.
Apart fr om the repeat cycles just mentioned befor e, the wRMS values of the RL06 96
×
96 and

Remote Sens. 2019 , 11 , 2116 13 of 22
60
×
60 time series ar e mostly almost identical. Periods where these values ar e notably larger ar e again
r elated to less harmful repeat cycles such as the long-lasting 107/7 r epeat orbit around December 2009.
Finally , also Figure 6 shows that the “GRACE single ACC” months ar e of much less quality than the
r est of the time series. At least, the RL06 solution for May 2017 is now of comparable quality (it must
be noted that for this solution GRACE-B ACC data is actually available and used).
Figure 6.
wRMS over the oceans (cm EWH) of DDK5 filter ed residuals relativ e to a climatology model
for the complete GFZ RL05a (r ed), GFZ RL06 (96
×
96, green), and GFZ RL06 (60
×
60, blue) time series.
3.4. Low Degree Harmonics
In this subsection, time series of selected low degree SH coef ficients are analyzed, starting with C
20
.
This coef ficient is known to be poorly estimated from GRACE (see, e.g., [
40
]), and it is common practice
to r eplace it, e.g., with estimates derived from SLR observations to geodetic satellites. Despite the
fact that the GFZ GRACE RL06 C
20
values have significantly improved compar ed to GFZ RL05a
(Figur e 7 a), a replacement of C
20
is still r ecommended for RL06 before using the time series for
geophysical interpr etation. A vailable SLR-based r eplacement time series which are consistent with
RL06 standar ds are, e.g., GRACE T echnical Note TN-11 generated by CSR [
41
], or a similar time series
pr ovided by GFZ [ 42 ] which is also shown in Figure 7 a.
T wo other coefficients r equiring special attention are C
21
and S
21
. When analyzing surface mass
variations fr om the GRACE SDS RL05 time series, W ahr et al. [
43
] r ecommended corrections to
these coef ficients to account for effects of the applied mean pole model. Since all three SDS RL06
time series including GFZ RL06 ar e pr ocessed based on a linear mean pole model which is conform
to the updated IERS2010 mean pole convention ( http://iers- conventions.obspm.fr/chapter7.php ),
this r ecommendation is not applicable anymore to these r eprocessed time series. Looking at the GFZ
RL06 C
21
time series in comparison to GFZ RL05a (Figur e 7 b), however , one can see an anomalous
behavior during the “GRACE single ACC” period. Although already the RL05a time series shows
lar ger amplitudes in that period, this is even more pr onounced in RL06. A similar behavior is visible
also for S
21
(Figur e 7 c). The reason for these anomalies in C
21
and S
21
is not yet fully understood
and subject to further investigation. As it is clearly corr elated with the use of ACC data transplant,
a possible explanation would be that it is due to inaccurate modeling of surface forces, potentially
in conjunction with an inappr opriate parametrization. First experiments at GFZ combining GRACE
and SLR on NEQ level have revealed pr omising r esults and might lead to a replacement time series,
similar to C
20
, to overcome these deficiencies in the near futur e. It should be mentioned here that
a GRACE+SLR combination would not be a novelty as, e.g., the GRACE solutions provided by the
CNES/GRGS gr oup are in fact alr eady based on a combination with SLR [ 15 ].

Remote Sens. 2019 , 11 , 2116 14 of 22
( a )
( b )
( c )
Figure 7.
T ime series of SH coef ficients C
20
(
a
); C
21
(
b
); and S
21
(
c
); each plot shows values of GFZ
RL05a (red), GFZ RL06 (96
×
96, green), and GFZ RL06 (60
×
60, blue); for C
20
, the SLR-based time
series König et al. [ 42 ] is shown additionally (black).
4. External V alidation
Due to the uniqueness of GRACE Level-2 pr oducts as observable for studies of Earth surface mass
transport and climate change, it is nontrivial to validate them against independent data or models,
and thus to r eliably assess the quality of differ ent GRACE time series in terms of signal content rather
than only assessing their internal noise level. In the following subsections, two methods to evaluate
the quality of the GFZ RL06 and RL05a time series by external data ar e presented.
4.1. OBP V alidation
First, the GFZ GRACE RL06 and RL05a solutions are independently validated by comparing
them with ocean bottom pr essure (OBP) in situ observations.
The OBP database used her e was initially compiled by Macrander et al. [
44
] and consists of
167 stations which ar e irr egularly scattered over the oceans covering the time period fr om 2002
thr ough 2010 with observation lengths for individual stations of up to eight years. The station data
ar e pr eprocessed as outlined by Por opat et al. [
7
] to obtain time series of OBP observations with
r emoved trends, tidal variability , outliers, and discontinuities at certain dates related to instr ument
issues including maintenance and battery r eplacement.
For the OBP validation, the GFZ RL06 and RL05a Level-2 solutions are post-pr ocessed as follows:
The C
20
coef ficients are r eplaced with GRACE T echnical Notes TN-11 and TN-07 [
40
], for RL06

Remote Sens. 2019 , 11 , 2116 15 of 22
and RL05a, respectively , the effects of glacial isostatic adjustment ar e corrected by subtracting
the model by A et al. [
45
], co-seismic signatures fr om three megathr ust earthquakes are r emoved
with estimates fr om the GOCO06s model [
46
], and appr oximated degree-1 coef ficients according to
Ber gmann-W olf et al. [
47
] ar e added. The DDK filter is applied to de-correlate the solutions: DDK4
is used for the long-term tr end component, wher eas DDK2 is used for the annual and semi-annual
components and for the r emaining residual monthly signals. Please note that for five monthly solutions
with particularly poor signal-to-noise ratio, the DDK1 filter is used. Finally , the monthly GAD
backgr ound model [ 48 ] including atmospheric surface pressur e and non-tidal OBP is added back.
These post-pr ocessed GRACE data ar e evaluated at the locations of the OBP in situ recor ders.
Regionally dif ferent linear tr ends, specifically caused by changing sea level, are r emoved. Since GRACE
data do not r epresent a point-measur ement, but an average over a large ar ea, areas of coher ent OBP
variability ar e identified and the GRACE OBP data ar e averaged over these areas [
49
]. The selection of
these ar eas follows [ 7 ].
T o compare GRACE and in situ OBP variations at the OBP in situ sites, relative explained variances
(defined as
σ 2
r = ( σ 2
in situ OBP − σ 2
in situ OBP - GRACE OBP ) / σ 2
in situ OBP )
and corr elation coefficients ar e
calculated fr om both time series. Generally , positive relative explained variances ar e observed for
about 35% of the OBP in situ stations (Figur e 8 a), indicating that GRACE-derived and observed OBP
variations corr espond rather poorly in many regions. However , impr ovements in relative explained
variance for GFZ RL06 compar ed to GFZ RL05a become visible in most regions (Figur e 8 c). The same
conclusion can be drawn for the corr elations, where a slight incr ease for GFZ RL06 can be seen as well
again in most r egions (Figure 8 d). Generally , correlation coef ficients between GRACE and in situ OBP
ar e within the range of 0.1 to 0.7 for most of the stations (Figure 8 b); the corr esponding 25th, 50th,
and 75th per centiles ar e 0.21, 0.34, and 0.54, r espectively . Overall, a slightly better performance of GFZ
RL06 over GFZ RL05a in explaining OBP variability over wide r egions is achieved.
( a )
8 0 °S
6 0 °S
4 0 °S
2 0 °S
0 °
2 0 °N
4 0 °N
6 0 °N
8 0 °N
[ G F Z R L 0 6 ]
7 5 5 0 2 5 0 2 5 5 0 7 5 1 0 0
r e l a t i v e e x p l a i n e d v a r i a n c e [ % ]

( b )
8 0 °S
6 0 °S
4 0 °S
2 0 °S
0 °
2 0 °N
4 0 °N
6 0 °N
8 0 °N
[ G F Z R L 0 6 ]
− 0 . 4 − 0 . 2 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0
c o r r e l a t i o n c o e f f i c i e n t

( c )
8 0 °S
6 0 °S
4 0 °S
2 0 °S
0 °
2 0 °N
4 0 °N
6 0 °N
8 0 °N
[ G F Z R L 0 6 - G F Z R L 0 5 ]
− 4 0 − 2 0 0 2 0 4 0
r e l a t i v e e x p l a i n e d v a r i a n c e [ % ]

( d )
8 0 °S
6 0 °S
4 0 °S
2 0 °S
0 °
2 0 °N
4 0 °N
6 0 °N
8 0 °N
[ G F Z R L 0 6 - G F Z R L 0 5 ]
− 0 . 3 − 0 . 2 − 0 . 1 0 . 0 0 . 1 0 . 2 0 . 3
c o r r e l a t i o n c o e f f i c i e n t

Figure 8.
(
a
) Relative explained variances
σ 2
r
at in situ OBP stations for GFZ RL06; (
b
) Correlation
coefficients between in situ OBP and GRACE OBP for GFZ RL06; (
c
) Differ ence of relative explained
variances for GFZ RL06 and GFZ RL05a; (
d
) Differ ence of correlation coef ficients for GFZ RL06 and
GFZ RL05a. For (
c
) and (
d
), re d colors indicate impr ovements of GFZ RL06 over GFZ RL05a; stations
with relative explained variances or corr elation coefficients < 0 for both RL06 and RL05a ar e marked
with white crosses.

Remote Sens. 2019 , 11 , 2116 16 of 22
4.2. GOCE Orbit T ests
As another independent validation, orbits of ESA ’s Gravity field and steady-state Ocean
Cir culation Explor er (GOCE) mission are used to compar e the quality of monthly GRACE gravity
solutions. The GOCE satellite [
50
], in orbit from Mar ch 2009 until November 2013, had a very low
orbital altitude of about 255 km and thus shows a rather high sensitivity to the Earth’s gravity field.
For these orbit tests, dynamic orbits are fitted to GOCE kinematic 3D orbit positions which
ar e taken as observations (i.e., not directly the GPS tracking data). These kinematic orbits
(Pr ecise Science Orbits) have been generated at AIUB [
51
] and ar e pr ovided within the GOCE High
Level Pr ocessing Facility . For this study , GOCE orbit tests have been carried out for four months
(November and December 2009, October and November 2010), each consisting of 30 individual GOCE
ar cs with a length of 1.25 days. The ocean tide model used her e is FES2014 [
28
] to SH d/o 100. The
r eference system and gravitational for ce modeling is done applying the IERS 2010 [
33
] conventions.
GOCE common mode accelerations ar e used during orbit computation instead of non-gravitational
for ce models. The scale factors of the common mode accelerations cannot be accurately estimated
per ar c due to the drag-fr ee contr ol system which has compensated most of the signal and are
ther efore fixed to one [
52
]. This value is accurate within 3%, as demonstrated by V isser and van
den IJssel [
53
]. The GOCE gradiometer works best in the measurement bandwidth of 10 to 200 s [
54
],
and consequently the common mode accelerations include an instrumental bias. Ther efore, three
common mode acceleration biases per ar c are estimated, one in each dir ection, in addition to the initial
state vector .
For each month, two versions of orbit fits ar e computed which are identical except for the
backgr ound gravity field model: The first version uses the corresponding GFZ RL06 monthly solutions,
the second one uses the GFZ RL05a solutions instead, both up to SH d/o 90. Due to the high
gravitational sensitivity of GOCE, the monthly GRACE models are filled up with SH coef ficients from
the long-term static GOCE model GO_CONS_GCF_2_DIR_R6 [
55
] up to d/o 240 to achieve r easonable
orbit fits at the level of few centimeters.
The r esults of the GOCE orbit tests ar e listed in T able 4 . When using GFZ RL06 instead of GFZ
RL05a as backgr ound model, the RMS values of the orbit fits are clearly r educed for all four months,
with r elative improvements of GFZ RL06 over GFZ RL05a ranging fr om 12% to 25%. The significant
dif ferences in the orbit fits pr ove that such kind of orbit validation tests are an appr opriate tool for the
validation of monthly GRACE gravity field solutions. For future validation purposes, it is planned to
extend the orbit validation to the complete GOCE mission period and to investigate whether orbits of
other Low Earth Orbiting satellites such as, e.g., CHAMP and Swarm can be used as well.
T able 4.
RMS of orbit fits [cm] for the time-variable GFZ RL05a and RL06 gravity field models and
(only for refer ence) for the static model GO_CONS_GCF_2_DIR_R6. RMS values ar e based on 3D
residuals and r epresent mean values of the 30 individual ar cs within a particular month.
Gravity Field Model Month
2009/11 2009/12 2010/10 2010/11
GFZ RL05a 8.39 9.14 7.53 7.40
GFZ RL06 7.39 6.84 6.24 6.21
GO_CONS_GCF_2_DIR_R6 3.56 3.37 3.82 3.76
5. Conclusions
GFZ has r epr ocessed an improved monthly gravity field time series for the complete GRACE
mission consisting of 163 gravity field models (Level-2 pr oducts) in the period from April 2002
thr ough June 2017. This GFZ GRACE RL06 time series incorporates a r eprocessed in-house GPS
constellation (orbits and clocks), r eprocessed Level-1B K-band ranging, star camera and acceler ometer
(ACC) transplant observations (L1B RL03 dataset provided by JPL), updated backgr ound models

Remote Sens. 2019 , 11 , 2116 17 of 22
for tidal (FES2014) and non-tidal (AOD1B RL06) mass variations, and a considerably modified
pr ocessing strategy including a dif ferent parametrization with (for most months) even less parameters
compar ed to the precursor GFZ RL05a. Key features of the new RL06 pr ocessing strategy are a
strict separation of GPS and K-band data editing, manual instead of automated sigma-based K-band
data editing, and omittance of a time-variable gravity background model during the gravity field
estimation step. Mai n dif fer ences in RL06 parametrization compared to RL05a ar e consistently
estimated parameters thr oughout all pr ocessing steps, less ACC parameters (biases and scale factors),
and –exclusively for the last months wher e ACC transplant data has to be used for GRACE-B (“GRACE
single ACC” period)–the estimation of a fully populated ACC scale factor matrix. Independent
validation by satellite laser ranging (SLR) observations r eveals a satisfying quality of the GRACE
orbits prior to gravity field adjustment with standar d deviations of SLR r esiduals < 20 mm for selected
high-quality stations.
W ith the new GFZ RL06 time series significant improvements have been achieved: The noise is
considerably r educed and, consequently , geophysical signals ar e better detectable and can be analyzed
at smaller spatial scales. Relative improvements over GFZ RL05a in terms of r esidual RMS variability
ar e about 40% for both DDK3 and DDK5 filtered solutions. Furthermore, the complete time series
is mor e homogeneous. Although the GFZ RL06 formal errors ar e still too optimistic for most of the
gravity field coef ficients, they exhibit a more r ealistic behavior , and also empirical errors in terms of
r esiduals relative to a climatology model ar e smaller than for GFZ RL05a. The quality of the gravity
fields within the “GRACE single ACC” period is clearly worse compar ed to the rest of the time series,
but r elative to RL05a, the RL06 solutions are also significantly impr oved here. Special attention needs to
be paid to the C
21
and S
21
coef ficients showing unrealistic amplitudes during that period. A combined
GRACE+SLR r eplacement time series for these coefficients might help to mitigate this issue, as first
investigations at GFZ have indicated. Regar ding the C
20
coef ficient, known to be poorly estimated from
GRACE, it is still advised to replace the values by external time series, e.g., derived fr om SLR. Such a
time series that is consistently pr ocessed with GRACE RL06 standards, is also pr ovided by GFZ [ 42 ].
External validation by means of comparison with in situ ocean bottom pressur e observations as
well as orbit tests with the GOCE satellite confirm that impr ovements have been achieved with GFZ
RL06 over RL05a, enabling thus a better understanding of phenomena in the Earth system related
to climate change. T o put the relative impr ovement from RL05a to RL06 in context with the r elative
impr ovements between all GFZ GRACE releases since RL01, Figur e 9 shows gravity field anomalies
for all pr evious GFZ GRACE releases exemplarily for the month August 2003. The corresponding
r elative improvements in terms of wRMS over ocean ar e as follows: RL01 to RL02: 14%, RL02 to RL03:
24%, RL03 to RL04: 4%, RL04 to RL05a: 0%, RL05a to RL06: 41%. This is another clear indication
of the remarkable impr ovements achieved with the GFZ RL06 repr ocessing and also depicts that
even after mor e than 15 years of the first instrument data release a substantial gain in the quality of
monthly GRACE gravity field pr oducts is possible thanks to repr ocessing efforts r egarding Level-1
and Level-2 pr oducts, but also improved backgr ound models and enhanced processing strategies.
Hence, repr ocessing of a GRACE RL07 time series is already planned, for which a final release of
Level-1 pr oducts will be available. Apart from using these new Level-1 data and possible backgr ound
model updates, the specific focus at GFZ for RL07–or other likely upcoming r eleases–will be on
the r eported C
21
/S
21
issue, as well as on a further reduction of noise as achieved by other gr oups
(see, e.g., [
14
]). Whereas modification or fine tuning of the parametrization is always a pr omising
option in view of impr ovements, in particular the application of an improved stochastic modeling of
err ors in observations and background models is envisaged.
A comparison between GFZ RL06 and r ecently published GRACE time series by other processing
centers is not the purpose of this work; however , such comparisons wer e already done in several
other studies: Göttl et al. [
56
] r eport an incr eased consistency of the SDS (CSR, JPL, GFZ) RL06 and
ITSG-Grace2018 solutions compar ed to the SDS RL05 and ITSG-Grace2016 solutions. Kvas et al. [
14
]
investigated the signal content of the SDS RL06 and ITSG-Grace2018 solutions by evaluating river

Remote Sens. 2019 , 11 , 2116 18 of 22
basin averages and conclude that all four solutions exhibit the same signal content. Adhikari et al. [
57
]
calculated sea-level fingerprints using the SDS RL06 time series and find that differ ences between
these thr ee solutions are within 1-sigma uncertainties.
−30 −24 −18 −12 −6 0 6 12 18 24 30
[cm]

Figure 9.
Gravity field anomalies in terms of cm EWH (DDK3 filtered) for the month 2003/08 for all
GFZ GRACE releases so far: RL01 (
top left
), RL02 (
top middle
), RL03 (
top right
), RL04 (
bottom left
),
RL05a ( bottom middle ), and RL06 ( bottom right ).
The GFZ GRACE RL06 monthly gravity field time series consists of fully unconstrained spherical
harmonic (SH) Level-2 pr oducts, i.e., no r egularization at all is applied, and is provided in two
versions as agr eed upon within the GRACE SDS: (1) up to SH degree and or der 96; and (2)
up to SH degree and or der 60. GFZ GRACE RL06 is available at GFZ’s Information System
and Data Center (ISDC) ar chive ( https://isdc.gfz- potsdam.de/grace- isdc/ ) along with r elated
documentation ([
12
]; Release Notes for GFZ RL06 Level-2 products ( ftp://isdcftp.gfz- potsdam.de/
grace/DOCUMENTS/RELEASE_NOTES/GRACE_GFZ_L2_Release_Notes_for_RL06.pdf ); GRACE
Level-2 User Handbook ( ftp://isdcftp.gfz- potsdam.de/grace/DOCUMENTS/Level- 2/GRACE_L2_
Gravity_Field_Pr oduct_User_Handbook_v4.0.pdf )).
GFZ GRACE RL06 pr ocessing standards and backgr ound models are also used for the initial GFZ
GRACE-FO Level-2 pr oduct r elease [
58
]. Moreover , GFZ GRACE/GRACE-FO RL06 Level-2 pr oducts
ar e the basis for GFZ’s web portal GravIS (Gravity Information Service, http://gravis.gfz- potsdam.de ),
jointly developed with the Alfr ed-W egener-Institut and TU Dr esden, where dedicated Level-3
pr oducts for hydrological, oceanic and polar ice-sheet applications are visualized and of fered
for download. Finally , the GFZ GRACE RL06 time series contributes to the newly established
International Combination Service for T ime-variable Gravity Fields (COST -G), a pr oduct center of the
International Gravity Field Service (IGFS).
Author Contributions:
Conceptualization, C.D.; Pr ocessing of GRACE orbits and gravity fields, C.D.; Pr ocessing
of GPS orbits, A.R.; Softwar e, C.D., M.M., G.M., K.H.N. and O.A.; V alidation of r esults, C.D., M.M., H.D., R.S.
and C.F .; W riting—Original Draft Preparation, C.D.; W riting—Review and Editing, M.M., F .F ., H.D., R.S. and
C.F .; V isualization, C.D., M.M. and R.S.; Supervision, F .F ., H.D. and R.K.; Project Administration, F .F .; Funding
Acquisition, F .F ., H.D. and R.K.
Funding:
This resear ch was partly funded by the German Ministry for Education and Research (BMBF) with
FKZ 03F0654A, and by the German Resear ch Foundation (DFG) within Research Gr oup 2736 NEROGRA V (New
Refined Observations of Climate Change from Spaceborne Gravity Missions).
Acknowledgments:
W e would like to thank the German Space Operations Center (GSOC) of the German
Aerospace Center (DLR) for pr oviding continuously and nearly 100% of the raw telemetry data of the twin
GRACE satellites. V aluable comments by four anonymous r eviewers helped to improve the manuscript and ar e
highly appreciated.

Remote Sens. 2019 , 11 , 2116 19 of 22
Conflicts of Interest:
The authors declare no conflict of inter est. The funders had no role in the design of the
study; in the collection, analyses, or interpr etation of data; in the writing of the manuscript, or in the decision to
publish the results.
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 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
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