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The Release 04 CHAMP and GRACE EIGEN Gravity Field Models 53

Table 3 SLR data and test arcs of the orbit computation tests

Satellite

Number of included SLR observations/data

period/tested arcs: number and lengths

CHAMP 358/October 2001/4 × 1.5 days

GRACE 592/September 2002/4 × 1.5 days

Table 4 SLR residuals (cm) after an orbit determination based on GPS-SST and accelerometer

data (CHAMP, GRACE) and K-band range-rate data (GRACE). The SLR data were not included

in the orbit adjustment

Satellite

Max. degree

used GGM03C EGM2008 EIGEN-5C

EIGEN-

CHAMP03S

EIGEN-

CHAMP05S

CHAMP 80 9.51 9.34 9.69 10.77 9.40

90 6.10 6.02 6.14 7.11 5.91

100 5.96 5.97 6.03 6.36 5.59

110 5.53 5.57 5.59 6.23 5.43

120 5.45 5.51 5.51 6.28 5.31

150 5.44 5.46 5.49 6.19 5.52

GRACE 80 6.54 7.27 6.44 11.54 6.92

90 5.05 5.57 4.93 11.34 5.48

100 5.20 5.54 5.09 11.03 5.42

110 5.31 5.45 5.19 11.45 5.56

120 5.28 5.46 5.15 11.51 5.48

150 5.27 5.43 5.14 11.51 5.45

The orbit ﬁts for CHAMP and GRACE were performed with the adjustment of

one scaling factor and one bias parameter per arc for each of the three accelera-

tion components in addition t o the orbital elements, GPS ambiguities and clocks.

Additionally for CHAMP one thruster parameter per arc and thruster pair and one

scaling factor per component and arc for the Lorentz force on the accelerometer

proof mass have been adjusted. In the case of GRACE one Range bias 1/rev per arc,

range acceleration and range-rate bias per revolution were adjusted for the K-Band.

Table 4 gives the orbit ﬁt residuals for the mean CHAMP models EIGEN-

CHAMP03S (blue column) and EIGEN-CHAMP05S (red column) in comparison

to the most recent global combined gravity ﬁeld models GGM03C (Tapley et al.,

2007), EGM2008 (Pavlis et al., 2008) and EIGEN-5C (Förste et al., 2008b). We

carried out our orbit computations for these two satellites with different maximum

degrees of the spherical harmonic coefﬁcients to investigate possible degree-related

differences between the tested gravity ﬁeld models.

For both satellites the obtained orbit ﬁt residuals for EIGEN-CHAMP05S are sig-

niﬁcantly smaller i.e. better than for EIGEN-CHAMP03S. In particular the obtained

residuals of GRACE (∼11 cm for EIGEN-CHAMP03S vs. ∼5.5 cm for EIGEN-

CHAMP05S above maximum used degree 80) are an impressive indication for the

strong improvement of EIGEN-CHAMP05S vs. EIGEN-CHAMP03S. Furthermore

54 F. Flechtner et al.

it is noticeable, that the obtained numbers for GRACE with the new EIGEN-

CHAMP05S as well as with the GRACE-based combined models are of the same

order of magnitude of about 5 cm. This ﬁnding indicates that our new CHAMP-only

model features no major performance difference with the compared GRACE-based

models for the investigated degree range up to 150 when using for LEO orbit com-

putations. Lastly, EIGEN-CHAMP05S show no signiﬁcantly different behaviour

compared to the combined models, when inspecting the dependency of the orbit

ﬁts on the maximum used degree.

To investigate the error of the mean EIGEN-CHAMP05S model we compared

the variability of partial solutions. For this purpose we computed two partial solu-

tions, namely from the accumulation of the odd as well as of the even months for

the i ncluded time span from October 2002 till September 2008. Figure 9 shows the

difference degree amplitudes between these partial solutions (black line) in com-

parison with the formal errors of EIGEN-CHAMP05S (red line). The values of the

difference degree amplitudes have been divided by 2 to take into account the dou-

ble number of observation in the EIGEN-CHAMP05S models with respect to the

partial s olutions. When taking the variability of partial solutions as measure for the

error of the obtained spherical harmonic coefﬁcients, it is remarkable that the formal

errors for EIGEN-CHAMP05S (red) till about degree 70 (wherefrom the regulariza-

tion starts) are almost of the same order of magnitude as the computed variability

Fig. 9 Difference degree amplitudes between CHAMP partial solutions (i.e. the difference

between the accumulated odd and evens months between October 2002 and September 2008) in

comparison to the formal errors of EIGEN-CHAMP05S. Additionally the degree amplitudes for

EIGEN-CHAMP05S and EIGEN-CHAMP03S are given

The Release 04 CHAMP and GRACE EIGEN Gravity Field Models 55

values. This indicates an optimum parameterization and a good internal consistency

of our CHAMP gravity ﬁeld processing.

Additionally the degree amplitudes of EIGEN-CHAMP05S and EIGEN-

CHAMP03S are given in Fig. 9 for comparison. It can bee seen, that the spectrum

of EIGEN-CHAMP05S contains more power beyond degree 60 compared to the

older EIGEN-CHAMP03S. This should be mainly caused by the increased number

of included measurement years (6 years f or EIGEN-CHAMP05S vs. ∼3.5 years

for EIGEN-CHAMP03S) and by an increased sensitivity due to the meanwhile

decreased altitude of the CHAMP satellite (∼350 km end of 2008 vs. ∼400 km end

of 2003, which was the end of the EIGEN-CHAMP03S measurement time span).

7 Summary and Conclusions

At GFZ release 04 (RL04) EIGEN (European Improved Gravity ﬁeld of the Earth

by New techniques) time series of monthly CHAMP and GRACE gravity mod-

els, pure weekly GRACE solutions and satellite-only and terrestrial data combined

static gravity ﬁelds of the Earth have been derived by homogeneous reprocessing for

nearly the whole CHAMP and GRACE mission periods. The updated background

models, processing standards and strategies led to signiﬁcant improvements of the

reprocessed gravity ﬁeld models. Both the monthly and static EIGEN-GRACE05S

gravity ﬁelds could be improved by about 60% (in terms of “factor above the pre-

launch simulated baseline error; Kim, 2000”). For the ﬁrst time, GRACE gravity

ﬁelds are provided with weekly resolution (up to degree and order 30 and aligned to

GPS calendar week) which may provide further insight into mass variations which

take place at ten-daily or even shorter time scales such as barotropic Rossby waves,

continental water storage changes or solid Earth and ocean tides. The monthly

EIGEN-CHAMP05S models show a high correlation to EIGEN-GRACE05S for the

long-wavelength components. The new static satellite-only and combined gravity

models EIGEN-5S and EIGEN-5C are complete to degree and order 150 and 360,

respectively. Independent comparisons with geoid heights determined point-wise by

GPS positioning and GPS levelling show notable improvements. Also, the unreal-

istic meridional striping patterns over the oceans in the precursor EIGEN models

could be much reduced. Therefore, ESA has decided to use both models as the

standard for ESA’s ofﬁcial data processing of the upcoming gradiometer satellite

mission GOCE.

In addition to the monthly EIGEN-CHAMP05S models a new 6-years mean

CHAMP-model has been computed. In particular orbit adjustment tests with

CHAMP and GRACE show a signiﬁcant improvement of this model with respect to

its precursor EIGEN-CHAMP03S.

These new RL04 EIGEN models provide an important data base to monitor

mass transport and mass distribution phenomena in the system Earth, such as the

continental hydrological cycle, ice mass loss in Antarctica and Greenland, ocean

mass changes or the ocean surface topography. Nevertheless, the GRACE base-

line mission accuracy has still not been reached by a factor of 7.5 (static ﬁeld)

56 F. Flechtner et al.

and 15 (monthly solutions), respectively. Therefore plans already exist for a fur-

ther consistent reprocessing of the complete CHAMP and GRACE time series.

This includes (a) reﬁnements in the observation models, (b) improvements of

the background models and (c) upgrade of the applied processing strategy and

standards.

The ﬁrst topic comprises the treatment of the accelerometer data after ﬁltering,

outlier removal and calibration as direct observations instead of measured surface

forces. Additionally, the accelerometer data shall be improved by analysis of var-

ious satellite induced effects such as heater and magnet torquer spikes, twangs

or penumbra-transitions. Finally, for GPS data processing the still missing integer

ambiguity ﬁxing for LEO satellites and phase wind-up and absolute phase center

corrections for ground and LEO GPS observations will be implemented. The back-

ground models will be completed by seasonal variations derived from the RL04 time

series as well as by improved tidal and non-tidal oceanic and atmospheric models.

As the integrated one-step approach turned out to give more reliable and precise low

degree harmonics (geocenter motion, Earth ﬂattening) compared to the “standard”

two-step approach (Zhu et al., 2004), also the processing strategy to derive GRACE

gravity ﬁelds has still room for improvements.

RL04 EIGEN models along with their calibrated errors and ancillary products

such as the corresponding mean atmospheric and oceanic non-tidal mass variations

as well as supporting documentation are or will be shortly available at the CHAMP

and GRACE Integrated System and Data Center (ISDC, http://isdc.gfz-potsdam.de)

at GFZ. Additionally the models can be downloaded from the ICGEM (International

Centre for Global Earth Models) data base at GFZ Potsdam (http://icgem.gfz-

potsdam.de).

Acknowledgment This is publication no. GEOTECH-1276 of the programme

GEOTECHNOLOGIEN of BMBF and DFG, grant 03F0436A.

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Orbit Predictions for CHAMP and GRACE

Krzysztof Snopek, Daniel König, and Rolf König

1 Introduction

Precise orbit predictions are service products to support SLR, pre-processing of

mission data and mission operations. In all cases it is necessary to know the position

of the satellite at some time in the future with a dedicated accuracy depending on

the application. Currently, GFZ delivers a suite of orbit prediction products for these

purposes for the Low Earth Orbiters (LEOs) CHAMP, GRACE-A and -B, and, since

June 2007 also for TerraSAR-X. These applications highly contribute to the success

of these missions as, e.g. in the end, SLR observations play an important role for

validation in Precise Orbit Determination (POD).

The orbit prediction system is running fully automated and it is robust

against various critical situations, e.g. hardware problems. Though a high per-

centage of the distributed orbit prediction products meet the requirements of

the users, as will be shown later in this article, a constant effort is put to

improve the quality which is monitored regularly by a Quality Control (QC)

subsystem.

The most demanding application of the orbit predictions is the laser tracking

of the above-mentioned satellite missions carried out by the International Laser

Ranging Service (ILRS; Pearlman et al., 2002) ground stations. For the acquisi-

tion of SLR data the required accuracy for these LEOs is about 70 m in along-track

direction that is equivalent to a 10-ms bias of the time the satellite becomes visible

over a station (i.e. the satellite is too early or too late), shortly the time bias. With

view on this quality criterion the QC is carried out. Based on the actual QC, the

frequency of the generation of orbit predictions is chosen; currently it is twice a day

for GRACE-A/-B and four times per day for CHAMP.

K. Snopek (B)

Helmholtz Centre Potsdam, GFZ German Research Centre for Geosciences,

Department 1: Geodesy and Remote Sensing, Telegrafenberg, 14473 Potsdam, Germany

e-mail: krzysztof.snopek@gfz-potsdam.de

F. Flechtner et al. (eds.), System Earth via Geodetic-Geophysical Space Techniques,

Advanced Technologies in Earth Sciences, DOI 10.1007/978-3-642-10228-8_5,



Springer-Verlag Berlin Heidelberg 2010

60 K. Snopek et al.

2 Orbit Prediction System

The orbit prediction software system consists of a set of UNIX shell scripts and

binary programs. The kernel of the whole system is the GFZ-own EPOS-OC (Earth

Parameter and Orbit System – Orbit Computation) software that carries out the

proper POD from recent tracking data and predicts the orbit by numerical orbit inte-

gration with an optimized dynamical model. All software components are regularly

upgraded. In general the orbit prediction algorithm comprises the preprocessing of

tracking and auxiliary data, the orbit adjustment and prediction, the generation of the

orbit prediction products, and the dissemination of the products, see also (Schmidt

et al., 2003).

2.1 Preprocessing

In the preprocessing part the observational data as well as some auxiliary data are

assembled and provided in EPOS-OC-readable format. On the basis of the assem-

bled data an EPOS-OC control ﬁle is created deﬁning as well the parameterisation

of the respective POD problem.

The main observational data used are orbit ephemerides available as on-board

navigation solution (NAV) or as near real-time orbits (NRT) from the mission

ground segment parts run in-house (chapter “Near-Real Time Satellite Orbit

Determination for GPS Radio Occultation with CHAMP and GRACE” by Michalak

et al., this issue). Originally, NAV solutions have been used for both CHAMP and

GRACE. Since the year 2007 NRT orbits are used as the primary source of orbit

ephemeris for CHAMP. The advantages of using NRT orbits instead of NAV solu-

tions is that they do not have to be downloaded from a remote place and that they

Fig. 1 Differences between a reference orbit (RSO) and a predicted orbit (solid line: NRT based,

dashed line: NAV based). Time advance 0.0 refers to the epoch of the last available observation

Orbit Predictions for CHAMP and GRACE 61

lead to smaller positional residuals in the observed part of the orbit prediction pro-

cess as revealed by Fig. 1. In addition to orbit ephemerides also SLR normal points

are used as observations.

The auxiliary data used comprise gravity ﬁelds of Earth, Sun, and Moon, Earth

orientation parameters, an atmospheric density and solar radiation pressure model

driven by solar and geomagnetic activity indices, an atmospheric gravity variation

model, ocean tides and solid Earth tides models, and a macro model of the respec-

tive satellite for modelling the atmospheric density and the solar radiation pressure

forces acting on its surface.

2.2 Orbit Determination

The proper calculation of the predicted orbit consists of two steps. In the ﬁrst step the

POD for that part of the orbit covered by observations (the “observed part”) is car-

ried out. The length of the observed part depends on the availability of observation

data; in general 1 day is used.

The accuracy of the predicted orbits of CHAMP is inﬂuenced by the observa-

tional data. In Fig. 1 the differences between a reference Rapid Science Orbit (RSO;

see chapter “Rapid Science Orbits for CHAMP and GRACE Radio Occultation Data

Analysis” by Michalak and König, this issue) and a predicted orbit, based one time

on NRT data and the other time based on NAV data, is plotted. As a RSO is a highly

accurate reference orbit with an accuracy of orbit positions on the level of a few cen-

timetres Fig. 1 clearly reveals that the predicted part is more accurate if the whole

predicted orbit is based on NRT data.

In the POD step, various model parameters are estimated allowing the adjustment

of the modelled perturbing forces acting on the satellite from the tracking data.

Among the parameterised orbit forces the atmospheric drag is the most critical one

in case of LEOs, it mainly inﬂuences the along-track error of the adjusted orbit.

Atmospheric drag parameters are set up every 6 h in the observed part resulting in

four values to be estimated.

Once the orbit adjustment of the observed part has converged the critical esti-

mated parameters as well as the RMS values of the residuals are checked for certain

thresholds. In case all requirements are met the second step of the orbit predic-

tion process is carried out by extrapolating the orbit of the observed part by pure

numerical forward integration using the estimated parameters stemming from the

ﬁrst step. The resulting orbit is called the “predicted part”. For the modelling of the

atmospheric drag the mean of the last three drag parameters of the observed part is

introduced into the predicted part as starting value of a linear function leading to

1.0 approximately 30 days later. The aim of this averaging is to make the predicted

part more stable. The histograms in Fig. 2 show a comparison of residuals for a

time advance of 12 h in along-track direction. The left histogram refers to predic-

tions without averaging of the atmospheric drag parameters; the right plot refers to

the case where the drag parameters are averaged as explained before. A signiﬁcant

62 K. Snopek et al.

Fig. 2 Comparison of residuals of predicted orbits in along-track direction 12 h (i.e. 0.5 d) after the

last available observation as compared to a reference orbit. Left histogram: residuals of predicted

orbits without extrapolation of atmospheric drag parameters; Right histogram: residuals in case of

extrapolation of atmospheric drag parameters

improvement in bias and standard deviation can be detected justifying the averaging

of the atmospheric drag parameters.

2.3 Products

The prediction products to be derived from the predicted orbits depend on their

application. Table 1 summarizes the prediction products generated by GFZ as well

as the corresponding archive used and the application intended. The main recipients

of GFZ orbit prediction products are the ILRS community and the telemetry stations

of GFZ and DLR (German Aerospace Centre, Cologne, Germany).

Prior to June 2008, beside Smithsonian Astronomical Observatory (SAO;

Pearlman et al. 1979) elements and Two-line elements (TLEs, 2009) the ILRS

required predictions as well in the standard “Tuned Inter-Range Vector” (TIRV,

Table 1 GFZ prediction products for CHAMP, GRAC E, and TerraSAR-X

Product Application Archive Comment

IRV + DRAG

function

SLR tracking CDDIS, EDC, ISDC Ceased after 2008

SAO Scheduling of satellite passes CDDIS, EDC, ISDC Ceased after 2008

CPF SLR tracking CDDIS, EDC, ISDC Since 2006

TLE Scheduling of satellite passes CDDIS, EDC, ISDC Ongoing

PDO CHAMP science data system ISDC Since 2000

Only for CHAMP