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546 P. Steigenberger et al.

2 Standards, Conventions, Parameterization, Models

The consistency of the technique-speciﬁc solutions generated within the GGOS-D

project is essential for a successful combination. Therefore, the deﬁnition of com-

mon standards is a prerequisite for a proper interpretation of the combined time

series and the only way to avoid misinterpretations due to differences in modeling.

As the solutions of the different techniques are computed with a variety of different

software packages, the common standards had to be implemented in these packages

as the ﬁrst step of the GGOS-D project. Based on the experiences and results of the

ﬁrst solution, an update of the standards has been performed for a second iteration.

For a combination of different solutions on the normal equation (NEQ) level as

it is done in the GGOS-D project, the parameterization of these parameters has to

be identical, see Table 1. Station and quasar coordinates as well as the lower har-

monics of the Earth’s gravity ﬁeld are represented by constant offsets per parameter

interval. Parameters with high temporal resolution (e.g., troposphere zenith delays)

are represented by continuous piece-wise linear functions (CPWLFs). The current

value of a parameter x at epoch t contributes to the neighboring parameter estimates

and x

at the epochs t

and t

as follows:

x(t) = x

− t

+ x

t − t

− t

(1)

This kind of parameterization has the advantage that there are no discontinuities

at the interval boundaries.

Table 1 Parameterization of the 2nd GGOS-D iteration. Settings of the 1st iteration are given in

parentheses. Only parameters involved in the combination are listed. CPWLF stands for continuous

piece-wise linear function

Station coordinates Constant daily/session-wise/weekly offsets for GPS/VLBI/SLR

Quasar coordinates Constant offsets (only 2nd iteration, ﬁxed for session solutions)

Earth rotation parameters Default solution: CPWLF with a parameter interval of 24 h

Subdaily solution: CPWLF with a parameter interval of 1 h (2 h)

Nutation parameters CPWLF w.r.t. the a priori model IAU2000A with a parameter

interval of 24 h

Troposphere parameters CPWLF for the wet part of the troposphere zenith delay with a

parameterintervalof1h(2h)forVLBIand2hforGPS

Troposphere gradients are modeled according to MacMillan

(1995) and represented by a CPWLF with a parameter interval

of 24 h (tilting model with wet Niell (1996) mapping function

for GPS, MacMillan (1995) for VLBI)

Wet VMF1 mapping function (Boehm et al. 2006b) for the

troposphere zenith delay (wet Niell, 1996 mapping function)

Lower harmonics of the Spherical harmonic expansion up to degree and order 2

Earth’s gravity ﬁeld (only 2nd iteration)

GGOS-D Technique-Speciﬁc Solutions 547

Table 2 Common modeling standards for the second iteration of GGOS-D

Station coordinates

Solid Earth tides IERS Conventions 2003, McCarthy and Petit (2004)

Permanent tide Not considered for coordinates

Pole tides Linear trend for mean pole offsets: IERS Conventions 2003

Ocean loading FES2004 including the center of mass correction for the

motion of the Earth due to the ocean tides,

http://www.oso.chalmers.se/~loading/

Atmospheric loading Not applied

Earth orientation parameters

A priori information Daily values of the C04 05 series

Subdaily ERP model IERS2003, McCarthy and Petit (2004)

Nutation model IAU2000A, Mathews et al. (2002)

Lower harmonics of the Earth’s gravity ﬁeld

A priori model EIGEN-GL04S1 (Förste et al., 2007) including temporal

variations of C

Troposphere modeling for radio techniques

Hydrostatic delay 6-hourly ECMWF grids,

http://mars.hg.tuwien.ac.at/~ecmwf1/GRID/

Hydr. mapping function Hydrostatic VMF1 (Boehm et al., 2006b)

Wet delay No a priori model, wet delay estimated (see Table 1)

Troposphere modeling for SLR

Troposphere model Mendes and Pavlis (2004)

Technique-speciﬁc effects: GPS

Phase center model Schmid et al. (2007),

ftp://igscb.jpl.nasa.gov/igscb/station/general/igs05_1421.atx

Antenna offsets ftp://igscb.jpl.nasa.gov/igscb/station/general/igs.snx

2nd/3rd order iono. corr. Applied according to Fritsche et al. (2005)

Technique-speciﬁc effects: SLR

Reﬂector offsets ILRS conform

Range biases For selected stations, ILRS conform

Arc length 7 days

Technique-speciﬁc effects: VLBI

Thermal deformations Applied, Nothnagel et al. (1995); Skurikhina (2001): mean

value of the temperature recordings during the VLBI

sessions used as station-speciﬁc reference temperature

The common standards for modeling are based on the recommendations of the

IERS 2003 conventions (McCarthy and Petit 2004) and the standards of the interna-

tional services International GNSS Service (IGS, Dow et al., 2005), International

Laser Ranging Service (ILRS, Pearlman et al., 2002) and International VLBI

Service for Geodesy and Astrometry (IVS, Schlüter et al., 2002). Table 2 lists

the standards of the second GGOS-D iteration. For several modeling options more

sophisticated models have been applied than those commonly used by the analysis

centers of the international services. For example, tropospheric mapping functions

based on numerical weather models (like the Vienna Mapping Function 1 – VMF1)

provide a more realistic modeling of the atmosphere compared to the empirical

models still widely used nowadays (e.g., also for the ﬁrst iteration of GGOS-D).

548 P. Steigenberger et al.

3 Global Positioning System

The GPS plays an important role in the combination of space-geodetic tech-

niques due to its dense and continuously observing tracking network. GPS provides

access to different parameter groups relevant for a rigorous combination, namely

geometric parameters (station positions, origin of the tracking network), atmo-

spheric parameters (troposphere zenith delays and gradients) and Earth orientation

parameters (polar motion, length of day and nutation rates). Two independent

GPS solutions with different software packages were computed at Deutsches

GeoForschungsZentrum (GFZ) Potsdam.

A modiﬁed version of the Bernese GPS Software (Dach et al 2007) was used to

process GPS observations of 202 and 241 stations for the 1st and the 2nd iteration,

respectively, starting with the raw RINEX (Receiver INdependent EXchange for-

mat) ﬁles. The processing scheme was deduced from an earlier GPS reprocessing

effort of TU Dresden and TU München (Steigenberger et al 2006). In addition to the

parameters listed in Table 1, GPS-speciﬁc parameters like ambiguities and satellite

orbits have to be estimated. The satellite orbits are represented by the six Keplerian

elements plus ﬁve radiation pressure (RPR) parameters (Beutler et al 1994) and

pseudo-stochastic pulses at 12:00 UT. Ambiguities are ﬁxed to integer numbers for

baselines up to 6,000 km with different methods (depending on the baseline length).

For the ﬁnal ambiguity-ﬁxed solution a no-net-rotation condition w.r.t. the reference

frame speciﬁed in Table 3 is applied. Besides the reference frame, also the models

for the antenna phase centers and the a priori RPR have been updated for the 2nd

iteration (see Table 3).

Table 3 Important differences between ﬁrst and second iteration of the Bernese GPS solutions

1st iteration 2nd iteration

Number of stations 202 241

Start time 1 January 1994

End time 24 April 2006 31 March 2007

Number of SINEX ﬁles 4,496 4,838

Reference frame IGb00 IGS05

Phase center model igs05_1365.atx igs05_1421.atx

A priori RPR model ROCK (e.g. Fliegel

and Gallini, 1996)

CODE (Springer, 2000)

For the second GPS solution, observations of a global network of 403 stations

have been processed using the EPOS-PV2 software (Gendt et al., 1999) improved

in the recent years and following the scheme described in Zhang et al. (2007). The

network consists of 216 IGS stations and 187 GPS stations located at or near tide

gauge benchmarks and analyzed within the IGS Tide Gauge Benchmark Monitoring

Pilot Project (TIGA). Vertical motions of TIGA GPS stations are important for cor-

recting tide gauge records in sea level change investigations. The models used follow

those in Table 2 with the following exceptions: the tropospheric modeling is based

on the Global Pressure and Temperature model (Boehm et al., 2007) and the Global

GGOS-D Technique-Speciﬁc Solutions 549

Mapping Function (Boehm et al., 2006a), and no 2nd and 3rd order ionospheric

corrections are applied. Initial values of geocentric coordinates and velocities of

206 stations are taken from ITRF2005 (Altamimi et al., 2007). Processing is per-

formed at daily intervals. Daily solutions are combined into weekly ones at the level

of NEQs. The solution includes weekly sets of GPS station coordinates and daily

values of Earth rotation parameters and their rates in SINEX format for the time

interval from January 1998 till December 2007.

4 Very Long Baseline Interferometry

The VLBI sessions between 1984 and 2007 have been analyzed independently

with two different VLBI analysis packages: At the Deutsches Geodätisches

Forschungsinstitut (DGFI) in Munich, a modiﬁed version of the OCCAM v6.1

software package (Titov et al., 2004) has been used, and the Calc/Solve soft-

ware (Petrov 2006) at the Institut für Geodäsie und Geoinformation (IGG) of the

University of Bonn. To ensure consistent processing, the two software packages

have been adapted in detail according to the GGOS-D speciﬁcations as described in

Sect. 2. With both software packages, the same VLBI sessions have been analyzed.

Only data of non-mobile telescopes with sufﬁcient observations during an adequate

time span have been used. The GGOS-D VLBI solutions consist of 2781 sessions

where group delay observations of 53 stations and 1954 radio sources have been

used.

Although great care has been taken to achieve consistency, there are remaining

analysis-speciﬁc differences between the two VLBI solutions. In each VLBI solu-

tion, relative offsets, linear and quadratic time derivatives of the atomic clocks at

the observing sites have to be estimated, where different reference clocks and clock

breaks may have been chosen. Furthermore, a slightly different set of observations

may have been used due to differences in the outlier rejection. In addition, sig-

niﬁcant differences in the weighting of the observations are used in both software

packages. At DGFI a reﬁned stochastic model has been used (Tesmer and Kutterer

2004). At IGG the initial measurement weights from the correlation process have

been used and modiﬁed session-wise to ensure t hat the χ

is approximately one for

each baseline. NEQs have been saved in SINEX format as input for further com-

bination efforts. These SINEX ﬁles include the whole parameter space except for

the clock parameters which have been reduced from the equation systems. No addi-

tional constraints have been applied to the remaining parameters which ensures that

the NEQs are completely undeformed.

Before adding both contributions to one combined VLBI solution, a number of

comparisons have been carried out to detect remaining differences of both individ-

ual solutions. As an example, Fig. 1 shows the mean height differences between

both individual solutions. The grey arrows illustrate the differences before the adap-

tation of both software packages, the black arrows after the adaptation. On average,

the height differences before the adaptation reach ±5 mm with clear systematic

behavior in the quadrants. The main reason for this is the different mean pole within

550 P. Steigenberger et al.

Fig. 1 Height differences between both individual solutions before adaptation of the software

packages (grey arrows) and after the adaptation ( black arrows)

the pole tide model. After the adaptation (black arrows) almost all offsets are smaller

than ±1 mm.

The VLBI intra-technique combination is based on datum-free NEQs. Each

individual observing session has been combined separately using the software

DOGS_CS (Gerstl et al., 2001).

One of the basic requirements for the combination based on NEQs is that the

systems have to use the same set of a priori values. Therefore, transformations are

carried out to refer all parameters to the same reference epoch, to the same reference

frame (ITRF2005, Altamini et al., 2007) and an identical set of a priori EOPs.

In a second step the suitability of the individual contributions for the combina-

tion is checked. For this purpose, a solution of the station positions is calculated

from each contribution. A contribution is rejected if the correction to the a priori

station positions is larger than 5 cm in the horizontal components and larger than

7.5 cm in the vertical component. For each individual session, a combined datum-

free NEQ system is calculated by adding the DGFI and IGG NEQs. The combined

NEQ system is then saved as SINEX ﬁle for combination with the other techniques.

5 Satellite Laser Ranging

SLR is vital for the deﬁnition of a Terrestrial Reference Frame (TRF) because it

is the only technique which deﬁnes the geocenter directly. SLR is also a strong

contributor to the network scale and to the determination of the low degree coefﬁ-

cients of the spherical harmonic representation of the Earth’s gravity ﬁeld (hereafter

shortly named “low degree harmonics”). The global SLR tracking network con-

sists of about 30 stations with some changes, stations closing down or new stations

showing up. In the GGOS-D project the global SLR tracking network is analyzed

by GFZ using the EPOS ( Earth Parameter and Orbit System) software package and

by DGFI with the DOGS (DGFI Orbit and Geodetic parameter estimation Software)

package (http://ilrsac.dgﬁ.badw.de/dogs/). The dynamical and measurement models

GGOS-D Technique-Speciﬁc Solutions 551

Fig. 2 Number of observations per week and RMS ﬁt of the weekly GFZ and DGFI solutions

are adopted according to the GGOS-D standards (see Sect. 2) and harmonized in

both software packages. The only difference concerns the data editing procedures

which explains some of the discrepancies between the two solutions (see Fig. 2). The

higher RMS values in the DGFI solutions are mainly produced from a few stations

with poor tracking performance, which are often edited in the GFZ solutions.

Both centers processed weekly arcs for the period October 1992 to January 2007

(GFZ) and November 1992 to May 2007 (DGFI), respectively, solving for weekly

stations coordinates and daily EOPs (polar motion and UT1). Additionally, both

solutions incorporate the low degree harmonics up to degree and order 2. In order

to overcome the datum defect, the coordinates, the EOPs, and the low degree har-

monics are endowed with an a priori sigma of 1 m or its equivalent. The solutions

are presented in form of SINEX products where GFZ delivers the NEQs regular-

ized with the a priori sigmas plus the a priori sigmas used in a separate NEQ, DGFI

provides the free (singular) NEQs directly.

In total 732 common weeks in the period from November 1992 until January

2007, are available using about 1.75 million SLR normal points to the geodetic

satellites Lageos-1 and -2. The quality of the orbital ﬁt slightly increases in the

observation period from 1.5 cm in the beginning to 0.9 cm since 2000 and are

comparable between the satellites and the software packages (Fig. 2).

The input of the weekly SLR combination consists of weekly solutions of DGFI

and GFZ presented as datum-free NEQs for weekly station coordinates, daily polar

motion and UT1 as well as for the lower harmonic coefﬁcients of the Earth’s grav-

ity ﬁeld up to degree and order 2 (C

). First investigations reveal that the solution

with estimated C

is not stable on a weekly basis, even when the respective mini-

mum constraints are included. Hence, the processing of weekly SLR combinations

is restricted to the determination of relative weights for both solutions, the mul-

tiplication of the given NEQs with the weights and the addition of the weighted

552 P. Steigenberger et al.

NEQs. The relative weighting procedure is based on the hypothesis that both solu-

tions deliver a nearly equivalent precision level for the core station coordinates. The

relative weight of DGFI solution is arbitrarily set to one, whereas the weight for GFZ

is determined by the sum of GFZ NEQ diagonals over the core stations divided by

the respective sum of DGFI NEQ. It turns out that the GFZ weights scatter between

3 and 0.7 for 1993 to 1999 and between 2 and 0.9 for 2000 to 2006. The combination

process consists of the following steps:

– Aligning the right hand sides of the NEQs to the reference values (SLRF2005 for

the station coordinates, C04 05 for the EOPs, and EIGEN-GL04S1 for C

– Minimum constraint solutions of both input NEQs with ﬁxing C

in order to ﬁnd

outliers mainly in the station coordinates. The minimum constraints are based on

three rotational rank deﬁciencies for the coordinates and on the offset deﬁciency

for UT1.

– Determination of weights, weighting the input NEQs, and combination of

weighted NEQs.

– Minimum constraint solution of combined NEQs with ﬁxing C

. This solution

is used for precision and comparison analysis.

– Storage of weekly combined NEQs and of weekly combined minimum constraint

solutions to SINEX ﬁles.

6 Summary and Conclusions

Consistent homogeneously reprocessed long-time series of the space geodetic tech-

niques GPS, SLR, and VLBI are the backbone of the GGOS-D project. The common

standards for modeling and parameterization described in Sect. 2 are essential for

a consistent combination and proper interpretation. Table 4 gives an overview of

Table 4 Technique-speciﬁc SINEX ﬁles of the 2nd GGOS-D iteration

Technique Institution Software Time period # ﬁles Resolution

GPS GFZ Bernese 01/1994–

03/2007

4,838 1 d

GPS GFZ EPOS-PV2 01/1998–

12/2007

515 7 d

SLR DGFI DOGS OC 01/1993–

05/2007

759 7 d

SLR GFZ EPOS 01/1993–

01/2007

732 7 d

SLR combined DGFI DOGS CS 01/1993–

12/2006

559 7 d

VLBI DGFI OCCAM 01/1984–

12/2006

2,728 1 d

VLBI GIB CALC/SOLVE 01/1984–

12/2006

2,707 1 d

VLBI

combined

GIB DOGS CS 01/1984–

12/2006

2,536 1 d

GGOS-D Technique-Speciﬁc Solutions 553

the GPS, SLR and VLBI SINEX ﬁles available from the solutions discussed in this

chapter. These solutions provide the basis for the generation of combined time series

and a TRF described in the chapters GGOS-D Consistent and Combined Time Series

of Geodetic/Geophysical Parameters and GGOS-D Global Terrestrial Reference

Frame.

Acknowledgment The efforts of IGS (Dow et al., 2005), ILRS (Pearlman et al., 2002), IVS

(Schlüter et al., 2002) are acknowledged. The authors like to thank J. Boehm for providing the

ECMWF troposphere delays and coefﬁcients of VMF1. This is publication no. GEOTECH-1283

of the programme GEOTECHNOLOGIEN of BMBF and DFG, Grants 03F0425A, 03F0425C,

03F0425D.

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GGOS-D Global Terrestrial Reference Frame

Detlef Angermann, Hermann Drewes, Michael Gerstl, Barbara Meisel,

Manuela Seitz, and Daniela Thaller

1 Introduction

Highly-accurate, consistent and long-term stable geodetic reference frames are

a fundamental requirement for the estimation of geodetic-geophysical parame-

ters for the Global Geodetic Observing System (GGOS). These requirements

are not fully satisﬁed with the currently available reference frames (e.g., the

International Terrestrial Reference Frame (ITRF) of the International Earth Rotation

and Reference Systems Service (IERS)). The latest version, the ITRF2005, has

been computed from a combination of time series of station positions and EOP’s

(Altamimi et al., 2007; Angermann et al., 2009). A remarkable progress has been

achieved compared to past realizations which were based on the combination of

multi-year solutions of the different space-techniques. However, t here are still

considerable deﬁciencies. The ITRF2005 input data are not fully consistent, the

standards and models were not completely uniﬁed amongst the analysis centres,

and the GPS solutions provided by the International GNSS Service (IGS) were not

homogeneously reprocessed.

Within the GGOS-D project, the observation time series for the different space

geodetic techniques were homogeneously processed by applying uniﬁed standards

for the modelling and parameterization (see chapter “Integration of Space Geodetic

Techniques as the Basis for a Global Geodetic-Geophysical Observing System

(GGOS-D): An Overview” by Rothacher et al., this issue). The GGOS-D terrestrial

reference frame (TRF) has been computed from a combination of long time series of

VLBI, SLR and GPS observations. The station positions and velocities (TRF) have

been estimated in a common adjustment with Earth Orientation Parameters (EOP)

and quasar coordinates. A major focus was on the development and implementation

of reﬁned combination strategies.

The paper is structured as follows: Sect. 2 gives some information on the

GGOS-D data that were used for the reference frame computation. In Sect. 3 the

D. Angermann (B)

Deutsches Geodätisches Forschungsinstitut, D-80539, München, Germany

e-mail: angerman@dgﬁ.badw.de

555

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_46,



Springer-Verlag Berlin Heidelberg 2010