EVALUATION OF GOCE-BASED GLOBAL GEOID MODELS IN

FINNISH TERRITORY Timo Saari and Mirjam Bilker-Koivula

Finnish Geospatial Research Institute (FGI), National Land Survey of Finland (http://www.fgi.fi)

Geodeetinrinne 2, FI-02430 Masala, Finland

Email: timo.saari@nls.fi, mirjam.bilker-koivula@nls.fi

RESULTS & CONCLUSIONS

The results of the evaluations are illustrated in three figures, where the models were evaluated up to three different degrees

and orders (d/o): 200, 240 and maximum.

At d/o 200 (Figure 3, left) improvements between the later models and earlier models are minor if not non-existent.

At d/o 240 (Figure 3, right) the later models perform clearly better → more data is included → better determination of

the higher d/o (>200).

The GOCE-based models perform better than EGM96 and equally with EGM2008 at d/o 200 (Figure 4, left). At 240 the

best satellite-only models are at the same level as the pre-GOCE high resolutions models in Finland (Figure 4, right).

The pre-GOCE high resolution models perform very well over Finland (Figure 4). The excellent performance is due to

the good high resolution terrestrial gravity data that was already available in the area of Finland for the models.

At d/o 240 and maximum (Figure 5) the latest GOCE and combined GOCE+GRACE models give standard deviations of

the height anomaly differences of around 15 cm and of gravity anomaly differences of around 10 mgal over Finland.

The best results are achieved with DIR5, TIM5 and GOCO05s, however, the best performance of the satellite-only

models is not usually achieved with the maximum coefficients (well seen with GOCO05s), since the highest coefficients

(above 240) are less accurately determined (Figure 5).

ACKNOWLEDGEMENTS This research has been funded by a grant of Vilho, Yrjö and Kalle Väisälä Foundation, and the ESA-MOST Dragon 3 contract No. 4000110315/14/I-BG.

INTRODUCTION &

OBJECTIVE

The start of the millennium has been an era of the

global gravity satellite missions. It started with the

Challenging Minisatellite Payload (CHAMP),

followed by the Gravity Recovery And Climate

Experiment (GRACE) and most recently the Gravity

field and steady-state Ocean Circulation Explorer

(GOCE). GOCE made its final observations in the

fall of 2013, by then it had exceeded its expected

lifespan of 20 months with 35 additional months due

to milder solar winds. The last six months of its

mission GOCE flew in much lower orbits than

originally planned. Thus, the mission was a huge

success, since GOCE not only collected more data but also denser data from the Earth’s gravitational field.

In this study the global geoid models produced by the GOCE mission are studied. Altogether 16 GOCE models and 7

combined GOCE+GRACE models are evaluated using Finnish terrestrial data to see how well the models perform relative to

each other, but also to see their absolute agreement with terrestrial data. The latest satellite-only models are also compared

against pre-GOCE high resolution global geoid models EGM96 and EGM2008 to see the effect of the GOCE mission in the

lower degrees and orders.

Figure 1. (GOCE) (image credit: European Space Agency).

Figure 5. Comparison of the height and gravity anomalies from the latest GOCE-based satellite-only models (GOCE and GOCE+GRACE) using coefficients up to

240/maximum against GPS-levelling and gravity data: standard deviations of the differences (m) and (mgal).

Figure 4. Comparison of the height and gravity anomalies from the latest GOCE-based satellite-only models (GOCE and GOCE+GRACE) and high resolution

(EGM96 and EGM2008) models using coefficients up to 200 (left) and 240 (right) against GPS-levelling and gravity data: standard deviations of the differences

(m) and (mgal).

Figure 3. Comparison of the height and gravity anomalies from the GOCE (HPF) models using coefficients up to 200 (left) and 240 (right) against GPS-levelling

and gravity data: standard deviations of the differences (m) and (mgal).

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Other GOCE-only models

• ITG-Goce02 (maximum degree and order 240)

Released data 01/11/2009 – 31/6/2010

• JYY_GOCE02S (maximum degree and order 230)

Released data 01/11/2009 – 31/08/2012

• JYY_GOCE04S (maximum degree and order 230)

Released data 01/11/2009 – 19/10/2013

Combined GOCE+GRACE models

• EIGEN-6S2 (maximum degree and order 260)

Released data GOCE 01/11/2009–24/5/2013, GRACE 2/2003–9/2012, LAGEOS 1985–2010

• GOCO01S, GOCO02S, GOCO03S and GOCO05S (maximum degree and order 280)

Released data GOCE 01/11/2009–20/10/2013 (TIM5), GRACE 2/2003–12/2013 (ITSG-Grace2014s)

• GOGRA02S and GOGRA04S (maximum degree and order 230)

Released data GOCE 01/11/2009–19/10/2013, GRACE 8/2002–8/2009

Models of the GOCE High-level Processing Facility (HPF) by ESA

• Direct (DIR) approach (maximum degree and order 300)

5 data levels – Released data 01/11/2009 – 20/10/2013

A priori data (EIGEN-5C (DIR1), ITG-Grace2010s (DIR2))

Complementary data from LAGEOS + GRACE for lower degrees and orders

• Time-wise (TIM) approach (maximum degree and order 280)

5 data levels – Released data 01/11/2009 – 20/10/2013

GOCE-only models

• Space-wise (SPW) approach (maximum degree and order 280)

3 data levels – Released data 11/2009 – 31/7/2012

GOCE-only models

A priori high resolution models (e.g. EGM2008) used for variance and covariance modelling

For more information see the website of the ICGEM (http://icgem.gfz-potsdam.de/ICGEM/modelstab.html)

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Figure 2. The coverage of the GPS-levelling and gravity datasets over Finland: EUVN-DA with 1st order precise

levelling network (left), NLS (middle) and gravity database of the FGI (right).

The gravity database of the Finnish Geospatial Research Institute (FGI, former Finnish Geodetic Institute) and two GPS-

levelling datasets were used as a ground truth. Both the gravity data and the GPS data were corrected for the land uplift

(vertical velocities from the NKG2005LU land uplift model) and converted to the epoch 2000.0. The datasets:

The FGI’s gravity database containing observations from 1938 to present.

The EUVN-DA dataset containing 50 GPS–levelling points (class 1) in Finland. The points have EUREF-FIN GPS

coordinates as well as levelled heights in the Finnish height system N2000.

The NLS GPS-levelling dataset by the National Land Survey of Finland containing 526 GPS–levelling points (classes 1

to 3). The accuracy and distribution of the points is not homogenous and the dataset partly overlaps with the EUVN-DA.

STUDY AREA, METHODS & DATASETS

MAJOR REFERENCES Bilker-Koivula, M. (2015): Assessment of high resolution global gravity field models for geoid modelling in Finland. In: Marti, U. (ed.): Proceedings of the International

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Mayrhofer, R., Krasbutter, I., Sansò, F. & Tscherning, C. C. (2011): First GOCE gravity field models derived by three different approaches. Journal of Geodesy. Vol. 85:11.

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Rudenko, S., Dettmering, D., Esselborn, S., Schoene, T., Förste, C., Lemoine, J. M., Ablain, M., Alexandre, D. & Neumayer, K. H. (2014): Influence of time variable

geopotential models on precise orbits of altimetry satellites, global and regional mean sea level trends. Advances in Space Research. Vol. 54:1. pp. 92–118. DOI

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Saari, T. & Bilker-Koivula, M. (2015): Evaluation of GOCE-based Global Geoid Models in Finnish Territory. Newton’s Bulletin. Nr. 5. In print.

The GOCE-based models were compared against the ground data. For the comparison, height anomalies and free-air gravity

anomalies were calculated from the global models using the pyGravsoft-software.