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REGIONAL ANALYSIS OF RECENT GLOBAL GEOPOTENTIAL MODELS:

A CASE STUDY IN TURKEY

Selda Demir1

Dr. R. Alpay Abbak2 1 Gaziosmanpasa University - Turkey 2 Selcuk University - Turkey

ABSTRACT

Geoid is an equipotential surface of Earth’s gravity field, which partially coincides with the mean sea level and extended inside continents. In the gravimetric geoid determination; global geopotential models (GGMs), digital elevation models and terrestrial gravity observations are combined in a proposed technique (e.g. Remove-Compute-Restore). The external Earth's gravity field is represented by a GGM that consists of the globally and homogeneously distributed terrestrial and satellite gravity measurements. Currently, CHAMP, GRACE, and GOCE satellite missions have been used to determine the gravity field. Satellite-based GGMs that mainly represent the long wavelength components of the gravity field can be evaluated externally by using terrestrial data such as ground gravity, GPS-leveling, etc. Then, the standard deviation of the differences (e.g. NGGM minus NGPS-LEV) is considered as the accuracy of the model. In this study, geoid undulations derived from recently published GGMs are compared with equivalents obtained from GPS-leveling data, and the accuracies of selected GGMs are investigated in the territory of Turkey. Numerical results show that GGMs combining GRACE and GOCE data are more accurate than the others. Keywords: CHAMP, GRACE, GOCE, Global Geopotential Model, GPS-Leveling data

1 INTRODUCTION

Physical geodesy aimed to determine the Erath’s gravity field and geoid which is an equipotential surface of gravity field. The geoid is a closed surface that overlaps the mean sea level, perpendicular to the direction of the vertical at each point. It is very important to determine geoid for earth sciences because the height of the points on the earth is measured from the geoid, which is considered as a reference surface. Thus height and depth are defined by geoid.

Geoid determination methods are divided according to the data groups used: astro-geodetic, gravimetric and GPS-leveling methods. In the gravimetric method, the study area can be regional or global. Evaluating homogeneously distributed gravitational observations throughout the earth produces global geopotential models in gravimetric method. Looking at the literature, there are more than 150 global potential models [4]. Global geopotential models are examined in three groups as satellite-only, combined, and tailored models. The satellite-based models have low level of accuracy, while the combined models have high accurate and resolution. For this reason, combined models are more useful in geodetic studies.

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In this study, the accuracy of the new generation global geopotential models obtained from current satellite missions (CHAMP, GRACE and GOCE) was investigated. Test models GGM05S (2014), HUST-Grace2016s (2016), ITU_GRACE16 (2016) and Tongji-GRACE01 (2016) from GRACE; ULUX_CHAMP2013s (2013) and EIGEN-CHAMP05S (2010) from CHAMP; GO_CONS_GCF_2SPW_R4 (2014) and JYY-GOCE04S (2016) from GOCE; GGM05G (2015) and ITU_GGC16 (2016) were chosen for the joint solution of GRACE and GOCE satellite data. The geoid undulations derived from these models were compared with those obtained from the GPS-leveling data. The results show that the models obtained from joint solutions of GRACE and GOCE data are more successful than the others.

2 GLOBAL GEOPOTENTIAL MODELS Evaluating homogeneously distributed gravitational observations throughout the earth produces global earth potential models. Different measurement methods and solution techniques have been developed to obtain the knowledge of the gravity field of the earth. The gravity field of the earth is determined globally with the help of dedicated satellites (CHAMP, GRACE, GOCE).

From 2000 onwards, artificial satellites began to be used to measure the gravity field of the earth with high precision. As the height of geodesic satellites increases, the strength of the signals to be received from the satellite decreases. The acceleration in low-orbit satellites equals 86% of the earth's surface acceleration and 6 % in others. Since other planets and the effect of sun will multiply away, this 6 % slice becomes even more obscure in other satellites [2]. As the satellite altitude decreases from the other side, due to atmospheric effects, the usage period decreases. Therefore, the satellite height must be the most convenient. It also makes it possible to obtain gravitational field information collected by satellites homogeneously from the entire earth. Today geodesic objectives can be traced through low earth orbit (LEO) such as CHAMP, GRACE and GOCE. These satellites are approximately 400 km from the earth. Models such as the geoid undulation that can be used to calculate the size of gravity field related to the earth's surface are global geopotential models created by using gravity data from all over the world. The geopotential model is essentially models with floor numbers calculated up to a certain degree and includes floors of the spherical harmonic series that best define the Earth's attraction potential [5].

Satellite tracking data obtained from CHAMP, GRACE, GOCE low-orbit satellite systems can be used to obtain information on the long wavelength components of earth gravity field. The satellite tracking technique based on the determination of the dynamic behavior of the suit expressed by the Kepler elements and the gravitational effect of the global gravitational field can be expressed in terms of spherical harmonic coefficients since they exhibit a harmonic behavior outside the masses. Gravitational potential takes the shape of

𝑉 = 𝑟,𝛳, 𝜆 =𝐺𝑀𝑅

𝑅𝑟

!!!!

!!!

(𝐶!" cos𝑚𝜆 + 𝑆!" sin𝑚𝜆)𝑃!"(cos𝜃)!

!!!

with the help of the coefficients that can be calculated from all over the world [3]. Parameters are defined as follows: G is gravitational constant, M is the masses of the

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earth, R is the equatorial radius of the earth, r is the radial component, 𝜃 is the pole distance, λ is the geocentric longitude, C!", S!" is the fully normalized spherical harmonic coefficients, P!" is the fully normalized Legendre polynomials, n, m is the degree and order of spherical harmonics, respectively.

The global model differs from the others due to its characteristics such as the degree of data source and analysis method. Therefore, it is possible to divide global potential models into various classes [1]. Satellite based models are obtained by determining the gravitational field by tracking the orbits of artificial satellites. Combined models are obtained by solving satellite altimeter data and terrestrial gravity data. Tailored models are obtained by using satellite-based models to expand spherical harmonic coefficients to a higher extent and to improve them locally.

3 NUMERICAL ANALYSIS

Satellite-based global geopotential models can be used to perform external accuracy analysis using terrestrial data. The standard deviation of the differences is called the accuracy of the models. In this application, the accuracy of geodetic undulations derived from recent global geopotential models compared with the equivalents obtained from GPS-leveling data and selected current global land potential models are investigated locally.

3.1 GPS-Leveling Data GPS-leveling observations are frequently used data sources for evaluation and validation of geoid models. In the case of numerical application, GPS-leveling data obtained from Map General Command has been utilized in the project carried out by Üstün and Demirel [7]. The application was carried out between the Antalya and Samsun tide gauge stations at the first leveling order of the Turkish National Vertical Control Network 1999 (TUDKA99) (Figure 1). The precision of the 47 GPS-Leveling points is determined to be less than 7 cm. The accuracy of the ellipsoidal heights of the points is 1-3 cm, and the accuracy of the orthometric heights determined by the level varies between 0.3 cm in Antalya and 6 cm in Samsun [6]. Over the course of time, the topographic structure is starting from the sea surface (maximum: 1512.07 m, average: 803.23 m).

3.2 Comparison Global geopotential models derived from ground gravity field data with the help of low orbit satellites such as CHAMP, GRACE and GOCE in the direction of geodetic purposes are published on the ICGEM website. The ICGEM website has more than 150 global geopotential models built up to date. Since every model produced contains more measurement and new measurement technology than before, it is inevitable that the last published ones reflect the gravitational field more realistically. The ICGEM data center offers users free text files with gfc extensions with spherical harmonic coefficients of the models.

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Figure 1. GPS-Leveling points used in regional analysis of global geopotential models

Information on the current global geopotential models selected for this study are given in Table 1. At least two current models have been selected from the global land potential models obtained with the help of CHAMP, GRACE and GOCE satellites, using at least two current models generated by each satellite, GRACE and GOCE satellites. When selecting models, the year of production, the data source and the degree of spherical harmonic opening are taken into consideration. Thus, it is aimed to analyze the performances of all satellite studies to determine the gravitational field and to investigate its development over time.

Table 1: Selected current global land potential models Model Name Year Degree Data Source Reference

EIGEN-CHAMP05S 2010 150 S(Champ) Flechtner et al, 2010 ULux_CHAMP2013s 2013 120 S(Champ) Weigelt et al, 2013 Tongji-GRACE01 2013 160 S(Grace) Shen et al, 2013 GGM05S 2014 180 S(Grace) Tapley et al, 2013 ITU_GRACE16 2016 180 S(Grace) Akyilmaz et al, 2016b HUST-Grace2016s 2016 160 S(Grace) Zhou Hao et al, 2016 GO_CONS_GCF_2_SPW_R4 2014 280 S(Goce) Gatti et al, 2014 JYY_GOCE04S 2014 230 S(Goce) Yi et al, 2013 GGM05G 2015 240 S(Grace,Goce) Bettadpur et al, 2015 ITU_GGC16 2016 280 S(Grace,Goce) Akyilmaz et al, 2016a

In order to evaluate the regional accuracy of the determined models, the geoid undulations were calculated as the result of the level measurements at the coordinates found by GPS measurement. Then, the text files of the gfc extensions that contain the

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global harmonic coefficients and the standard deviations of these coefficients for each model selected from the ICGEM website have been acquired. The textual reference information found in the resulting text files has been cleared. The new files created for each model are evaluated in a program; and the geoid undulations of the models are calculated. Taking the latitude, longitude and geoid undulation from the calculated data, The geoid undulations of 47 points obtained from GPS-leveling data are compared. The minimum, maximum, median, mean, root mean square errors (RMS) and standard deviation of differences between global model and GPS-leveling data were investigated. The results of the accuracy analysis of selected global geopotential models are given in Table 2.

As can be seen from RMS according to Table 2, as the degree of the global model increases, compatibility with the GPS-leveling data is increasing. When the results are examined, the worst accurate models are formed by the CHAMP satellite data. Although there is almost 10 years of data available for the CHAMP fit, there is no significant improvement in the accuracy of the models. Since this data does not increase the accuracy of the models generated, this data has left its place to GRACE and GOCE satellites. If you look at models created with GRACE satellites, it shows higher accuracy than CHAMP satellites.

When only the last satellite mission GOCE satellites models are examined, it is seen that other satellites have achieved the best results in a shorter period than the data collection period. These results are the closest satellite to the earth and the contribution of developing technology is great. Grading the gravity field data of the earth with the gradient meter contained in the GOCE satellites in high accuracy.

Table 2: Accuracy test of various global models with GPS-leveling data [m]

Model Name Data Source Min. Max. Median Mean RMSE Std.

EIGEN-CHAMP05S S(Champ) -2.317 2.859 -0.22 -0.291 1.380 1.364

ULux_CHAMP2013s S(Champ) -1.105 2.604 -0.318 0.053 0.903 0.912

GGM05S S(Grace) -2.257 1.656 -0.028 -0.083 0.834 0.839

HUST-Grace2016s S(Grace) -2.254 1.824 0.139 0.002 0.777 0.786

ITU_GRACE16 S(Grace) -5.217 3.049 0.451 0.222 2.095 2.106

Tongji-GRACE01 S(Grace) -1.823 1.475 -0.094 -0.021 0.675 0.682

GO_CONS_GCF_2_SPW_R4 S(Goce) -0.742 0.42 -0.065 -0.063 0.277 0.273

JYY_GOCE04S S(Goce) -0.907 0.863 -0.052 -0.062 0.395 0.395

GGM05G S(Grace,Goce) -0.935 0.618 -0.145 -0.061 0.354 0.353

ITU_GGC16 S(Grace,Goce) -0.625 0.499 -0.051 -0.039 0.257 0.257

According to the analysis results, the accuracy of GO_CONS_GCF_2_SPW_R4 sediment model obtained by GOCE satellite data is 0.273 m, and the accuracy of ITU_GGC16 model is calculated as 0,257 m from GRACE and GOCE combined data.

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ITU_GGC16 model accuracy is specified as the highest model. It appears that the GRACE data for the selected models are less than those for the combined models.

4 CONCLUSIONS In this study, the definitions, theories and concepts related to the global geopotential models are explained and the regional accuracies of the most recent data and the oldest data have been tested from satellite missions. As a result of the tests, it has been tried to determine the most suitable global geopotential model to determine regionally. For this purpose, the geoid undulations derived from the satellite-based global geopotential models are compared with the geoid undulations calculated from the GPS-leveling data. As a result of the evaluations, the long-term results of the CHAMP fit did not show significant improvements in determining the gravity field of the earth. Comparisons show that GRACE models have more accurate than GOCE models. With the development of science and technology, it is understood that GOCE gravity field, the last satellite to determine gravitational field, provides high accuracy in determining long wavelength components. Finally, it is thought that the highest accurate model ITU_GGC16, obtained by combining GRACE and GOCE data, can be used as a reference global model in the calculation of gravimetric geoid models. Developments in satellite data have been so promising. By continuing to work in this area, more accurate geopotential models can be created. In near future it is appears that the time consuming leveling operations are not required to determine physical heights from mean sea level.

5 REFERENCES [1] Abbak R. A., Evaluation Of Global Geopotential Models By Spectral Methods And Improvement Locally For Geoid Determination, PhD Thesis, Institution of Natural and Applied Sciences, Selcuk University, Konya/TURKEY, 2011.

[2] Aydın C., Physical Geodesy Course Notes, Yıldız Technical University, İstanbul/TURKEY, 2014.

[3] Hofmann-Wellenhof, B., Moritz H., Physical Geodesy, Springer-Verlag, Wien, 2005.

[4] ICGEM, International Centre for Global Earth Models (ICGEM), http://icgem.gfz-potsdam.de/ICGEM/, 2017.

[5] Türen Y., Geoid determination using astrogeodetic leveling: A case study in Konya, Master Thesis, Institution of Natural and Applied Sciences, Selcuk University, Konya/TURKEY, 2010. [6] Üstün A., An investigation on contribution of GPS to global and regional height systems: A Case study of GPS/leveling between Antalya and Samsun tide gauges, PhD thesis, Institution of Natural and Applied Sciences, Yıldız Technical University, İstanbul/TURKEY, 2002. [7] Üstün A., Demirel, H., Long-Range Geoid testing by GPS-Leveling Data in Turkey, Journal of Surveying Engineering, vol. 132(1), pp 15-23, 2006.