An investigation on the contribution of GOCE satellite mission to regional geoid modelling in Turkey

The Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite was launched on March 2009 and it completed its mission in November 2013. Over 30 Global Geopotential Models (GGM) have been published using data collected by GOCE with various combinations of data sets. With the contribution of dedicated gravity field satellite missions and improved methodologies, computation of precise geoid model that can replace the existing vertical datum is possible. Some countries, such as Canada, adopted geoid-based vertical datum which facilitates the use of GNSS technologies to derive orthometric heights from ellipsoidal heights precisely. Currently, there are ongoing height modernization efforts to re-define the vertical datum in Turkey. Through this modernization, methodological developments and new approaches are needed to be investigated as well as acquiring the optimum data set to determine a centimeter accuracy geoid model. In the first part of this study, the evaluation of the performance of the recent GOCE-only and GOCE-GRACE models using four different GPS/Levelling data sets in Turkey are presented. Direct (DIR), Time-wise (TIM), Space-wise (SPW), GOCO and GOGRA models are evaluated. In order to make the models comparable with the observation dataset, spectral enhancement method is applied. In the calculation of geoid heights, high-frequency components of the gravity field are computed from EGM2008 and Residual Terrain Model (RTM). The standard deviations of the evaluated models are compared with the combined model EGM2008. As a result of the assessment of global geopotential models, the contribution of GOCE in the medium wavelength is obvious. There are significant improvements in the releases of the models. In the second part of the study, the models DIR R5, TIM R5 and GOCO05S, which shows superior agreement with the GPS/Leveling data sets, are used in the computation of regional geoid via the classical Remove-Compute-Restore (RCR) and KTH approach, also known as the Least Squares Modification of Stokes' formula (LSMS), to clarify the contribution of GOCE mission to the gravimetric geoid modeling in Turkey. The theoretical differences of the two geoid modelling methods are provided with their performance comparisons based on numerical results. The geoid models are tested using 30 GPS/Levelling benchmarks distributed through the whole Turkey, besides the local validation is carried out in the Marmara region using 81 GPS/Levelling benchmarks. In RCR method, the standard deviations of the geoid models that are computed with GOCE models show the same performance compared to that of EGM2008 at the same degree. The best results are achieved when the optimum degree of global geopotential model is used. In KTH method, the best results are achieved when the cap size is 0.1o and EGM2008 is used up to 360 degree and order. Additionally, GOCE models performed better in the geoid modelling compared to EGM2008 at the same degree. The standard deviation of the geoid computed with the maximum degree of the model is smaller than that of the optimum degree of the model. So it can be said that KTH method minimizes the effect of the low quality terrestrial gravity data using the high-frequency information of the global geopotential model. The best standard deviations are found as 22.4 cm and 17.6 cm (before fitting the geoid models to regional vertical datum) using RCR and KTH methods at 30 GPS/Levelling points, respectively. After the corrector surface fitting is applied at GPS/Levelling data sets using different parametric models, the performance of the models are compared to each other and Turkey Geoid (TG03). At 30 TUTGA points, 4-parameter Helmert similarity transformation model shows better results and the standard deviations are 21.2 and 16.6 cm for RCR and KTH methods respectively. The standard deviation of TG03 is 16.1 cm for the same data set. At 81 TUTGA points, the performance of RCR model is better than KTH model. However, both model cannot reach the accuracy of TG03 which is 6.3 cm. The best standard deviation is achieved when the 5t h degree polynomial model is used, but the cross-validation results revealed that the optimal model is the 3rd degree polynomial model. At IGNA points, the performance of KTH model is slightly better than RCR model. There is no significant difference in terms of standard deviations for 3rd , 4t h and 5t h degree polynomial models. Thus, 3rd degree polynomial model is preferred as optimal. The validations at the test points confirms this result as well. the Both models outperform the TG03 in that region about 4 cm. The validations at Izmir points shows that the best model is 5t h degree polynomial model for RCR and KTH. The standard deviations for RCR and KTH are 6.9 cm and 7.2 cm at the test points. TG03 performs better than both models. In conclusion, the computed geoid models are not accurate enough to be used for transforming ellipsoidal heights to orthometric heights because of the low accuracy of the terrestrial gravity data. Additionally, in order to make more clear statements about the performance of the RCR and KTH methods in Turkey, a better set of GPS/Levelling points whose distribution represents the changes of the topography must be used.