Geoid modeling for Klang Valley using least square modification of stokes formula with additive corrections

Abstract

The accuracy of the geoid model is critical in providing accurate earth surface information. Many modification procedures have been developed in recent decades to obtain accurate local geoid models. Furthermore, satellite-based positioning techniques, particularly the Global Navigation Satellite System (GNSS), have been widely used, and more emphasis has been placed on the precise determination of geoid models. The main objective of this study was to improve the quality of the geoid model in a small area. The Klang Valley, with an area 2,500 square kilometres, was selected as an area of interest. A total of 1,258 terrestrial, 878 airborne gravity data, 3-arc Shuttle Radar Topography Mission (SRTM) model and Earth Gravitational Model 2008 (EGM2008) as well as 45 benchmarks were used to develop the Klang Valley Gravimetric Geoid Model (KTHKVGM2020Grav). The selection of the Global Gravitational Model (GGMs) was assessed based on terrestrial gravity data and GNSS levelling. The EGM2008 is the best model for this study, with an accuracy of ±0.122m and ±0.851m, respectively. Meanwhile, the SRTM model was assessed based on GNSS and benchmark with an accuracy of ±3.117m and ±3.024m, respectively. The gravity dataset was assessed with anomaly residuals based on ten mGal outliers that caused 181 terrestrials and 41 airborne gravities eliminated. Using the Tscherching/Rapp model and correlated method, the Klang Valley boundary problem value for signal and noise variance on EGM2008 was set at 10,800 maximum degrees. Consequently, the EGM2008 optimum upper limit, M, and upper limit of modification parameter, L was 2,190 maximum degrees. Capsize, ?0 of the study area was 0.1 degree as a minimum bias with variance error, ten mGal of the terrestrial gravity anomaly, ??g. All datasets were gridded using the Kriging method with patching node encompassing cell interpolation. After additive estimations, the height of the KTHKVGM2020Grav geoid model was estimated between -5.011m and 3.998m, respectively. The KTHKVGM2020Grav geoid model was evaluated with 45 GNSS levelling stations and obtained ±11mm accuracy. Meanwhile, the KTHKVGM2020Grav geoid model successfully fitted into Peninsular Malaysia Geodetic Vertical Datum (PMGVD) using 35 GNSS levelling stations after correlating with four transformations parameters. Klang Valley fitted geoid model (KTHKVGM2020fit) succeeded with ±5mm level accuracy. This study has demonstrated that the geoid model developed using the KTH approach provides better quality vertical reference than other methods, especially for a small area, such as Klang Valley.