Abstract
This study presents a solution of the ‘1 cm Geoid Experiment’ (Colorado Experiment) using spherical radial basis functions (SRBFs). As the only group using SRBFs among the fourteen participated institutions from all over the world, we highlight the methodology of SRBFs in this paper. Detailed explanations are given regarding the settings of the four most important factors that influence the performance of SRBFs in gravity field modeling, namely (1) the choosing bandwidth, (2) the locations of the SRBFs, (3) the type of the SRBFs as well as (4) the extensions of the data zone for reducing the edge effect. Two types of basis functions covering the same spectral range are used for the terrestrial and the airborne measurements, respectively. The non-smoothing Shannon function is applied to the terrestrial data to avoid the loss of spectral information. The cubic polynomial (CuP) function which has smoothing features is applied to the airborne data as a low-pass filter for filtering the high-frequency noise. Although the idea of combining different SRBFs for different observations was proven in theory to be possible, it is applied to real data for the first time, in this study. The RMS error of our height anomaly result along the GSVS17 benchmarks w.r.t the validation data (which is the mean results of the other contributions in the ‘Colorado Experiment’) drops by 5% when combining the Shannon function for the terrestrial data and the CuP function for the airborne data, compared to those obtained by using the Shannon function for both the two data sets. This improvement indicates the validity and benefits of using different SRBFs for different observation types. Global gravity model (GGM), topographic model, the terrestrial gravity data, as well as the airborne gravity data are combined, and the contribution of each data set to the final solution is discussed. By adding the terrestrial data to the GGM and the topographic model, the RMS error of the height anomaly result w.r.t the validation data drops from 4 to 1.8 cm, and it is further reduced to 1 cm by including the airborne data. Comparisons with the mean results of all the contributions show that our height anomaly and geoid height solutions at the GSVS17 benchmarks have an RMS error of 1.0 cm and 1.3 cm, respectively; and our height anomaly results give an RMS value of 1.6 cm in the whole study area, which are all the smallest among the participants.
Highlights
The unification of physical height systems is an essential geodetic application of the Earth’s gravity field
The results contribute to the ‘1 cm Geoid Experiment,’ which enables a comparison of our SRBFbased results to thirteen independent solutions calculated within other approaches, such as least-squares collocation (LSC)
The cubic polynomial (CuP) function is applied to the airborne data as a low-pass filter, and the smoothing features of this type of spherical radial basis functions (SRBFs) are used for filtering the high-frequency noise in the airborne data
Summary
The unification of physical height systems is an essential geodetic application of the Earth’s gravity field. 99 Page 2 of 19 and geocentric positions X can be transformed to geopotential numbers CP and ellipsoidal heights h, respectively (Ihde et al 2017). The determination of potential values as IHRS coordinates may be performed following the strategies applied for the (quasi-) geoid modeling. According to Ihde et al (2017), the target uncertainty of W (X) should be at the 10−2 m2/s2 level (equivalent to around 1 mm for physical heights). The reliability of the potential estimation undergoes the same limitations of the precise (quasi-) geoid modeling. A high-resolution and high-precision (quasi-) geoid model is the key for the realization of the IHRS
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