Abstract
High precision geoid determination is a challenging task at the national scale. Many efforts have been conducted to determine precise geoid, locally or globally. Geoid models have different precision depending on the type of information and the strategy employed when calculating the models. This contribution addresses the challenging problem of combining different regional and global geoid models, possibly combined with the geometric geoid derived from GNSS/leveling observations. The ultimate goal of this combination is to improve the precision of the combined model. We employ fitting an appropriate geometric surface to the geoid heights and estimating its (co)variance components. The proposed functional model uses the least squares 2D bi-cubic spline approximation (LS-BICSA) theory, which approximates the geoid model using a 2D spline surface fitted to an arbitrary set of data points in the region. The spline surface consists of third- order polynomial pieces that are smoothly connected together, imposing some continuity conditions at their boundaries. In addition, the least-squares variance component estimation (LS- VCE) is used to estimate precise weights and correlation among different models. We apply this strategy to the combined adjustment of the high-degree global gravitational model EIGEN-6C4, the regional geoid model IRG2016, and the Iranian geometric geoid derived from GNSS/leveling data. The accuracy of the constructed surface is investigated with five randomly selected subsamples of check points. The optimal combination of the two geoid models along with the GNSS/leveling data shows a reduction of 21 mm (~20%) in the RMSE values of discrepancies at the check points.
Highlights
High precision geoid determination is a challenging task at the national scale
Regional geoid models are developed by combining short, medium and long wavelength components derived from a digital elevation model (DEM), terrestrial and space gravity data, low degree global geopotential models, satellite altimeter measurements, GNSS/leveling data and so on
To enhance the geoid model precision, we aim to combine different regional and global geoid models and the geometric geoid model derived from GNSS/leveling network
Summary
To approximate a 2D function values using a smooth spline surface, LS-BICSA can be introduced as a reliable and flexible method [Amiri-Simkooei et al, 2018]. LS-BICSA is based on the pure bi-cubic spline functions, but in the least squares sense. The spline surface consists of third-order polynomial pieces that are smoothly connected together having some continuity conditions at their boundaries. The connecting knots must be defined by the user at the boundaries of the surface patches. To better explain the appropriate patch sizes, the required number of boundary knots and hard constraints, the reader is referred to Amiri-Simkooei et al [2018]. The user may impose some hard constraints into the functional model. The least squares cubic spline approximation (LS-CSA) can be introduced to approximate the 1D data in the least squares sense. B-spline automatically applies all continuity constraints, whereas LS-BICSA imposes only the user-specified constraints
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