Development of a precise local quasigeoid model for the city of Krakow – QuasigeoidKR2019

Abstract

A geoid or quasigeoid model allows the integration of satellite measurements with ground levelling measurements in valid height systems. A precise quasigeoid model has been developed for the city of Krakow. One of the goals of the model construction was to provide a more detailed quasigeoid course than the one offered by the national model PL-geoid2011. Only four measurement points in the area of Kraków were used to build a national quasigeoid model. It can be assumed that due to the small number of points and their uneven distribution over the city area, the quasigeoid can be determined less accurately. It became the reason for developing a local quasigeoid model based on a larger number of evenly distributed points. The quasigeoid model was based on 66 evenly distributed points (from 2.5 km to 5.0 km apart) in the study area. The process of modelling the quasigeoid used height anomalies determined at these points on the basis of normal heights derived through levelling and ellipsoidal heights derived through GNSS surveys. Height anomalies coming from the global geopotential model EGM2008 served as a long-wavelength trend in those derived from surveys. Analyses showed that the developed height anomaly model fits the empirical data at the level of single millimetres – mean absolute difference 0.005 m. The developed local model QuasigeoidKR2019, similar to the national model PL-geoid2011, are models closely related to the reference and height systems in Poland. Such models are used to integrate GNSS and levelling observations. A comparison of the local QuasigeoidKR2019 and national PL-geoid2011 model was made for the reference frame PL-ETRF2000 and height datum PL-KRON86-NH. The comparison of the two models with respect to GNSS/levelling height anomalies shows a triple reduction in the values of individual quartiles and a mean absolute difference for the developed local model. These summary statistics clearly indicate that the accuracy of the local model for the city of Krakow is significantly higher than that of the national one.

A crossvalidation-based comparison of kriging and IDW in local GNSS/levelling quasigeoid modelling

“…Spatial distribution of the GNSS/levelling points used for modelling purposes is shown in Figure 1. Details as to GNSS and leveling measurements and accuracy issues are reported in Banasik et al (2020).…”

“…The goal of this study is to compare these two methods differing in complexity of theory and computational effort and should not be directly connected to the one of Banasik et al (2020) which was a kind of quasi-geoid model development report. The comparison itself is made in cross-validation mode with varying steering parameters of the methods, i.e., structure function and number of nearest neighbours in case of kriging/LSC, and power parameter (exponent) and number of nearest neighbours in case of IDW.…”

Research on gravity field modelling and gravimetry in Poland in 2019–2022

“…The maximum difference between models and empirical GNSS/levelling data reaches up to 14 mm for the local model and 44 mm for the national model. The mean absolute difference of 5 mm for the local model and 16 mm for the national model was obtained (Banasik et al, 2020).…”

Influence of reference stations on the stability of the geodetic control network during deformation determination in the area of Kadzielnia in Kielce

“…They record continuous (permanent) signals coming from satellites at a fixed measurement interval. The recorded data are made available to interested users (Banasik et al, 2008). The appropriate location of the reference stations provides the opportunity for full use.…”