Riga quasi - geoid model
As of April 15, 2021, a new quasi-geoid model RIGA′20 is available, which has been developed by the City Development Department of the Riga City Council (hereinafter - RDPAD).
When determining the normal height in the implementation of the European Vertical Reference System (hereinafter - EVRS) for the territory of Latvia in the Latvian normal height system in the epoch 2000.5 (hereinafter - LAS-2000.5) with global positioning, the national quasi-geoid model is used. If another quasi-geoid model is used, the developer shall verify its accuracy by performing control measurements and assessing the accuracy of the model in a chamber.
RDPAD has performed a model accuracy check and submitted its results and model assessment to the Latvian Geospatial Information Agency (hereinafter - the Agency) for publication on the Agency's website.
Brief summary of the accuracy test of the quasi-geoid model RIGA′20
Connected and checkpoints
Four points of the N1 class of the State Geodetic Network and eleven points of the local network have been used as connected points with the normal height in the implementation of EVRS in the administrative territory of the city of Riga (three of these points have been created by leveling).
Four N1 class points of the State Geodetic Network Leveling Network and two local network points were used as model accuracy test points with normal height in the implementation of EVRS in the administrative territory of Riga city.
The values of the interconnected points have been determined by conducting global positioning observations at the fifteen N1 class and local network points of the National Geodetic Network (or at outcrops in their immediate vicinity) in the period from 2019 to 2020.
The values of the checkpoints were determined in the period from September 2020 to March 2021 by conducting Global Positioning Observations at six N1 class and local network points of the National Geodetic Network.
In addition, 45 points were selected for real-time test measurements, of which 26 points of the National Geodetic Network and 19 points of the local network. Measurements were performed in the global positioning base station systems “Latvian Positioning System” (hereinafter - LatPos) and “EUPOS-RIGA”.
At the aligned and test points, global positioning measurements were performed in post-processing mode, accumulating data for 4 hours. The 15 points used for matching are located in the GNSS_RIGA20_SP.dat file. The 6 points used in the test are located in the GNSS_RIGA20_VP.dat file.
Global positioning measurements in real time were performed in the LatPos system, in total 37 points, and in the EUPOS-RIGA system, in total 45 points.
Two independent observations were made at each station, each observation consisting of 10 sessions, 10 measurements in each session with an interval of 1 second. The nearest station solution was used. For seven points, real-time observations were made on extensions approximately 60 m away. For the outlets, the normal elevation is determined by geometric leveling, according to the accuracy of leveling class 2, and the height is determined against the nearest leveling mark.
Bernese Software 5.2 program with precise satellite ephemeris and independent vector principle was used for global positioning calculations for aligned and test points for which the geodetic height was determined by collecting data for 4 hours in post-processing mode.
The geodetic height of the test points is determined as the average of all measurements, excluding gross errors.
Comparison of normal height values
At the points of the leveling network and the local network used for the test, where the global positioning has been performed by post-processing, the height standard deviation from the GVT within one sigma is up to 3 mm. Normal height differences range from -15 to 7 mm. *
At the points of the leveling network and local network used for the test, where the global positioning was performed by real-time measurements in the LatPos system, the standard deviations within one sigma are up to 10 mm. Normal height differences range from -14 to 25 mm, with an average value of 9 mm.
At the points of the leveling network and local network used for the test, where the global positioning was performed with real-time measurements in the EUPOS-RĪGA system, the standard deviations within one sigma are up to 15 mm. Differences in normal heights range from -17 to 26 mm, with a mean value of 5 mm.
The standard deviations obtained in the test of the quasi-geoid model RIGA′20 in post-processing and real-time mode show that the accuracy of the quasi-geoid model RIGA′20 ensures the acquisition of basic geospatial data for the performance of Riga city municipality functions and tasks in the city land area.
The Agency's review of the developed model and its development report revealed the following shortcomings:
- The systematic deviation between the results obtained in RTK measurements in LatPos and EUPOS-RĪGA networks is not systematic in the GNSS test measurement report chapter “Real-time quasi-geoid test”, page 15. In the same chapter, p. the following incorrect explanation of accuracy is included: “The interval of normal height differences obtained in the EUPOS-RĪGA system is similar to the obtained interval in the LatPos system, which confirms that the observed standard deviation does not always determine the measurement accuracy.”;
- the model has been developed for the administrative territory of the city of Riga, and its accuracy assessment fully applies only to it. There is no explanation for the need for 6 km of coverage outside the city limits. The coverage of the model outside the administrative boundaries of the city of Riga must be equal to the length of a double data step;
- the quasi-geoid model has not been compared with previously developed models that cover its territory (for example, LV'14, LV'98). For example, the orientation of RIGA'20 and LV'14 surfaces is similar in the whole territory of connected points; RIGA'20 in the whole territory is higher than LV'14 in the range of 0.02-0.07 m, the average difference is about 0.04 m (see pictures). It would be advisable to compare the models using the new checkpoints. An analysis of these differences would help identify improvements to the model compared to older models;
Figure 1. Locations of constructed profiles. Symbols: I - checkpoints; II - connected points; III - RIGA'20 coating; IV - constructed profiles.
Figure 2. Constructed profiles in the territory of RIGA'20 connected points. Comparison of model height anomalies values.
* Verification of the quasi-geoid model is performed by comparing the empirical height anomalies of the model with those obtained by field measurements. Elevation anomalies are values used by geodetic programs to transition from geodetic (ellipsoidal) to normal elevation in both global positioning tools and data calculation programs.
When assessing the compatibility of a quasi-geoid with an altitude reference system, it should be taken into account that the altitude system, matched and checkpoints, and global positioning measurements are also realized with some certainty. The obtained normal heights for the joint and test points shall be evaluated at least five times better than the obtained geodetic height, therefore their influence on the final assessment shall be excluded.