Combining Levelling with GPS Measurements and Geoid Information

Combining Levelling with GPS Measurements and Geoid Information Urs Marti, Andreas Schlatter and Elmar Brockmann Federal Office of Topography, Seftigenstrasse 264, CH-3084 Wabern, Switzerland ABSTRACT The demand of using GPS for height determination and to replace expensive levelling measurements in regions where not the maximum accuracy is needed, requests a height system in which levelling and GPS in combination with geoid information lead to compatible results. The new kinematic height system LHN95 of Switzerland should fulfil this task. The geoid of Switzerland CHGEO98 with an accuracy of 3 to 5 cm over the whole country is available since 1998 and all the levelling measurements since 1902 are now available in digital form and have been evaluated in a kinematic adjustment process. More than 120 levelling bench marks are also connected to the national GPS network, which has been re-measured in 1998. This gives us in a first step an excellent data set for comparing and analysing the different results. In a second step we will try to include the orthometric heights obtained out of GPS and the geoid into the adjustment of the levelling network. This should strengthen the solution over long distances. In addition to these more general investigations two special GPS campaigns have been performed in mountainous regions where we wanted to test the possibilities to replace levelling by GPS measurements. The evaluation revealed promising results but also that much attention has to be paid on the GPS evaluation method. Especially the modelling of the influence of the troposphere plays a major role. Just with standard models it is not possible to get satisfactory results. More sophisticated modelling methods have to be applied. 1. INTRODUCTION One of the main problems of surveyors today is the accurate height determination. Levelling over longer distances is usually too expensive and too time consuming and therefore the users prefer the much cheaper GPS method. Of course, they have to apply the correction of an accurate geoid or quasigeoid model to get orthometric or normal heights which are usually used as national height systems. But this arises the problem that in general, these heights are not in accordance with the heights obtained out of levelling. The simple reason for this discrepancy is the simple fact that all the implied data sets (GPS, levelling, geoid) show smaller or larger random and systematic errors. The goal for a national height system therefore has to be a common treatment of the 3 data sets and to reach consistency between them. The simple condition, that the ellipsoidal height has to be equal to the sum of orthometric height and the geoid undulation has to be fulfilled. Only under these circumstances it is possible to replace levelling by cheaper GPS measurements at least in regions where not the highest accuracy is needed. A first step in this direction has to be - a good connection between the GPS and the levelling networks through many GPS/levelling stations - an accurate geoid model - and a detailed analysis of the involved data sets and the differences between them 2. The available data sets 2.1 The national GPS network The Swiss national GPS network LV95 was originally established between 1989 and 1994. Since then it is systematically densified and consists today of about 240 principal and densification points. 22 of these points form the permanent GPS network AGNES (Automated GPS Network of Switzerland). The whole network was re-measured in 1998 and the results assured us that the accuracy of the network is clearly better than 1 cm in position and about 1 to 3 cm in height [Gubler et al, 1999]. The network and its connection to the national levelling network is displayed in fig. 1. 0 km 20 km 40 km 60 km 80 km 100 km Fig. 1: The national GPS network LV95 (including the permanent network AGNES) and its connection to the levelling network LHN95. GPS/levelling stations are marked with circles. 2.2 The national Levelling network The national first and second order levelling network (LHN95) has a length of about 4000 km and contains about 11'000 bench marks [Marti et al. 2001]. All measurements in this network since 1902 are available in digital form and most of the lines are at least observed in 2 epochs. This allows us to treat LHN95 as a kinematic network and to estimate vertical movements. LHN95 is an orthometric height system but in order to assure the data exchange with neighbouring countries, normal heights are available as well. The orthometric heights are obtained out of the geopotential numbers by division through the mean gravity along the plumbline, which itself is estimated out of surface gravity and a density model of the upper Earth's crust. The accuracy of LHN95 is about 0.7 mm/km or about 1 cm/100 km. 2.3 The geoid of Switzerland The 3rd data set involved is the geoid model of Switzerland CHGEO98 [Marti, 1997]. It is available also in form of a quasigeoid. For its determination, about 600 astronomically observed deflections of the vertical and 70 connections between GPS stations and levelling bench marks were used. Gravity measurements were only used in the step of downward continuation. Furthermore the same mass models as in the calculation of orthometric heights were used in the remove/restore step. These are mainly a 25-meter DEM and density models for crustal structures. After reducing the measurements from the effects of topographic masses, the residuals were interpolated by means of least squares collocation. The final geoid was calculated by re-adding the effects of the mass models. The result revealed an accuracy of 2 to 3 cm in the flatter areas and of about 5 cm in the Alps. This could be verified by a comparison with independent GPS/levelling stations and by a comparison with the European gravimetric geoid EGG97 [Denker and Torge, 1997]. These two totally independent solutions showed (at least in flatter areas) an accordance of better than 5 cm. 3. Comparison of the data sets For about 120 stations all the 3 quantities ellipsoidal height, orthometric height and geoid undulation are available and we can form differences of the orthometric height out of levelling minus orthometric heights out of GPS and the geoid without applying offset or tilt parameters. These differences are displayed in fig. 2. Another comparison on the level of normal heights and height anomalies gave slightly better results since the density distribution in the Earth's crust is of no importance. But, in our case, these differences between the two comparisons are really small (up to 1 cm) and so it is not worth to discuss both of them. In most parts of the country the differences are smaller than 3 cm, which indicates that levelling, the geoid and GPS yield rather consistent results. In flatter areas the agreement is even better than 2 cm. But all the same, there are regions with systematic differences of more than 5 cm. This is mainly the case in the Southeast of Switzerland, but also in the North a systematic trend of the residuals of up to 4 cm exist. The most reasonable explanation up to now is that these differences are caused mainly by local problems of the geoid. It seems less likely that the problem is caused by systematic errors of the levelling because of the small residuals of the adjustment of the levelling network. A systematic trend of the GPS can most probably be excluded as well. The entire GPS network LV95 was remeasured in 1998 [Gubler et al., 1999] and great attention was paid to troposphere modelling and therefore also to height determination. Only small systematic differences of up to 5 cm to the original result of 1995 could be detected which may explain some of the differences in the North but they do not explain the differences in the South and Southeast. A common adjustment of all the 3 data sets has not been performed yet. The principal problems that have to be resolved first are the detection and elimination of systematic errors, a reasonable weighting between the different types of observations but also to get the full variance-covariance information of the geoid. A first approach for this common adjustment can be found in [Kotsakis et al. 1999]. 0 km 20 km 40 km 60 km 80 km 100 km 5 cm Fig. 2: Differences between orthometric heights out of levelling and orthometric heights out of GPS and geoid information. 4 The Possibilities of Substituting Levelling by GPS One of the main goals of a common treatment of levelling, GPS and the geoid is to substitute expensive levelling through cheaper GPS measurements at least in regions where not the highest accuracy is necessary. In order to prove the capability of GPS for height determination, two test campaigns were carried out in 1998 on 4 consecutive days: the first one in the Emmental, a pre-Alpine hilly region with height differences of up to 500 metres and the second one at the Sustenpass, in a high Alpine area with height differences of up to 1700 metres. Static GPS measurements were carried out since it was obvious from the beginning that kinematic methods would not give the requested accuracy. But since GPS should remain a cheaper method than levelling, no enormous effort was put into the observations. A total of about 65 levelled stations were observed in day and night sessions of 3 to 12 hours. Mainly the impact of troposphere modelling, cut-off angle, session length, topography and GPS evaluation software was tested. Alpine-scale height differences observed by GPS are biased mainly by a mismodelling of the troposphere. In collaboration with the Institute of Geodesy and Photogrammetry ETH Zurich (A. Geiger), zenith path delays were computed from meteorological data (ANETZ data) of the Swiss Meteorological Institute (SMI) using the 4-dimensional modelling software called COMEDIE [Hirter, 1998]. Comparisons between GPS and levelling were performed by transforming the GPS ellipsoidal heights into orthometric heights using the geoid model CHGEO98. The campaigns were designed to answer the following questions: - The impact of different processing strategies and different troposphere models (different a-priori models, estimation of tropospheric zenith path delays from GPS observations, introduction of zenith path delays from COMEDIE) on the GPS height estimation. - Impact of data analysis of different GPS processing packages. Commercial packages and the scientific package Bernese 4.1. [Beutler et al. 1996] were used. - Impact of the session length on the height estimates. - Accuracy of the GPS heights compared with levelling / geoid information. 4.1 The test campaign Emmental The Emmental measurements were carried out in June 1998 to investigate the possibility of replacing second and third order levelling in hilly regions by GPS and a geoid model. The test network consists of a total profile length of 44 km with a total height difference of about 300 m following a recently re-measured levelling line of the national levelling network LHN95. The evaluation of this GPS network has been performed with several software packages and by varying as many parameters as possible. Some characteristics of the results can be summarised as follows: - for baselines longer than 10 km, a L3 solution has to be used; a L1/L2 solution gives no accurate heights. - to obtain good heights, a weighting of the GPS observations with zenith angle or a higher cut-off angle has to be used - Troposphere parameter estimation out of GPS is not reliable for sessions shorter than 3 hours - commercial software packages give comparable results with a standard evaluation with the Bernese software - The best height repeatability is obtained by using the COMEDIE troposphere model - using a standard Saastamoinen troposphere model gives a rather good height repeatability but the result shows a height bias compared to the COMEDIE solution 5 0 600 -5 650 700 750 800 850 900 950 1000 -10 -15 -20 -25 -30 -35 Saastamoinen Comedie -40 -45 Station Height [m] Fig. 3: Results of the Emmental Test Campaign: Comparison of the ellipsoidal heights (GPS) corrected for geoid undulations with orthometric heights from levelling using: a) standard troposphere model (Saastamoinen; solid grey line), b) 4D meteo model (COMEDIE; dashed black line) After the GPS evaluation the obtained ellipsoidal heights were corrected with the geoid and then compared to the orthometric heights from levelling. The principle results can be seen in fig. 3: If we use a standard meteo model the heights obtained out of GPS and geoid can be biased of up to 10mm/100 m height difference. When we use a more sophisticated meteo model such as COMEDIE, the results are in very good agreement with levelling. The bias disappears completely. This also proves that the GPS repeatability is not a reliable indicator for detecting height biases. 4.2 The test campaign Sustenpass The test network Sustenpass consists of a profile of 48 km in length with a total height difference of about 1700 m following the pass road. The 30 GPS stations are connected to a recently re-measured national 2nd order levelling line. The observations have been performed on 3 days in July 1998 in 9 sessions with a length between 3 and 12 hours. An important role in the analysis of the result plays the height profile shown in fig. 4 at left, where we have to distinguish between the West (Wyler) and the East (Wassen) side. The results of the GPS evaluation and the repeatability were not very different from the Emmental campaign and do not need to be discussed here. Because of the big height differences the repeatability was in general worse but it were the same strategies that lead to the best results. The conclusions from the analysis of the GPS heights corrected for the geoid and their comparison with the orthometric heights from levelling are as follows: - The modelling of the troposphere was much more difficult due to the difficult topography and the distribution of the meteo sites. The results from the two flanks are not homogeneous. - When standard troposphere models (Saastamoinen) were used, the height estimates are biased by up to 3 mm per 100 m. - When using the 4D meteo model (COMEDIE), the agreement between GPS heights and levelled heights is better on the west side (diff. < 4 cm) and worse on the east side (diff. < 9 cm) of the pass (see fig. 4). The bias in the height scale can not be eliminated completely even with long observation sessions. - Of course, the Sustenpass is not only a difficult region for GPS campaigns, but also for levelling and the geoid determination. Therefore it is not sure that the detected biases are a consequence of the GPS results only. The levelling and the geoid as well, are not be supposed to be free of systematic errors. 80 60 2400 Sustenpass Legend 2200 Levelling line 40 Rässegg Rinderboden Test network markers 2000 LV95 densification points Sustenbrüggli Steingletscher 1800 Height [m] 20 Himmelrank Hochrainplanggen Hell Wendenwasser II 1000 2000 1500 2500 Färnigen 1400 -40 Meien Wendenwasser I 1200 0 500 -20 Fleschboden Feldmoos 1600 Gadmen Husen -60 Käppeli 1000 Wassen Hopflauenen 800 -80 Wyler -100 600 0 5 10 15 20 25 30 Levelling distance [km] 35 40 45 50 Wyler - Saastamoinen Wassen - Saastamoinen Wyler - Comedie Wassen - Comedie -120 Station Height [m] Fig. 4: Test network Sustenpass: Height profile (at left) and comparison of the ellipsoidal heights (GPS) corrected with geoidal undulations with orthometric heights from levelling for the two sides of the Sustenpass (Wyler: western part; Wassen: eastern part) using: a) standard troposphere model (Saastamoinen; solid line), b) 4D meteo model (COMEDIE; dashed line). 4.3 Consequences of the test campaigns When special attention is paid to the tropospheric corrections, the use of GPS for the densification of height networks in flat and pre-Alpine areas with height differences smaller than 500 m is promising. In order to avoid severe biases in the height scale, standard troposphere models should not be used. Excellent results were obtained when a new 4D meteo model (COMEDIE) using regional meteo data was applied. In Alpine networks with large height differences, height determination by GPS is still a difficult task. Even the most sophisticated tropospheric models are not yet capable of eliminating systematic influences from tropospheric refraction. The results of these test campaigns revealed that the substitution of levelling is possible under the following conditions: - no extreme topography - relative accuracy demands are not very high (about 1 cm over 30 km). - special attention is paid to troposphere modelling. A standard model is not suitable. - even with the most sophisticated troposphere models only suitable for scientific GPS software, it is still a very difficult task to get a good accuracy in high mountainous areas. - several hours of GPS measurements are necessary to obtain sufficient results. - appropriate parameter choice in the GPS evaluation. 5 Summary, Conclusions The national levelling network LHN95 is ready to be used and rigorous orthometric heights are available on all 1st and 2nd order levelling lines. About 120 levelling benchmarks are also connected to the GPS network LV95 and can be used to detect discrepancies between levelling, GPS and the geoid model CHGEO98. The 3 data sets GPS, levelling and the geoid are in agreement of 2 cm in flatter areas and up to 8 cm in some regions in the Alps. Usually this is sufficient for the daily work of the surveyors. These differences are not randomly distributed over the country but some regional trends seem to exist. They are supposed to be caused mainly by long wavelength errors of the geoid, systematic errors in levelling or GPS are less probable or at least smaller. This implies that it is perhaps worth to consider a new geoid determination including some options that were not included in the geoid model CHGEO98 such as the full integration of gravity measurements, the use of a global model or the integration of the newest GPS/levelling measurements. Until now, GPS, levelling and the geoid are only compared among each other. A combined adjustment of all 3 data sets has not been performed yet. The main reasons that prevent us from these step are that systematic errors have to be eliminated first, that a reasonable weighting has to be found and that the full variance-covariance information for the geoid is not available. The two test campaigns in the Emmental at the Sustenpass showed that levelling can be replaced by GPS under some circumstances when accuracy demands are not too high and a accurate geoid or quasigeoid model is available. In regions with extreme height differences it is extremely difficult to bring GPS and levelling into agreement. The main reason for this is the influence of tropospheric refraction on GPS but also on levelling. Therefore much attention has to be paid to troposphere modelling in the GPS evaluation. But even if the GPS results show a good repeatability in height, we can not be sure to get a good agreement with levelling. Depending on the chosen parameters in the GPS evaluation we can get biases in the order of 1 cm per 100 meter height difference. Parameters like the cut-off angle and the weighting of the observations with their zenith angle are of major importance in the height determination with GPS. 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