Estimation of the geopotential value Wo for the local vertical datum of continental Greece using EGM08 and GPS/leveling data Grigoriadis VN, Kotsakis C, Tziavos IN, Vergos GS Department of Geodesy and Surveying Aristotle University of Thessaloniki Session 5: Establishment and Unification of Vertical Reference Systems International Symposium on Gravity, Geoid and Height Systems (GGHS2012), 9-12 October 2012, Venice, Italy
PRESENTATION OUTLINE -2- • O BJECTIVES • M ETHODOLOGY • T HE H ELLENIC V ERTICAL D ATUM • A VAILABLE D ATA • N UMERICAL R ESULTS • C ONCLUSIONS Estimation of the geopotential value Wo for the local vertical Grigoriadis VN, Kotsakis C, – datum of continental Greece using EGM08 and GPS/leveling data Tziavos IN, Vergos GS
OBJECTIVES -3- Estimate the geopotential value Wo for the local vertical datum of continental Greece using a methodology based on Helmert heights and geopotential models in order to allow the connection to other local, national, continental and global height systems . Estimation of the geopotential value Wo for the local vertical Grigoriadis VN, Kotsakis C, – datum of continental Greece using EGM08 and GPS/leveling data Tziavos IN, Vergos GS
METHODOLOGY -4- Problem setup Benchmarks Terrestrial i = { 1, 2, …, j} Network Local Vertical datum W=W o H i (orthometric heights - leveling) φ i , λ i , h i (position – GNSS methods) W o (geopotential value) g i , W i (geopotential model) Estimation of the geopotential value Wo for the local vertical Grigoriadis VN, Kotsakis C, – datum of continental Greece using EGM08 and GPS/leveling data Tziavos IN, Vergos GS
METHODOLOGY -5- By modeling physical heights as Helmert-type orthometric heights: LVD W W helm o i H i 5 helm 0.0424 10 H g i i LS estimate of LVD’s zero -height level helm helm p y W H g i i i i i ˆ LVD i W o p ‘weights’ i i Estimation of the geopotential value Wo for the local vertical Grigoriadis VN, Kotsakis C, – datum of continental Greece using EGM08 and GPS/leveling data Tziavos IN, Vergos GS
METHODOLOGY -6- Method’s rationale W j W i W k helm helm W W H g i i i i W ˆ LVD i W W o W W k j 2 p W min Estimate the LVD zero-height level such that: i i i Estimation of the geopotential value Wo for the local vertical Grigoriadis VN, Kotsakis C, – datum of continental Greece using EGM08 and GPS/leveling data Tziavos IN, Vergos GS
METHODOLOGY -7- Advantages Does not rely on the use of geoid heights and thus is not affected by ‘geoid modeling errors’ . Insensitive to the uncertainty of surface gravity values (g i ), i.e. the accuracy of g i is not critical and has a small affect to the computed W o . H i dH dg i i 5 0.0424 10 H g i i Even an extreme gravity error of 20mGal at mountainous areas (e.g. H=2000m) will affect the height value by 4cm. Estimation of the geopotential value Wo for the local vertical Grigoriadis VN, Kotsakis C, – datum of continental Greece using EGM08 and GPS/leveling data Tziavos IN, Vergos GS
NUMERICAL RESULTS -8- Advantages LVD W W helm o i H The residuals obtained after the i 5 helm g 0.0424 10 H i i adjustment can be utilized for studying adjustment the error characteristics associated to the physical heights ˆ LVD W o Additional Notes Assumption: Physical heights conform to Helmert-type orthometric heights Results obtained from the above methodology may also be tested with corresponding results from other alternative techniques that may employ different geopotential models Estimation of the geopotential value Wo for the local vertical Grigoriadis VN, Kotsakis C, – datum of continental Greece using EGM08 and GPS/leveling data Tziavos IN, Vergos GS
HELLENIC VERTICAL DATUM -9- The Hellenic VD was established by the Hellenic Military Service No scientific documentation is publically available Unknown Wo value associated with the Hellenic VD The accuracy of H is not realistically known Height values are considered to refer to the tide-gauge station located in the Piraeus port (Athens) – measurements period 1933- 1978. Estimation of the geopotential value Wo for the local vertical Grigoriadis VN, Kotsakis C, – datum of continental Greece using EGM08 and GPS/leveling data Tziavos IN, Vergos GS
AVAILABLE DATA -10- GPS/Leveling BMs 1542 points ( mainland ) X, Y, Z (ITRF00, t=2007.236) from HEPOS/GPS campaign Helmert-type ortho heights from Hellenic Military Service Stations with identified blunders/outliers have been removed GPS Accuracy ( 1σ): 1 -4 cm (horiz) 2-5 cm (vert) Ortho heights accuracy: unknown Estimation of the geopotential value Wo for the local vertical Grigoriadis VN, Kotsakis C, – datum of continental Greece using EGM08 and GPS/leveling data Tziavos IN, Vergos GS
NUMERICAL RESULTS -11- Data preparation Mean tide to tide-free conversion for orthometric heights using: 2 H H 29.6sin 9.9 [ cm ] TF M Computation of g at each benchmark using: T g r computed from EGM08 All computations were carried out in a tide-free system Computations for EGM08 were made using Pavlis&Holmes software Estimation of the geopotential value Wo for the local vertical Grigoriadis VN, Kotsakis C, – datum of continental Greece using EGM08 and GPS/leveling data Tziavos IN, Vergos GS
NUMERICAL RESULTS -12- Un-weighted LS estimate ˆ LVD 2 2 W 62636859.37 ?.?? m /s o helm ( 1/ ) p H Weighted LS estimate i i ˆ LVD 2 2 62636860.16 ?.?? m /s W o ˆ LVD 2 2 Difference: 8 cm ! W 0.79 m /s o (*) estimated zero-height level of the Hellenic mainland LVD as given by Sima et al. (EUREF 2009): ˆ LVD 2 2 W 62636859.44 m /s o Estimation of the geopotential value Wo for the local vertical Grigoriadis VN, Kotsakis C, – datum of continental Greece using EGM08 and GPS/leveling data Tziavos IN, Vergos GS
NUMERICAL RESULTS -13- ˆ LVD W o Height threshold for Difference used BMs Weighted Un-weighted helm ( p 1/ H ) i i < 200 m, 514 pts 62636860.04 62636860.20 ~ 1.6 cm < 500 m, 866 pts 62636859.90 62636860.19 ~ 3.0 cm < 1000 m, 1308 pts 62636859.65 62636860.17 ~ 5.3 cm < 1500 m, 1487 pts 62636859.45 62636860.17 ~ 7.3 cm < 2000 m, 1535 pts 62636859.37 62636860.16 ~ 8.1 cm Estimation of the geopotential value Wo for the local vertical Grigoriadis VN, Kotsakis C, – datum of continental Greece using EGM08 and GPS/leveling data Tziavos IN, Vergos GS
NUMERICAL RESULTS -14- Evidence of a ˆ LVD W o height-correlated Height threshold for Difference bias in the data used BMs Weighted Un-weighted helm ( p 1/ H ) i i < 200 m, 514 pts 62636860.04 62636860.20 ~ 1.6 cm < 500 m, 866 pts 62636859.90 62636860.19 ~ 3.0 cm < 1000 m, 1308 pts 62636859.65 62636860.17 ~ 5.3 cm < 1500 m, 1487 pts 62636859.45 62636860.17 ~ 7.3 cm < 2000 m, 1535 pts 62636859.37 62636860.16 ~ 8.1 cm Estimation of the geopotential value Wo for the local vertical Grigoriadis VN, Kotsakis C, – datum of continental Greece using EGM08 and GPS/leveling data Tziavos IN, Vergos GS
NUMERICAL RESULTS -15- More robust estimates Evidence of a ˆ LVD W o due to data weighting height-correlated Height threshold for Difference bias in the data used BMs Weighted Un-weighted helm ( p 1/ H ) i i < 200 m, 514 pts 62636860.04 62636860.20 ~ 1.6 cm < 500 m, 866 pts 62636859.90 62636860.19 ~ 3.0 cm < 1000 m, 1308 pts 62636859.65 62636860.17 ~ 5.3 cm < 1500 m, 1487 pts 62636859.45 62636860.17 ~ 7.3 cm < 2000 m, 1535 pts 62636859.37 62636860.16 ~ 8.1 cm Estimation of the geopotential value Wo for the local vertical Grigoriadis VN, Kotsakis C, – datum of continental Greece using EGM08 and GPS/leveling data Tziavos IN, Vergos GS
NUMERICAL RESULTS -16- Even more robust Evidence of a ˆ estimates due to data LVD W o height-correlated Height threshold for weighting Difference bias in the data used BMs Weighted Un-weighted helm 2 ( p 1/ ( H ) ) i i < 200 m, 514 pts 62636860.04 62636860.12 ~ 0.8 cm < 500 m, 866 pts 62636859.90 62636860.12 ~ 2.2 cm < 1000 m, 1308 pts 62636859.65 62636860.12 ~ 4.8 cm < 1500 m, 1487 pts 62636859.45 62636860.12 ~ 6.8 cm < 2000 m, 1535 pts 62636859.37 62636860.12 ~ 7.6 cm Estimation of the geopotential value Wo for the local vertical Grigoriadis VN, Kotsakis C, – datum of continental Greece using EGM08 and GPS/leveling data Tziavos IN, Vergos GS
NUMERICAL RESULTS -17- W o -reduced Helmert ortho heights (adjusted residuals from unweighted LSA) ˆ LVD W W ˆ o i helm LVD 2 2 e H W 62636859.37 m /s i i o helm g i 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 (m) (m) 0 0 -0.1 -0.1 -0.2 -0.2 -0.3 -0.3 -0.4 -0.4 -0.5 -0.5 0 500 1000 1500 0 500 1000 1500 2000 2500 Point no. Ortho height (m) max = 0.429 m min = -0.456 m mean = 0.000 m σ = 0.150 m Estimation of the geopotential value Wo for the local vertical Grigoriadis VN, Kotsakis C, – datum of continental Greece using EGM08 and GPS/leveling data Tziavos IN, Vergos GS
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