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Building an unified height basis for both continental and marine territories of Vietnam without using mean sea level Prof. Dr. Sc. Pham Hoang Lan Vietnam Association of Geodesy, Cartography and Remote sensing

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In order to overcome the principle disadvantages of the height system based on traditionally using the mean sea level there is supposed in this paper building an unified height basis for both continental and marine territories of Vietnam by use of Molodenskys theory of the normal height. For this purpose there were chosen 3 points in the coastal zone and 2 points on the off-shore islands where the geodetic height has been determined from GPS and the height anomaly has been computed from the gravimetric measurements in Vietnam in combination with different Earth gravitational models. Summary

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In result there were established 5 control stations with an accuracy of 0.2 - 0.3 m for the future height foundation in Vietnam without using the changeable mean sea level. There is also considered the distance between surfaces of the local and the world quasi-geoids along the coastal zone of Vietnam. Summary

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Since beginning of the 20 th century in the Vietnam’s territory there were built several leveling lines with a starting origin chosen at local mean sea level. In 1929 the first tide gauge has been established in Hon Dau - Hai phong ( 28 0 40’; 106 0 49’) and accepted as National height origin for Vietnam. Because of historic situation in 1954 - 1975 in the south part of the country there was used the mean sea level at Ha Tien tide gauge ( 10 0 32’; 104 0 28’). Status of the National height network in Vietnam

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After the unification of the country the National height network built in the north part during 1959 - 1964 with four orders of accuracy and the origin in Hon Dau has been developed over the whole country. A height value of benchmarks was simply accepted equal sum of observed leveling differences from the origin. Only in 1996 for the first time gravimetric corrections have been introduced by use of the gravity anomalies averaged for standard blocks of 5’x 5’ and accordingly height values were reduced to the normal height system. Status of the National height network in Vietnam

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In result of adding measurements in lack regions and improving observation quality in general the Vietnam’s National height network has today’s status with 13 first order and 44 second order leveling lines which formed 6 first order closed loops, 2 second order closed loops and 36 joint closed loops. The influence of gravity field has been taken into consideration by use of gravity measurements carried out along leveling lines. The unit weight rms is evaluated equal 0.92 mm for the first order and 2.29 mm for the second one. Status of the National height network in Vietnam

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The minimum rms is 3.26 mm for the first and 5.56 mm for the second order. The maximum rms is 34.47 mm and 38.29 mm for the first and second order accordingly. So the Vietnam’s National height network of first and second orders has an even and dense construction, high accuracy with an origin at the mean sea level of Hon Dau tide gauge and is reduced to the perfect normal height system. But, because of undertaking the mean sea level as a height origin the considered height network has some disadvantages. Status of the National height network in Vietnam

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Firstly, being transfered from a starting point far in the North a height value of south benchmarks differs more and more from its height value concerned to the local mean sea level. The actual measurements show the difference between height values derived from Hon Dau and Ha Tien tide gauges reaches 0.16 m. This caused known inconveniences for south coastal zones of the country in using topographic maps with height values reduced to Hon Dau. Status of the National height network in Vietnam

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Secondly, having one starting point the height network can’t be confidently controlled and adjusted for improving its accuracy quality especially in such stretched country as Vietnam. Moreover, the established National height system works only for the continental territory, but no more for the islands and territorial waters of the country. Finally, as it is well known, the sea level is not invariable, but rising under climate change. Status of the National height network in Vietnam

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Above mentioned disadvantages of the existing National height network should be overcome by building an unified height basis for both continental and marine territories of Vietnam without using mean sea level as discussed below. Status of the National height network in Vietnam

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Proposed solution is based on using the normal height recommended in Molodensky’s revolutionary theory for study of the Earth’s physical surface and gravity field without any hypothesis about its inner structure. The normal height has been initially interpreted by Molodensky as height of the first approach of the Earth’s actual surface above the surface of the normal ellipsoid. This approach surface had a later name of telluroid suggested by Hirvonen. Theoretical grounds of solution

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The normal height is designated as H and can be understood as the difference between the geodetic height h and the height anomaly ( fig. 1). Theoretical grounds of solution Fig.1. Main surfaces of the Earth

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We have: H = h - . (1) In essence the height anomaly is a distance of physical surface of the Earth from telluroid. It can be determined by solving the fundamental equation of physical geodesy and is expressed by the integral formula with gravity anomaly values g given for whole globe as follow: Theoretical grounds of solution

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The geodetic height h can be acquired by sattelite positioning technology like GPS or GLONASS. It is important to use the same ellipsoid for counting both geodetic height and height anomaly. It also should be remined that the normal height has not to be determined by use of the traditional levelling in combination with gravity measurements because in this case we again face to the mean sea level problem. Theoretical grounds of solution

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In order to realize the proposal there were chosen 3 points along coastal zone: DSON (20042’;106047’); QNAM (15051’;107056’); VTAU (10024’;107009’) and 2 points on off- shore islands: BLV (20008’;107044’) and COND (8040’;106034’). For determination of geodetic coordinates of the points there were used dual frequency GPS receivers. Observation sessions lasted continuously at all the points since march 22 up to march 24, 2009. Realization of the proposal

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Data processing has been carried out by use of the BERNESE 5.0 program including 4 IGS stations available around Vietnam such as KUNM (China), NTUS (Malaysia), PIMO (The Philippines) SHAO (China). RMS error of the coordinates in ITRF were evaluated equal 2 mm. Gravimetric height anomalies have been defined through air free gravity anomalies for standard blocks of 5’x 5’ averaged from actual measurements in gravimetrically studied regions with rms error of about 3 mgal and interpolated by use of collocation in lack regions with rms error of about 6 mgal. Realization of the proposal

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The total number of used standard blocks is 4217. The “remove - restore“ technique was applied with five models of the Earth gravity field such as EGM-96, EGM-2008, ggm03c, EIGEN-GLO4C and EIGEN-5C and the digital terrain model SRTM 30. The 3D Least Square Collocation method with the main package GravSoft and additional softwares Matlab R 2009a and Surfer has been used for calculating gravimetric height anomalies. Realization of the proposal

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Finally, for five mentioned above points there were obtained the normal height values with their rms errors: 0.30 m for BLV, 0.25 m for DSON, 0.20 m for QNAM, 0.25 m for VTAU and 0.30 m for COND. The received result may be considered as a multi - origin and unified height basis first time built in Vietnam for both continental and marine territories without using mean sea level. The accuracy of normal heights can be significantly increased by use of more and better heterougeneous observation data available in the next future such as satellite altimetry, satellite gradientometry and other modern measurement technologies. Realization of the proposal

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The continental points DSON, QNAM, VTAU were chosen to coincide with the benchmarks of the National height network, so it is possible to calculate for them a difference between the normal height values determined by two various ways: traditional levelling and GPS levelling. Corresponding differences are: -1.92 m, 0.98 m and -2.63 m. They represent a distance between the local and the world quasi- geoid surfaces at the considered points and have been received for first time in Vietnam. Realization of the proposal

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