Temporal and Spatial Investigation of the Different Geodetic Methos in terms of Evaluating Elevation

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Temporal and Spatial Investigation of the Different Geodetic Methods in terms of Evaluating Elevation Change Bengisu Gelin, Sefa Onur DĂźndar 2015-2016 Bachelor Degree Graduation Project YÄąldÄąz Technical University, Geomatics Engineering, Turkey, Istanbul bengisugelin@gmail.com, sefaonurdundar@hotmail.com Supervisor: Prof. Dr. UÄ&#x;ur DoÄ&#x;an Abstract.

In the engineering applications, using geoid as a reference surface is a fundamental necessity since it is an equipotential surface. Different geodetic methods can be solution to determine the height from surface to the mean sea level. In this study, orthometric heights and height differences between assigning network sites on the study area were determined using three geodetic methods; Global Navigation Systems (Real Time Kinematic and static) and levelling. These methods were applied two diverse application areas which one of them is flat (platform1) and the other is sloping land (platform2) to observe the effect of slope.

In these network sites, static measurements with GPS for 3 hours and kinematic measurements (5s, fixed) by connecting to ISKI-CORS were done.

After ellipsoidal heights were obtained with the data sets, orthometric heights were calculated with using EGM08 geoid model. Besides, levelling measurements were carried out and the orthometric heights were determined with least squares method.

All measurements were compared with each other and the results were handled for two different measurement areas, flat and sloping land. The investigation indicates cm degree differences for all comparisons.

Introduction.

BĂ–HHBĂœY.

•To convert the epoch following formula is used: đ?‘‰đ?‘Ľ đ?‘‹(đ?‘‡) đ?‘‹(đ?‘‡0) [đ?‘Œ(đ?‘‡) ] đ?‘‡đ?‘ˆđ?‘‡đ??şđ??´ = [đ?‘Œ(đ?‘‡0) ] đ?‘‡đ?‘ˆđ?‘‡đ??şđ??´ + (đ?‘‡ − đ?‘‡0 ) [đ?‘‰đ?‘Ś ] đ?‘‡đ?‘ˆđ?‘‡đ??şđ??´ đ?‘‰đ?‘§ đ?‘?(đ?‘‡) đ?‘?(đ?‘‡0)

Which T0 is TUTGA reference epoch and Vx,Vy,Vz are velocities. •Standard deviations ĎƒÎ”X, ĎƒÎ”Y, ĎƒÎ”Z of every independent bases are calculated and result should be, Ďƒ ΔX, Ďƒ ΔY, Ďƒ ΔZ ≤ Âą (10 mm + 1 ppm) •Geodetic coordinates (φ, Îť, h) and standard deviations of bases after the adjustment are calculated. Standard deviations of the geodetic coordinates should be; Ďƒ φ, Ďƒ Îť ≤ Âą 3.0 cm, Ďƒ h ≤ Âą 5.0 cm TUTGA. Turkish National Fundamental GPS Network (TUTGA) has been establish between 1997-1999 and revision surveys has been done because of the high seismicity after 1999. In this research, ITRF96, initial reference frame of TUTGA, was used. Therefore, all measurements were translated to ITRF96 as it is said in Code of Production of Large Scale Map and Map Information. TUTGA also contains IGS stations such as ISTA which is used in our investigation as a reference station.

According to BĂ–HHBĂœY (Code of Production of Large Scale Map and Map Information) which includes fundamental rules of surveying in Republic of Turkey, the following criteria should be provided.

Evaluation of the GPS measurements: Figure 1. General Distribution of TUTGA Stations

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EGM08.

The new geoid model for Turkey (Turkish Hybrid Geoid 2009) have computed by using Earth Gravitational Model 2008, new surface gravity observations, satellite altimetry-derived gravity over the sea and high-resolution digital terrain model. However, we only access Turkish Geoid 2003 via General Command of Mapping. Hence, we decided to use EGM08 geoid model since it is reliable in terms of closeness to the newest Turkish Geoid Model.

has 580 m distance and %3.45 slope percentage (20 m elevation change).

Figure 3. Platform 1 (101, 102, 103, 104, 105, 106, 107) and Platform 2 (104, 201, 202, 203, 204, 205, 206) indicates sites of flat and sloping areas respectively. 104 is the common site for the two networks.

Instruments.

Figure 2. EGM08 Geoid Heights for the Globe

TUSAGA-Active.

The Turkish RTK CORS Network is called TUSAGA-Active which is controlled by two control stations, Photogrammetry and Geodesy Administration of the General Directorate of Land Registration and Cadastre as a master control station, and General Command of Mapping of Turkey as a headquarters. One of the TUSAGAActive stations, ISTN, was used as a reference station for the adjustment of measurements.

In the static GPS measurements (~3hr), Trimble Netr9 receivers and Trimble precise geodetic antennas (Zephyr) were used. Measurements that obtained in this method, post-processed using Leica Geo-Office software.

Figure 4. One of the generated points, 104, while doing static measurement.

In the levelling measurements, Leica model levelling instrument was used.

Study Area.

Two different networks, one is a sloping land and the other is a flat land, each consist of seven sites, have been designed in Yildiz Technical University Davutpasa Campus, Istanbul, Turkey. While flat land has 419.8 m distance and %0.48 slope percentage (1.58m elevation change), sloping land Address Offices in Brussels : Rue du Nord 76, BE – 1000 Bruxelles. Tel +32/2/217.39.72 Fax +32/2/219.31.47 E-mail: maurice.barbieri@clge.eu - www.clge.eu EU-Transparency Register of interest representatives - 510083513941-24

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Evaluation.

Methods.

1. Static GPS Measurements.

Static measurements (~2-3 hours) were done on the generated points on 26.02.2016. First seven points, between 14.30 and 17.45, and the second seven points, between 17.50-20.30, were measured with 10º elevation angle and 15s recording range in the scope of the investigation. During the evaluation phase of the measurements ISTA station, which is one of the IGS stations; ISTN Station which is one of the TUSAGA-Active Stations and the data of YLDZ station working continuously on the roof of the Yıldız Technical University Civil Engineering Faculty and related to EUREF has been supplied and used. YLDZ, ISTA and ISTN stations were fixed, information of antennas was taken from National Oceanic and Atmospheric Administration of U.S. government, precise ephemeris was imported into the project by GPS week and day from"https://igscb.jpl.nasa.gov/components/prods _cb.html" website (For 26.02.2016 Friday, GPS week is 1885 and GPS day is 5; for 27.02.2016 Saturday, GPS week is 1885 and GPS day is 6).

After satellite data were improved, by using fixed coordinates, the stable coordinates of 13 points were obtained (Hofmann-Wellenhof et al., 2008) in ITRF96 reference system without ambiguity problem.

In the beginning of the evaluation, there were five stations namely ISTN, ISTA, YLDZ, KARB and SLEE which has 6.05km, 14.149km, 75.2m, 39km, 61.922km distance from generated points respectively. (Figure 6) However, the fact that we used Leica Geo-Office software and it does not remove atmospheric effects, 20km from the generated points were determined as a border to avoid ionospheric effects, therefore ISTN, ISTA and YLDZ were accepted as fixed coordinates.

As a result, ellipsoidal heights of the generated points are evaluated. Furthermore, geoid heights were found with the EGM08 geoid model using the obtained geographical coordinates and the transition to the orthometric height was achieved.

Process of the generated points related to the fixed coordinates resulted standard deviations of independent bases, σΔX, σΔY, σΔZ (Table 1); geodetic coordinates of the generated points and their standard deviations (Table 2).

Figure 6. Five Selected stations, ISTA, ISTN, YLDZ, SLEE, KARB, to be used as reference stations for adjustment calculations.

Figure5. Improved satellite data for generated point 103.

White parts indicate operations carried out to get the best resolution.

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Table 1. Standard deviations of the bases between fixed points and generated points.

Std. Std. Dev. Dev. Station Point (cm) Station Point (m) ΔX

ISTA

206

0.28 ΔX

ISTA

104

h 113.4581 m

h

112.6441 m

0.24 ΔZ

0.12 ISTA

103

0.28

ΔY

0.2

ΔY

0.16

ΔZ

0.23 ΔZ

0.28

ΔX

ISTA

204

0.16 ΔX

ISTA

102

101 φ 41°01'25.99516"N 0.11 201 φ 41°01'29.58009"N 0.0009 28°53'27.94009"E 0.0007

ΔZ

0.25 ΔX

Coordinates

λ

0.09

205

Coordinates

Std. Dev. (cm)

λ 28°53'20.17609"E 0.08

0.22 ΔY ISTA

No

Std. Dev. (cm) No

0.13

ΔY ΔX

Table2. Geodetic Coordinates (φ, λ, h) of generated points and their standard deviations.

0.3

0.22

0.0019

102 φ 41°01'27.16967"N 0.18 202 φ 41°01'28.09421"N 0.0012 λ 28°53'21.82798"E 0.13

λ

28°53'30.50850"E 0.0009

h 113.7969 m

h

110.7370 m

0.38

0.0024

103 φ 41°01'28.46736"N 0.17 203 φ 41°01'25.95267"N 0.0013 λ 28°53'23.28849"E 0.12

λ

28°53'33.66690"E 0.001

h 113.7849 m

h

106.8747 m

0.36

0.0028

ΔY

0.12 ΔY

0.17

ΔZ

0.14 ΔZ

0.29

λ 28°53'26.10719"E 0.05

λ

28°53'35.97422"E 0.0007

0.18

h 114.1265 m

h

102.9471 m

ΔX

ISTA

203

0.22 ΔX

ISTA

101

104 φ 41°01'31.04482"N 0.07 204 φ 41°01'23.09882"N 0.001

0.15

0.002

ΔY

0.16 ΔY

0.11

ΔZ

0.2

ΔZ

0.18

λ 28°53'27.15298"E 0.18

λ

28°53'39.55023"E 0.0012

0.27

h 114.5335 m

h

96.4864 m

ΔX

ISTA

202

0.19 ΔX YLDZ

206

ΔY

0.14 ΔY

0.22

ΔZ

0.17 ΔZ

0.24

ΔX

ISTA

201

0.15 ΔX YLDZ

205

0.24

ΔY

0.11 ΔY

0.2

ΔZ

0.14 ΔZ

0.22

ΔX

ISTA

107

0.2

ΔX YLDZ

204

0.13 ΔY

0.11

ΔZ

0.21 ΔZ

0.13

ISTA

106

0.39 ΔX YLDZ

203

0.21

ΔY

0.24 ΔY

0.15

ΔZ

0.35 ΔZ

0.19

ΔX

ISTA

105

0.4

ΔX YLDZ

202

0.49

0.0033

106 φ 41°01'33.91050"N 0.25 206 φ 41°01'20.19568"N 0.0015 λ 28°53'28.48824"E 0.17

λ

28°53'44.35319"E 0.0013

h 114.6706 m

h

94.1670 m

0.48

0.0037

107 φ 41°01'36.02458"N 0.14 λ 28°53'30.57997"E 0.09 h 115.0129 m

0.25

0.15

ΔY ΔX

105 φ 41°01'32.40615"N 0.25 205 φ 41°01'21.25331"N 0.0016

0.18

ΔY

0.22 ΔY

0.13

ΔZ

0.37 ΔZ

0.16

For the static measurements of the generated points, it was reached the result that the standard deviations of the all bases lower than the threshold value (10 mm) which is set by BÖHHBÜY. (Table 1) Furthermore, standard deviations of latitude and longitude (σφ, σλ), and standard deviations of ellipsoidal height (σh) are less than the limit values which are 3 cm and 5 cm respectively. (Table 2.)

In the second step, orthometric heights were attained using geoid undulations which are obtained from EGM08 via the well-known formula that indicates the relation between ellipsoidal and orthometric height; h= H+ Nj Here h, H and Ni are the illustration of the ellipsoidal height, orthometric height and geoid undulation respectively.

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Connected levelling was done for the flat area with 0.6 mm error closure and closed levelling was applied for sloping area with 2cm error closure using Leica model levelling instrument. After following processes were done such as adjustment and detecting outliers, orthometric heights were reached as in Figure 9.

Figure 7. Transition between Ellipsoidal and Orthometric Height for platform 1 (A) and platform 2 (B). Ellipsoidal Height calculated via post process of the 2-3 hours static GPS measurements; geoid height obtained from Earth Geoid Model 2008.

Figure 9. Orthometric Heights of generated points determined with least square method in platform 1 (A) and platform 2 (B).

We also compared redundancy of these two areas.

To be able to achieve it, following formulas and criteria were considered. ri = 1 - QiiPi

(1)

Qii = (A.Qxx.AT)

(2)

đ?‘ 0

Pi = diag(đ?‘ 1 ,

Figure 8. Orthometric heights of generated points and height differences between them, attaining from static measurements, for platform 1 (A) and platform 2 (B).

đ?‘ 0 đ?‘ 2

đ?‘ 0

‌ ‌ . . đ?‘ đ?‘› )

(3)

Where ri is redundancy, Pi is weighted matrix, Qii is weighted coefficient matrix of adjusted measures, A is matrix of coefficient, Qxx is weighted matrix of coefficient, s0 is unit length (1km) and s1, s2,.., sn are distances among points as km.

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STUDENT CONTEST 2018 0 â&#x2030;¤ ri < 0.01 uncontrolled measure 0 .01 â&#x2030;¤ ri < 0.10, poorly controlled measure 0.10 â&#x2030;¤ ri < 0.30 adequately controlled measure, 0.30 â&#x2030;¤ well-controlled measure.

As a result, it was reached that all measures were in well controlled part of the criteria above. However, when redundancy of flat area and sloping area were compared, it has been attained that measures of flat area were more well-controlled than the sloping area.

Figure 10. Redundancy values of Platform 1 (A) and platform 2 (B).

Transformation between ITRFs are obtained by following standard model, đ??ˇ đ?&#x2018;&#x2021;đ?&#x2018;Ľ đ?&#x2018;&#x2039;đ?&#x2018; đ?&#x2018;&#x2039; đ?&#x2018;&#x2026;đ?&#x2018;§ [đ?&#x2018;&#x152;đ?&#x2018; ] = [đ?&#x2018;&#x152; ] + [đ?&#x2018;&#x2021;đ?&#x2018;Ś] + [ â&#x2C6;&#x2019;đ?&#x2018;&#x2026;đ?&#x2018;Ś đ?&#x2018;?đ?&#x2018; đ?&#x2018;? đ?&#x2018;&#x2021;đ?&#x2018;§

â&#x2C6;&#x2019;đ?&#x2018;&#x2026;đ?&#x2018;§ đ??ˇ đ?&#x2018;&#x2026;đ?&#x2018;Ľ

đ?&#x2018;&#x2026;đ?&#x2018;Ś đ?&#x2018;&#x2039; â&#x2C6;&#x2019;đ?&#x2018;&#x2026;đ?&#x2018;Ľ] [đ?&#x2018;&#x152; ] đ??ˇ đ?&#x2018;?

Where X, Y, Z are the coordinates of current ITRF and Xs, Ys, Zs are coordinates in other frames which is want to transform.

Figure 11. Orthometric heights of generated points and height differences between them obtained by kinematic measurements connecting ISKI station for platform 1 (A) and platform 2 (B).

3. CORS-TR. In this section Kinematic (5 epoch(s)) measurements were done for all points on the two areas by connecting ISKI Station. Then, since CORS-TR is in ITRF2005, epoch 2005 but TUTGA-99A is in ITRF96 epoch 2005, we obtained heights both in ITRF96, epoch 2005 and in ITRF96, epoch 2005 to see if there are any differences between them. In the end, it has been reached same orthometric heights by using EGM08.

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Results.

Height differences obtained from Static GPS measurements, levelling and Kinematic measurements by connecting to ISKI-CORS were compared each other and demonstrate in Figure 12.

Although some effects that may create multipath in the point selection were tried to be avoided, since flat land, namely platform 1, is located on a treelines road on either side, the multipath effect in this region showed itself as an error. In comparison, the difference between the elevation changes on platform 1 is expected to be less; however, results of the sloping land, platform 2, was better in terms of closeness of elevation change comparison.

Despite this negativity, it was determined that all of the measurements made within the threshold values given in BÖHHBÜY. As a result of the investigation, it was concluded all comparisons belongs to the points on platform 1 are below 3 cm in all but 3 values and it was seen that highest values of elevation change differences between leveling-static, leveling-kinematic and static-kinematic measurements are 2.68±0.51 cm; 3.04±0.51 cm and 4.44±0.5 cm respectively.

(Figure 12, part A) In platform 2, it was also seen that highest values of elevation change differences between levelingstatic, leveling-kinematic and static-kinematic measurements are 1.715±0.47 cm; 2.35±0.47 cm and 3.16±0.47 cm respectively. Besides, it was determined that 72% of the comparisons were below 1 cm. (Figure 12, part B)

Figure 12. Differences of height differences and their standard deviations, for Leveling-Kinematic, Leveling-Static and Static-Kinematic on platform 1 (A) and platform 2 (B)

When the average value of differences between the elevation changes is ~0.8488 cm takes into account for in a region of 580 m distance and 20 m total elevation change, it has been reached as a conclusion that it can be used all three geodetic methods in engineering studies that do not require high accuracy, within the error bounds.

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References.

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