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Research article
Determination of the accuracy of leveling route based on GNSS/leveling and Earth gravitational model data SGG-UGM-2 at some typical regions in Vietnam
BUI THI HONG THAM, PHI TRUONG THANHH
Hanoi University of Natural Resources and Environment, Hanoi, Vietnam
How to cite this article: Bui Thi Hong Tham, Phi Truong Thanh. Determination of the accuracy of leveling route based on GNSS/leveling and Earth gravitational model data SGG-UGM-2 at some typical regions in Vietnam. Journal of Mining Institute. 2024. Vol. 265, p. 34-44. EDN UGMFEW
Abstract. This paper presents the accuracy of leveling routes determined by using GNSS/leveling at three grades and Earth gravitational model data SGG-UGM-2 in four regions of Vietnam by calculating the difference between the measured height anomalies and the model of pairs of points. The calculation is made based on the total points of three grades for four regions (99 in the Northwest, 34 in the Red River Delta, 130 in the Central Highlands, and 96 in the Mekong River Delta) with the leveling routes, connected between pair of points in each region are 189, 92, 294, and 203. The calculated results of the percentage of accuracy of the leveling routes of the four regions have shown that most of the leveling routes are satisfactory (grades I-IV, and technical leveling). The determination of the accuracy of the leveling route is completely applicable to other areas when the points have simultaneous ellipsoid and leveling heights and it also helps managers and surveyors to predict the accuracy of the height points when the above-mentioned leveling routes are connected and to take reasonable measures when implementing the project.
Keywords: Earth gravitational model; GNSS/leveling; height; accuracy; SGG-UGM-2
Acknowledgment. The article was written as part of the project TNMT.2022.562.04 by the Ministry of Natural Resources and Environment (MONRE), Vietnam.
Received: 25.06.2022 Accepted: 20.06.2023 Online: 29.11.2023 Published: 29.02.2024
Introduction. A height system is a one-dimensional coordinate system used to determine the metric distance of some points from a reference surface along a well-defined path, termed simply the height of that point [1]. Corresponding to the reference surface will give the type of height: the geoid reference surface will give the orthometric height, and the quasigeoid reference surface will give the normal height (also known as the leveling height). The reference surface is the ellipsoid which will give the ellipsoid height.
Most countries in the world have used the normal height system as the national height system. This height system is concretized by benchmarks (called national height points) buried in the field. The normal heights of benchmarks are determined based on the starting surface which is the average sea level for many years. National height points are control points serving the construction of all kinds of works for the socio-economic development, security, and defense of each country.
To establish topographic maps, cadastral maps, construction of civil and industrial works, traffic works, irrigation, mining, etc., height points are built. These points are connected with the national benchmarks from the leveling routes, and leveling closed loops. Therefore, if we know the accuracy of the leveling routes, we can predict the height accuracy of the connection points with those national height points.
In order to determine the accuracy of the leveling routes to achieve grade, it usually takes the following steps: measure in the field; process measurement data to calculate the mean square error
per one km leveling route; compare the mean square error per one km leveling route with the permitted measurement error for leveling grades [2-6].
The accuracy of the leveling route is determined after the process of measuring and processing data, which wastes time and money, especially if the leveling route does not reach the required accuracy. Therefore, the idea of this study is to determine the accuracy of the leveling route without having to take measurements in the field. To carry out this study, the Earth gravitational model and GNSS/leveling data were used.
An Earth gravitational model (EGM) is a set of geopotential coefficients used in a spherical harmonic expansion to create a global potential surface to coincide with the Mean Sea Level (MSL). This model is used as the reference geoid in the WGS. Basically, Earth gravity model data are provided in two formats: as a series of spherical harmonic coefficients determining the model and as a geoid height of the point which have a coordinate. A GNSS point that has an ellipsoid height and leveling height is called a GNSS/leveling point.
GNSS/leveling data and Earth gravitational model play an important role in studies of the geoid, and national height systems and it is the input data source to carry out studies, such as:
The GNSS/leveling data is used to evaluate the accuracy of the global gravity model such as: evaluating and comparing models GOCE, EGM2008 in the Mediterranean area [7], Japan [8]; evaluating models EGM08, EIGEN-6C4, GECO in Iran [9], Turkey [10]; evaluating model EGM2008 [11]; comparing model XGM2019e with XGM2016, EIGEN-6C4, EGM2008 [12]; compare models EGM2008 and EGM96 in Iraq [13]; evaluating model EGM2008, EIGEN-6C4, XGM2019e_2159 in Korea [14]; comparing model EIGEN-6C4 with EGM2008 in Europe, USA, Canada, Brazil, Japan, Czech Republic and Slovakia [15]; evaluating the accuracy of models EGM2008, EIGEN-6C4, GECO, and SGG-UGM-1 in Kenya [16]; evaluating models EGM2008, EIGEN6C4, and GECO in the Aegean region [17]; evaluating models EGM96, EGM84, and EGM2008 in Iraq [18]; comparing models EGM96 and EGM2008 in Iraq [19]; comparing models OUS-91A, EGM96, and EGM2008 in Egypt [20]; evaluating model EGM2008 in Bangladesh [21]. GNSS/leveling data was used to build local geoid models such as in Iraq [19], Turkey [22], Evboriaria, Benin City (Nigeria) [23].
GNSS/leveling data were used to correct the global gravity model and build a local geoid model: the model EGM2008 and GNSS/leveling data to build a local geoid model in Indonesia [24], Nigeria [25], Vietnam [26], Turkey [27], Egypt [28], China [29], the USA [30]; model EIGEN6C4, leveling data, GNSS to build a local geoid model in Uganda [31].
GNSS/leveling data and the global gravity model were used to build the height system in Italy [32], the GNSS/leveling data and the model EGM2008 to build the height system in Palestine [33]; the GNSS/leveling was together with GOCE data to estimate the height reference system in Canada [34].
GNSS/leveling data, global gravity model and other data were used to build local geoid model: GNSS/leveling together with EGM2008 data, digital terrestrial model to determine geoid model in Mexico [35]; GNSS/leveling together with EIGEN-6C4 gravity data to build geoid model in Qatar [36]; GNSS/leveling together with GOCE data to build geoid models in the state of Sao Paulo (Brazil) [37]; GNSS/leveling together with model data XGM2019e_2159, digital terrestrial model ACE2 GDEM to build geoid model in Egypt [28]; GNSS/leveling together with model data EGM2008, EIGEN-6C4, gravity data, high-resolution topographic data, bathymetric data to build geoid model in Vietnam [38].
GNSS/leveling data and Earth gravitational model are indispensable factors when studying height-related issues in countries. It is an input data source to support evaluating the accuracy of the global gravity model, building the national height system, and the local geoid model.
In this study, based on the GNSS/leveling data and Earth gravitational model, the theoretical basis for determining the accuracy of the leveling routes is presented logically and rigorously. Based on the collected data, the experimental areas are selected as the areas in the territory of Vietnam.
Theoretical basis. The relationship between the ellipsoid height h and the normal height H is presented by the formula
ZGNSS/leveling ~ h -H , (1)
where CG^s/being - height anomaly of point i.
The height anomaly value can also be determined based on the Earth gravitational model. To determine the accuracy of the leveling route connecting the national GNSS/leveling points, the value of the height anomaly when determined according to the GNSS/leveling data is compared with the corresponding data taken from the Earth gravitational model.
Suggested ZLdei is the height anomaly of the point i extracted from the Earth gravitational model. The formula for calculating the height anomaly of the point i is written as follows:
AZ, = ZGNSS/leveling - Zmodel = h -H - Zmodel. (2)
Calculate the average value of the deviation of height anomaly according to the following formula
n ■ l
AZaverage = Z A? /«, (3)
i = 1
where n - is point numbers.
The deviation of the pair of points i and j (Fig. 1) are calculated according to the following formula
A?ij =AZj -AC'. (4)
Combination of formula (2) and (3), get
AZj = h - h -(W - H' )-(Z model - Zmodel ) . (5)
Assign formulas
Ahv = h - h; AW = Hj - H;
AZj = Zj - Z' ■ AZ= Ah'j - AH'j
AZmodel Zmodel Zmodel; AZGNSS/leveling Ah ,
(6)
2
* l y * get the equation
V \ f
V \ f S
The weight of the equation (6) is calculated according to the ",■,> " * formula
^ / ^ J \ ^ 1
t \ X P'J=—, (8)
• where D - is the distance between points i and /, km.
The mean square error of the height anomaly difference over Fig.i. Pairs of points one kilometer is calculated according to the following formula
1
[ PAZ ' AZ;
q
(9)
where q - is the number of pairs of points used to perform the calculation.
The national standard on building height networks, the permited error for leveling route, leveling closed loop according to the grade are specified. In Vietnam, for mountainous areas, the permited error for leveling route, leveling closed loop of grades I, II, III, IV is 3>/L, 5>/L, 12^/L , 25^L (L is in mm); respectively; for in the plains, these errors are 2%[b , , 10>/L, 2oVL, respectively; for technical leveling, the error is 50^L (L is in km).
Vietnam is a country which has mostly low hills and mountains, with plains making up about a quarter of the area. Based on topography and economic development, Vietnam is divided into the following regions:
• Northwest region - terrain with many high mountain ranges;
• Northeast region - low hills;
• Red River Delta - relatively flat terrain, it is the economic center of the northern region of Vietnam;
• North central coast - mixed topography of mountains, hills and plains;
• South central coast - low mountains and plains;
• Highlands region - diverse topography, includes: high mountains, plateaus and large plains;
• Southeast region - midlands and low hills;
• Southwest region or Mekong River Delta - terrain is relatively flat, quite low compared to sea level, often affected by tides.
According to the national standard on building height networks, with different topographical areas, the error of leveling route, leveling closed loop according to their grades is different. Therefore, the areas having a typical topography of Vietnam are selected for research including: Northwest, Red River Delta, Central Highlands, Mekong River Delta. Data sources used in the analysis include GNSS/Leveling data and Earth gravitational model data.
GNSS/leveling data. The points number of national GNSS/leveling in each experimental area is listed in Table 1. The leveling and geodetic heights of the GNSS/leveling points are detailed in Table 2.
Table 1
GNSS/ leveling points
Region Number of GNSS/ leveling points Total
Grade I Grade II Grade III
Northwest 35 16 48 99
Red River Delta 20 11 3 34
Highlands 24 26 80 130
Mekong river Delta 13 52 31 96
Data of GNSS/leveling points
Table 2
Points number Point index B0 L0 h, m H, m
1 I(BMT-APD)12 12.28926 107.59477 907.6780 907.9755
2 I(BMT-APD)1-2 12.65835 108.02837 431.3888 431.2042
3 I(BMT-APD)16 12.10935 107.65618 833.2335 832.9730
4 I(BMT-APD)22 11.99578 107.51564 732.3017 732.6708
End of Table 2
Points number Point index B0 L0 h, m H, m
5 I(BMT-APD)25 11.93166 107.42908 575.1619 576.0473
6 I(BMT-APD)3 12.58108 107.84340 358.1393 358.6506
7 I(BMT-APD)6 12.49414 107.74019 580.5556 581.0788
8 I(BMT-NH)11-1 12.80411 108.54048 468.5150 466.5640
9 I(BMT-NH)17-1 12.73304 108.75417 423.7629 420.9371
10 I(BMT-NH)22 12.58583 108.85847 561.2232 557.7819
351 III(TT-GR)4 9.95520 105.36885 -5.6633 0.9933
352 III(TT-HN)2 10.92092 105.42574 -4.3237 4.1669
353 III(TT-TS)1 10.25559 105.16435 -5.4807 2.6149
354 III(TV-LS)9 9.71773 106.42700 -0.1141 2.0210
355 III(TY-VD)9 9.22404 104.81945 -6.3808 0.4914
356 III(UM-HDB)7 10.52037 104.70823 -8.4336 2.0185
357 III(VL-MC)7 10.23367 106.18661 -2.0257 1.8265
358 III(VT-PS)5 9.37355 105.39224 -4.1265 1.1779
359 III(VT-VC)7 9.29983 105.93297 -1.2964 1.4918
Earth gravitational model data. The Earth gravitational model SGG-UGM-2 is the latest model published in 2020. The data of this model can be accessed at the website of the International Center for Global Earth Models (ICGEM) (http://icgem.gfz-potsdam.de/tom). Height anomaly data of GNSS/leveling points got from the Earth gravitational model are listed in Table 3.
Table 3
Height anomaly data of GNSS/leveling points got from Earth gravitational model
Points number Point index Z SGG —U GM—2' m Points number Point index ZSGG—UGM—2 ' m
1 I(BMT-APD)12 -0.6568
2 I(BMT-APD)1-2 -0.4138 351 III(TT-GR)4 -6.9711
3 I(BMT-APD)16 -0.0710 352 III(TT-HN)2 -9.1764
4 I(BMT-APD)22 -0.6639 353 III(TT-TS)1 -8.7063
5 I(BMT-APD)25 -1.1798 354 III(TV-LS)9 -2.4782
6 I(BMT-APD)3 -1.0340 355 III(TY-VD)9 -7.1055
7 I(BMT-APD)6 -1.0081 356 III(UM-HDB)7 -11.1486
8 I(BMT-NH)11-1 1.3586 357 III(VL-MC)7 -4.1515
9 I(BMT-NH)17-1 2.3220 358 III(VT-PS)5 -5.4536
10 I(BMT-NH)22 3.0755 359 III(VT-VC)7 -3.1043
Results and discussions. The accuracy of the leveling routes is carried out according to the following steps:
1. Calculate the height anomalies from measurement data GNSS/leveling ZoNss/ieveiing (formula (2).
2. Calculate the deviation of hight anomaly between the measured height anomalies and model AZ'. The mean value of high anomaly AZaverage is calculated in formula 3.
3. Calculate the deviation of height anomalies of the pairs of points A Z (formula (5).
4. Calculate the weight of the leveling route P (formula (8).
5. Calculate the mean square error of the height anomaly difference per kilometer (formula (9) for each leveling route and for four regions.
6. Calculate the permited error for each leveling route wpemited.
7. Compare the mean square error of the height anomaly difference per kilometer of each leveling route with the permited error.
The calculated results in steps 1 and 2 are shown in Table 4 and Fig.2.
Table 4
Height anomalies from measurement data GNSS/leveling and their deviation and the model value
Points number Point index Z GNSS/leveling , m AÇ ', m Points number Point index Z GNSS/leveling , m AÇ ', m
1 I(BMT-APD)12 -0.2975 0.3593
2 I(BMT-APD)1-2 0.1846 0.5984 351 III(TT-GR)4 -6.6566 0.3145
3 I(BMT-APD)16 0.2605 0.3315 352 III(TT-HN)2 -8.4906 0.6858
4 I(BMT-APD)22 -0.3691 0.2948 353 III(TT-TS)1 -8.0956 0.6107
5 I(BMT-APD)25 -0.8854 0.2944 354 III(TV-LS)9 -2.1351 0.3431
6 I(BMT-APD)3 -0.5113 0.5227 355 III(TY-VD)9 -6.8722 0.2333
7 I(BMT-APD)6 -0.5232 0.4849 356 III(UM-HDB)7 -10.4521 0.6965
8 I(BMT-NH)11-1 1.9510 0.5924 357 III(VL-MC)7 -3.8522 0.2993
9 I(BMT-NH)17-1 2.8258 0.5038 358 III(VT-PS)5 -5.3044 0.1492
10 I(BMT-NH)22 3.4413 0.3658 359 III(VT-VC)7 -2.7882 0.3161
<3
1.2 0.8
0.4
0.0
-0.4 -0.6
<3
0.6
0.4
0.2
0.0
Number of GNSS/leveling points
1 15 29 43 57 71 85 99 113 127 Number of GNSS/leveling points
<3
1.0
0
0.6
0.4
0.2
0.0
1.0
0.8 0.6
¥ 0.4 0.2 0.0
1
6 11 16 21 26 31 Number of GNSS/leveling points
1 16 31 46 61 76 Number of GNSS/leveling points
91
b
a
1
d
c
0
Fig.2. Height anomaly of model SGG-UGM-2 with the height anomaly of the GPS/ leveling: a - Northwest; b - Red River Delta; c - Central Highlands; d - Mekong River Delta
Figure 2 shows that the topography of the four regions is generally higher than the model SGG-UGM-2. The average value of the deviation of height anomaly of the GNSS/leveling points between the measurements and model makes in the Northwest 0.4249 m, Red River Delta 0.6369 m, Central Highlands 0.4638 m, and Mekong River Delta 0.3588 m.
The calculated results in steps 3 and 4. From the GNSS/leveling points at the four regions, the leveling routes are formed based on pairs of points with the number of routes in the Northwest region 189, Red River Delta 92, Central Highlands 294, and Mekong River Delta 203. The measured height anomaly values and models of GNSS/leveling routes are shown in Table 5.
Table 5
The deviation of height anomalies of the national GNSS/leveling of pairs of points
Points number Start point End point D, km AZ GNSS/leveling ' m AÇmodel = m AÇ«, m P
1 I(BMT-APD)12 I(BMT-APD)16 21.0 -0.5580 -0.5858 0.0278 0.048
2 I(BMT-APD)12 III(DBS-DL)3 23.4 0.3530 0.1683 0.1847 0.043
3 I(BMT-APD)12 III(QS-DN)2 29.8 -1.1846 -1.2386 0.0540 0.034
4 I(BMT-APD)12 III(BDS-QP)5 33.0 -0.7274 -0.4316 -0.2958 0.030
5 I(BMT-APD)22 I(BMT-APD)25 11.8 0.5163 0.5159 0.0004 0.085
6 I(BMT-APD)22 I(BMT-APD)16 19.8 -0.6296 -0.5930 -0.0366 0.050
7 I(BMT-APD)25 I(BMT-APD)30 24.0 0.9462 0.9868 -0.0406 0.042
8 I(BMT-APD)25 III(BGM-MH)3 32.7 1.6841 1.8078 -0.1237 0.031
9 I(BMT-APD)3 I(BMT-APD)6 14.8 0.0119 -0.0259 0.0378 0.068
10 I(BMT-APD)3 III(BDS-QP)5 21.3 -0.9412 -0.8088 -0.1324 0.047
767 III(TT-HN)2 II(HN-AB)7 23.7 -0.7255 -1.0619 0.3364 0.042
768 III(TT-TS)1 II(CD-VC)8 32.3 -0.1642 -0.5622 0.3980 0.031
769 III(UM-HDB)7 III(OD-CN)1 26.1 -0.7561 -0.6581 -0.0980 0.038
770 III(VL-MC)7 II(TL-TV)5-1 17.5 -0.6959 -0.6593 -0.0366 0.057
771 III(VL-MC)7 II(MT-TV)6-1 17.6 -0.1647 -0.1954 0.0307 0.057
772 III(VL-MC)7 III(LH-TH)1 21.6 0.3888 0.4602 -0.0714 0.046
773 III(VL-MC)7 I(VL-HT)273A 23.1 -0.3478 -0.3374 -0.0104 0.043
774 III(VL-MC)7 II(TX-TL)25 24.9 1.1117 1.1544 -0.0427 0.040
775 III(VL-MC)7 I(VL-HT)284A 29.2 -1.1320 -0.9975 -0.1345 0.034
776 III(VT-PS)5 II(SC-PL)34 20.7 0.9892 0.9625 0.0267 0.048
777 III(VT-PS)5 II(SC-PL)15 21.9 0.6785 0.5949 0.0836 0.046
778 III(VT-VC)7 II(ST-PL)2 27.5 -0.7561 -0.6581 -0.0980 0.036
The calculated results from steps 5 to 7. The mean square error of the height anomaly difference over 1km of the four regions is calculated according to the formula (9):
„ , . /0.0526
for Northwest region = J « ±0.0516 m;
for Red River Delta region = J^^^^^ ~ ±0.0249 m;
for Central Highlands region mm = for Mekong River Delta region =
0.2368
294
±0.0284 m;
0.0521 ' 203
±0.0160 m.
To determine the accuracy of each leveling route, it is necessary to define two types of errors:
• the mean square error of the height anomaly difference over one km shows the accuracy of the leveling route that is calculated according to the formula (9); in case if it has only one leveling route, q = 1 and P = 1 and the mean square error of the height anomaly difference over 1 km will be calculated according to formula m= ^A^A1 J;
• the permitted error is also caculated for each leveling route based on the topography of the area. If the terrain is plain, the value of L = 1.1D (distance between two points), if the terrain is mountainous, the value of L = 1.3D.
The error value for each leveling routes is shown in Table 6.
Table 6
Error of the leveling routes
Points number Start point End point |rnkm|, mm Absolute value of permitted error, mm Achieved grade of leveling route
Grade I Grade II Grade III Grade IV Technical leveling
1 I(BMT-APD)12 I(BMT-APD)16 27.8 15.7 26.1 62.7 130.6 313.6 Grade III
2 I(BMT-APD)12 III(DBS-DL)3 184.7 16.5 27.6 66.2 137.9 330.9 Technical
3 I(BMT-APD)12 III(QS-DN)2 54.0 18.7 31.1 74.7 155.6 373.3 Grade III
4 I(BMT-APD)12 III(BDS-QP)5 295.8 19.7 32.8 78.7 163.9 393.3 Technical
5 I(BMT-APD)22 I(BMT-APD)25 0.4 11.8 19.6 47.0 97.9 235.0 Grade I
6 I(BMT-APD)22 I(BMT-APD)16 36.6 15.2 25.4 60.9 126.9 304.5 Grade III
7 I(BMT-APD)25 I(BMT-APD)30 40.6 16.8 27.9 67.0 139.6 335.1 Grade III
8 I(BMT-APD)25 III(BGM-MH)3 123.7 19.6 32.6 78.3 163.0 391.3 Grade IV
9 I(BMT-APD)3 I(BMT-APD)6 37.8 13.2 21.9 52.6 109.6 263.1 Grade III
10 I(BMT-APD)3 III(BDS-QP)5 132.4 15.8 26.3 63.1 131.5 315.6 Technical
767 III(TT-HN)2 II(HN-AB)7 336.4 10.2 20.4 51.1 102.1 255.4 Unsatisfactory
768 III(TT-TS)1 II(CD-VC)8 398.0 11.9 23.8 59.6 119.2 298.0 Unsatisfactory
769 III(UM-HDB)7 III(OD-CN)1 98.0 10.7 21.4 53.6 107.2 268.1 Grade IV
770 III(VL-MC)7 II(TL-TV)5-1 36.6 8.8 17.6 43.9 87.8 219.5 Grade III
771 III(VL-MC)7 II(MT-TV)6-1 30.7 8.8 17.6 44.0 87.9 219.9 Grade III
772 III(VL-MC)7 III(LH-TH)1 71.4 9.8 19.5 48.8 97.6 243.9 Grade IV
773 III(VL-MC)7 I(VL-HT)273A 10.4 10.1 20.2 50.4 100.9 252.1 Grade II
774 III(VL-MC)7 II(TX-TL)25 77.8 10.5 20.9 52.4 104.7 261.8 Grade IV
775 III(VL-MC)7 I(VL-HT)284A 42.7 11.3 22.7 56.6 113.3 283.2 Grade III
776 III(VT-PS)5 II(SC-PL)34 134.5 9.5 19.1 47.7 95.4 238.5 Technical
777 III(VT-PS)5 II(SC-PL)15 26.7 9.8 19.6 49.1 98.2 245.4 Grade III
778 III(VT-VC)7 II(ST-PL)2 83.6 11.0 22.0 55.0 110.0 274.9 Grade IV
The sum of leveling routes corresponding to the grades for each region in Table 6 is listed in Table 7. The number of leveling routes of each grade in four regions are calculated as the number of leveling routes of each grade divided by the total number of leveling routes of each respective region.
Table 7
Number of leveling routes achieved grades and percentage of accuracy
Region Number of leveling routes achieved grades Accuracy, %
Satisfactory Unsatisfactory
Grade I Gradell Grade III Grade IV Technical leveling Unsatisfactory Total Grade I Grade II Grade III Grade IV Technical leveling
Northwest 13 7 25 45 68 31 189 6.9 3.7 13.2 23.8 36.0 16.4
Red River Delta 9 7 15 28 30 3 92 9.8 7.6 16.3 30.4 32.6 3.3
Central Highlands 31 15 62 97 85 4 294 10.5 5.1 21.1 33.0 28.9 1.4
Mekong River Delta 16 14 35 51 67 20 203 7.9 6.9 17.2 25.1 33.0 9.9
The percentage of accuracy of the leveling routes of the four regions of Vietnam show that most of the leveling routes in the four regions are satisfactory (grades I-IV and Technical leveling). The highest grade that can be obtained for the leveling routes in all four experimental regions is grade I.
Conclusions. The results of determining the accuracy of the leveling routes from GNSS/leveling data and Earth gravity model SGG-UGM-2 at four regions - Northwest, Red River Delta, Central Highlands, Mekong River Delta - by calculating the difference between the measured height anomalies and the model of pairs of points with the leveling routes, connected between pair of points in each region showed that most of the percentage of accuracy of the leveling routes of the four regions are satisfactory.
The effect of determining the accuracy of leveling routes allows to save time and money, since there is no need to take measurements in the field. The determination of the accuracy of the leveling route is completely applicable to other areas if the points have both geodetic and leveling heights.
From these results, managers and surveyors can predict the accuracy of the elevation points when the above-mentioned leveling routes are connected to take reasonable measures when implementing the project.
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Authors: Bui Thi Hong Tham, PhD, Dean, https://orcid.org/0000-0002-3932-4040 (Hanoi University of Natural Resources and Environment, Hanoi, Vietnam), Phi Truong Thanh, Associate Professor, Dean, ptthanhdc@hunre.edu.vn, https://orcid.org/0000-0003-0421-6557(Hanoi University of Natural Resources and Environment, Hanoi, Vietnam).
The authors declare no conflict of interests.
