Reliability assessment of three topographic methods for generating digital elevation models (DEMs)

Rodrigo Roblero-Hidalgo; Jorge Flores-Velázquez; Jesús Chávez-Morales; Aurelio Reyes-Ramírez

Scientific article

Received: 31 December 2019

Accepted: 21 July 2020

DOI: https://doi.org/10.5154/r.inagbi.2020.01.005

Abstract

Introduction: A digital elevation model (DEM) allows for the analysis of specific features on the earth's surface in three dimensions. The engineering DEM is useful to evaluate resources and design management strategies.

Objective: To evaluate the technical-operational feasibility of generating DEMs from total station (TS) topographic surveys, GPS RTK and aerial photogrammetry using an unmanned aerial vehicle (UAV).

Methodology: A 20x20 m grid was traced in a plot without vegetation (1.4 ha) located in Montecillo, Estado de México, and topographic surveys were carried out with three methods, from which DEMs were generated for graphic and statistical evaluation and by tracing contour lines.

Results: The estimated statistical errors were 0.15, 0.15 and 0.02 m, for TS vs. UAV, GPS RTK vs. UAV and TS vs. GPS RTK, respectively.

Study limitations: The instruments used and the geographical conditions of central Mexico may be a reason for variation when extrapolating the results with other devices.

Originality: A methodology is provided to generate DEMs accurately. The results allow the user to make reasoned choices based on the equipment available.

Conclusion: The DEMs generated with TS and GPS RTK data have a smaller error than the one obtained from UAVs. The use of UAV helps in the representation of the terrain, since it generates a dense cloud of points that strengthens the procedure for topographic surveys.

Keywords: accuracy, topographic method, drone, orthomosaic.

Resumen

Introducción: Un modelo digital de elevación (MDE) permite analizar rasgos específicos sobre la superficie terrestre en tres dimensiones. El MDE en ingeniería es útil para evaluar recursos y diseñar estrategias de manejo.

Objetivo: Evaluar la viabilidad técnica-operativa de generar MDE a partir de levantamientos topográficos con estación total (ET), GPS RTK y fotogrametría aérea usando un vehículo aéreo no tripulado (VANT).

Metodología: Se trazó una cuadrícula de 20 x 20 m en una parcela sin vegetación (1.4 ha) ubicada en Montecillo, Edo. de México, y se realizaron levantamientos topográficos con tres métodos, a partir de los cuales se generaron los MDE para su evaluación gráfica, estadística y mediante el trazo de curvas de nivel.

Resultados: Los errores estadísticos estimados fueron de 0.15, 0.15 y 0.02 m, para ET vs. VANT, GPS RTK vs. VANT y ET vs. GPS RTK, respectivamente.

Limitaciones del estudio: El instrumental usado y las condiciones geográficas del centro de México pueden ser motivo de variación al momento de extrapolar los resultados con otros dispositivos.

Originalidad: Se proporciona una metodología para generar MDE con precisión. Los resultados permiten al usuario tomar decisiones razonadas en función del equipo con el que dispone.

Conclusión: Los MDE generados con datos de ET y GPS RTK tienen un error menor que el obtenido a partir de VANT. El uso del VANT ayuda en la representación del terreno, ya que genera una densa nube de puntos que fortalece el procedimiento para levantamientos topográficos.

Palabras clave: precisión, método topográfico, dron, ortomosaico.

Introduction

A digital elevation model (DEM) is the graphical representation of databases containing a numerical format of terrain elevations. A DEM shows, in a simplified and numerical way, the geometry of a part of the terrain surface (Mena-Frau, Molina-Pino, Ormazábal-Rojas, & Morales-Hernández, 2011), which can be represented by a set of values indicating points on the surface, and its geographical location is defined by X (longitude), Y (latitude) and Z (altitude) coordinates. It has been agreed that these points are regularly spaced and distributed according to a pattern that, in general, is located in a geographical projection such as the Universal Transverse Mercator (UTM) (Zhoua & Chenb, 2011).

The techniques to carry out topographic surveys with less error are the total station (TS) and GPS RTK; the development of unmanned aerial vehicles (UAV) have enriched the traditional techniques to improve them; this because they generate greater detail of the surface from images or videos taken during the flight. The evolution of computer systems, technological advances in UAV systems and strategies for processing large volumes of data promote research and application (Escalante-Torrado, Cáceres-Jiménez,& Porras-Díaz, 2016). The increasingly recurrent use of UAVs has diversified their application (Colomina & Molina, 2014); however, the basic products generated are images and videos (Ojeda-Bustamante et al., 2016). In this study, their application is focused on the processing needed to obtain orthomosaics and DEMs from photographic images obtained with an airborne camera.

The applications of DEMs obtained from UAVs are diverse, some of which are the generation of terrain models with topographic use (Liu, Liu, Zou, Wang, & Liu, 2012) and surface models in coastal areas (Long et al., 2016), used in agriculture (Mesas-Carrascosa et al, 2015), in forest engineering (Leduc & Knudby, 2018) and archaeology (Toschi et al., 2015), landslide studies (Permata et al., 2016), and monitoring of mine extraction (Wang et al., 2014), of disaster areas (Bendea et al., 2008), and infrastructure damage (Vázquez-Paulino& Backhoff-Pohls, 2017). The objective of this study was to evaluate the technical and operational feasibility of generating DEMs from images obtained with a camera transported in a UAV, and from topographic surveys with TS, as a direct measurement method, and with a geographic positioning system (GPS RTK). Survey errors were compared and evaluated using statistical indicators to clarify advantages and disadvantages.

Materials and methods

Description of the study area

MDEs were carried out on a plot located at the Colegio de Postgraduados, Campus Montecillo, Texcoco, Estado de México, with an area of 1.4 ha (Figure 1 and 2). The equipment used for the topographic surveys were: TS (CST Berger CST305R), GPS RTK (Sokkia GRX1) and camera for the UAV (Phantom 4 pro) (Table 1).

Figure 1
Location of the plot studied (Colegio de Postgraduados, Mexico).

Figure 2
Twenty m grid drawn in the field.

Table 1
Specifications of the topographic equipment.

A grid with 20 m separation in both directions (X, Y) was drawn on the ground. At each junction, a plummet tool was placed at ground level and it was marked with a target (36 control points), so that they could be visible at 28.7 m flight height and have a ground pixel resolution of 2.74 cm∙pix^-1, with a flight time of 5 min, an overlap of 80%, a focal length of 3.61 mm and an electronic shutter (Figure 2).

As a reference point (level bank) to start the ground survey, control points were set with the GPS RTK, the following UTM coordinates of zone 14N were selected: XG_base = 510 685.680 m, YG_base = 2 152 639.377 m and ZG_base = 2 239.327 masl. Subsequently, with the GPS RTK, the 36 checkpoints marked on the ground were raised. The reference point obtained with GPS RTK was used for the survey with TS. This method is considered the reference method for comparing the errors obtained with GPS RTK and photogrammetry. For the photogrammetric survey, a digital camera was used, transported in a UAV (Table 1). The procedure for the flight was suggested by Ojeda-Bustamante et al.(2016), which consists of a flight plan of the trajectory that the UAV will follow to take the photographs at a certain height, in this case 28.7 m. This plan is established in Pix4Dcapture and the images obtained will be treated to obtain the mosaic from which the DEM is generated.

Each method has a processing step in which the information of the UTM coordinates for each point of the grid (i = 1, 2, 3, ..., 36) is obtained (Table 2). With the GPS RTK, the coordinates of the points marked in the field were obtained, as well as the table of attributes of each point, which was exported to *.shp format. The generation of the DEM was possible from the *.shp file, from which a triangular facet network or triangle irregular network (TIN) was elaborated and converted to raster mode; from this, the DEM (n = 3 083 342 cells) was generated containing the values of the UTM coordinates (longitude [XG_i], latitude [YG_i] and altitude [ZG_i]).

Table 2
Universal Transverse Mercator coordinates (UTM, from zone 14N) obtained with three topographic survey methods.

Point	Total Station			GPS RTK			Unmanned aerial vehicle
i	XE_i	YE_i	ZE_i	XG_i	YG_i	ZG_i	XV_i	YV_i	ZV_i
1	510 610.475	2 152 731.599	2 238.514	510 610.522	2 152 731.499	2 238.525	510 610.630	2 152 731.541	2 238.382
2	510 624.827	2 152 727.436	2 238.750	510 624.896	2 152 727.354	2 238.757	510 625.009	2 152 727.408	2 238.639
3	510 644.290	2 152 722.450	2 238.873	510 644.323	2 152 722.332	2 238.873	510 644.379	2 152 722.427	2 238.837
4	510 663.664	2 152 717.380	2 238.970	510 663.642	2 152 717.284	2 238.943	510 663.716	2 152 717.357	2 238.938
5	510 682.654	2 152 711.740	2 239.081	510 682.694	2 152 711.646	2 239.060	510 682.664	2 152 711.764	2 239.008
6	510 701.896	2 152 706.119	2 239.183	510 701.884	2 152 706.014	2 239.150	510 701.860	2 152 706.104	2 238.990
7	510 696.142	2 152 687.027	2 239.101	510 696.144	2 152 686.935	2 239.097	510 696.124	2 152 687.058	2 239.108
8	510 677.019	2 152 692.462	2 239.034	510 677.037	2 152 692.364	2 239.030	510 677.028	2 152 692.463	2 239.126
9	510 657.602	2 152 697.614	2 238.996	510 657.614	2 152 697.496	2 238.985	510 657.641	2 152 697.558	2 239.095
10	510 638.307	2 152 702.941	2 238.852	510 638.380	2 152 702.882	2 238.853	510 638.407	2 152 702.959	2 238.963
11	510 619.092	2 152 708.342	2 238.715	510 619.186	2 152 708.259	2 238.732	510 619.261	2 152 708.289	2 238.767
12	510 604.776	2 152 712.444	2 238.642	510 604.847	2 152 712.339	2 238.647	510 604.933	2 152 712.372	2 238.583
13	510 599.001	2 152 693.325	2 238.607	510 599.079	2 152 693.251	2 238.605	510 599.177	2 152 693.253	2 238.625
14	510 613.611	2 152 689.539	2 238.737	510 613.689	2 152 689.479	2 238.748	510 613.777	2 152 689.469	2 238.847
15	510 632.757	2 152 684.177	2 238.851	510 632.770	2 152 684.099	2 238.839	510 632.814	2 152 684.108	2 239.031
16	510 651.952	2 152 678.753	2 238.907	510 651.970	2 152 678.678	2 238.893	510 652.015	2 152 678.703	2 239.130
17	510 671.176	2 152 673.282	2 238.992	510 671.194	2 152 673.200	2 238.983	510 671.172	2 152 673.264	2 239.177
18	510 690.451	2 152 667.849	2 239.107	510 690.470	2 152 667.757	2 239.103	510 690.410	2 152 667.792	2 239.177
19	510 684.846	2 152 648.640	2 239.105	510 684.889	2 152 648.606	2 239.091	510 684.853	2 152 648.570	2 239.147
20	510 665.441	2 152 654.111	2 238.971	510 665.480	2 152 654.058	2 238.959	510 665.418	2 152 654.047	2 239.161
21	510 646.234	2 152 659.474	2 238.898	510 646.260	2 152 659.416	2 238.921	510 646.243	2 152 659.386	2 239.133
22	510 626.901	2 152 664.990	2 238.806	510 626.940	2 152 664.925	2 238.809	510 626.952	2 152 664.881	2 239.002
23	510 607.654	2 152 670.154	2 238.721	510 607.679	2 152 670.078	2 238.725	510 607.768	2 152 670.025	2 238.829
24	510 593.197	2 152 674.242	2 238.603	510 593.242	2 152 674.160	2 238.603	510 593.310	2 152 674.106	2 238.614
25	510 587.249	2 152 655.132	2 238.537	510 587.334	2 152 655.123	2 238.544	510 587.388	2 152 655.025	2 238.512
26	510 602.386	2 152 650.859	2 238.624	510 602.454	2 152 650.826	2 238.627	510 602.554	2 152 650.739	2 238.706
27	510 621.500	2 152 645.078	2 238.752	510 621.577	2 152 645.061	2 238.759	510 621.620	2 152 645.037	2 238.898
28	510 640.709	2 152 639.405	2 238.813	510 640.738	2 152 639.356	2 238.794	510 640.788	2 152 639.317	2 238.986
29	510 660.052	2 152 634.361	2 238.907	510 660.081	2 152 634.327	2 238.907	510 660.004	2 152 634.288	2 239.040
30	510 679.468	2 152 629.564	2 238.996	510 679.474	2 152 629.511	2 238.992	510 679.398	2 152 629.481	2 239.031
31	510 673.829	2 152 610.339	2 239.123	510 673.869	2 152 610.335	2 239.113	510 673.761	2 152 610.264	2 238.941
32	510 658.811	2 152 614.818	2 238.835	510 658.823	2 152 614.817	2 238.831	510 658.768	2 152 614.760	2 238.868
33	510 639.463	2 152 619.831	2 238.705	510 639.533	2 152 619.833	2 238.701	510 639.487	2 152 619.761	2 238.815
34	510 620.146	2 152 624.857	2 238.635	510 620.161	2 152 624.858	2 238.631	510 620.186	2 152 624.757	2 238.719
35	510 600.958	2 152 630.379	2 238.595	510 601.016	2 152 630.326	2 238.594	510 601.057	2 152 630.188	2 238.584
36	510 581.769	2 152 635.956	2 238.554	510 581.881	2 152 635.931	2 238.533	510 581.924	2 152 635.806	2 238.364

From the two support points placed with the RTK GPS the survey was carried out with the TS. To do this, the points XE_base = 510 675.793 m, YE_base = 2 152 609.461 m and ZE_base = 2 239.346 masl were set, and as a support point to orientate the TS and to start taking the points that were placed in the field were XE_reference = 510 699. 029 m, YE_reference = 2 152 686.294 m and ZE_reference = 2 239.355 masl; all in UTM coordinates zone 14N.The information was processed as with the generation of the raster DEM with GPS RTK. Also in this case the information of the UTM coordinates (longitude [XE_i], latitude [YE_i] and altitude [ZE_i]) was standardized for each point of the grid (i = 1, 2, 3, ... 36) (Table 2).

The processing of the images acquired with UAV was done with the Agisoft PhotoScan program (Agisoft, 2019). The total of photographic images generated in *.jpg format was 77, which were imported and aligned; with this the point cloud, the triangular facet mesh and the orthomosaic were created, for which ground control points were necessary (1, 6, 16, 21, 22, 31 and 36). As a product of the processing, the DEM was obtained in raster format (*.grid), which contains the information of the UTM coordinates (longitude [XV_i], latitude [YV_i] and altitude [ZV_i]) (Table 2).

Results and discussion

From the points obtained (Table 2 and Figure 2) the three topographic methods used were compared; for this purpose the three variables (X, Y, Z) representing a point in the terrain surface were considered.

X coordinates

When comparing the variable X of the topographic methods, Figures 3 shows that all three methods have an R² = 1, a P value of 2.2 x 10^-16 for a 95 % confidence level and a residual standard error of 0.022 m between GPS and TS, 0.041 m between TS and UAV, and 0.041 m between GPS and UAV. Therefore, it is considered that there is no significant variation in the length measurements in the three methods.

Figure 3
Comparison of Mercator Universal Transverse coordinates (UTM, from zone 14N) longitudinal (X variables) between the three surveying methods: total station (TS; XE_i), GPS RTK (XG_i) and unmanned aerial vehicle (UAV; XV_i).

Y coordinates

When comparing the Y variable of the survey methods, it is observed that the three techniques have an R² = 1, a P value of 2.2 x 10^-16 for a 95 % confidence level and a residual standard error of 0.018, 0.041 and 0.043 m, for TS vs. GPS RTK, TS vs. UAV and GPS RTK vs. UAV, respectively (Figure 4). Therefore, it is considered that in Y measurements there is no significant difference between the different methods.

Figure 4
Comparison of Mercator Universal Transverse coordinates (UTM, from zone 14N) latitudinal (Y variables) between the three surveying methods: total station (TS; YE_i), GPS RTK (YG_i) and unmanned aerial vehicle (UAV; YV_i).

Z coordinates

Z coordinate show there is a difference between the different methods. When comparing TS vs. GPS RTK it is observed that R² is 0.996, with a residual error of 0.010 m and a P value of 2.2 x 10^-16 for a confidence level of 95 %, which indicates a concordance of 99 %. On the other hand, when comparing UAV vs. TS it is observed that there is a R² = 0.743, a residual error of 0.098 m and a P value of 1.44 x 10^-11 for a 95 % confidence level; likewise, it was obtained a R² = 0.756, a residual error of 0.092 m and a P value of 5.72 x 10^-12 for the same confidence level when comparing UAV vs. GPS RTK.

When analyzing the differences between the variables and for each method, we obtain that when comparing the topographic survey with ST vs. UAV an absolute error of X = 0.061 m, Y = 0.065 m and Z = 0.047 masl is expected, and with GPS RTK vs. UAV an error of X = 0.020 m, Y = 0.002 m and Z = 0.050 masl is expected (Table 3).

Table 3
Statistics of reading differences of variables (X, Y, Z) when comparing three survey methods.

TS = total station; UAV = unmanned aerial vehicle.

Contour line map

Figures 6 and 7 represent the contour lines generated at 0.1m with the DEMs obtained with each surveying method. The contour lines obtained from TS and GPS RTK surveys are coincidental, and different from those obtained with UAV, which coincides with that reported in Figure 5. It would be pertinent to carry out more tests with UAVs, but with more stable flight devices than those used to achieve a better description of the points on the ground surface, as well as programs with image processing methods that impact on a DEM that better represents reality.

Figure 5
Comparison of Mercator Universal Transverse coordinates (UTM, from zone 14N) altitudinal (Z variables) between the three surveying methods: total station (TS; ZE_i), GPS RTK (ZG_i) and unmanned aerial vehicle (UAV; ZV_i).

Figure 6
Digital elevation model: a) total station and b) GPS RTK.

Figure 7
Digital elevation model: c) unmanned aerial vehicle (UAV) and d) continuous scanning using UAV.

Statistical analysis

DEM were compared based on the square root of the root mean square error (RMSE), as analyzed by Komarek, Kumhalova, and Kroulik (2016), and Polat and Uysal (2017). The above is to quantify the magnitude of the deviation of the values obtained in the DEM using UAV in Z variable (elevation), assuming that X and Y variables are coincident according to the DEMs obtained from TS and RTK GPS.

R M S E = \sqrt{\frac{\sum_{j = 1}^{n} {(z_{j} - Z_{j})}^{2}}{n}}

[1 ]

Where z_j is the elevation obtained using UAV (m), Z_j is the elevation obtained with TS or GPS RTK(m),j = 1, ..., n is the number of each cell (non-dimensional) and n is the number of cells in the raster of the three DEMs.

The estimation of Equation 1 was performed with map algebra of the three DEM rasters (ArcMap [ESRI, 2016]), obtaining the numerator of the function for each cell of the raster estimated. To apply the sum and obtain the number of cells of the raster in the zone spatial analysis tool, the data were exported to a table to sum the values of the squared height differences and obtain the number of cells analyzed (Table 4).

Table 4
Comparison of surveying methods in relation to the square root of the mean square error (RMSE).

TS = total station; UAV = unmanned aerial vehicle.

Comparative methods	Number of cells in the raster	$\sum_{j = 1}^{n} {(z_{j} - Z_{j})}^{2}$	RMSE
TS vs. UAV	3 083 342	70 293	0.151
GPS RTK vs. UAV	3 083 342	64 573	0.145
TS vs. GPS RTK	3 083 342	1 101	0.019

Table 4 shows that RMSE when comparing TS vs. UAV is ±0.151 m, GPS RTK vs. UAV is ±0.145 m, and TS vs. GPS RTK is ±0.019 m.

Gupta and Shukla (2018) report an error of 0.44 between DEM generated with UAV and with TS, which indicates a 65 % difference to the error found in this study. Komarek et al. (2016) obtained an RMSE = 0.29 m when comparing DEM obtained from UAV and GPS RTK, showing a difference of 47 % with respect to the error found in this study. Polat and Uysal (2017) showed an RMSE = 0.171 when generating DEM with UAV and GPS RTK, which agrees with the results obtained in this study, since there is a difference of only 11.7 %.

The MDE obtained from each topographic survey technique does not present significant differences (P ≤ 0.05) in the variables X, Y and Z, which indicates that it is indistinct to use one or another method to generate the MDE with the exposed methodology. When using the equipment analyzed in this study (TS, GPS RTK and photogrammetry), the average error estimated in the variable X is ±0.041 m, and in Y is ±0.043 m. However, in the Z variable the difference is ±0.098 m when compared with X, and with Y it increases by 127 %, so this difference defines the use that will be given to the DEM.

The RMSE statistic of TS vs. UAV is ±0.151 m, of GPS RTK vs. UAV is 0.145 m and of TS vs. GPS RTK is 0.019 m, which indicates that the traditional methods TS and GPS RTK maintain reliability with respect to the photogrammetric method analyzed.

Conclusions

The different surveying methods (ST, GPS RTK and photogrammetry) used to generate a DEM do not differ statistically. According to the conditions described in the study, the user can make a reasoned decision depending on the equipment available and on the application of generating the topography. Furthermore, it was determined that the three methods are reliable, since the traditional methods (TS and GPS RTK) show minor errors compared to photogrammetry using UAV; however, the methods complement each other because it is indispensable to take control points in the field for the georeferencing of DEMs. X and Y coordinates have a lower error, compared to the Z axis in UAVs. For further studies, it is proposed to carry out the survey at different flight heights, and to analyze the error due to the increase in pixel size and surface coverage conditions.

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Author notes

*Corresponding author: jorgelv@colpos.mx, tel. 5959520200, ext. 1176.

Variable	TS vs. UAV			TS vs. GPS RTK			GPS RTK vs. UAV
Variable	X	Y	Z	X	Y	Z	X	Y	Z
Maximum	0.070	0.190	0.192	0.022	0.118	0.033	0.108	0.138	0.172
Minimum	-0.182	-0.031	-0.236	-0.112	-0.002	-0.023	-0.113	-0.123	-0.237
Average	-0.061	0.065	-0.047	-0.041	0.063	0.004	-0.020	0.002	-0.050
Standard deviation	0.079	0.048	0.117	0.031	0.035	0.012	0.061	0.070	0.114