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. 

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]).

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).

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).

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.

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 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.