1 Introduction

Nowadays, it is increasingly common to use unmanned aerial vehicles (UAVs) or, more broadly, unmanned aerial systems (UAS) for missions that result in the acquisition of high-resolution imagery. These images offer great material from which a digital surface model (DSM), digital elevation model (DEM) [1, 2] or orthomosaic [3, 4] can be created relatively quickly and easily. UAS systems enable us to obtain spatial information from a wide area of interest, and the obtained data are detailed and of high resolution. UAS systems can thus be ranked between space-based remote sensing and detailed in situ measurements in environmental monitoring systems [5]. The widespread availability and decreasing cost of such flying equipment has led to its increased use in scientific research, to, for example monitor soil erosion [6], detect and conduct spatial analyses of periglacial landforms [7], perform detailed geomorphological mapping [8], monitor coastal dune change [9, 10], analys karst landforms [11] or conduct a multi-faceted analysis of the Antarctic ecosystem [12]. This technique is also often used in mining [13,14,15], monitoring various natural geohazards and phenomena [16, 17], detecting of agricultural crops or trees [18, 19] and, dam and riverbed erosion [20], modelling topographic features [21], updating cadastral data [22], estimating solar irradiation [23], researching cultural heritage and archaeology [24, 25] and monitoring traffic [26, 27]. All of these activities require specific data of adequate accuracy.

The quality of the final product (UAV-DEM/DSM, orthomosaic) depends on the initial image acquisition, and ground sampling distance (GSD, i.e. spatial resolution of the UAV images) is a fundamental element of successful image processing. GSD is affected by many factors, including the flight height and path, the employed sensor (RGB, multispectral/hyperspectral) [28], lighting conditions (sun angle and cloud cover) [29] and, the terrain surface cover. Furthermore, the resulting model accuracy also depends on camera pitch [30, 31], image overlap [32], flight trajectory [33], camera calibration method [34, 35] and the software used for reconstruction [36]. Besides the above technical aspects related to designing and executing a UAV mission, additional measurements can be applied to improve the quality of UAV data. Standard methods to increase the accuracy of DEMs/DSMs derived from UAV measurements consist of using ground control points (GCPs), which are points measured in the field, during pre-processing and independently using high precision geodetic GNSS RTK [37,38,39,40,41]. UAV methods are sometimes combined with terrestrial laser scanning (TLS) systems [42,43,44]. Some authors apply multi-view stereopsis (MVS) techniques combining photogrammetry and computer vision with ground control points collected using a Differential Global Positioning System (DGPS) [45]. However, UAV-mounted (on-board) GNSS RTK are utilised in an increasing number of assignments [32, 35]. Unfortunately, UAV cameras equipped with a GNSS RTK or LiDAR receiver are still expensive (prices start at $25,000—$30,000).

There is also a more advanced approach to measuring the same area from different altitudes and angles, which leads to much better results [46]. Although the highest possible accuracy is required from models created on the basis of UAV measurements, it often occurs that high precision (centimetre/decimetre) is not absolutely necessary. Similar insights emerge in the relevant literature [see 47]. Based on such an assumption, the aim of this paper is to vailidate the final accuracy of UAV-DEM and UAV-DSM, which were created based on image data from UAV flights. These models were created using the simplest method, without ground control points (GCPs) measured earlier in the field with GNSS RTK equipment. Accuracy is considered here in two directions: vertical accuracy (calculated on the basis of airborne laser scanning [ALS] data) and horizontal accuracy (calculated on the basis of high-resolution orthophotomaps). The author is interested in mathematical and statistical accuracy, specificallythe extent to which the model obtained from UAV flights differs from reality. The article focuses on two issues: 1) the extent to which the heights of digital models created from UAV data differ from ALS reference models (with an elevation accuracy of ± 0.1 m) and 2) the extent to which the locations of objects are shifted horizontally compared to orthophotomaps acquired from the national geoportal (with a resolution of 5 cm × 5 cm). The results of the study make it possible to determine the order of magnitude of accuracy errors to be expected when using this type of data in environmental studies.

2 Study area

The study area is located in southern Poland, in the Katowice Upland (mesoregion) and the Silesian-Cracow Upland (subprovince), which belong to the strip of Polish Uplands [48]. The midpoint of the research area is situated at 50.3∘ N latitude and 19.1∘ E longitude. This area covers over 82 km2 (Fig. 1). The land cover [49] is mainly of an anthropogenic character: artificial anthropogenic surfaces occupy the majority of the vast area (urban fabric: 38%; industrial, commercial and transport units: 12%; green urban areas: 7%; mines, dumps and construction sites: 1%); the second group comprises agricultural areas (arable land: 31%), and the third group is forests (ca. 10%). The geomorphological background is made up of two large plateaus separated by a floodplain in the southern part. The northern part of the area consists of river terraces and residual hills (due to rock hardness) in the northwest. Moreover, many anthropogenic landforms exist, especially in the centre and south of the area. Anthropogenic flats, subsidence basins, embankments and flood embankments occur near artificial river channels [50]. The local relief is 136 m and the average altitude is 277 m a.s.l. The highest elevations, St. Dorothy Hill (381 m a.s.l.) and Parcina Hill (355 m a.s.l.), are located in the northwestern part of the area; the lowest place, an old coal mine area (238 m a.s.l.), is located in the southwestern part. The main drainage river is Przemsza, with its tributaries and a fragment of Brynica with its arm Wielonka (Fig. 1). This area is diverse enough to show different types of landforms; however, at the same time, it has well-recognized topography, which constitutes the reason for its selection. Twenty-one test sites were selected for detailed research (Fig. 1). These test sites can be divided into three types by surface relief: areas with low, medium and high relief. Areas with low relief (relative heights of 0–10 m) include test fields 1, 4, 8, 9, 10, 11, 13, 14 and 18. Areas with medium relief (relative heights of 11–20 m) are represented by test fields 5, 6, 7, 12, 17 and 19. The last group (high relief, relative heights > 20 m) includes test fields 2, 3, 15, 16, 20 and 21.

Fig. 1
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Study area and locations of the test sites 1–21

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3 Source data

To avoid any misunderstanding, terms used in the following text will first be clearly defined. A digital elevation model (DEM) is understood as a digital representation of elevations of a topographic surface in the form of a georectified area-based grid covering bare earth [51]. A digital surface model (DSM) is in turn a DEM that represents the upper surface of a landscape, including any vegetation (trees, bushes, etc.), buildings and other surface features [52]. In this study, both DEM and DSM are in the form of raster images consisting of rectangular grids with a defined size (i.e. spatial resolution). The models used in the research have basically the same internal structure (data recording format and resolution) and differ only in how they obtain the elevation data, which are the basis for the creation of the elevation models.

3.1 UAV data

The UAV data consist of 21 sets of photos corresponding to the 21 test sites. All the images were obtained using the DJI Mavic 2 Pro UAV missions, which took place in November—January 2020/2021 and April—May 2022. The basic details of the UAV system and the flights: flight altitude 75 m, flight speed (5 m/s), side overlap (70%), frontal overlap (80%), margin (15 m), photo mode (timed interval shot), camera type (Hasselblad L1D-20C), metering mode (center weighted average), the shutter was between 1/320 and 1/800, the ISO was between 100 and 200 (depending on the lighting conditions) and the image pixel was 2.03 cm × 2.03 cm. Each mission assumed the approximate range of the flight area to be 250 m × 250 m; the number of photos taken ranged between 190 and 220 and the flight mission time was about 10 min. After the missions were completed, the data were processed using the AgiSoft MetaShape Professional software [53]. Once the photos were uploaded and Align Photos were taken, a dense cloud was created. The digital surface model (UAV-DSM) and orthomosaic were generated based on this cloud. The final stage was the filtration of Classify Ground Points to obtain a digital elevation model (UAV-DEM). The simplest method of creating terrain models and orthomosaics was used: aerial data processing without ground control points (GCPs). Finally, based on the UAV photos the following data were created for all 21 test sites: orthomosaics in natural colours with a spatial resolution of 5 cm × 5 cm, a digital surface model (UAV-DSM) and a digital elevation model (UAV-DEM) with a resolution of 0.25 m × 0.25 m. The final test sites ranged from 3.3 ha to 15.9 ha, with an average of 10.4 ha (0.1 km2). The spatial distribution of all the test sites is presented in Fig. 1.

3.2 ALS data

The airborne laser scanning (ALS) data are the elevation data in the form of binary files in LAS format [54] containing a cloud of points with X, Y and Z coordinates derived from ALS in April 2019. These data were recorded in accordance with the LAS standard 1.2 [55]. These files contain, among other things, class information for the point and the intensity of reflections in three ranges of the visible part of the electromagnetic radiation spectrum corresponding to the red, green and blue colours (RGB values) obtained from the aerial photographs. The LAS files have a minimum density of 12 points/m2 and average height accuracy of ≤ 0.1 m. The correctness of the classification of points is not less than 95%. All of the points are in the Polish plane coordinates system PUWG-1992 (EPSG:2180) and the height coordinate system PL-EVRF2007-NH [54]. Each LAS file covers an area of around 0.5 km × 0.5 km. One used 48 LAS files with a total area of 15.5 km2. Table 1 summarises the information about the applied classification values and the number of points in each class. The average point spacing in all the LAS files ranged from 0.15 to 0.22 m. Therefore, theALS-DSMs and ALS-DEMs were created at a resolution of 0.25 m × 0.25 m. The ALS-DEMs were made based on only class 2 points (ground).

Table 1 ALS data point classes
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3.3 TOPO-DEM

Four sheets of the topographic maps at a scale 1:10,000 [56] were the primary data for creating the TOPO-DEM. Altogether, most of the contour lines (750 km in total) and all the 362 height points were digitised from the maps. Since the scale of the source maps was 10,000 (if the smallest polygonal object on the map is 1 mm × 1 mm, it measures 10 m × 10 m in reality), a DEM with a resolution of 10 m × 10 m was built. Like the other DEMs, the TOPO-DEM was made in the PUWG-1992 (EPSG: 2180) Polish plane rectangular coordinate system, and the heights of points relate to the Normal Height System Kronsztadt 86 [57]. The Topo-to-Raster tool from ArcGIS Toolbox [58] was utilised to generate the TOPO-DEM. This technique creates hydrologically correct DEMs and is based on the ANUDEM algorithm developed by Hutchinson [59]. This method applies an interpolation process specifically designed to create a surface that more closely represents a natural drainage surface and better preserves ridgelines and stream networks from input contour data. Therefore, all the watercourses and water reservoirs with an area of ≥ 500 m2 were used as break lines together with contours and height points to support the interpolation process.

3.4 Orthophotomaps

An orthophotomap is a raster cartometric image of the land surface, that results from the orthogonal processing of aerial photographs or satellite scenes. High-resolution (5 cm × 5 cm) orthophotomaps from flights in May 2021 were used for this research. These accuracy raster data were made in the PUWG-1992 (EPSG: 2180) Polish plane rectangular coordinate system in real colours (RGB). These orthophotomaps are official high-resolution reference images obtained from the Geoportal of the Spatial Information Infrastructure [60] conducted by the Head Office of Geodesy and Cartography in Warsaw.

4 Methods

As one of the main goals of this research was to determine the quality of DEMs, DSMs and orthomosaics based on UAV measurements, their vertical and horizontal accuracy was assessed as precisely as possible.

ALS-DEM and ALS-DSM reference data created with the LiDAR altitude data [54], were used to assess the vertical accuracy of the UAV-DEM and UAV-DSM. These data are currently the most accurate freely-available reference height data for this study area (see Subsection 3.2). These data were taken from the Geoportal of the Spatial Information Infrastructure [60]. Additionally, based on previous research [61], it was decided to use the TOPO-DEM (see Subsection 3.3) from this area for comparison. To show the quantitative elevation differences between the models and their spatial distribution, differential models were made for the DEMs (UAV-DEM vs ALS-DEM) and DSMs (UAV-DSM vs ALS-DSM). The result conformity index proposed by Szypuła [62] was also applied. This index expresses how the percentage of the grid cells of the interpolated DEM follow the same grid cells of the reference DEM with a given height tolerance. In addition, four additional flights were performed for test site 13 to analyse the variation in the results within one defined area. Morover, 10 ground control points (GCPs) were measured on this test site in the field and used to calculate the UAV-DEM/DSM and orthophotomosaic. GCPs were measured using ComNav T300 GNSS RTK equipment with a horizontal accuracy of 0.01 m and vertical accuracy of 0.02 m.

High-resolution orthophotomapswere employed to assess the horizontal accuracy (location of the X and Y coordinates) of the UAV orthomosaic. The horizontal displacement (shift) of the UAV orthomosaics compared to the orthophotomaps was measured. The shift measurements were made based on points that: 1) were located on the ground (intersections, road lanes, street ligh lamp bases, square corners, curbs, sewage pits, etc.) and 2) were unambiguously identified on UAV orthomosaics and orthophotomaps. For each of the 21 test areas, 10—28 points were measured, reaching a total of 371 points.

In the last stage, the UAV orthomosaics were georeferenced using orthophotomaps. Moreover, the shift measurements were repeated in the same points to verify the extent to which the horizontal accuracy of the UAV orthomosaic would increase.

The development of UAV data and the creation of relevant UAV-DSMs, UAV-DEMs and UAV orthomosaics was conducted using the AgiSoft MetaShape Professional software [53]. The Polish plane coordinate system PUWG-1992 (EPSG:2180) and height coordinate system PL-EVRF2007-NH [57] were used in the creation of all the resulting data (models and orthophotomaps).

The creation of the TOPO-DEM and ALS DEM/DSM and all analyses, calculations and visualisations were performed in the ArcGIS environment [58]. All of the important software processing settings are in Table 2. Figure 2 presents a workflow which shows the main stages of the work: A – data preparation, B – creation of the models/orthomosaics, C – accuracy calculation.

Table 2 Software used and the processing settings
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Fig. 2
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Workflow with the main work stages: A – data preparing, B – creating the models/orthomosaics, C – accuracy calculating

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5 Results

5.1 Characteristics of the altitude data

To address the models’quality issues, it is necessary to first look at the altitude data that describe them. Table 3 summarises the basic altitude characteristics of the DEMs based on data from the UAV, ALS and topographic maps. A first glance at the data shows that the elevation relationships in all three types of DEMs are similar. The minimum heights for the UAV-DEMs and ALS-DEMs differ by 2.5 m on average; the average differences in the maximum heights for the same models amount to 3.1 m, while the mean heights differ by an average of 2.4 m (Table 3). This shows the order of magnitude of height differences related to the minimum and maximum values. The standard deviation (STD) values for UAV-DEMs and ALS-DEMs are very similar, which confirms the substantial similarity in the distribution of distance from the mean value and the variability of the height value in the data set itself. The greatest differences in the minimum, maximum and mean heights were observed for test sites 16 and 20, while the smallest ones were observed for test sites 8 and 20 (Table 3). Despite this, the spatial image of the surface relief shows a high agreement of topographic details for all the test sites (Fig. 3). The only differences are related to the imperfect filtering of areas that are usually wooded, an anthropogenic dump in the middle of the area (Fig. 3B) or buildings (Fig. 3D).

Table 3 Altitude characteristics of the DEMs
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Fig. 3
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Example of DEMs of the test site no. 16 (A), 21 (B), 8 (C) and 20 (D)

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As for the TOPO-DEM, despite the obvious difference in resolution compared to the UAV-DEM, Table 3 shows very similar minimum, maximum and mean values of both models. This confirms the author's earlier observations [see 61] that, despite its lower resolution, the DEM created on the basis of the topographic maps generalises the topography very well while maintaining the characteristic elements of the terrain surface.

Table 4 presents the altitude characteristics of the UAV-DSMs and ALS-DSMs. The differences between the minimum, maximum and mean values, which are much higher than for the analogous DEMs, can be easily observed. This is mainly due to individual objects such as trees, power lines, chimneys and buildings (see Fig. 4B, C) which were recorded incorrectly or left unrecorded on the UAV data. On average, the mean values of the UAV-DSMs and ALS-DSMs differ by only 2.2 m (Table 4). As with the DEMs, the spatial image of the topography mapped on the UAV-DSMs is very accurate (Fig. 4).

Table 4 Altitude characteristics of the DSMs
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Fig. 4
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Example of DSMs of the test site no. 4 (A), 7 (B), 10 (C) and 14 (D)

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5.2 Elevation accuracy

In statistics, the term “error” means a departure from a known, correct value [63]. To determine the differences between the elevation values obtained from the model and the real situation, one can employ field measurements or apply reference data. In these studies, the ALS-DEM and ALS-DSM with a confirmed height accuracy of 10 cm were used as reference data [54]. There are many standards that can be used to calculate the differences (errors) between models [39, 64, 65]; however, the mean absolute error (MAE), the root-mean square error (RMSE) and the result conformity index were applied in this study. The MAE measures the average magnitude of errors in a set of predictions without considering their direction (+ or -). It is the average of the absolute differences between an actual observation (ALS models) and prediction (UAV models) at a set of points used for calculation. All individual differences have equal weight [66]. The RMSE also measures the average magnitude of error. It is the square root of the average of squared differences between an actual observation and prediction at control points.

The RMSE is the most frequently used characteristic determining the degree of accuracy or the measure of conformity between a set of estimates and the actual values [67]. It expresses the dispersion of frequency distribution of variances between reference elevations and DEM data. The main difference between these indicators is that the RMSE is a measure of the typical difference between two models cell by cell, and the MAE is the average of all absolute errors.

Table 5 shows the calculated altitude differences between the UAV-models and ALS-models. Column “differences” indicates that the ALS model has been subtracted from the UAV model. As for the DEMs, the height differences range from -9 m to + 19 m.

Table 5 Elevation differences between UAV- and ALS-models
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These may seem like major differences, but a look at the spatial image (see Fig. 5) shows that these are only single places (trees or buildings). These major errors should be considered as outliers. The MAE and RMSE values are much more important. Only in one case (test site 21) did these values exceed 10 m, while the majority did not go beyond 2 m, with the mean value for all test sites being 2.7 m (Table 5). In general, the greater the difference between the MAE and the RMSE, the greater the variance in individual errors in the sample. The RMSE values are slightly greater than the MAE, which suggests that all the errors are of the same magnitude [68]. The MAE and RMSE values for the DSMs look alike, so the overall error distribution for the areas is very similar. The differences only appear in extreme values, which, do not have a significant impact on the entire data set, because the average values (MAE and RMSE) are almost identical to those for the DEMs (Table 5, Fig. 6). Generally, it can be stated that the average height accuracy of UAV based DEMs and DSMs is 2.7–2.8 m. The MAE values are almost identical to the RMSE values, which indicates that most of the errors in the models have similar values (the set is not statistically differentiated). This is additionally confirmed by the differential models (Figs. 5 and 6).

Fig. 5
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Example of differential DEMs of the test site no. 16 (A), 21 (B), 8 (C), 20 (D)

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Fig. 6
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Example of differential DSMs of the test site no. 4 (A), 7 (B), 10 (C), 14 (D)

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The last indicator used to assess the altitude accuracy in spatial terms was the results conformity index [after 62]. Result conformity values express the percentage of the grid cells of the interpolated model (UAV-DEM) that are in accordance with the same grid cells of the reference model (ALS-DEM) within a given accuracy. This index is based on differential models and through its nature (value ranges), it somehow generalises the image of height errors, making the differential model more spatially readable. On the other hand, it presents a quantitative statement: the percentage share of the area occupied by individual ranges of error values.

Due to the large errors that occurred in the UAV-DSM models, it was decided that the result conformity index would be calculated only for UAV-DEMs versus ALS-DEMs models, as shown in Table 6. The calculations were made for the given ranges of errors (differences) in height. It appears that the places with the smallest errors (range from -0.5 m to + 0.5 m) for all 21 test sites amount to 21% on average. If the range of the smallest altitude errors is extended from -1 m to + 1 m, it will cover a total average area of 41% of each UAV-DEM. The largest area (52%) is occupied by errors above + 1 m. This means that half of the area of each UAV-DEM is 1 m or more above the actual ground surface on average. The areas with an error of -1 m and below occupy an average of less than 17% (Table 6).

Table 6 Index of the result conformity of the DEMs
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On the other hand, the spatial distribution of the result conformity index values looks interesting (Fig. 7). First of all, as mentioned above, the areas occupied by the largest positive errors dominate. Secondly, errors often appear concentrically in the form of circles centred in the middle of the area (Fig. 7). Circular height errors are related to flat or slightly sloping areas, usually ploughed fields or low meadows (test sites 1, 4, 6–11 with a local relief of 6–12 m). The majority of significantly inclined areas (test sites 2, 3, 15–16, 21 with a local relief of 22–35 m) or completely flat ones with buildings (test site 14 is a parking lot) have positive errors of above 1 m (Fig. 7). The areas containing meadows with tall grasses (test sites 18, 19) are characterised by the greatest chaos in terms of the distribution of height differences. Nevertheless, these are the most accurate models: the error range from -0.5 to + 0.5 m has the largest share (34–47%; see Table 6).

Fig. 7
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Result conformity maps of the all 21 test site DEMs

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5.3 Horizontal accuracy

High-resolution reference images (orthophotomaps) were used to analyse the horizontal accuracy (shift errors) of the UAV orthomosaics. Both the UAV orthomosaics and orthophotomaps had the same resolutionof 5 cm × 5 cm. For each test site, 10 to 28 distinctive, uniquely identified points were selected on each pair of images. The difference in the position of each point on the UAV orthomosaic relative to its position on the reference orthophotomap was measured. Then, based on the shift values, an interpolation was performed to see the spatial shift distribution (Fig. 8). A total of 371 points were measured. Table 7 shows the obtained shift values, which ranged from 0.18 m to over 5 m, while for test sites they ranged from 1.1 m to 3.6 m on average. The average value obtained from all the 371 measurements was 2.1 m. This seems to be a good resultas official tests revealed that the best accuracy of GPS Navstar amounts to 1.8–2.8 m [69], and 3.1 m for GLONASS [70, 71]. The UAV used for the measurements (DJI Mavic 2 Pro) utilises two GNSS systems simultaneously (GPS and GLONASS), and position precision in this case ranges from 2.3 to 4.6 m [72].

Table 7 Shift errors of the UAV orthomosaics
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As for the spatial distribution of the shift errors, the smallest values (max 1.7 – 2.6 m) were recorded for test site 1, 3, 18 and 21, and the mean error was 1.1—1.5 m (Table 7). While for test sites 1 and 18 this is related to the occurrence of the smallest height errors, the other two test sites ( 3 and 21) are characterised by positive errors of height over the entire surface (see Figs. 7, 8 and Tables 5, 6). On the other hand, the largest shift errors (max > 5 m) that we noticed concern test sites 4, 10 and 11, mean 2.4 – 3.2 m. It is interesting that these three test sites represent areas with low relief (local relief < 1 m, see Table 3). When analysing the maps of all the test sites with shift errors (Fig. 8), it is difficult to notice any spatial regularity—regardless of the surface coverage or topography. Some authors note that the centre of the orthomosaic has higher positional precision than areas along the edges [40]. It is likely that more survey points distributed more symmetrically across the area would have provided more comprehensive information, but unfortunately this was often not possible due to the lack of distinctive reference points.

Fig. 8
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Shift error maps of the all 21 test sites

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6 Discussion

The vertical and horizontal accuracy obtained results are similar to the research of Crume [73]. His tests showed that the Mavic 2 Pro used, for a flight at an altitude of 50 m, for frontal overlap of 70% and side overlap of 60%, achieved an elevation error of about 1.8 m and a horizontal error of about 1.2—1.5 m. Its errors are smaller, probably due to the 1/3 lower flight altitude and the associated higher resolution of the images (1.37 cm).

UAV systems usually measure altitude using an internal barometric sensor with an above ground level (AGL) reference. This means that the DJI Mavic system records each time elevation compared to its take-off point, not an absolute elevation [72]. In view of this fact, the range of measurement error (spread of values) between successive flights was assessed. For this purpose, four additional flights were conducted (numbers 2, 3, 4, 5) for test site 13. The results of these flights are shown in Table 8. The differences between the minimum, maximum and mean values for successive flights range from 1.5 to 5.5 m. These are, of course, extreme values, as the STD values were 0.5—0.7 m, which shows a similar distribution of values across the entire data set.

Table 8 Altitude characteristics of the test site no. 13
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In the next step, a UAV-DEM and UAV-DSM were created using all the images from flights 2, 3, 4 and 5 (Table 8, flights 2–5). The UAV-DEM and UAV-DSM calculated in this way did not show better performance; the values were similar to the other four models. This means that an increased number of images does not improve the quality of the created models.

In addition, 10 GCPs were measured using ComNav T300 GNSS RTK equipment with high accuracy (horizontal 0.01 m, vertical 0.02 m). It was decided to assess the accuracy UAV models would have with GCPs (Table 8, flight GCPs). The differences in altitude values for the UAV-DEM (GCPs) compared to the ALS-DEM do not exceed 0.2 m. The UAV-DSM (GCPs) is different mainly because of the changes that occurred in the study area over thethree years (since the ALS measurements were made). This can easily be seen in the spatial image (Fig. 9D) in the southern part of the area, where a new housing development has been built. The calculated RMSE value for the UAV-DEM (GCPs) was 0.68 m, and the MAE value was 0.47 m. These values are comparable to the results of other authors [see 74]. For the UAV-DEM without GCPs for the same test site (13), the RMSE was 1.4 m and the MAE was 1.1 m (see Table 5). This is confirmed by the results obtained by other researchers [see 75], who achieved a vertical accuracy result of 2.5–3 m for the RMS and MAE. Thus the UAV-DEM with GCPs has only twice the vertical accuracy of the UAV-DEM without GCPs. On the other hand, the value of the RMSE for the UAV-DSM was 2.01 m, and the MAE was 1.29 m; for the same UAV-DSM without GCPs, the RMSE was 2.3 m and the MAE was 1.7 m. Thus, the statistical accuracy results are almost identical for the UAV-DSM with and without GCPs. In general, it can be said that the range of the values for the UAV-DSM is comparable to, for example, archaeological studies see [76], where DSM accuracy ranges from -4.6 to 15.4 m.

Fig. 9
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Comparison of UAV GCPs models (A, D) with ALS models (B, E) and result conformity maps (C, F) for test site no. 13

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Analysis of the result conformity showed that for the UAV-DEM with GCPs, areas with ± 0.5 m accuracy occupied almost 64% of the area, and areas with ± 1.0 accuracy occupied more than 90% (Fig. 9C). This is a much better result than for the UAV-DEM without GCPs, where areas with ± 0.5 m accuracy occupied 31% of the area, and areas with ± 1.0 m accuracy occupied around 55% (Table 6, test site 13). For the UAV-DSM, the largest area (over 40%) was occupied by areas with an error of more than 1 m. Areas with ± 0.5 m error covered around 13%, and areas with ± 1.0 m error covered around 50% of the total area. This agrees with the research of Kulhavy [77] and Unger [78], who noted that a UAV system measuring altitude with an internal barometer tends to overestimate the height.

The processing analysis revealed that the types of distortion recorded and shown in Fig. 7 were probably related to the standard calibration settings of the DJI Mavic Pro. Some UAS systems (including Mavic 2 Pro with the integrated Hasselblad L1D-2C camera) need processing modifications [75]. The standard pipeline for processing that allows software to optimise the internal camera parameters and recalculate or optimise the position and orientation of the photographs only resulted in a domed SfM point cloud (radial distortion). Kalacska et al. [75] also point out that the exact model of the Mavic 2 Pro despite having a superior camera to other UAV systems (i.e. the Mavic Pro or the SkyRanger), generates an unexpected amount of relatively high errors.

The calculated mean shift errors ranged from 1.1 to 3.6 m, and they are typical for orthomosaic made without GCPs, as has been confirmed by other researchers [79] or [75]. Having the measured GCPs at my disposal, I also decided to verify the horizontal accuracy of the orthomosaic made based on GCPs. Shift errors turned out to be very small and amounted to only 0.02 to 0.15 m with a mean value of 0.04 m and STD of 0.03 m. This is a very good result that is in line with expectations, but unfortunately requires precise measurements of ground control points.

Although to the study aimed to avoid interfering (through post-processing) with the material obtained from the UAV flights, we decided to verify the extent to which the horizontal accuracy would improve if the UAV orthomosaic was georeferenced based on orthophotomaps. As an experiment, the test sites with the smallest errors in horizontal accuracy (1, 3) and with the largest errors (9, 11, 12—see Table 7) were checked. The georeferencing tool in the ArcGIS software was used to perform first order polynomial (affine) transformation, and nearest neighbour without compression was used as the resample type. The measurements of the position difference were made again for the same points on the selected five test sites. The results are presented in Table 9. Except for one maximum error (test site 1) all the shift errors decreased. On average, the horizontal accuracy was between 0.25 and 0.90 m, which is a very good result for materials of this resolution.

Table 9 Shift errors for referenced UAV orthomosaics
Full size table

7 Conclusions

The advantages of working with UAV survey data without GCPs include the speed of data acquisition, low cost, simple post-processing (most of it is automatic), high resolution of data, measurement capabilities in difficult or inaccessible areas, and the relatively large area that can be measured. The disadvantages are relatively short flight time on a single battery, the need for good weather conditions when measurements are taken, and (sometimes) too low vertical and location accuracy. Obviously, it is the research profile that determines quality of the spatial data. Data obtained from UAV systems can be successfully used for automatic landform recognition [see 80, 81], because the accuracy of the calculated DEMs and DSMs is sufficient. The research of Dachauer et al. [82] is a good example in which the obtained DEM has exactly the same resolution (about 0.25 m × 0.25 m) and is accurate enough to capture the large crevasse structures. Given the advantages of UAVs compared to other devices (e.g. low cost, applicable to inaccessible areas; [83]), this study shows that UAVs provide a reliable and effective method for gathering data for aerodynamic roughness length estimation on glaciers. Morover, UAV-based SfM photogrammetry without GCPs has a special advantage in places where there are no possibilities to measure GCPs (i.e. assessment of marsh geomorphology in highly seasonal climates [84]).

The average elevation accuracy of all the created UAV-based DEMs/DSMs is approximately 2.8 m. The ± 1 m accuracy involved an average of 41% of the area of each model, while half of the area of each model displayed height values overestimated by 1 m or more on average. Despite this, the spatial image of the surface relief on the obtained models shows high conformity of topographic details with reality. The only differences that occur are related to elements of infrastructure (chimneys, high voltage lines, and buildings) or areas with medium (shrubs) and high (trees) vegetation, which are often inappropriately filtered when creating the orthomosaic.

As for the horizontal accuracy, the obtained shift values range from 0.18 m to more than 5 m, with an average of 1.1 m to 3.6 m for the test sites. The average value generated from all the measurements was 2.1 m. Interestingly the analysis showed that UAV orthomosaics have a much better quality for identifying details than orthophotomaps of the same resolution (5 cm × 5 cm). Additionally, fast georeferencing of UAV data based on reference orthophotomaps increased horizontal accuracy by several multiples. This could be a simple and quick method to significantly improve the quality of UAV data, provided that high-resolution orthophotomaps are available. Additional UAV-DEM/DSM and orthophotomosaics calculated with GCPs showed very minor errors (horizontal: mean 0.04 m; vertical: MAE 0.47 m). Surprisingly, the vertical accuracy is only twice as good as for models without GCPs. It is important to remember that the presented results for creating DEMs/DSMs and orthophotomosaics without GCPs and the associated vertical and horizontal accuracies refer to a specific UAV system (Mavic 2 Pro), which provides a certain benchmark. The use of more professional and, above all, newer UAV systems, together with the conscious application of processing settings, maybe will yield much higher accuracies than those reported here.