Interactive comment on “ Evaluating the Potential of PPK Direct Georeferencing for UAV-SfM Photogrammetry and Precise Topographic Mapping

Abstract. Images captured by Unmanned aerial vehicle (UAV) and processed by Structure from Motion (SfM) photogrammetry are increasingly used in geomorphology to obtain high resolution topography data. Conventional georeferencing using ground control points (GCPs) provides reliable positioning but the geometrical accuracy critically depends on the number and spatial layout of the GCPs. This limits the time- and cost-effectiveness. Direct georeferencing of the UAV images with differential GNSS, such as PPK (Post-Processing Kinematic), may overcome these limitations by providing accurate and directly georeferenced surveys. To investigate the positional accuracy, repeatability and reproducibility of digital surface models (DSMs) generated by a UAV-PPK-SfM workflow, we carried out multiple flight missions with different camera/UAV systems. Our analysis showed that the PPK solution provides the same accuracy (mean: ca. 0.01 m, RMSE: ca. 0.03 m) as the GCP method. Furthermore, our results indicated that camera properties (i.e., focal length, resolution, sensor quality) have an impact on the accuracy but planimetric and altimetric errors remained in the range of 0.011 to 0.024 m. By analysing the repeatability of DSM construction over a time period of a few months, our study demonstrates that a UAV-PPK-SfM workflow can provide consistent, repeatable 4D data with an accuracy of a few centimetres without the use of GCPs. An uncertainty analysis showed that the minimum level of topographical change detection was ca. ±0.04 m for a high-end DSLR camera and ca. ±0.08 m for an action camera (for a flight height of 45 m). The level of detection substantially improved when reducing the UAV flight height. This study demonstrates the repeatability, reproducibility and efficiency of a PPK-SfM workflow in the context of 4D earth surface monitoring with time-laps SfM photogrammetry. As such, it should be considered as an efficient tool to monitor geomorphic processes accurately and quickly at a very high spatial and temporal resolution.



2
We do think that an assessment of the repeatability, reproducibility and efficiency of a PPK-SfM workflow in the context of 4D earth surface monitoring with time-lapse SfM photogrammetry is timely and highly relevant for geomorphological research. There is some recent research on the accuracy of PPK direct georeferencing but not in the context of 4D monitoring.
The consistency of data generation over longer monitoring periods and how uncertainty is propagated is crucial for geomorphological applications. This is the main focus of this paper. In addition, we would like to emphasize that we do not 5 repeat 'well-established principles in relation to camera properties. Rather we focus on two typical UAV-camera setups: We are convinced that an evaluation of the performance of a micro-drone equipped with an action camera (low-cost and very high portability) versus a heavy professional UAV equipped with a reflex camera is relevant for the readership of your journal.
Based on these comments, we have substantially rewritten the introduction and method sections following the suggestions made here. We have also addressed the issues of novelty and transferability. In our answers to the detailed comments below, 10 we discuss how these improvements were implemented.
2) With the paper focussed on PPK direct georeferencing for UAV surveys, the introduction would be well served by focussing on this. With UAV-SfM approaches not being so new, substantial regions of text (e.g. up to P 3), which introduce the broader aspects and uses of UAV photogrammetry could be condensed into a few sentences or a single paragraph. The introduction would be strengthened by incorporating Table A1 into the main text and critically evaluating the progress of PPK controlled 15 UAV surveys so far. Consideration of established use of this approach for crewed aircraft could be covered briefly. Inclusion of the recent PPP work by Grayson et al. (2018;DOI: 10.1111/phor.12259)and references included within itwill also strengthen this section.
We have rewritten the introduction section and focused more on PPK direct georeferencing. We also removed the introduction of other DEM acquisition methods. Table A1 was presented and discussed in the introduction as Table 1 to improve the 20 description of the state-of-the-art in relation to PPK and the problem statement. The PPP work by Grayson et al. (2018;DOI: 10.1111/phor.12259) was included in Table 1 as well as a PPK work by Padró et al. (10.1016Padró et al. (10. /j.jag.2018. 3) One aspect of the work is an exploration of predictors for survey repeatability. The rationale for some of the selections could be strengthened here, and the utility of tie point density (which is shown to explain <50% of the variance for one camera) 25 more critically considered. How useful is this, given that the analysis only appears to work for one camera and requires deployment of GCPs to determine the relationship? The number of tie points retained per image is usually a software setting that can be varied. Consequently, any parameterisation of repeatability would be software and UAV system dependent.
Furthermore, other more important parameters are not considered. Within the bundle adjustment, measurement precision for a tie point is related to the number and angles of observationshow do these vary? The authors cite James et al. (2017) who 30 show how point coordinate precision varies spatially and can be linked directly to these photogrammetric factors and other georeferencing factors within the adjustment. Consequently, maps of 3D point precision can be determined without any GCPs. The work here would be strengthened by discussing the authors 'spatialised error' approach in context with the 3D precision maps of James et al. (2017). The authors could also consider the findings of Mosbrucker et al (2017;DOI: 10.1002/esp.4066)

within the discussion (or introduction).
We have completely reworked this section and we now use two approaches to estimate precision for the change detection analysis: observational (i.e. CP-derived) precision and Monte Carlo-derived precision (using the workflow proposed by James 5 et al 2017). The analysis are presented in Fig. 5 and Fig. A3 and are discussed on page 18. 4) Comparison of results from different cameras (S4.2; particularly the last paragraph) dominantly reflects established relationships between camera/flight parameters and conventional survey design principles. In my view, this material should form the rationale behind the survey design, and be given within the introduction or methods sections. Placing this within the discussion detracts from the newer aspects of the work (the PPK). 10 We have reduced these contents and discussed more about how camera properties impact on SfM output precision and accuracy.
We retained some discussion about the low FOV feature. It not only determines the survey design, but also affects the tie point matching due to a more intense radial distortion, which affects the accuracy.
To deeper understand what difference comes out from the low FOV feature regarding to tie point precision, we carried out some additional flight survey using the low FOV action camera. In this survey, we used a denser flight plan to have a higher 15 overlap and we clipped the images to retain the central area of each image. The new dataset has a much lower radial distortion.
We also down-sampled the resolution of the DSLR dataset to have the same GSD as the action camera images, this allowed us to evaluate the variate (GSD or FOV) controlling tie point uncertainties (P19).
Both precision map exhibited spatialized pattern, we thereby infer that the low FOV resulted in the non-spatialized precision of the action camera dataset. It also indicated that the low FOV affected tie point matching. With a diagonal FOV of ca. 43º , 20 one tie point can be observed simultaneously by 7-12 images for DSLR camera in our case, while 60-80 images for the action camera which are from wider imaging angles.

5) Throughout, when discussing results from different cameras, I suggest that a dimensionless approach based on pixels (or 25
ground sampling distance) is also used. This could be used to assess the quality of the photogrammetric networks achieved, and to generate insightagain, see previous work, including that of Mosbrucker et al. (2017). I would actually see a much more detailed assessment of the PPK performance as providing the most useful (i.e. transferrable) insight.
We presented the accuracy results of each survey using density plots, showing the CP residuals on X, Y and Z directions. The units were given in both meters and pixels. The pixels were calculated based on GSD at corresponding flight height. We expressed the accuracies in pixels to standardize the RMSEs in terms of the expected error incurred from GSD. The CP XYZ RMSEs for the DSLR camera corresponds to ca. 4-15 pixels. However, it should be noted that the GSD for the DSLR camera is extremely fine (0.006 m) due to the low flight height, and this is much finer than the width of the markers used on the CP 5 (0.02 m) or the precision of the CPs. As a result, the XYZ RMSEs for the action camera were better and within a range of 1 to 5 pixels. The extreme high GSD (down to 6 mm) makes it difficult to compare it to reported accuracies in terms of pixels.
However, by reporting both pixels and meters, and by discussing the specific conditions of our analysis, we hope we have sufficiently addressed the issue of transferability.  James et al. 2017aJames et al. -http://dx.doi.org/10.1016James et al. /j.geomorph.2016 resulting from overweighting the GCPs in that case). Details of the a priori assigned camera position precisions used in the 15 adjustments need to be provided and, given that they are often optimistically estimated, the effects of diluting the estimates could be explored.
We added the images residuals plot in the appendix, showing the shift between the original image positions and the optimized position after BBA process. The DSLR images had a smaller SD than the action camera images, indicating that the action camera images had higher random error regarding the BBA process. 20 Figure. Residuals on the images and CPs in planimetric view. Vectors give the horizontal residual component magnified by ×500 for DSLR survey (left) and ×100 for action camera survey(right). With inset mean value and standard deviation of the image residuals.
As for the image overlap outlines of the DSLR datasets, we agreed that the camera positions might have been over-constrained.
However, the shift between areas where constructed from the two adjacent images was less than 2 cm, which can be eliminated by applying a LoD threshold. In order to find a balance between the camera accuracy (BBA liberty) and the tie point reliability 5 for the PPK solution, we implemented a test of setting different camera accuracy (from 0.01 m to 1 m) and validated the precision by CP residuals and corresponding Monte Carlo extracted values. We found a strong relation between precision and camera accuracy. It indicated that for direct georeferencing, the precision of tie points was determined by camera accuracy, which means that the camera accuracy should be wisely set. It should be noted that the overlap outlines were only observed in the low FOV DSLR dataset, whereas the fisheye action camera output had no such outline effect. 10

Figure. The relationship between precision and camera accuracy.
We also explored the relation between tie point uncertainty and tie point density. From the figure we inferred that denser tie points generally lead to robust positioning of tie points. It implies that areas with relatively higher tie point density are of higher probability to be accurate and precise in the SfM output. With increased survey (images) density, the accuracy can be 15 further improved when using RTK/PPK precise positioning, before which photogrammetric considerations are the limiting factors.  We have modified this figure and add an image of GCPs.
All figures need to be checked for readability of the text labels. In particular, all map figures have scale and other labels which 10 are far too small to be readable, and font sizes vary substantially across the figures. Labels must be readable: more consistent font sizes, of at least 9 point, will help.
We have adjusted the size of figures to make it more readable.  DoDsrepresent image overlaps etc for the DSLR but not for the action camera.
We have rephrased the caption, i.e., spatialized error threshold for DSLR camera and constant error threshold for action camera.

Fig 7b LoD before/after lines indistinguishableneeds more careful visualisation.
We have adjusted the size. 5 Fig. 8 Colour scale given to four decimal places could be tidied up.
We have modified the figure to have the same decimal.

The paper "Evaluating the Potential of PPK direct Georeferencing for UAV-SfM Photogrammetry and Precise Topographic
Mapping" fits the scope of the journal and I consider that the paper is very interesting for the Earth Surface Dynamics ' 5 readership. Moreover, it is a well-written paper, with very interesting results and rigorous validations. However, some minor revisions and comments must be fixed before the final publication: Below, we show how we have revised the manuscript in light of these comments and recommendations.
Scientific comments: 10 1) Introduction (section 1) and Discussion (section 4.2): There is a very recent publication where it is compared the accuracy of different PPK approaches and other positioning alternatives, using DLSR cameras (10.1016/j.jag.2018.10.018). This could be in the introduction and in the discussion, since this research follows a similar workflow.
We have followed the suggestion and added the work by Padró et al. (10.1016Padró et al. (10. /j.jag.2018). We will also include the PPP work by Grayson et al. (2018;DOI: 10.1111/phor.12259) in Table 1 to strengthen the advance in direct georeferencing. 15

2) P6 (section 2.3.2): Why did you not post-processed the static GNSS measurements?
The positioning measurement of GCPs was conducted using Reach RS in RTK mode, for which the differential correction data was transmitted via mobile IP network (the same approach for determining the base station coordinate). The Reach RS + GPS pole setup could provide a better control of antenna placement and reduce disturbance. We also tested the precision of 20 the RTK solution by repeatedly measuring a fixed point near our department (12 km from the study field and 20 km from the BRUS station), and the error was ca. 0.010 m in XYZ. We thereby determined GCPs by RTK solution.

3) P7 (section 2.4.2): What was the interpolation method used in the DSM generation (TIN, bilinear, bicubic)?
It is the mean altitude from the point cloud data which is assigned to the DSM raster values. We added this information in the 25 revised manuscript (P9L2-3). After initial processing of pix4d, the software will generate a file with optimized position information based on the distortion 30 model. The external camera parameters are given by: T = (Tx, Ty, Tz) the position of the camera projection center in world coordinate system. 9 R the rotation matrix that defines the camera orientation with angles ω, φ, κ (PATB convention.) If X = (X, Y, Z) is a 3D point in world coordinate system, its position X' = (X', Y', Z') in camera coordinate system is given by: This was automatically computed in the initial processing, and the external camera parameters can be derived from the output 5 "txt." file.
We have substantially rewritten the section to include the detailed approach for obtaining precision map (section 2.5.2-2.5.3). We have strengthened this discussion (section 4.2).

6) P5 (section 2.3.1): Finally, the authors set the trigger interval in seconds, but they do not detail the rover velocity. Then, if 15
the v is specified the reader could know how many meters lag between image captions and, if the GNSS rate is given,the distance between GNSS records.
The rover velocity is determined when the front-overlap, flight height, trigger interval and the camera parameter (especially horizontal FOV) are preset. Given that the trigger interval for DSLR camera (EOS) was 2 s and action camera (GoPro) was 4 s, the velocity was ca. 4.5 m/s and 2.8 m/s, respectively. The corresponding distance between each capture were 9 m for EOS 20 and 11 m for GoPro. The image information can also be derived from the GPS logging or Pix4D output log after initial postprocessing.

Referee #3
General comments: The manuscript evaluated the repeatability of PPK UAV flight missions for precise topographic mapping. It is well structured and well written providing sufficient literature background and state-of-the-art methods. Results are presented from different 5 perspectives and discussed broadly. The manuscript provides a contribution to the current debate of emerging PPK UAV data acquisition workflows that can be of interest to the readership of Earth Surface Dynamics. However, I encourage the authors to revise the manuscript based on some minor comments.

Scientific comments: 10
1) Compared to the entire manuscript, the introduction is very long, and some paragraphs could be more concise as most of the text builds on the general knowledgebase (e.g. general camera parameters, exterior orientation). Even though the authors stress the aims of the research, the novelty of this contribution is a bit fuzzy, as much research in this field has been done already. Efficiency is mentioned as one of the main objectives; however, there is little evidence on this in the results/discussion section as those parts mainly focus on repeatability/reproducibility. 15 We have compacted the introduction and improved its focus, readability (section 1).
2) Comparing metrical horizontal/vertical residuals of datasets with different GSD might not be the best approach, and normalized residuals could be more appropriate.
We will follow the suggestion and Referee #1 has similar comment to use a dimensionless approach. We have reorganized 20 and summarized the datasets in Table 2 to better present the results. Note: Repeated flight missions were marked as F_a and F_b. The missions showed in the list were used parallel flight plan.
The accuracy results of each survey were presented using density plots (Fig. 4), showing the CP residuals on X, Y and Z directions. The units were given in both meters and pixels. The pixels were calculated based on GSD at corresponding flight height. 5 3) Line 3 page 6: Can you provide more information on the decision not to use a crossflight pattern or a single perpendicular strip as recommended by various authors?
The UAV autonomy (flight duration) is an important factor to take into account. A crosshatch pattern could improve accuracy by providing multi-angle images and increased overlap. However, it doubles the survey time and battery consumption, and 10 may average out systematic bias in positioning. We therefore only used parallel flight lines in the main text. We also wanted to investigate the large-FOV (field of view) action camera, so as to find a better solution for accuracy/efficiency ratio.
For the surveys we implemented, we did flights using 'crosshatch' pattern. However, to simplify the manuscript we only used the 'parallel' flight pattern, which were listed in Table 2. We can also provide the results of 'crosshatch' missions, as a comparison between the two flight patterns. We noticed that for the PPK direct georeferencing, a crosshatch pattern had slightly 15 better performance on the altimetric accuracy.

4) Did your UAVs also record attitude parameters? In the manuscript, you should make clear why you used some observations of the external orientation parameters and others not.
We apologize that this was not clear. Our cameras used a separate system without connection to IMU, so the images only 5 contained positional information without attitude parameters. We have rephrased the method section to make it clear.

5)
You used Pix4D as a kind of black-box program. Which settings did you choose for camera calibration and the accuracy for geotagging information?
We added details in 2.4.2 Point Cloud and DSM Generation. 'The horizontal and vertical accuracy were both set as 0.05 m. 10 We kept the remaining settings as default as 3D maps template, i.e., full keypoints image scale, automatic targeted number of keypoints and standard calibration method.' The artificial quadratic pattern of the DSLR camera were observed especially for the low-FOV camera. With a diagonal FOV ca. 43º , one tie point can be observed simultaneously by 7-12 images for EOS camera in our case. While we compared the output with the large-FOV camera GoPro and one single point can be captured by 60-80 images from wider angle. This had different effects on the BBA process, e.g., GoPro output had no such outline effects. Though the image overlap outlines shift in our case is ca. 2 cm, which can be eliminated by applying DoD threshold. We have added related discussion. 20 7) Some results are not very clear to the reader. I recommend extending the results section with some more explanation to enhance readability.
We have followed this suggestion and have rewritten the result section.

1) Figures: Check consistency of font and readability of legends
We have adjusted the size to improve the readability.
2) There are some typos and grammar mistakes -I recommend English proofreading prior to publication.
We have corrected these typos. Abstract. Images captured by Unmanned aerial vehicle (UAV) and processed by Structure from Motion (SfM) 10 photogrammetry are increasingly used in geomorphology to obtain high resolution topography data. Conventional georeferencing using ground control points (GCPs) provides reliable positioning but the geometrical accuracy critically depends on the number and spatial layout of the GCPs. This limits the time-and cost-effectiveness. Direct georeferencing of the UAV images with differential GNSS, such as PPK (Post-Processing Kinematic), may overcome these limitations by providing accurate and directly georeferenced surveys. To investigate the positional accuracy, repeatability and reproducibility 15 of digital surface models (DSMs) generated by a UAV-PPK-SfM workflow, we carried out multiple flight missions with two different camera/UAV systems: a small-form low cost micro-UAV equipped with a high FOV action camera and a professional UAV equipped with a DSLR camera. Our analysis showed that the PPK solution provides the same accuracy (MAEmean: ca. 0.012 m, RMSE: ca. 0.03 m) as the GCP method for both UAV systems. Furthermore, our results indicated that camera properties (i.e., focal length, resolution, sensor quality) have an impact on the accuracy but planimetric and altimetric errors 20 remained in the range of 0.011 to 0.024 m. By analysing the repeatability of DSM construction over a time period of a few months, ourOur study demonstratedemonstratesd that a UAV-PPK-SfM workflow can provide consistent, repeatable 4D data with an accuracy of a few centimetres without the use of GCPs. However, a few flights showed vertical bias and this could be corrected using one single GCP. We further evaluated different methods to estimate DSM uncertainty and show that this has a large impact on cm-level topographical change detection. Tie pointAn uncertaintyies were derived from Monte Carlo 25 simulations to acquire spatially explicit analysis showed that the minimum level of topographical change detection was ca.
±0.04 m for a high-end DSLR camera and ca. ±0.08 m for an action camera (for a flight height of 45 m). We also showed that camera properties (i.e., focal length, resolution, sensor quality) have a large impact on the tie point uncertainties. The DSM reconstruction and surface change detection based on a DSLR and action camera were reproducible: the main difference lies in the level of detail of the surface representations. The level of detection substantially improved when reducing the UAV 30 flight height. This study demonstrates the repeatability, reproducibility and efficiency of aThe PPK-SfM workflow in the context of 4D earth surface monitoring with time-laps SfM photogrammetry. As such, it should should be considered as an efficient tool to monitor geomorphic processes accurately and quickly at a very high spatial and temporal resolution.

Introduction
During the past decade, Unmanned Aerial Vehicless (UAV'ss) or Unmanned Aerial Systems (UAS's) have emerged as a very valuable tool for aerial surveying (Passalacqua et al., 2015;Tarolli, 2014). An important application in geoscience is the 5 generation of hHigh-resolution topography (HRT) data (i.e., point clouds, digital surface models-DSMs or digital elevation models-DEMs) from 2D imagery using Structure from Motion (SfM) and Multi-view Stereo (MVS) photogrammetry (Eltner et al., 2016;James and Robson, 2012). Compared to satellite-or airborne-based sensing approaches, the UAV's provide important advantages, more specifically they provide a considerably higher spatial resolution at a relatively low cost in combination with a high versatility in terms of sensors and data collection. With the capability of detecting topographical 10 change at a very high resolution and accuracy, the UAV-SfM framework has become an increasingly used tool or Unmanned Aerial Systems (UAS) are increasingly used in geomorphological research . They are currently used as tools to for the monitoring of landslides (e.g., Clapuyt et al., 2017;Turner et al., 2015), overland flow erosion (e.g., Eltner et al., 2017;Pineux et al., 2017), river dynamics (e.g., Hemmelder et al., 2018) and vegetation dynamics (e.g., Candiago et al., 2015).
However, the inter-comparison of UAV-SfM photogrammetric products requires very accurate georeferencing. So far, the use 15 of ground control points (GCPs) surveyed with precise GPS systems or total stations is generally employed for accurate geodetic positioning. The GCP-based georeferencing method has been widely proven to be a solid solution for accurate georeferencing (Hawkins, 2016;James et al., 2017;Turner et al., 2016). However, GCPs need to be placed as a network and this comes at a cost as it is time consuming. Furthermore, the accuracy depends on the quantity and distribution of GCPs (Sanz-Ablanedo et al., 2018). When used in a monitoring study, additional issues arise from the fact that GCP's can move (weather 20 impact or surface deformations). Finally, a major limitation arises from the fact that GCP's cannot be placed in poorly accessible terrain due to practical or safety reasons (e.g., swamps, landslides or glaciated areas).
Direct georeferencing based on high precision GNSS is key to overcome this issue, but it requires the accurate geotagging of aerial images at the exposure time. WithinDuring the last several years, the development of high-quality IMU and GNSS technology and dedicated RTK (Real Time Kinematic) and PPK (Post-Processing Kinematic) solutions for UAVs has may 25 provide enabled the accurate measurements of UAV/camerathe position and orientationEO parameters. By double differencing the phase ambiguities between two GNSS/GPS receivers, atmosphere propagation delay and receivers clock errors can be eliminated. RTK positioning requires a stable radio (or internet) link between a base and the UAV, and this can sometimes be challenging due to radio link outages and/or GNSS signal blocks. PPK, in contrast, processes the information after the flight and there is thus no risk of data loss due to link outages. In addition, precise ephemeris data of GNSS satellites is available 30 3 during post processing, PPK offers the advantage that positioning can be based on previous and future GNSS data, which can often provide a more consistentaccurate solution. The utilization of such an approach has the potential to avoid or mitigate eliminate the need for GCPs . Several studies already investigated the application of RTK/PPK direct georeferencing by the integration of sensor orientation with onboard RTK-GPS (Fazeli et al., 2016;Forlani et al., 2018;Stöcker et al., 2017). In a study performed by Gerke and Przybilla (2016), the block orientation accuracy could significantly be enhanced by using an 5 on-board RTK-GNSS solution. With an enabled RTK-GNSS and cross flight pattern, the best scenario reached a final horizontal geometric accuracy of 4 cm. Recently, both georeferencing methods are gradually matured and can deliver centimeter-level accuracy in geomorphological applications (Table A1Table 1). However, to our knowledge the accuracy and repeatability of HRT products derived from RTK/PPK in the context of longer-term 4D earth surface monitoring with timelaps structure-from-motion photogrammetry has not been quantified. 10 Camera position and orientation are defined as exterior orientation (EO) parameters. The coordinates of the camera projection center at the exposure time are typically measured by the on-board GNSS receiver, and are then introduced as constraints in the bundle block adjustment, or are used to compute the transformation from the SfM arbitrary reference to the mapping system . Typically, single GNSS receivers of consumer-grade UAVs are not able to deliver sub-meter level positioning accuracy.
Therefore, the use of ground control points (GCP) surveyed with precise GPS systems or total stations is generally employed 15 for accurate geodetic positioning. The GCP-based georeferencing has been widely proven to be a solid solution for accurate georeferencing . However, GCPs need to be placed and surveyed and this comes at a cost as it is time consuming. Furthermore, the accuracy strongly depends on the number of GCP's used and their spatial layout (Sanz-Ablanedo et al., 2018). When used in a monitoring study, additional issues arise from the fact that GCP's can move (weather impact or surface deformations).
Finally, a major limitation arises from the fact that GCP's cannot be placed in poorly accessible terrain due to practical or 20 safety reasons (e.g., swamps, landslides or glaciated areas).
High resolution topography (HRT) data (i.e., point clouds, digital surface models-DSMs or digital elevation models-DEMs) can be acquired using different techniques (e.g., Light Detection and Ranging (LIDAR), Synthetic Aperture Radar (SAR), Structure from Motion (SfM), etc.). The main advantage of LIDAR and SAR is that both techniques are not limited by 25 illumination or cloud/canopy cover . However, they are of high operation costs and produce very large datasets that are difficult to interpret. Alternatively, SfM and Multi-view Stereo (MVS) provide low-cost options for acquiring HRT . The combination of UAV-based aerial photos and SfM algorithm enables to reconstruct three-dimensional (3D) surface models based on a set of digital RGB images from different perspectives . Geomorphic processes can thus be quantified using multi-temporal aerial photogrammetry . However, it is essential to understand the utility, limitations, and particularly the accuracy of HRT derived 30 from these techniques.Research has shown that tThe accuracy and precision of photogrammetry also SfM-generated HRT data depends on many other factors, including camera/image quality, camera calibration, flight plan designcharacteristics, camera 4 modelling methodology, SfM algorithms, and surface texture and albedo, etc. georeferencing strategy. SfM The bundle block adjustment (BBA) process determines the 3D positions of key features/points presented in the overlapping part of multiple images by recognizing and matching keypoints (hereafter referred to as tie points, i.e., keypoints that can be identified on two or more images). In a next step, then calculates the exact relative position locations and orientations of the camera are estimated by performing a fit and minimizing the error through the tie keypoints (Triggs et al., 2000). The . abovementioned factors 5 affects the identification of the tie points, which are infrequently reported, but important, nevertheless. Therefore, the accuracy of traditional photogrammetric data depends heavily on control quality, whereas SfM accuracy is also strongly affected by image characteristicsthis process is closely related to the image quality as well as the accuracy and precision of the image georeferencing (Mosbrucker et al., 2017).
The selection and configuration of cameras are of special interest in UAV photogrammetry.Camera type and settings are key 10 factors determining image quality and 3D cloud construction . Digital cameras equipped with high quality sensors (e.g., a DSLR camera) provides better image quality due to higher resolution and reduced image noise whenrelative to compared to a more portable and smaller sensor (e.g., a compact or action camera), which and this results in high quality DSMs (Eltner and Schneider, 2015;Micheletti et al., 2015;Mosbrucker et al., 2017). The focal length relates to radial distortion and associated calibration of the camera lens (Rosnell and Honkavaara, 2012;Sanz-Ablanedo et al., 2012). While small focal length (or wide-15 angle) leads to a large field of view (FOV), which therefore requires a less dense flight plan for a given lateral overlap, these images are subject to increased radial distortion, which can degrade accuracy (James and Robson, 2014;Mosbrucker et al., 2017). Some studies have investigated the impact of focal length on DEM accuracy (Clapuyt et al., 2016), but mainly on DEM reproducibility. Furthermore, the distance between sensor and surface also determines ground sample distance (GSD), which impacts on accuracy. Eltner et al. (2016) showed in a review of 54 studies that the error of SfM-derived DSMs increased 20 nonlinearly with an increasing surface to camera distance (Eltner et al., 2016). Another constraint to SfM accuracy is radial distortion and associated calibration of the camera lens . The distortion is highly correlated to the lens focal length, which also determines the camera's field of view (FOV). While small focal lengths (or wide-angle) is common to provide a large FOV which could reduce the flight plan density for a given overlap in UAV photogrammetry, these are subject to increased radial distortion and smaller scale for a given object distance, which can degrade accuracy (James and Robson, 2014a; Mosbrucker 25 et al., 2017). Some studies have investigated the impact of focal length on DEM accuracy (Clapuyt et al., 2016), but mainly on DEM reproducibility. An optimal configuration, corresponding to specific research needs, on the accuracy of aerial photogrammetry remains poorly quantified until now. Furthermore, it should also be noted thatFrom an operational point of view, camera weight is a critical variable as it determines the size and weight of the UAV system. tThere is a large difference in weight between DSLR (0.5-1.5 kg) and action cameras (0.05-0.15 kg) and this has large implications, not only for flight 30 autonomy (and hence spatial coverage), but also the choice of the UAV platform. Small action cameras can be mounted on small 'micro' drones, which offer the advantage of a much higher portability and applicability, as they are subjected to less 5 stringent UAV flight regulation (e.g., in Belgium, a flexible class 2 UAV operation license certificate allows for a maximum flight height of 45 m and a weight limit of 5 kg (UAV + payload)).
Camera position and orientation are defined as exterior orientation (EO) parameters. The coordinates of the camera projection center at the exposure time are typically measured by the on-board GNSS receiver, and are then introduced as constraints in the bundle block adjustment, or are used to compute the transformation from the SfM arbitrary reference to the mapping system 5 (Barazzetti et al., 2010). Typically, single GNSS receivers of consumer-grade UAVs are not able to deliver sub-meter level positioning accuracy. Therefore, the use of ground control points (GCP) surveyed with precise GPS systems or total stations is generally employed for accurate geodetic positioning. The GCP-based georeferencing has been widely proven to be a solid solution for accurate georeferencing (Hawkins, 2016;James et al., 2017;Turner et al., 2016). However, GCPs need to be placed and surveyed and this comes at a cost as it is time consuming. Furthermore, the accuracy strongly depends on the 10 number of GCP's used and their spatial layout (Sanz-Ablanedo et al., 2018). When used in a monitoring study, additional issues arise from the fact that GCP's can move (weather impact or surface deformations). Finally, a major limitation arises from the fact that GCP's cannot be placed in poorly accessible terrain due to practical or safety reasons (e.g., swamps, landslides or glaciated areas).
Within the last several years, the development of high-quality IMU and GNSS technology and dedicated RTK (Real Time 15 Kinematic) and PPK (Post-Processing Kinematic) solutions for UAVs may provide accurate measurements of the EO parameters. By double differencing the phase ambiguities between two GNSS/GPS receivers, atmosphere propagation delay and receivers clock errors can be eliminated. RTK positioning requires a stable radio (or internet) link between a base and the UAV, and this can sometimes be challenging due to radio link outages and/or GNSS signal blocks. PPK, in contrast, processes the information after the flight and there is thus no risk of data loss due to link outages. In addition, PPK offers the advantage 20 that positioning can be based on previous and future GNSS data, which can provide a more consistent solution. The utilization of such an approach has the potential to eliminate the need for GCPs . Several studies already investigated the application of RTK/PPK direct georeferencing by the integration of sensor orientation with onboard RTK-GPS (Fazeli et al., 2016;Forlani et al., 2018;Stöcker et al., 2017). In a study performed by Gerke and Przybilla (2016), the block orientation accuracy could significantly be enhanced by using an on-board RTK-GNSS solution. With an enabled RTK-GNSS and cross 25 flight pattern, the best scenario reached a final horizontal geometric accuracy of 4 cm. Recently, both georeferencing methods are gradually matured and can deliver centimeter-level accuracy in geomorphological applications (Table A1).
The quality of UAV survey output is typically analyzed using the spatial patterns of errors in DSMs, and this includes both the accuracy and the reproducibility of DSM generation. Errors propagate when differences of DSMs (DEM of differences, DoD's) are computed to quantify topographic change. Given the uncertainty inherent in individual DSMs, how to distinguish real 30 geomorphic changes from noise, and how well these uncertainties are considered control the reliability of interpretation. In order to isolate and quantify the uncertainty error that is associated with the topographic reconstructions, reproducibility 6 assessments are critical aspects of monitoring landform changes over time (Brasington et al., 2000;Wheaton et al., 2010).
However, until now the repeatability of direct PPK-based georeferencing for SfM-derived point clouds and/or DSMs has not been thoroughly evaluated. Past research has shown that a RTK-SfM workflow is repeatable (Forlani et al., 2018), but the flights analysis waswere based on repeated flights conducted over a done in a very short time frame: i.e. with very similar satellite constellation, base station setup and and light conditions. It remains uncertain to what extent a PPK-SfM workflow 5 may provide consistent 4D data when survey conditions are variable, e.g. when monitoring over longer periods of time (e.g. weeks or even, months). This is particularly relevant for geomorphological applications that require centimetric precision such as rill erosion or soil roughness monitoring (d' Oleire-Oltmanns et al., 2012;Eltner et al., 2015). A second issue is the platform: Cheap low-cost, easy-deployable RTK-enabled micro-UAV's (smallform ca. 25×25 cm, weight 1.4 kg) equipped with small cameras have recently become available, but their accuracy and repeatability, relative to professional UAV systems (large-10 form ca. 80×80 cm, weight 4.5 kg) equipped with high-end camera's remains poorly quantified. In particular, the influence of the UAV/camera setup on the minimum level of topographical change detection should be quantified in order to guide geomorphological applications.
The main objective of this study is thereby to quantify the (i) repeatability, (ii) reproducibility and (iii) efficiency of the PPK-SfM framework in the context of 4D earth surface monitoring with time-laps structure-from-motion photogrammetry where 15 centimetric precision is required. More specifically, we aim to (i) assess the accuracy and repeatability of PPK and Non-PPK solutions in georeferencing to examine the capability of using PPK without the need for GCPs, (ii) assess the reproducibility of surface topography change detection using PPK solutions for two different UAV/camera setups (i.e., with a DSLR camera and versus a high FOVan action camera), (iii) investigate the factors controlling the errors associated with surface reconstructions and (iiiv) evaluate different approaches to estimate uncertainties using PPK solutions and their implications 20 for surface change detection/demonstrate the potential of the approach for geomorphological research requiring high precision using a case-study.

Study Site
The study site is located in an agricultural area (1.7 ha) in the Belgium loess belt, ca. 40 km southeast of Brussels, Belgium 25 ( Fig. 1). It is characterized by a slightly undulated terrain with an altitude range between 207 m to 210 m a.s.l. and by very gentle slopes (mean slope: 1°). The site is partially cultivated while other parts are covered by grass. The surface was classified into five classes, i.e., bare soil, short grass, shrub, road and hay stacks. 7 2.2 Hardware Setup

Platforms and Payloads
We evaluated (i) a high-payload UAV system equipped with a DSLR camera and (ii) a consumer-grade UAV equipped with a fisheye action camera. The high-payload aerial system is a custom-built Hexacopter and is equipped with a DJI A2 flight controller. The platform has an effective payload of 4 kg and an autonomy of ca. 15 minutes. This UAV was equipped with a 5 Canon EOS 550D camera (18 Megapixels, 5184 × 3456 pixels, with Canon EF 28 mm F/2.8 lens). The consumer-grade UAV was a DJI Phantom 3 Advanced Drone. We removed the DJI camera/gimbal system and mounted a Hero GoPro 3 camera (12 Megapixels, 4000 × 3000 pixels, with 2.92 mm F/2.8 123° HFOV lens) (Fig. 2). Both platforms are equipped with a compact multi-GNSS RTK receiver (Reach RTK kit, Emlid Ltd) with RTK/PPK capability as described below.

PPK-GPS Module 10
During the UAV flights, a Reach RS (Emlid Ltd) base station was mounted on a tripod located in the north of the test area as base station to provide positioning correction input. The maximal distance between the UAV and the base station was 220 m.
The receiver of the base is configured to log the raw data in a RINEX file at 5 Hz using the satellite GPS, GLONASS and GALILEO. We did not use a fixed position for the base station, but randomly positioned in an area of ca. 10 × 10 m for each flight. Both UAVs were equipped with a Reach GNSS receiver to log the raw data as UBX format using GPS and GLONASS 15 satellites. The antenna model was Tallysman's TW2710, which covers the GPS L1, GLONASS G1, BeiDou B1, Galileo E1, and SBAS (WAAS, EGNOS, and MSAS) frequency bands. The antenna was mounted on an aluminum plate, with the center right above the camera lens center to minimize the offset the shift between the antenna phase center and camera projection center. The antenna height was 22.5 cm and this difference between the antenna and camera projection center was considered during the post-processing. No lever-arm corrections were considered, but the offset between the camera and the GPS receiver 20 was considered in the camera position assuming a constant vertical offset (see below). Because of the small magnitude of the physical offset vector (0, 0 and 22.5 cm in X, Y and Z in the body frame, respectively), typical tilting during flights would only propagate to a camera position error of about 1 cm, which is close to the expected GPS positioning error of about 2-3 cm.
For the high-payload UAV, we used the hotshoe of the camera to timemark the pictures with a GPS event that are logged on a Reach GNSS device mounted on the UAV. As the action camera has no hotshoe, we built an electronic system to integrate 25 and synchronize the GPS with the action camera. To this end, a single board computer (SBC) is used as a trigger by transmitting an electrical signal to both the camera and GPS unit. To eliminate the lag between the shutter opening time of the camera and the GPS recording time, we quantified the delay between the electrical signal and the shutter opening by integrating a LED light in the circuit. Several delay times were tested until the LED light was visible on the images taken by the action camera.
This procedure resulted in a system where the geotagging was accurately synchronized with the GPS time. For both 30 8 UAV/camera systems, we did not build a link between the UAV-IMU and camera. As a result, the images only contained positioning information without attitude parameters.

Flight Planning
Flight missions were planned using the Autopilot app (Hangar Technology, 2018). The side overlap was set to 80%. The 5 frontal overlap was defined by the speed of the UAV and the camera trigger interval which was set at 2 s for DSLR camera and 4 s for action camera, which resulted in a frontal overlap of ca. 90% for both systems.
Flight mission arrangements are summarized in Table A2Table 2. Three flights (including repeated flights) were performed conducted three timesbefore a part of the study area was plowed. These flights were conducted (from late March to early April, 2018) at a constant height of 45 m above the take-off point leading to a ground sample distance (GSD) of less than 0.63 cm 10 and 3.11 cm for the DSLR and the action camera, respectively. The configuration of the three missions was kept constant to test the reproducibility of the resulting DSMs. At the end of the survey period (6 April), the farmland was plowed leading to a change in surface roughness. To acquire higher GSD and detect ground surface change, we set the flight height at 35 m for DSLR camera and 20 m for action camera respectively for this mission. Flight mission arrangements are summarized in Table   A2. It should be noted that we did not usethe missions were performed using simple parallel rather than cross-hatch flight 15 pattern, as the latter mission setup can mask systematic bias. cross-flight patterns as this may average-out positional errors.

Ground Control Points
Sixteen fixed targets were distributed evenly across the study area before the survey as control points (Fig. 2)

Georeferencing Configuration
The open source software package RTKLib was used for computing differential positioning (Takasu and Yasuda, 2009). Raw GPS data from the UAV-mounted cameras and the base station were then extracted and corrected by post-processing using RTKLib. We verified the consistency of the estimated camera positions using PPK by evaluating different satellite elevation 5 masks (15° and 20°) and methods (i.e., fix and hold versus continuous mode).
We extracted A PPK solution allows various georeferencing configurations by changing the positioning mode in RTKLib, and this enables us to evaluate the performance of both PPK-GPS or and single GPS solutions for the camera position estimates.
To assess the accuracy of different georeferencing options, datasets were processed with four configurations, i.e., single GPS, single GPS + 8 GCPs, PPK only, and PPK + 1 GCP. For the conventional methods using GCPs and single GPS, we used the 10 RTKLibon-board single GPS solution to acquire the images coordinates, and selected half of the targets as 3D GCPs during block control processing. The remaining control points were then used as checkpoints. The setup of GCP/CP is shown in Figure 3. In the single GPS + 8 GCPs scenario, the eight selected GCPs were evenly distributed in the survey area. In the PPK + 1 GCP scenario, cross validation was used. We selected one point as a GCP while the remaining targets where then used as CPs and this bundle adjustment processing was repeated sixteen times. The accuracy assessment was based on the average 15 error of the cross-validation.

Point Cloud and DSM Generation
The geotagged images were processed with the Pix4D Mapper software (www.pix4d.com). The software uses the SfM algorithm to generate 3D point clouds, DSMs and orthophoto mosaics of the surveyed area. The procedure consists of three main steps: (i) Initial Processing, (ii) Point Cloud generation, and (iii) DSM and orthomosaic generation. First, the photographs 20 are aligned using a point matching algorithm that automatically detects matching points on overlapping photographs and uses these points to simultaneously solve for exterior orientation (EO) parameters. With additional position information that is available for the images or GCPs, the software then georeferences the model and refines the camera calibration by minimizing the error between the modeled locations of the points and the measured locations, meanwhile, non-linear deformations within the model are corrected. Pix4D reports the offset between calculated and measured GCP locations afterwards, providing an 25 initial estimate of model accuracy Camera accuracy is a key parameter allowing users to set how accurate the coordinates of images can be, which would affect the determination of estimated camera positions in the BBA process. Considering the precision of PPK GPS (ca.0.02 m) and the antenna angle movement caused by UAV attitude during flying, we set the horizontal and vertical accuracy both as 0.05 m.
We used the Pix4D 3D maps template for the remaining settings, i.e., full keypoints image scale, automatic targeted number 30 of keypoints and standard calibration .method. After initial processing, Pix4D generates a dense 3D point cloud at a given quality and resolution. In order to maintain highlight the characteristics of the original data, the clouds were not processed or filtered nor smoothed. Gridded From these point clouds, DSMs and Orthophoto mosaic were then generated based on the mean altitude of these point clouds. The 3D outputs (i.e., point clouds and DSMs) used for reproducibility assessment were georeferenced using the PPK method (and no GCP were considered). The corresponding GSD grid resolutions of the DSMs were less than 0.031 m for the action camera and 0.006 m for DSLR camera at the flight height of 45 m. 5

Accuracy Assessment
The aAbsolute accuracy test validation was performed using the CPs (which were not used in the cloud generationBBA process) by computing comparing the differences between the coordinates of the 16 CPcheckpoints in the 3D cloud and with those reference values measured in the field by RTK-GNSSNSS. Mean values absolute error (MAE) and the root mean square 10 error (RMSE) and standard deviation of the differences of the differences were computed for each flight to: (i) assess the accuracy of SfM outputs with different georeferencing configurations (ii) assess the precision of PPK-SfM reconstruction considering CPs as static references during the observation period (i.e., with variable satellite constellation, light conditions and base station setup), and (iii) detect whether there are internal systematic shifts and block deformations in the SfM output.

Precision Maps Based on Monte Carlo SimulationError Source Exploration 15
To demonstrate how tie points uncertainty can vary spatially, we implemented a Monte Carlo approach that enabled precision maps to be produced when using SfM-based software. Following the workflow by James et al. (2017), the processing was

Repeatability and Reproducibility AssessmentDSM Uncertainty Characterization
To robustly distinguish real changes of DSM/DEM differencing from the inherent noise (Fuller et al., 2003), DoD uncertainty 10 must be considered. Regardless of the approach used to generate DSM/DEMs, the process of accounting for DoD uncertainty follows a consistent progression via three steps: (i) quantifying the error surface (δz) of each individual DSM surface (ii) propagating the identified uncertainties into the DoD (δuDoD) and (iii) assessing the significance of the propagated uncertainty (Wheaton et al., 2010). The tie points differ between each repetition of the survey, and therefore we analyze the error propagation at the DSM level. There are two primary ways to build an error surface. The combined error can be calculated as 15 a single value for the entire DoD based on the average RMSE of each DEM if spatially-explicit estimates of the error do not exist. This method assumes that the errors in each cell are random and independent. Alternatively, a spatially variable error can be considered for both DEMs independently (e.g., Wheaton et al., 2013). The individual error in the DSMs can be propagated into the DoD as: where δuDoD is the propagated error in the DoD as minimum level of detection threshold (LoDmin)., and δzref and δzref are the individual error in referenced DSM and compared DSM, respectively.
To define a spatially variable confidence interval associated with each measurement and combining the uncertainties, a prescribed confidence level (95% in the following) is used to estimate locally the measurement accuracy and precision. The registration error (reg) is considered and assumed isotropic and spatially uniform, as the systematic bias in georeferencing may 25 exist Afterwards, the significance of uncertainties in DoD predicted elevation changes are typically expressed. The propagated uncertainties (i.e., δuDoD) are used to define an elevation change threshold as minimum level of detection threshold (LoDmin).
In practice, a user-defined confidence interval can be applied to indicate the reliability of threshold (e.g., Brasington et al., 2003;Wheaton et al., 2013). If the estimate of δz is a reasonable approximation of the individual error, Eq. (1) can be hereby modified to: 30 Where reg is the relative overall registration error between the surveys. LOD95% is the level of detection at 95% confidence interval..

Repeatability and Reproducibility Assessment
Using the aforementioned DoD method to assess the repeatability of DSMs, two datasets collected on the same day were selected: (i) DSMs from repeated surveys using the DSLR camera on 5 April; (ii) DSMs from surveys using the action cameras on 30 March (Table A2). As the earth surface represented by these DSMs was not subject to any change, differences should theoretically be close to zero and have a narrow Gaussian distribution indicating uncertainty/noise inherent to the approach. 5

UAV-based Monitoring of Surface Change
As mentioned above, the bare soilfarmland was plowed on 6 April, leading to surface roughness and volume change. Surveys on 5 April and 6 Aprilimplemented before and after the representing field conditions before and after the plowing plowing were compared to detect the change. In this case study, the PPK dataset was potentially subjected to higher reg error, while PPK + 1GCP scenario might be able to substantially mitigate the reg error. Therefore, a reg value was used based on the CP 10 RMSEs for the PPK dataset, whereas the PPK + 1GCP dataset was regarded with negligible reg error. In that case, the assessment of the constant and spatialized LoD were carried out: a DoD using a survey-wide LoD based on the Z-RMSE on CPs and a spatialized LoD based on the Monte Carlo altimetric precision. A zoomed-in area as well as a transect was sampled to illustrate the surface change using the LoDmin thresholds (Fig. 67). The sediment budget was subsequently assessed by computing DoD between DSMs, using the Geomorphic Change Detection (GCD) software (Wheaton et al., 2010). The GCD 15 software provides the capability of segregating and quantifying those uncertainties independently in each DEM and propagating them through to the DEM of difference. For each DEM, we set aforementioned two uncertain surfaces in the change detection between surveys. 1 GCP. For the action camera, the CP RMSEs for the GCP solution are better than 1 pixel for X, Y and Z coordinates. The CP RMSEs for the PPK solutions were slightly higher than for the GCP solution, but in the range of 0.5-1.4 pixels for the X, Y and Z coordinates. The values reported here are very close to the estimated error of the PPK solution. For both the mean error and SD, they were in the same order of magnitude for the single GPS + GCP, PPK and PPK + 1 GCP solutions. For datasets derived from the action camera, the accuracy (mean error) of the single GPS configuration was 1.53 m in the horizontal and 3.89 m in the vertical. The precision (SD error) of the single GPS When using single GPS + GCP, the accuracy was substantially enhanced to cm-level, and the absolute mean errors were less than 0.028 m. For both cameras, PPK + 1 GCP showed similar planimetric accuracy and better altimetric accuracyshowed slightly better results for the action camera than the DSLR datasets, i.e., 0.04 m, 0.05 m and 0.12 m in X, Y and Z. When using single GPS + GCP, the accuracy was substantially 5 enhanced to cm-level, and the absolute mean errors were less than 0.02 m. The PPK and PPK + 1 GCP configurations also showed accuracies of ca. 0.03 m. For the PPK solution, adding 1 GCP did not affect the accuracy.. Adding 1 GCP improved the accuracy of the altimetric CP RMSE of the PPK solution by 20% to 30%. The standard deviation for the mapping errors (SD error) are very similar for both cameras and PPK and GCP solutions (0.02--0.04 m), while as expected, the precision was substantially less good for the single solution (0.24--0.35 m). 10 Figure 4 shows the CP residual distributions for each survey for the PPK solution. As reported above, the overall accuracies and precisions among the surveys were robust within a range of 0.10 m, regardless of dates and missions. The planimetric accuracies of the surveys were robust (with little bias) and the errors were close to 0zero. In contrast, the altimetric accuracy showed a much higher uncertainty among the surveys with substantial bias for some flights. Similar results were obtained for 15 both camera setups, i.e., altimetric errors showed larger variation than planimetric errors. We can also express the accuracies in pixels to standardize the RMSEs in terms of the expected error incurred from GSD. The CP XYZ RMSEs for the DSLR camera corresponds to ca. 4--15 pixels. However, it should be noted that the GSD for the DSLR camera is extremely fine (0.006 m) due to the low flight height, and this is much finer than the width of the markers used on the CP (0.02 m) or the precision of the CPs. As a result, the XYZ RMSEs for the action camera were better and within a range of 1 to 5 pixels.The 20 positional accuracy validation shows a planimetric and altimetric error less than 0.03 m with the DSLR camera and 0.08 m with the action camera when using a PPK solution (Table 2). Both the DSLR and action camera can deliver a mean planimetric error of less than 0.027 m while the altimetric error for the action camera ranges from -0.04 to 0.05 m, which is substantially larger than DSLR surveys Analysis of the distribution of check point residuals derived from the surveys, shows that about 40% of the error is within the -0.01 m and 0.01 m interval (i.e., absolute error lower than 1 cm) for the DSLR surveys. A similar proportion was found for the action camera (Fig. A1). The 25th and 75th percentiles were -0.012 m and 0.019 m for the action camera and -0.009 m and 0.015 m for DSLR camera. The check point residuals for the DSLR surveys are distributed more closely around the mean, as 30 14 all the errors are smaller than 0.05 m. For the data derived from the action camera, the residuals are substantially more dispersed (  Fig. A1).

PPK Tie Point Error Correlative Analyses andPprecision Maps Spatial Variation
For soil surface change detection, it is important to quantify the precision of each surface. Here, we compare different methods to quantify precision. Figure 5 shows tie point precision maps derived from the Monte Carlo (MC) simulations. Spatial patterns 5 can be observed from the DSLR precision map, where shrub area have higher uncertainties while non-vegetated areas were modelled more precisely. The DSLR dataset had a much better precision and smaller range (0 to 0.05 m) when compared to the MC simulations for the action camera dataset. For the action camera, the precision ranged between 0 and 0.25 m. In contrast to the results obtained for the DSLR camera, the precision map for the action camera did not exhibitshow a clear structured spatial pattern. The boxplots represent the CP-derived precision based on the 5 repeated surveys (16 CPs were used in each 10 survey) (Fig. 5 c and d). The DSLR precision maps derived from the MC simulations are in line with the empirical precision derived from the CPs (i.e., 0.01 to 0.03 m). The slightly higher mean and range obtained for the empirical precision reflects the fact that for the MC analysis, only uncertainty in camera position was considered, while the empirical estimates reflect all sources of variability (i.e., positioning uncertainties, differences in image quality between surveys, etc.). In contrast, the action camera MC precision was substantially higher than the precision derived from the repeated CP surveys. In other words, the 15 observational precision estimates were smaller than those estimated from the MC analysis.
The stepwise multiple regression analyses indicated that the tie point density was significantly correlated to the measurement error for the DSLR dataset (p <0.001), while no correlation with any of the studied variables was found for the action camera dataset. The number of images visible was excluded because of collinearity with tie point density (Table A1). A regression model was constructed to relate tie point density to error (Fig. 4a), and this single factor could explain 42% of the observed 20 variability in error for the DSLR dataset. No other variables were retained in the model. Based on the MC precision maps, spatially propagated error estimates can be generated for the repeated surveys (Fig. A16). The spatially distinct errors can be quantified, where shrubs area had larger error of detection (0.031 m). The distribution of errors also showed lower precision for shrubs. For the rest of surface types, the MC precision was around 0.02 m. For the action camera dataset, no clear spatialized pattern was found and a spatially uniform precision is therefore a good approximation.in the precision map. We thereby 25 assumed that there was no significant spatialized uncertainty for the action camera in this case.
Based on this density-error regression model, spatially explicit error estimates were generated for the repeated surveys with the DSLR camera (Fig. 5). The error is spatially structured with larger errors in shrub areas and smaller errors in non-vegetated areas. The propagated error shows a similar pattern and has a mean value of 0.056 m, which represents the average detection limits of the DSLR camera at this survey height (45 m) and under the given surface conditions (Fig. 5b). 30 Figure 6 shows the DoDs when using (i) an average and spatially constant error and (ii) when using a spatialized error map. The histogram shows a unimodal distribution and shows a high repeatability with a mean shift of ca. 0.019 m and a SD of ca. 0.018 m between the two repeated survey outputs. When using a constant error threshold, 94.2% of the area is in the range of LoDmin, i.e., -0.042 to 0.042 m (Fig. 6a), and larger differences are visible for the shrub and grassland 5 areas. When using the spatial explicit error for thresholding, a larger error threshold is allocated in vegetated areas due to lower tie point densities, and this results in a relatively tolerant change detection in these regions. When applying a reasonably conservative 95% confidence interval, the DoD is close to zero, indicating a reliable repeatability and reproducibility of the survey.

Repeatability
The DoD map derived from the action camera shows a very different pattern. The 95% confidence interval is ±0.163 10 m and has a SD value of 0.039 m, and this is substantially larger than those derived from the DSLR dataset (Fig. 6b).
As discussed above, a spatialized error threshold for the action camera could not be derived.

Soil sSurface Cchange dDetection
In order to illustrate the potential of PPK in high resolution surface change detection, we evaluate various approaches and camera setups. At the end of the monitoring period, Tthe surface of the study area changed substantially as a result of plowing. 15 The DSMs of the plowed area (before and after plowing) were analyzed (Fig. 67). It should be noted that the flight height after plowing was reduced (35 m and 20 m for the DSLR and action camera, respectively). For the PPK datasets, when the mean XYZ RMSE was used to estimate the reg registration error considered, the threshold was high and substantially using CP RMSEs improved the reliability but reduced the sensitivity in change detection. For the PPK + 1GCP datasets, we observed that the bias (particularly in Z direction) was removed and we therefore set the registration reg error to zero.was substantially 20 mitigated. We then applied Bboth a spatially uniformconstant DoD threshold (based on the CPs RMSE) and a spatialized ly variable error surfaces (based on MC precision) were applied. Note that due to the With the different flight altitudes (35 m and 20 m for the DSLR and action camera, respectively), the DoD thresholds were similar for both cameras. Similar change detection can be obtained using the constant DoD for both cameras (Fig. 67aa). As reported above, the MC precision showed lesssmaller uncertainties for the DSLR dataset than for the while higher uncertainties for action camera dataset, leading to 25 different levels of detection for both datasets. The zoomed-in area showeds the detail of the surface changes along a profile and its DoD threshold (Fig. 67b). The DSLR camera provided much more detail when thancompared to the profile generated by the action camera. Nevertheless,A a significant surface change could be detected for both approaches when using the LoDmin threshold. We assessed the volume changes over the area of interest while considering the LoD thresholds. Regarding the PPK solution, the volume estimations of the two camera datasets had significant difference due to the existed bias. For the PPK + 30 1GCP datasets. wWhen using a constantspatially uniform (i.e. constant average) LDoD, the DSLR dataset resulted in a total volume lowering of 8.17 ± 2.70 m 3 , while a volume increase of 175.50 ± 76.33 m 3 was detected due to changes in bulk density and the construction of ridges. The action camera dataset evaluated the volume decrease at 6.16 ± 2.36 m 3 , while 191.77 ± 99. 18 m 3 accumulated (Fig. 9c). When using MC DLoD, the estimated volume of changes was 155.96 ± 35.05 m 3 for DSLR camera and 92.60 ± 66.5 m 3 for action camera. Both DSLR and action camera obtained similar estimation using constant LDoD. The MC LDoD for DSLR datasets resulted in more significant surface changes thanwere more robust than those obtained for the action camera estimationdataset.
After the repeated surveys, the surface of the study area changed substantially as a result of plowing. The DSMs of the plowed area (before and after plowing) were also analyzed (Fig. 7). It should be noted that the flight height after plowing was reduced 5 substantially (35 m and 20 m for the DSLR and action camera, respectively). Due to the lower flight heights, the DoD thresholds are similar for both cameras. Although the overall spatial patterns match, the action camera provides a less detailed picture and is not able to detect significant changes in a large part of the study area (Fig. 7a). The zoomed-in area shows a detail of the surface changes along a profile (Fig. 7b). The DSLR camera resulted in much more roughness and level of detail when compared to the profile generated by the action camera. Nevertheless, a significant surface change could be detected for 10 both approaches when using the LoDmin threshold. To illustrate the potential of the approach, we assessed volume changes over the plowed area of interest using the GCD software (Wheaton et al., 2010) while considering the DoD thresholds. The DSLR dataset evaluated that a total volume of 10.31 ± 2.70 m 3 was lowered, while 186.06 ± 76.33 m 3 of the area experienced a volume increase due to changes in bulk density and the construction of ridges. The action camera dataset evaluated the decreased volume at 9.34 ± 2.36 m 3 , while accumulated equaled 203.85 ± 99. 18 m 3 (Fig. 7c). Accordingly, the estimated net 15 volume of difference by DSLR and action dataset were 175.76 ± 76.38 m 3 and 194.51 ± 99.21 m 3 , respectively. The similarity in the detected volume changes suggests that the PPK-SfM workflow provides reproducible results.

Accuracy and pPrecision of PPK sSolution in Ddirect gGeoreferencing
Our study focused on the accuracy and precision of PPK solutions for direct georeferencing. Results indicated that the DSM 20 generated by a PPK solution can deliver topographic models with an accuracy below 0.015 m without the use of ground control points (i.e., DSLR camera (EOS): 0.63 cm px -1 GSD, 0.011 m planimetric error and 0.012 m altimetric error). The performance of the action camera provides ca. 0.03 m accuracy (Fish-eye lens, 3.11 cm px -1 GSD, 0.019 m planimetric error and 0.024 m altimetric error). The PPK direct georeferencing approach provided centimeter level accuracy and precision under longer time provided results that are comparable to those that can be obtained using GCPspanduring a 14-day monitoring campaign where 25 light conditions, image quality and GPS satellite constellation changed. Thiss, i.e., with RMSEs of 0.01-0.02 m. This indicatinges es that the that direct georeferencing with accurate positioning and orientation is capable to replace the conventional ground control method and allows for the acquisition of(GCPs) and acquire robust centimetric HRT data and acquire centimetric accuracy. As already indicated by manyprevious studies, single on-board GPS are not sufficientprovides for sub-meter level accuracy (Turner et al., 2012a). The quality of GCP-based georeferencing depends on the number and 30 distribution of GCPs (Sanz-Ablanedo et al., 2018). The accuracy is can be improved by introducing more and densely distributed GCPs, which would induces a tradeoff between survey time and quality of surface reconstruction (Eltner et al., 2016;Smith et al., 2016). Areas with poor distributions of GCPs or lower control precision could be vulnerable to systematic errors . For example, in remote glacier studies (Kraaijenbrink et al., 2016), GCPs can generally only be located at the glacier periphery, which is unfavorable for internal accuracy. In contrast, precise direct georeferencing of aerial 5 surveys (kinematic GNSS) provides an evenly distributed control framework as each image can be regarded as a control point. Figure A12 exhibited the planimetric image residuals between the original image positions and the optimized positions after BBA process. ItThis showeds that the image residuals were evenly distributed and had standard deviation of only a few centimetresa mean value close to 0 for both cameras, indicating there wereas little bias forduring the image georeferencing process. The DSLR images had lesssmaller SD of positional residuals than those of the action camera images, indicating that 10 the action camera images had higher random error regarding the BBA process.
In this study, our experiments showed that a high quality GNSS receiver mounted on an aluminum plate that is positioned as far as possible from the UAV electronics can provide reliable accuracy and precision in positioning camera locations. Initial tests showed that the GPS data quality is very vulnerable to interferences from the UAV motors and electronics and special attention should be given to shielding. The PPK positioning (without a single GCPs) of camera positions was shown to provide 15 the same level of accuracy and precision as a GCP solution in this our studycase. thoughNevertheless, there might be biases in the PPK GNSS position estimation due to false solutions which can remain undetected (e.g., false fix in resolving ambiguities). An approach to detect this is to check the accordance between 'Fix and hold' and 'Continuous' resolution in integer ambiguity in RTKLib.). Implementing one GCP did not always improve the results in our study: on average the addition of a single GCP did slightly reduce the overall RMSEs. , neverthelessGiven that it is difficult to assess the quality of the PPK 20 solution without independent observation, we recommend that using at least one GCP (or one single fixed point throughout the monitoring) could beprovides a robust way the best operational compromise to detect perturbations of the GPS signal. Forlani et al. (2018) balanced the advantage of an RTK/PPK versusand a GCP solution and assessed reported that for the RTK + 1 GCP configuration, the vertical bias was greatly reduced. However, iIt should be noted that applying one GCP only moves the overall project to the approximate location without internal georeferencing.our system integration did not result in a 25 consistent bias and we did not observe false solutions.

Comparison of DSLR andversus Action Camera in Photogrammetry
As for the cameras we used in this study, the main differences were related to the focal length, image resolution and quality.
The action camera with shorter focal length (2.92 mm) provides a larger field of view (diagonal FOV: 149.2°) but is characterized by radial optical lens distortions. The vertical errors derived from sixteen individual check points were all below 30 0.07 m indicating that the 'doming' effect can be greatly eliminated or mitigated benefitting due tofrom the dense and precise control of camera positions.correcting the lens-distortion effects during the image processing greatly eliminated the deformation of the short focal lens (fish-eye) camera. The DSLR camera, due to the a larger APS-C sized imagers, higher focal length and higher resolution, together with the complete control of the ISO, shutter speed and aperture settings, produced much less noise and better overall picture quality. These differences led to better GSD and image contrast. We observed that this assisted greatly in recognizing and matching tie points. For instance, at 45 m the same flight height, the DSLR dataset has a 5 higher tie point density (mean: 213.5 points m -2 ) than action camera (mean: 12.1 points m -2 ) and the detailed images help improve finding and matching tie points.
To visualize the two camera setup outputs and assess the potential of soil roughness measurement in different surface type, we derived two representative transects (Fig. 67b). Due to a higher GSD, the DSLR-derived data showed abundant and sharp details, while data from the action camera werewas relatively smooth. It should be noted that due to the large FOV, the action 10 camera required a flight plan that was much less dense than for the DSLR camera (about half), indicating that a much larger area (about double) could be surveyed in the same time. However, this larger spatial coverage comes at the cost of ground resolution. A lower distance between the camera sensor and the surface is required for the action camera to obtain the same GSD as DSLR camera (for the GoPro and EOS cameras used in this study, the flight height ratio to obtain the same GSD equals 1:3.5, and the consumed time ratio was ca. 1:1.5). For the design and In practical implementation of UAV surveys, it 15 is crucial to take the sensor weight and size into account, as well as the payload and endurance of UAV platform. We found that with a light, small, highly portable and low-cost UAV equipped with a very simple camera and RTK/PPK GPS system, very good results in terms of accuracy and precision are possible (RMSE of ca. 1 pixel). In addition,Proper selection of devices depends on specific application scenarios, UAV regulations and accuracy/precision requirements. T taking advantage of the large FOV of the compact action camera, it is feasible to cover more area but at the cost of GSD and accuracy. 20

Precision eEstimates
Precision estimates based on Monte Carlo simulation are feasible approach to reveal the uncertainty of SfM reconstruction.
Although there was We observed some inconsistencyies between the MC-derived precision and CP-derived precision estimates.
The observational, precision for the DSLR dataset was slightly worse than those obtained from the MC estimates. wWe attribute this to the fact that CP itself can be regarded as a key feature which is easy to recognize in the BBA process. In 25 addition, the observational precision reflects all sources of uncertainty while the MC only considered the camera position It would result in MC uncertainties at CP positions lower than it could actually be. It explained the relatively higher MC precision than the CP precision for the DSLR datasets.. HoweverIn contrast, the MC precision of action camera dataset was much lower than the CP precision, which might results from the high radial distortion feature of the high FOV lens and the lower GSD.
To clarifyidentify which factor (high GSD or low FOV) results incontrols the precision estimates,spatialized precision map, 30 we pre-processed the images usingin two methods (i) down-sample the DSLR images to have the same GSD as action camera images (ii) clipped the action camera images to have the same FOV as DSLR images (For that, we implemented an additional flight mission for the action camera using thea denser flight path but smaller region). Precision maps were then generated using Monte Carlo simulation (Fig. A23). With a lower GSD, the spatializedprecision pattern offor the DSLR dataset remained withbut showed increased uncertainties. In contrast, the while clipped low FOV action camera images revealed a clear spatial pattern for the precision estimates. Based on this analysis, we suggest that Therefore, we assumed thata higher GSD increased 5 the robustness of the tie point matching and hencethus improved the precision. It is possible thatHowever, the tThe large FOV of the action camera has also enablesing wide imaging angles to a single tie point, whichsome advantages that may to some extent compensate the difficulties for the identification of key features due to the lower GSD image quality difference. Using a fisheye camera allows larger angles between homologous rays and convergent imaging that may minimize systematic errors James et al., 2017) or may provide a better determination of the internal geometry camera calibration,, at least if appropriate 10 parameters model calibration are introduced in the bundle adjustment. It should be noted that the radial distortion induced by the fisheye featurelens is more severe ion the edges of the images., This which would increases the uncertainties in tie points orientatingon and this may explain the higher magnitude of tie point uncertainties (Fig. 5b). Therefore, a tip for using such type of cameras for aerial photogrammetry is to relatively lower the flight height and increase the overlap.
Another feature of the low FOV DSLR camera was that the image overlap outlines clearly existed. It suggested that camera 15 positions may have been over-constrained in the processing when we set the camera accuracy as 0.05 m. With increased camera accuracy (e.g., 0.1 m), the quadrate outline can be mitigated whilst the accuracy may degrade due to a weaken control of camera position. We explored how precision varied with different camera accuracy using DSLR dataset. The camera accuracies were set as 0.01 m, 0.03 m, 0.05 m, 0.1 m, 0.15 m, 0.2 m, 0.5 m and 1 m. The precisions were validated using CP residuals and corresponding MC extracted values (Fig. A3). The strong correlations indicated the precision of direct georeferencing is 20 highly dependent on camera accuracy. Therefore, a prudent selection for camera accuracy is required. In our case, we maintained the rigorous constraint since the outline shifts were ca. 0.02 m, which can be eliminated by applying LoD threshold.This feature may explain the observed absence of a significant correlation between error and tie point density for the action camera (Table A3). We performed an additional analysis to verify this by only using half of the images (i.e., we removed one out of every two images) of the action camera dataset: the results showed that the error (based on sixteen control points) 25 did not increase when using a substantially decreased tie point density.
Our result showedIt can be noticed that the 'artificial quadratic pattern' in overlapping area between adjacent images had less uncertaintya correlation exists between tie point density and accuracy for the low FOV DSLR dataset. Although the number of images was excluded in the multiple linear analyses, we found this factor to be strongly correlated to tie point density 30 ( Fig. 5aFig. 8). We inferred that denser tie points generally lead to robust positioning of tie points (Fig. A4). It implies that areas with relatively higher tie point density are of higher probability to be accurate and precise in the SfM output. In contrast 20 to the low focal length action camera with a large FOV, a single tie point is normally captured by only 7-12 images, where more tie points are found in the intersecting area while less are found below the image positions. This results in a structured pattern in tie point density and suggests that anWith increased in survey (images) density, may further improve the accuracy can be further improved when using RTK/PPK precise solutionspositioning, before which photogrammetric considerations are the limiting factors. However, a substantial part of the observed error still remained unexplained. Since we could not identify 5 other controlling factors, we postulate that these errors are random errors, which are constrained by the GSD, color and contrast, and limitations of the SfM algorithm.
To visualize the two camera setup outputs and assess the potential of soil roughness measurement in different surface type, we derived two representative transect (Fig. 7b). Due to a higher GSD, the DSLR-derived data showed abundant and sharp details, while data from the action camera were relatively smooth. It should be noted that due to the large FOV, the action camera 10 required a flight plan that was much less dense than for the DSLR camera (about half), indicating that a much larger area (about double) could be surveyed in the same time. However, this larger spatial coverage comes at the cost of ground resolution.
A lower distance between the camera sensor and the surface is required for the action camera to obtain the same GSD as DSLR camera (for the GoPro and EOS cameras used in this study, the flight height ratio to obtain the same GSD equals 1:3.5). Our surveys at different flight heights indicated that a better accuracy and precision can be obtained with lower flight height (Table  15 2), which was also reported by Eltner et al. (2016). However, lower flight height means a denser flight plan and lower flight speed for a given constant side/front overlap. We calculated the required survey time for both cameras to obtain the same GSD, image overlap and survey area by adjusting flight height and speed. To obtain the same GSD, the action camera requires a lower flight altitude while at the same time, its larger FOV allows to space the flight lines more widely, relative to the DSLR camera. For a same GSD, the time ratio of the DSLR to action camera was ca. 1:1.5 for the camera models used here. In 20 practical UAV survey, it is crucial to take the sensor weight and size into account, as well as the payload and endurance of UAV platform. Proper selection of devices depends on specific application scenarios, UAV regulations and accuracy/precision requirements. Taking advantage of the large FOV of the compact action camera, it is feasible to cover more area at the cost of GSD and accuracy.

Application of UAV-SfM Framework for Surface cChange Ddetection 25
Using an average RMSE to estimate the registration error resulted in poor estimates of surface change. This was related to the fact that the PPK solution provided results with substantial bias in the Z direction for a few flights. The repeatability assessment showed that the use of a flight specific registration error, based on 1 GCP, could remove the bias. Furthermore, tThis study showed that the approach is repeatable as both UAV-camera setups resulted in used obtained similarhere resulted in similarestimation inof 3D surface data to quantify 3D topography change changess. To obtain a robust change detection, in 30 addition to improve the survey accuracy, it is also crucial to set a proper uncertainty threshold (LoD). Our results indicated 21 that the approach to estimate the LoD (i.e. MC-based versus CP-based) could substantially affect the estimationresults, especiallyparticularly for small scale, high resolution applications (i.e. that require centimetric precision) detection (centimetric level). In this study, the LoD95% for the DSLR camera was ca. ±0.08 m and while it was ca. ±0.16 m for the action camera at a flight height of 45 m. Lower flight altitude, and hence a higher GSD resulted in a better change detection. For a flight altitude of 20 m, the LoD95% for the action camera was reduced to ca. ±0.09 m. Areas where the tie point density was low resulted in a 5 poor DSM reconstruction. Therefore, the generation of DSMs depends strongly on the characteristics of the measured surface.
It is also important to understand the effect of effects potential accuracy of different types of surfaces on the SfM output, particularly in a region with a 'complex' surface, including e.g., vegetation area, and rough objects and surface with few key features. Vegetation has long been recognized as a source of error in photogrammetry (Lane et al., 2000;Messinger et al., 2016), and in this study the vegetated areas show larger errors than bare soil (Fig. 5). For dense vegetationdue to with the 10 cluster of leaves, the wind caused movement and illumination change and this increased the complexity of the imagery, leading to difficulties in isolating tie points (Harwin and Lucieer, 2012). We showed that carrying out topographic change detection using Applying a spatially explicit error thresholds in topographic change detection can help improvinges the reliability and sensitivity because it takes into account the factors controlling the error.
Our study showed demonstrates that the PPK positioning is a robust solution for monitoring surface change and estimating 15 sediment budgets at very high spatial and temporal resolution. This technique can be very advantageous when it comes to monitoring large areas that are poorly accessible or require repeated surveying (Clapuyt et al., 2017;Eltner et al., 2016). It is also worthy of attention to properly select the UAV platform depending on survey demands.
A relatively cheap RTK/PPK-enabled micro UAV (small-form 25×25 cm, weight 1.4 kg, autonomy 15 minutes) provided similar accuracy and repeatability as a professional multirotor UAV system (large-form 80×80 cm, weight 4.5 kg, autonomy 20 15 minutes). Based on our analysis, we suggest that using a micro-drone/action camera setup is suitable for large scale monitoring (e.g., gully erosion, landslides, glaciers, etc.) when a high GSD areis not needrequired. When considering taking account of a scene's 3D geometry, the high FOV prevailsalso assists in for recording features exposed along vertical facades (e.g., vertical cliff face) from nadir-view photogrammetry. Furthermore, in countries with strict UAV regulations and/or inaccessible regions (e.g., mountains) a light-weight system can be more easily transported on the field than a large UAV 25 system. The DSLR camera setup can be used when high resolution is needed, for example for soil roughness assessment, sheet and tillage erosion, solifluction, riverbank erosion, etc. Finally, a key step in PPK positioning is to obtain GPS data from a statoinarystationary base station. In this study, we used an internet-enabled system to geolocate the base station for each flight.
For areas where an internet is absent or unreliable, and long-term monitoring is required, we suggest to setsetting up a permanent reference point that can be used to position a local base station (e.g., a concrete pole). 30 The UAV-SfM framework is increasingly used in geomorphology to accurately capture the Earth's surface. Our study showed that the application of PPK (Post-Processing Kinematic) in direct georeferencing can provide cm-level accuracy and precision which results in a ith greatly improved field survey efficiency. Furthermore,, it is a robust method that was demonstrated to and this without the need to survey a single GCPits robustness was manifested to be repeatable among multiple dates and 5 surveys. We investigated the positional accuracy and the repeatability of DSMs by repeating the same flight plans. The PPK solution had a similar accuracy (MAEmean: ca. 0.021 m, RMSE: ca. 0.03 m) as the traditional approach using georeferencing based on GCP's. Nevertheless, some flights were characterized by a vertical shift which could be mitigated using a single GCP. We also evaluated two UAV-camera setups (with differences in UAV size/weight, portability, camera focal length, resolution and sensor quality) and showed that the tie point uncertainties are very different camera properties (i.e., focal length, 10 resolution, sensor quality) have a large impact on the accuracytie point uncertainties. Nevertheless, Tthe DSM reconstruction and surface change detection based on a DSLR and action camera were reproducible: the main difference lies in the level of detail of the surface representations. Using low-altitude flights (<45 m) it is possible to detect surface change using a PPK-SfM workflow with a threshold below 5 cm, even with a low-cost action camera.We found thatUsing tie point density pPrecision estimates are critical to assess significant changes between two surfaces. We evaluated different methods to estimate 15 precision and registration errors and found that Monte Carlo simulations  where the camera position uncertainty is considered provide a robust way to estimate for was significantly related to the error of the topography reconstruction for the DSLR camera. By exploiting the relation between error and tie point density, we demonstrated that a spatially explicit LDoD thresholds for low-FOV cameras., can greatly improve surface change detection. Overall, the PPK-SfM workflow overcomes some of the main limitations of GCPs, and providing es a high-precision and high-efficiency 20 solution in surveying and geomorphological applications.         includes or removes one independent variable at each step, based (by default) on the probability of F (p-value). "enter" method forces variables introduced in one step in order of decreasing tolerance. For action camera dataset, no variables were entered the regression equation using "stepwise" method. Therefore, the variables were introduced by "enter" method. (a)