Centimetric Accuracy in Snow Depth Using Unmanned Aerial System Photogrammetry and a MultiStation

: Performing two independent surveys in 2016 and 2017 over a flat sample plot (6700 m ), we compare snow-depth measurements from Unmanned-Aerial-System (UAS) photogrammetry and from a new high-resolution laser-scanning device (MultiStation) with manual probing, the standard technique used by operational services around the world. While previous comparisons already used laser scanners, we tested for the first time a MultiStation, which has a different measurement principle and is thus capable of millimetric accuracy. equal 0.02 0.30 m, but decreases to 0.06–0.17 m when areas of potential outliers like or river beds are excluded. Compact and portable remote-sensing devices like UASs or a MultiStation can thus be successfully deployed during operational manual snow courses to capture spatial snapshots of snow-depth distribution with a repeatable, vertical centimetric accuracy. UAS reads 0.97, 1.00, and 0.99 for the 2016 winter survey, the 2017 winter survey, and the summer survey, respectively. These results show that UAS and MS can provide a map of snow depth distribution with similar, competitive accuracy. In light of this high agreement, only UAS (for which we produced a DSM) was benchmarked against manual probing.


Introduction
Monitoring snow distribution has important implications for both water resources management and risk prevention [1]. The amount of snow can be quantified indirectly as snow depth (HS, in m), or directly as snow water equivalent (SWE, in mm w.e. or kg/m , see [2]). Both variables are often measured with snow pits and manual probing [2], which are both time consuming and risky in avalanche-prone, remote areas. HS can be also measured using ultrasonic [3] or laser [4] sensors, while SWE can be monitored using snow pillows [5] or cosmic rays [4]. The significance of local measurements has been often debated [6,7,8,9,10], especially in view of the marked spatial variability of snow processes [11,12,13,14]. To partially take this variability into account, snow manual measurements are often performed along snow courses and then averaged to provide a more representative estimation of available SWE and snow depth [15].
Remote sensing has recently emerged as a non-invasive alternative for monitoring snow water resources. Remote sensing captures the spatial and temporal patterns of snow and thus overcomes the potential undersampling of point measurements and the long surveys needed for snow courses [16,17]. Existing methods include Terrestrial Laser Scanner (TLS, Several attempts of using Unmanned Aerial Systems (UASs) on snow have been recently carried out. These systems are commonly used for high-resolution surveys [29,30,31,32,33,34,35,36,37,38] as they allow flights to be performed in an automatic way [39,40]. The miniaturization of imaging and positioning sensors also reduces the payload and thus enables flights up to about one hour long [41]. The increasing use of UAS is also related to the improvement of Structure from Motion (SfM) and its combination with algorithms for automatic tie points extraction such as Scale Invariant Feature Transform (SIFT) [42] and Speed-Up Robust Feature (SURF) [43], which automatically reconstruct three-dimensional models from sequences of two-dimensional images [44,45]. These feature-based algorithms give several reliable matchings even in case of bad-textured surfaces [46,47].
Existing works employing UAS on snow or glaciers report an expected Root Mean Square Error (RMSE) for HS below 30 cm (e.g., see [28,48,49,50,51,52,53,54,55]). Larger errors are attributed to vegetated areas [28, 50,52]. However, the performances of UAS on snow have mostly been quantified using datasets at low density [48,49,50,51,52] or mixed fresh-old snow and bare-ice surface textures [55], whereas only [54] and [28] present comparisons with a TLS under different illumination conditions. Snow tends to form homogeneous surfaces and therefore the identification of homologous points on different images of the photogrammetric block can be highly uncertain [55,56,57,58], especially in case of high-resolution images where each frame covers only a small area. This ambiguity represents one of the biggest challenges for UAS-based photogrammetry compared to a TLS. UAS flights may also suffer from strong wind, which is a frequent, yet variable condition in mountain areas, while a TLS needs several stationing points to https://www.mdpi.com/2072-4292/10/5/765/htm 6/30 map snow depth over an irregular terrain, hence a longer survey. These shortcomings are likely among the reasons why most operational services around the world prefer traditional, manual Section 2 introduces the case study and the instrumentation used. Section 3 presents the processing methods and the results. Section 4 and Section 5 report discussions and conclusions, respectively.

The Case Study
The study area is located nearby the Belvedere glacier (Piedmont region, Italy, 45 57 10.85 , 7 55 5.22 , 2070 m a.s.l) and extends for about 6700 m ( Figure 1). The site is characterized by sparse rocks and grass with no trees. The area is also crossed by two streams. While the topography is quite homogeneous (maximum variation of ∼7 m in correspondence of the highest rocks), the bare-ground coverage is variable and this enables to investigate the variability of sensor performances with different topographic features, representative of Alpine headwater catchments.  The photogrammetric blocks were georeferenced using Ground Control Points (GCPs), represented by black-and-white square targets (0.30 × 0.30 m). The position of both the summer and winter GCPs is given in the same reference frame, which is necessary to compute HS by means of a differentiation of photogrammetric DSMs. Therefore, three geodetic networks were realized and measured in the field, combining MS and GNSS measurements. GNSS measurements were only used to georeference the three surveys, while the MS (used in its Total Station mode) was used to measure all the GCPs. To correctly georeference the surveys, each of them was referred to some permanent GNSS stations, known in the ETRF2000(08) reference frame. The final adjustment leads to a centimetric accuracy for the position of GCPs for both cases in the global ETRF2000(08) reference frame.

MultiStation Scans
The  accuracy is very well preserved when changing the incidence angle between 0 and 80 degrees.
During the winter campaigns discussed in this paper, the zenith angles measured with the MS were in the range between 121 and 92 degrees (2016) and between 117 and 88 degrees (2017).
The lowest value corresponds to some rocks emerging from the snowpack. The zenith angle coincides with the supplementary of the incidence angle when the terrain can be considered horizontal. Because of the flat topography and the morphology of the investigated site, small horizontal variation produced insignificant variation in the final DSM.

Manual Probing
Point measurements of snow depth were performed using portable stakes (aluminum, diameter ∼1 cm, resolution 1 cm). A regular grid of points was defined and materialized in the field using ropes. The grid was composed by 12 (10) courses in 2016 (2017); the average spacing between measurement points on the same course was ∼5 m, which aimed at reasonably capturing the variability of snow depth at plot scale. Each measurement took a few minutes and about two hours were needed to complete the manual survey. Both surveys were performed between 1 and 4 PM local time, meaning that snow surface was undisturbed during UAS and MS measurements (Table 1). This time span, however, introduced a slight decrease in the measured snow depth with time due to snowmelt (see Section 3). The position of each probing point was measured using the MS (centrimetric precision), thus guaranteeing the co-registration with the GCPs used for the photogrammetric processing and with the MS point clouds.

UAS Photogrammetric Blocks: Processing
The photogrammetric blocks of the three surveys were processed using Agisoft Photoscan As stated before, searching correspondences (tie points) on snow may introduce large uncertainty, and for this reason an higher overlapping was used for the 2016 winter flight.
However, we verified that the automatic algorithm performed very well also on quite homogeneous surfaces such as snow; for this reason the overlapping for 2017 flight was similar to that of the summer 2016 survey. Choosing the best overlapping is again the result of a trade off between high tie point multiplicity and wide baseline. While the first is necessary for image matching algorithms, the latter guarantees a satisfactory intersection between homologous rays.
Both configurations (winter 2016 and winter 2017) allowed us to reach an accuracy of the order of one GSD, which means that the two solutions are characterized by the same level of accuracy.
Of course, processing time will be lower if the photogrammetric block is composed by less images.
Each block was processed separately, following the standard photogrammetric procedure.
First, tie points were extracted from multiple images and the External Orientation (EO) parameters were computed, constraining the block with the GCPs previously measured (bundle block adjustment). The accuracy of each GCP was specified for each coordinate, in agreement with the precision obtained from the geodetic network adjustment. Following this procedure, we  Table 2.   No bare-soil survey was performed during summer 2017.

UAS vs. MultiStation
For each survey, we compared the MS scans with both photogrammetric products, i.e., dense point clouds and DSMs. We first performed a cloud to cloud comparison (C1), meaning that the clouds of points from UAS and MS were directly compared. Second, we compared the MS cloud with the UAS-based computed DSM (C2) as DSMs are largely used as final products in snow applications [62]. We avoided a DSM to DSM comparison between MS and UAS as this would have been affected by uncertainties connected to each DSM generation. The MS scans were surveyed using the same geodetic network used for measuring the GCP, which guarantees the co-registration between the datasets. C1 was performed by computing the height difference between each point of the MS scan and its nearest neighbour in the photogrammetric point cloud, which was found basing on the shortest 3D distance. Because the photogrammetric point cloud has some gaps due to shadows or poor matching over some areas of the snow surface, any resulting couple of points with a distance greater than 0.03 m in the horizontal plane was not included in the statistics. This corresponds to setting a maximum horizontal search radius of 0.03 m, which is assumed as the maximum acceptable distance between points on different datasets that make them physically correspondent. C2 was performed by interpolating the UAS DSM in correspondence of the horizontal coordinates of the MS point clouds and then comparing this interpolated height with that measured by the MS.    The horizontal range in Figure 4a excludes few locations with a significantly larger residual (see Figure 4b) because these points are characterized by a very small relative frequency. These larger biases are expected in shaded areas or depressions (see Figure 3) and are mostly evident in C2, which means that they are generally the result of interpolation, i.e., DSM creation.   Table 4). Because the measurement protocol as well as the manual probe were the same for all the courses, this discrepancy cannot be easily explained by a measurement error. While the differences are clustered along these courses, no evident spatial pattern in vegetation or soil coverage emerges that could clearly explain this mismatch.  cm thick). Between January and April 2016, the snowpack increased up to ∼150 cm, but both melt-freeze and rain-on-snow events occurred over the study area, especially in early April. Both processes, together with water retention at layer transitions due to capillary barriers [63], favor the development of ice layers [64]. While no pit was excavated during this first field survey due to time constraints, ice layers were observed close to the two streams crossing the study area,

UAS vs. Manual Probing
where the snow cover was patchy. The random occurrence of ice layers, coupled with slope redistribution of water in snow [65], may have impeded the full penetration of manual probes into snow, hence a systematic underestimation of snow depth [66].
During the second field survey in 2017, the mean difference between HS and HS was equal to 0.01 m, with a standard deviation equal to 0.20 m. This translates into a RMSE equal to 0.20 m (see Table 5). The maximum difference is equal to 0.52 m, while the minimum is equal to −1.08 m. During this second survey, the locations of maximum and minimum differences were more clearly correlated with topography, corresponding either to bushes or to the stream bed, which are both conditions that are prone to noise in manual probing as well as in DSMs. Both bushes and streams present complex elevation differences between winter and summer DSMs that may not be entirely due to snowpack, including potential micro-topographic variations in the surface of stream beds due to seasonal transport of sediments or larger rocks. This complicates the comparison at these specific locations as probing is expected to reach the ground surface, while HS is the result of a differentiation between DSMs (e.g., photogrammetry reconstructs the surface of bushes, whereas probes are supposed to reach the underlying ground surface). If these outliers are removed from the sample, RMSE, minimum difference, and maximum difference decrease to 0.06 m, −0.72 m, and 0.19 m, respectively. One pit was excavated close to the study area during this second snow survey and no ice layer was found at any depth. Table 5. Statistics of the differences between UAS and manual measurements in 2017.
Results are reported with or without outliers (8 samples out of 115).

Discussion
Our   [67,68], knowledge of snow depth distribution can also potentially be converted to SWE via empirical regressions [69] or dynamic models [62]. In this context, portable, low-cost techniques, such as UAS and a MS, can fill an important gap between laborious, manual measurements and large-scale surveys at lower resolution using satellites or manned aircrafts. Yet, snow-density estimates using models currently represent the most important source of uncertainty when converting LiDAR-based snow depth to SWE [70]: coupling these devices with co-located measurements of density is therefore an important direction of future development.

Conclusions
We