Microscale variability of snow depth using U . A . S . technology

Introduction Conclusions References

The spatial distribution of snow depth and snowpack mass content, in the form of Snow Water Equivalent, SWE, has been widely measured and modeled, both at the local, slope and catchment scale (Grünewald et al., 2010).Modeling approaches include statistical attempts, such as Carroll and Cressie (1996), Elder et al. (1998), Erxleben et al. (2002), Anderton et al. (2004), Molotch et al. (2004), Dressler et al. (2006), López Moreno and Nogués-Bravo (2006), Skaugen (2007) and Bavera et al. (2014), and physically-based models, e.g.Lehning et al. (2006Lehning et al. ( , 2008)).These works have improved our knowledge about, e.g. the relevance of single forcings in determining the distribution of the snow cover on complex terrains (Anderton et al., 2004).In addition, they provide a useful tool to estimate the impact of future modifications of climate on the Earth system (Bavay et al., 2009(Bavay et al., , 2013)).Nonetheless, many input data are usually needed, together with great computational efforts (Bavera et al., 2014).
On the experimental side, automatic snowpack mass dynamics monitoring has been traditionally run by means of point devices, such as snow pillows (Cox et al., 1978), cosmic ray counters (Morin et al., 2012) and ultrasonic depth sensors (Ryan et al., 2008).
These sensors are usually placed in areas that are believed to be suitable locations for representative measurements at wider scales (i.e.unaffected by local heterogeneities).Nonetheless, Grünewald and Lehning (2014) demonstrate that, usually, point stations on flat areas tend to overestimate catchment mean snow depth, and that representa-Introduction

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Full tive cells are usually randomly located, i.e. impossible to be determined a priori.These represent important drawbacks of point weather stations in the study of snowpack dynamics (see again Grünewald and Lehning (2014) and references therein).Moreover, these are usually affected by systematic and random errors (Cox et al., 1978;Fassnacht, 2004;Johnson, 2004), that decrease the actual precision of measurements with respect to instrumental resolution (Avanzi et al., 2014b).
Here, we have investigated the possibility of using Unmanned Aerial Systems (U.A.S., sometimes also referred to as drones) to measure snow depth patterns within a small mountainous basin at cm resolution.U.A.S. represent an alternative to aforementioned techniques to automatically, cheaply (Colomina and Molina, 2014)  DSM of the bare soil has been collected, while during the second one, on 11 April 2014, the same area has been surveyed to determine the DSM of the snow cover.Then, calculating the vertical differences between the two DSMs (Deems et al., 2013), the spatial distribution of snow depth has been derived, and compared with manual measurements at 12 points.These locations have been randomly chosen.Successively, the snow volume accumulated over the area was determined.This has been compared to the ones provided by classical interpolation techniques (namely arithmetic mean, inverse distance weighting, Thiessen method and kriging) of point measurements.
In Sect.2, we describe the study area, while in Sect.3, we provide some information about the U.A.S. technology, the design of the two surveys, the comparison with point measurements, and the spatialization techniques used as a matter of comparison.Section 4 gives results and discussion, while in Sect. 5 conclusions are given, and some outlooks are illustrated.

The study area
The case study is located in the western Val Grosina valley, Lombardy region, northern Italy.It is nearby the Malghera lake, ∼ 46 • 20 2 N, ∼ 10 • 7 14 E, 2320 m a.s.l.The approximate extent of the study area is 300 000 m 2 .In Fig. 1, the location of the study area is given, together with the topographic map of the bare soil, produced by the local regional administration.Figure 1 shows that site topography is relatively homogeneous.
The study area has been selected according to the following criteria: (1) it must have a quite high elevation (> 2000 m a.s.l.), to guarantee an adequate snow thickness at the end of the accumulation season; (2) it must be easily accessible during all the seasons; (3) it must be interested by seasonal snow, so that the DSM acquired during autumn represents the 3-D surface of the soil.Introduction

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U.A.S. technology and design of the surveys
The use of U.A.S. is nowadays rapidly increasing (Eisenbeiss, 2009;Watts et al., 2012;Colomina and Molina, 2014).Some examples include ecology (Dunford et al., 2009;Koh and Wich, 2012), coastal engineering (Delacourt et al., 2009) or geomorphological mapping (Lejot et al., 2007;Hugenholtz et al., 2013).See Colomina and Molina (2014) for an exhaustive review.These systems provide an airborne support for sensors operating at different wavelengths.The support can autonomously determine its position in a 3-D reference system.Therefore, it is able to reproduce a pre-arranged flight plan.This let for autonomous, repeteable, cheap (Colomina and Molina, 2014) and low-risk surveys to be run, even in high-wind and hard climate conditions (Funaki et al., 2008).In optical surveys, usually they use compact digital cameras, due to the limited payload (say ∼ 10 2 g).Nonetheless, these are affected by higher deformations as compared with those of photogrammetric calibrated cameras (Pollefeys et al., 1999;Remondino, 2006;Stretcha et al., 2010;Sona et al., 2014).The U.A.S. used in the two surveys is a light-weight fixed wing SwingletCAM system (SenseFly ).It is characterized by a limited weight (< 500 g) and size (wingspan equal to 80 cm).These features make it suitable to perform photogrammetric flights over limited areas (about 1 km 2 ) at very high resolutions (3-7 cm of Ground Sample Distance -GSD).The SwingletCAM is able to perform pre-planned flights in a fully automated mode.The device continuously analyzes data from the onboard GPS/IMU and takes care of all aspects of the flight mission.However, the operator can always recover full control of the system itself.The system incorporates a compact camera Canon Ixus 220HS (12 Mp and fixed focal length of 4.0 mm) which can acquire images at a GSD of some cm (depending on flight height).
In the two field surveys, the GSD was set to 4.5 cm.Thus, we obtained an average flight height of 132 m a.g.l.(the range of the height values is between 130 and 135 m).

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Full Furthermore, in order to gain the maximum stereoscopy and to avoid uncovered areas, forward and side overlaps were set to 80 %.Following this approach, from six to seven strips were necessary to cover the area of interest.

Comparison with point measurements
In what follows, we compare estimates of snow depth obtained by the SwingletCAM at some points where point manual measurements are operated using snow poles.The locations of these measurements have been randomly chosen.Snow poles have been often used since the beginning of snow field surveys to determine snow depth amount at a point, in the context of snow density and SWE determination (Church, 1933).Although they represent the most direct way to measure this quantity, the long time needed to operate these surveys (Deems et al., 2013) have caused their partial replacement with automatic devices.A comparison with probe measurements has been often used to assess the performances of alternative techniques to describe snow depth dynamics (Deems et al., 2013).However, no specific rule or common practice exists in the literature to determine the minimum number of manual snow depth measurements, over a given area, needed to evaluate the performances of a given technique.study area.These point measurements allowed to make a statistical evaluation (i.e.calculating mean and SD) of the performances of U.A.S. in retrieving snow depth at a generic point within the study area.

Spatial interpolation techniques
Spatial interpolation techniques are methods used in the literature to produce continuous maps of attributes starting from some point values.These methods have been widely used in snow hydrology applications to produce maps of snow depth variability (López Moreno and Nogués-Bravo, 2006) starting from point values of the same variable.These techniques include, among others, (1) the Inverse Distance Weighting mehod (IDW), that calculates the attribute at a given location as a function of the distance between that point and the locations where known values are given (Erxleben et al., 2002;Fassnacht et al., 2003;López Moreno and Nogués-Bravo, 2006;Bavera et al., 2014), ( 2) Thiessen method, that associates the data at a given location to a certain subset of points close to it (Elder et al., 1991), (3) Kriging, which estimates the unknown values by previously estimating (or assigning) a certain law of variation of the variable in space (the so-called variogram, Carroll and Cressie, 1996;Balk and Elder, 2000;Erxleben et al., 2002;López Moreno and Nogués-Bravo, 2006), (4) Cokriging, that adds to the variogram additional predictors, such as elevation or aspect (López Moreno and Nogués-Bravo, 2006), ( 5) Cokriging of the residuals (Erxleben et al., 2002) and ( 6) Spline, that estimates unknown values by using a function that minimizes surface curvature (López Moreno and Nogués-Bravo, 2006).Moreover, global methods such as regression-tree models, multivariate statistical analysis or linear models have been also applied (Erxleben et al., 2002;Fassnacht et al., 2003;Anderton et al., 2004;Dressler et al., 2006;López Moreno and Nogués-Bravo, 2006;Bavera et al., 2014), sometimes combined with remote sensed images (such as in Harshburger et al., 2010).
Here, we consider some classical spatial interpolation techniques, and we compare their estimates of snow volume with the one obtained using U.A.S.These techniques 1054 Introduction

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Full are inverse distance weighting, Thiessen method, and ordinary Kriging.In addition, we will consider also the arithmetic mean of snow depth measured at poles.

Surveys realization
For both the two surveys, the flight lasted around 15-20 min.In the survey made on 26 September 2013, the U.A.S. collected a block of 47 images divided in 6 strips.Due to the high image overlap, all the ground points are visible in many images (from 3 to 9, see the left panel of Fig. 2).Thirteen pre-signalized Ground Control Points (henceforth, GCPs), measured through GPS rapid static survey, allowed the referencing of the block and the accuracy analyses.The SD of the three coordinates of GCPs are around 3 cm in the horizontal components, and 5 cm in the vertical one.
In the survey run on 10 April 2014, the U.A.S. collected a block of 84 images divided in 12 strips (6 regular strips as in the autumn survey plus 6 cross strips).Fourteen pre-signalized GCPs, measured through a GPS static survey and theodolite, allowed the referencing of the block.This set of GCPs is different from the one used during the first survey.We chose points that were reasonably distributed over the area, and we referred them to the same reference frame.Based on this survey, GCPs coordinates have been estimated with a SD of about 1 cm.
The blocks of images were processed using the Agisoft Photoscan software.It is a 3-D modelling software, carrying out the image relative orientation, together with the self-calibration, in an arbitrary reference system, which is often obtained using a minimum constraint coming from the approximate orientation provided by the telemetry.Firstly, for each block of images, the position of the camera for each image is determined searching common points on the images.Then the extraction of topographic points (which represent a cloud of points), and the rejection of outliers are made for Introduction

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Full each survey.The subsequent use of GCPs allows translating and rotating the photogrammetric blocks in a specific reference frame, i.e.ETRF2000.We report in Fig. 2 the location of camera photos and their overlap for each of the two surveys.In particular, the left panel regards the survey made on September 2013, while the right panel refers to the survey run during April 2014.Colors indicate the number of images covering each area.It is well known that the precision in coordinates estimation increases with an increasing number of images in which a point is present (Remondino and El-Hakim, 2006).In this perspective, most of the study area has been imaged at least by 3 or 4 images.Clearly, the overlap increases at the center of the study area.In that area, points have been imaged by a number of images ≥ 9.

DSMs production
Using the Agisoft Photoscan software, we have obtained orhophotos and DSMs of the two surveys from the clouds of points as 3-D polygonal meshes.
Figure 3a and c, shows the orthophoto for the autumn and the spring survey, respectively.Figure 3b and d, describes the related DSMs, both characterized by a pixel size of 5 cm.Red lines depict contour lines (10 m interval).
The autumn ortophoto (Fig. 3a) shows high coherence with the topographic map in scale 1 : 10 000, produced by the regional administration, and reported as background.For example, rivers and Malghera Lake outlet are correctly located.This consideration holds from the quantitative point of view, because contour lines of the topographic map (in black) and those of DSM (in red) are in agreement (see Fig. 3b).
As for the spring survey (Fig. 3c and d), a comparison with the topographic map is not straightforward, because of snow depth coverage.Nevertheless, rivers and lake outlet seems to have been correcty positioned, since they correspond to clear depressions in snow coverage.The snow depth surface on this area is interested by patchy coverage of sand dust transported by wind storms.This is visible as brown areas in the ortophoto (Fig. 3c), and has been of great help in referencing the images of the spring survey, providing common points on photographs.Clearly, the associated DSM shows contour Introduction

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Full lines which are different from the ones obtained during the September survey.This is an effect of snow depth presence on the ground.This causes a slight reduction in topography irregularities, too.

Point snow depth retrieval
We report in Table 1 a comparison between manual (H M ) and U.A.S. based (H U.A.S. ) snow depth measurements.Manual measurements are associated with a standard resolution of ±1 cm.The average difference between measurements is equal to −7.3 cm, with an associated SD of 12.8 cm.This result shows that the U.A.S. technique is able to locally estimate the snow depth values with a precision of ∼ 10 cm.Part of this difference could be explained by slight differences in the position of manual measurements and U.A.S. estimates.Nonetheless, this precision is comparable with the order of magnitude of the precision (instrumental resolution and noise effect) of many automatic sensors currently installed for point measurements of the same variable (Avanzi et al., 2014b).Legend scale shows that micro-topographic differences can be equal to ∼ 2-3 m.This illustrates the importance of sampling resolution, the extreme variation of accumulation dynamics of snow depth, and the scarce representativeness of point measurements (Grünewald and Lehning, 2014).

Distributed estimation of snow depth
The snow depth value at poles positions varies between 1.48 and 2.11 m.This represents a reduced variability with respect to the complete range of variation of U.A.S. snow depth values.On the one hand, the location of poles was randomly chosen, and snow depth spatial patterns are hardly predictable a priori (Grünewald and Lehning, 2014).On the other hand, additional investigations are necessary to assess U.A.S. performances in case of, e.g.shallow or patchy snow cover conditions.
Table 2 proposes a comparison of average/maximum/minimum snow depth and the estimated volume of snow depth using different spatial resolutions of the DSMs: 5, 10, 20 cm.Clearly, an increase of the spatial resolution would increase the number of pixels.Nevertheless, this would marginally affect the values of average/maximum/minimum snow depth, as also the estimated volume of snow.We can suggest a spatial resolution of 20 cm as a good trade off between the number of pixels considered and the description of the snow micro-topography.However, as a matter of continuity throughout the manuscript, we will use the DSM with a spatial resolution of 5 cm in the comparison with the classical interpolation techniques.

The comparison with classical interpolation techniques
Table 3 reports the comparison between the estimated snow volume using a set of simple interpolation techniques of the 12 snow depth poles (namely, arithmetic mean, IDW, Thiessen method and ordinary Kriging) and the estimation of snow volume operated by the U.A.S. system.The snow volume plays a key role in estimating the total amount of water in the snow form.
Results show that the differences among the estimates of different interpolation techniques are rather reduced.These are ∼ 1000 m 3 , with the total volume equal to ∼ 360 000 m 3 .Nonetheless, all these techniques greatly underestimate the snow vol-Introduction

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Full ume estimated by the U.A.S. system (∼ 460 000 m 3 ).The average percentage difference in snow volume estimation, with respect to the one estimated by the U.A.S. system, is equal to ∼ 21 %.In terms of absolute values, the average difference is ∼ 96 350 m 3 .Considering an average bulk snow density of 450 kg m −3 (measured at the same location during the April survey by means of a snow pit), this would entail an absolute difference in SWE estimation of ∼ 43 358 m 3 .
It is worth recalling that the considered area has a very reduced extension with respect to the usual distance between gauged sites in instrumental networks (see e.g.Fassnacht et al., 2003).This result shows that the assessment of snow depth microtopography has clear impacts on many applications of scientific as well as engineering interest (such as water availaibility estimation for civil usage and/or energy production), and cannot be easily neglected.From this perspective, U.A.S. systems confirm to be able to easily, cheapily, and semi-automatically return a more refined representation of snow depth.
Table 3 shows that all interpolation techniques return an underestimated volume of snow.This should be considered as a case-specific result, that is due to the choice of pole positions.In fact, Fig. 4 shows that manual measurements were taken in areas that were not characterized by very high snow cover.Since evaluating a-priori representative locations is very difficult (Grünewald and Lehning, 2014), and since they could even vary from year to year basing on snow redistribution dynamics, this result shows again the advantage of using a directly distributed estimation instead of relying on a simplified representation of snow topography.

Conclusions
For the first time, we have here assessed the possibility of retrieving snow depth microscale variability by means of a photogrammetry-based survey using a U.A.S. technology, over a small alpine area (∼ 300 000 m 2 ).For this purpose, we run two surveys.
The first one, during September 2013, allowed to reconstruct the topography of the

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Full bare soil.This survey will not be necessary for future assessment of snow distribution in the same area.Then, during April 2014, a second survey allowed to reconstruct the microscale variability of snow depth, by vertical differentiation of the maps.Results show that: (1) ortophoto and DSM of autumn survey are in agreement with the topographic map available for the study area; (2) the average difference between manual and U.A.S. based measurements of snow depth is competitive with typical precisions of point measurements (average difference equal to −7.3 cm, with an associated SD of 12.8 cm); (3) the evaluation of snow depth volume (hence, SWE) using classical interpolation techniques of point values of snow depth is severely biased (average difference in snow volume estimation, with respect to the one estimated by the U.A.S., equal to ∼ 21 %).
The U.A.S. technology has some interesting potentialities within the framework of available methods to reconstruct the spatial variability of snow surface.In fact, this device allows to obtain semi-automatic, quick and repeteable surveys of limited areas (∼ 300 000 m 2 ), with a very high vertical precision (SD ± 0.128 m in the vertical direction).Although the device that we used here needs the operator to assist it during takeoff operations, other devices (currently not available to the authors) can take off and land in an autonomous way, and can cover much wider areas.This could let repeated (say, daily) surveys to be autonomously obtained, even without needing a operator to reach (or point from the distance) the target area.This, together with the possibility to substitute, or integrate, optical sensors with sensors at different wavelenghts, could represent in the future an alternative to automatic point stations to directly obtain distributed measurements of snow variables.Moreover, attempts have been already made to design supports that are able to resist to harder climatic conditions (Funaki et al., 2008), such as strong winds, that would make unfeasible a survey using the same sensor used here.Future developments should compare the performances of this technique with the ones obtained by other remote sensing approaches, in similar conditions.Moreover, performances should be assessed during different weather conditions (such as during

TCD Introduction
Full  Full  Full Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | and autonomously reconstruct a high-resolution Digital Surface Model (hereinafter, DSM) of a given area (Watts et al., 2012).Thus, they potentially allow to obtain an automatic and detailed description of snow depth variability.We chose as a field test the bare plateau around the Malghera lake, within the western Val Grosina valley (around 2300 m a.s.l.), northern Italy.A double airborne survey of this area, at the beginning and end of the accumulation season, was designed.During the first one, on 26 September 2013, the Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | As an example, Machguth et al. (2006) included 19 measurements of snow depth with snow probes and 20 snow pits in the assessment of helicopter-borne GPR performances over two glaciers in the Alps (area ∼ 17.3 km 2 ), Prokop et al. (2008) used automatic measurements and 90 bamboo sticks to record snow depth changes and to compare with laser scanning and tachimetry estimations over a ∼ 200 m × 200 m area, Bavera and De Michele (2009) considered 170 point snow depth measurements to validate snow distribution estimations at a basin scale (area 325 km 2 , snow cover interesting 2/3 of the total surface), while Gutmann et al. (2012) and Nievinski and Larson (2014) used manual measurements from either 4 or 1 snow poles respectively to evaluate GPS-based estimations of snow depth.In this framework, we operated 12 poles measurements over ∼ 300 000 m 2 , i.e. approximately one measurement every 25 000 m 2 .No automatic device was available in the Introduction Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Figure 4
Figure 4 reports a map of snow depth distribution over the study area, obtained making the difference of the elevations of the maps reported in Fig. 3. Different colors indicate different values of snow thickness (see the legend scale reported in the figure).Black dots indicate the location of the 12 manual measurements (already used in Sect.4.3).Snow depth shows a remarkable micro-topographic variability over the considered area, although this is rather limited in extension (around 300 000 m 2 ), and characterized by bare soil and scarce vegetation.Most of the central area is characterized by an alternation of low and high values of snow thicnkess, that would be completely missed by sampling at poles positions, only.Clusters of high values of snow depth correspond to the location of rivers, or depressions in micro-topography.On the contrary, low snow depths are observed on topographic local maxima.

Figure 1 .Figure 2 .Figure 3 .Figure 4 .
Figure 1.Location of the study area in western Val Grosina valley, Lombardy region, northern Italy.In the right panel, it is reported the topographic map of the area in scale 1 : 10 000, with isolines every 10 m and the elevation (in m) of some points of interest.