**2. Methods**

The purposes of this study required the investigation of different components and the integration of different data sources (Figure 1). The accomplishment of the declared objectives was approached selecting a study site where ground-based cameras were positioned for a decade. The first part of the effort was devoted to the analysis of the available terrestrial dataset. In this case, the selection of the most appropriate procedure was obtained considering the automated procedures and the supervised methods in order to check the overall performance of automated solutions under different conditions of illumination and snow coverage. Secondly, the collection of different satellite products provided

the material useful for evaluating the potential impact of terrestrial photography on the estimation of snow extent from remotely sensed data.

**Figure 1.** Description of the workflow followed in the manuscript. While the green boxes represent the considered data sources, the other colored boxes constitute the final products obtained by the different procedures required for the estimation of the Fractional Snow Cover.

## *2.1. Study Area*

The considered study area (Figure 2) is located in the Italian northeastern Alps (Lago di Cavia, Falcade, Italy). The webcam (46◦2124" N, 11◦4920" E, WGS84) was positioned in a ski resort at 2200 m above the sea level. The study site is characterized by a snow cover duration almost complete from mid-November to late April, a melting season completed at the beginning of June and occasional snowfall in the rest of the year [22]. The selection of the site for the camera setup was supported by the topographic behavior of the location, which is an almost flat area with a soft slope where an artificial water body is located. The presence of an important ski facility and the managemen<sup>t</sup> of this water resource outline the importance of this location.

## *2.2. Camera Setup*

The webcam system was provided by Sistemi Video Monitoraggio S.r.l. (Romito Magra-SP) using a digital camera (Olympus C765). The camera was deployed at 2 m above the ground. The camera was featured by 4-megapixel sensor and a 1/2.5" CCD, the focal length was 6.3 mm and images were saved in the jpeg data format with an 800 × 600 pixel resolution. Data logging and transmission were provided by specific hardware placed into a waterproof case and the power supply was ensured by the direct connection to the electric mains and by photovoltaic panels with a buffer battery. Data transfer was performed using an intranet connection with the receiving station located in Arabba through a mobile connection. The Veneto Regional Agency for Environmental Protection and Prevention developed a webcam section in the website (www.arpa.veneto.it) that supported the near-real-time availability of the images. The field of view defined by the camera perspective considered an area

of about 5000 m<sup>2</sup> with a maximum distance from the camera up to 180 m. The camera acquired all-year-round images every 1 hour since 2004 to 2013. For this study, we considered a "complete" dataset with about 8000 images where every melting season was included in order to have a large range of snow cover and illuminating conditions. In addition of that, we defined a "small" dataset with 30 images dating back to 2008 and 2009, which included a large variability in terms of illuminating conditions and snow cover.

**Figure 2.** The study site of Cima Pradazzo (**a**), close to Falcade (Italy). Panoramic view of the camera (**b**) with the considered mask in red. The orthorectified views of the camera (**c**): the grey shaded area with red contour shows the camera view projected on the ground; and the colored lines indicate the pixel grids of the different satellite products.

#### *2.3. Terrestrial Image Classification*

Following the guidelines developed for the analysis of multispectral remotely sensed images, the classification issue can be approached using different principles depending on the methods for measuring the spectral matching or the spectral similarity: the deterministic-empirical methods and the stochastic approaches [23]. The deterministic measures include the spectral angle, the Euclidean distance and the cross-correlation of spectral vectors in the hyperspectral space. The stochastic measures evaluate the statistical distributions of spectral reflectance values of the targeted region of interests. Within this framework, a large variety of classification methods that can be grouped from different perspectives [24].

## 2.3.1. Supervised Methods

The requirement for the automated solution is a "parametric" method, based on a "per-pixel" classification about the presence of snow cover. The description of the pixel content must be definitive and, consequently, a "hard" classifier is necessary. Furthermore, the classification process cannot be iterative and specific for a single image. Consequently, the generalization for different images, under different illumination conditions, can be obtained with a "supervised" classifier, which considers a "training" Region Of Interest (ROIs) associated with the theoretical "white" snow. Looking at the

supervised methods, we can include classifiers that are sensitive to the user experience during the definition of the region of interests and to the selection of discriminant parameters between snow and not snow. Some methods are associated with the threshold selection defined by the statistics of the identified ROIs. This is the case, for example, of the Parallelepiped classifier (PA), where the user defines a threshold based on the standard deviation. Some other approaches consider the probability associated with a specific ROI [25], calculating the Euclidean distance for the Minimum Distance (MD) method, the Mahalanobis distance for the Mahalanobis classifier (MA), and the covariance-based discriminant function for the Maximum Likelihood method (ML). These algorithms are all implemented in the commercial suite ENVI version 4.7 (Exelis Visual Information Solutions, Boulder, Colorado).

## 2.3.2. Blue Thresholding

Within the group of automated methods, there is a well-established method that is currently in use for snow-cover purposes with some limitations: it is a linear classifier based on thresholding of the blue channel (BT) that was introduced by [26] in the Snow-noSnow software. The method is based on the frequency counting of the blue component, and its hardness is associated with the definition of snow-not-snow limit looking at increments in the blue-channel histogram. This method has been used in several studies and it has shown some limitations. The illuminating conditions, the surface roughness and the distance from the camera are critical issues that affect the performance on retrieving snowed covers [27]. These limitations are the grounds of research for a higher performing method that possibly increases the depth of analyzing RGB imagery.

## 2.3.3. Spectral Similarity

The approach proposed in this paper is based on measuring the spectral variations in a 3D color space where reference endmembers are a theoretical "white" snow and a theoretical "black" target. The parameters estimated in this vector system are the spectral angle defined by [28] and the Euclidean distance [21], respectively calculated considering white and black references. While the parameter based on the Spectral Similarity (SS) represents an independent spectral feature, the Euclidean distance of the vector can be defined as a brightness-dependent feature. The involvement of all the three-color components will support the increase of surface types that can be discriminated: snow, shadowed snow and not snow. The proposed approach (Figure 1) was developed in the R programming environment [29].

The first step consists of rearranging the three-color components of each pixel into a new two-dimensional vector space, mathematically defined as follows:

$$\theta = \arccos \frac{P\_{\mathbb{R}} R\_{\mathbb{R}} + P\_G R\_G + P\_B R\_B}{\sqrt{P\_{\mathbb{R}}^2 + P\_G^2 + P\_B^2} \sqrt{R\_{\mathbb{R}}^2 + R\_G^2 + R\_B^2}} \tag{3}$$

The spectral angle *θ* in Equation (3) represents the relative proportion of the three-pixel components ( *PR*, *PG* and *PB*) in relationship to the reference composition ( *RR* = 1, *RG* = 1 and *RB* = 1). The angle varies from zero, which can be associated with a "flat" behavior of colors (R = G = B), to *π* 2, referring to a very dissimilar behavior from the theoretical "white" reference.

$$
\Delta = \sqrt{P\_R^2 + P\_G^2 + P\_B^2} \tag{4}
$$

The spectral distance Δ in Equation (4) is conversely an estimation of the vector length in the RGB space. It can range from 0 (black) to 1.73 (white) and it can be associated with the Euclidean distance from a "black" reference RGB composition ( *RR* = 0, *RG* = 0 and *RB* = 0). While this parameter is sensitive to the brightness of colors, the spectral angle is invariant with brightness [23]. The outcome of this step consists in the frequency counting of pixels considering the two spectral components with a 0.05 resolution. Furthermore, the total number of included pixels ( *ftot*) and the area included in the cluster perimeter ( *Pf*) were estimated.

The second step of the procedure consists in discriminating clusters from the obtained frequency distribution, and a watershed algorithm [30] can support this segmentation phase. Each cluster was fitted with a normal distribution in order to retrieve modes (defined by *μ*Δ and *μθ*) and deviations (*<sup>σ</sup>*Δ and *σθ*). If clusters are very close to each other, they can be combined in one larger group depending on their probability to be discriminated using the Mahalanobis distance. The criteria adopted for the definition of the cluster perimeter was based on the pixel frequency *f*(<sup>Δ</sup>, *<sup>θ</sup>*) higher than the Poisson error of the adjacent pixel *f*(<sup>Δ</sup>, *θ*) (Equation (5)).

$$f(\Delta t, \theta t) > \sqrt{f(\Delta, \theta)}\tag{5}$$

The procedure for the delimitation of the cluster perimeter was implemented using a per-pixel method following [31].

The final step consists in the identification of the surface type (snow, not snow and shadowed snow). This step was defined observing the frequency distributions of pixels in the defined spectral space (Figure 3). It was possible to detect that snow covers were generally characterized by higher *θ* angles and lower Δ values than not-snow covers. Snowed centroids (defined by *μ*Δ and *μθ*) were generally positioned where angles were higher than 0.9 and distances were lower than 0.1.

**Figure 3.** Examples of two different snow-not-snow mixtures. Colored polygons identified areas of clusters in presence of two different situations: partial (**a**) and full (**b**) snow cover. Lower plots are frequency distribution of pixels at the different spectral angles (*θ*) and spectral distances (Δ).

Furthermore, the range of cluster values ( Δ*max*, Δ*min*, *θmax* and *θmin*) were characterized by short distance variations compared to angles in the case of snow-covered surfaces. From this point of view, clusters with limited perimeters ( *Pf* < 0.04) and a high number of included pixels ( *ftot* > 50 of the analyzed pixels) described surfaces with homogeneous reflective behavior, as expected for snow-covered surfaces. The second rule that can be considered includes clusters with limited perimeters ( *Pf* < 0.04) and consistent number of included pixels (10 < *ftot* < 50 of the analyzed pixels). The optical behavior of those clusters must be coupled to their centroid position that must have low spectral angles (*μ*Δ < 0.5). These constraints describe, also in this case, clusters characterized by a homogeneous spectral behavior coherent with a snow-covered surface. The third rule that completes the classification procedure consisted on estimating the range of Δ between the defined clusters in the

image and on defining a threshold ( *T*Δ) that discriminates snow and other surface types. Two situations can occur for defining clusters above the threshold as snow-covered surface: one with multiple clusters (Equation (6)) and one with a single polygon (Equation (7)).

$$
\mu\_{\Lambda} > \max \Delta\_{\max} - \min \Delta\_{\min} \tag{6}
$$

$$
\mu\_{\Lambda} > 0.8 \tag{7}
$$

Once performed the classification, the amount of snow-covered surface was obtained adding the contribution of each cluster identified as snow covered. Furthermore, the quality of the final output was checked by the target area over the 10-year series of images. From this perspective, the ground control points were used to estimate eventually-induced shifting of the target view, and also to control the occurrence of adverse meteorological conditions (fog, clouds, intense raining/snowing) that could affect the image. Finally, the dataset was filtered from artifacts coupling this analysis to some basic tests about the file corruption and the image resolution.
