Water Resources Research

Metrics for assessing snow surface roughness from digital imagery

Authors


Abstract

[1] Digital image profiles of snowpack surfaces were acquired concurrently with 1-cm resolution manual measurements. The manual measurements confirmed that unaltered digital images accurately represented a two-dimensional roughness profile of the snowpack surface. Roughness indices, such as random roughness, that have been used to represent soil surfaces were computed, and their utility for quantifying snowpack surface roughness is illustrated. Variogram analysis was used to determine the fractal dimension and scale break. Surface characteristics were a function of the scale, with a rough snow surface and graupel yielding similar results. A relatively smooth snow surface showed no crystal-scale features and had a fractal dimension approaching that of a random surface.

1. Introduction

[2] Snow surface roughness is a measurement of the variability of surface microtopographic features. It is a function of crystal type, deposition conditions, and age (metamorphism and temperature history). The roughness of the snow surface exerts an important control on the transfer of wind energy to the surface, with important effects on snow transport and redistribution and latent and sensible heat exchanges. Development and standardization of measurement and classification techniques for snow surface roughness would add a physical basis for estimation of the z0 roughness parameter used in energy balance computation, and could potentially increase the accuracy of snow transport, hydrologic, and climatic models.

[3] Roughness of different Earth surfaces has been measured at various scales, including the microtopography (millimeter to centimeter resolution) of soils related to tillage and erosion practices [e.g., Kuipers, 1957; Currence and Lovely, 1970] and the macrotopography (usually meter resolution) of seafloors related to their formation [e.g., Swift et al., 1985; Briggs, 1989; Lyons et al., 2002]. These investigations have developed several different surface profiling techniques and roughness analysis indices and measures. For soil, pin boards with either single or multiple probes measure vertical distance relative to an established datum in either one or two dimensions manually, electronically or with photography [Currence and Lovely, 1970]. These vertical distances have also been measured using laser scanners [Huang et al., 1988] and stereoscopic imagery [Welch et al., 1984; Swift et al., 1985], and the digital data have been used to derive digital elevation models [Rieke-Zapp et al., 2001]. Munro [1989] assessed snow roughness on a glacier using eddy correlation and physical measurements. Herzfeld et al. [2003] assessed snow surface patterns at a 0.1 mm resolution covering an area of 100 m by 100 m.

[4] Once surface data have been measured, various indices and measures are developed to describe roughness. A variety of roughness indices designed to describe surface variation as a single value have been outlined [Currence and Lovely, 1970; Huang, 1998]. These include the random roughness (RR) which is the standard deviation of the elevations from the mean surface [Kuipers, 1957], the sum of the absolute slopes (RM) between various distance intervals [Currence and Lovely, 1970], and the product of the microrelief index (MIF) (mean absolute deviation of elevation from a reference plane) and the peak frequency (number of elevation peaks per unit transect length) [Romkens and Wang, 1987].

[5] Roughness measures are designed to quantify the spatial structure of the surface. These include the semivariance [Brown, 1987], autocorrelation [Huang, 1998], and power spectral density [Currence and Lovely, 1970]. Semivariance is computed between elevation points of equal distance and the plot of the semivariance versus the lag distance between elevation pairs is called a variogram. In log-log space, linear segments indicate power law scaling, and the power law slope can be used to compute the fractal dimension (D), equal to the dimensional space plus one minus one half of the exponent or power of the relationship. A change in slope between power law variogram segments defines a scale break (SB), indicating a change in driving processes at that length scale [e.g., Deems et al., 2006]. Often the semivariogram becomes random (D = 2 for a profile) at separation distances greater than a SB. To analyze larger snowpack roughness features (>0.1 m horizontal and >1 cm vertical), Herzfeld [2002] used variograms, called a first-order vario function, and subsequently a second-order vario function to investigate the variability of a variogram.

[6] To assess snowpack surface roughness, we captured digital images of the snow surface against a board partially buried into the snowpack, as has been done in some previous studies. For example, Elder et al. [2009] used 1.5-m-long boards that yielded a resolution of ±1 mm. Löwe et al. [2007] identified snow surface roughness at a subcrystal scale (∼0.1 mm) by defining the optimal gray scale threshold between the snow and a scaled target. This paper presents methods (1) to determine snowpack surface roughness from digital imagery and (2) to estimate several different roughness indices and measures. The snowpack surfaces derived from digital imagery are compared to manual measurements, and the sensitivities of various roughness metrics are examined.

2. Methodology

2.1. Manual Roughness Measurements and Image Capture

[7] The snow surface was measured using a 1-m-long snow board partially driven into the snowpack surface. Manual vertical measurements with a resolution of 1 mm were taken at 1-cm horizontal intervals along the 1-m-long board (Figure 1). The relative datum was the top of the board; this was corrected during image analysis. A digital photograph was taken of the board-snow interface including the ends of the board. The camera was always positioned the same distance from the board and yielded the same resolution. The digital photograph of the surface was taken by the person shown on the right of Figure 1 with the camera being held at the snow surface. For this study, photographs were taken with a Sony Cybershot® DSC707 camera (2560 × 1920 resolution) from 1.25 to 1.3 m. The lens was kept in wide-angle mode (focal length of 10 mm). The f-stop ranged from f/4 to f/6.3 with an exposure time from 1/400 to 1/500 s.

Figure 1.

Photograph of the manual measurement of the “rough” snow surface. The digital photograph of the surface was taken by the person shown on the right with the camera being held at the snow surface.

[8] Three board-snow data sets were analyzed (Figures 2a2c). The board-snow interface having the larger undulations was considered “rough” snow (Figure 2a); while the interface with the smaller undulations was considered “smooth” snow (Figure 2b). Both these data sets were collected 3 March 2005 at Pingree Park, Colorado, and had at a 0.4 mm vertical resolution. The two images were approximately perpendicular to each other, with the smooth snow being exposed to more persistent wind than the gusting wind experienced over the rough snow. The third interface, at a 0.1 mm vertical resolution, was from a “graupel” event on 15 April 2006 near Cameron Pass, Colorado (Figure 2c).

Figure 2.

Digital photographs of black snow board pushed into (a) “rough” snow, (b) “smooth” snow, and (c) graupel.

2.2. Image Processing

[9] The digital photographs included areas beyond the edge of each snowboard. To rectify the 1-m-long snow board, the image was manually cropped at the vertical edge of the snowboard. The top of the image was cropped below the top of the snowboard. The image was then converted into an 8-bit gray scale tagged image format file and adjusted manually to remove snow on the board or snow fall captured in the image foreground. Using the ARC/INFO® software, the image was converted into an ARC GRID file and then into an ASCII text file of digital numbers.

[10] The snow-board interface was identified as being the location of the largest change in adjacent values of the digital number (DN) for each column of pixels. For blurry images, the largest DN may not determine the actual interface, so a manual threshold was assigned for the whole image. This is typically 128 for an 8-bit image, which is analogous to setting the image contrast at 100%. The effect of using various manual DN thresholds was tested for the rough snow interface.

2.3. Image Analysis

[11] Once a snow interface was converted to a series of Cartesian coordinates, the X and Y data were detrended such that the best fit line through the transformed data had a slope of zero and a y intercept of zero. Detrending can remove variations at the board scale or larger. However, the camera and/or board may not be level which may yield photographs with a sloping surface. This can create a bias whereby the results are dominated by nonexistent elevational artifacts. This detrending allows a comparison of roughness indices (RR, RM, MIF) and roughness measures (fractal analysis, autocorrelation). Similar to work by Currence and Lovely [1970], the RM index was computed at 1, 2, 3, 10, and 20 cm intervals on the basis of the manual measurements resolution.

[12] Since the distance from the camera to the board-snow interface varied, the widths of the pixels also varied from maximum values at the edges to a minimum value at the middle. To assess this, the rough image was parabolically stretched considering the computed distance from the board to the camera, and the resultant interface was compared to the unstretched and manual images. To reduce vertical pixel stretching, the camera was held as close to the snow surface as possible without obscuring the interface by snow surface features in the foreground. To remove bias when the board was not plumb, the image was clipped to below the top of the snow board. Since it was difficult to assess if the interface was plumb, the interface lines were detrended to minimize bias for comparison.

3. Results

[13] The rough snow surface extracted from digital imagery was well correlated with the manual measurement (Figure 3a), with a Nash-Sutcliffe coefficient of 0.91 [Nash and Sutcliffe, 1970]. For the smooth snow surface (Figure 3b), the Nash-Sutcliffe coefficient was −0.43 implying that it was more appropriate to represent the manual surface using an average elevation value from the manual surface than using the digital image. The digital image highlights the small-scale variations but the larger-scale (>1 cm) variations are dominant for the rough surface but not for the smooth surface. As illustrated by the Nash-Sutcliffe coefficient, the digital rough snow surface was approximately 10% less rough than the manually attained surface, while the opposite was observed for the smooth surface, for which the digital interface was 50% more rough (Table 1). The RM index was computed using both pixel and centimeter intervals, yielding less than 1% difference.

Figure 3.

Snow surface plot derived from 1-cm horizontal manual measurement and 0.5-mm horizontal digital photography for the (a) rough and (b) smooth snow examples and 0.1-mm horizontal digital photography for the (c) graupel snow example, as per Figures 1a, 1b, and 1c, respectively.

Table 1. Roughness Indices for the Different Snow Surfacesa
BoardRRRMMIFSinuosity
  • a

    RR is the random roughness, RM is the sum of absolute slopes, and MIF is the product of the microrelief index and the peak frequency. The sinuosity is the distance to width ratio. Note that the graupel surface was only estimated digitally.

Rough-digital10.6291118.41.22
Rough-manual11.8313020.71.03
Smooth-digital1.279781.011.56
Smooth-manual0.8786320.6681.00
Graupel-digital0.6413820.4571.57

[14] With the exception of sinuosity, the rough snow indices are greater than those of the smooth snow, which in turn are greater than for the graupel image (Table 1). When the roughness indices are compared, there are no obvious relationships between the different indices, but they do illustrate the same trends. The roughness measures show similarities between the rough and graupel surfaces (Table 2), especially at the larger scale and for the graupel at finer than 0.2 cm (Figure 4).

Figure 4.

Variograms for the rough, smooth, and graupel snow.

Table 2. Roughness Measures for the Different Surfacesa
BoardDSB (cm)Autocorrelation
Short RangeLong RangeShort RangeLong Range1 pixel1 cm
  • a

    D is the fractal dimension at short and long ranges and SB is the scale break at the upper limit of the range. The autocorrelation is computed over a lag of 1 pixel or measurement and over 1 cm for the digital measurements. There is no obvious scale break for the smooth snow surface measured manually (NA means not available).

Rough-digital1.481.368400.9990.971
Rough-manual1.431.338400.9770.977
Smooth-digital1.911.971110.7700.264
Smooth-manualNA1.97NANA0.4320.432
Graupel1.891.378130.9400.444

[15] The variograms for the rough snow manual and digitally derived surfaces are similar, and are also similar to the graupel surface (Figure 4 and Table 2). The scale breaks have the same value for the digital and manual rough surfaces, with similar fractal dimensions. The variogram for the digital smooth snow shows that the surface approaches random (D = 1.91 to 1.97), as is seen for the small-scale graupel surface (D = 1.89). There is little spatial structure for the manual smooth snow, as the best fit power function would only explain 10% of the variability (Figure 4).

[16] For the rough snow surface, the autocorrelation is approximately the same for the digital image at a 1-cm resolution and for the manual measurement (Table 2). The digital smooth snow surface is autocorrelated at the 0.5 mm resolution, but less autocorrelated at 1cm than the manual surface (Table 2). This is similar to the graupel surface which is dominated by small, subcrystal-scale roughness elements rather than larger features.

[17] The estimation of the rough snow surface is affected by the digital number threshold (DNthreshold) used (Table 3). With DNthreshold less than 40 or greater than 130, variations in the snow surface or the board appear. As well, the snow surface becomes more random (i.e., D is larger; Table 3) because of the addition of random noise.

Table 3. Fractal Analysis for the Rough Snow as a Function of Digital Number Threshold
DNthresholdDSB (cm)
Short RangeLong RangeShort RangeLong Range
  • a

    The digital number threshold (DNthreshold) range from 40 to 130 is equivalent using the maximum change in digital number (ΔDN).

201.691.881545
301.861.60940
40–130/ΔDNa1.481.36840
140N/A1.51N/A45
1501.641.43530
1601.851.761555

4. Discussion

[18] The surface roughness indices and measures showed roughness on the basis of the minimum resolvable scale, which is illustrated by the manual (1-cm resolution) and digital (0.5-mm resolution) measurements. Graupel had a fractal dimension (D = 1.37) similar to the rough snow (D = 1.33 to 1.36), while approaching random (D = 1.89) at the crystal resolution similar to the digital smooth snow surface (D = 1.91). At a resolution greater than 1 cm, the smooth snow became random (D = 1.97). All roughness indices (Table 1) varied but supported these trends. Sinuosity (Table 1) varies as a function of resolution and overall roughness of the surface.

[19] The digital imagery yielded resolution two orders of magnitude finer than manually derived snow surfaces. The imagery illustrates crystal-scale (or in the graupel image, subcrystal-scale) resolution variations. However, for a rough snow surface, larger-scale undulations dominate over the finer variations and thus have a greater influence on the magnitude of roughness metrics. Snow surface roughness at fine scales or distances tends toward a random spatial pattern (Figure 4). At larger distances, in particular greater than 8 cm, variability increases because of the larger-scale undulations (Table 2). This randomness at short distances was also observed in snow depth data [Deems et al., 2006]. The resolution [e.g., Nyquist, 1928] and extent [e.g., Fassnacht and Deems, 2006] of the imagery, combined with the magnitude of surface variation (e.g., rough, smooth in Figure 2), dictated the scale over which spatial coherence was resolved and thus governed the applicability of results.

[20] Bertuzzi et al. [1990] stated that although the standard deviation (RR) measure is easily applied, no standard procedure has been established to consider the effects of slope and oriented roughness, which makes comparison of this roughness index for different studies difficult. We addressed this issue by detrending of the snow surface data derived from the snow board to yield a slope, y intercept, and mean of zero.

[21] Parabolic stretching of the digital image to correct for the variation in distance from the camera lens to the snow board produced minimal effects on the final product. We found that detrending the surface had a greater effect. This is also true for considering the plumbness of the snowboard in the snow surface. When multiple parallel interfaces are to be photographed, the elevation of the top of the board should be surveyed.

[22] Snow surface roughness identification tends to be easier than the classic soil roughness analysis. Various problems exist with soil roughness identification. For example, Wagner and Yu [1991] noted that operator error could exist for manual or electronic measurements using a pin board, and images with poor resolution or lighting [also Huang, 1998] can cause difficulties when distinguishing between pins. The data presented herein represents roughness differences from 1 mm to 50 cm that are at a finer resolution than the soil pin boards. Because of the greater contrast of snow against the black board (black-white contrast), as opposed to soil against background, the image quality in this paper is substantially better than the soil roughness profiles.

[23] Late in the season, it was necessary to use a rubber mallet to drive the board into the snow. It is important to minimize the disturbance of the snow surface by using a board with a sharp edge. Additional tests were conducted to examine the contrast between the snow and three different boards: a natural wood board, a wood board painted black, and a quarter inch thick piece of rigid plastic painted black. The contrast between the natural wood board and the snow was insufficient, and using 100% contrast or the maximum DN did not allow identification of the snow surface as well as with the black plastic board because of its more uniform color. When manipulating blurry images, we found that using a specific threshold was better than using the maximum DN to delineate the actual surface. Shading from the board or falling snow in the image can present additional problems which must be addressed individually. In particular, we found the following important to consider: (1) images that blur the interface cannot be interpreted by identifying the maximum DN change so these poor quality images should be retaken or discarded; (2) during a heavy snowfall, especially when large flakes are falling, it may be necessary to cover the area between the camera and the snow board interface; and (3) the board needs to be kept clean; that is, snow needs to be removed from its surface between each image acquisition.

5. Conclusions

[24] The digital images of a 1-m black board inserted perpendicularly into the snow surface were useful for quantifying and assessing snow surface roughness at a resolution of 1 mm or less. These images are individually manipulated, but assessments of roughness are similar regardless of the method used to identify the snowpack surface roughness. The surface roughness extracted from digital imagery was similar to manual measurements at a 1-cm resolution, and this imagery can resolve finer-scale variations.

[25] The roughness indices used here (random roughness, sum of absolute slopes, microrelief index, and fractal dimension) allow quantitative comparison of surface roughness over scale ranges from 1 mm to 1 m, and serve to highlight important scales at which observed roughness changes character, potentially indicating scales at which controlling processes change.

[26] This study also identified methodological techniques for digital estimation of surface roughness in field environments. A black plastic board of uniform composition, i.e., not plywood, is preferred as a background for digital imaging to maximize the contrast, and the board must be firm to rigid and thin to penetrate the snow surface with minimal disruption. The optimal method to identify the digitally based surface roughness is using a maximum change in the digital number, however blurriness in an image requires using a threshold digital number or setting the contrast to 100%. Roughness indices and measures are useful for illustrating physical features, regardless of inadequacies in image quality.

Acknowledgments

[27] Mark Corrao was supported in part by Northwest Management, Inc. The manual data were collected by the WR406 Seasonal Snow Environments class at Colorado State University in March 2005.

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