1. Introduction

The specific surface area (SSA) is an essential microstructural parameter for the characterization of sintered materials such as snow (Reference GermanGerman, 1996). The SSA of snow changes during isothermal and temperature-gradient metamorphism (Reference Schneebeli and SokratovSchneebeli and Sokratov, 2004; Reference Legagneux and DominéLegagneux and Dominé, 2005) and determines the radiative properties of snow (Reference WarrenWarren, 1982; Reference Leroux, Deuzé, Goloub, Sergent and FilyLeroux and others, 1998). The SSA is a highly relevant parameter for the catalytic effect caused by photochemical properties (Reference Dominé and ShepsonDominé and Shepson, 2002). It is also likely that the permeability of snow (Reference Albert and PerronAlbert and Perron, 2000) is determined by SSA, as Reference GermanGerman (1996) shows is true for other sintered materials.

In this paper, SSA (mm^–1) is defined as the ratio between surface area and the volume of the ice phase.

Natural snowpacks consist of morphologically different layers (Reference ColbeckColbeck, 1991). The complexity of the stratigraphy (Reference Pielmeier and SchneebeliPielmeier and Schneebeli, 2003; Reference Sturm and BensonSturm and Benson, 2004) usually precludes a detailed and exhaustive sampling of snow to determine SSA. Current methods of determining SSA, such as adsorption (Reference Legagneux, Cabanes and DominéLegagneux and others, 2002), microtomography (Reference BrzoskaBrzoska and others, 2001; Reference Schneebeli and SokratovSchneebeli and Sokratov, 2004) and stereology (Reference MatzlMatzl and Schneebeli, 2006), are restricted to relatively small snow samples and confined to essentially point measurements. These methods also require a cold laboratory, and are relatively timeconsuming. Thus, a method that could deliver spatial information on natural snow profiles while requiring only simple equipment would make the measurement of SSA more accessible. Such a method could also be extremely valuable in initializing and validating numerical simulations of snowpack metamorphism (Reference Brun, Martin, Simon, Gendre and ColéouBrun and others, 1989; Reference Lehning, Bartelt, Brown, Fierz and SatyawaliLehning and others, 2002).

Reference Warren and WiscombeWarren and Wiscombe (1980) used Mie theory to describe the optical properties of snow in the near-infrared (NIR) spectrum. Based on this theory, the reflectance between wavelengths of 750 and 1400nm is controlled largely by snow grain size. The influence of snow density can be neglected, as the interparticle distances between the grains are still large compared with the wavelength. According to Reference Dozier, Kaitowski and DeckerDozier (1992), the grain-size effect dominates in the NIR spectrum as long as the snow density is <650 kgm^–3. Impurities influence the reflectance of snow only in the visible spectrum, but not in the NIR spectrum (Reference Warren and WiscombeWarren and Wiscombe, 1980; Reference Leroux, Lenoble, Brogniez, Hovenier and De HaanLeroux and others, 1999). As a consequence, the dependence of snow reflectance on grain size is used in remote sensing to map grain size in the surface snow layer (Reference Dozier, Schneider and McGinnisDozier and others, 1981; Reference Nolin and DozierNolin and Dozier, 2000). Reference Giddings and LaChapelleGiddings and LaChapelle (1961) speculated that the most appropriate definition of the optically relevant grain size of snow could be derived from the volume:surface ratio, the inverse ratio of the SSA. This speculation has yet to be verified experimentally. Reference Grenfell and WarrenGrenfell and Warren (1999) reviewed previous works on the importance of the volume: area ratio for explaining optical properties of snow and clouds. But Reference MitchellMitchell (2002) showed theoretically that the SSA could be directly converted to an effective optical diameter. This suggests that SSA provides a direct link between optical and structural snow properties. Reference Wiesmann, Mätzler and WeiseWiesmann and others (1998) correlated scattering and absorption coefficients at microwave frequencies to the correlation length of snow particles. Reference MätzlerMätzler (2002) showed that correlation length is equivalent to SSA per total volume.

In a related but different problem, there is no simple way to document the stratigraphy observed in a snow pit. The translucent snow profile (Reference BensonBenson, 1962; Reference Good and KrüsiGood and Krüsi, 1992) is perhaps the best-known attempt to map layer features more quantitatively. The translucent profile delivers a clear delineation of boundaries between layers, but the transmitted light intensity cannot be interpreted in a unique fashion, because transmissivity depends not only on grain size but also on snow density (Reference Zhou, Li and StamnesZhou and others, 2003) and section thickness. Experiments comparing NIR photographs on film and translucent profiles showed the feasibility of using an NIR photographic method (Reference Haddon, Schneebeli, Buser, Frost and McNeilHaddon and others, 1997), but analogue photographs were cumbersome to process quantitatively. Here we describe a new method based on NIR digital photography that can be used to determine the SSA and map the pit stratigraphy. The NIR reflectance was compared with measured values of SSA for precisely located snow samples. The correlation between the two measurements was about 90%, with an uncertainty of 3–15%, where the uncertainty increases with increasing SSA. Based on this correlation function we have calculated the SSA for the NIR images. The SSA can be mapped with a spatial resolution of approximately 1mm in an image covering a profile wall with a size up to 1 m². Even thin layers, which can hardly be detected by traditional methods, can thus be detected in the images.

2. Method

The correlation between SSA and snow reflectance required an experimental design that allowed measurement of both parameters for the same snow samples. The reflectance of a snow profile wall was measured using digital photography in the NIR spectrum (section 2.1). Subsequently, snow samples containing specific layers were taken from the same snow wall. The SSA of the snow samples was determined using stereological methods (section 2.2) described by Reference MatzlMatzl (2006). The reflectance of these samples was calculated from the NIR images. Reflectance and SSA were correlated for easily distinguishable and preferably homogeneous layers (section 2.3). Figure 1 illustrates the experimental design. The correlation function was then used to calculate the SSA for the whole NIR image of the snow-pit wall.

Fig. 1. (a) NIR image of a snow-pit wall with four calibration targets (i) in the corners. The locations of the sample containers are marked with a black frame. (b) Magnification of the NIR image at one sample location. The vertical distribution of the reflectance signal for this sample is calculated based on the pixel intensity of the targets (i). (c) Image covering the same snow-pit wall with the inserted sample containers (ii). The surface section of one sample is displayed (d) and also the corresponding measured specific surface area (SSA) values.

2.1. NIR photography

The camera used for the digital photographs was a Kodak DCS420ir with a 20mm Nikkor lens. A gelatine filter (Kodak Wratten 87c) was placed over the charge-coupled device (CCD). The wavelength of the detected light ranged from 840 to 940 nm. The distance between camera and profile wall varied between 1.5 and 2.0 m, resulting in pit wall photos varying from 0.5 to 1.0m². Before the photographs were taken, the profile wall was cut carefully with a saw and smoothed with a rounded-edge wooden board about 20cm in width.

To compensate for tilting or turning of the camera with respect to the profile wall, a geometrical correction was performed on the digital image. The correction required at least three targets, inserted in the profile wall with a known distance to each other and a known geometry (Fig. 1a). The nearest-neighbour method was used to transform the target coordinates in the digital image congruently with their original geometry and distance.

The calibration targets were manufactured of Spectralon greyscale standards with NIR reflectances of 50% and 99%. Alongside the geometrical correction, these reflectance values corrected illumination variations by interpolation between the 50% targets and subtracting the interpolation from the original image. The NIR reflectance, r, of the snow was calibrated with regard to the pixel intensities of the targets:

(1)

where i is the intensity of each pixel and a and b are determined by a linear regression on the pixel intensities of the greyscale standards. The coefficient of deviation of the reflectance from the calibrated image measured at the white targets is 2.6%.

After photographing the smoothed wall, a second image of the profile wall was taken, including the inserted containers of the snow samples (Fig. 1c). The comparison of the two images allowed us to define the exact sample coordinates in the first image. The reflectance signal was calculated by averaging horizontally over the 65mm width of the image covering the sample location (Fig. 1b), thereby producing a graph of SSA with height.

3. Results

Figure 2 gives an overview of all the measured parameters. Density and SSA are stereological estimates from the segmented surface section, while the reflectance is calculated from the NIR image. Corresponding layers are marked for the SSA and the reflectance signal.

Fig. 2. Surface section and NIR image of two snow samples and the derived density, specific surface area (SSA) and reflectance signals. For sample 2 the absolute height of the surface section and the NIR image vary. The grey bands mark visually identified layers.

In total, 29 samples were obtained from field measurements. For each sample, we identified between one and three layers for which mean reflectance and SSA were measured. Figure 3 shows the scatter plot of reflectance and SSA for all layers. For a comparison with existing data we choose values published by Reference Warren and WiscombeWarren and Wiscombe (1980), Reference Dozier, Kaitowski and DeckerDozier (1992) and Reference Sergent, Pougatch, Sudul and BourdellesSergent and others (1993) at 890 nm. We transformed the optical sphere diameter, d, used in these publications to SSA using:

Fig. 3. Scatter plot of measured specific surface area (SSA) values vs reflectance with a fit (solid line; Equation (3)). The dotted line indicates the relationship between reflectance at 890 nm and SSA based on published values by Reference Wiscombe and WarrenWiscombe and Warren (1980), Reference Dozier, Kaitowski and DeckerDozier (1992), and Reference Sergent, Pougatch, Sudul and BourdellesSergent and others (1993).

(2)

To avoid an overweighting of the intermediate reflectance class, we grouped our data in reflectance classes of 5%. Six measurements per class were randomly selected. The regression was calculated based on these stratified samples. The scatter plot shows an exponentially growing relationship between SSA and reflectance, r.

(3)

where A = 0.017 ± 0.009 mm^–1 and t = 12.222 ± 0.842. The correlation coefficient, R ², is 90.8% at a significance level p<0.002. The error increases with increasing SSA from 4% at an SSA of 5 mm^–1 to about 15% for SSA values of about 25 mm^–1. Alternatively, a linear fit of the reflectance vs square root of grain diameter was tried, based on the simplified equation in Reference Wiscombe and WarrenWiscombe and Warren (1980). In this case the correlation coefficient, R², is 89.5% at a significance level p <0.0001.

The scatter plot of density and SSA for the same snow layers shows that we included snow types with a wide range of densities and SSA values (Fig. 4). It can also be seen that low-density snow covers the whole range of measured SSA, and samples with a low SSA cover a wide range of densities.

Fig. 4. Scatter plot of SSA and density.

Figures 5 and 6 show a quantitative two dimensional (2-D) mapping based on Equations (1) and (3). Figure 5 also shows a conventional hand profile. The photograph corresponds with the hand profile. Note that the ice crust at a height of 73cm and the boundary at 36cm are very distinct. Not only layers are mapped but also gradual transitions (e.g. that between 57 and 60cm height). The SSA varies between 1 mm^–1 for the lower parts of the profile and for the ice crust, and 27 mm^–1 for the upper parts of the profile.

Fig. 5. SSA mapped for a snow-pit wall combined with a traditional hand profile. Larger boundaries are marked with a dotted line.

Figure 6 shows an NIR image with inhomogeneous illumination. The upper-left part of the profile is too bright. However, it is still possible to recognize features such as the melt crust in the upper third of the profile or the infiltration zone below.

Fig. 6. SSA mapped for a snow pit with inhomogeneous illumination.

4. Discussion

The SSA and reflectance of a wide range of snow types were measured. An increasing reflectance is correlated with an exponentially increasing SSA. We did not observe any systematic difference between snow type and the fitted line. This result supports the assumption of Reference Giddings and LaChapelleGiddings and LaChapelle (1961) that SSA is the most important parameter determining snow reflectance in the NIR spectrum.

The comparison with data published by Reference Wiscombe and WarrenWiscombe and Warren (1980), Reference Dozier, Kaitowski and DeckerDozier (1992) and Reference Sergent, Pougatch, Sudul and BourdellesSergent and others (1993) shows good agreement with our observations for SSA values below approximately 20 mm^–1 (Fig. 3). There are three possible explanations for the difference for SSA values greater than 30 mm^–1. (i) The calibration targets may have had a lower reflectance than specified because of staining caused by field use. However, post-calibration indicates that this effect is not more than 2%. (ii) Our estimated average wavelength (890 nm) is underestimated. Because the NIR sensitivity of the camera CCD is unknown, this is a reasonable explanation. Comparison with figure 9 in Reference Wiscombe and WarrenWiscombe and Warren (1980) shows that our curve is steeper than expected for 890 nm. (iii) The measured light intensity was not only reflectance but also light that passed the snowpack from the snow surface, as the snow surface behind the profile was not always completely shaded. Because the snow samples showing a large SSA value were mostly obtained close to the surface, such an influence cannot be excluded.

The comparison between density and SSA (Fig. 4) shows a loose correlation between these properties, as high SSA values are usually related to low densities and vice versa. For densities from approximately 150 to 300 kgm^–3 a wider range of SSA values can be observed. This makes a direct correlation, as suggested by Reference NaritaNarita (1971) and Reference Legagneux, Cabanes and DominéLegagneux and others (2002), very uncertain in this density range. Snow classes 1–3, which include new snow, partly decomposed snow and rounded snow, are well discriminated by a steadily decreasing surface area. Snow classes 4–8, which indicate stronger metamorphism, are not well discriminated and cover a larger range of SSA and reflectivity.

The correlation function between reflectance and SSA was used to calculate the SSA for the NIR images. The images of the snow profiles (Figs 5 and 6), especially when combined with a manual profile, show that variations in the SSA reflect the layering of a snow cover in great detail. The method ‘visualizes’ layers well and shows the slight vertical and horizontal structural variations that are otherwise difficult to record by conventional field methods. Even very small local differences in the SSA are visible (e.g. an infiltration zone in Fig. 6).

This method could be improved in several ways. A homogeneous and diffuse illumination of the profile wall is essential, because the digital correction of an inhomogeneous illumination is not possible without losing the context to absolute reflectance. We found that in the field such heterogeneities in the illumination are not detectable by eye. Figure 6 shows such uncontrolled reflections. The upper-left part of the profile was too bright, which makes a quantitative interpretation of this part difficult. The shading for diffuse illumination must cover at least 0.5m behind the profile wall, and must extend over the side walls of the pit. The method could also be improved by the use of a flat-field correction. A second image, where a target of constant colour brightness covers the whole profile wall, is subtracted from the first image. This method even corrects for very local illumination heterogeneities and may be used instead of the digital interpolation between the reference targets, as was used in this study.

We conclude that the current technique allows us to visualize relative differences of SSA at a very high resolution. The SSA on a 2-D image can be measured with an uncertainty of about 15%. The proposed improvements could significantly enhance this result.

The ability to measure SSA in two dimensions opens up the possibility of linking micro- and macroscale measurements of snow structure. SSA of individual layers as well as the stratigraphy of the snow cover is crucial for physical and chemical models. Because of the widespread use of SSA to parameterize air permeability and thermal conductivity of sintered materials (Reference GermanGerman, 1996), it can be expected that this should also be possible for snow. Such an extension of the present work would be very useful in initializing and calibrating numerical models that simulate the transport and transformation processes occurring in a snow cover.