Micro-computed tomography (μCT) allows the full 3-D microstructure of snow to be reconstructed. μCT measurements of snow result in a gray scale, which was filtered using a Gaussian filter (σ=1 voxel, support = 1 voxel, following ) and then segmented into a binary image. The threshold for segmentation was constant for each sample and determined visually. After segmentation, the binary image contains the full microstructure and allows the derivation of the volume fraction ϕi of the snow sample, which is then related to the density ρ of snow by ρ=ρiceϕi in terms of the density ρice=917kgm-3 of ice. The main uncertainty of the μCT density lies in the segmentation of grayscale images into binary images.

Density cutters provide a gravimetric measurement, where density is calculated by weighing a defined snow volume which is extracted from the snow using a cylinder-, wedge-, or box-type cutter. Figure  shows the three different types of cutters which were used during the workshop: (a) a 100 cm3 box cutter, 6cm×3cm×5.5cm, originating from the Institute of Low Temperature Science, Japan, now known as the Taylor–LaChapelle density cutter, manufactured by snowhydro (http://www.snowhydro.com/products/column4.html) and WSL-SLF; (b) a 100 cm3 cylinder cutter, 3.72 cm inner diameter and 9.2 cm in height, constructed from an aluminum cylinder with one end sharpened to cut cleanly through the snow; and (c) a 1000 cm3 wedge cutter, 20cm×10cm×10cm, manufactured by Snowmetrics (http://snowmetrics.com/shop/rip-1-cutter-1000-cc/). All three cutter types are typically inserted horizontally to extract snow samples; the cylinder cutter can be inserted vertically as well to extract snow samples from thin layers (detailed in the next paragraph). In addition to these three cutters, a larger cylinder cutter of inner diameter 9.44 cm and length 55 cm (also vertically inserted into the snow) was used to determine the snowpack average density. The main uncertainties for the density cutters lie in the compaction of light snow while inserting the cutter into the snowpack and in losing parts of snow samples, especially those which consist of fragile facets and depth hoar .

After the stratigraphic arrangement of the snowpack was identified (see Sect. ), density measurements were made within each layer. The 100 cm3 cylinder cutter inserted vertically down through the snow to a preplaced crystal screen (see also ) was used to extract snow samples within stratigraphically defined layers. Samples were weighed using an ACCULAB Pocket Pro 250-B scale with a resolution and nominal accuracy of ±0.1 g. Each density measurement is repeated twice and the average of both samples taken as either layer or sublayer density. The density of layers, the height of which are less than the cylinder length, can be calculated using the ratio of the layer height and the cylinder length. However, layers thinner than about 2 cm are aggregated to adjacent upper or lower layers and cannot be resolved with regard to density except when the hardness of the layer itself, or of an adjacent layer, is greater than a hand hardness index of 3 (i.e., one finger, see ). In such a case, a sample may be cut out of the snow and density can be estimated by measuring its dimensions and weight. If the sample contains two layers, the softer one may then be gently scraped away to determine the density of the harder layer. Using both measurements yields the density of the softer layer. Such measurements are prone to large errors (≥10 %), even by a skilled observer. Three melt–freeze crusts or ice lenses were determined in this manner.

Conversely, where vertical layer thickness was larger than the cylinder length, seamless sampling down the layer was required to determine its mean density. In that case, densities at sublayer scale may be obtained within a layer. Finally, depth averaging the layer densities over the full profile yields the snow water equivalent (SWE) of the snowpack.

The density per layer or traditional stratigraphy is termed “cylinder cutter” hereafter, as only the cylinder cutter was used in this study to determine the density per layer. All other devices (box and wedge cutter, μCT) were operated without consideration of snowpack layering or stratigraphy, i.e., with constant vertical resolution (see also Sect. ).

Thirteen snow blocks of 40 cm × 40 cm in area and between 10 and 36 cm in height were used in this study. The major grain types of the snow blocks were facets (n=7), rounded grains (n=3), and depth hoar (n=3), as classified according to . All blocks were measured using the μCT and the 100 cm3 box-type density cutter in the laboratory, at a constant air temperature of -10 ∘C. μCT samples were taken from depths between 2.9 and 6.8 cm from the surface of the block. Up to three samples were taken per block; two samples were extracted using a 35 mm diameter sample holder, and one using a 20 mm diameter sample holder. Samples in the 35 mm sample holder were scanned with a resolution of 0.018 mm, within the scanned volume of 153 mm3, whereas samples in the 20 mm sample holder were scanned with a resolution of 0.010 mm within the scanned volume of 103 mm3. The representative cubic volume to derive density from μCT measurements is around 1.253 mm3 . Continuous box cutter measurements were performed from the snow surface to the bottom of the snow block with a vertical resolution of 3 cm, leading to a maximum of eight measurements per block. For comparison with μCT densities, the uppermost three cutter measurements (0–9 cm snow depth) were analyzed, to avoid any misalignment with the location of the μCT measurements. An overview of the lab measurements is given in Table .

The field site was a tennis court in St. Moritz (46.4757∘ N, 9.8224∘ E) which is surrounded by forest, and is fenced, wind-sheltered, and flat, and as such showed a very homogeneous natural snowpack. For instance, wedge cutter measurements, where two profiles were performed within 20 cm horizontal distance, showed a mean difference of 7 kgm-3 or 2 % of the mean wedge cutter density. All density measurements were performed within less than 3 m horizontal distance of each other. Field measurements were made on 11 and 12 March 2014 (Table ). Warm temperatures caused surface melt after the measurements during the first day, leading to densification of the uppermost layers and to more pronounced crust and ice layers on the second day. Measurements were made between 04:00 and 09:00 each day, while the snowpack was still dry.

To analyze a profile completely from top to bottom by means of μCT, five blocks of 20cm×20cm×30 cm were extracted from the snowpack on 11 March. Snow blocks were quickly transported to the lab and each block was sampled using 35 mm diameter sample holders, leading to a total of 18 μCT samples for the whole vertical profile. Each sample was scanned with a resolution of 0.018 mm within a scanned volume of 10.8mm×10.8mm×2.16 mm. Scans were performed with a vertical overlap of 50 %. The density was then resampled in a depth window of 1.08 mm. Field μCT samples were evaluated using the classic segmentation approach (Sect. ). Three types of density cutters (Sect. ) were used in the field. Measurements using the cylinder cutter (densities per layer) and wedge cutter were made on 11 March, and box cutter measurements were made on 12 March. All measurements were performed within 2 m horizontal distance of each other.

As the stratigraphy is defined by several properties, density alone is always an insufficient parameter for the traditional stratigraphy. Here we demonstrate that the traditional stratigraphy often shows much sharper boundaries than the density measurements would indicate (Fig. ). Traditional stratigraphy showed a highly detailed representation of specific types of density variations such as ice layers in the upper part of the profile, contrasted by a very coarse representation in the lower part; only one single layer was determined from 90 to 130 cm depth (Fig. ). Nevertheless, three sublayers could be identified within this layer, the density difference of which could not be explained by inter-sample variability (4.2 kgm-3 or 1.1 %). While the sublayer densities of 382, 400, and 418 kgm-3 from top to bottom reproduced the trend of both box and wedge cutter measurements, the cylinder cutter did not represent these variations. Further, the wedge cutter did not represent the variations measured by the box cutter, and the box cutter did not represent the variations measured by the μCT. Figure  illustrates this fact: on the one hand, layer boundaries, which were defined following the traditional stratigraphic approach , appeared less distinct in the μCT, and on the other hand, the higher resolution methods resolved a high degree of variability within a layer. We would like to point out here that sharp boundaries, as introduced by the observer, compared to the very smooth evolution of the high-resolution measurements, may introduce a significant bias in numerical simulations, when observed snow profiles are used as initial conditions. The effect of different stratigraphic representations on microwave emission modeling was unambiguously demonstrated. estimated the error in retrieved snow depth from passive microwave simulations to be up to 50 % due to neglecting stratigraphy. showed that the bias of a three-layer representation of a tundra snowpack with respect to microwave emission was half of the bias for a single-layer representation. For the validation of snow cover models, mentioned the fact that more layers are produced by the models than are typically observed in a snow profile to be critical.

The fact that the higher resolution methods resolved a higher degree of density variation is closely related to the measurement volume of the different instruments. For instance, the measurement volume of the μCT (153 mm3=3375 mm3=3.375 cm3) is around 3 % of the measurement volume of the 100 cm3 box density cutter. A larger measurement volume is connected to a smoothing of the measured density profile, as thin layers are averaged within the measurement volume. This explains the lower variability of the box cutter density profile, compared to the high-frequency density variations resolved by the μCT, and is also true for the lower variability of the 1000 cm3 wedge cutter compared to the box cutter. As the measurement volume of the μCT was sufficiently large to be representative (1.253 mm3=1.95 mm3, , Sect. ), these high-frequency density fluctuations are not an artifact of a small measurement volume.

Spatially discontinuous near-surface ice layers decreased the agreement between different field measurements (Table ). Box and wedge cutters did not fully resolve the ice layers in the field, in contrast to the stratigraphic method.

Ice layer densities were determined by careful measurement of an extracted ice layer. Uncertainties remain in measurements of ice layer densities using this technique, largely due to the triaxial volume measurement of an irregular-shaped ice sample in combination with the precision of the in situ mass measurement (±0.1 g) relative to the mass of the sample. When using the box and wedge cutter, ice layers represented only a small part of the sampled snow volume. The box cutter showed two distinct density peaks, but with values of 409 and 405 kgm-3, these measurements were lower than the layer densities of 567 and 760 kgm-3 for the upper and lower ice layers, respectively (Fig. ). In contrast, the wedge cutter did not show any significant density peaks. The perceived lack of ice lenses in the 1000 cm3 wedge cutter is due to them representing a much smaller proportion of the sampled volume than the other methods. However, uncertainties in measurements of ice layer densities are poorly constrained. Previous measurements have produced a wide range of densities values, such as 630 to 950 kgm-3 in the Canadian Arctic and 400 to 800 kgm-3 in seasonal snow on the Greenland ice sheet . Unfortunately, no ice layer was present in the samples measured by the μCT. The large variability in ice layer density measured by different instruments in this study suggests that this topic needs further investigation towards the development of a more precise measurement technique, especially due to the significance of this measurement for radiative transfer modeling .

In addition, ice layers evolved during the two field days. On the first day, the ice layers were very heterogeneous and horizontally discontinuous. After that, warm temperatures and melt in the uppermost layers led to more pronounced and continuous ice layers on the second day. The SMP provided evidence for the thickening of the ice layers. To avoid breaking the sensor, the SMP immediately stops measuring once a force threshold of 41 N is reached, which means that the layer is too hard for the instrument to penetrate. The SMP force threshold of 41 N was reached for 31 % (4 out of 13) and 56 % (13 out of 23) of the measurements on the first and second day, respectively.

For the μCT measurements, the blocks were extracted on the first day when ice layers were less pronounced. The μCT data showed no evidence of distinct ice layers in these blocks. Density peaks, however, were found in the lower part of the profile, e.g., at 80 cm snow depth (Fig. ). These density peaks correspond to melt–freeze crusts consisting of larger aggregated structures.

The unresolved variation represents the density variation within a layer. This variation is not captured by the measurement methods with coarser vertical resolution and cannot be reconstructed. The unresolved variations were up to 7.7 %, averaging the μCT densities to match the traditional layers, with a standard deviation of 5.0 %, expressed as percentage of the mean μCT density. On average, an unresolved density variation of 7.7 % seems tolerable, but it becomes a critical variable as the loss of small density variations will propagate through all parametrizations which are based on density, such as permeability (e.g., ) or thermal conductivity (e.g., ). Figure b illustrates this: the high-resolution density profile of the μCT sample no. 9 loses all of its detail if measured with the vertical resolution of the box cutter. The temperature gradient inside the snowpack depends on variations of the thermal conductivity caused by variations in density . Losing density variation means losing local maxima and minima in temperature gradient, and therefore missing the driver for potential crystal faceting and weak layer formation. also mentioned the limited resolution of a traditional snow profile as a major drawback for the characterization of weak layers. Density variations are also known to have a large influence on mechanical properties and on microwave signatures as they act as interfaces for wave reflection .