**1. Introduction**

The microstructure of snow is an important parameter for the modelling of microwave emission and optical reflectance [1–3], and it is therefore also important for remote sensing applications. However, a parameter describing all snow properties, including size, shape, bonding, and the orientation of snow grains, is not simple to define. The parameters most often used for that purpose are traditional grain size [4], correlation length [3,5], optical grain size [6,7], and specific surface area (SSA) [8,9]. Several methods exist to measure these directly or indirectly, but this study concentrates only on the reflectance-derived, in-situ methods.

Snow reflectance at near infrared (NIR) and short-wave infrared (SWIR) wavelengths, especially over 1000 nm, is dominated by grain size [6]. Optical effective grain size is defined as the diameter of spheres having equal optical properties compared with the original grains [6,10]. SSA is defined as the surface area of the air–ice interface per unit mass (unit m<sup>2</sup> kg−1) [9,11]. Optical grain size and SSA are related by Equation (1):

$$SSA = \frac{6}{\rho\_{\rm ice} \, D\_0} \tag{1}$$

where *ρice* is the density of ice and *D*0 is the optical grain size, which is derived based on equations in [9,12] as presented by [13]. Grain shape has been shown to affect the reflectance-derived SSA in many wavelengths [10,14,15], and [16] presented a modelling study concerning the influence of grain shape on albedo-derived SSA, resulting in 20–25% error.

DUal Frequency Integrating Sphere for Snow SSA (DUFISSS) was presented by [13]. It uses 1310 nm and 1550 nm lasers and an integrating sphere to measure hemispherical reflectance from the snow sample surface, which was converted to SSA [13,17]. The error of the SSA measurement was 10% based on [13]. The measurement method is similar to that of the IceCube, which is described in Section 2.2. The Profiler of Snow Specific Surface area Using SWIR reflectance Measurement (POSSSUM) and the Alpine Snow Specific Surface Area Profiler (ASSSAP) [18] are also based on the same principle. A contact spectroscopy method is presented by [7] to observe the optical grain diameter from a vertical profile of snowpack based on reflectance measurements of a band near 1030 nm by using a FieldSpec FR and attached modified Contact Probe (ASD Inc., Longmont, CO, USA). The derivation of optical grain size was based on an ice absorption model by [2]. The optical grain size and traditional grain size had poor correlation with less robust results for rounded grains, which is assumed to relate to the effect of grain shape. A review of past field experiments, where reflectance or albedo is compared to some of those parameters describing snow microstructure, is presented next.

Near infrared photography at 850–1000 nm is a method to observe SSA from reflectance as presented by [19]. The correlation between reflectance and SSA was reported to be 0.9 and the inaccuracy of SSA 15%. A clear correlation between hemispherical reflectance derived from measured nadir SWIR spectral reflectance of snow from FiedSpec FR 350–2500 nm (ASD Inc., Longmont, CO, USA) and SSA measured with Brunauer Emmett Teller (BET) analysis [9,20] was presented by [8]. Additionally, they did not find any effect from grain shape on the results. A correlation between grain size and a ratio of 1160 nm and 1260 nm hemispherical reflectance is showed by [21]. The accuracy of average grain size estimation was presented to be ±0.2 mm. Spectral albedo was measured with the Autosolexs instrument (400–1050 nm) to estimate SSA [22]. The accuracy of SSA depended on the solar zenith angle and the leveling of the instrument, and error was presented to be 15%. The SSA derived from Autosolexs had poor correlation with ASSSAP measurements; however, the wavelength and vertical resolutions of the instruments were different. The Automatic Spectro-Goniometer is presented for hemispherical–directional reflectance measurements [23]. The measurements were compared with Discrete Ordinates Radiative Transfer Program for a Multi-Layered Plane-Parallel Medium (DISORT)-modelled reflectance by using spheres with radii equal to the surface-area-to-volume ratio derived from stereological analysis, resulting in model underestimation with a maximum mean root-mean-square error (RMSE) of 0.09% for 1300 nm. A study where albedo was modelled with DISORT based on SSA measured with DUFISSS resulted in 1.1% difference to measured albedo with FieldSpec pro JR (ASD Inc., Longmont, CO, USA) [24]. It is estimated that 1% error in albedo corresponds approximately with 15 m<sup>2</sup> kg−<sup>1</sup> error in SSA [16]. In addition, the optical diameter of snow grains with data derived from near infrared photography or FieldSpec (ASD Inc., Longmont, CO, USA) spectral albedo or reflectance observations is researched by [25–29]. Grain size or size distribution was measured traditionally or from image-processing of microphotography.

The presented methods from previous studies are primarily intended for measuring reflectance from the surface of the snowpack, and they are not suitable for measuring vertical profiles except for contact spectroscopy with the Contact Probe and near-infrared photography. Since solar radiation is subject to variability, originating from, for example, zenith angle and cloud cover, it is beneficial that the instrument used includes an internal light source for stable illumination. A newly developed instrument, QST (ASD Inc., Longmont, CO, USA), was tested for performing rapid measurements of vertical snow profiles. The hand-held instrument measures almost bidirectional reflectance with similar optical geometry to that of the Contact Probe. The instrument was tested on taiga snowpack in the Arctic Space Centre of the Finnish Meteorological Institute in Sodankylä in northern Finland. QST has been used previously for other purposes such as the detection of ion concentrations in soil [30] and heavy metal pollution in soil [31]. Snow measurements are more challenging due to the deeper penetration depth of the radiation, the fragile structure of the snowpack, and melting of the snow.

Previous results of SSA measurements from a taiga snowpack in Sodankylä include the comparison of SSA and optical grain size to modelling results. The optical grain size derived from SSA measurements of IceCube was compared to SNOWPACK [32–34] modelled optical grain size in [35,36]. SNTHERM [37,38], SNICAR [39], and MOSES [40] modelled optical grain sizes were compared to IceCube-derived optical grain size by [37]. Moreover, the spectral reflectance of a taiga snowpack has previously been measured with a portable Field Spec pro JR spectrometer in the Sodankylä area and a similar mast-based spectrometer located at the same area as the measurements performed for this study [41,42]. In addition, measurements of bidirectional reflectance factor have been performed with a goniospectropolariphotometer [43,44].

The aim of this study was to test the suitability of the QST instrument for measuring the reflectance of snow, and the main conclusion of the study was that an empirical relationship between SSA and QST reflectance exists. The paper has the following structure: Section 2 presents field measurements and methods, results are presented in Section 3, and discussion is made in Section 4.

#### **2. Materials and Methods**

Snow measurements have been performed at the Intensive Observation Area (IOA) in Sodankylä in northern Finland since 2006 (Figure 1) for the calibration, validation, and development of remote sensing instruments and interpretation algorithms. Vegetation in the cleared area among sparse pine forests consists of lichen, moss, heather, crowberry, and lingonberry, whose growth rate is approximately 0.4 cm per year in the snow pit area [45]. Typically, the average maximum snow depth (~80 cm) occurs in late March. The average air temperature is below 0 ◦C from November to April, and the average wind speed is low (1–2 m s<sup>−</sup>1) in the area as described in [35]. Several automated instruments measuring snow, soil, radiation, and meteorological parameters are installed in the IOA, in addition to manually recorded snow pit measurements [35]. The data set for this study was taken from snow pit measurements made in spring 2017 (22 February, 7 March, 16 March, 21 March, and 3 April) with clear or partially cloudy sky conditions.

**Figure 1.** (**a**) Location of Sodankylä in northern Finland; (**b**) snow pit measurement site in Sodankylä.

#### *2.1. Layers, Traditional Grain Size, and Density*

Horizontal layers of the snowpack were defined manually with a brush and toothpicks. Layers were defined according to visual appearance, grain type, grain size, hardness, and wetness. Macrophotography-based, traditional grain size, the largest extent of an average grain [4], was estimated from macro-photographs taken against a 1 mm reference grid. The density profile was measured every 5 cm with a 10 cm × 10 cm × 5 cm rectangular sampler and digital scale with ±1 g accuracy. More detailed information of the methods is presented by [35].

#### *2.2. SSA with IceCube*

The reflectance and SSA was observed with IceCube manufactured by A2 Photonic Sensors, Grenoble, France. IceCube measures the hemispherical reflectance of a 1310 nm laser from the snow sample surface (Figure 2a). A photodiode observes diffuse radiation from the integrating sphere originating from the laser and reflected from the sample. The snow sample is collected with a spatula (or a specific tool), packed into the sample holder to reach a minimum density of 200 kg m −3, and the surface is levelled (Figure 2b). The sample holder is 2.5 cm high and 6 cm in diameter. Software provided by the manufacturer converts the observed voltage value to reflectance using the calibration results. The instrument is calibrated for every measurement occasion using reference plates of different reflectivity. The calibration curve is fitted to the six calibration measurements. Determination of SSA from the reflectance is based on DISORT modelling and depends also on optical parameters of the integrating sphere [13]. In this study, the SSA samples were taken in 3 cm intervals from the vertical profile of the snowpack. A more detailed description of the IceCube measurement procedure is presented in [35] and a discussion on measurement errors is presented in [46].

Additional testing of the measurement accuracy occurred on 21 March 2017. The measurement of each sample from the profile was repeated three times with IceCube by rotating the sample in the azimuth direction between measurements. In addition, three samples were taken from both the surface layer and the depth hoar layer to test the effect of the sampling procedure and packing density. Those samples were also weighed to determine the sample density.

**Figure 2.** (**a**) The IceCube measurement; (**b**) the IceCube sample; (**c**) the QualitySpec Trek (QST) measurement from the snowpack vertical profile; (**d**) the QST measurement from sampled snow.

#### *2.3. Reflectance with QualitySpec Trek*

QST is a portable spectrometer manufactured by ASD Inc., Longmont, CO, USA (Figure 2c,d). QST measures the almost bidirectional reflectance of NIR and SWIR radiation at 350–2500 nm wavelengths with a spectral resolution of 9.8 nm at 1400 nm. The instrument has three detectors: 350–1000 nm (512-element silicon array), 1001–1785 nm (InGaAs photodiode), and 1786–2500 nm (InGaAs photodiode). The instrument also has an internal light source and internal gray scale reference

for optimization and wavelength calibration. The light source is a Quartz Tungsten Halogen bulb with a color temperature of 2870 K ±33 K. Illumination and viewing geometry is presented in Figure 3. The window of QST is approximately 1 cm in diameter, and the whole window is illuminated by the internal light source. The window and materials inside the instrument are designed to minimize specular reflections. The angle from the instrument window to the light source is 55◦ and the angle to the fiber optic is 78◦. The fiber optic cable has a field of view of 25◦, which means that the field of view is 0.82 cm on the window of the instrument. The Contact Probe [7] has the same measurement geometry as QST. Additional calibration is made before every measurement occasion with a separate white reference plate. The reference plate is attached in front of the instrument window with magnetic plugs. It is important that the white reference plate is clean and that the manufacturer provides information for cleaning and replacing the plate. Full-spectrum dark reference is measured also during the start-up with an internal shutter, the light source is turned off, and the white reference is plugged. The dark reference (background) value is subtracted from raw data prior to the reflectance calculation. The sample count averaging time can be set to 1, 2, 5, or 10 s. The instrument scans the entire wavelength range 10 times per second and produces an average of those. The sample is set to physical contact with the instrument window (Figure 2c,d and Figure 3), so cleaning of the window between the measurements is therefore required. A measurement is stored by pushing a trigger button. Sound signals for starting and finishing the measurement notes when the instrument needs to be in stationary position with the (snow) sample. The most recent data is shown on the screen. Audio note recording is possible after the measurement. The instrument also stores coordinates and elevation from the internal GPS for each sample. Automatic and manual data storage options are available. The resulting reflectance is absolute reflectance (reflectance normalized with reference reflectance). Since the instrument is commercial, calibration data and data from the single spectrums before averaging are not available.

The measurement procedure included a white reference measurement, instrument setup (choosing how many times the wavelength range is scanned for averaging), and snow measurement (repeated). Cleaning of the window was rarely needed. Automatic data storage was used. The integration time for a measurement was set to 1 or 2 s. A longer integration time meant more averaged spectrums and therefore less noise for an acquisition. On the other hand, the instrument remained steadier in snow with a shorter integration time. Two procedures related to how the instrument can be used are (1) vertical reflectance profile from the snowpack of the snow pit wall and (2) reflectance from the snow surface without digging a snow pit. The measurements were made with the first procedure from the snowpack profile by pushing the instrument window steadily against the snow pit wall during the measurement (Figure 2c). The window had physical contact to the snow so that the distance between the snow and fiber optic cable was always constant and the measurement configuration did not change. The measurements were made at approximately 2–5 cm intervals from the vertical profile. Some of the IceCube samples were also measured with QST by pushing the window against the snow in the middle of the sample surface (Figure 2d).

**Figure 3.** Illumination and viewing configuration. Fiber optic and light source have the same azimuth angle. Fiber optic cable has 25◦ field of view. Diameter of the window is approximately 1 cm.

#### *2.4. Methods for Comparison of QST and IceCube Measurements*

Reflectance profiles were measured with QST from both the snowpack and the sampled snow on 21 March and 3 April 2017. The two profiles were measured with different height intervals, and therefore both profiles were linearly interpolated for every centimeter (no extrapolation). A comparison presented in Section 3.3 was made only for the heights where both interpolated reflectance values existed.

The empirical relationship between SSA and reflectance was studied with 1160 and 1260 nm reflectance-dependent coefficient Q, which is the ratio of reflectance at the bottom of the ice absorption feature and the reflectance change in the ice absorption feature. The absorption coefficient of ice is larger at 1260 nm than at 1160 nm. Q is calculated with Equation (2) as

$$Q = \frac{R\_{1260}}{R\_{1160} - R\_{1260}} \tag{2}$$

where *R*1160 is reflectance at 1160 nm and *R*1260 is reflectance at 1260 nm.

Similarly, interpolation was also needed to compare SSA and reflectance-derived Q from the same heights of snow. Linear interpolation without extrapolation was made for SSA when the reflectance profiles from the snowpack were studied. For 21 March, the values from the first of the three SSA measurements of the same sample were used. The comparison presented in Section 3.4 was made with interpolated SSA values from the same heights as the original reflectance profile measurements from the snowpack. Interpolation was not needed in the case of the reflectance profile from sampled snow because the same samples were measured with both instruments.

Clearly erroneous reflectance values measured with QST were removed from the analysis (>0.1 difference to the closest value without fitting to other values around). One of those was from the snowpack profile in 16 March (63 cm height), another one was from the snowpack profile in 21 March (70 cm height), and the two last ones were from the sampled snow in 21 March (48 and 51 cm height).
