2.1. The HISSGraS instrument

HISSGraS was designed to measure the SSA of snow grains on site (Fig. 1). The characteristics of HISSGraS are: (1) lightweight (1.7 kg, including the battery), (2) handheld size (L 287 mm long × 109 mm high × 104 mm wide), (3) measuring the snow surface or a snow pit face directly through a glass window installed in front of an integrating sphere (IS) (Fig. 1, top right) and (4) recording the measured data and GPS measurement position automatically on a memory card. The measurement duration for a single data point is less than 1 s. These enable HISSGraS quick field measurements. HISSGraS can also measure SSA of snow samples collected using the same sampling cup and procedure as the IC. A cylindrical snow core, 30 mm thick, is extracted using a snow sampler and then inserted into a sampling cup with a depth of 25 mm using a piston. Any excess snow is carefully removed with a snow spatula to provide a fresh surface. The use of a sampling cup during the sampling procedure could introduce errors in SSA measurements. Martin and Schneebeli (Reference Martin and Schneebeli2023) discussed how particles artificially created during the sampling procedure using a sampling cup in SSA measurements with the IC method sometimes led to overestimated SSAs when compared to SSAs derived from X-ray microtomography. Additionally, Gallet and others (Reference Gallet, Dominé, Zender and Picard2009) pointed out that snow samples with low density and high SSA (>66 m² kg⁻¹) could produce artifacts, where incident light hits the walls or bottom of the sampling cup, causing underestimated SSAs. Therefore, performing SSA measurements directly on a snow surface or a snow pit face using HISSGraS (as described in (3)) is expected to minimize errors related to these technical issues.

Figure 1. Direct measurement of a snow pit face with the HISSGraS instrument. A black cloth covers the snow surface to protect against stray light from solar radiation entering the HISSGraS instrument. The inset photo at top right shows the front of the HISSGraS and the glass window (snow window) installed in the open port of the IS. The diameter of the window aperture is 25 mm. The inset photo at bottom right shows HISSGraS with a sheltering disk attached to prevent stray light from penetrating through the snow surface during the snow surface measurements. The diameter of the sheltering disk is 150 mm.

When measuring directly at the snow surface or a snow pit wall, the snow window of HISSGraS is gently pressed against the target snow surface or snow pit face, creating a contact of approximately 5 to 10 mm in depth, ensuring that the snow microstructure is not significantly disturbed. To prevent stray light from entering during snow pit measurements, a black cloth was placed over the snow surface (Fig. 1). For all HISSGraS measurements directly at the snow surface, a sheltering disk (bottom right of Fig. 1) was utilized to prevent stray light interference. After conducting tests to assess the impact of stray light under direct solar illumination without the sheltering disk, we observed no significant differences in the HISSGraS output. As a result, we chose not to use a sheltering disk when measuring directly at the snow pit wall (main picture in Fig. 1). It is worth noting that achieving a perfect seal of the snow window against the snow pit face can be challenging in case the snow layers containing ice formations or large, hard ice grains.

The basic measurement principle of the HISSGraS instrument is the same as that of the IC instrument (Gallet and others, Reference Gallet, Dominé, Zender and Picard2009). HISSGraS uses an IS to measure the reflectance of the target snow R _s at the wavelength of the laser diode used as the light source (λ _L = 1310 nm). The interior wall of the IS is painted with BaSO₄, and the laser diode illuminates the target snow through a snow window (Fig. 1). To obtain the reflectance of the target snow, the light intensity on the IS wall is measured with an InGaAs photodiode detector. Then, the measured light intensity is converted to R _s using calibration data obtained for six different Spectralon diffuse reflectance standards (DRSs). Because the beam intensity output from a laser diode generally has temperature dependence, HISSGraS records the temperature of the laser diode (T _L) together with the output signal from the detector to correct the T _L dependence of the laser power. Figure 2a shows the T _L dependence of the HISSGraS output signals for the six Spectralon DRSs (#1–#6) obtained during field observations (see Section 3) and used for calibration data. The temperature dependence of the HISSGraS output, as illustrated in Figure 2a, is approximately 1.2% K⁻¹ within the temperature range of −2 to 12°C. In contrast, the InGaAs photodiode used in this study exhibits a temperature dependence of approximately ± 0.1% K⁻¹ at 25°C. Therefore, it is reasonable to attribute the temperature dependence observed in Figure 2a to the laser's temperature sensitivity. Ideally, this calibration procedure should be performed before and after each set of SSA measurements (we did so in this study), because air temperature variations, for example, during the observation might influence SSA profile measurements conducted in a snow pit, but the relationship between T _L and the HISSGraS output signal can also be determined by using calibration data obtained in a cold laboratory. The dashed curves in Figure 2a are fitted using a cubic polynomial function at six reflectance values of Spectralon DRSs, from which the relationships between the output signal and six reflectance values shown by closed circles in Figure 2b are obtained. Although we show the HISSGraS output signal–T _L-corrected reflectance R _S relationships for T _L at 5°C intervals (Fig. 2b), the relationship can be determined for any T _L from the temperature-dependence curves shown in Figure 2a. From those closed circles, the solid curves shown in Figure 2b are furthermore fitted with a cubic polynomial function, which are the relational equations to obtain the T _L-corrected reflectance R _s from the HISSGraS output signal. HISSGraS only emits a laser beam during SSA measurements due to battery consumption and safety reasons, whereas IC always emits a laser beam continuously. It is recommended for IC to warm up with laser emission sufficiently before taking SSA measurements. We allowed the HISSGraS device itself to warm up for 30 min before conducting measurements in this study, while the laser only emits during the actual measurement process. As demonstrated in Figure 2a, which was generated from all calibration data collected over the entire observation period, a consistent relationship between laser power and temperature is evident. Therefore, errors stemming from the lack of laser warm-up are expected to be minimal. HISSGraS is conceptually similar to InfraSnow; however, it employs different wavelengths. Given that the light penetration depth at 1310 nm for HISSGraS is shallower than that at 950 nm for InfraSnow, HISSGraS provides SSA information for a shallower snow layer (approximately several millimeters) compared to InfraSnow (approximately several centimeters). Since InfraSnow does not have a glass window in front of the integrating sphere, it is expected to nondestructively measure the SSA of the snow surface or snow pit face, including wet snow.

Figure 2. (a) Laser temperature (T _L) dependence of the HISSGraS output signal calibrated by using six Spectralon DRSs (#1–6) obtained during the in situ field observation period from 27 February to 4 March 2022 at Nakasatsunai, Hokkaido, Japan. The reflectances of DRSs #1–6 at laser wavelength λ _L = 1310 nm are 5.1, 10.7, 19.3, 48.6, 71.0 and 98.3%, respectively. Curves (dashed lines) were fitted to the calibration data (HISSGraS output signal–T _L relationship; open circles) using a cubic polynomial function. (b) Relationships between the HISSGraS output signal and reflectance for different T _L values (5°C intervals). The solid curves were fitted to the data calculated from the fitting curves shown in (a) for DRS reflectances #1–6 (closed circles) using a cubic polynomial function.

2.2. SSA retrieval algorithm

2.2.1. Structure of the IS and illumination properties of the target snow

Figure 3 illustrates the structure of the IS and the illumination properties of the snow by the light emitted from the laser diode in the IS. The direct laser beam as a light source initially illuminates the target snow surface through the glass snow window in front of the HISSGraS instrument and is reflected diffusely into the IS. After the first reflection, multiple diffuse light reflections occur in the IS; thus, the target snow is illuminated hemispherically with diffuse light (Fig. 3a). These illumination processes occur with a single laser emission. The photodiode detector observes the light intensity on the interior wall of the IS. The first reflectance of the target snow is the nadir directional reflectance ($\dot{r}$) and the second, diffuse reflectance is the hemispherical reflectance (r). The theoretically expected reflectance of the target snow R _s is expressed as:

(1)$$R_{\rm s} = f_{\rm f}^\downarrow r + ( {1-f_{\rm f}^\downarrow } ) \dot{r}, \;$$

where $f_{\rm f}^\downarrow$ is the diffuse fraction of the total illumination of the target snow. The value of $f_{\rm f}^\downarrow$ can be calculated using $\dot{r}$, r, the IS structural parameters given below, the interior wall reflectance of the IS (ω = 0.925) at λ _L, and the laser emission fractions initially striking the target snow ($\dot{f}\;$ = 0.885) and the IS wall ($1-\dot{f}$) (Hidović-Rowe and others, Reference Hidović-Rowe, Rowe and Lualdi2006; Gallet and others, Reference Gallet, Dominé, Zender and Picard2009) as:

(2)$$f_{\rm f}^\downarrow = \omega s\displaystyle{{\dot{\,f}\dot{r}\alpha {\rm} + ( 1 \hbox{-} \dot{\,f}) \{ {1-( {s + d} ) } \} } \over {1-( {s + d} ) -\omega \alpha [ {1-\{ {d + ( {1-r} ) s} \} } ] }}.$$

Figure 3. Schematic illustrations of laser light paths in the IS and its components: (a) Pathways of light emitted from the laser diode and the illumination conditions of the target snow. The direct beam emitted from the laser diode is indicated by black arrows, and the reflected light by the target snow and the interior wall of the IS is shown with pink arrows. The laser direct beam illuminates the interior wall of the IS, extending beyond the snow window. The detector measures the intensity of the reflected light on the opposite interior wall of the IS. (b) Structural parameters of the IS components. The surface area fractions of the components are d, photodiode detector; s, snow window; h, laser diode; and α, reflective IS wall. ω represents the reflectivity of the IS wall and $\dot{f}$ is the fraction of light initially striking the target snow (pink-colored area) relative to the total laser emission (orange-colored area).

The structural parameters of the IS are shown in Figure 3b, which are the surface area fractions of the photodiode detector (d = 0.010102), target snow window (s = 0.066987), laser diode (h = 0.010102), and reflective IS wall (α = 0.91281), where d + s + h + α = 1. The value of ω was measured directly using HISSGraS with a BaSO₄ reflectance standard, the same material as the IS wall. The measurement of f was conducted under condition where no external light entered the IS from the snow window.

Eqns (1) and (2) relate the reflectance of the target being measured (R _s) to the signal detected by the photodiode. To obtain SSA from R _s, the two types of reflectances, $\dot{r}$ and r, at λ _L as a function of SSA are calculated with a radiative transfer model (Aoki and others, Reference Aoki, Aoki, Fukabori and Uchiyama1999, Reference Aoki2000), where $\dot{r}$ is calculated for direct beam illumination to the nadir direction from the laser diode, and r is calculated for the diffuse illumination from the IS wall. The relationships between SSA and $\dot{r}$ and between SSA and r are obtained, which will be shown in the following section. Finally, R _s is derived as a function of SSA by using Eqns (1) and (2).

2.2.2. Snow grain shape model

The radiative transfer calculations to establish the R _s–SSA relationships involve three steps. The first step is to calculate the single-scattering parameters of the snow grains, utilizing both spherical and nonspherical snow grain shape models. We calculated the spherical model using Mie theory with a log-normal size distribution (Aoki and others, Reference Aoki, Aoki, Fukabori and Uchiyama1999, Reference Aoki2000) and the nonspherical model using the Voronoi shape model (Ishimoto and others, Reference Ishimoto2012, Reference Ishimoto2018). Using X-ray micro-computed tomography data for various types of snow grains, Ishimoto and others (Reference Ishimoto2018) showed that the single-scattering parameters of fine snow particles can be accurately parameterized by a Voronoi column model and those of coarse snow particles by a Voronoi aggregate model. The transition from the Voronoi column shape to the Voronoi aggregate shape occurs at an SSA-equivalent sphere grain radius (r _VA = 3/(ρ _iceSSA)) between r _VA = 50 μm and r _VA = 200 μm, where ρ _ice is ice density and the unit of SSA is area per unit weight. The validity of this Voronoi column/aggregate grain shape model for retrieving snow grain size has been confirmed by observations using a ground-based spectral radiometer in Hokkaido, Japan (Tanikawa and others, Reference Tanikawa2020). In this study, as the nonspherical grain shape model, we used the same Voronoi column/aggregate model used by Ishimoto and Others (Reference Ishimoto2018) and Tanikawa and Others (Reference Tanikawa2020).

In the second step, we calculated the relationships between snow reflectance $\dot{r}$ and r at λ _L and the SSA of snow using a multiple scattering radiative transfer model (Aoki and others, Reference Aoki, Aoki, Fukabori and Uchiyama1999, Reference Aoki2000). This calculation involved inputting the single-scattering parameters of the snow grains determined in the first step. The relationships between the reflectance and SSA for both spherical and nonspherical (Voronoi) snow grain shape models are shown by solid curves in Figures 4a and b, respectively. These curves were fitted with quintic polynomials to match the discrete values obtained through theoretical calculations using a radiative transfer model. When viewing horizontally at the same SSA value, the curve for r is higher than that for $\dot{r}$. As the third step, for each grain shape model, we calculated the R _s–SSA relationships from $\dot{r}$ and r by Eqn (1) (Figs 4a and b, dashed curves). Then, we compared the R _s–SSA relationships obtained with the spherical and Voronoi models with that for IC (Eqn (7) in Gallet and others, Reference Gallet, Dominé, Zender and Picard2009). The R _s–SSA relationship curve for the HISSGraS spherical model mostly overlaps with the IC curve, but we consider this agreement to be merely fortuitous. For R _s < 50% (SSA < 52 m² kg⁻¹), the curve obtained with the Voronoi model is lower than those obtained with the spherical model and the IC curve, but the relationship is reversed for R _s > 50%. This reversal occurs because of the change of the Voronoi model from the aggregate to the column shape as SSA increases. We used these relational equations to convert the T _L-corrected HISSGraS-measured reflectance R _s at λ _L to SSA.

Figure 4. Relationships between snow reflectance at λ _L = 1310 nm and SSA of snow grains calculated with a radiative transfer model using a (a) spherical or (b) Voronoi (nonspherical) grain shape models. Solid curves in (a) and (b) show the relationships of SSA with nadir directional reflectance ($\dot{r}$) and hemispherical reflectance (r), and the dashed curves show the HISSGraS reflectance (R _s)–SSA relationship calculated with Eqns (1) and (2). (c) The HISSGraS R _s–SSA relationships calculated with the spherical and Voronoi models (HISSGraS (Sph.) and HISSGraS (Vor.), respectively; i.e. the dashed curves from (a) and (b)), and the IceCube R _s–SSA relationship (Gallet and others, Reference Gallet, Dominé, Zender and Picard2009). In each panel, quintic polynomial curves were fitted to the values theoretically calculated with the radiative transfer model (symbols) (Aoki and others, Reference Aoki, Aoki, Fukabori and Uchiyama1999, Reference Aoki2000).

3.1. Observation site

SSA measurements were conducted together with snow pit observations from 27 February to 4 March 2022 in a flat snowfield at Nakasatsunai (42°38.4′N, 143°6.6′E; 251 m a.s.l.) in Hokkaido, Japan (Fig. 5). The fieldwork was conducted during 08:00–12:30 local time (LT) (Fig. 6) to synchronize with satellite overpasses, including the Second Generation Global Imager (SGLI) on the Global Change Observation Mission-Climate (GCOM-C) satellite and the Moderate Resolution Imaging Spectroradiometer (MODIS) on Terra satellite. The snow height during the observation period was 54–65 cm, and the daily maximum air temperature was above 0°C from 27 February to 2 March and just below 0°C on 4 March (Table 1). Because it snowed strongly on 3 March, field observations were not conducted at the Nakasatsunai site on that date, although SSA measurements for the snow surface, consisting of precipitation particles, were performed during 15:00–16:00 LT near the facility at Kamisatsunai, 1.5 km away from the Nakasatsunai site (Fig. 6).

Figure 5. Location of the Nakasastunai observation site (42°38.4′N, 143°6.6′E; 251 m a.s.l.), Hokkaido, Japan. The ground-surface at the 450 m × 520 m observation site was flat farmland.

Figure 6. Relative timing of snow pit observations and SSA measurements at Nakasatsunai from 27 February to 4 March 2022. The lengths of the color bars indicate the actual time period in which the corresponding measurements were performed. Snow temperature (T _s) profiles were measured during time periods indicated with color bars A, B, C and D. The occurrences of snow grain shape and snow density are marked with SS and ρ_s, respectively. SSA measurements are indicated by the abbreviation of the corresponding measurement instrument or method: IC, HIS_s and BET represent SSA measurements carried out on snow samples using IceCube, HISSGraS and BET method, respectively, while HIS_d indicates SSA measurements directly performed on the snow pit wall or at the snow surface using HISSGraS. Multipoint direct surface SSA observations conducted with HISSGraS are marked as HIS_dmp. The top right inset shows the abbreviations of the snow parameters and SSA measurement methods and their corresponding colors.

Table 1. Snow and meteorological conditions during the observation period at Nakasatsunai

Snow height and weather conditions were measured in situ at the first snow pit observation every day, which is marked with ‘A’ in Figure 6, and air temperatures are instantaneous values observed at the local time given in the table with the Automated Meteorological Data Acquisition System station of the Japan Meteorological Agency at Kamisatsunai, located 1.1 km from Nakasatsunai.

3.2. SSA and snow pit observations

At Nakasatsunai, we performed in situ SSA measurements with the HISSGraS and IC instruments, snow sampling for later laboratory measurement with the BET method, and snow pit observations and other observations for the satellite validation experiment, including spectral albedo, bidirectional reflectance, and infrared radiation. The relative timing of the snow pit observations, SSA measurements, and snow sampling for BET method measurements are shown in Figure 6. SSA profile measurements were first performed with both the IC and HISSGraS instruments on snow samples collected from a snow pit face at 3-cm intervals with the same 25-mm-deep sampling cup used for IC-based measurements (‘IC&HIS_s’ in Fig. 6). Subsequently, SSA profile was measured applying HISSGraS directly on the snow pit wall, though on a new pit face (‘HIS_d’ in Fig. 6). Snow was sampled for the BET measurements (‘BET’ in Fig. 6) from another, nearby snow pit; thus, the snow samples used for the BET measurement were different from those used for IC and HISSGraS measurements. For the BET measurements, snow samples of 12–25 g were collected in stainless steel pressure cells (internal volume, 42 mL) that were immediately immersed in liquid nitrogen at the field site and transported to a temporary laboratory established at Kamisatsunai. The SSAs of the snow samples were measured on the same day as the samples were collected with a portable BET instrument based on methane adsorption (described in detail in Hachikubo and others, Reference Hachikubo2014). Between SSA profile measurements, we measured surface snow SSAs in the same area applying both IC and HISSGraS (HIS_s) on snow samples (marked, respectively, as IC and HIS_s in Fig. 6) and HISSGraS directly on the surface (HIS_d in Fig. 6). SSA profiles measured with IC and HIS_s on snow samples, with HIS_d, and with the BET method on snow samples are plotted in Figure 7. Surface snow SSAs, measured with the same methods used for the SSA profiles, were not synchronous with BET method measurements. After the other SSA measurements on 2 and 4 March, multipoint surface SSA observations were conducted with HIS_dmp at 110 and 108 points, respectively, along a route approximately 4.5 km long around the snow pit area in the same farm field. No snow pit observations were performed on 3 March because of strong snowfall, and SSA was measured only on surface snow composed of precipitation particles. On 28 February and 2 March, SSA profile measurements with IC and HIS_s were conducted separately at different times for the upper and lower layers in the snow pit. SSA profile observations with IC or HIS_s took approximately 30 min per 20 snow samples, whereas SSA profile observations with HIS_d on the same snow pit wall took approximately 3 min; thus, HIS_d observations required only ~1/10 of the time required for IC and HIS_s.

Figure 7. Vertical profiles of SSA measured on the snow pit face with the HISSGraS, IceCube and BET methods during the observation period. Four different HISSGraS SSA profiles are shown, calculated using the spherical snow particle shape model (Sph.) and the Voronoi snow particle shape model (Vor.) from measurements of snow samples (HIS_s) collected from a snow pit and direct measurements (HIS_d) on the snow pit face. In (d, e), the mean (blue dot, purple triangle), minimum and maximum (bars) surface SSA observation results derived from multipoint HISSGraS direct measurements (HIS_dmp) on 2 and 4 March are shown just above the values at surface layer of SSA profiles.

Snow pit observations were performed approximately 15 m away from the snow pits used for SSA measurements on each day of the observation period except 3 March, when there was strong snowfall (Fig. 6). The snow pit observations included the vertical profiles of snow temperature (T _s), snow shape (SS), snow density (ρ _s), optically equivalent snow grain size measured with a magnifying glass (as defined by Aoki and others, Reference Aoki2000, Reference Aoki, Hachikubo and Hori2003), liquid water content, and snow microphotograph. The three components after optically equivalent snow grain size are excluded from Figure 6 because they are not addressed in the paper.