Snow Grain Research Articles

A new snow bidirectional reflectance distribution function model in spectral regions from UV to SWIR: Model development and application to ground-based, aircraft and satellite observations

A generalized and flexible snow Bidirectional Reflectance Distribution Function (BRDF) model is proposed to describe the snow anisotropic properties in the spectral ranges from UltraViolet (UV) to Short-Wave InfraRed (SWIR). The new development belongs to the Fast and Accurate Semi-analytical Model of Atmosphere-surface Reflectance (FASMAR) family. FASMAR is developed, applied to and validated by ground-, aircraft- and satellite observations. FASMAR is a kernel-driven BRDF model. It contains four major kernels: isotropy kernel, asymptotic radiative transfer kernel, single-scattering kernel, and auxiliary kernels. These kernels enable FASMAR to characterize the angular-dependent scattering features and wavelength-dependent absorbing patterns of the snow BRDF properties. The comparison between FASMAR and RossThick-LiSparseReciprocal-Snow (RTLSRS) model were performed using radiative transfer simulations, ground-, aircraft- and satellite observations at selected wavelengths 380, 480, 670, 870, 1220, and 2200 nm. For Solar Zenith Angle (SZA) smaller than 70°, FASMAR shows somehow better accuracy compared to the RTLSRS model. FASMAR’s accuracy keeps quite stable for large SZAs (SZA larger than 70°). The relative difference between FASMAR calculations and radiative transfer simulations is within 5% for wavelengths between 380 and 2200 nm. A similar accuracy of FASMAR is observed compared to aircraft BRDF measurements, with a relative difference of less than 5%. FASMAR also shows good agreement with ground-based and satellite observations, with correlation coefficients larger than 0.9 and relative errors smaller than 2% for UV–vis and 4% for NIR-SWIR spectral ranges. The comparisons additionally reveal that the accuracy of FASMAR is not strongly affected by the a priori knowledge of the snow grain size. FASMAR can provide snow BRDF estimation with good accuracy in spectral regions from UV to SWIR under all observation/illumination geometries. FASMAR is used support the operational retrieval of the snow properties from satellite observations.

Long‐Term Rain Attenuation Measurement for Short‐Range mmWave Fixed Link Using DSD and ITU‐R Prediction Models

AbstractSeveral millimeter Wave (mmWave) bands, which suffer from rain attenuation, were identified in the World Radiocommunication Conference 2019 (WRC‐19) for fifth generation (5G) radio networks. In this paper, long‐term attenuation is measured over typical building to building radio links in the built environment, which constitute two 36 m links along a direct link and an indirect side link at 25.84 and 77.54 GHz and a 200 m link at 77.125 GHz. The attenuation was also estimated using precipitation data from a high end accurate disdrometer weather station using the drop size distribution and the International Telecommunication Union (ITU) models. The results indicate that attenuation using Mie theory is in agreement with the ITU model for most of the rainfall events; with higher attenuation being measured than predicted when snow grains and raindrops mix. Raindrops with diameter between 0.1 and 4 mm indicate that the dominant raindrops have considerable influence on the measured attenuation, especially at light and moderate rainfall events. The maximum distance factor restriction of 2.5 in ITU‐R P.530‐17 is shown not to be suitable for short‐range fixed links as it excessively underestimates attenuation.

Sensitivity of Antarctic surface climate to a new spectral snow albedo and radiative transfer scheme in RACMO2.3p3

Abstract. This study investigates the sensitivity of modeled surface melt and subsurface heating on the Antarctic ice sheet to a new spectral snow albedo and radiative transfer scheme in the Regional Atmospheric Climate Model (RACMO), version 2.3p3 (Rp3). We tune Rp3 to observations by performing several sensitivity experiments and assess the impact on temperature and melt by incrementally changing one parameter at a time. When fully tuned, Rp3 compares well with in situ and remote sensing observations of surface mass and energy balance, melt, near-surface and (sub)surface temperature, albedo and snow grain specific surface area. Near-surface snow temperature is especially sensitive to the prescribed fresh snow specific surface area and fresh dry snow metamorphism. These processes, together with the refreezing water grain size and subsurface heating, are important for melt around the margins of the Antarctic ice sheet. Moreover, small changes in the albedo and the aforementioned processes can lead to an order of magnitude overestimation of melt, locally leading to runoff and a reduced surface mass balance.

The Determination of the Snow Optical Grain Diameter and Snowmelt Area on the Greenland Ice Sheet Using Spaceborne Optical Observations

The optical diameter of the surface snow grains impacts the amount of energy absorbed by the surface and therefore the onset and magnitude of surface melt. Snow grains respond to surface heating through grain metamorphism and growth. During melt, liquid water between the grains markedly increases the optical grain size, as wet snow grain clusters are optically equivalent to large grains. We present daily surface snow grain optical diameters (dopt) retrieved from the Greenland ice sheet at 1 km resolution for 2017–2019 using observations from Ocean and Land Colour Instrument (OLCI) onboard Sentinel-3A. The retrieved dopt are evaluated against 3 years of in situ measurements in Northeast Greenland. We show that higher dopt are indicative of surface melt as calculated from meteorological measurements at four PROMICE automatic weather stations. We deduce a threshold value of 0.64 mm in dopt allowing categorization of the days either as melting or nonmelting. We apply this simple melt detection technique in Northeast Greenland and compare the derived melting areas with the conventional passive microwave MEaSUREs melt flag for June 2019. The two flags show generally consistent evolution of the melt extent although we highlight areas where large grain diameters are strong indicators of melt but are missed by the MEaSUREs melt flag. While spatial resolution of the optical grain diameter-based melt flag is higher than passive microwave, it is hampered by clouds. Our retrieval remains suitable to study melt at a local to regional scales and could be in the future combined with passive microwave melt flags for increased coverage.

A New Index for Snow/Ice/Ice‐Snow Discrimination Based on BRDF Characteristic Observation Data

AbstractThe field observation data of ice‐snow (the ice covered by snow) is scarce, causing a poor understanding of its characteristics and some uncertainty in ice process simulation. Using a multi‐angle observation instrument, we conducted a field investigation and measured the snow/ice/ice‐snow Bidirectional Reflectance Distribution Function. Both snow and ice have the typical feature of forwarding scattering, and the scattering intensity is governed by their properties (i.g., snow grain size, liquid water content, and transparency). The characteristics of ice‐snow are similar to snow when a small amount of fresh snow is deposited on the ice surface, but will change significantly when the surface snow is metamorphic (melt or refreezing). This change can affect the monitoring accuracy of snow and ice using remote sensing data. In this study, a Normalized Difference Ice‐Snow Index (NDISI) was developed using two bands (i.e., 1,080–1,120 nm and 1,760–1,800 nm). We applied spectra from different regions to verify the ability of NDISI and its application for distinguishing ice‐snow. This work should be helpful for the fine classification between snow, ice, and ice‐snow. It can support a more accurate simulation of ice phenology.

Raman Spectroscopy-Based Assessment of the Liquid Water Content in Snow.

In snow, water coexists in solid, liquid and vapor states. The relative abundance of the three phases drives snow grain metamorphism and affects the physical properties of the snowpack. Knowledge of the content of the liquid phase in snow is critical to estimate the snowmelt runoff and to forecast the release of wet avalanches. Liquid water does not spread homogeneously through a snowpack because different snow layers have different permeabilities; therefore, it is important to track sudden changes in the amount of liquid water within a specific layer. We reproduced water percolation in the laboratory, and used Raman spectroscopy to detect the presence of the liquid phase in controlled snow samples. We performed experiments on both fine- and coarse-grained snow. The obtained snow spectra are well fitted by a linear combination of the spectra typical of liquid water and ice. We progressively charged snow with liquid water from dry snow up to soaked snow. As a result, we exploited continuous, qualitative monitoring of the evolution of the liquid water content as reflected by the fitting coefficient c.

Snow albedo reductions induced by the internal/external mixing of black carbon and mineral dust, and different snow grain shapes across northern China

Previous studies have indicated that black carbon (BC) potentially induces snow albedo reductions across northern China. However, the effects of other light-absorbing particles (LAPs, e.g., mineral dust, MD), snow grain shape, or BC–snow mixing state on snow albedo have been largely ignored. Here we evaluate the BC- and MD-induced snow albedo reductions and radiative forcings (RFs) using an updated Snow, Ice, and Aerosol Radiation radiative transfer model, considering all of the potential factors that can be derived from the field observations across northern China. The results highlight that the LAP-induced albedo reductions for nonspherical snow grains are 2%–30% less than those for spherical grains. Furthermore, BC–snow internal mixing can significantly enhance albedo reduction by a factor of 1.42–1.48 relative to external mixing, with snow grain radius ranging from 100 to 1000 μm. The mean regional BC + MD-induced snow albedo reductions are amplified by the increase of snow grain radius, ranging from 0.012 to 0.123 for fresh snow to 0.016–0.227 for old snow. Finally, we discuss the relative contributions of BC and MD to the albedo reductions and RFs, highlighting the dominant role of BC in reducing snow albedo across northern China.

Time Series X- and Ku-Band Ground-Based Synthetic Aperture Radar Observation of Snow-Covered Soil and Its Electromagnetic Modeling

The snow water equivalent (SWE, a measurement of the amount of water contained in snow packs) is an important variable in earth systems. Microwave remote sensing provides a possible solution for estimating the SWE globally. To support radar SWE retrieval, the snow backscattering theory needs to be studied; the forward simulation model needs to be validated against natural snow observations. In this study, a one-winter experiment to observe the time series backscattering coefficient of snow-covered bare soil is reported. This is the first long time series snow-covered soil backscattering experiment that was measured by an imaging radar. The backscattering coefficient was observed at three frequencies covering the X-band and dual-Ku bands, which are of great interest to the snow remote sensing community and are used for SWE estimation in mountains. The calibration of the synthetic aperture radar (SAR) system was conducted manually and carefully to ensure high-quality radar observation data. The observations from our experiment show that in general, the time series backscattering signature of snow-covered terrain is mainly driven by soil freezing, snow grain size growth, and snow accumulation processes. The time series observations for dry snow are modeled by backscattering models with model inputs directly calculated from field measurements. Our simulation results indicate that the time series radar backscattering at three frequencies and four polarizations can be simulated with high accuracy, including the cross-polarization channels. This study provides some key understanding of the time series signature of radar backscattering from snow and provides some key implications for SWE retrieval from radar observations.

Global Snow Depth Retrieval From Passive Microwave Brightness Temperature With Machine Learning Approach

Current global snow retrieval algorithms based on spaceborne microwave measurements inherit noticeable biases and uncertainties regarding spatial distribution and temporal variations. In this article, we present an improved spatiotemporally dynamic global snow depth retrieval algorithm to account for the heterogeneity of snowpacks in different seasons worldwide. The proposed model adopts nonlinear machine learning to retrieve snow depths from passive microwave measurements and other auxiliary information. We indirectly characterized the variation in snow grain size using the daily profiles of the temperature gradient within the snowpack. In addition, a zoning and multitemporal modeling strategy was employed to reduce the bias and uncertainty caused by snow heterogeneity across different ecoregions and seasons. The proposed model was implemented to retrieve the global daily snow depth from 2001 to 2010. The results were validated by <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> observations and compared with the NASA Advanced Microwave Scanning Radiometer for EOS (AMSR-E) snow water equivalent product (AE_DySno). Satisfactory accuracy was achieved for different ecoregions with regard to daily, monthly, and yearly validations (the root-mean-square error (RMSE) varied from ~7.5 to ~12 cm; the Pearson correlation coefficient <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R$ </tex-math></inline-formula> ranged from 0.75 to 0.85). The results of ten trials indicated the promising stability of the proposed model in different ecoregions with small variations in RMSE and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R$ </tex-math></inline-formula> values. Compared with the AE_DySno products, the estimation results did not exhibit the overestimation problem and provided snow depth patterns with greater spatial heterogeneity, showing RMSEs ~5 cm lower and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R$ </tex-math></inline-formula> values ~0.3 higher than those of the AE_DySno products.

Angle of repose of snow: An experimental study on cohesive properties

The angle of repose is a measure reflecting the internal friction and cohesion properties of a granular material. In this paper, we present an experimental setup and measurements for the angle of repose of snow for seven different snow samples over a large range of temperatures. The results show that the angle of repose is dependent on the fall height, the temperature, and the grain size of the snow. These variables are quantified, and their interdependencies are separately studied. With increased snow temperature, the angle of repose increases, and this can be explained by the presence of a liquid layer on ice that can be thermodynamically stable at temperatures below the melting point of water. With decreasing grain size the angle of repose also increases which is expected since the cohesive energy decreases more slowly than the grain mass. For increasing fall height, the snow grains generally accelerate to larger collisional velocities, yielding a smaller angle of repose. In general, the dimensionless cohesion number was found to largely reflect the dependencies of the variables and is therefore useful for understanding what affects the angle of repose. The results demonstrate that the drag force and collision dynamics of ice grains are important for understanding how snow accumulates on a surface, for example if one desires predicting snow accretion by simulating a dispersed cloud of snow.

Measurements and Modeling of Optical-Equivalent Snow Grain Sizes under Arctic Low-Sun Conditions

The size and shape of snow grains directly impacts the reflection by a snowpack. In this article, different approaches to retrieve the optical-equivalent snow grain size (ropt) or, alternatively, the specific surface area (SSA) using satellite, airborne, and ground-based observations are compared and used to evaluate ICON-ART (ICOsahedral Nonhydrostatic—Aerosols and Reactive Trace gases) simulations. The retrieval methods are based on optical measurements and rely on the ropt-dependent absorption of solar radiation in snow. The measurement data were taken during a three-week campaign that was conducted in the North of Greenland in March/April 2018, such that the retrieval methods and radiation measurements are affected by enhanced uncertainties under these low-Sun conditions. An adjusted airborne retrieval method is applied which uses the albedo at 1700 nm wavelength and combines an atmospheric and snow radiative transfer model to account for the direct-to-global fraction of the solar radiation incident on the snow. From this approach, we achieved a significantly improved uncertainty (&lt;25%) and a reduced effect of atmospheric masking compared to the previous method. Ground-based in situ measurements indicated an increase of ropt of 15 µm within a five-day period after a snowfall event which is small compared to previous observations under similar temperature regimes. ICON-ART captured the observed change of ropt during snowfall events, but systematically overestimated the subsequent snow grain growth by about 100%. Adjusting the growth rate factor to 0.012 µm2 s−1 minimized the difference between model and observations. Satellite-based and airborne retrieval methods showed higher ropt over sea ice (&lt;300 µm) than over land surfaces (&lt;100 µm) which was reduced by data filtering of surface roughness features. Moderate-Resolution Imaging Spectroradiometer (MODIS) retrievals revealed a large spread within a series of subsequent individual overpasses, indicating their limitations in observing the snow grain size evolution in early spring conditions with low Sun.

In Situ Determination of Dry and Wet Snow Permittivity: Improving Equations for Low Frequency Radar Applications

Extensive efforts have been made to observe the accumulation and melting of seasonal snow. However, making accurate observations of snow water equivalent (SWE) at global scales is challenging. Active radar systems show promise, provided the dielectric properties of the snowpack are accurately constrained. The dielectric constant (k) determines the velocity of a radar wave through snow, which is a critical component of time-of-flight radar techniques such as ground penetrating radar and interferometric synthetic aperture radar (InSAR). However, equations used to estimate k have been validated only for specific conditions with limited in situ validation for seasonal snow applications. The goal of this work was to further understand the dielectric permittivity of seasonal snow under both dry and wet conditions. We utilized extensive direct field observations of k, along with corresponding snow density and liquid water content (LWC) measurements. Data were collected in the Jemez Mountains, NM; Sandia Mountains, NM; Grand Mesa, CO; and Cameron Pass, CO from February 2020 to May 2021. We present empirical relationships based on 146 snow pits for dry snow conditions and 92 independent LWC observations in naturally melting snowpacks. Regression results had r2 values of 0.57 and 0.37 for dry and wet snow conditions, respectively. Our results in dry snow showed large differences between our in situ observations and commonly applied equations. We attribute these differences to assumptions in the shape of the snow grains that may not hold true for seasonal snow applications. Different assumptions, and thus different equations, may be necessary for varying snowpack conditions in different climates, suggesting that further testing is necessary. When considering wet snow, large differences were found between commonly applied equations and our in situ measurements. Many previous equations assume a background (dry snow) k that we found to be inaccurate, as previously stated, and is the primary driver of resulting uncertainty. Our results suggest large errors in SWE (10–15%) or LWC (0.05–0.07 volumetric LWC) estimates based on current equations. The work presented here could prove useful for making accurate observations of changes in SWE using future InSAR opportunities such as NISAR and ROSE-L.

Investigating the Kokhanovsky snow reflectance model in closerange spectral imaging

The internal structure of the snow and its reflectance function play a major contribution in its appearance. We investigate the snow reflectance model introduced by Kokhanovsky and Zege in a close-range imaging scale. By monitoring the evolution of melting snow through time using hyperspectral cameras in a laboratory, we estimate snow grain sizes from 0.24 to 8.49 mm depending on the grain shape assumption chosen. Using our experimental results, we observe differences in the reconstructed reflectance spectra with the model regarding the spectra's shape or magnitude. Those variations may be due to our data or to the grain shape assumption of the model. We introduce an effective parameter describing both the snow grain size and the snow grain shape, to give us the opportunity to select the adapted assumption. The computational technique is ready, but more ground truths are required to validate the model.

Retrieval of Snow Albedo and Total Ozone Column from Single-View MSI/S-2 Spectral Reflectance Measurements over Antarctica

We proposed a simple algorithm to retrieve the total ozone column and snow properties (spectral albedo and effective light absorption path) using the high spatial resolution single–view MSI/S-2 measurements over Antarctica. In addition, the algorithm allows the retrieval of the snow grain size on a scale of 10–20 m. This algorithm should be useful for the understanding of intra-pixel total ozone and snow albedo variability in complement to satellite observations performed on a much coarser spatial resolution scale (0.3–1 km and even larger spatial scales).

The Broadband Albedo of Snow

The asymptotic radiative transfer theory is used to derive the analytical approximation for the broadband albedo of pure and polluted snow surfaces. The technique for the determination of the effective snow grain size and also the snow specific surface area from the shortwave broadband albedo measurements is proposed.

Spectral Albedo of Dusty Martian H2O Snow and Ice

AbstractRecent evidence of exposed H2O ice on Mars suggests that this ice was deposited as dusty (&lt;∼1% dust) snow. This dusty snow is thought to have been deposited and subsequently buried over the last few million years. On Earth, freshly fallen snow metamorphoses with time into firn and, if deep enough, into glacier ice. While spectral measurements of martian ice have been made, no model of the spectral albedo of dusty martian firn or glacier ice exists at present. Accounting for dust and snow metamorphism is important because both factors reduce the albedo of snow and ice by large amounts. However, the dust content and physical properties of martian H2O ice are poorly constrained. Here, we present a model of the spectral albedo of H2O snow and ice on Mars, which is based on validated terrestrial models. We find that small amounts (&lt;1%) of martian dust can lower the albedo of H2O ice at visible wavelengths from ∼1.0 to ∼0.1. Additionally, our model indicates that dusty (&gt;0.01% dust) firn and glacier ice have a lower albedo than pure dust, making them difficult to distinguish in visible or near‐infrared images commonly used to detect H2O ice on Mars. Observations of excess ice at the Phoenix landing site are matched by 350‐μm snow grains with 0.015% dust, indicating that the snow has not yet metamorphosed into glacier ice. Our model results can be used to characterize orbital observations of martian H2O ice and refine climate‐model predictions of ice stability.

Snow features on sea ice in the western Arctic Ocean during summer 2016

ABSTRACT Arctic sea ice and its snow cover are important components of the cryosphere and the climate system. A series of in situ snow measurements were conducted during the seventh Chinese Arctic expedition in summer 2016 in the western Arctic Ocean. In this study, we made an analysis of snow features on Arctic sea ice based on in situ observations and the satellite-derived parameter of snow grain size from MODIS spectral reflectance data. Results indicate that snow depth on Arctic sea ice varied between 19 and 241 mm, with a mean value of 100 mm. The mean density of the snow was 340.4 kg/m3 during the expedition, which was higher than that reported in previous literature. The measurements revealed that a depth hoar layer was widely developed in the snow, accounting for 30%∼50% of the total snow depth. The equivalent snow grain size was small on the surface and large at the bottom in snow pits. The average relative error between MODIS-derived snow grain size and in situ measured surface snow grain size is 14.6%, indicating that remote sensing is a promising method to obtain large-scale information of snow grain size on Arctic sea ice.

Improving snow depth estimation by coupling HUT-optimized effective snow grain size parameters with the random forest approach

Snow cover is highly critical for global water and energy cycles because of its wide areal extent, high reflectivity and good thermal insulation. Knowledge of snow conditions, e.g., snow water equivalent (SWE) and snow depth, is significant to hydrologic and climatologic processes. Spaceborne passive microwave (PMW) data, namely, brightness temperature (TB), have been in use for snow depth and SWE retrieval at the global scale since 1978. However, the sensitivity of TB to these parameters is complex due to snow metamorphism (e.g., snow grain size, GS), which limits the feasibility of many existing algorithms characterizing snow. This study presents a new methodology to retrieve snow depth over China by coupling a microwave snow emission model with a random forest (RF) machine learning (ML) technique. An effective GS value (effGS), a prior snowpack descriptor, was optimized utilizing the Helsinki University of Technology (HUT) model by minimizing the difference between AMSR2 observations (18.7 and 36.5 GHz) and HUT simulations. Five elaborately selected independent variables, including vertical polarized TB differences (TBD) between 18.7 and 36.5 GHz (TBD18.7V&36.5V), 10.65 and 36.5 GHz (TBD10.65V&36.5V), longitude, elevation and effGS, together with the target variable, snow depth, were applied to train the RF model, and then the 10-fold cross-validation (10-CV) approach was employed for performance validation using station data during the period from 2012 to 2018. The results indicated that (1) inclusion of effGS in RF greatly enhanced the overall performance in snow depth estimation; (2) the trained RF model performed better on a temporal scale than on a spatial scale, with unRMSEs of 1.81 cm and 3.17 cm, respectively; (3) specifically, the fitted RF algorithm partially addressed the overestimation in shallow (≤ 20 cm) snowpacks and underestimation in deep (> 20 cm) snow conditions when compared with the established RF algorithm based solely on predictor variables but without effGS. To evaluate the predictive power of the RF algorithm trained with samples in 2017 and 2018, spatially independent station measurements during the period from 2012 to 2016 and field survey data collected from January 2018 to March 2019 were used for validation. Additionally, the RF estimates were compared with two widely used satellite products (AMSR2 and GlobSnow-2). The validation results showed that RF estimates were closer to the in situ data than the other two satellite products. This study demonstrated the potential utility of combining the snow emission model with an ML approach to improve snow depth estimation.

Optimal estimation of snow and ice surface parameters from imaging spectroscopy measurements

Snow and ice melt processes are a key in Earth's energy-balance and hydrological cycle. Their quantification facilitates predictions of meltwater runoff as well as distribution and availability of fresh water. They control the balance of the Earth's ice sheets and are acutely sensitive to climate change. These processes decrease the surface reflectance with unique spectral patterns due to the accumulation of liquid water and light absorbing particles (LAP), that require imaging spectroscopy to map and measure. Here we present a new method to retrieve snow grain size, liquid water fraction, and LAP mass mixing ratio from airborne and spaceborne imaging spectroscopy acquisitions. This methodology is based on a simultaneous retrieval of atmospheric and surface parameters using optimal estimation (OE), a retrieval technique which leverages prior knowledge and measurement noise in an inversion that also produces uncertainty estimates. We exploit statistical relationships between surface reflectance spectra and snow and ice properties to estimate their most probable quantities given the reflectance. To test this new algorithm we conducted a sensitivity analysis based on simulated top-of-atmosphere radiance spectra using the upcoming EnMAP orbital imaging spectroscopy mission, demonstrating an accurate estimation performance of snow and ice surface properties. A validation experiment using in-situ measurements of glacier algae mass mixing ratio and surface reflectance from the Greenland Ice Sheet gave uncertainties of ±16.4 μg/gice and less than 3%, respectively. Finally, we evaluated the retrieval capacity for all snow and ice properties with an AVIRIS-NG acquisition from the Greenland Ice Sheet demonstrating this approach's potential and suitability for upcoming orbital imaging spectroscopy missions.

Calculation of the contact area between snow grains and ski base

Gliding friction depends on the contact area between ski and snow. Therefore, we computed the contact area of a single grain with the ski base by solving the static contact problem. The calculations were done at randomly selected positions on two ski bases, various snow grain radii, and various loadings. The relative single grain contact area with the ski base was 0.03–6.0% of the snow grain’s cross section. Contact area and pressure increased with decreasing snow grain radius and increasing load. The contact pressure exceeds the strength of ice, presumably causing fracture of parts of snow grains. Resulting debris may partly remain in the interface between ski and snow and thus reduce friction.