It is well understood that the distribution and quantity of liquid water in snow is relevant for snow hydrology and avalanche forecasting, yet detecting and quantifying liquid water in snow remains a challenge from the
micro- to the macro-scale. Using near-infrared (NIR) spectral reflectance
measurements, previous case studies have demonstrated the capability to
retrieve surface liquid water content (LWC) of wet snow by leveraging shifts in the complex refractive index between ice and water. However, different models to represent mixed-phase optical properties have been proposed, including (1) internally mixed ice and water spheres, (2) internally mixed water-coated ice spheres, and (3) externally mixed interstitial ice and water spheres. Here, from within a controlled laboratory environment, we determined the optimal mixed-phase optical property model for simulating wet snow reflectance using a combination of NIR hyperspectral imaging, radiative transfer simulations (Discrete Ordinate Radiative Transfer model, DISORT), and an independent dielectric LWC measurement (SLF Snow Sensor). Maps of LWC were produced by finding the lowest residual between measured reflectance and simulated reflectance in spectral libraries, generated for each model with varying LWC and grain size, and assessed against the in situ LWC sensor. Our results show that the externally mixed model performed the best, retrieving LWC with an uncertainty of
The distribution and quantity of liquid water within a snowpack, introduced by rain and/or melt, are relevant for multiple snow-related applications including snow hydrology, remote sensing, and avalanche forecasting. In terms of snow hydrology, water is an indicator of snow energy balance and snowmelt timing; the change in phase from ice to water indicates that the cold content of the snowpack is depleted and that energy balance inputs are contributing to melt (DeWalle and Rango, 2008). Rain on snow can accelerate this process by contributing large energy inputs into the snowpack over a short amount of time (Mazurkiewicz et al., 2008). Water at the surface will also lower snow albedo, initiating a positive feedback loop that increases absorbed solar radiation, the main driver of snowmelt (Gupta et al., 2005). For active and passive microwave remote sensing of snow, the presence of water alters microwave signatures because of the large difference in relative permittivity between liquid water and ice (i.e., dry snow). For active microwave sensors, wet snow causes characteristic changes in microwave backscatter and reduces penetration depth (Shi and Dozier, 1992), while for passive sensors, the emissivity of the snow surface is increased (Walker and Goodison, 1993). For avalanche forecasting, the infiltration of liquid water into the snowpack impacts snow stability (Conway and Raymond, 1993). The strength of the snowpack can be increased at lower water content, where grains form well-bonded clusters, but reduced at higher water content, when water flow through pore space deteriorates a significant number of snow grain bonds, resulting in relatively cohesionless particles (Colbeck, 1982). Although it is recognized as a critical snow property across the cryospheric sciences, liquid water content (LWC) measurements in a snowpack are notoriously difficult to accurately quantify due to the high spatial and temporal variability in liquid water distribution.
Here, the utility of mapping LWC in situ using near-infrared hyperspectral
imaging (NIR-HSI) and radiative transfer model inversion is assessed. This
approach leverages the segments of the near-infrared (NIR) spectrum where
the optical properties of liquid water, hereafter referred to as water, vary
from those of ice. To date, wet snow has been modeled using effective spheres with a known radius, referred to as the effective grain radius (
Although different mixing model representations have been proposed and
demonstrated (Green et al., 2002; Hyvarinen and Lammasniemi, 1987), no study has quantitatively compared the different approaches or compared LWC retrievals to established LWC measurement methods. Without intercomparing or validation, the best approach for retrieving LWC from NIR spectral reflectance has yet to be determined. Additionally, radiative transfer
approaches to retrieving
Water infiltration through snow is a spatially and temporally complex process, controlled by water saturation level, snow microstructure, and topography. Generally, water infiltration is described by two primary mechanisms: homogenous matrix flow and heterogeneous preferential flow. Matrix flow is described as the semi-uniform vertical movement of water, while preferential flow is made up of concentrated water pathways that follow the path of least resistance that can extend deep into the snowpack, ahead of the matrix flow (Schneebeli, 1995). Although gravitational forces primarily drive vertical movement of water in snow, large amounts of water can be diverted horizontally due to stratigraphic layers in the snowpack, such as ice crusts or capillary barriers (i.e., fine grains over coarse grains) (Waldner et al., 2004; Webb et al., 2021; Eiriksson et al., 2013). As the snowpack becomes less stratified throughout the melt season, the general pattern transforms from preferential flow to homogenous flow (Webb et al., 2018).
The complexity of water movement through snow makes observations and measurements challenging. Early observations of water flow patterns through snow were made using dye tracers (Seligman et al., 1936; Gerdel, 1954), a method which is still used today. Dye tracers provide a spatial visualization of water infiltration that has been used to study processes such as preferential flow (Schneebeli, 1995; Waldner et al., 2004) and capillary barriers (Avanzi et al., 2016). While these methods remain primarily a qualitative visualization technique, Williams et al. (2010) quantified the three-dimensional (3D) spatial distribution of meltwater within a 1 m
In situ measurements of LWC in snow have traditionally been measured by
centrifugal separation (Kuroda and Hurukawa, 1954), melting calorimetry (Yosida, 1940), freezing calorimetry (Jones et al., 1983), and the dilution method (Davis et al., 1993). A more detailed summary of these methods can be found in Stein et al. (1997). Generally, these methods are difficult to perform and time-consuming and have only been occasionally used since their introduction. More commonly, LWC is measured using dielectric methods at frequencies ranging from 1 MHz to 1 GHz by leveraging the large differences in the relative permittivity (
Previous non-destructive measurements of LWC in snow have been made using remote sensing techniques. Like dielectric sensors, active and passive microwave sensors leverage the difference in relative permittivity between water, ice, and air. At the ground-based scale, upward-looking ground-penetrating radar (upGPR) has been used to measure the volumetric LWC directly above antennas buried below a snowpack (Schmid et al., 2014). At the spaceborne scale, active and passive microwave sensors have been used to make classification maps of wet or dry snow at spatial resolutions on the order of tens of meters (e.g., Lund et al., 2020; Walker and Goodison, 1993). Similarly, in the optical wavelengths, the shift in absorption patterns of ice and water across the NIR have been leveraged to map surface LWC (Green et al., 2002), which is the primary method of interest in this work.
Absorption in the optical wavelengths is described by the imaginary part of
the complex refractive index. Although the absorption patterns across the
NIR are similar between ice and water, there are shifts that distinguish the
different phases. The spectral complex refractive index for ice (Warren and Brandt, 2008) and water at 0
Complex refractive index of ice and liquid water at 0
Inversion of radiative transfer models is commonly used in remote sensing
applications to retrieve physical snow properties from measured spectra, and
many modeling approaches have been proposed. Hyvarinen and Lammasniemi (1987) modeled the reflectance of wet snow using a collection of spheres with radius
To date, three radiative transfer approaches for simulating the reflectance
of wet snow have been proposed: (1) mixed-phase spheres, hereafter referred to as “
A schematic of three ice and water optical mixing models used to simulate the reflectance of wet snow.
Three optical property mixing models were used to simulate the bidirectional
reflectance of wet snow across a range of
Liquid water content and effective grain radius retrieval and assessment workflow.
Snow reflectance in the NIR was mapped with a Resonon Inc. Pika NIR-320 near-infrared hyperspectral imager. A brief description of the instrument follows (for a more detailed description see Donahue et al., 2021). The imager has a spectral resolution of 4.9 nm, measuring 164 bands across the NIR region from 900–1700 nm. The imager constructs a 2D image containing the full spectrum in each pixel by collecting the image line by line, known commonly as a “push broom” or “line” scanner. Thus, to collect an image, the camera needs to be moving (translating or rotating) relative to the scene, or the scene needs to be moving relative to the imager. Here, both types of image acquisition techniques are used. In the laboratory, a linear scanning stage was used to move the sample beneath the sensor, while in the field, a rotational stage mounted on top of a tripod was used to scan the snowpit wall.
The SLF Snow Sensor (FPGA Company, 2018), hereafter referred to as the “SLF sensor”, is a capacitance sensor that is placed on the snow surface to measure the relative permittivity. This is used to determine snow density and LWC in dry snow and wet snow conditions, respectively. The factory calibration for the LWC measurement is based on an empirical equation derived from reference measurements of snow with varying wetness and density using the dilution method (Davis et al., 1985) and weighted volumes. The sensor measures a snow surface area of
The hyperspectral imager was mounted onto the Resonon benchtop linear scanning stage, which positions the imager on a stationary tower above a linear translating stage where samples are placed (shown in Fig. 4a). The lens of the imager is surrounded by four halogen lamps, and both are positioned for nadir viewing and illumination. The halogen lamps and lens of the imager were at a height of 38 and 47 cm above the snow surface, respectively. This quasi-monostatic configuration results in a bidirectional reflectance measurement in each pixel of the image when calibrated using a white reference panel. A large Spectralon ® 99 % reflectance panel was placed at the same height as the surface of the snow samples and filled the imager's entire field of view, such that each snow sample was calibrated from radiance to reflectance on a pixel-by-pixel basis. This method of calibration is ideal for hyperspectral imaging because it minimizes effects to illumination imperfections across the scene.
Schematic of laboratory setup.
Snow samples were prepared in the laboratory using laboratory-made and collected natural snow to generate a dataset with a range of grain types
including precipitation particles (PP), decomposing and fragmented precipitation particles (DF), rounded grains (RG), melt forms (MF), and faceted crystals (FC) (Fierz et al., 2009). The dry snow density, measured by weighing the sample container with a known volume and using the SLF sensor, ranged between 115 and 510 kg m
Laboratory snow samples (reported
n/a stands for not applicable.
For each snow sample, an initial image was taken while the cold room was at
To demonstrate the applicability of the NIR-HSI method for retrieving LWC
and
The imager was mounted onto the Resonon outdoor field system, which includes a tripod-mounted rotational stage, and was placed 110 cm from the snowpit wall. The snowpit wall was illuminated with two 500 W halogen lamps mounted on a tripod, line-powered (120 V AC) through the weather station. The lights were placed perpendicular to the wall at a distance of 90 cm, similar to the laboratory setup presented in Donahue et al. (2021). For controlled lighting conditions, sun light (direct and diffuse) was blocked by placing an opaque tarp over the top of the snowpit. A detailed schematic of the field setup is shown in Fig. 5. For a pixel-by-pixel calibration of the NIR-HSI measurements from radiance to reflectance, a 36 % spectrally flat reflectance calibration tarp was hung in front of the snowpit wall, completely covering the field of view of the imager and ROI of the snowpit.
Images of the wall were taken at 13:00 MST, at which time there were few clouds, and the air temperature was 10
Schematic of the near-infrared hyperspectral imaging setup in the field for measurement of liquid water content across a snowpit wall. The area at the bottom 40 cm of the snowpit was not imaged and is shown with hatched lines.
Immediately following imaging, LWC measurements were made with the SLF sensor along a vertical profile at 5 cm increments. For optimal LWC measurements, the SLF sensor requires the dry snow density; however, the snow was already wet, and therefore the dry snow density could not be obtained. Instead, the density of the snow from the adjacent density cut measurement was used, which introduced a small error in the LWC measurement. Following the methodology proposed by FPGA Company (2018), this error was corrected by subtracting the mass of water from the wet snow density based upon the initial LWC. The updated density was used to calculate an updated LWC using the empirical calibration equation. This calculation was repeated, with each iteration returning a smaller change in snow density. Through multiple iterations it converges on the dry snow density and corrected LWC.
To simulate the optical properties of snow, the single-scattering optical
properties of constituents (ice, air, water, and impurities) as well as their relative arrangement to one another must be represented. The scattering properties of a single particle are described using three dimensionless optical parameters: (1) the absorption efficiency
First, the
Simulated bidirectional reflectance of snow using three optical mixing models: (1)
For each model clean snow is assumed, and the effects of light-absorbing
particles (LAPs, i.e., dust and soot) are not considered (discussed further in Sect. 5.3.1). The single-scattering optical properties were calculated for
To generate a spectral library to match to measured spectra, directional-hemispherical reflectance for each mixing model was simulated
using a general-purpose 16-stream plane-parallel Discrete Ordinate Radiative Transfer model (DISORT; Stamnes et al., 1988). DISORT allows the user to define optical properties of multiple layers; here, a single optically thick layer was used since the penetration of NIR light into the snowpack is shallow. Optical property inputs for this layer included single-scattering albedo, defined as the ratio of the scattering efficiency and extinction efficiency
The output from DISORT was directional-hemispherical reflectance, whereas NIR-HSI measurements are bidirectional reflectance. This is a suitable approach because of the experimental setup: the NIR-HSI measurements were made at nadir illumination and viewing angles and calibrated using a Lambertian white reference target. Under these conditions, snow is nearly Lambertian, allowing for a direction comparison, which would not be the case for non-nadir viewing angles, given that snow heavily favors forward scattering (Dumont et al., 2010).
To simultaneously retrieve LWC and
Example of a measured NIR-HSI spectrum, retrieved simulated spectrum using the interstitial sphere model, and the residuals at each band.
Additionally,
The LWC retrieved from NIR-HSI was compared to the SLF sensor across seven samples, spanning a wide range of initial dry snow grain sizes from
approximately 100 to 900
An example of the LWC maps produced as melt progressed in a single snow sample is presented in Fig. 8. These examples are of the same ROI and show LWC retrieved using the interstitial sphere model. The initial image (Fig. 8a) was taken at the start of the experiment, when the snow was dry, and 98 % of pixels (10 450 pixels) retrieved 0 % LWC. The other 2 % of pixels (267 pixels) retrieved 1 % LWC, which was found to be due to sensor noise. The remaining images in Fig. 8 capture melt progressing through 5 % (Fig. 8b), 10 % (Fig. 8c), and 16 % (Fig. 8d) mean LWC, and the corresponding SLF sensor measurement is noted in each panel. Additionally, the distribution of values also broadens with increasing LWC, shown in the per-pixel distribution of LWC for each image in Fig. 8e. The summary statistics show melt progression, as expected, but the maps allow visualization and quantification of melt initiation and LWC distribution. The melt features that begin to develop in early time steps can be tracked to later time steps (e.g., Fig. 8c to d).
The full performance comparison across all datasets is summarized in Fig. 9, which plots LWC from the SLF sensor against that from each mixing model
applied across all samples. To help visualize the difference between
experiments, the comparison points are symbolized by different colors as well as marker size that varies with the mean initial dry snow
Comparison of LWC measured with the SLF Snow Sensor versus the mean LWC retrieved from NIR-HSI using the residual method. Three optical property mixing models are compared using the same datasets:
Liquid water content retrieval results from the laboratory (reported
For the two samples with the smallest initial
For the remaining samples, ranging from 176–898
Using the residual method, all mixing models retrieved similar grain size
values because the grain size retrievals are primarily dependent on the
absolute reflectance driven by ice absorption. Here, we present results from
the interstitial sphere model because it performed best in the LWC retrieval. For initial dry snow conditions, the
Mean effective grain radius (
Results from the snowpit at Bridger Bowl Ski Area.
Although a controlled laboratory environment is ideal for identifying the
best-suited optical mixing model, the primary applications for this method
would be in situ field studies, motivating the field-based testing of the
The maps were processed using each of the mixing models introduced above, but based on the laboratory findings, only retrievals from the interstitial sphere model are presented here. The SLF sensor measurements were taken along the left side of the ruler (gray stripe or NaNs down the center of snowpit), represented as the dashed red box in Fig. 11c. For comparison, LWC was depth-averaged in pixels covering the area of the SLF sensor measurements (red line in Fig. 11d) in addition to the depth average LWC across the entire width of the snowpit (gray line in Fig. 11d). The mean LWC, standard deviation (
Liquid water content retrieval results from the field.
For comparison, when processed with the coated sphere model the LWC reached
the model limit at 25 % over much of the scene. The
The high resolution of the maps shows how stratigraphy influences
The interstitial sphere and
The coated sphere model performed reasonably in the pendular regime, where water is contained in menisci held in between the ice particles, but then considerably overestimated LWC in the funicular regime. The coated sphere model was chosen over the interstitial sphere model by Green et al. (2002), based on visual inspection, considering the bands in the ice absorption feature centered at 1030 cm, which encompasses only part of the distinct shifts between ice and water that are present in the complex refractive index across the NIR (Fig. 1). This study used a greater number of NIR bands that span multiple distinguishable shifts between ice and water, which is a more robust approach.
For small snow grains of PP (Sample 1) and DF (Sample 2) crystal type, LWC
retrievals did not perform well using any of the models, one potential
reason being that PP and DF crystal types are complex shapes, and reflectance
may not be accurately represented using spheres. Using a ray tracing model,
Picard et al. (2009) showed that grain shape can influence reflectance.
Although it is possible to have wet PP and DF crystal types (e.g., rain on
snow), low-density dendritic snow crystals are more commonly found at
temperatures well below freezing (Judson and Doesken, 2000). It is far more common for wet snow to contain larger rounded grains primarily because the presence of water rapidly increases the rate of snow grain growth, especially through melt and refreeze cycles. Small RG (Sample 3), having only slightly larger
Interestingly, for the largest grains, Samples 6 and 7, the highest LWC
measurements from the SLF sensor are
Effective grain radius (
The scaled band area method assumes dry snow, but in remote sensing and field applications there is typically no a priori knowledge of snow wetness; thus comparing
In the wet snow case, the absorption feature centered at 1030 nm shifts to
shorter wavelengths and broadens. Similar to the comparison for dry snow, the fixed wavelength range and continuum line of the scaled band area method fail to fully capture the wet snow absorption feature, resulting in a reduction in the scaled band area. This result is shown in the spectral reflectance example (Fig. 12c) and is responsible for the decreasing
All the mixing models examined in this study are approximate representations of the relative arrangement of ice and water in wet snow. The spherical particle approximation used in this study to represent wet snow is a reasonable approach because ice grains in the presence of water tend to be rounded. The arrangement of ice and water, on the other hand, is dependent on the level of water saturation; therefore using a single mixing model to determine the LWC across a large range of water saturations results in inherent uncertainty. Since no a priori knowledge of snow wetness is known when taking NIR-HSI measurements, the goal of this research only aims to find the modeling approach that has the best retrieval of LWC across ranges commonly found in natural environments when compared to an established dielectric-based instrument.
Simulations of clean snow reflectance, assuming no LAPs, were valid for the laboratory experiments; however snow in natural environments contains varying concentrations of LAPs. Since LAPs predominately effect the visible part of the spectrum (Nolin and Dozier, 2000), it is unlikely that typical concentrations would impact this retrieval method. However, at high concentrations of LAPs their impact extends into the NIR, and in extreme cases this can make the ice absorption feature more shallow (Skiles et al., 2018), which would increase uncertainties in this retrieval method.
There is uncertainty in the measurement of absolute spectral reflectance, the accuracy of which is important for using the residual method. To minimize this uncertainty in the laboratory, spectral measurements were taken with consistent lighting conditions and at close proximity, resulting in near-perfect conditions, which was ideal for the comparison study. Similarly, uncertainties related to lighting conditions in the field experiment were minimized by blocking all sunlight with an opaque tarp and illuminating the snowpit wall with a known lighting source. This approach is recommended and is used with other optical methods, such as contact spectroscopy (Painter et al., 2007; Skiles and Painter, 2017). Using natural light in a standard snowpit orientation (i.e., facing away from the sun) would make the conversion from radiance to reflectance challenging because the snowpit wall is unevenly illuminated by diffuse light and would need to be accounted for in the radiative transfer modeling. Additionally, there may not be enough light on the snowpit wall for imaging; however, this was not tested here.
Similarly, if the orientation of the imager or light source is off-nadir, this needs to be accounted for in the radiative transfer modeling such that the measured and simulated spectra are comparable. Here, we did not image the bottom 40 cm of the snowpit because positioning the camera and lights off-nadir would introduce errors in the comparison to the simulated spectra at nadir viewing, which is discussed in more detail in Donahue et al. (2021). However, the full snowpit could be imaged in nadir orientation by digging a larger snowpit such that the camera and lighting source are farther away from the snowpit wall or by using a tripod that lowers closer to the ground.
Additionally, the residual method benefits from the high signal-to-noise ratio (1885) and spectral resolution (4.9 nm) of the instrument used here. For application of this method at the airborne or satellite scales, spectral measurements contain more noise than those in the laboratory and require atmospheric and topographic correction, introducing additional uncertainty into absolute reflectance values. Although not within the scope of this study, instruments at these scales also need to account for water vapor in the air, which is discussed further in Green et al. (2006). Finally, due to the relatively minor shift in NIR reflectance, this approach is likely not suitable for mixed pixels (not pure snow), which become more common as spatial coverage and pixel sizes increase.
Dielectric instruments, including the SLF sensor used here, have their own
uncertainties. Based on the empirical calibration of the SLF sensor (FPGA Company, 2018), the RMSE of the LWC measurement is
Acquiring a vertical profile of LWC, using any instrument, requires digging a snowpit and exposing the sidewall. The atmospheric exposure can change snow properties and introduce uncertainties to the measurement. Shea et al. (2012) observed that a statistically significant change in the surface temperature across a snowpit wall occurred within the first 90 s of exposure, providing evidence that atmospheric equalization affects the surface temperature more strongly than from heat behind the snowpit wall. Here, the snowpit was isothermal, and the air temperature was above freezing (10
Controls on liquid water movement through snow include LWC, grain size, and
wet snow metamorphism (Hirashima et al., 2019). Multi-dimensional snowmelt models have been developed to represent the relationship between grain growth and water percolation (Hirashima et al., 2014), but limited observations for validation at large spatial scales currently exist. Being able to coincidently map
Coincident
There is also broader relevance for the assessment and development of snow property retrievals from measured spectral reflectance with upcoming satellite imaging spectrometer missions. These include the Surface Biology and Geology (SBG) imaging spectrometer mission and the Copernicus Hyperspectral Imaging Mission (CHIME). Although algorithm suites have been developed to retrieve snow properties from airborne imaging spectroscopy (Painter et al., 2013), LWC is not a standard part of the retrieval and has only been demonstrated as a case study (Green et al., 2002). Time series mapping of LWC could be used to monitor melt initiation and how it varies with slope, aspect, and elevation.
The results in this study show that the externally mixed interstitial sphere model performs best when compared to a dielectric LWC measurement instrument, relative to the previously proposed
For the
The field application of the NIR-HSI method produced maps that reflect the general understanding of what a snapshot of a snowpit would look like during snowmelt progression but mapped the stratigraphy of snow properties (i.e., LWC and grain size) at much higher resolution relative to standard profile-based observations. The retrieved LWC was found to be slightly higher than that measured by the SLF sensor, which was attributed to both the inability to determine the dry snow density and the high level of detail in the maps that could not be captured by the volume-averaged dielectric sensor.
Data will be available upon request from the lead author.
CD conceptualized the study, collected laboratory and field data, conducted DISORT model simulations, and analyzed the results. SMS provided the hyperspectral imager, assisted with data collection, and advised CD during conceptualization and DISORT model simulations. KH acquired funding for this research, was responsible for project administration, and supervised CD throughout the study. CD wrote the original draft manuscript, and all co-authors contributed during review and editing.
The contact author has declared that neither they nor their co-authors have any competing interests.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This research was supported by the NASA New Investigator Program award 80NSSC18K0822. Additionally, S. McKenzie Skiles was supported by the NSF CZO-Net award EAR-2012091. We thank Joseph Shaw for providing the Resonon linear scanning stage used in this study. We thank Michael Dvorsak and Ladean McKittrick for their assistance in the laboratory. We thank Pete Maleski and the Bridger Bowl Ski Patrol for allowing us to conduct fieldwork at the Alpine Weather Station and for transporting our instruments into the field. We acknowledge the use of the Subzero Research Laboratory in the Department of Civil Engineering at Montana State University. We thank Ryan Webb and Chander Shekhar for providing insightful comments that helped improve this paper.
This research has been supported by the National Aeronautics and Space Administration (grant no. 80NSSC18K0822). S. McKenzie Skiles was funded by the National Science Foundation award EAR-2012091.
This paper was edited by Carrie Vuyovich and reviewed by Chander Shekhar and Ryan Webb.