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

Abstract

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.

Estimating snow accumulation and ablation with L-band InSAR

“…The lower elevations showed no accumulation in the InSAR retrievals, and this was confirmed by both the HQ met snow depth sensors and snow pit (Figure 8b). These results illustrate the ability to Corresponding research by Webb et al (2021b) investigated the relationship between dielectric permittivity and LWC for both dry and wet snow conditions in the Jemez Mountains. With ρ s ranging between 261 to 309 kg m −3 and ϵ s between 1.26 to 1.39, snowpack LWC would range approximately between 3% to 5%.…”

“…This validates figures presented in Leinss et al (2015), which state that at L-band (1.26 Ghz), and a ρ s of 300 kg m −3 , the radar signal can penetrate between about 10 m at 1% LWC and 1 m at 10% LWC. The high quality of the phase signal even with relatively high LWC shows promise for the overall performance of NISAR and it's 6 AM and 6 AM sun-synchronous orbit even when snowpacks contain some LWC (Webb et al, 2021b). By processing the 12-26 February pair, we've shown that coherence can be held and quality snow phase information can be obtained at a 14 day temporal baseline, even in the presence of melt.…”

Arctic Tundra Lake Drainage Increases Snow Storage in Drifts

“…We observed a good correlation between probe and GPR measurements (Figures 3a and 3b), and the calibrated snow radar velocity (0.189 ± 0.023 m ns −1 ) has an uncertainty of ∼12%. However, our calibrated velocity is slower than observed in previous works, typically between 0.23 and 0.25 m ns −1 (e.g., Bradford, Harper, & Brown, 2009; McGrath et al., 2022); and it is also slower than expected for a snow density of 360 kg m −3 using empirical relationships that correlates dry snow density and radar velocity (e.g., Kovacs et al., 1995; Tiuri et al., 1984; Webb et al., 2021). This discrepancy may be attributed to differences in snow properties at the Arctic lowland compared to, for example, alpine mountains.…”

“…GPR has been widely applied in snow investigations across different regions, including alpine mountains (e.g., Bradford, Harper, & Brown, 2009; McGrath et al., 2022), Arctic Coastal Plain of Alaska (e.g., Wainwright et al., 2017), Greenland (e.g., Gacitúa et al., 2013; Jaedicke & Sandvik, 2002), boreal regions (e.g., Gusmeroli & Grosse, 2012), and Antarctic sea ice (e.g., Pfaffhuber et al., 2017). The snow radar velocity can be calibrated based on direct snow depth probe measurements; the radar velocity in dry snow is fundamentally controlled by the snow density (Tiuri et al., 1984; Webb et al., 2021).…”

Snowpack relative permittivity and density derived from near‐coincident lidar and ground‐penetrating radar

“…We categorized surveys as dry or wet based on the presence of any LWC noted in snow pits and corroborated by pit temperatures (Appendix A.2; Figure S2). Relative permittivity estimates obtained in dry‐snow conditions (all surveys, except the 7 April and 27 May 2021 surveys) were then converted to density using the Kovacs et al (1995), Kuroiwa (1954), and Webb et al (2021) equations and compared to in‐situ density measurements to calculate the RMSE and Pearson correlation coefficient to determine the most representative equation.…”