Liquid-water content and water distribution of wet 1 snow using electrical monitoring

Abstract. Snow exists in a wide range of temperatures and around its melting point snow becomes a three-phase material. A better understanding of wet snow and the first starting point of water percolation in the seasonal snowpack is essential for snow pack stability, snow melt run-off and remote sensing. In order to induce and measure precisely the liquid water and the corresponding dielectric properties inside a snow sample, an experimental setup was developed. Using microwave heating at 18 kHz allows the use of dielectric properties of ice to enable heat to be dissipated homogeneously through the entire volume of snow. A desired liquid water content inside the snow sample could then be created and analysed in a micro-computer tomography. Based on the electrical monitoring a promising perspective for retrieving water content and water distribution in the snowpack is given. The heating process and extraction of water content are mainly dependent on the morphological properties of snow, the temperature and the liquid water content. The experimental observation can be divided in three different heating processes affecting the dielectric properties of snow for different densities: (1) dry snow heating process up to 0 °C indicating a temperature and snow structure dependency of the dielectric property of snow; (2) wet snow heating at stagnating temperature of 0 °C and the presence of uniformed distributed liquid water changes the dielectric properties. The presence of liquid water decreases the impedance of the snow sample until water starts to percolate; and (3) the start of water percolation is between 5–12 water volume fraction depending on the snow density and confirms the literature findings. The onset of water percolation initiated an inhomogeneity in snow and water distribution, strongly affecting the dielectric properties of the snow. These findings are pertinent to the interpretation of the snow melt run-off of spring snow. These laboratory measurements allow to find the narrow range of the starting point of water percolation in coarse-grained snow and to extract the corresponding dielectric properties which is important for remote sensing.


liquid water on the snow microstructure is essential. It influences radar and microwave 43 attenuation, sub-surface exploration, remote sensing, radar altimetry, electrical 44 grounding, atmospheric electrical fields and electrostatic charging by precipitation and 45 blown particles (Mellor, 1977). Liquid water in snow is also a critical factor for 46 estimating the hazard of wet snow avalanches and the transmission of melt-water 47 The core of the snow heater is a Red Pitaya STEM 125-14 using for signal generation 133 and data acquisition, and is controlled via Standard Commands Programmable 134 Instruments SCPI in Matlab. The low voltage sinusoidal input signal with a frequency 135 of 18 kHz is generated by a high-speed digital to analog converter and is amplified 136 afterwards to stabilizes the electrical potential in the circuit. A step-up transformer 137 transforms the low primary voltage to a high secondary voltage of around 350 V 138 applied to two copper plates inducing the dielectric heat into the snow sample. The 139 surface of the copper plates is electrically insulated to prevent Joule heating of the 140 snow sample. The snow sample was placed into a polyoxymethylene (POM) ring 141 (diameter = 60 mm, distance = 13 mm) and inserted between the two capacitor plates. 142 The snow sample and the capacitor are thermally insulated with extruded polystyrene 143 foam (XPS) with a thickness of 120 mm to prevent radial conductive and convective 144 heat losses. 145 The applied sinusoidal waveforms of voltage U(t) to the copper-plates is attached to a 146 differential probe and is measured galvanic sorted with a 100-fold attenuation. The 147 current I(t) from the plate is measured via a shunt resistor. The phase shift j(t) 148 between the sinusoidal waveforms of voltage and current is measured between the 149 circuit's input and circuit's output signal. An input protection circuit prevent the analog 150 to digital converter from damage in case of a short circuit. The voltage connection 151 between the low and high voltage part is measured via a shunt resistor. This 152 connection defines the star point of the circuit and makes sure that the second part of 153 the circuit doesn't thrift away. It is the only star point preventing the circuit from circular 154 currents. A negative temperature coefficient element is placed one centimetre inside 155 the snow sample to measure the temperature. A low pass filter is applied to block the 156 noise of the capacitor. 157 The total power PRMS(t) between the two copper-plates is calculated based on the root-158 mean-squared voltage URMS(t), current IRMS(t) and the measured phase difference j(t) The impedance RRMS(t), describing the resistant of the snow sample, between the two 161 copper-plates is given by The uncertainties of the temperature T(t), current IRMS(t), voltage URMS(t), phase shift 164 j (t), total power consumed P(t), and density of the snow measured by weighting are:

Tomography experiments 167
A cooled micro-computer tomograph (CT; Scanco Medical µ-CT80) at a cold Gaussian filter (s = 1.4, support = 3) was applied to reconstruct the micro-CT images. 173 The volume was segmented to a binary image by classifying each voxel by ice or air. 174 The threshold for the segmentation process was chosen such as that the manually 175 measured density did not deviate more than 12 % from the CT-density in the 176 segmentation process (Riche and Schneebeli, 2013). Each scan took around 2.7 h. 177 Absorption by water and ice are almost identical (Lieb-Lappen et al., 2017), and are 178 hardly to separate in the segmentation process. Therefore, the water creation on the 179 snow surface was extracted by superposition of two micro-CT scans. One scan was 180 taken before the heating process and the second one afterwards. Before the second 181 micro-CT scan, the wet snow sample was shock frozen at -30 °C to preserve the snow 182 structure. This allowed us to easily visualize and to extract the water creation on the 183 surface of the ice matrix with an uncertainty of 4 %. 184

Method 185
The phenomena involved in microwave heating of snow are volumetrically absorption 186 of electromagnetic energy to achieve self-heating uniformly and rapidly, which is 187 characterized by the density of the snow. The dielectric power absorption P is equal 188 to the total power consumed PRMS, given by: 189  which depends on the frequency f, snow density rs, and snow temperature Ts.

197
The heating efficiency is an important factor to evaluate the heating process. It is 198 defined as the ratio of energy absorbed by the heated sample to that radiated from the 199 microwave source [Ali, 2016] given by: 200 where ms is the mass of the snow sample, cp the specific heat capacity, T0 and T1 the 202 initial temperature and melting temperature at 0 °C, and t1 the time until temperature 203 reached 0 °C. 204 The liquid water mass fraction for each timestep t, is calculated by the fraction of the 205 measured dissipated latent heat and total latent heat needed for the phase change: 206 where hlatent = 334 kJ kg -1 is the latent heat for the phase change from ice to water and 208 where rs, ri and rw are the snow, ice (917 kg m -3 ) and water (999.9 kg m -3 ) density.

212
The uncertainties of xmass and xvol are 10 % due to the uncertainty of the power (±0.005 213 W) and density measurement (±20 kg m -3 ). 214

Results 215
Deionized water with a conductivity of » 0.2 µS cm -1 was used to produce natural 216 identical snow (Schleef et al., 2014) in a cold laboratory at -20 °C. The produced snow 217 was sieved into sample holders (mesh size: 2 x 2 mm) and was sintered at a 218 temperature of -2 °C for two to five days to allow the snow crystals to form a uniform 219 grain size. A hydraulic press compressed the snow to densities between 400 and 600 220 kg m -3 to represent snow packs in spring ( Bartelt and Lehning, 2002). We analysed in 221 total seven different snow samples. 222 The measured electrical properties between the two copper-plates were strongly 223 influenced by the temperature, water content, and density of the snow sample. The 224 higher the snow density and the water content in the snow was, the stronger the 225 measured electrical properties were affected, shown in Table 1. Figure 3  The snow temperature, density and water content strongly affected the impedance 242 and the total power consumed by the snow sample. The impedance decreased with 243 increasing temperature, water content, and density, vice versa for the total power 244 consumed, shown in Table 2. Figure 4 shows a typical calculated total power PRMS(t) The heating efficiency was affected by heat loss at the wall and decreases with higher 256 snow density. The microwave power did not directly penetrate into the snow samples 257 but also through the air space of the pores. As a result, the reflection of microwave 258 power on the interface, which was caused by the relative permittivity mismatch 259 between the air and the sample led to limited heating efficiency. As the frequency of 260 18 kHz was in the range of the optimal snow heating frequency between 10 and 100 261 kHz depending on the snow density (Bader and Kuroiwa, 1962 The start of water percolation was between 5-12 water volume fraction depending on 269 the snow density. Dense snow absorbed more microwave energy leading to higher

Discussion 291
Our major experimental results are summarized in Fig. 4 and 6, and in Table 2 and 3. 292 The dominant sources of absolute errors in the measurement of the water mass and 293 volume fraction in the snow were the snow density and the inaccuracy in the power 294 measurement. Especially, at snow densities below 450 kg m -3 this might cause 295 deviations of ± 1 % in the water mass and volume fraction measurement. However, at 296 higher snow densities the relative errors were considerably less. 297 The snow structure and the water content had a major impact on the electrical 298 properties showing the same behaviour like in the work of Camp and LeBraque (1992). 299 In both works the electrical power increased with increasing water content and drops 300 at one point again. Based on the findings we divided the heating process in three 301 areas, shown in Fig. 9:  Further, at higher density the structural connections between ice crystals were less 308 destructed by the pore volumes. This allowed a higher rate of flow of electric charge 309 leading to a higher electric current. Additionally, the electrical potential between the 310 two copper-plates was less affected by the pore volume leading to a more stable 311 voltage and smaller phase shift between voltage and current. As a result, the electrical 312 conductivity increased resulting in a lower impedance and a higher electrical energy 313 transfer. 314 (2) Wet snow: Snow was becoming a particularly complicated medium because the 315 introduction of liquid water caused rapid changes of the important material properties. 316 The temperature stagnated at 0°C and the presence of uniformed distributed liquid 317 water changed the dielectric properties of the snow sample. Additionally, the liquid 318 water layer at the surface allowed the mobility of protons resulting in stronger rate of 319 flow of electric charge and therefore enhanced the electrical conductivity. This reduced 320 the impedance of the two-phase material significantly leading to a decrease of the 321 impedance and phase shift, and an increase in electric current and power. 322 Based on the findings, water percolation occurred over a narrow range of values in 336 coarse-grained snow (see Table 3) and was initiated at around 5-8 % of the mass 337 volume (see Table 3). For high snow densities where the surface-to-volume ratios 338 were small, our results were lower than found by Coléou and Lesaffre (1998). 339 (2) they fully saturated the snow sample for about 5 minutes. Therefore, the surface 342 tension of water had an additional effect, like a suction effect, holding more water in 343 the pore space. In our approach water could not be held immobile as the percolation 344 started earlier at the smooth ice surface. 345 Although the micro-CT measurements (see Fig. 7) showed a snow sample after the 346 water percolation point, still preferential spots of water accumulation inside the snow 347 structure could be seen. Three interesting observations were visible after percolation: 348 (1) No water film around the snow structure but isolated smaller and larger water 349 accumulations were visible indicating that phase change from ice to water were 350 happening on preferential spots on the ice crystal. However, it has to mention that the 351 pixel resolution was too coarse to detect an additional thin water film around the snow 352 structure. The created water led to a stronger rounding of the ice crystals and the 353 dendritic structure further disappeared. Nevertheless, no big change in grain shape 354 was observable due to the high density. (2) The gravity had no influence on the 355 orientation of the accumulated water on the ice crystal. It is apparent that the water 356 was uniformly distributed on the single ice crystals. The water droplets were too small 357 to be distracted by the gravity. (3) Single water accumulation links between single 358 neighbouring ice crystals can be seen. The refreezing of the snow sample after the 359 experiment led to single crystals agglomeration and a growth in size of snow crystals 360 (Colbeck and Davidson, 1973). 361 The electrical heating procedure developed to incrementally melt snow in order to vary 362 the water content and to analyse the created water non-destructive in a micro-CT 363 worked very well. Improving the experimental setup that the frequency can be 364 increased to the GHz-MHz regime for a short period of time, the exact dielectric snow 365 https://doi.org/10.5194/tc-2020-56 Preprint. Discussion started: 3 May 2020 c Author(s) 2020. CC BY 4.0 License.
property based on the snow morphology and water content can be extracted. This will 366 allow to improve remote sensing and field measurements on the snow-water-367 equivalent Denoth, 1972, Koch et al., 2014). 368

Summary and Conclusion 369
We designed, fabricated, and tested an experimental setup for in-situ time-lapse Our results and conclusions indicate that there is a need for additional validation. 394 Specially, it would be crucial to not only look at the density but also at the specific 395 surface area of the snow at a given density which also affects the capillary forces and 396 https://doi.org/10.5194/tc-2020-56 Preprint. Discussion started: 3 May 2020 c Author(s) 2020. CC BY 4.0 License. therefore the starting point of water percolation. Ideally, the entire snow sample will be 397 tomographically measured before the experiment to extract the morphological 398 parameters. The primarily micro-computer tomography (CT) result (Fig. 7) shows first 399 promising visualization of the preferred spots of liquid water in three-dimensional 400 space without destroying the snow structure. However, more detailed measurements 401 are needed to make stronger statements about preferential spots of water 402 accumulations inside the snow sample.     Additionally, the CT sample holder with the 34 mm capacitor is shown. 561