KEYWORDS: Snow physics, electromagnetic properties, hydraulic properties

STRUCTURAL PHASE CHANGES OF LIQUID WATER IN ALPINE SNOW

A. Denoth *Institute of Experimental Physics, University of Innsbruck, Austria

ice, water and air - influences both the ele~magnetic and hydraulic response, and this 0a way to experimentally determine water geetry in the different saturation regimes.Experimental results of a ten-year field study agiven. Field measurements have been carriedout in the Alpine regions of the Stubai Alps inAustria, whereby only old or fim-type snow hbeen used with mean grain sizes exceeding 1mm in diameter and which is characterized byseveral melt - freeze cycles.

2. METHODS AND MATERIALS

Electromagnetic and hydraulic meaments have been done with old or fim-typeAlpine snow with mean grain sizes exceedingmm. Grain shape and size has been derivedfrom a photographical analysis of the individusnow samples (Denoth, 1982b); snow liquidwater content, W, has been measured by abrated dielectric probe (Denoth, 1994), snowrosity, <1>, has been calculated from the measUlied density, and snow water saturation S hasbeen calculated according to S = W/<1>.Electromagnetic measurements have been dusing a free-space technique, with the snow

* Institute of Experimental Physics, University ofInnsbruck, Technikerstrasse 25/4, A-6020 Inns­bruck, Austria. E-mail: armin.denoth@uibk.ac.at

Independent of the stage of metamorph­ism, liquid water in snow exists generally in dif­ferent geometric arrangements depending onthe amount of water present: the pendular regi­me with two different sub-zones, the funicular re­gime, a pendular-funicular transition zone andthe regime of complete saturation (Colbeck,1982; Denoth, 1982a). The pendular regime ischaracterized by isolated closed water bodiesand ranges from the adsorbed-liquid limit tosaturations at which some of the water bodiescoalesce. Recently, the existence of closed ring­shaped water bodies within the pendular regimeof Alpine snow which has experienced severalfreeze-thaw cycles has been proved (Denoth,1999). The funicular regime at higher saturationsshows continuous liquid paths throughout thepore space with an isolated and trapped gas­eous phase. The actual arrangement and geo­metry of the individual components of wet snow -

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1. INTRODUCTION

ABSTRACT: The way free water is arranged in the complex texture of Alpine snow is measuredseries of different methods: Broadband electro-magnetic measurements ranging fromfrequencies up to the microwave K-Band regime directly allow the detection of the geom •structure of the water bodies; hydraulic measurements - measurements of water percolation throor water drainage off an Alpine snow cover - show a significant change of water movcharacteristics which are caused by changes in the water geometrical configuration (structuralchanges) due to the natural variation in the free water saturation. Structural characteristics ofbodies included in snow are reflected by the dielectric depolarization fadors, the special case of .shaped water inclusions is reflected by the magnetic permeability.Field measurements have been carried out in the Alpine regions of the Stubai Alps, Austria, whemetamorphism of these Alpine snow covers is characterized by several melt-freeze cycles. Itthe existence of 4 main regimes of water saturation characterized by different structural propertiesthe free water bodies: the pendular zone with closed isolated water bodies, a funicular zoneconfluent water bodies, a transitional zone where isolated water bodies begin to merge, and aregime included in the pendular zone characterized by the existence of ring-shaped waterExperimental results of a ten-year field study are presented.

Fig.1 Free-space technique. H1, H2: hom an­tennas, I,R, T: incident, reflected and transmittedsignal.

sample placed in between two high-gain micro­wave hom antennas. The principle of operationis shown in Fig.1. Reflected and transmitted sig­nals are measured in the frequency range of 6up to 16 GHz by a network analyzer, modelHP8510A. Based on Fresnels formulae, snowdielectric permittivity, E = E' - LE", and magneticpermeability, ~ = ~'- L~", have been derivedfrom the measured total reflection and trans­mission coefficients. Data analysis to deducestructural parameters of the liqUid water com­ponent is based on the effective-medium modelof Polder and van Santen (1946). In this modelthe geometry ofthe solid 0ce) and the liquid(water) components are described by three-axialellipsoidal bodies, and are characterized by thecorresponding depolarization factors, G1,G2, andG3, with LGj =1. Measured snow magnetic per­meability is interpreted in terms of the induceddiamagnetic effect of conducting water ringsaround contact zones of ice grains (Denoth,1999), whereby the fraction of total water for­ming the rings has been used as fitting para­meter. So, the geometrical shape of the waterinclusions and the amount of water collected inthe special shape of pendular rings can bederived from electromagnetic measurements.

It is obvious that changes in water geometry andarrangement affects the flow characteristics ofwater in snow. Consequentely, additional infor­mation as to the lower limit of the funicular zoneor as to the range of bound or immobile waterWithin the pendular zone can be obtained. So, inaddition to the electromagnetic measurements,water movement through snow has been studied

Fig.3. Dependence of shape factor G2 on liquidwater saturation.

Water saturation S ['Ill]

Fig.2. Dependence of shape factor G1 on liquidwater saturation.

: .

40

40

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30

30

funicular zone

funicular zone

20

20

W8Ier s8lUflllion S ['Ill]

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10

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40 zone

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1200 , :. . ..: .: ; ~ ;.....

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... .i 25 ·f>: .... ··'1[. 20 ..: - -.- .. -......•..................................... _ .... --

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Electric and magnetic permeability of atotal of 151 snow samples has been measuredin the frequency range of 6 to 16 GHz, wherebywater saturation S of the natural snow samplesvaried from 0% to 40%. Based on Polder andvan Santens effective medium model the charac­teristic shape factors, Gi, have been calculatedusing least-square fitting routines. Fig.2 andFig.3 show the dependence on water saturationof G1 and G2, respectively. Regions, wheresignificant changes in the shape factors can beobserved are marked by arrows.

in the field by long-term drainage and percola­tion experiments. To be independent on the ac­tual weather conditions, natural melting and/orprecipitation rates have been simulated. experi­mental setup and data evaluation is describedby Wilhelm et al. (1992).

3. EXPERIMENTAL RESULTS

,--­I,

!

253

10 12 ,. 16

water sfJIuralion S ['l>]

Fig.4. Dependence of magnetic loss on watersaturation.

Both shape factors, G1 and G2. vary significan­tely with water saturation: funicular and pendularsaturation regimes are clearly separated by atransitional zone ranging from S -8% to -13% ofthe pore volume. Within the pendular regime atliquid saturations S lower than a critical satura­tion, Se, [Se:::: 4%], a subzone is formed charac­terized by a strongly decreasing shape factor G1:

G1~ O. In the subzone 0 < S < Se capillaryforces and surface tension may be dominant andcontrol the geometric shape of the water inclusi­ons. for S > Se , gravity forces may play the do­minant role.The dependence of magnetic loss IJ" on watersaturation is shown in Fig.4 for a selected fre­quency of f = 14 GHz. Regions. where significantChanges in the 'induced'diamagnetic losses canbe observed are marked by arrows.

A detailed analysis of long-term drainage andpercolation experiments shows. that the 'gravityflow' theory (Colbeck, 1971) is suitable to modelwater flux through (homogeneous) snow only forinitial saturations less than approximately 14% ofthe pore volume; for higher saturations consider­able higher initial fluxes are observed. This maybe explained by the formation of an additionalflux in an spacially unstable channel system builup by merging water bodies in the pendular-funi­cular transition zone. Consequentely, an upperlimit of S :::: 14% for water saturation of the transi­tional zone is also confirmed by hydraulic mea­surements. In addition to the measurement ofwater flux. water saturation has been recordedautomatically, and it approaches asymptoticallya limiting value Sj with Sj = S(u* ~ 0): Sj :::: 4%. Itmay be of interest, that Sit the irreducible watersaturation, compares excellent to the crititcal sa­turation, Se, derived by electromagnetic measu­rements, and Se and Sj may be identical. Conse­quentely, the saturation zone 0 < S ~ Se == Sjwithin the pendular regime is characterized bythe domination of caplillary / surface forces overgravitational forces.

Measurements of the electromagneticand hydraUlic response of wet coarse-grainedAlpine snow - which has experienced freeze­thaw-cycles - confirm the existence of ring -

4. CONCLUSION

1.9::: ....A.i=15%,..

1.2 . ,. I ~ .. ·t··· ..

.~ ::: I.-.~.< :S < 11% :... .. ., ..

0.6 ,.........~~.~,;t:: ,.T.. :.. :· .0.4 >;:~: , .

:~~ .0.2·· .. ···· .. · .. ····· • ~_ .: : : :~'..:.o~:..~ .....o~ : , -

t·

Fig.5. Variation of relative water flux u* with timefor initial saturations of S=15% and S<11 %.

respectively. To be independent on the actualinitial hydraulic conditions of a specific experi­ment. the measured quantities flux u and timethave been related to intrinsic quantities Uo andto: u* = uluo , t* = tIta.

.......... -.;....

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. . .. : ~ funicular

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Compared to the low intrinsic magnetic permea­bility of bulk water, the relative high apparentmagnetic losses are caused by electrically con­ducting ring - shaped water bodies. The range ofexistence, however, is limited to low water satu­rations, well within the pendular regime: for satu­rations less than approximately 5% more or lessall the free water seems to be arranged in ring­like structures. For saturations exceeding :::: 8%magnetic losses decrease drastically, indicatinga merging of water rings whereby closed sphero­idal water bodies are formed. This transitionalzone is followed by a zone characterized byIJ" = 0. and this zone compares favorably withthe funicular zone defined by the shap factors Gj.

Fig.5. shows a typical characteristic of watervolume flux u* shown vs. time t* for two differentinitial water saturations, S<11%, and S=15%.

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h ed water bodies for saturations less than a~~I saturation Sc ~ 4%, where surface forcesd minate over gravity forces. This regime is part~the pendular regime which extends to a satu-

o fon of S ~ 8%, characterized by the increasing~ ~ortance of gravity forces. The transition from~~e pendular regime to the funicular regimeccurs in a relatively broad range of saturations~tween ~8% and ~1~ %, ~n~ is charact~rizedby merging water bodies bUlldmg up contmuous

liquid paths.

5. ACKNOWLEDGEMENTS

The Wintersport Tirol AG' is thanked forsupporting in part the field experiments made inthe Stubai glacier area.

6. REFERENCES

Colbeck, S.C., 1971. One-dimensional waterflow through snow. CRREL Res. Rep.296, Hanover, NH.

Colbeck, S.C., 1982. The geometry and per­mittivity of snow at high frequencies. J.Appl.Phys. 53(6),4495-4500

Denoth, A., 1980. The pendular-funicular liquidtransition in snow. J.Glac. 25/91, 93-97

Denoth, A., 1982a. The pendular-funicular liquidtransition and snow metamorphism.J.Glac., 28, 99, 357-364

Denoth, A., 1982b. Effect of grain geometry onelectrical properties of snow at frequen­cies up to 100 MHz. J.AppI.Phys., 53,11,7496-7501

Denoth, A., 1994. An electronic device forlong-term snow wetness recording.Annals Glac., 19, 104-106

Denoth, A., 1999. Wet snow pendular regime:The amount of water in ring-shapedconfigurations. CRST 30,13-18

Polder, D. and J.H. van Santen, 1946: The ef­fective permeability of mixtures of solids.Physica 12, 5, 257-271

Wilhelm, T., Rechenmacher, J., and A. Denoth,1992. Transport of water and dye tracersthrough snow. Proc. ISSW 1992, 365­370

255

[EXTENDED ABSTRACT]

Charles Fierz* and Michael Lehning

KEYWORDS: snow cover simulation, snow cover structure, snow texture, snow physical pro

3 SNOW COVER MODELING

Figure 1: Settlement and temperaturesensor laid on top of the snowpack before asnowfall. The sensor is clipped onto thevertical guiding and depth measuring wires.

frame across which a continuous tungstis stretched to record temperature. Its sideare clipped to two vertical wires serving asguides and electric connectors to deterrn'sensor's depth. As snowfall buries the sethe latter settles with the underlying sn(Weilenmann, 1999).

A full description of SNOWPACK is bey0n4the scope of this paper and the reader is refe"­to the publication by Lehning et al. (1_Nevertheless it is worth mentioning 118important properties and processes such asthermal conductivity and viscosity as well 8$bond and grain growth are based on miClO"structural model formulations. Each of these haSits own free parameter which has to be adjustedfrom experimental data. However, because e.g.conductivity and bond growth are related, aconsistent set of parameters must be found.

*Corresponding author address: Charles Fierz,Swiss Federal Institute for Snow and AvalancheResearch, FIOelastrasse 11,CH-7260 Davos Dorf, Switzerland;phone: +41 81 41701 65; fax: +41 81 41701 10;E-mail: fierz@slf.ch

INTRODUCTION

During the exceptional winter 98/99,7 speciallydesigned sensors were used to recordcontinuously both snowpack settlement and snowtemperature in situ at the SLF study siteWeissfluhjoch/Davos, 2540 m a.s.1. The viscousbehavior of quite different snow layers could thusbe monitored under large and rapid naturalloading.

It is well known that snow texture effectssettlement of the snowpack. New snow, layers ofeither small rounded grains or larger faceted andcup-shaped crystals as well as wet snow allshow different viscous behaviors. In snow-covermodels, this effect is taken into account eitherassigning each type of snow a distinct viscositylaw, or e.g. as function of temperature anddensity or by modeling snow viscosity completelyin terms of microstructure parameters such asgrain and bond size, bond neck length,coordination number and density. The latterapproach was chosen in the Swiss snow-covermodel SNOWPACK.

These in situ measurements as well asexperiments done in the cold laboratory allowedto find a consistent set of parameters to improvemodel performance.

2 IN SITU MEASUREMENTS

Swiss Federal Institute for Snow and Avalanche Research SLFFIOelastrasse 11, CH-7260 Davos Dort, Switzerland

EFFECT OF SNOW TEXTURE ON SNOWPACK SETTLEMENT RAT

One of the sensors used for this study isshown in Figure 1. It consist of a balsa wood

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