AD- A256 299 9R *UIIUIUIIII•

0P Determination of the Water Content of

Snow by Dielectric Measurements

Paul R. Camp and David R. LaBrecque July 1992

a-, DTIC

S ELECTE

OCT23 

1992 U

92 1 039227801
The dielectric properties of wet and dry natural snow were studied In the

frequency range of 50 Hz to 100 kHz to deterrnlne wfether measurements

made In this frequency range might prove useful in evaluating the water

content of snow. Dielectric heating at 20 kHz proved a very useful means of

modifying the water content from 0 to 30% by weight. Six different natural

snows were used in these experiments. Meltwater was analyzed for conductivity, pH, and Impurity content. In addition to developing Information on the

dielectric properties of wet and dry snow, we measured the changes produced

in dry snow by altering Its density overthe range of 0. 11 to 0.66 g/cm3.Details

of the experimental technique and the data obtained are fully reported. Our

results do not lead to optimism about the usefulness of measurements In this

frequency range alone for the determination of water content.

For conversion of SI metric units to U.SJBrltlsh customary units of measurement consult ASTM Standard E380, Mfr Ptce Gukde, published by the

American Society for Testing and Materials, 1916 Race St., PhIladelphia, Pa.

19103.

This report Is printed on paper that contains a minimum of 50% recycled

material.
Special Report 92-18 U

U.S. Army Corps

of Engineers

Cold Regions Research &

Engineering Laboratory

Determination of the Water Content of

Snow by Dielectric Measurements

Paul R. Camp and David R. LaBrecque July 1992

Accesion For

N-IS CR INDC ,

B y .. .................... .......... ........

A•, ~Lbiy •., Cccdbs

Dis•t t Av2l N . or S ,.ca

Prepared for

OFFICE OF THE CHIEF OF ENGINEERS

Approved for public release; distrbution is unlimited.
PREFACE

This report was prepared by Paul R. Camp, Professor, of the Department of Physics, University

of Maine at Orono, and David R. LaBrecque of Micro Physics, Old Town, Maine. Funding for this project was provided by DA Project 4A762784AT42, Design, Construction and Operations Technology

for Cold Regions, Task FS, Work Unit 032, Mesoscale Prediction in Denied Areas.

The authos thank Kurt Knuth and Gary Koh of CRREL for technically reviewing the manuscript

of this report. They also express their appreciation to Ronald Atkins of CRREL for many hours of

technical discussion during the progress of this work as well as for review of the manuscript.

The contents of this report are not to be used for advertising or promotional purposes. Citation of

brand names does not constitute an official endorsement or approval of the use of such commercial

produ'ts.
CONTENTS

Page Preface .......................................................................................................................................... ii

Introduction .................................................................................................................................. 1

Background .................................................................................................................................. 4

Literature review ..................................................................................................................... 4

M odeling by com puter ....................................................................................................... 4

Com puter tools for data m anagem ent and interpretation ........................................................ 6

Experim ental design ..................................................................................................................... 7

D ielectric m easurem ents ........................................................................................................ 7

Sam ple water content ......................................................................................................... 7

M onitoring dim ensional change ............................................................................................ 7

O verall design .......................................................................................................................... 8

Sam ple preparation and properties ............................................................................................... 11

H arvest and storage ................................................................................................................. 11

Properties ................................................................................................................................. 12

Control experim ents ..................................................................................................................... 12

Electrode m aterials .................................................................................................................. 12

Sam ple distribution in the cell ............................................................................................... 12

Effects of pressure ................................................................................................................... 12

D ielectric experim ents for wet and dry snow ............................................................................. 13

Experim ents on aged snow .................................................................................................... 13

Experim ents on new snow .................................................................................................... 17

D iscussion ................................................................................................................................ 17

The effect of density ..................................................................................................................... 27

Conclusions and recom m endations .......................................................................................... 32

Technique ................................................................................................................................ 32

M eltw ater ................................................................................................................................. 33

D ry snow ................................................................................................................................. 33

W et snow ................................................................................................................................. 33

A nnotated Bibliography ............................................................................................................... 34

Appendix A : D ata table ................................................................................................................ 37

A bstract ........................................................................................................................................ 39

ILLUSTRATIONS

Figure

1. Approximate dielectric constants of ice and water as a function of frequency at 00C ....... 2

2. Approximate electrical conductivities of ice and water as a function of frequency ........... 2

3. U nit cube ............................................................................................................................. 3

4. Example of matching a model to experimental results using data available from dielectric spectrum of portland cement paste cured for one day ............................................ 4

5. Example of matching a model to experimental results using data available from dielectric spectrum of portland cement paste cured for 35 days ....................... 5

6. Equivalent parallel capacitance and conductance as functions of frequency for the network show n .................................................................................................................... 5

7. Properties of the netw ork show n ........................................................................................ 6

8. M easurem ent cell for experim ents 1, 2 and 3 ................................................................... 8

iii
Figure Page

9. Measurement cell for experiments 10-16 .......................................................................... 9

10. Circuit arrangement for measuring dielectric properties of wet snow ............................. 10

11. Photomicrographs of snow samples I through V .............................................................. 11

12. Temperature, power level, and sample thickness as a function of time during a typical

experim ent ...................................................................................................................... 13

13. Electrode separation vs percent water for sample 3 ........................................................ 13

14. Dielectric spectra for sample 1 for indicated water contents ............................................ 14

15. Dielectric spectra for sample 2 for indicated water contents ............................................ 15

16. Dielectric spectra for sample 3 forindicated water contents ............................................ 16

17. Dielectric spectra for sample 13 for indicated water contents .......................................... 18

18. Dielectric spectra for sample 16 for indicated water contents .......................................... 19

19. Dielectric spectra for sample 10 for indicated water contents ......................................... 20

20. Dielectric spectra for sample 16 for indicated water contents ......................................... 21

21. Dielectric spectra for sample 12 for indicated water contents ......................................... 22

22. Dielectric spectra for sample 14 for indicated water contents ......................................... 23

23. Dielectric spectra for sample 15 for indicated water contents ......................................... 24

24. Logl0 low-frequency conductivity and loglo low-frequency dielectric constant for

various snows vs pH of the melt water ....................................................................... 25

25. Concentrations of sodium and chloride ions vs conductivity of the meltwater for various

snow s .............................................................................................................................. 25

26. Logl0 percent water vs logl 0 dielectric constant at 5 kHz .............................................. 25

27. Micrometer cell used for variable density experiments ................................................. 28

28. Conductivity and dielectric constant as functions of frequency for sample 5 ................. 29

29. Conductivity and dielectric constant as functions of frequency for sample 6 ................. 29

30. Conductivity, and dielectric constant, as functions of frequency for sample 7 ............... 29

31. Conductivity, and dielectric constant as functions of frequency for sample 8 ................ 30

32. Conductivity and dielectric constant as functions of frequency for sample 9 ................. 30

33. Conductivity and dielectric constant at 50 Hz vs density for the samples indicated

by the num ber ............................................................................................................ 30

34. Conductivity, a, and dielectric constant, K, at 500 Hz vs density for the samples indicated

by the num ber ............................................................................................................. 31

35. Conductivity, a, and dielectric constant, K, at 5 Hz vs density for the samples indicated

by the num ber ............................................................................................................. 31

36. Conductivity, o, and dielectric constant, K, at 50 kHz vs density for the samples indicated

by the num ber ............................................................................................................. 31

37. Conductivity, o, at 50 kHz minus that at 50 Hz vs density for dry snow ........................ 31

38. Dielectric constant at 50 kHz minus that at 50 Hz vs density for dry snow .................... 32

39. Logl 0 K vs logl 0 density for dry snow samples ............................................................. 32

40. Log1 0 K vs logl 0 density for samples 10-16 having water contents between I and 3% .... 32

TABLES

Table

1. Properties of snows used ................................................................................................ 10

2. Sam ple data ......................................................................................................................... 12

3. Polynomial fit to data for samples 10-16 ....................................................................... 26

4. Cole plot parameters for the various samples ................................................................ 27

5. Cole plot parameters for the various samples ................................................................ 28

iv
Determination of the Water Content of Snow by

Dielectric Measurements

PAUL R. CAMP AND DAVID R. LABRECQUE

INTRODUCTION Figure 1 shows the approximate dielectric constant

for ice at 0°C as a function of frequency (solid line). The

Knowledge of the free water content of snowfields is dielectric constant of water is also shown (dashed line).

important in snow mechanics, hydrology, avalanche It would appear that one might easily determine the

control and in satellite imagery interpretation. Various water content of the snow by combining a very low fretechniques for determining the water content of snow quency measurement of effective dielectric constant (in

have been employed, but these measurements must be which the contributions of the water and the ice are nearmade by teams in the field. Direct methods reviewed by ly equal) and a high-frequency measurement in which

Boyne and Fisk (1990) include melting and freezing they are very different. However, avarietyofthingsdiscalorimetry, alcohol calorimetry and ionic dilution. tort the low-frequency end of the ice spectrum, as is

Electrical methods have focused on measurements of shown by the dotted line. These include impurities and

the dielectric properties at frequencies at which the di- electrode polarization effects. As frequency increases,

electric constant of water is high and that of ice is low, the importance of these anomalies decreases but we get

generally above 1 MHz. These methods, reviewed by into the dispersion part of the curve where the calculaDenoth et al. (1984), also involve field studies because tions become more difficult.

they require an independent measurement of density. Figure 2 shows the approximate dispersion with freClearly, it would be highly desirable to be able to make quency of the conductivity of pure ice (solid line) and of

free water determinations by remote sensing orby auto- pure water calculated from the relaxation (dashed line).

matic instruments that can be interrogated remotely Again one might hope to be able to infer the relative

without the need for field measurements. amounts of water and ice in a sample by measurements

A wide spectrum of frequencies has been explored at two frequencies, one well below the ice dispersion

for electrical methods of determining the free water and one above. However, as is shown in Figure 2, the

content of snow, the most popular being the UHF or low-frequency end of the dispersion flattens out due to

microwave ranges. It is here that water has a high dielec- the DC conductivity of ice and to the presence of other

tric constant (about 88 at 00

C) and ice a low dielectric low-frequency dispersions. Moreover, both the DC

constant (about 4), thus providing good contrast to conductivity of ice and the strength of the dispersion are

reveal the presence of water. Typically these measure- sensitive to impurities in the ice. More important still,

ments focus on the behavior at one frequency only. In the DC conductivity of water is dominated by ions. The

this study, we have chosen to see what might be learned thermal dissociation of water alone gives pure water a

from measuring the dielectric response over the low- resistivity at room temperature of 5 x 105 ohm-m. Disfrequency range in which ice has a Debye dispersion. solved CO2 from the atmosphere can decrease this to

Our thought was that by knowing the dispersion prop- 2 x 104 ohm-in. The respective conductivities are also

erties of ice, measurements at several frequencies over shown in Figure 2 as dashed lines. Since additional imthe dispersion region might provide simultaneous equa- purity will raise the conductivity even further, this

tions the solution of which would yield the water con- baseline is very strongly dependent on impurities. We

tent without an independent measurement of density. conclude that the measurement of dielectric constant is

The argument is given in more detail below, more promising than that of dielectric loss.
too - ........... ..

atr

10 f

7

5

3

2

2 3 5 7 1 0 3 

1 0 4 

1 0 5

Frequency (Hz)

Figure I1. Approximate dielectric constants of ice and water as afunction of

frequency at OC (extrapolated from Camp et al. 1967).

10-4.

a(ohm-m)- 1

I. ) Distilled water

(p = 2xl 04 ohm-m) _.----

fo 20 kHz

10 Ice 10- 8 i/

........... S. . - Conductivity water

(p= 2 x 105 ohm-m) Calculated

104- from /0^ ,relaxation /7 (use scale

.5 2 3 57 at right) 

*

103 

104 

105

Frequency (Hz)

Figure 2. Approximate electrical conductivities of ice and water as afunction ofI

frequency. Dashed line to the right shows the conductivity of pure water calculatedfrom its relaxation spectrum (use scale at the right for these values) (data

from Camp et al. 1967).

2
Although the low-fre- Hippel 1972). Perhaps this can be overcome by making

SI i quency measurements measurements at several different frequencies through- / may be distorted by elec- out the Debye dispersion range and using these to effec- /1:f /A trode and other phenom- tively project the true low-frequency value.

ena as mentioned, it now To illustrate the -eornetrical problems, we refer

T appears possible to use again to Figure 3. If instead of placing electrodes on the

---------- measurements in the dis- top and bottom of the cube, we place them on the left-

/ persion region in a fairly hand and right-hand sides, we have an entirely different

, ,, simple way. The advent geometry. The air, water and ice are now in series in-

, , of inexpensive, hand- stead of in parallel. Our measurements would give

held, programmable com- entirely different values, as

puters makes possible the

-i -I 11 rapid interpretation of this C meas_1

Figure 3. Unit cube, more complicated data. l/CA+ 1/Cw+ l/Ci

It can be automated in the

field, almost in real time. instead of CA + Cw + Ci in the parallel case.

As shown in Figures I and 2, the dielectric properties As a specific illustration, let us supposefA = 0.8,f1 =

of ice change rapidly in the dispersion range, while 0.15 andfw = 0.05. For the parallel case (eq 1), using ki

those of water are essentially constant. Thus we should (low) = 100, k, = 88, and ki (high) = 3.5,

be able to separate the effects of water and ice by measurements at different frequencies. We pick an overly Cmeas (low freq) = 20.2cv

simplified case for illustration.

Let us suppose that the various components of a sam- Cmeas (high freq) = 5.73Ej.

pIe, ice, water and air, could be modeled as acting in

parallel as shown in Figure 3, a unit cube. If electrodes In the series case , we would have,

are applied at the top and the bottom, the contributions

to the measured capacitance of each material would be Cmeas (series) = r0 l (3)

in parallel. LetfA,fw, andfi, be the volume fractions of fA + f/ki + fJkw 3

each material and CA, Cw and Ci the partial capacitances

due to air, water and ice. respectively. Using F-0 as the Cmea (low freq) = 1.247F-o

permittivity of free space (air) and kw and ki as the

dielectric constants of water and ice, we have C mea- Cmeas (high freq) = 1. 86cO.

sured (Cm) given by

These approximate the two extreme cases for the possiCm = CA + Cw + Ci = E0(fA + kvJ, + k/). (1) ble grain structure of snow, parallel columns and series

plates. Thus, from the measurements themselves, one

Also might be able to infer something about the grain structure. However, the situation is even more complicated

fA Jw +fA = 1 (unit cube). (2) than this. Temperate snow is a complex structure of

grains of ice of various shapes in series and parallel

Since ki (high frequency) is very different from ki combinations with water that has electrical conductiv-

(low frequency), if we measure C at both high and low ity as well as dielectric constant. (This is also a problem

frequencies, we have three different independent equa- with microwave measurements.) Thus in the end, the

tions and thrce unknowns. Therefore, we should be able measurements must be calibrated against samples hayto solve for fA, fw and .i, without an independent ing known properties. But these complicating factors

measurement of density. Unfortunately the situation is have their positive side as well. If we measure at a nummore complicated for two basic reasons. The first is ber of points over the range of the Debye dispersion, we

electrical and has already been touched on. The second might be able to develop a set of profiles each of which

is geometrical, is uniquely characteristic of a specific water content,

The electrical problem with capacitance measure- density and snow structure. The studies reported here

ment is that the low frequency capacitance is complicat- were undertaken to explore this possibility.

ed by electrode and impurity effects and the possibility In this specific effort, we have been so far unsuccessof very low-frequency dispersions for ice, which have ful. However, in the process, we have developed what

been reported in the literature (Camp et al. 1967, Von we believe is a significant tool for studies of wet snow,

3
some useful insights into the process involved, and a Modeling by computer

body of specific information concerning the dielectric Because any electrical analog we might make inproperties of snow, both wet and dry, in this frequency volves the series-parallel interconnection of resistors

region. In order to make this information generally and capacitors, an interactive computer program has

available and useful we give in this report a rather de- been developed (using Microsoft Quick-Basic, version

tailed account of our experiments and their results. We 4) that allows us to model resistance to capacitance

have found no such extensive information in the liter- circuits of almost any complexity. If we have a model in

ature and hope that this work will provide a useful basis mind, we can try it out and plot its capacitance and confor theoretical or further experimental studies. ductance spectrum. We can also go to the other extreme

and find out how tinkering with a circuit will change its

characteristics. Figures 4 and 5 are examples of the first

BACKGROUND process. We happened to have available dielectric spectra for portland cement samples and a model that had

Literature review been proposed to describe two different states of curing.

A computer search was conducted covering the fol- By adjusting parameters, we were able to fit the data for

lowing databases and years: "Information Service for cement cured only one day (Fig. 4) and cement cured 35

Physics and Engineering (INSPEC)," 1969-1989; and days (Fig. 5). Figures 6 and 7a are examples of the

"Engineering Index," 1970-1989. This was supple- second process. We asked whether it was possible to

mented by a manual search of the CRREL abstracts for create from resistors and capacitors alone a network that

the years available to us. 1961-75. We are indebted to would have a dispersion curve in which the capacitance

Ronald Atkins who has provided us with further titles would drop (and the conductance would rise) over a

from the CRREL abstracts. All references that we have wide frequency range, not as frequency squared, but as

found useful to this line of study are included in the frequency toalowerpower(as happens in snow). These

Annotated Bibliography. figures show that it can be done. Figure 6 shows that by

Log Cp(F) Log Gp(S)

-4 0

-5 -

-6 -2

-7 -3

105 F 100f)

-8 -4

-9 20 2. Id°F

~ 2O(~ 200f

-10 -6

1 2 3 4 S 6 7

FRECJENCY

Figure 4. Erample of matching a model to experimental results using data available from dielectric

spectra of portland cement paste cured for one day.

4
Log Cp(F) Log Gp(S)

-5-

-2

"1" ,] -5

-10 F 

--4

2 3 4 5 6 7

FREQUENCY

Figure 5. Example of matching a model to experimental results using data available from dielectric

spectra of portland cement paste cured for 35 days.

--37

-7

-7

1 2 3 4 5 6 7 8

Frequency (Hz)

Figure 6. Equivalent parallel capacitance and conductance as

functions offrequency for the network shown.

5
Log Cp(F) Log GP(S)

:",Cpl D~pI

-9"

-4 .1-12 /7

1 2 3 4 5 6 7 e

Frequency (H)

a. Equivalent parallel capacitance and conductance as functions

offrequency for the network shown.

600

400 ... ...... 5 K. . ....

00K.*

-200 .

-4003 . . . . . . . . . . . . .

•-600.

-600I I

0 200 400 600 800 1000 1200

K'

b. Cole plot for the network of 7a.

Figure 7. Properties of the network shown.

doubling C per section and keeping G co.,stant, the total torted for this distribution of Debye relaxations. Both of

capacitance can be made to fall as the first power of the these features show up in our data for snow.

frequency from about 200 Hz to 20 kHz. Figure 7a

shows that if C is "alved and G is doubled for each Computer tools for data management

succeeding section the total C falls and the total G rises and interpretation

as the square root of frequency over about three de- Each snow experiment involved ihe collection, procades. Figure 7b shows how the Cole semicircle is dis- cessing and organization of a large variety of data. 6i
These data included time, sample temperature, plate the water content of a particular sample which remains

separation, snow parameters, power measurement and undisturbed in the test cell. To this end, we have develdielectric properties as a function of frequency. The oped a method of electrically melting the sample itself.

data entry, processing and organization was simplified In doing this, two things are important: the heat genby the use of a computer spreadsheet (Quattro by Bor- erated must be uniformly deposited in the sample and it

land)on a standard IBM AT microcomputer. The spread- must be measurable with sufficient precision. Direct

sheet was used for the calculation of snow water con- current heating, perhaps the simplest approach, is unsattent. During the dielectric heating of the snow, the isfactory because once a liquid path has been created,

power was calculated from the current, voltage and ionic conduction will cause most of the heat to be dephase measurements. Numerical integration of power posited along that path, which will become larger and

during the heating process determined the heat input larger. To ensure that the energy is uniformly deposited

and thus the water content. The spreadsheet was also in the ice itself, we use the heating due to dielectric loss

used in calculating the conductivity and dielectric con- in the ice. Thus we choose a frequency of the order of,

stants, and the data for the logarithmic graphs and the or higher than, the Debye dispersion frequency for ice

Cole plots. (fD). If we used microwave heating, we would again

To further analyze the data, an interactive, curve- find water absorbing much of the energy. Moreover,

fitting program was written in Microsoft Quick-Basic, microwave heating would be hard to monitor.

version 4.This program finds the parameters giving the We have chosen 20 kHz as our working frequency.

best fit for a set of data to any type of polynomial speci- The power is monitored by measuring the voltage apfled by the user. plied to the sample, the current through it and the phase

angle between them. A Singer model LT PS-I1 oscillator

EXPERIMENTAL DESIGN and power amplifier supplies up to 1600 V at 20 kHz

from a 780-ohm source. Thus arbitrary increments of

Dielectric measurements heat can be added to a sample in situ and dielectric measMeasurements were made of equivalent parallel urements can be made after each increment without

capacitance Cp and equivalent parallel conductance Gp disturbing the sample. The circuit arrangement is shown

using a General Radio 1615A bridge in the three- in Figure 10.

terminal mode. The sample holders are shown in Fig- The most difficult aspect of this procedure is the

ures 8 and 9. The signal source was a General Radio measurement of the phase angle, which changes signifi1210-C oscillator and the detector was the General cantly with time. At the start, we monitored this using a

Radio 1232-A tuned amplifier and null detector. The dual trace oscilloscope. More recently, we have been

sample cells were placed inside an electrically shielded provided by CRREL with a Wavetek model 750 phase

oven, which was itself inside a commercial chest type meter. We now use both. In two cases, we checked our

freezer. The oven temperature was controlled by a water content as calculated by power measurement

Cole-Palmer model 2159 Versatherm controller using against alcohol calorimetry. In one, the energy calculaa thermistor sensor. Sample and oven temperatures tion gave a 20% water content and the alcohol caloriwere monitored by Yellow Springs Instrument linear- meteravalueof23%.Intheothertheenergycalculation

ized thermistors with digital readout on Keithley model gave 5% and the alcohol calorimetry 7.8%. To check

160 voltmeters. All probes were calibrated against a further on the alcohol calorimetric technique, we simHewlett-Packard 2802-A platinum resistance thermo- ply added 5% and 10% water to snow samples at 00 C

meter and zeroed in a common ice bath. and found that alcohol calorimetry gave us 7.4% and

14.5% readings respectively. This error was consistent

Sample water content with the higher readings given above and gives us

An obvious way to prepare snow of known water greater confidence in our power measurement procecontent is simply to add to dry snow at 00 C known dure than in our alcohol calorimetry.

amounts of water also at 00C. However, there are prob- We appreciate the comment of a reviewer who has

lems with this method. One of these is obtaining uni- called our attention to the fact that E. Brun (1989) had

form mixing. Another is that if either the snow or the previously used dielectric heating at 20 kHz to change

water is too cold, some of the water will freeze. If the the water content of snow by melting. In that paper,

water is slightly too warm, some of the ice will melt. Brun did not discuss his measurement of power.

Most importantly each time the watercontent is chaaged,

we must work with a new and possibly fundamentally Monitoring dimensional change

different sample that inevitably will be mixed and In preliminary experiments, we used a capacitance

packed differently. What we would like to do is to vary cell that had vertical plates 10 cm square separated by 2

7
To linear transducer

I 6 inn.

3/8 in Brs /j /// 7

2 Snow sample I in.

1 in.

Styrofoam Thermistor bead

Lucite centering rod Copper foil 1 2 3

10 cm

Figure 8. Measurement cell for experiments 1, 2 and 3. The electrodes are thin

copper foil.

cm. A vertical structure was used so that if waterdrained a continuous record of the position of the top plate. This

away from the top of the sample, good electrical contact also allowed us to correct for changes in sample thick- would be maintained over most of the sample and a ness when calculating conductivity and dielectric congood average measurement would still be made. How- stant.

ever, we found that even a very small amount of moisture caused the sample to shrink away from the plates. Overall design This we attribute to capillarity at low water contents. At Except where noted, all the measurements reported high water contents, there was also shrinkage due to the here were made using one of two sample cells. The first melting of ice. Thus we changed our basic design to a is shown in Figure 8. The housing is made of building- horizontal cell (Fig. 8) and included in it a device for grade dense Styrofoam having an R value of 6 for a I - monitoring the sample thickness by mechanically link- in. thickness (thermal conductivity of 0.024 W/m K). ing the top plate to a high resolution potentiometer on The electrodes are of thin copper foil to minimize the

top of the sample cell. The resistance of the potentiome- heat capacity. They are unguarded for fringing cap- ter was monitored on a chart recorder, which provided acitance. The guard terminal of the bridge is connected

8
To distance transducer

1 in. 0.25 in.

t ' Snow sample

1 in. Stn o e otyrofoam

trica 25y iaad ta vin. si

4% 1 3 2 .i 

Figure 9. Measurement cell(for experiments 10-16. In experiment w0, segments 2, 3 and

4 were guards and in experiments 11-16, segments 3 and 4 were guards and I and 2 connected together.

to the aluminum case of the oven. On top of the upper temperature of the sample. Figure 9 shows the design of

electrode and insulated from it both thermally and elec- the second cell that we used. This was a guarded cell

trically is a brass disk that provides a constant gravita- using 1/4-in. stainless steel electrodes. The loading protional loading of 1027 N/m2 (about 0. 15 lb/in.2). This is vided by this cell was 306 N/m2. In all other respects it

done to ensure that all samples in these experiments was very similar. (We show later that loading itself has

have the same packing, thus eliminating one possible a negligible effect on our measurements except as it

variable. A rod from this plate drives the precision changes density. The density of each sample was sepapotentiometer to provide displacement measurements rately measured.) Each cell itself was placed inside a

as the sample thickness changes. A thermistor bead in thick walled aluminum "oven,"which was in turn inside

contact with the bottom of the bottom plate monitors the the commercial freezer. The oven was wound with re9
Position I Heat

2 Measure

1 2

T To

° e-1 bridge :c Sample LC

20-kHz.0

source

: ,..Rc04 ( (Current)

S~Phase

Figure 10. Circuit arrangement for measuring dielectric properties of wet snow.

sistance wire through which DC current was passed to conductivity requires an accurate knowledge of sample

maintain the desired temperature. This was controlled dimensions, which are used in calculating the cell

by a thermistor sensor and Cole-Palmer Model 2158 capacitance and the effects of fringing. The dominant

temperature controller. The oven temperature was inde- uncertainty is in sample thickness. We estimate a compendently monitored and was normally maintained at bined uncertainty of 10% in absolute value and a reso-

-1 (±0.5) °C. lution of better than 1%. Density is measured by weighFigure 10 is a diagram of the electricai connections ing the sample to better than 1% and measuring its

to the test cell. Stray capacitances due to shielding of the thickness after the cell has been assembled. The absoleads, etc., are shown in dotted lines. Since the source is lute accuracy is estimated to be 10%, the accuracy of

of low impedance, C1 has negligible effect. Because of changes about 0.1%. We can resolve a change of thickthe bridge design, C2 and C3 can be neglected. Because ness of 0.01 mm while thickness is accurate to 1 mm.

RI is so small, it has a negligible effect on the measure- Temperatures are ordinarily measured with an accuracy

ment of V and C4 of this magnitude can be neglected. ofO.2°C and a resolution of 0.01 °C. Overall we believe

The performance characteristics are as follows: Cr our water content is accurate to 0. 1 times the reading

and Gr are ordinarily measured to 4 or more significant ±+0.5%, and our values for conductivity and dielectric

figureswithanaccuracyof0.1%overmostoftherange. constant are accurate to 10% of the reading with a

However, to translate this into dielectric constant and resolution of better than 1%.

Table 1. Properties of snows used.

Harvest data Melt Anal•ysis (p1) (eq 1)

Snow Date Temp (glcnrn) pH al Ca Mg K Na NH4 C1 NO3 S04

IA March 89 0.42 4.5 169

granular

IB March 89 0.52 6.04 3.56 227 10.7 4.3 74.4 1.6 70 10.5 203

Granular

iI 30 Dec 89 -8 0.38 4.27 2.80 11.5 3.3 4.3 52.6 nd 56 45.8 21

very fluffy

Ili 30 Jan 90 -2 0.41 5.36 0.305 5.0 nd" 1.5 1.7 nd 3 19 5

IV 5 Feb 90 -15.5 0.32 5.0 0.534 7.0 nd 1.3 1.3 nd 4 8.2 6

light fluff

V 25 Feb 90 -8 0.27 4.82 0.865 19.0 1.6 4.3 7.4 nd I I 13.4 17

fine & floc.

Vi** 31 Mar90 0 5.64 0.17 0.1 nd 4.8 nd nd 6 0.6 3

wet

Density as measured on 14 April 1990.

t Units of conductivity are milli (ohm-meters) -I or milli S/rn.

** Snow VI not used in measurement- reported here.

tt No data.

10
1 mm

VIVOI

1 mr bl 

p 41

M% 4
Properties we would always be comparing different samples. Thus

One or more samples of each snow harvesi were we used a cell with a bottom plate of copper and changed

melted and the conductivity and pH of each determined, the top plate without disturbing the sample. Top plates

In addition an impurity analysis was made. The results of aluminum, copper, stainless steel and a blocking

are summarized in Table 1. Not surprisingly, there is a electrode formed by insulating the top plate with a very

strong correlation between the NaCl concentration and thin layer of polyethylene were used. Measurements

the conductivity of the melt. It may also be of interest were made from 50 Hz to 50 kHz with very similar

that the charge of the total anions minus the total cations results in each case. The maximum difference in Cp,

is positive for the twolowest pHsnows and negative for which was found at 50 Hz, was only 12%. That in Gp

that having the highest value, was only 8%. We conclude that the electrode contribuSince the same snow harvest was used for a number tion was not a serious problem.

of experiments at different times and since properties

such as density and grain size vary with time, each Sample distribution in the cell

specific sample is identified by an (arabic) experiment Anotherconcem was thatourresults might be signifnumber. Table 2 is an index to the samples. icantly influenced by an undetected variation of the

distribution of snow in the cell. Snow was typically

Table 2. Sample data. placed in the cell as evenly as possible and then leveled

Measurement with a blade. To test the distribution we built the cell of

Experiment date Snow Code Experiment Figure 9 using stainless steel electrodes (this became

1 5 Sept 89 IA 8/89-A K o % W our cell of choice for later experiments). The top elec2 I1 Sept 89 IA 9/89-B K c % W trode was one piece, 10 cm in diameter. The bottom

3 15 Sept 89 IA 8/89-C K a % W plate comprised a central disk surrounded with three

1/90-A Test run of concentric rings with about one millimeter of insulation

1/90-B Test 

no interest run of between them. The central disk and each ring had ar

no interest area of 20 cm 2. By connecting all of the elements but

4 24 Jan 90 11 1/90-C Density one to the guard circuit, we were able to measure each

5 31 Jan 90 III 1/90-D Density region of the sample in turn without disturbance.

Loose guard ring Several experiments with snow and one using wet

6 31 Jan 90 111 I/90-E Density

7 5 Feb 90 IV 219-A e sand suggested a possible small radial decrease inp

8 8 Feb 90 I1 2/90-B Density and Gp, with the largest variation at low frequencies.

9 12 Feb 90 1B 2/90-C Density This induced us to use greater care in uniformly filling

10 1 Mar90 V 3/90-A Ka%W the cells.

!1 12 6 Mar 90 IV 3/90-B Ka%W

12 

6 

7 

Mar 

Mar 

90 

90 IV if 3/90-C 3/90-C K go%w% We also considered the possibility of an azimuthal

13 8 Mar 90 1B 3/90-D K a % w variation of snow distribution. To test for this possibil14 9 Mar 90 I11 3/90-E K a % W ity, we made a top plate that was segmented like a pie.

15 15 Mar 90 11 3/90-F K a % W We were able to sample one segment at a time and found

16 20 Mar 90 IB 3/90-G K o % W no significant azimuthal variation. This test also verified the uniformity of the test samples themselves.

CONTROL EXPERIMENTS Effects of pressure

As explained earlier, a standard sample loading was

At various times during our experiments, questions used to eliminate possible variations due to pressure

arose about possible sources of error. Each time we tried effects. However, the following experiment was done to

to devise experiments to check these. Although they explore the matter. A sample was measured with the

were conducted as the questions arose, they are grouped standard load. Then incremental loads of 500 g were

together in this section. added and the sample remeasured with each addition.

Each time the samples became slightly more comElectrode materials pacted and the values of Cp and Gp increased by 2-3%.

A recurrent question in our early experiments was But when all the extra loading was removed, the values

whether part of the dispersion we were seeing was an remained almost unchanged. We conclude that the

electrode effect characteristic of the electrode material. observed increases were due to increases in density, not

To explore this, we varied electrode materials. A prob- pressure. Later experiments on the effect of density (VI

lem with just using cells of various materials is that then B) confirm the large effect of density.

12
20 Sample 9/89-C 24

Thickness

S~H

| 10 G

0!F

Power

A B

010

0]

19

-8 1-18

10 30 50 70 90 110 130

Time (min.)

Figure 12. Temperature, power level, and sample thickness as a function of time

during a typical experiment

DIELECTRIC EXPERIMENTS FOR minutes as if the sample were relaxing slightly after beWET AND DRY SNOW ing loaded. Then the gradual packing at zero degrees,

followed by a sharp decrease at C as ice melts followed

Experiments on aged snow by successive decreases at E and G. These last two deBecause it was late December 1989 before we were creases do not stop abruptly with the cessation of power.

able to harvest fresh snow,many of our experiments had Moreover, the rate of drop is not as great as the first,

to use snow that had been harvested in the previous even though the power is larger. We suggest that capilMarch (snow I). This snow had already been on the lary forces may play a significant role in the first and that

ground for a week or more before it was collected. Con- the others are dominated by volume loss due to melting

siderable metamorphosis had already taken place when and rearrangement of the grains. The situation is illusit was first used. Its characteristics are listed in Table 1. trated in Figure 13 in which the electrode separation is

Figure 11 is a microphotograph of its structure taken in shown to change as the water content is changed by

March of 1990 when it was almost ayear old. At the time heating.

of these measurements, a typical grain dimension was Data for samples 1,2 and 3 are shown in Figures 14-

about 2 mm. For these experiments, cell I (Fig. 8 ) was 16. These measurements were all made using cell I with

used. 24

Figure 12, a plot of temperature, power and sample

thickness, illustrates how the experiments were con- E2

ducted. The sample was placed in the cell at about -60C, " 2

which was placed in the "oven" at -0.5°C. At this time, o 22........................

a measurement of Cp and Gp as a function of frequency

(a frequency scan) was made. " 21.........................

Over the first 32 minutes, the sample warmed slowly u)

to about -3°C at which point (point A), the 20-kHz T• 20

power was turned on and left on until B, heating the 0.

sample internally almost to zero. A second frequency ,

scan was then made. At about 62 minutes (point C), the 0 2 4 6 8 10 12

heating power was again turned on briefly until D. % Water

During this time ice was melted. Again a frequency scan Figure 13. Electrode separation vspercent water

was run, followed by another heat pulse, etc. Note the for sample 3, which shows the sample shrinking

gradual rise in the sample thickness for about the first 30 as percent water increases.

13
In

o 91

LrJ

LL..

ci -

q7. W

>1 001

V -4

>1 ~Q6

0 6 

'-

In W. Z

I i7

UIn 0 0 IIn

I. Ii S0
0

In

-u Z

0

IIt 4.%

A0

C. . "' 

' xI

q o - -

in '-

0 : '0 

0

p ~0

o -0.

q (N

_ _ _ _ _ _ __ _°__ 

...................... . ......... ... ,

8 o

0 0•' 0V 0

(,N-N/HO) kiAIAion(INOO 00"1 .-Y. • 

15
xw

L3.

rL&J. Y.

7n § 

N 0

C -D

NN

o~ E.oo

o~~ a .o

* "-

0

J. S.

0

ZA x~.

I~. ~ -

-~Q.

vi vi w

I 1a 1 C2 3 E4c

,ýN ~ ~ ~ ~ ~ C -VH)klloOO 0

16~3
copper foil electrodes. The curves for the log 10conduc- sample was heated to very close to zero using 20 kHz, as

tivity vs log10 frequency changetheircurvaturein going explained, and measured again. Thereafter, increments

from dry snow to even slightly damp snow. Then the of heat were added to melt some snow, and frequency

predominant change is a steady rise of the values with scans were run after each increment. Figures 17-23

water content. The increase with frequency is slow and show the data for these samples both as plots of the log

almost linear. The curves for the logl0 of apparent di- conductivity and logl0 dielectric constant vs log freelectric constant k also show a sudden change in going quency and as Cole diagrams. These data, while coverfrom dry snow to wet snow. Here again there is strong ing the same general range of values, differ in detail

sample-to-sample similarity except for the highest fre- from one another and from the earlier measurements.

quency points of sample 1. The log 10 of K falls roughly

in proportion to the log 10 of frequency. It was shown in Discussion

the Modeling by Computer section that this type of dis- Our major experimental results are summarized in

persion in both the dielectric constant and conductivity Figures 14-23. Numerical values are tabulated in Apis characteristic of a system having a number of Debye pendix A. For detailed information concerning the proprelaxations in parallel, each having a different relaxa- erties of any particular sample, see Tables 1 and 2. The

tion time. This is also seen in the Cole plots (Fig. 14- dominant source of absolute error in the measurement of

16c-f). conductivity and dielectric constant is the sample thickWe have used above the term "apparent dielectric ness. This is less than 10%. However, the conductance

constant" because at low frequencies we frequently find and capacitance were measured to 0.1% or better. We

values greatly exceeding that for pure ice or pure water. believe that the major source of error in the water content

Thus the microscopic geometry of the sample must be was inaccuracy in the power measurement. This might

very different from the geometry of our cell. There may cause an error between samples such that one sample

be conducting paths that make the effective plate area measured at 8% might have the same water content as

much greater than the true plate area and the effective another measured at 10%. But measurements on the

plate separation small. By the same argument, the term same sample should be ordered so that the relative errors

"effective conductivity" might be used. In the interest of are considerably less.

brevity, we will drop the word "effective" in the re- The general features of the dielectric data for all

mainder of this report. samples show a rather large low-frequency conductivity

The data for these three samples, all from snow LA, rising monotonically with frequency. This is compatible

form a consistent set for 10 different watercontents. For with a conductivity made up of two parts, a frequencyzero water content, they result in almost identical spec- independent ionic conductivity (protons) to which is

tra, giving us confidence in the reproducibility of our added a conductivity resulting from one or more dielecexperiments. When the water contents of different ex- tric dispersions. The dielectric constant data show these

periments are close, the spectra are very similar. This dispersions more clearly and indicate a range of dispertends to confirm our estimates of the reliability of the sions. The Cole plots show a range of dispersions in the

water content (± 1%). They were all taken within a space low-frequency range centered in the region of 100-200

of 10 days. The data for samples 13 and 16 (Fig. 17 and Hz and often a range of dispersions in the kilohertz

18) are for snow sample 1B, which was harvested with range. In general, both the conductivity and the dielecsample IA but from a different region and has a different tric constant rise with water content. On many samples,

conductivity and pH. These data were taken six months there is a change in curvature from concave up to conlater than those for snow IA and with the cell of Figure cave down on the logl 0 conductivity and log 10 dielectric

9. The figures are very different indeed, a fact that is constant vs frequency plots as the sample changes from

discussed in the Discussion below., dry to wet.

For dry snow, there appears to be a general tendency

Experiments on new snow for the low-frequency conductivity to be proportional to

After the winter snowfall began, we were able to ex- the H+ ion concentration and for the low-frequency

periment with different snows. For all of these we used dielectric constant to be proportional to the square root

the stainless steel cell of Figure 9. The center plate and of the H+ concentration. This is shown in Figure 24, in

first ring were connected together as one electrode and which are plotted the 50-Hz values of log conductivity

the outer two electrodes connected to the guard. (In the (circles) and log dielectric constant (crosses) as funccase of sample 10, all three outer rings were connected tions of pH (the negative log H' ion concentration) of the

to guard.) The procedure was essentially the same as meltwater of the various snows. Other ionic impurities

that used in A. First, frequency runs were made on the seem to have little effect. This suggests that the lowsample when it was several degrees below zero, then the frequency conductivity is the result of proton hopping.

17
in

9Z.,

I.I inN

Pi'Z !2

.9 x.

AN

ciN

NnN

In _ _ _ _ _ _ _ _

ve f C ~ - -I N

en q AIX

Cl 0 - -

Ia -n c

NOO

0 zi

x~ - .. ... a - . -8- W!N

40 40

L&J~ C kiidl V-R O 00- -. p -OO 

18 --
o -X

0Y

in SIXr

x

... .. .. .. ..O .. . .. . .. . .. . .. . N. 

viz--

CA..

en -ý

'in)

pi Z~ S, n C n 4,

trwI

19(X L6-

____ ____ ____ ____ 0

_j

2W a 40 p" C4

1-(M-H)~ 00.um:nN ) 0 19.
C~C

LL.

43 E

Co..

0 C.

0>.9i~i

aJ~

Q >- x .C

wn L

W Z.

r. K 

2 8 8 00 ___ __

)I 001

Inn

in L

20~
s.3

x L:

sxxr . tn

:3 x

CR..

aJ -

00

Cx 4 :

I. C4 

2 0u 04 C4

N4 001

q xCx

*fi -. .

W~ C2

.O3..

a~j U.

3-.

.in q

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(.4

__ _ _ __ __ _ __ _ q ~ CD

L c,

1.(R-rHO) AmVU1nflNOO 001

21
lei

* I Ix

x

ON t

.0 f4

X..

en I

* I -

so4 CI

U..

N.0

C2 Q.

U -x

..... .... ..... .... ....

>1 001 . 7 

O .x

X, Q

x Q

x

LLIR S-R ~

ax

xS

-x 0~ C_ _ _ _ _ -

in ~ 0 0 .

0 In 0 In

,(m-mHO)(* uijoOO 0

22
.8 .3

x • e 'R N =

x )k*r

°C3,

u .

SnX

0 x . . .

ft eqx •q

001• .>1 

SnIn

~ * R

.x

inr

.4 X

* x In

X .-

"-. K.

ri -x ".

en~~i S n a '

Z

I • - I I

23.

w

o w

0 ~x

4.~

in F.: ~

,-4nRHZ AiwioaNG.- .-

23-
in

x.

.9.

x

x

0 La

x . . .*

C4 -a! '

(4 .. . . .

x . .

C44 =*V w

x C

X~

- . .

or

in -

M x

4!

.. . .. . .. .. . .. . ... . . .. . . . 1.-

1 1 1 a

,-(y4-riH- Aimn- 00 : le

24a~.
Ogo10o log10 K

-4.5I 0.5

M IA IV TI TB

A-

-5.0 - 1.0 /

Ka H* 10=

-5.5 K W-1.5 IA m

-6.0 - 2.0

-6.5 - -- 2.5 •.1.0 ,-

0 "v IV I

-7.0 0 3.0 II A

- 7.5 I I I 0.15I l I I I I ,I

4.0 4.5 5.0 pH 5.5 6.0 6.5 10 10K (5 kHZ)10 100

Figure 24. Loglo low-frequency conductivity (left-hand Figure 26. Logjo percent water vs loglO dielecscale)andlogjolow-frequencydielectric constant(right- tric constant at 5 kHz for the snows indicated by

hand scale)for various snows vs pH of the meltwater. Roman numerals.

80 1 (Fig. 14-16) and snow IB (Fig. 17, 18). The very low,

Bxc low-frequency conduction of the latter exposes strucb60 ................. X ....... ture in the log o vs logl0 frequency curve, which is

,fl ÷, obscured by the high low-frequency conduction of C I a) 40..........................sample IA. The conductivity of the melt is dominated by

the ions of NaCI except at its lowest concentrations 0rS 20 ......................... where the H' ion may play a role. This can be seen in

V Table l and Figure 25.

0 1 The water-content experiments all produced ordered

sets of data. Even experiments on different samples of 0 50 100 150 200 250 300 350 400 the same snow gave results that fit together rather well. Meltwater Conductivity (gS/M) In all, both the conductivity and dielectric constant

Figure 25. Concentrations of sodium and chlor- increased as water content increased. Thus it is tempting

ide ions vs conductivity (! kHz) of the meltwater to take vertical cuts of these data to see if, at a single frefor various snows. quency, a relation can be found between either parameter and the water content. Figure 26 is such a cut. It

These data have been corrected for temperature. To shows the variation with water content of the dielectric

correct for density is more tenuous because, as will be constant at 5 kHz on a log-log plot. For a given snow, the

seen, ourdensity effect measurements gave rather ragged data fall in a well-ordermd sequence on a straight line.

curves and were all made at -9"C. When we do attempt Where we report data on niore than one sample of the

to correct for density, the points are moved as indicated same snow, different symbols are used for each sample

by the arrows. Except for snow V, the general tenden- but the points fall on nearly the same lines. This consiscies remain. But the effect on snow V is catastrophic. tency builds confidence in our techniques. However, no

Possibly grain size plays a role here because samples IV two different snows lie on the same line. We have found

and V, for which the correction is largest, are the no slice of this kind that appears to be useful for detersamples with the finest grains. Exploring the questions mining water content. Although there is an easily mearaised by Figure 24 may be a fruitful area for future surable variation of both the dielectric constant and

research. conductivity spectra with water content, no relation has

The relationship between low-frequency conduc- been found that works well with all snows. There appear

tance of the snow and the hydrogen ion concentration to be too many variables to sort out.

helps to explain the great difference between snow IA We have tried several strategies to discover a way to

25
Table 3. Polynomial fit to data for samples 10-16.

Polynonial fit Average

Experiment Snow Meltwater Melt Density Temp (T) AF"°.5

+BF°0 +CF0 -5 percent

number number (a) (pH) (g/ImL) or % 11•0 A B C relative error

10 V 68 4.8 0.182 T=--4.5 674.07 -7.585 0.0315 13.8

10 V 68 4.8 0.182 T=-2 532.39 -3.651 0.0170 1.8

10 V 68 4.8 0.8 675.41 -5.683 0.0234 4.2

10 V 68 4.8 1.7 609.69 -3.725 0.0161 1.0

10 V 68 4.8 2.7 640.11 -3.756 0.0157 0.7

10 V 68 4.8 3.7 718.70 -4.366 0.0167 2.2

11 IV 42 5 0.265 T=-5 370.94 1.292 -0.0005 5.2

11 IV 42 5 0.265 T = -5 234.33 4.388 -0.0115 0.2

11 IV 42 5 0.8 443.06 3.377 -0.0111 3.9

I1 IV 42 5 2.5 512.71 3.279 -0.0114 5.6

11 IV 42 5 2.9 511.56 3.849 -0.0151 6.1

II IV 42 5 3.6 542.40 3.970 -0.0149 6.1

12 II 220 4.27 0.36 T=-2 634.04 4.019 -0.0055 2.8

12 11 220 4.27 0.36 T = -4 508.96 8.705 -0.0241 1.8

12 II 220 4.27 0.7 1263.95 7.472 -0.0327 4.6

12 II 220 4.27 2.1 1743.51 6.002 -0.0348 6.0

12 II 220 4.27 3.3 2269.86 2.865 -0.0302 6.3

12 II 220 4.27 4.0 2331.67 3.313 -0.0359 6.1

13 lb 294 6.05 0.423 T = -3.5 83.21 10.048 -0.0239 1.3

13 Ib 294 6.05 0.423 T= -25 93.32 11.561 -0.0298 0.6

13 lb 294 6.05 0.5 48.83 16.842 -0.0505 2.1

13 lb 294 6.05 1.3 39.39 21.434 -0.06q1 1.5

13 lb 294 6.05 1.8 45.76 25.563 -0.0856 1.3

13 lb 294 6.05 2.3 40.62 28.591 -0.0985 1.2

14 III 24 5.36 0.391 T=-5 240.13 6.089 -0.0178 0.8

14 I11 24 5.36 0.391 T=-5 207.33 8.457 -0.0263 1.9

14 111 24 5.36 0.9 355.49 10.704 -0.0397 6.6

14 Ii 24 5.36 1.6 423.59 11.452 -0.0440 6.6

14 111 24 5.36 1.9 457.73 11.788 -0.0461 6.7

14 I11 24 5.36 2.1 464.52 12.482 -0.0493 6.5

15 11 220 4.27 0.372 T=-7 1134.67 -9.124 0.0424 9.5

15 ii 220 4.27 0.372 T= -5 613.35 6.700 -0.0188 3.8

15 11 220 4.27 0.3 1141.45 4.213 -0.0172 4.2

15 I1 220 4.27 1.2 1563.68 -0.001 -0.0059 3.2

15 I1 220 4.27 2.3 2309.29 -7.400 0.0134 2.7

15 I! 220 4.27 3.2 2933.29 -14.816 0.0344 0.4

16 lb 294 6.05 0.422 T = -8.5 19.59 10.429 -0.0239 3.1

16 lb 294 6.05 0.422 T= -5 86.51 12.178 -0.0309 0.9

16 lb 294 6.05 0.5 32.84 18.490 -0.0556 2.1

16 lb 294 6.05 0.7 31.82 19.470 -0.0592 2.2

16 lb 294 6.05 0.9 29.27 20.694 -0.0641 2.2

16 lb 294 6.05 1.1 25.21 22.366 -0.0708 2.6

use our data to determine water content of snow. De- frequency in hertz and A, B and C are the parameters

spite clear trends of the dielectric data with water con- (see Table 3). We could fit the data for samples 1,2 and

tent, they are not free enough from variations due to 3 with an equation Af-I+ Bf"0"5 + C. However, we

other parameters to allow us to work backward from were unable to find a three-parameter polynomial form

dielectric measurements to water content. One scheme which would fit all of our data. Note that the snow used

was to fit our dielectric constant data with a polynomial in samples 1, 2 and 3 was of type IA, having very large

of as low an order as we could in the hope that the grains and large conductivity.

coefficients would serve to catalog our samples. If there Another approach was to use the data describing the

were orderly variations in these that could be related to form of the various Cole plots, that is, the center frewater content, then we might have a useful tool. We quencies of the majorgroups ofdispersions, the strengths

found that we could fit all of our data for samples 10-16 of these groups as indicated by the diameters of the Cole

using an equation, Af-0 "

5 + B + Cf 0.5, where f is the circles, and the distance below K"= 0 of the centers of

26
Table 4. Cole plot parameters for the various samples.

Low dispersion High dispersion

Sample Snow Condition Temp. f S H f S H

no. type (ohmr-m) pH or %W Hz pF pF Hz pF pF

I la 1.69E-03 4.4 T=-6 60 160 40 150 220 15

I la 1.69E-03 4.4 3.5 100 1200 520 500 420 110

I la 1.69E-03 4.4 24.0 70 3600 1000 200 3600 700

1 la 1.69E-03 4.4 38.0 110 4600 350

2 la 1.69E-03 4.4 T= -4.5 100 230 25

2 la 1.69E-03 4.4 9.7 120 1600 400 1000 700 110

2 la 1.69E-03 4.4 28.6 200 4800 600

3 la 1.69E-03 4.4 T=-4.5 110 250 45

3 la 1.69E-03 4.4 T=-0.2 110 140 30

3 Ia 1.69E-03 4.4 2.5 110 940 280

3 la 1.69E-03 4.4 5.7 200 1120 310

10 V 8.60E--04 4.8 T = -4.5 120 96 20

10 V 8.60E-04 4.8 T=-2 160 70 8

10 V 8.60E-04 4.8 0.8 170 96 22

10 V 8.60E-04 4.8 3.7 180 104 22

1I IV 5.30E-04 5 T=-5 150 780 14

11 IV 5.30E-04 5 T=-0.6 170 34 7

11 IV 5.30E--04 5 0.8 200 56 12

11 IV 5.30E-04 5 3.6 280 80 21

12 II 2.80E-03 4.27 T=-2 150 120 41

12 11 2.80E-03 4.27 T=--4 150 66 I1

12 II 2.80E-03 4.27 0.7 150 140 5

12 11 2.80E-03 4.27 4.0 210 260 30

13 lb 3.73E--03 6.05 T =-3.5 190 12 1 30000 8

13 lb 3.73E-03 6.05 T = -25 200 16 3 30000 12 2

13 lb 3.73E-03 6.05 0.5 250 12 2.5 20000 15 2

13 lb 3.73E-03 6.05 2.3 250 16 4 18000 26 3.5

14 111 3.00E-04 5.36 T=-5 110 56 0 5000 22 6

14 111 3.OOE-04 5.36 T=-0.5 150 24 3 6000 15 2.5

14 ill 3.00E-04 5.36 0.9 280 44 10 5000 24 4

14 ili 3.00E-04 5.36 2.1 300 64 17 5000 28 4

15 II 2.80E-03 4.27 T=-7 130 160 30

15 11 2.80E-03 4.27 T = -0.5 190 96 22

15 II 2.80E-03 4.27 0.3 260 160 45

15 I1 2.80E-03 4.27 3.2 180 420 130

16 lb 3.73E-03 6.05 T = -8.5 120 5 1 30000 8 1

16 lb 3.73E-03 6.0 T = -0.5 200 1I 0 25000 12 2

16 lb 3.73E-03 6.05 0.5 200 10 3 21000 16 3

16 lb 3.73E-03 6.05 1.1 180 12 3 20000 16 2

Notes:

S = Strength of the dispersion (diameter of Cole circle).

H = Displacement of the center of the circle below t' = 0.

f = Frequency corresponding to center of circle.

these circles (which is an indication of the breadth of the THE EFFECT OF DENSITY

distribution of the dispersions). In the case of two

groups of dispersions, this would require a total of six A series of experiments in which samples of dry

parameters per sample. These data are given in Table 4. snow at -9°C were subjected to unconfined compresNo strong dependence on water content is evident, al- sion was undertaken to determine how sample density

though there does seem to be a clear tendency for the affected the dielectric properties. A guarded ring cell,

strength of the dispersions to increase with water con- oneelectrodeof which wasdriven by amicrometer, was

tent for those samples having no clear high-frequency constructed of stainless steel (Fig. 27). The cell was

dispersion. Again we find a profound difference be- placed on its side in an aluminum box which was loosely

tween snow IA and all of the others. filled with snow. Bridge measurements were then made

27
Snow loaded here

T a

3m. 27. ,nis°-

LuIile All Stainless Steel

1/4 in.Xl4 1/4 in. Except as Shown

0.25 in.

Guard Ring Support Posts

Epoxy

Bottom Plate

i1.5 in..

Figure 27. Micrometer cell usedfor variable density experiments.

Table R. Cole plot parameters for the various samples, -9pC.

Snow Freq K a Density Snow Freq K a Density

Sample type (Hz) ratio ratio ratio Sample type (Hz) ratio ratio ratio

9 1 50 2.8 5.0 1.4 6 Iii 50 4.5 22.4 2.1

500 2.6 4.6 500 4.3 14.2

5 K 2.3 4.6 5 K 2.6 8.5

50 K 1.2 2.6 50 K 1.4 3.2

8 11 50 1.4 13.5 1.8 7 IV 50 22. 157 6.0

500 1.6 11.2 500 6 48

5 K 1.4 8.5 5 K 9 24

50 K 1.02 4.9 50 K 7 8.1

5 Iii 50 7.9 27 2.4 Averages for samples 5 through 9 omitting 7

500 6.4 17 50 4.2 17. 1.93

5 K 3.0 10.8 500 3.7 12.

50K 1.4 4.8 5K 2.3 8.1

50 K 1.26 3.9

28
at 50 Hz, 500 Hz, 5 kHz and 50 kHz. The micrometer results are shown in Figures 28-36. Figures 28-32 show

was turned to somewhat compress the sample and a new frequency spectra for conductivity and dielectric confrequency spectrum was run. This process was repeated stant with density as a parameter. Both increase someseveral times to produce data over a range of densities. what regularly with density in a mannerroughly proporIn all, samples of four different snows were run in this tional to the initial magnitude. The scatter in the data

manner with two different samples of one snow. The from sample to sample is emphasized when the conduc2a (AMS/rn) K

.54 .5454

6 .4o l jfl

10.....................8....20 e.. .. .. .. .. .....

848

.4,0 150..... .. .. .. .. .. ...

LO II OGFECYIIC

Figure 28. Conductivity, o, and dielectric constant, K, as functions of

frequency for sample S. Density in g/cmn3 is shown as a parameter.

.29 1200

2 (50 .46 K.Srn) 

.2 2 3

10 . P4

1.5 2 2.5 3 ,5 4 .5 1.5 2 2. 3 45 4 .' 5

LOG FOJ LOG POM

Figure 28. Conductivitya and dielectric constantK as functions rqec of 

frqecfor sample Density 5. in g/cm3 is shown as a parameter.

2 a"' •s/M) .46 K

10 .1. . .8. . . . . ..... .. 10

.39

39

33

4 .-. . . . . . . . .28.0 40

~~28

6 . .. /.. 4. . ........

20 . 228

.231

1.5 2 25 3 35 4 4.5 5 1.5 2 25 3 55 4 45 5

LOG FFABCY LOG F1WUDCY

Figure 29. Conductivity and dielectric constant as functions of frequency

for sample 6. Density in g/cm3 is shown as a parameter.

ar tjsrn) .6 2 K

105

.33 33...........

40.2b..... .. . .. ..

1522531315414155 1.52 25 335 445 5

LOG F1EMDCY LOG R1EIM1C

Figure 30. Conductivity and dielectric constant as functions of frequency

for sample 7. Density in glcm3 is shown as a parameter.

29
50 a ( rn) .56 20D 6K

30 A~44 0

.44.3

3 .3 ... . . .

103

x ~. - .: . . . . . .03 . .. .

.31

U 2 2.5 3 35 4 455 1.5 2 2.5 3 35 4 45 5

LOG F1EM LOG F

Figure 31. Conductivity anddielectric constant asfunctions of frequency

for sample 8. Density in glcm3 is shown as a parameter.

a0 I" S/m) .5 , 35.56 K

15 .. . . . .... . . .. ... ... . . . . . .. . . . .

4747 25.A7.....I. ............

10....... ... 44 ......... ......... J~.44 4

155 .

0 I I I I I

1.5 2 5 3 35 4 425 5 1.5 2 25 3 35 4 4.5 5

LOG FRMLECY LOG FMMW

Figure 32. Conductivity and dielectric constant asfunctions of frequency

for sample 9. Density in glcm3 is shown as a parameter.

tivity and dielectric constant are plotted against density the trends and the variability. At the bottom of Table 5

for three given frequencies with the sample as a para- is given the average for the first four samples, which

meter (Figures 33-36). Sample 8 (snow IB) is clearly have approximately the same density range. This gives

anomalous as is sample 9 (snow II) to a lesser extent. an overall idea of how density differences among samEach snow behaves in a fairly orderly way but each is ples may affect their dielectric response.

somewhat unique. To illustrate this more fully, Table 5 Figure 37 is a plot of the difference between the congives the ratio of K for maximum density to K for mini- ductivity at 50 kHz and that at 50 Hz vs density for dry

mum density and the same for conductivity. This shows snow. This difference in conductivity is roughly pro-

' 35 . . . . . . . . . . . . . . . . . . . . . . 5 25~~ .~ . .~ ... . .. . . . . . 0 . . . . . 7

0 

550 8.. . ... ..

2 0 . . . . . . .. ..... . . . . . 6... 

'0 15 . . . . . . . . . . . . .1 0 . .. . . . .

C 7 o

( ... .10 9

5 -5 .. . . 5 M . . . . . . .

0 0 I

0.1 0.2 0. 4 0.5 0.6 0.7 a.1 0.2 0.3 0.4 0.5 0.6 0.7

Density (g/cm3) Density (g/cm3)

Figure 33. Conductivity and dielectric constant at50 Hz vs density for the samples indicated

by the number.

30
40 50 7

35 5

30 o(•40

5 .. . . . . . . U ). o •. . . . .

~25 0

30

0 15 7 20 - . . . -

10

5 6 50

. 9 0 f 0

0Q 0.2 0.3 0.4 0.5 0.6 0.7 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Density (g/cm3) Density (g/cm3 )

Figure 34. Conductivity, a (pS/m) and dielectric constant, K, at 500 Hz vs density for the

samples indicated by the number.

40 B 20

c9

1 2 0 o L C 1 .O . .. . . .• . .. . . .. . . . . . . . . . . - C. 58.... . "" 7 .7 0C

15 0 0i7

. . 9 o~ 6

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Density (g/cm3) Density (g/cm3)

Figure 35. Conductivity and dielectric constant at 5 Hz vs density for the samples indicated

by the number.

50 7 9

8 E6

408

C. 4. ... . ... . . . . 6. C

.2 56

/5 2 ........................

00

.~0 .

0.1 0.2 0.3 0.4 C.2 0.6 0.7 0.1 0.2 0-3 0.4 a.5 0.6. W.

Density (g/cm3) Density (g/cm3)

Figure 36. Conductivity and dielectric constant at 50 kHz vs density for the samples indticated

by the number.

213

IZ 16 . . . . . . . . . g. . . .

x

5

'1-1

8 4 . . . . . . . . . . . . . .. . . . . . . ..

,. 1 2 =8 . . . . .; 8.. 5 . - . . .

61 .... ........ 0.5 ....... 0.1 0. 0.3 0.4 0. . S .

. .. .. . % 8 . 9 .. . . . . . ..

Figur 36. Conducty m) at5 O kHz minus that at5Hzvs density

2 n................. t h7 .. (g/cm3)for dry snow. The numbers refer to

0o-,-- '5 1 1 density experiments at -9 C . The * are 0 0.l 0.2 U3 0.4 0.5 0.6 0.7 from samples 10-16 in the temperature

Density range from -2 °( to -5C°(.

31
2501

5

200 - 5

U, • .. . . . . .'5 5 . 7 8 8. ..

.n 150 .. . .. . . . . . .•. . 7 . . . . . -150

to 5

a Figure 38. Dielectric constant at 50 kHz S 50 . . . . . .. . . *! -. . . . . . . . . . . . . .

7 6 * minus thatat5OHz vsdensityfordry snow.

7 , 699 , 9, 9 , Points * are for samples 10-16. The num0 0.1 0.2 o03 0.4 0.5 0.6 0.7 bers indicate samples used in the density

Density experiments.

1.4

9

1.29 *9

1 8 ý58 7

68507

* 6*

0.6 . ..... 7 . .5 ......... .. ...

7

L4 1 I Figure 39. Log to K (at 5 kHz) vs logto den-

-1 -a8 -- 6 -(14 -02 0 sity for dry snow samples numbered as

Log Density (g/cm3) shown (-9 C).

1.5

S~X •, 1 . . . . . . . " ." v . . . . .. . . . . . . .

S0Figure 40. Log -0 K (at 5 kHz) vs log /o density for samples 10--16 having water con0 tents between I and 3%. Where more than

-1 -08 -06 -0.4 -(2 0 one X appearsfor a given density, the highLog Density (g/cm3 ) er the mark, the higher the water content.

portional to density, not surprising when one considers possible more than a rough estimate of density from

that it represents the parallel sum of the conductances measurements of a or K. Similar data for samples havwhich appear in all of the Debye dispersions making up ing a small water content, from 1% to 3%, are shown in

the sample. Because each sample has a different dis- Figure 40. The same tendency is present; but the values

tribution of dispersions, we would expect each to be- of K are shifted upward by roughly 50% from those for

have differently in detail. Note that the data converge dry snow.

toward the origin as they should. We were surprised that

a similar plot of the dielectric constant difference vs

density (Fig. 38) showed a very broad scatter and only CONCLUSIONS AND RECOMMENDATIONS

a very general tendency to increase with density. Detailed discussion will be found in each appropriHowever for dry snow close to the melting point, we ate section. Here we summarize our major observations

see in Figure 39 that the log10 of dielectric constant at 5 and comment on possibly useful further studies.

kHz increases nearly proportionally to the logl 0 of

density. Thus the dielectric constant at 5 kHz is roughly Technique

proportional to the density. Unfortunately, the band of The electrical heating procedure developed for invalues in both Figures 37 and 39 is too broad to make crementally melting the snow in order to vary the water

32
content works very well. By improving the power meas- centration and seems quite insensitive to other ions (see

urement. particularly by improving the measurement of Fig. 24). Thus proton hopping seems to be the dominant

phase, controlofwatercontent can be mademore sensi- process. If this were a surface conductivity, we would

tive. While the accuracy of the present system was ade- expect a large effect of grain size,of which we fiuid a hint

quate to our needs, greater precision might make possi- in the discussion of Figure 24. At -9'C, we would not

ble very useful experiments. For example, at tempera- expect large surface conductivity for ice, but it might be

turesclosetothemeltingpoint, the surface properties of important as the melting point was approached. As

ice are believed to change markedly. The mobility of noted above, our mechanism for heating would seem

protons near the surface is greatly enhanced and the well suited to such studies.

material is often said to become "liquid like." One It was shown in Figure 37 that the difference between

would like to study this phenomenon in a system like the high-frequency conductivity and the low-frequency

snow in which the surface-to-volume ratio is high. conductivity was roughly proportional to density but

Well-controlled electrical heating of the kind we have that the proportionality was different for different samused should make it possible to change the temperature pies. No such relation seemed to hold for the differences

of the whole sample uniformly at temperatures close to in dielectric constant. But there was a proportionality

0°C. Dielectric measurements should then be respon- for the dielectric constant measured at 5 kHz.

sive to changes in the surface properties. Pressure of itself seems to have little or no effect on

Our technique of monitoring the electrode separa- the dielectric properties of dry snow. This would indition also makes it possible to study the dimensional cate that the contact pressure between grains plays only

changes of a system under constant load as the water a small role in determining the electrical properties of

content changes. We suggest that interesting mechani- dry snow. (This tentative result should be followed up

cal information about snow, and possibly othersystems, by more extensive experiments.) However, the change

may be obtained by exploring dimensional changes in in density resulting from pressure is very important.

this way, particularly at temperatures close to the melt- Although based on only five different snows, our

ing point. We believe that this technique could be made measurements suggest that the low-frequency conducmore sensitive with more sophisticated apparatus and tivity of dry snow is proportional to the hydrogen ion

that an effort at such improvement would be worth- concentration and that the low-frequency dielectric

while, constant is proportional to the sq,'are root of the hydroThe consistency of the data gives some confidence in gen ion concentration. To explore this further would

the reliability of the technique. Forexample. the data for seem to be a fairly simple and useful project. If proton

samples 1, 2 and 3. all from snow IA, form a consistent hopping is the dominant process for low-frequency

set for 10 different water contents. Their spectra at zero conduction in dry snow, activation energy measurewater content and approximately the same temperature ments in this region might provide some confirmation

are very nearly the same (see Fig. 14-16). and useful information relating to bulK and surface

processes. This too should be a straightforward experiMeltwater ment.

Room temperature analysis of the meltwater of the

various snows shows a wide range of impurities, Ca and Wet snow

SO4 being the most abundant ions. The details are given

in Table I. Figure 25 shows that the conductivity is Mechanical

dominated by NaCI except at the lowest values. It may Because of the sensitivity of our apparatus for meaalso be of interest that the total anions minus the total suring the thickness of the sample, we were able to

cations is the most positive for the lowest pH and most monitor the dimensional change as the water content

negative for the two highest values of pH. We believe increased. There was a steep change at the start and then

that a continuing program of routine collection and a rather uniform change as the water content increased.

analysis of fresh snow might be useful. Much analysis The steep change at the start we attribute to capillarity

of this kind is done in connection with acid rain studies, and possibly to liquid-like surface states as the temperabut in the work with which we are familiar, rain and tureapproachesveryclosetozero.Ourtechniqueseems

snow are sometimes collected together and periodically well suited to studying this process in more detail.

analyzed.

Electrical

Dry snow We have developed a body of data for five different

For dry snow (at about -90C), the low-frequency snows which is as detailed and complete as time and

conductivity is proportional to the hydrogen-ion con- facilities permitted. It is presented in a form making it

33
availaDle for further analysis. The dominant properties Freezing calorimetry, alcohol calorimetry, dilution and

affecting the dielectric spectra are water content, densi- capacitance are compared and believed to be accurate to

ty and pH of the melt water. Grain size seems to be im- 2-3% water content.

portant, but we do not have enough detailed information Brun, E. (1989) Investigation of wet-snow metamortobe sure. Ionic impuritiesdo not appear toplaya strong phism in respect of water content. Annals of Glaciology,

role in dry snow but they seem to make a major con- 13: 22-26.

tribution to the meitwater conduction when their abun- A study of the grain growth in snow as a function of time

dance is high. at different water contents. The water content was Experiments on dry snow indicated that the inter- a ifrn ae otns h ae otn a

granular gnaperimentssu 

pressure was 

wasnot dre 

not imptanted i d therninther t controlled by melting a portion of the sample by dielec- important in determining the tric heating at 20 kHz. Little detail is given.

dielectric properties. It would be useful to explore this

for wet snow. Camp, P., W. Kiszenick and D.A. Arnold (1967) ElecThe dielectric properties vary strongly with water trical conduction in ice. USA Cold Regions Research

content. Both conductivity and dielectric constant in- and Engineering Laboratory, Research Report 198.

create but not in the same manner from sample to sam- Bulk and surface dielectric properties of hijgie crystal

ple. This is not surprising considering the complexity of ice from --60 to melting in the frequency range DC to

the system. We have explored two different approaches 100 kHz.

to searching for useful regularities in it. In one, we at- Colbeck, S. (1978) Difficulties of measuring the water

tempted to fit all of our data with a three-parameter saturation and porosity of snow. Journal of Glaciology,

power law polynomial, each sample to be characterized 20(82): 189-201.

by different coefficients. (Our thought was that if there Analyzes the errors inherent in many types of measurewere three important properties, they might be sepa- Anaz The errors inherent many in types omsrable in this way.) We were able to fit much, but not all, tent, tent, water te fator saturation ang and porosity eorosin are liquidw discussed.

of our data with one equation. In the other approach we

analyzed our data in terms of Cole plot parameters Colbeck, S. (1973) Theory of metamorphism of wet

(Table 4). In neither did we establish a method by which snow. USA Cold Regions Research and Engineering

these data might be used to evaluate the water content of Laboratory, Research Report 313.

an unknown sample. However, we think it might be A fundamental treatment using thermodynamics to preinteresting to try to deconvolute these spectra by assum- dict the rate of grain growth in snow.

ing that water content, density, grain size and possibly Denoth, A., A. Fogler, P. Wieland, C. MAtzler, H.

hydrogen ion concentration each affect the spectra in its Aebischer, M. Tiuri and A. Sihvola (1984) The comparown characteristic way and that they combine in a linear ative study of instruments for measuring the liquid

way to produce the measured spectra. water content of snow. Journal of Applied Physics,

56(7): 2154-2160.

ANNOTATED BIBLIOGRAPHY A review of measurement methods at high frequencies.

Denoth, A. (1982) Effect of grain geometry on electrical

Ambach, W. and A. Denoth (1975) On the dielectric properties of snow at frequencies up to 100 MHz. Jourconstant of wet snow. In Proceedings, Snow Mechanics nal of Applied Physics, 53(11): 7496.

Symposium, April 1974. IAHS-AISH Publication No. Measurements in the range I MHz to 100 MHz show

114. that grain size and distribution are important.

Measurements in the frequency range: I to 20 MHz. At Denoth, A. and A. Foglar (1986) Recent developments

f Ž 20 MHz the authors suggest W = czl(Eoo'l) -2.221 of snow moisture dielectric devices. Presented at Interwhere W = free water content, at = density. national Snow Science Workshop, Lake Tahoe, CaliAmbach, W. and A. Denoth (1972) Studies on the die- fornia, October 1986.

lectric properties of snow. Zeit:chriftfiirGletscherkunde Reviews measurement techniques at high frequencies

and Glazialgeologie. VIII, Hett 1-2: 113-123. and comments on their applicability. Good recent referUse Wiener's formula for describing dielectric constant ences.

of snow as a mixture. Depends on a linear relation be- Evans,S.(1965) Dielectric rnopertiesof iceand snowtween oo,' and density. A review. Journal of Glaciology, 5(42): 773-792.

Boyne, H. and D. Fisk (1987) Comparison of snow Provides an excellent guide to the literature before

cover liquid water measurement techniques. Water Re- 1965. His data on wet snow are mostly at microwave

sources Research, 23(10): 1833-1836. frequencies. Uses Weiner's formula for mixtures and

34
considers complex permittivities. Reviews the general phase. Other polynomials are discussed.

subject of ice, snow and water. Little on wet snlow. Perla, R. and J. Banner (1988) Calibration of capaciFisk, D. (1986) Method of measuring liquid water mass tance cells for measuring water in snow. Cold Regions

fraction of snow by alcohol solution. Journal of Glaci- Science and Technology, 15: 225-231.

ology, 32(112): 529-530. Uses acid dilution to calibrate water content. Natural

Describes the technique in sufficient detail for others to snow measured at 1 MHz.

use. Claims accuracy of 0.3% volume liquid water. Pradhan, B.P. and R.C. Gupta (1964) Dielectric conKuroiwa, D. (1962) Electrical properties of snow. In stants of mixtures. Dielectrics, 1(4): 195-200.

Physics and Mechanics of Snow as a Material. USA Theory of complex dielectric constants for different

Cold Regions Research and Engineering Laboratory, shapes, data formixtures of ZnO, silicon, and magnesia.

Cold Regions Science and Engineering Monograph II- Sadiku, M. (1985) Refractive index of snow at microB, Chapter J, p. 63-79. wave frequencies. Applied Optics, 24(4): February 15.

An excellent review of the work on electrical properties Uses Weiner's formula with a form factor which inof snow up to 1962. Considers the real and imaginary creases with water content.

parts of the dielectric constant in both the audio and microwave regions. Treats both dry and wet snow. Sihvola, A.H. and J.A. Kong (1988) Effective permittivity of dielectric mixtures. IEEE Transactions on Meredith, R. (1959) Studies on the conductivities of Geoscience and Remote Sensing, 26(4): 420-429. dispersions. University of California, Berkeley. Calculation at 1 GHz for different shaped particles as a

A basic theoretical and experimental study of two- function ate content. r 

phas sysems.function of water content. phase systems.

Olhoeft, G. (1979) Electrical properties (of rocks). In Von Hippel, A. (1972) Dielectric and mechanical reInitalh Repoe rt of th) EPetica popesics Labofraoryks. n sponse of ice Ih single crystals and its interpretation. Initial Report of the Petiophysics Laboratory (G.R. Journal of Chemical Physics, 57(6): 25602571.

Hunt et al., Ed.). Geological Survey Circular 789, p. - Summarizes vigorous research over a period of many 26. years. Accepts the Bjerrun defect model for normal volGives a very useful summary of the theory of dielectric ume polarization of ice but suggests mechanical losses

processes in rocks and similar materials and describes result ume polarizaio from Frenkel ofic defects. For ts much mchanicalxlosse more extensive

the apparatus used. Effects of water content included. coverage of his experiments and the underlying physPerla, R. (1990) Real permittivity of snow at 1 MHz and ics, refer to the author's Technical Reports 8 and 9,

00C. Submitted to Journal of Glaciology. Massachusetts Institute of Technology, 1970 and 1971.

Measured 200 samples of natural and artificial snow. Watt, A.D. and E.L. Maxwell (1960) Measured electriFinds data fit and empirical function e = Evjgj-0.43 vAvI cal properties of snow and glacial ice. Journal of Re-

- 5 0VIVw - 100 VAVW, where e is real permittivity, ii = search of the National Bureau of Standards, 64d(4).

A, 1, or W (air, ice or water); vj is the volume proportion Gives experimental data on natural snow, 200 Hz to 100

of each phase and ej, is the dielectric constant of each kHz, at snow temperatures of 0

0C but no water content

(or density) measurements. Considers glacial ice. Uses

four electrode techniques to measure conductivity.

35
APPENDIX A. DATA TABLE

Sample Density Temp ('C) LogK LogK LogK LogK Logo Logo Logo Logo

no. (glcm3 ) or % H20 50 Hz 500 Hz 5 kHz 50 kHz 50 Hz 500 Hz 5 kHz 50 kHz

1 0.42 T=-6 2.473 1.620 1.122 0.802 -5.539 -5.344 -5.161 -4.824

IA 1 0.42 3.5% 2.835 2.223 1.476 0.455 -4.695 -4.636 -4.481 -4.343

1 24.0% 3.698 2.837 1.866 1.062 -3.965 -3.884 -3.784 -3.736

1 38.0% 3.821 2.932 1.893 1.238 -3.837 -3.711 -3.617 -3.568

2 0.42 T =-4.5 2.380 1.538 1.154 0.807 -5.547 -5.377 -5.191 -4.801

IA 2 9.7% 3.332 2.623 1.796 0.785 -4.348 -4.272 -4.127 -4.002

2 28.6% 3.811 2.987 1.982 1.118 -3.814 -3.725 -3.637 -3.598

3 0.42 T = -4.5 2.378 1.678 1.171 0.821 -5.588 -5.393 -5.158 -4.806

A 3 T=-0.2 2.240 L.641 1.234 0.831 -5.414 -5.317 -5.123 -4.753

3 2.5% 2.881 2.203 !.503 0.777 -4.690 -4.614 -4.472 -4.310

3 5.7% 3.068 2.409 1.634 0.840 -4.531 -4.454 -4.299 -4.172

4 0.264 T = -9 2.029 1.364 0.954 0.689 -5.585 -5.520 -5.397 -5.032

4 0.317 T=-9 2.460 1.742 I.LOO 0.737 -5.078 -4.990 -4.909 -4.699

11 4 0.366 T = -9 2.635 1.996 1.279 0.823 -4.806 -4.730 -4.645 -4.465

4 0.396 T = -9 2.808 2.063 1.325 0.867 -4.739 -4.643 -4.568 -4.395

4 0.432 T=-9 2.887 2.134 1.385 0.900 -4.637 -4.548 -4.414 -4.310

5 0.228 T = -9 1.457 0.885 0.595 0.320 -7.106 -6.685 -6.222 -6.632

5 0.337 T = -9 1.927 1.282 0.798 0.427 -6.260 -5.987 -5.692 -5.286

111 5 0.405 T=-9 2.222 1.517 0.911 0.465 -5.917 -5.666 -5.407 -5.124

5 0.476 T=-9 2.319 1.626 0.996 0.442 -5.770 -5.535 -5.282 -5.037

5 0.543 T = -9 2.356 1.692 1.077 0.469 -5.681 -5.456 -5.189 -4.951

6 0.225 T = -9 1.383 0.929 0.667 0.376 -6.972 -6.664 -6.169 -5.483

6 0.246 T = -9 1.330 0.990 0.710 0.394 -6.630 -6.452 -6.032 -5.443

111 6 0.281 T=-9 1.450 1.099 0.790 0.407 -6.380 -6.230 -5.864 -5.314

6 0.328 T=-9 1.607 1.216 0.870 0.476 -6.156 -6.027 -5.696 -5.215

6 0.463 T=-9 2.034 1.565 1.075 0.511 -5.621 -5.510 -5.241 -4.971

7 0.111 T -- 9 1.343 9.901 0.524 0.228 -7.115 -6.632 -6.231 -5.657

7 0.166 T =-9 1.325 0.859 0.585 0.317 -6.004 -5.959 -5.833 -5.471

IV 7 0.248 T=-9 1.580 1.001 0.651 0.404 -5.611 -5.573 -5.501 -5.249

7 0.497 T=-9 2.213 1.628 0.915 0.485 -5.013 -4.965 -4.881 -4.792

7 0.662 T = -9 2.137 1.649 0.987 0.462 -4.999 -4.952 -4.846 -4.751

8 0.309 T = -9 2.068 1.3"44 0.951 0.665 -5.581 -5.485 -5.344 -5.014

8 0.355 T = -9 2.029 1.280 0.903 0.687 -5.068 -5.039 -5.00 i -4.820

1i 8 0.440 T = -9 2.018 1.403 0.992 0.678 -4.656 -4.647 -4.630 -4.527

8 0.500 T = -9 2.249 1.572 1.081 0.680 -4.513 -4.498 -4.478 -4.384

8 0.564 T=-9 2.219 1.551 1.101 0.673 -4.452 -4.437 -4.413 -4.326

9 0.423 T=-9 1.087 0.967 0.910 0.711 -7.410 -7.128 -6.436 -5.159

9 0.441 T=-9 1.230 1.098 1.026 0.733 -7.091 -6.884 -6.181 -5.017

[B 9 0.470 T = -9 1.351 1.209 1.122 0.758 --6.938 -6.734 -6.006 -4.912

9 0.504 T=-9 1.477 1.326 1.232 0.791 -6.799 -6.589 -5.850 -4.799

9 0.564 T = -9 1.539 1.379 1.276 0.798 -6.708 -6.494 -5.778 -4.740

10 0.182 T=-4.5 2.001 1.250 0.674 0.391 -5.852 -5.704 -5.564 -5.289

10 0.182 T = -0.2 1.865 1.297 0.712 0.402 -5.697 -5.590 -5.454 -5.221

V 10 0.8% 1.975 1.363 0.757 0.408 -5.789 -5.649 -5.483 -5.226

10 1.7% 1.922 1.370 0.784 0.415 -5.794 -5.656 -5.474 -5.208

10 2.7% 1.943 1.396 0.809 0.417 -5.788 -5.649 -5.453 -5.191

10 3.7% 2.000 1.431 0.851 0.410 -5.758 -5.615 -5.410 -5.166

II 0.265 T=-5 1.761 1.206 0.825 0.452 -6.074 -5.932 -5.666 -5.215

11 0.265 T=-5 1.572 1.166 0.838 0.457 -5.731 -5.682 -5.522 -5.151

IV II 0-8% 1.793 1.392 0.939 0.459 -5.915 -5.789 -5.483 -5.113

!I 2.5% 1.841 1.460 0.975 0.480 -5.901 -5.769 -5.443 -5.084

II 2.9% 1.839 1.471 0.987 0.441 -5.896 -5.762 -5.425 -5.084

11 3.6% 1.864 1.495 1.011 0.488 -5.872 -5.734 -5.403 -5.075

37
Sample Density Temp (9C) LogK LogK LogK LogK Logo Logo Logo Logo no. (g/cm3

) or % H20 50 Hz 500 Hz 5 kH: 50 kHz 50 H: 500 H: 5 kH: 50 kH:

12 0.36 T=-2 1.990 1.484 1.106 0.749 -5.273 -5.239 -5.120 -4.814

12 0.36 T=-4 1.893 1.505 1.149 0.747 -5.329 -5.284 -5.137 -4.807

12 0.7% 2.239 1.839 1.351 0.765 -5.209 -5.120 -.4.907 -4.618

12 2.1% 2.363 1.968 1.435 0.781 -5.041 -4.968 -4.764 -4.513

12 3.3% 2.470 2.066 1.499 0.799 -4.916 -4.843 -4.651 -4.428

12 4.0% 2.480 2.078 1.512 0.759 -4.854 -4.786 -4.608 -4.401

13 0.423 T=-3.5 1.348 1.112 0.981 0.706 -6.950 -6.646 -6.109 -5.080

13 0.423 T=-25 1.395 1.174 1.033 0.725 -6.947 -6.635 -6.052 -5.023

IB 13 0.5% 1.391 1.239 1.147 0.760 -7.192 -6.865 -5.996 -4.909

13 1.3% 1.439 1.327 1.234 0.790 -7.198 -6.848 -5.876 -4.822

13 1.8% 1.511 1.402 1.305 0.822 -7.159 -6.800 -5.776 -4.747

13 2.3% 1.540 1.443 1.347 0.830 -7.164 -6.787 -5.723 -4.708

14 0.391 T=-5 1.607 1.209 0.917 0.503 -6.764 -6.395 -5.829 -5.195

14 0.391 T = -5 1.560 1.249 0.976 0.545 -6.327 -6.174 -5.734 -5.128

14 0.9% 1.730 1.460 1.101 0.536 -6.679 -6.270 -5.586 -5.044

14 1.6% 1.800 1.518 1.145 0.546 -6.639 -6.211 -5.517 -5.002

14 1.9% 1.829 1.546 1.165 0.549 -6.632 -6.183 -5.489 -4.983

14 2.1% 1.840 1.557 1.181 0.549 -6.621 -6.176 -5.471 -.4.975

15 0.372 T=-7 2.226 1.546 1.028 0.734 -5.636 -5.487 -5.301 -4.941

15 0.372 T = -0.5 1.943 1.559 1.140 0.720 -5.020 -4.993 -4.900 -4.696

15 0.3% 2.1gl 1.774 1.271 0.739 -4.973 -4.938 -4.816 -4.602

I1 15 1.2% 2.325 1.870 1.328 0.755 -4.951 -4.906 -4.773 -4.553

15 2.3% 2.488 2.006 1.410 0.774 -4.845 -4.791 -4.651 -4.456

15 3.2% 2.600 2.072 1.463 0.779 -4.774 -4.722 -4.584 -4.392

16 0.422 T =-8.5 1.149 1.013 0.957 0.714 -1.399 -7.107 -6.351 -5.102

16 0.422 T=-5 1.375 1.192 1.049 0.752 -6.638 -6.447 -5.988 -4.998 IB 16 0.5% 1.379 1.259 1.178 0.792 -7.175 -6.873 -5.985 -4.878

16 0.7% 1.395 1.278 1.198 0.804 -7.194 -6.885 -5.962 -4.855

16 0.9% 1.411 1.300 1.221 0.812 -7.222 -6.896 -5.934 -4.832

16 1.1% 1.433 1.325 1.250 0.823 -7.222 -6.901 -5.895 -4.802

38 *U.S. GOVERNMENT PRINTING OFFICE: 1992-800-063160014
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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

I July 1992

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Determination of the Water Content of Snow PE: 6.27.84A

by Dielectric Measurements PR: 4A762784AT42

6. AUTHORS TA: FS

WU: 032

Paul R. Camp and David R. LaBrecque

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION

REPORT NUMBER

Department of Physics, University of Maine, Orono, Maine

MicroPhysics, Old Town, Maine

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

Office of the Chief of Engineers U.S. Army Cold Regions Research

Washington, D.C. 20314-1000 and Engineering Laboratory Special Report 92-18

Hanover, N.H. 03755-1290

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Approved for public release; distribution is unlimited.

Available from NTIS, Springfield, Virginia 22161.

13. ABSTRACT (Maximum 200 words)

The dielectric properties of wet and dry natural snow were studied in the frequency range of 50 Hz to 100 kHz to determine

whether measurements made in this frequency range might prove useful in evaluating the water content of snow. Dielectric

heating at 20 kHz proved a very useful means of modifying the water content from 0 to 30% by weight. Six different natural snows were used in these experiments. Meltwater was analyzed for conductivity, pH, and impurity content. In addition

to developing information on the dielectric properties of wet and dry snow, we measured the changes produced in dry snow

by altering its density over the range of 0.11 to 0.66 g/cm 3. Details of the experimental technique and the data obtained are

fully reported. Our results do not lead to optimism about the usefulness of measurements in this frequency range alone for

the determination of water content.

14. SUBJECT TERMS 15. NUMBER F PAGES

4,- 3

Dielectric measurement Liquid water content Snow 16. PRICE CODE

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