Physical measurements of sea ice

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RESEARCH AND..DEVELOPMENT REPORT
REPORT 825
11 FEBRUARY 1958

PHYSICAL MEASUREMENTS OF SEA ICE

J.H. BROWN AND E.E. HOWICK

U.S. NAVY ELECTRONICS LABORATORY, SAN DIEGO, CALIFORNIA
A BUREAU OF SHIPS LABORATORY

G78 Hoday / 1

THE PROBLEM

Study the physical properties of sea ice to ascertain those properties which may
be pertinent to naval operational needs.

RESULTS

An initial study, in the Bering Sea, of such sea-ice properties as density, salinity,
air-bubble distribution, size and distribution of crystal grains, and elastic moduli,
was accomplished. Two sites were involved, in 1954 and 1955.

RECOMMENDATIONS

1. Conduct a study of the variation of all parameters over one entire ice season
at one location, attempting to relate the plate-wave velocity variation with the
state of the sea ice and the state of the sea ice with its breaking properties.

2. Obtain heat-transfer information by making continuous measurements over a
complete ice season of (1) temperature gradients through an ice sheet with a snow
cover, (2) wind gradients above the ice sheet, (3) wet and dry temperature gradi-
ents above the ice sheet, and (4) the net radiation.

ADMINISTRATIVE INFORMATION

Work was done under SW-01102, NE 121217-847.1 (NEL L6-1, Part 1), by mem-
bers of the Special Research Division. This report covers work performed in Feb-
ruary and March 1954, and March and April 1955, and was approved for publi-
cation 11 February 1958.

The authors are greatly indebted to the crew of the USCGC NORTHWIND for
assistance rendered, and particularly to the UDT and EOD groups which partici-
pated in the Bering Sea Expeditions in the winter of 1954 and 1955. Appreciation
is also expressed to all members of the Submarine and Arctic Research Branch,
particularly Dr. W. K. Lyon for his encouragement and technical assistance; L. L.
Morse for his technical assistance in the seismic instrumentation; A.C. Walker
for his assistance in general instrumentation; and R. N. Rowray for his help in
analyzing data.

CONTENTS

page
2 INTRODUCTION

3 ELASTIC-WAVE THEORY

5 MEASUREMENTS, WINTER 1954 BERING SEA EXPEDITION
7 MEASUREMENTS, WINTER 1955 BERING SEA EXPEDITION
19 SUMMARY

23 RECOMMENDATIONS

23 REFERENCES

301 004055

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ILLUSTRATIONS

page figure
5 1 Wenner method of dc resistivity measurements
6 2 Schematics of equipment layout on ice sheet (1954)
9 3 Schematics of equipment layout on ice sheet (1955)
9 4 Density profile of ice sheet, site No. 1 (1955)

10-11 5-7 Sea-ice salinity profiles

12-13 8-10 Temperature profiles through ice and snow

14-15 11-12 Crystal grain size distribution for various ice samples
16-17 13-14 Air-bubble size distribution for various ice samples
18 15 Conducted heat flow through snow-covered ice sheet

TABLES
page table

6 1 Seismic data taken in 1954

8 2 Longitudinal plate-wave velocity data taken in 1955

8 3 Ice thickness calculated from seismic method vs measured ice thickness, 1955
19 4 Resonant rod measurements of sea ice, 1955

21 5 Apparent dc resistivity measurements

INTRODUCTION

A knowledge of the physics of sea ice is essential to arctic naval operations. The
measurements reported here are one phase of a major continuing study being con-
ducted by the Navy Electronics Laboratory to furnish geophysical data on the
arctic regions which will be of value in naval operations in that area.

A survey of the literature’?:? (see References at end of report) in 1953, con-
cerning the longitudinal plate-wave velocity in fresh-water ice, showed a signifi-
cant variation in velocity. At that time there were no data on longitudinal plate-
wave velocities in sea ice; however, since that time one article on the subject has
been published,* indicating that if variations existed in the longitudinal plate-
wave velocity in sea ice, these variations would be related to certain physical
properties of the ice.

During the Winter 1954 Bering Sea Expedition and the Winter 1955 Bering
Sea Expedition, measurements were made of the longitudinal plate-wave velocity.
In 1954, the location of the ice sheet in which measurements were made was
60°20’ N, 168°38’ W; and in 1955 the ice sheet, although variable in position
during the several days measurements were being made, occupied the position
63°05’ N, 166°09’ W. In 1955, in addition to the measurement of the longitudinal
plate-wave velocity, other physical properties of the ice which might be of sci-
entific interest were measured. The investigation of other sea-ice parameters in-
cluded: (1) sampling profiles of density, temperature, salinity, air bubble, and
crystal grain; (2) measurement of the longitudinal wave velocity in ice rods;
(3) measurement of the frequency of air-coupled flexural waves to determine ice
thickness; and (4) resistivity measurements.

The information obtained from these two surveys represents point data; that is,
data which were taken at a given point in a relatively short time interval.

ELASTIC WAVE THEORY
Mechanical Properties

From the theory? of elastic waves in an isotropic medium, the longitudinal
plate-wave velocity is given by the relation

V, = {E/[p(1 — o*))}*/”?
where
E = Young’s modulus
pi = density of medium (ice)
o = Poisson’s ratio

The shear wave velocity, Vs, = (u/pi)1/*, in which » = E/[2(1 + o)] where » =
shear modulus.

If the medium is isotropic and the above two wave velocities can be detected,
then the elastic properties of the medium can be described by any two elastic con-
stants of the above equations. It should be noted that V, is a function of two elastic
constants whereas V,,;, is a function of only one elastic constant. In addition, both
of these wave velocities are a function of density.

The longitudinal wave velocity for rods, in which the diameter of the rod is
small in comparison to its length, is given by the relation®

V, = (E/pi)/?

From the plate velocity and the rod velocity equations, the following relation can
be written:
psf l= Oy

which gives the plate-wave velocity in terms of the rod velocity.
The theory of flexural waves’ in a floating ice sheet over deep water gives the
relation for the phase velocity C as

co (1/3)? V5? + {Upro/ pid 81/ (4x?) }
1+ (pw/pi) [= C?)/V 2-7? (2ary) 3

where
y= 4Af/c
H = thickness of ice sheet
f = frequency of flexural wave
C = phase velocity
pw = density of underlying water
pi = density of ice
\ = wavelength in ice
Vi» = velocity of longitudinal wave in water
V, = velocity of longitudinal plate wave in ice
g = acceleration of gravity

Flexural waves are usually generated by an explosive shot being placed in the
ice or in the air above the ice. The frequency of these waves changes with the
varying velocities of the shots. However, if the explosive shots are set off in the
air or on the surface of the ice, the frequency remains constant. Theory’ shows
these constant-frequency waves build up to a maximum amplitude, and then fall
off rapidly in amplitude. The point of maximum amplitude represents the passage

of the air wave. These waves are called air-coupled flexural waves. The equation
for y becomes
Ya = Hf if Cc

from which the ice thickness can readily be determined.

Other Physical Properties
HEAT FLOW THROUGH A SNOW-COVERED ICE SHEET

The heat flow per unit time per unit area through a snow-covered ice sheet,
which is bounded on one side by an isothermal reservoir of water and on the other
side by the atmosphere, is given by the relation®

w = —k (0T/0Z)
where
w = heat flux
k = thermal’ conductivity
T = temperature
Z = thickness of the ice sheet

When the thermal conductivity is not constant but varies through the ice sheet,
the ice sheet and the corresponding snow cover must be divided into thin layers.
By a consideration of the thermal conductivity of each individual ice layer, it is
possible to write the following relation for the heat conducted through the snow-
covered ice sheet

es Tn Ti Bes, T,— Ti

S (Zn/kn) (ZA EN(Z2y >) eZ ES)

n=1

RESISTIVITY OF SEA ICE

The resistivity method of measuring the resistance of sea-water ice consists of
sending an electric current into the ice sheet and measuring the potential between
a set of electrodes placed in the ice within the effective area of the current. The
Wenner method? of electrode arrangements (fig. 1) was used in making the
measurements.

Theoretical investigations based on the distribution of electric current in the
ground are nearly all based on the assumption that the layers are horizontal and
homogeneous in the horizontal plane. If the ground has uniform electrical prop-
erties for an infinite distance in a vertical direction, the resistivity, using the elec-
trode arrangement in figure 1, is given by

p= 27a (V/I)

where
p = resistivity in ohm-centimeters
a = electrode separation in centimeters
V = voltage in millivolts
I =current in milliamperes

For the case of nonuniform properties in a vertical direction, the equation no
longer gives the true resistivity. In such a case, the resistivity determined from the
measurements is called the apparent resistivity.

MILLIAMPERES

[

BATTERY SUPPLY MILLIVOLTS

CURRENT
ELECTRODE

POTENTIAL
ELECTRODE

POTENTIAL CURRENT
ELECTRODE ELECTRODE

Figure 1. Wenner method of dc resistivity measurements.

MEASUREMENTS, WINTER 1954 BERING
SEA EXPEDITION

Equipment and Procedures

Measurements of the longitudinal plate-wave velocity and of the ice thickness
by the air-coupled flexural-wave method were made in a sea-ice sheet. The equip-
ment consisted of Electro-technical model EVS 2-A geophones, a six-channel Brush
recorder, modified Brush amplifiers with limiters, and a shot-break circuit em-
ploying a portable transmitter-receiver radio system. The icebreaker lay to in the
ice sheet for a period of one to three days at three locations. At the first two
Stations, insufficient data were obtained because of difficulties encountered with
equipment operation in cold temperatures. At the third station, satisfactory rec-
ords were obtained.

Two sets of geophones, 91.44 meters (100 yards) apart, were buried in the ice
for detecting the longitudinal plate-wave velocity. Each set consisted of three geo-
phones oriented in the three vector directions. No effort was made to obtain dis-
persion curves, since the ship was at each location for only a short time. Hence,
it was decided to standardize on 457.2 meters (500 yards) and 914.4 meters (1000
yards) as the distance from the first geophone set to the point where the explosive
charges were detonated. Two additional geophones were placed on top of the ice
sheet for detecting the air-coupled flexural waves. The surface of the ice sheet
was, in general, very smooth. Measurements made in this ice sheet are presented
in table 1. Figure 2 presents a schematic arrangement of geophones and shot-blast
stations.

TABLE 1. Seismic data taken in 1954.

Mean Measured

Longitudinal | Air-Coupled Ice Thickness
Plate-Wave | Flexural Wave | Calculated Ice | with Probable Size of
Range Velocity Frequency Thickness Error TNT Charge
(meters) | (meters/sec) (cps) (cm) (cm) (Ibs)

2740 + 60
2553 + 60

912 15

912 2553 + 60
1003 2495 + 60
910 2603 + 60
2615 + 60

HORIZONTAL-TRANSVERSE
< TO WAVE FRONT

A HORIZONTAL-LONGITUDINAL
TO WAVE FRONT

e VERTICAL-TRANSVERSE

TO WAVE FRONT

83.8

SHOT BLAST STATION

457.2 METERS

a» 28

HUMMOCKED ICE
AREA (LESS THAN 1%)

ZA SHOT BLAST —

ICE THICKNESS MEASUREMENTS (CM)

457.2 METERS
81.3
83.8 sq} ~@
GEOPHONES SET 91.4 METERS
IN ICE
GEOPHONE SET ON TOP
e
4 a © OF ICE IN SNOW
SHIP POSITION,
WINTER 1954

Figure 2. Equipment layout on ice sheet (1954).

MEASUREMENTS, WINTER 1955 BERING
SEA EXPEDITION

Equipment and Procedures

MECHANICAL PROPERTIES

The icebreaker USCGC NORTHWIND (WAGB-282) lay to in the ice from
23 March to 5 April. Again measurements were made of the longitudinal plate-
wave velocity and of the air-coupled flexural wave frequency. The seismic equip-
ment consisted of a Consolidated Engineering Corporation type 5-101B, 14-channel
recording oscillograph. The galvanometers used in the oscillograph had a resonant
frequency of 375 cps. Nine of the amplifiers were type GN amplifiers made by
Engineering Laboratories, Inc., modified to give a uniform frequency response
from 11 cps to 1000 cps. Five amplifiers were designed and built at NEL to pro-
vide a uniform frequency response from 3 cps to 5000 cps. Eleven geophones of
Engineering Laboratories, Inc., type GS-100 were used. These geophones had a
resonant frequency of 27.5 cps. Two Brush C-23 hydrophones were used to detect
the water wave velocity. The shot-break signal was transmitted through field tele-
phone wire to the recorder.

Three sets of geophones were placed 91.4 meters (100 yards) apart. Each set
consisted of three geophones, one for each vector direction. In addition, two geo-
phones were set on top of the ice sheet, and two hydrophones were placed under
the ice sheet in the water. The explosive charges were detonated at a distance
of 457.2 meters (500 yards) and 914.4 meters (1000 yards) from the nearest set
of geophones. The general surface of the ice sheet was flat; however, the over-all
ice sheet consisted of two sections which had been rafted together into one ice
sheet. Thus, two sets of geophones were not in the same sheet as the one in which
the explosive charges were set off. The results of these measurements are pre-
sented in tables 2 and 3. A schematic arrangement of geophones and shot-blast
stations appears in figure 3.

Density profile measurements were made on a sample of ice taken from the area
of Site 1 (fig. 4). The density measurements were made immediately after taking
a core sample of ice by the direct method of weighing and measuring the dimen-
sions of the sample of ice.

Salinity profiles were made at Site 1 and Site 2 (figs. 5, 6, and 7). The size of
each sample was selected to assure a representative quantity. Chlorinities were
determined by the titration method and then converted to salinities by the use of
the Knudsen hydrographical tables.

It should be noted that errors exist in the determination of salinities by this
method." The error in this method, which is well within practical limits, is
apparently less than 0.1°/ 0.

Vertical temperature profiles through the ice sheet were made at Site 2 at the
time of the explosive shots. The results are presented in figures 8, 9, and 10 for
each day the tests were conducted. Thermistors were used as the thermal elements.

Profiles of the crystal grain size of a sample of ice were taken at Site 2. A graph
of the distribution of grain sizes is presented in figures 11 and 12. An Eastman
Kodak photo-copyer with 1.5-power magnification was used to photograph the
ice samples, which were placed under a calibrated grid between cross polaroid
plates.

TABLE 2. Longitudinal plate-wave velocity data TABLE 3. Calculated ice thickness from seismic method vs meas-
taken in 1955. ured ice thickness for 1955.

Mean Measured

Longitudinal
Plate-Wave

Ice Thickness,

Range Velocity Calculated Ice} with Probable
Date (meters) | (meters/sec) Range Thickness Error
(meters) (cm) (cm)

3-27-1955 2191 + 40

2132 + 40 3-27-1955 69.2 + 1.8 1

2118 + 40 69.2 + 1.8 1 TNT

2271 +40 105.9 + 23.6 1 TNT

2147 + 40 105.9 + 23.6 1 TNT
69.8 + 1.0 10 TNT

ESE 948+168 | 10 TNT

2164 + 40
2272 + 40
2248 + 40
2217 + 40
2261 + 40
2219 + 40

3-30-1955 69.2 + 1.8
105.9 + 23.6
69.2 + 1.8
69.2 + 1.8
69.2 + 1.8
114.8 + 29.5
105.9 + 23.6
105.9 + 23.6

4-2-1955 69.2 + 1.8
114.8 + 29.5
105.9 + 23.6
105.9 + 23.6

69.2 + 1.8

2219 + 40
2193 + 40
2140 + 40
2154 + 40

4-2-1955 2305 + 40
2219 + 40
2238 + 40
2286 + 40
2255 + 40
2266 + 40
2213 + 40
2210 + 40
2271 + 40
2219 + 40
2198 + 40
2225 + 40
2155 + 40
2179 + 40

114.8 + 29.5
105.9 + 23.6
94.8 + 16.8

HORIZONTAL-TRANSVERSE

< SNOW COVER (APPROX. 16.5 CM THICK)
TO WAVE FRONT

TO WAVE FRONT
e VERTICAL-TRANSVERSE
TO WAVE FRONT

A HORIZONTAL-LONGITUDINAL

719
SHOT BLAST STATION

457.2 METERS

SHOT BLAST STATION

457.2 METERS
73.7

AREA WHERE ONE ICE SHEET
HAS BEEN PUSHED UNDER
ANOTHER ICE SHEET

ICE THICKNESS MEASUREMENTS (CM)

DEPTH IN ICE SHEET (CM)

65.0

SET IN ICE
71.1

183 METERS
NO. 12 HYDROPHONE IS 2 FT
' BELOW BOTTOM OF ICE SHEET
NO. 13 HYDROPHONE IS 20 FT 0.85 0.90 0.95
va BELOW BOTTOM OF ICE SHEET DENSITY (GMS/CM')
SHIP POSITION,
SITE 2 WINTER 1955

Figure 4. Density profile of sea ice sheet,

i ) 1 6
Figure 3. Equipment layout on ice sheet (1955). ake No» 1 CE 2>)

SNOW COVER (APPROX. 16.5 CM THICK)

© SALINITY OF
| SNOW SAMPLE
i

DEPTH IN ICE SHEET (CM)

SALINITY (°/00)

Figure 5. Sea-ice salinity profile, site No. 2 (1955).

10

SNOW COVER (APPROX. 19 CM THICK)

fo)
1 SALINITY OF
| SNOW SAMPLE

DEPTH IN ICE SHEET (CM)

10
SALINITY (°/00)

Figure 6. Salinity profile of sea ice sheet, site No. 2 (1955).

SNOW COVER (APPROX. 5 CM THICK)

SALINITY OF 2
SNOW SAMPLE

8
|

DEPTH IN ICE SHEET (CM)

10
SALINITY (°/00)

Figure 7. Salinity profile of sea ice sheet, site No. 1 (1955).

1

12

27 MAR 55

WATER
| |

® 8 +8 =0 —§ © 6
TEMPERATURE (°C)

—I5 —10 —5

Figure 8. Temperature profile through ice
sheet and snow cover, site No. 2 (27 Mar
55).

7

AIR

2 APR 55
1040

WATER WATER
t '
3 15 = =s ay Ae as) Oo
TEMPERATURE (°C) TEMPERATURE (°C)
Figure 9. Temperature profile through ice Figure 10. Temperature profile through
sheet and snow cover, site No. 2 (30 and ice sheet and snow cover, site No. 2 (2 Apr

31 Mar 55). 55).

13

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SNOW-ICE INTERFACE

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N Nn nN nan Nn i>
= N o ~~ Pe) 0

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ICE-WATER INTERFACE

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CRYSTAL GRAIN LENGTH (

Crystal grain size distribution for ice samples of Z-axis orientation.

Figure 12.

15

16

Profiles of the air-bubble distribution in ice were made at Site 2. Figures 13
and 14 show the distribution of air bubbles for various samples of ice. The East-
man Kodak photo-copyer was used again to photograph the ice samples for air-
bubble content. A low-power microscope was used to photograph the smaller air
bubbles, with the ice samples placed under a grid graduated in 0.5 mm.

The longitudinal wave velocity of a sea-ice rod was measured by the resonant-
rod method. The radius of the rod, obtained by coring, was small in comparison
to its length. The rod was allowed to reach a temperature equilibrium over a
period of two or three days. A Hewlett-Packard audio signal generator, model
205 AG, was used to drive a balanced armature which, in turn, was coupled to a
2-inch-diameter plate attached to one end of the ice rod. An earphone was attached

to the other end of the rod to detect the waves generated. The signal from the
earphone was fed into a Ballantine vacuum-tube voltmeter.

36

SNOW-ICE INTERFACE

32

Pere 10

=
ou
4 ae 20
28 <= = i ——-—
=x
eooeeoeo 30 WD,
S
: ue
a I ——— we 40 O
2 24 ty 9 5
= : ce
Z = o. 50 3
o a fi e}
w 2 = 3 a
=z 3 Z 60
> 20 5 wy
g ‘A Gan eee: g
: f <q
ce 5 2 = 70 £
= 3 : a
wn =
= = 80
a =
216 = =
a : c = 87.5
uo : rp - ~ =
fe) :
[-4 = YS
wa =
3 a s ICE-WATER INTERFACE
3 12 = a

Oe ee)

ae
apnea of

“== eo.

SLL sree
*e0nerreeg
0

fe) 1/8 1/4

3/8 1/2 5/8 3/4 7/8
DIAMETER OF BUBBLE (MM)

Figure 13. Air-bubble size distribution for ice samples of X-Y-axis orientation, site No. 2.

40
36 i.
SNOW-ICE INTERFACE
32 penne — 2 =
noneseseca 10 =
o
== iG
28 aie
w
a eocce 30 ¥
iG wy uo
= 5 fe)
5 aa i 40 fo)
ia 24 3 = wi —
o o
w =
50 9g
3 a
eZ 60 9
& 20 Z
Es <
n &B
ig 700
a
GI ¥
=)
[-)
5 16 cd ee 80
[-4
wi
a
=
2 ICE-WATER INTERFACE
12
8
4
tnseaneay
0 —l we ba
0 1/8 1/4 3/8 1/2 5/8 3/4 7/8 1

DIAMETER OF BUBBLE (MM)

Figure 14. Air-bubble size distribution for ice samples of Z-axis orientation, site No. 2.

17

18

HEAT FLUX (CAL/CM /SEC)

.235 x 10°
.225 x 10-* = TT +
.215 x 10-7

.205 x 10-? il
-195 x 10-3 + TT
185 x 10° I !
175 x 10-3 + + |
-165 x 10-3 | 7
-155 x 10°
145 x 10-3
-135 x 10-3
-125 x 10-7
M5 x 10-3 { He
-105 x 10-7
.095 x 10-3

.085 x 10- + al

UB IT" 1800 | 0400 | 1400 | 0000 1000 | 2000 0600 | 1600 [0000 | 1200 0000 0800 1800 0400
0000 ©0900

OTHER PHYSICAL PROPERTIES

HEAT FLOW MEASUREMENTS THROUGH AN ICE SHEET. Since the
thermal gradients from the water through the ice sheet, the snow cover, and the
atmosphere were measured for the state of the ice, it was decided to measure the
conducted heat flow per unit time per unit area through a sea-ice sheet with a
snow cover. The measurements were made at Site 2 and the data are presented
in figure 15.

27 MARCH 28 MARCH 29 MARCH 30 MARCH 31 MARCH 1 APRIL 2 APRIL

|

ai
=

Figure 15. Conducted heat flow through snow-covered ice sheet, site No. 2.

RESISTIVITY MEASUREMENTS IN SEA ICE. Resistivity measurements
were made in the ice sheet at Site 2. Brass rods were driven into the ice sheet to
serve as electrodes. A switching device, which was designed to reverse the polarity
of the electrodes at each successive reading, was used to reduce the polarizing
effect on the electrodes. A 6-volt and a 12-volt lead storage battery were used as
the power supply for the system.

SUMMARY

Mechanical Properties

In comparing the results of 1954 and 1955 in tables 1 and 2, a difference of 300
to 400 meters/sec exists in the longitudinal plate-wave velocity. In Oliver, Crary,
and Cotell’s work,* variations in the plate velocity are of the order of 500
meters/sec. These variations are significant and can be attributed only to differ-
ences in the internal structure of the sea-ice sheet. In comparing the longitudinal
plate-wave velocity obtained by seismic methods (table 2) with the longitudinal
plate-wave velocity obtained by excitation of a long rod (table 4), a difference

TABLE 4. Resonant rod measurements of sea ice for 1955.

Longitudinal Plate-
Wave Velocity
(assuming o = 0.33)
(meters/sec)

Young’s Modulus
E
X 101° dynes/cm?

Rod Length | Resonant Frequency} Rod Velocity

(meters) (meters/sec)
3040 + 10

2330
2370 3040 + 10 3220+ 10

2200 2930 + 10 3110 + 10
2520 3000 + 10 3180 + 10
1475 2830 + 10 3000 + 10

Temperature Range: —18°C to —15°C

3050 + 10 3240 + 10

3000 + 10 3180 + 10

3220 + 10

in the plate velocity of the order of 700 to 800 meters/sec is obtained. These re-
sults are contrary to the results of Ewing, Crary, and Thorne, Jr.” on lake ice, in
which they found no significant difference in the plate-wave velocity when deter-
mined either by use of thin rods or by the seismic method. Poisson’s ratio, which
is not critical in this relation, is assumed to be 0.33. The rods of ice were obtained
with the long axis normal to the ice sheet. The rods were stored for several days
at a temperature between —18°C and —15°C. The temperature gradient in the
ice sheet was —8°C at the top of the sheet to —2°C at the bottom of the sheet,
as is shown in figures 8, 9, and 10. The difference in temperature of the order of
10°C between the ice sheet and the rod might indicate that the temperature of
the sea ice has more than a second-order effect on the elastic constants, whereas
temperature appears to have only a second-order effect with fresh-water ice.’
Another reason for the discrepancy between the longitudinal plate-wave velocity
of the ice sheet and the longitudinal plate-wave velocity as calculated from the
rod velocity might be due to attenuation and dispession. In this case, the faster
high-frequency waves would be attenuated first* in the ice sheet as they emanate
from the shot point; hence, at various distances from the shot point, a change in
the velocity would be detected. However, with the short length of the ice rods,
the high-frequency waves should be detected. Malmgren’* reports sea-ice densities

19

20

between 0.857 gm/cm? and 0.923 gm/cm’, a difference of 0.066 gm/cm*. The dif-
ference in density could contribute to a variation in the longitudinal plate-wave
velocity of the order of 150 meters/sec. The measurements presented in this re-
port do not show such a large variation of density. It is evident that although
density variation contributes to a change in the longitudinal plate-wave velocity,
it is not the major contributor. In 1954 and 1955, measurements were made in
smooth and in rough ice. An indication of the smoothness of the ice is shown by
the probable error of ice thickness measurements from tables 1 and 2.

One set of geophones was placed in an area of rafted ice in 1955. The plate
velocities from this geophone set were lower. The size of the charge which was
used appeared to have no effect on the plate velocity, provided it was sufficiently
large to generate the waves.

Attempts to measure shear wave velocities were unsuccessful, as it was im-
possible to identify positively the shear wave from the complex waves recorded.

Tables 1 and 3 show the results of ice-thickness measurements determined from
air-coupled flexural wave frequencies. When compared with measured ice thick-
ness, the results for an area of smooth ice show, in general, an ice thickness ap-
proximately 10 centimeters less than the measured value. The difference probably
is due to the effect of the bottom layer of the ice sheet which is a weak slush type
of ice. For data taken in an area of rafted ice, the results from calculated ice thick-
ness are less accurate. The probable error in these tables gives an indication of
the unevenness of the ice-sheet surface.

Efforts were made in 1955 to collect data on the independent parameters which
would aid in defining the state of sea ice. State of the ice is defined here as being
a function of a set of independent parameters, such that when these parameters
have some given value, the physical properties of the ice are fixed; that is, the ice
has a given state. If one of these parameters should vary, then the ice would assume
a different state. If the sea ice state can be defined by some dependent parameter
p; and further, if p is some function of 2 independent parameters such that

2 = f(a 25 35 & 05:6 Gn)

then any infinitesimal change in one or more of the independent parameters re-
sults in a change of the sea-ice state.

At NEL, studies are being made on sea ice in an effort to determine which are
the independent parameters. In the work covered in this report, the parameters
which have been considered are density, salinity, air-bubble distribution, crystal
grain size, crystal grain distribution, and the elastic moduli.

.The two salinity profiles taken at Site 2 are in agreement. Site 1 and Site 2 did
not appear to be located in the same ice sheet, and the variation in the salinity
profiles at these two sites seems to indicate that the thermal history of each sheet
was quite different.

A density profile was made only at Site 1. The profile shows a distinct variation
in density but there appears to be no correlation with any of the other parameters.
The average density through the ice sheet is 0.90 gm/cm*. This value is used in
all calculations in the report.

The profiles of air-bubble distribution, as presented in figures 13 and 14, show
that the size of the maximum number of air bubbles per unit area is below 0.1
mm. The general shape of the curves does not appear to have any correlation with
depth in the ice sheet.

The profiles of the crystal grains, as presented in figures 11 and 12, show the
relation between the size of the crystal grain and the size distribution per unit
area. For nearly all depths in the ice sheet, the highest percentage of crystal grain
size lies in the 0.5 mm to 1.0 mm region.

Other Physical Properties

CONDUCTED HEAT FLOW THROUGH AN ICE SHEET
WITH A SNOW COVER

Figure 15 shows the conducted heat flow per unit area from the water through
the ice sheet, the snow cover, and into the atmosphere. The data cover a period
of one week from 27 March to 2 April 1955. Resistance-wire thermometers and
Western Electric type 14B thermistors served as the thermal elements and meas-
urements were made with a Leeds and Northrup type S bridge. Malmgren’s'
values for the thermal conductivity of ice are used in the calculations. The thermal
conductivity value for snow is the average value found in Dorsey.!° The measure-
ments represent a preliminary heat-transfer study,,in which the convective heat
flux, the evaporative heat flux, and the heat of ice formation have not been
measured.

RESISTIVITY MEASUREMENTS IN SEA ICE

The apparent resistivity measurements in sea ice represent a preliminary survey
of techniques and necessary instrumentation. The apparent resistivities (table 5)
show a wide variation with increase in electrode spacing. The ice thickness in the
area of these measurements showed an average value of 84.0 cm (33 inches). The

TABLE 5. Apparent dc resistivity measurements.

Separation of
Electrodes Potential | Current Resistivity
E 191 a(E/I)
(ohm-cm)

21

22

results indicate the effect of salinity variations in the ice sheet on the apparent
resistivity values. As electrode spacing is increased, the distribution of electric
current spreads vertically downward into the ice sheet and to the water beneath
the ice. The low resistivity value with a minimum electrode separation of 7.62
cm (3 inches) indicates the high salinity content of the ice at or near the surface.
The apparent resistivity calculations indicate a maximum value at an electrode
spacing of approximately 60.9 cm (2 feet). As electrode separation is increased
beyond 60.9 cm (2 feet), the apparent resistivity falls off rapidly, indicating the
shunting effect of the sea water path of higher conductivity. The measurements
were taken within a temperature range of —5°C to —2°C. Because of the short
period of time in which field measurements could be made, it was impossible to
obtain a more complete temperature-resistivity profile. In comparing the data
obtained with the results of a more complete study of another group,’® it appears
that the measurements are reasonably consistent with those of the other group
within a temperature range common to the results of each group.

RECOMMENDATIONS

1. A study should be made of the variation of all parameters over one entire ice
season at one location. In conjunction with this survey, an attempt should be made
to relate the plate-wave velocity variation with the state of the sea ice and the state
of the sea ice with its breaking properties.

2. Continuous measurements over a complete ice season should be made of:
(1) the temperature gradients through an ice sheet with a snow cover, (2) wind
gradients above the ice sheet, (3) wet and dry temperature gradients above the ice
sheet, and (4) the net radiation. This would give the heat transfer through an ice
sheet by three different methods. From these measurements the thermal conduc-
tivity of the sea-ice sheet, the surface albedo, and the exchange coefficients at the
air-snow or ice boundary can be determined.

REFERENCES

1. T.C. Poulter Geophysical Studies in the Antarctic Stanford Research Insti-
tute, [1950] p. 27.

2. M. Ewing, et al. “Propagation of Elastic Waves in Ice. Part I’ Journal of
Applied Physics vol. 5, no. 6, June 1934, pp. 165-168.

3. N.E. Dorsey Properties of Ordinary Water-Substance in all its Phases: water-
vapor, water, and all the ices Reinhold, 1940, p. 461.

4, J. Oliver, et al. “Elastic Waves in Arctic Pack Ice” American Geophysical
Union. Transactions vol. 35, no. 2, April 1954, pp. 282-292.

5. J.B. Macelwane and F.W. Sohon Introduction to Theoretical Seismology
Wiley, 1936, pp. 89-105.

6. Rayleigh, Lord The Theory of Sound 2d ed., Dover, 1945, vol. I, pp. 242-254.

7. F. Press, e¢ al. “Air-coupled Flexural Waves in Floating Ice” American Geo-
physical Union. Transactions vol. 32, no. 2, April 1951, pp. 166-172.

8. L.R. Ingersoll, et al. Heat Conduction; with engineering, geological, and
other applications McGraw-Hill, 1954, p. 3.

9. M.B. Dobrin Introduction to Geophysical Prospecting McGraw-Hill, 1952,
pp. 292-297.

10. H. U. Sverdrup, et al. The oceans, their physics, chemistry, and general bi-
ology Prentice-Hall, 1942, pp. 216-219.

11. F. Malmgren Ox the Properties of Sea-Ice (Norwegian North Polar Expe-
dition with the Maud 1918-1925, Scientific Results vol. 1, no. 5) n.d. pp. 7-14.

12. T.D. Northwood “Sonic Determination of the Elastic Properties of Ice”
Canadian Journal of Research sec A, vol. 25, no. 2, March 1947, pp. 88-95.

13. F. Malmgren On the Properties of Sea-Ice (Norwegian North Polar Expedition
with the Maud 1918-1925, Scientific Results vol. 1, no. 5) n.d. pp. 15-18.

14. F. Malmgren On the Properties of Sea-Ice (Norwegian North Polar Expedition
with the Maud 1918-1925, Scientific Results vol. 1, no. 5) n.d. pp. 64-65.

15. N.E. Dorsey Properties of Ordinary Water-Substance in all its Phases: water-
vapor, water, and all the ices Reinhold, 1940, p. 483.

16. W. J. Dichtel and G. A. Lundquist Az Investigation into the Physical and
Electrical Characteristics of Sea Ice Naval Ordnance Laboratory [1950].

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