Sea Ice

Part I. Bulk Salinity Versus Ice Floe Thickness

Austin Kovacs June 1996

CRREL REPORT 96-7
Abstract: Mathematical expressions have been established for estimating the bulk salinity of Arctic and

Antarctic sea ice vs. ice floe thickness. The ice salinity

vs. thickness relationships are based on data for over

400 sea ice cores compiled from numerous sources.

The results show that the bulk salinity of first-year sea

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Cover: Logging of a sea ice core in the field. After extraction from the ice sheet, the ice core is quickly removed

from the ice core barrel and placed on a cutting board, not on the snow, which can draw brine from the ice. The

core length is measured. Small holes are then drilled about 2–3 cm deep into the core side at 20-cm increments

and a thermistor is inserted in each hole to determine the in-situ temperature of the ice sheet. Closer spaced

measurements may be required near the ice sheet surface, top of the ice core, to better define the temperature

gradient in the region. The core is next cut into lengths using the cut-off saw, which is mounted at the end of the

cutting board, and the axial length of the ice cylinder then is determined (in this case, using a dial gauge

measurement jig located beside the notebook). The ice sample is next weighed on an electronic balance and

then placed in a sealed plastic bag or container for later melting and salinity measurements. Air and ice sheet

temperature, ice porosity and processing time are factors that effect the loss of brine from the ice core during

logging. Upward flow of seawater through the permeable ice remaining at the bottom of a borehole will flush

brine from the ice. When this ice is finally removed by coring, its brine concentration may have changed

appreciably and the subsequent salinity measurement would be in error.

ice decreases in an exponential trend with ice sheet

thickness. A similar trend reoccurs as the winter ice

passes through the melt season. The expression for the

bulk salinity SB in ‰ for first-year sea ice from 10 to

200 cm thick is SB = 4.606 + 91.603/TF, where TF is

the ice floe thickness in centimeters.
CRREL Report 96-7

Sea Ice

Part I. Bulk Salinity Versus Ice Floe Thickness

Austin Kovacs June 1996

Approved for public release; distribution is unlimited.

US Army Corps


of Engineers

Cold Regions Research &


Engineering Laboratory
PREFACE

This report was written by Austin Kovacs, Research Civil Engineer, Applied

Research Division, Research and Engineering Directorate, U.S. Army Cold Regions

Research and Engineering Laboratory (CRREL), Hanover, New Hampshire.

The author acknowledges, with thanks, Dr. Lewis Shapiro of the University of

Alaska and Dr. Donald Perovich of CRREL for their unpublished sea-ice bulk salinity

vs. ice sheet thickness data. He thanks Dr. Martin O. Jeffries of the University of

Alaska for providing the tabulated ice salinity vs. thickness data from his published

figures. The review comments of Dr. Anatoly M. Fish of CRREL, Dr. Walter Spring of

Mobil Research and Development Corp., Dr. Wilford F. Weeks of the Geophysical

Institute, University of Alaska—Fairbanks, and Dr. Brian Wright of B. Wright and

Associates Ltd. are also acknowledged.

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 products.
CONTENTS

Page

Preface ..................................................................................................................... ii

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

Ice floe brine volume and salinity ....................................................................... 4

Estimating ice floe salinity ................................................................................... 6

Summary ................................................................................................................. 12

Literature cited ....................................................................................................... 13

Abstract .................................................................................................................. 17

ILLUSTRATIONS

Figure

1. Sea-ice crystal structure ............................................................................. 1

2. Sea-ice core sections.................................................................................... 2

3. Over 1-m-long stalactite that formed as a result of cold brine

drainage into the sea at the bottom of an ice floe .............................. 3

4. Three columnar sea-ice crystals with unaligned c-axes ........................ 3

5. Major 17-cm brine wave migration event observed in Antarctic

fast-sea ice ............................................................................................... 4

6. Sea-ice bulk salinity vs. floe thickness as reported by Cox and

Weeks ....................................................................................................... 5

7. Sea-ice bulk salinity vs. ice sheet thickness and growth time .............. 5

8. Sea-ice bulk salinity and growth rate vs. floe thickness........................ 6

9. Sea-ice bulk salinity vs. growth time ....................................................... 6

10. Comparison of Ryvlin’s empirical equation for estimating

sea-ice bulk salinity vs. floe thickness ................................................. 7

11. Beaufort Sea first-year ice bulk salinity vs. floe thickness .................... 7

12. Sea-ice bulk salinity vs. floe thickness as calculated with Ryvlin’s

equation for 31.5 and 34‰ seawater ................................................... 8

13. Ryvlin’s equation for calculating sea-ice bulk salinity vs. floe

thickness where parameter 

a is constant and varied to match

the regression curve through the Beaufort Sea ice data in

Figure 11 .................................................................................................. 8

14. Antarctic first-year sea-ice bulk salinity vs. floe thickness data of

Jeffries (1994)........................................................................................... 9

15. Ryvlin’s equation for calculating sea-ice bulk salinity vs. floe

thickness, where parameter 

a is constant and varied to match

the regression curve through the Antarctic sea-ice data in

Figure 14 .................................................................................................. 9
Figure Page

16. Sea-ice stable salinity and the sea-ice seawater salinity ratio vs.

growth rate .............................................................................................. 9

17. Antarctic first-year sea-ice bulk salinity vs. floe thickness data

collected from several sources ............................................................. 10

18. All Arctic and Antarctic first-year sea-ice bulk salinity vs. floe

thickness data compiled from numerous sources ............................. 10

19. Comparison between the regression curve passed through all the

bulk salinity vs. ice floe thickness data in Figure 18 and the

field data in Figure 7 .............................................................................. 11

20. Beaufort Sea multiyear ice bulk salinity vs. floe thickness ................... 11

21. Beaufort Sea and Antarctic multiyear sea-ice bulk salinity vs. floe

thickness .................................................................................................. 12

22. All Arctic and Antarctic multiyear sea-ice bulk salinity vs. floe

 thickness data ........................................................................................ 12
INTRODUCTION

When seawater freezes, small, flat platelets of

fresh ice are first to form. As this ice mass grows,

the platelets commingle and bond one to another

to form a compliant, highly saline slush called

grease ice. With sustained freezing temperatures,

the platelet mass thickens and grows together,

forming an ever-stiffening ice cover. During this

ice growth process most of the seawater is displaced, but between the platelets of pure ice a

seawater concentrate called brine becomes entrapped. This entrapment causes the ice to be

salty: the salinity of the surface layer of the new

ice can be greater than 40‰ (Martin 1979, Kasai

and Ono 1984, Ono and Kasai 1985).

Many factors affect the thickness of the

platelet or frazil ice layer, including growth

rate, sea state, ice pack motion, and under-ice

turbulence. However, under relatively quiescent conditions and after the frazil ice layer

has “stabilized,” the stage is set for the growth

of congelation ice. At first, the growing ice

platelets, <0.5 mm thick, are randomly oriented, but in time they become more and more

ordered, grow wider, and stack one against

another. They freeze together in layered groups

to form individual ice crystals. Due to thermodynamic factors, preferred platelet growth in

seawater is vertical (Weeks and Ackley 1989).

Therefore, over a short growth span the ice

crystals become “vertically” aligned, with the

parallel platelet array having a predominantly

horizontal c-axes alignment. The ensuing

growth structure is called congelation ice. The

number and size of the vertical ice platelets in

any crystal vary with growth rate, as does the

volume of brine trapped between the fresh-ice

platelets (Cox and Weeks 1988, Weeks and

Ackley 1989).

Brine entrapment originates in the root area

(Fig. 1) of the 1- to 5-cm-thick mushy region called

the SK or skeleton layer (Harrison and Tiller 1963)

or crystallization front (Cherepanov 1975). In this

growth zone the individual ice platelets extend

into the seawater, like fingers on a hand, and are

typically less than 0.25 mm thick and more than 1

cm wide. As each dendritic platelet grows thicker

at its root, it freezes to its neighbor. A high growth

rate at this stage (>2 cm/day) results in platelets

less than 0.5 mm thick, but at low growth rates

(<0.5 cm/day) the platelets can grow to be 1.6

mm thick, with a related increase in crystal size

(Weeks and Hamilton 1962a,b; Page 1966; Nakawo

and Sinha 1984). During this crystal formation

Sea Ice

Part I. Bulk Salinity Versus Ice Floe Thickness

AUSTIN KOVACS

Figure 1. Sea-ice crystal structure.

d


– 











     

   

    

 









     













Fresh Ice


Platelet a


– Gas

Brine

SK Ice


~ 1 to 5 cm c-axis


Direction

Basal


 

Plane















Columnar


Ice













b


–



















































c


–

Brine


Pockets

Root


Zone

a ≤ b < c
 – – –

d ~ 0.25 to 1.25 mm (avg 0.7)


–

a ~ 0.1 to 0.3 mm; b ~ 1 to 5 × a; c > 5 × a
 – – – – –  Frozen Interface

Seawater Interface
Figure 2. Sea-ice core sections (from Morey et al. 1984).

process the seawater at the ice growth interface is

replaced by supersaturated brine that slows the

rate of solidification. As with the frazil/granular

surface ice layer, some brine and gas become

trapped between the platelets, as depicted in Figure 1. As the ice sheet continues to grow and

becomes colder, the film of brine between the ice

platelets reduces in volume due to expulsion and

drainage processes as well as the freezing out of

fresh water from the brine to the surrounding ice

surface. The now-isolated brine inclusions are

called brine pockets. They are frequently described

as ellipsoids, but in fact can have rather complex

geometries, depending on ice growth rate and

temperature.

Brine expulsion and drainage occur along a

flow route that resembles the trunk and branches

of a tree, called a drainage tube and channels,

respectively. A vertical drainage tube and channel system in Beaufort Sea congelation ice is

shown in Figure 2. From 1.5-m-square ice blocks

removed from 1- and 1.8-m-thick ice sheets in the

Beaufort Sea, I found the drainage tubes at the

bottom of the ice to be spaced 5 to 17 cm apart,

but they average 10 cm apart. These spacings are

in agreement with the findings of Martin (1979),

Wakatsuchi (1983), and other investigators.

Wakatsuchi also reported that the spatial density

of brine tubes depends on the growth rate. The

faster the growth rate, the more drainage tubes

per unit area. The brine channel inclination varies

from 40° to 54°, but averages 45° (Lake and Lewis

1970, Criminale and LeLong 1984).

Brine drainage is high during initial ice formation, but as the ice sheet thickens and becomes

colder, brine flow decreases and much of the drainage system is transformed into a series of brine

and gas cells separated by necks of ice (Doronin

and Kheisin 1975). The salinity at any given depth

now decreases slowly during the remainder of

the growth season. Drainage systems form again

during the melt season (Nakawo and Sinha 1981).

Near-freezing temperatures and solar radiation

heating cause melting, “corrosion pockets” form

in the ice surface, and internal melting occurs at

crystal boundaries, old brine drainage routes,

flaws, etc. (Bennington 1967, Cox and Schultz

1980). The corrosion pockets contain liquid with a

high salt concentration originating, for example,

from the salt residue of the >50‰ salinity brine

that was ejected to the surface during initial ice

sheet formation (Burke 1940, Zubov 1945, Martin

1979, Drinkwater and Crocker 1988, Perovich and

Richter-Menge 1994), from the typically high-salinity frazil or granular ice surface layer (Martin

1979) or from brine concentrated in an ice surface

layer formed as a result of ice sheet flooding. The

enriched brine then melts into the ice sheet, reopening or enlarging the old drainage systems as

the brine wave descends to the sea. The cold,

high-salinity (60 to 70‰) drainage (Lewis and

Milne 1977) is followed by increasingly fresher

flow resulting from the pure-ice melt or is replaced by an upward flow of less dense seawater

(Edie and Martin 1975). Depending on the brine

temperature and volume flux and seawater current velocity, on exiting the ice the brine drainage

can freeze the seawater around the periphery of

the descending brine plume, forming long, delicate, thin-walled hollow ice stalactites (Fig. 3) that

2

a. Vertical sea ice core showing relative configuration of

brine drainage feeder channels (1) extending outward at

≈ 45° from the brine drainage tube (2).

b. Horizontal section across a brine drainage tube. Radiating out from the central brine drainage tube area (1) are

numerous brine drainage feeder channels (2).
on occasion can extend up to 6 m below the bottom of the sea ice (Page 1970, Dayton and Martin

1971, Martin 1974, Lewis and Milne 1977,

Grishchenko 1988).

As reported in Kovacs and Morey (1980), the

growth of congelation sea ice in calm water results in a structure in which the c-axes of the

crystals are randomly oriented in the horizontal

plane. This is depicted in Figure 4. However, if a

current exists under the ice sheet, selective ice

platelet growth and therefore crystal fabric orientation occurs, in which the horizontal c-axes of

the ice crystals become aligned with the current

(Kovacs and Morey 1978, Weeks and Gow 1978,

1979; Langhorne and Robinson 1986). The significance of this alignment is that it renders the ice

sheet horizontally anisotropic, and this in turn

affects the electromagnetic (Campbell and Orange

1974; Kovacs and Morey 1978, 1979; Morey et al.

1984) and mechanical (Anderson 1963, Payton

1966, Wang 1979, Timco et al. 1991, Kovacs 1993)

properties of the ice. Many other investigators

have observed preferred c-axis alignment in sea

ice. Perhaps most notable is Cherepanov (1975),

who made wide-area sea-ice observations in the

seas north of Russia, and, more recently, Gow et

al. (1982), who verified that similar sea-ice c-axis

alignment occurs in Antarctic congelation sea ice.

While the above description of first-year seaice growth does not encompass the many structure variations that can occur due to such factors

as snow loading and flooding, thick frazil-ice

components (e.g., Cherepanov and Kozlovskiy

1973a,b; Martin 1981; Gow et al. 1987), and large

interlaced ice platelet layers, as found, for example, in Antarctic sea ice (e.g., Cherepanov and

Kozlovskiy 1973a, Dieckmann et al. 1986, Eicken

and Lange 1989, Jeffries and Weeks 1993), it does

reveal that sea ice is a multicomponent material.

It is composed of fresh ice, brine, and gas inclusions and solid salt crystals (Sinha 1977, Marion

and Grant 1994). The volume of fresh ice is by far

C-axis

Orientation

Parallel Fresh Ice 

Platelets

Brine and Gas

Pockets

Figure 4. Three columnar seaice crystals with unaligned caxes. The crystal boundaries

are highly irregular.

Figure 3. Over 1-m-long stalactite

that formed as a result of cold brine

drainage into the sea at the bottom

of an ice floe.

3
the largest fraction, typically in excess of 95%. Sea

ice is classified by age (first-year, second-year,

and multiyear) and by morphology (flat, ridge,

rafted, etc.). Variations in growth, melt, and deformation processes result in ice formations of

complex shape and structure and variable brine

and gas content. The sea ice may also contain

foreign matter such as sediment (e.g., Barnes et al.

1984, Kempema et al. 1989) and microscopic algae

and diatoms (e.g., Sutherland 1852; Wright and

Priestley 1922; Usachev 1949; Buinitskii 1965, 1974;

and many others more recently).

ICE FLOE BRINE VOLUME

AND SALINITY

A number of factors affect the volume of brine

that is initially incorporated into the sea ice. Foremost is the salinity of the seawater, the ice growth

rate and structure. Under extreme cold conditions, accelerated growth occurs, and more brine

tends to be entrapped in the ice at the bottom of

the ice sheet (e.g., Malmgren and Sverdrup 1927,

Burke 1940, Zubov 1945, Weeks and Lee 1958,

Nakawo and Sinha 1981) and for congelation ice

the ice platelets that form each ice crystal are

narrower (e.g., Weeks and Hamilton 1962a,b; Page

1966; Nakawo and Sinha 1984). As the ice sheet

thickens, the rate of growth slows due to the decreasing rate at which heat is transferred from the

bottom of the ice to the atmosphere (Makshtas

1984, Maykut 1986). This heat exchange is further

reduced with increasing snow cover. The net effect is that less brine entrapment occurs as the ice

increases in thickness. Over time, very gradual

brine migration occurs toward the warmer seawater (Whitman 1926, Zubov 1945, Kingery and

Goodnow 1963, Bennington 1967, Untersteiner

1968, Nakawo and Sinha 1981). An explanation

for this continued brine migration is the dissolution of ice by the brine at the warmer bottom end

of a brine pocket and a refreezing of water at the

colder upper end of the pocket. This migration

and associated brine drainage gradually reduce

the bulk salinity of the ice from an initial value of

as much as 25‰ for ice 5 cm thick to about 5‰

for first-year ice about 2 m thick.

Accelerated brine drainage can occur under

warming conditions. The enriched brine from the

top of the ice sheet can move downward like a

wave slowly descending through the ice sheet.

During the descent the general form of the wavelet is preserved, but the amplitude (that is, the

brine volume) gradually decreases. This is due to

brine pockets intercepting the drainage network

and draining to the sea in advance of the following brine wave. This drainage phenomenon, illustrated in terms of a very smooth ice sheet salinity distribution profile, is shown in Figure 5.

The salinity (brine) migration wave shown is very

fast, about 0.8 cm/day. Migration rates one to two

orders of magnitude lower may be more typical

for winter sea ice, based on the velocity assessments presented by Weeks and Ackley (1989), who

give an in-depth review of sea-ice salinity and

brine entrapment and migration processes. In addition, it is difficult, at best, to see this movement

in the similar data of Nakawo and Sinha (1981),

and a rate of 1 mm/day may be estimated from

Shapiro and Weeks (1993, Figure 9).

A widely cited study on the bulk salinity variation in sea ice is that of Cox and Weeks (1974). In

this study average or bulk salinity data for winter

Beaufort Sea ice was collected from a number of

sources. Their plot of the salinity vs. ice thickness

data clearly shows a decrease in bulk salinity with

increasing ice floe thickness (Fig. 6). The available

data seemed to justify representing the bulk salinity vs. ice floe thickness trend by the two linear

curves shown in Figure 6. However, many natural phenomena tend to follow exponential-like

distributions. Sea-ice bulk salinity vs. floe thickness appears to be one of them.

Figure 5. Major 17-cm brine wave migration event observed in Antarctic fast

sea ice between 14 May and 5 June

(after Doronin and Kheisin 1975).

5 6 7 89

0

40

80

120

5 Jun

14 May

17 cm

D, Depth (cm)

S , Ice Salinity (‰) i

4
rapid decrease in bulk salinity as the ice

sheet grew to about 0.5 m thick and a

gradual decrease in bulk salinity thereafter.

Other early reports also confirm that

this bulk salinity vs. floe thickness trend

applies to Antarctic sea ice. Fedotov

(1973) measured the bulk salinity of the

fast ice in Alasheev Bight during the

growth period. His results are presented

in Figure 8. The bulk salinity was found

to be about 25‰ in the 5-cm-thick ice

but dropped rapidly to about 7.5‰ when

the ice was 0.5 m thick. At the end of the

measurement period (about 170 days),

the ice was 150 cm thick and the bulk

salinity had decreased to about 5‰.

Doronin and Kheisin (1975) presented

results for the bulk salinity of Antarctic

fast sea ice during the growth and melt periods

(Fig. 9). This figure again shows a rapid decrease

in the bulk salinity during the first growth month,

followed by a gradual decrease until the onset of

the melt season in October. At this time another

rapid decrease in the bulk salinity began, which

ended in December. The ice sheet’s bulk salinity

had by then decreased to about 2‰, a value representative of Arctic multiyear sea ice of similar

thickness.

Figure 6. Sea-ice bulk salinity vs. floe thickness as reported by Cox and Weeks

(1974).

20

15

10

5

0

1 Jan 1 Feb 1 Mar 1 Apr 1 May

Avg. Ice Thickness (cm)

24 54 85 90 95

S , Bulk Salinity (‰) B

Date of Determination

Figure 7. Sea-ice bulk salinity vs. ice sheet thickness and growth

time (after Weeks and Lee 1958).

In the mid-1950s, Weeks and Lee (1958) published their observations on the bulk salinity of

an ice sheet vs. ice thickness and growth time

(Fig. 7). The abrupt step in the curve through the

data occurred as a result of a flooding event during which seawater infiltrated the snow cover.

Had this not occurred, one could visualize that

the trend of the curve before the step would have

continued to decrease to a salinity of about 5‰

by May. In any event, the data clearly reveal a

5

k 5/4

16

12

8

4

0 100 200 300 400

S , Bulk Salinity (‰) B

T , Floe Thickness (cm) F

First-Year Ice

Multiyear Ice S = 14.237 – 0.194T B F

S = 7.879 – 0.016T B F
30

20

10

0 50 100 150

150

100

50

0

S , Bulk Salinity (‰) B

G , Growth Time (days) T

T , Floe Thickness (cm) F

r = 0.989 2

S = 4.371 + 158.329/T – 321.604/TF

2

B F

2 r = 0.998

T = – 1.905 + 0.466 G /1 – 0.004G F TT

Figure 8. Sea-ice bulk salinity and growth rate vs. floe thickness

(after Fedotov 1973).

10

8

6

4

2

0 M A M J J A SO N D J

S , Bulk Salinity (‰) B

Growth Time

Figure 9. Sea-ice bulk salinity vs. growth time (after Doronin

and Kheisin 1975).

The decrease in bulk salinity vs. time shown in

Figures 7 and 9 was also observed during laboratory studies of brine entrapment processes

in NaCl ice (Cox and Weeks 1975) and in natural sea ice by Fukutomi et al. (1951) and Blinov

(1965).

These reports clearly indicate that the bulk salinity of natural and laboratory-grown saline ice

decreases rapidly with increasing thickness or time

during the early growth phase, followed by a

second rapid decrease in the bulk salinity during

the early part of the melt season. Because of the

latter decrease, the bulk salinity data for “warm”

or “old” sea ice should not be combined and analyzed with “cold” first-year sea ice data.

ESTIMATING

ICE FLOE SALINITY

Ryvlin (1974) was one of the first to

express the bulk salinity SB vs. ice floe

thickness TF trend empirically. His formula takes into consideration the salinity

of the seawater Sw and the ice sheet

growth rate GR as follows:

 

S S S SS Bw R

a T e R w = − F ( ) + ( ) 1 0 5 – .

(1)

where SR = SBF/Sw = salinity ratio

SBF = final bulk salinity at end of

growth season

 

a = growth rate coefficient, reported to vary from 0.35 to

0.5, e.g., at GR ≥ 4 cm/day,

 

a = 0.35, and at GR ≤ 0.5

cm/day, 

a = 0.60.

Ryvlin suggests that where GR is not

known, one may assume the value of 0.5

for a. He also found empirically that SR is ≈

0.13. Using a value of 0.5 and 34‰ for a

and Sw respectively, and an unknown value

for SBF, Ryvlin compared eq 1 with his and

Weeks and Anderson’s (1958) first-year sea

ice SB vs. TF field data, as shown in Figure

10. In this comparison, the agreement between the empirical estimate and field measurements is extremely good throughout

the entire ice floe thickness range. The question is, does this agreement hold for other

data sets?

To evaluate Ryvlin’s equation, we first

compiled unpublished first-year Beaufort

Sea ice SB vs. TF data that was provided

by Perovich (five cores for TF <25 cm)

and Kovacs (30 cores), along with published data

from Gow and Weeks (two cores, 1977), Tucker et

al. (five cores, 1984), and Meese (nine cores, 1989)

(Fig. 11). The salinity of the Beaufort Sea near the

Alaska coast is 31.5‰. The purpose of using data

from just one location is that the salinity of the

water is a parameter that affects ice salinity (Weeks

and Lofgren 1967, Ryvlin 1974). This can be seen

in Figure 12, where the only parameter varied in

eq 1 was the seawater salinity. The fixed parameters used in eq 1 to create the curves in Figure 12

were 0.5 for 

a and 0.13 for SR. For an end-ofgrowth-season ice thickness of 200 cm, SB is

4.44‰ and 4.12‰ for an Sw of 34‰ and 31.5‰,

respectively. For this example, the seawater sa6
eq 1 does not fit the data. This is surprising, given the good agreement shown in

Figure 10.

At 200 cm the regression curve in Figure 11 gives a value of 5.50‰ for SB. Dividing this salinity by Sw = 31.5‰ gives a

value for SR of 0.175, not 0.13 as Ryvlin

determined from his data analysis. Using

this new SR value along with his suggested

growth rate coefficient of 0.5 in eq 1 brings

the Ryvlin curve into good agreement with

the regression curve between TF = 125 and

200 cm. However, there is still a significant

difference between eq 1 and the regression

curve where TF is less than about 50 cm. To

bring the two curves into agreement, coefficient 

a has to vary with TF. This is shown

in Figure 13, where the lower curve represents eq 1 with only SR changed from 0.13

to 0.175 and the upper curve represents

both the regression line through the data

in Figure 11 and eq 1 with SR = 0.175 and

coefficient 

a varied as shown.

To verify the need to vary SR and a in eq

1, I analyzed the SB vs. TF data collected by

Jeffries (1994) in the Amundsen and

Bellingshausen Seas, Antarctica, in late

winter. Unlike the predominantly congelation sea-ice data from the Arctic (Beaufort

Sea) the Antarctic sea-ice data are from ice

sheets having a predominantly frazil, large

interlaced platelet and infiltrated snow ice

structure. Core data on ice up to 200 cm

thick with a mean temperature below –3°C

were selected. The latter ensured that the

ice was “cold” and not melting. Their data

from 74 ice cores are shown in Figure 14.

The representative regression curve

through the data is of the same form as the

one through the Beaufort Sea ice data in

Figure 11. It is important to note that the regression curve at TF = 200 cm gives SB = 5.41

vs. 5.50‰ for the Beaufort Sea data. Given the

fact that the Antarctic seawater salinity is 34‰*

vs. 31.5‰ for the southern Beaufort Sea, one

would expect these SB values to be reversed for

reasons previously discussed. This unexpected

result suggests that the sea-ice data for the

linity difference caused an 8% difference in the

bulk sea-ice salinity.

The regression curve through the Beaufort Sea

SB vs. TF data (Fig. 11) is, for all intents and purposes, horizontal after an ice thickness of about

150 cm. Therefore, SBF may be determined from

the regression curve at any TF after 150 cm with

minor effect on the results of eq 1. For consistency, SBF at TF = 200 cm is used in this report.

Running below the regression line, and most

of the data, in Figure 11 is the curve derived using

eq 1 and an Sw of 31.5‰ (Fig. 12). Even though

the number of data points is limited (and nonexistent for a TF of 25 to 50 cm) it is apparent that

* M. Jeffries (1995), Geophysical Institute, University of Alaska, Fairbanks, and S. Jacobs (1995),

Lamont-Doherty Geological Observatory of Columbia University, Palisades, New York, personal communications.

20

15

10

5

0 50 100 150 200

T , Floe Thickness (cm) F

S , Bulk Salinity (‰) B

S = (2.242 + 20.556/T )2

B F

r = 0.840 2

S D = 1.45

S = 31.5 ‰ (Beaufort Sea) w

Figure 11. Beaufort Sea first-year ice bulk salinity vs. floe thickness. The lower curve represents the results of Ryvlin’s equation for 31.5‰ seawater.

Figure 10. Comparison of Ryvlin’s empirical equation for estimating sea-ice bulk salinity vs. floe thickness, with field data

(after Ryvlin 1974).

40

20

0 40 80 120

S , Bulk Salinity (‰) B

T , Floe Thickness (cm) F

Weeks and Anderson

Ryvlin

20 60 100

30

10

7
Arctic (Fig. 11) and Antarctic (Fig. 14) are not

sufficient to fully define the SB vs. TF trends or

that the effect of the seawater salinity difference on SB is masked by the scatter in the data

and/or ice structure differences. Perhaps as important is the regression curve selected to represent the data. Statistically, two regression curves

may fit the data with nearly the same correlation

coefficient r2 value, but they give different SB values at 200 cm. In any event, since the regression

curves (Fig. 11 and 14) lie well within each other’s

standard deviation, there is no statistically significant difference between them. Given this reasoning, it would seem that the Arctic and Antarctic sea ice SB vs. TF data can be combined.

Also shown in Figure 14 is the curve derived

from unmodified eq 1 (Fig. 12). As with the Beaufort Sea data, the curve does not fit the data.

Taking the regression curve (Fig. 14) value for

SBF = 5.41‰ at TF = 200 and dividing this salinity

by Sw = 34‰ gives an SR of 0.159. Using this

value in eq 1 gives the lower curve in Figure 15.

Varying coefficient 

a at the TF increments shown

in Figure 15 causes the Ryvlin equation to give SB

vs. TF values that match the regression curve

through the Antarctic data (Fig. 14). Both the modified Ryvlin and regression curves are represented

by the upper curve in Figure 15.

The fact that growth rate coefficient a needs

to vary with TF is not surprising. Ryvlin indicated

as much in his description of a in eq 1. A further

indication of the need to vary a can be seen in

Figure 8. Here the time to grow successive increments of ice is shown to increase with thickness.

In short, the heat flux through growing sea ice

decreases exponentially with thickness and likewise reduces the rate of ice growth (Makshtas

1984, Maykut 1986) and brine entrapment. The

20

15

10

5

0 50 100 150 200

T , Floe Thickness (cm) F

S , Bulk Salinity (‰) B

S = 34 ‰ (Amundsen and Bellingshausen Seas w )

S = 31.5 ‰ (Beaufort Sea) w Figure 12. Sea-ice bulk salinity vs. floe thickness

as calculated with Ryvlin’s equation for 31.5 and

34‰ seawater.

20

15

10

5

0 50 100 150 200

T , Floe Thickness (cm) F

S , Bulk Salinity (‰) B

0.220 = a

0.320

0.375

0.400

0.450

a = Varied

a = 0.5 Figure 13. Ryvlin’s equation for calculating seaice bulk salinity vs. floe thickness where parameter 

a is constant (lower curve) and varied (upper curve) to match the regression curve through

the Beaufort Sea ice data in Figure 11.

8
20

15

10

5

0 50 100 150 200

T , Floe Thickness (cm) F

S , Bulk Salinity (‰) B

S = 34 ‰ (Amundsen and Bellingshausen Seas) w

S = 5.369 + 1646.132/T 2

B F

r = 0.777 2

S D = 1.17

Figure 14. Antarctic first-year sea-ice bulk

salinity vs. floe thickness data of Jeffries

(1994). The upper curve is the regression

fit to the data. The lower curve represents

the results using Ryvlin’s equation for

ice grown in 34‰ seawater.

Figure 15. Ryvlin’s equation for calculating sea-ice bulk salinity vs. floe thickness,

where parameter 

a is constant (lower curve)

and varied (upper curve) to match the regression curve through the Antarctic seaice data in Figure 14.

Figure 16. Sea-ice stable salinity and the

sea-ice seawater salinity ratio vs. growth

rate.

20

15

10

5

0 50 100 150 200

T , Floe Thickness F

S , Bulk Salinity (‰) B

0.225 = a

0.270

0.350

0.475

0.520

0.550

a = Varied

a = 0.5

20

16

12

8

4

0 2 4 6 8 10 12 14

0.6

0.4

0.2

0

G , Growth Rate (cm/day) R

S , Stable Salinity (‰) s

r = 0.96 2

S = 5.60 G R

0.48

s

S D = 0.90

S D = 0.03

S = 0.17 G R

0.49

r = 0.96 2

R

S = = Salinity Ratio SB

w S R

9
tions in sampling techniques that may exist

between different research groups and to ensure that the ice sampled grew in seawater of

the same salinity. In the comparison between

this data set and the Beaufort Sea data, it was

found that the effect of seawater salinity on

ice salinity was not statistically discernible.

Therefore, it seems reasonable to combine

the Antarctic SB vs. TF data of Jeffries (1994)

with the Antarctic data of Fedotov (1973),

Wakatsuchi (1983), Gow et al. (1987),

Makshtas (1984), Eicken (1992), Gow et al.

(1992), Ackley et al. (1993), and Veazey et al.

(1994). These data, 315 points, are plotted in

Figure 17. There is considerable scatter in the

data, which can be due to a number of factors: natural growth rate variations (Fig. 16),

brine drainage during coring and processing, errors in salinity determination, variations in ice type (infiltrated snow, frazil, platelet and columnar ice), and morphology, such

as layered rafted ice. The salinity errors could

arise from errors in measuring the ice-core

temperature and melt conductivity, measurements that are required for calculating ice

salinity. The regression curve through the data

in Figure 17 probably gives a better assessment of Antarctic sea ice SB vs. TF than the

curve in Figure 14 because of the increase in

the number of data points from 74 to 315.

Combining now the data in Figure 17 with

the Arctic data in Figure 11 along with firstyear sea ice SB vs. TF data collected at Thule,

Greenland, and Hopedale, Labrador (Weeks

and Anderson 1958), Fram Strait (Gow et al.

1987), Port Clarence, Alaska (Kovacs and

Kalafut 1977), and Elson Lagoon, Pt. Barrow,

Alaska (L.H. Shapiro* 1994, personal contribution, eight measurements), the distribution shown in Figure 18 is obtained. Interestingly,

the regression curve through the combined data

gives nearly the same SB vs. TF values as the curve

in Figure 17. For example, at 200 cm both equations give 5.07‰ for SB, while at 15 cm the difference is only 0.30‰. This is well within experimental error, and suggests that for most purposes

the bulk salinity vs. thickness of undeformed firstyear sea ice grown in Arctic and Antarctic seawater with a salinity of about 31 to 34‰ will be very

similar. Refinements and standardization of sampling techniques may one day allow us to see the

Figure 17. Antarctic first-year sea-ice bulk salinity vs. floe

thickness data collected from several sources.

20

10

0 50 100 150 200

T , Floe Thickness (cm) F

S , Bulk Salinity (‰) B 30

r = 0.683 2

S = 4.644 + 86.660/T B F

S D = 1.46

20

10

0 50 100 150 200

T , Floe Thickness (cm) F

S , Bulk Salinity (‰) B 30

r = 0.730 2

S = 4.606 + 91.603/T B F

S D = 1.47

Figure 18. All Arctic and Antarctic first-year sea-ice bulk

salinity vs. floe thickness data compiled from numerous sources.

latter, of course, affects the salinity of the ice. This

is illustrated in Figure 16, which shows the stable

salinity of sea ice vs. growth rate. The data,

from measurements made on Arctic and Antarctic sea ice (Nakawo and Sinha 1981, Wakatsuchi

1983), clearly reveal that the salinity of sea ice

decreases exponentially with decreasing growth

rate. Therefore, the growth rate coefficient for natural sea ice is not a constant, but varies with ice

thickness. The scale on the right side of Figure 16

shows the salinity ratio of the ice vs. growth rate.

As expected, this ratio is not a constant, but also

varies with ice salinity.

In Figure 14 only the Antarctic sea ice data of

Jeffries (1994) were used, to eliminate any varia- * Geophysical Institute, University of Alaska, Fairbanks.

10
20

15

10

5

0

1 Jan 1 Feb 1 Mar 1 Apr 1 May

Avg. Ice Thickness (cm)

24 54 85 90 95

S , Bulk Salinity (‰) B

Date of Determination

as boxes in Figure 19 with an interconnecting

curve. The agreement is good, considering that

ice sheet flooding in January affected ice

growth and morphology.

The results in Figure 18 are representative

of first-year sea ice during the growth season.

In the melt season, ice salinity decreases due

to accelerated brine drainage and flushing.

Disregarding impurity effects, the speed and

intensity of the melt process are highly dependent on thermodynamic factors such as

air temperature, solar radiation intensity, snow

cover, and rain, as well as the thickness of the

ice. These factors govern how fast meltwater

forms on the ice surface and the speed at which

solar radiation melts the ice around brine channels, pockets, and flaws to help open up the

drainage networks leading to the sea. As indicated in Figure 9, spring melt conditions can

cause the bulk salinity of the ice to decrease by

50% in one month. At high latitudes, where summer melting is not as intense, the process of ice

freshening is slower. Here, more than one melt

season may be required to achieve the reduction

in ice salinity shown in Figure 9. In lower latitudes, the melt season is longer and sufficiently

intense to completely melt the ice cover. Because

the degree of ice freshening in one season is highly

variable, the salinity of second-year and older ice

also varies, but the trend is decidedly to a lower

bulk salinity for older ice.

Bulk salinity vs. second- and multiyear ice floe

thickness data collected in the Beaufort Sea by

Kovacs and Mellor (1971), Cox (1972*), Kovacs et

Figure 19. Comparison between the regression curve passed through all the bulk salinity vs. ice floe thickness data in Figure 18 and

the field data in Figure 7. The squares mark

the locations of the ice thicknesses used in the

regression equation given in Figure 18.

6

4

2

0

200 400 600 800

T , Floe Thickness (cm) F

S , Bulk Salinity (‰) B

r = 0.626 2

S = 1.40 + 121139.64/TF

2

B

Figure 20. Beaufort Sea multiyear ice bulk salinity vs. floe

thickness.

effect of seawater salinity variation as well as

first-year sea ice morphology and structure differences on the bulk salinity of the ice. The literature certainly shows that this can be done under

controlled conditions (Cox and Weeks 1975, Weeks

and Lofgren 1967) and during focused field measurement programs where the highly variable thermodynamic conditions controlling sea ice growth

are measured and accounted for (e.g., Nakawo

and Sinha 1981, 1984; Wakatsuchi 1983; Eicken

1992). In the interim, Figure 18 provides a good

indication of the bulk salinity of first-year sea ice

vs. thickness.

It may be of interest now to see how the regression curve in Figure 18 fits the data in Figure 7.

Using the five ice thicknesses given in Figure 7

and the equation in Figure 18, the bulk ice sheet

salinity was calculated. These values are shown * Only published as shown in Figure 6.

11
water has a higher salinity than in the southern

Beaufort Sea. Therefore, the Antarctic sea ice

could have a higher salinity due to this possible exchange, if all other parameters are the

same.

When multiyear sea ice SB vs. TF data

from Fram Strait (Gow et al. 1987) are added,

the distribution changes again, as shown in

Figure 22. The scatter in the data between 200

and 300 cm also increases. Some of the lower

salinity values from Fram Strait could have

resulted from sampling lower-salinity melt-pool

ice. Whatever the reason for the lower SB values, Figure 22 does indicate that sea ice that

has survived one or more melt seasons can

freshen to where the bulk salinity is 1 to 2‰.

SUMMARY

Sea ice salinity data collected in Arctic and

Antarctic waters indicate that the bulk ice-sheet

salinity decreases with increasing ice floe thickness following a negative exponential-like

trend. New ice about 0.05 m thick has a bulk

salinity of about 25‰. The bulk salinity of the

ice decreases rapidly to about 6‰ at an ice

thickness of about 0.5 m. After this, the bulk ice

salinity continues to decrease, but at a highly

reduced rate, to about 5‰ at the end of the

growth season for ice more than 1.5 m thick.

Reasons for the salinity decrease are related to

ice structure, rate of ice growth, and brine migration processes. The first and second reasons

are related, in that as the ice thickness increases,

the growth rate slows because the heat exchange from the ice bottom to the atmosphere

is reduced. Slower growth results in the formation of larger freshwater ice platelets and larger

ice crystals with proportionately fewer brine inclusions. Thus, the ice salinity is lower. Brine migration processes lead to the gradual drainage of

brine from the ice to the sea and a freshening of

the ice.

Significant scatter and a paucity of data precluded establishing a definitive relationship between seawater salinity and ice sheet structure

and the bulk salinity of the sea ice.

A significant decrease in ice floe bulk salinity

occurs during the melt season. Depending on

many factors, including the solar intensity during

the melt season, the bulk salinity of a first-year

sea-ice floe can decrease from about 5‰ to about

2‰. This transition to second-year ice separates

6

4

2

0

200 400 600 800

T , Floe Thickness (cm) F

S , Bulk Salinity (‰) B

F S = 1.80 + 99810.49/T 2B

r = 0.438 2

Arctic

Antarctic

al. (1973), Cox and Weeks (1974), Kovacs (data on

file), and Meese (1989) are shown in Figure 20.

The obvious trend is to lower SB values with increasing ice thickness.

When the higher SB vs. TF data for Antarctic

multiyear ice (Gow et al. 1987) are added to the

Beaufort Sea data the curve through the combined data shifts up slightly for the thicker ice

(Fig. 21). The higher Antarctic SB values may be

due to ice structure, thermodynamic differences

during the melt season, or differences in seawater

salinity. When the denser brine drains out of the

sea ice during the melt season, some of the drainage system can be reoccupied by seawater (Niedrauer and Martin 1979). In the Antarctic, the seaFigure 21. Beaufort Sea and Antarctic multiyear sea-ice

bulk salinity vs. floe thickness.

6

4

2

0

200 400 600 800

T , Floe Thickness (cm) F

S , Bulk Salinity (‰) B

S = 1.85 + 80217.97/TF

2

B

r = 0.222 2

Figure 22. All Arctic and Antarctic multiyear sea-ice bulk

salinity vs. floe thickness data.

12
the two ice types according to their bulk salinity.

For this reason the two ice types’ bulk salinity vs.

thickness data should not be combined, as previously reported, in an analysis of ice floe salinity–thickness trends.

The Ryvlin relationship for determining the

bulk salinity vs. ice floe thickness is difficult, at

best, to use since the growth rate parameter is not

a constant, but is shown to vary with ice thickness.

The bulk salinity vs. ice floe thickness trend for

winter sea ice is well represented by the expression SB = 4.606 + 91.603/TF shown in Figure 18.

This expression is applicable to both cold Arctic

and Antarctic first-year sea ice grown in seawater

of ~31 to 34‰ salinity. The expression should not

be used for such southern sea ice environments as

the Gulf of St. Lawrence, where winter freeze–

thaw cycles are common, and of course the lowsalinity Baltic Sea, where ice salinities are typically less than 1‰ for ice as thin as 0.2 m.

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June 1996

Sea Ice: Part I. Bulk Salinity Versus Ice Floe Thickness

Austin Kovacs

U.S. Army Cold Regions Research and Engineering Laboratory

72 Lyme Road CRREL Report 96-7

Hanover, New Hampshire 03755-1290

U.S. Army Cold Regions Research and Engineering Laboratory

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24

Ice floes Salinity Sea ice

UNCLASSIFIED UNCLASSIFIED UNCLASSIFIED UL

Mathematical expressions have been established for estimating the bulk salinity of Arctic and Antarctic sea ice

vs. ice floe thickness. The ice salinity vs. thickness relationships are based on data for over 400 sea ice cores

compiled from numerous sources. The results show that the bulk salinity of first-year sea ice decreases in an

exponential trend with ice sheet thickness. A similar trend reoccurs as the winter ice passes through the melt

season. The expression for the bulk salinity SB in ‰ for first-year sea ice from 10 to 200 cm thick is SB = 4.606 +

91.603/TF, where TF is the ice floe thickness in centimeters.