Journal of Glaciology, Vo!.
20,
No. 84, 1978
THE EQUILIBRIUM STATE OF THE EASTERN H A LF OF
THE ROSS ICE SHELF*
By
ROBERT
H.
THOMAS
{Institute for Quaternary Studies, University of Maine at Orono, Orono, Maine 04473 ,
U.S.A .)
and
CHARLES
R.
BENTLEY
(Geophysical and Polar R esearch Center, Univer sity of Wisconsin, Madison, Wisconsin 53 706,
U.S.A. )
ABSTRACT. M eas urements of ice thi ckness, veloc ity, snow accumul a tion rates, and surface strain-rates
a re used to examine the state of equilibrium of three fl o w ba nds of the Ross I ce Shelf. Th e a nalysis gives the
rate of thi cke ning of the ice shelf in terms of the basal freezing rate, which is unknown. However, indirect
evid ence suggests that the basal flux ranges from a s mall va lue of freezing in the south to a melting rate of
a bout o ne meter of ice per year a t the ice front. Hthese va lues are correct then the flow band in the south-east
corner of the ice shelf a ppears to be thi ckening at a n average valu e of (34 ± 15) cm of ice p e r yea r. Persistent
thi ckening at t his ra te must lead to grounding of la rge a reas of the ice shelf. This wou ld r es trict drainage
from W est Antarctic ice streams w hi ch feed this part of the ice shelf and these would te nd to thicken and
adva nce their g rounding lines into the ice shelf. Furth e r north, nea r the RISP bore-hole site, t he ice shelf
is probably in equilibrium. Th e la rgest Aow band is to the south and east of Roosevel t Island , and this a lso
may be in eq uilibrium if the re is signifi cant bottom m e ltin g from ice sh e lf tha t is more tha n 100 km from the
ice front.
R EsuME. L'etat d'eqllilibre de la moitie orientale dll R oss I ce Shelf. P a r d es m esures d'epa isse ur d e glace, de
vitesse, d 'accumul ation d e neige, et d e vitesse d e d eformation en surface, on examine I'etat d 'equilibre d e
trois band es d'ecou lement du R oss I ce Shelf. L 'a na lyse donn e la vitesse d 'epaiss issement d e la glace en
fon ction d e la vitesse d e co nge lat ion it la base qui est in co nnue. Cependant, d es indices indirects suggerent
que le flux basal varie depui s un e fa ible valeur d e co ngela ti on d a ns le sud jusqu 'it un e vi tesse de fusion
d 'enviro n un m et re d e glace par a n sur le front du g lacie r. Si ces estimations sont correctes, a lo rs le courant
de glace du coin Sud-Est d e la ba nquise semble s'epaiss ir a u rythme m oye n d e (34 ± 15) c m d e g lace pa r an .
U n epa iss isse m ent persistant a cette vitesse d evra it co nduire it a ppu yer sur le sol d e larges zones de la
banquise. Cec i restreind rait le dra in a ge par les cOUl·a nts d e glace de l' Ouest d e l'Antarctique qui nourrissent
cette pa ni e d e la banquise; ces cO Ul·ants tendent it s'e pa iss ir et it avancer l eur ligne d e decoll e m ent du rond
vers I' in terie ur d e la ba nquise. Plus loin a u Nord , pres du site de forage du RJSP, la glace est probablement
e n eq uilibre. L es plus g rands cO Ul·a nts d 'ecoul em ent sont vers le Sud et l'Est d e Roosevel t I sla nd et peuvent
a uss i erre en eq uilibre s' il ya un e fu sion au fond sig nifi cati ve a pa rtir de la banqu ise it plus d e 100 km du
front g lacia ire.
ZUSAMMENFASSUNG . Der GleichgewichtsZllstand der listlichen Hlilfte des R oss-Schelfeises. Zur U ntersuchung
des G leich ge wichtszustandes drei e r St rome d es R oss-Schel feises we rd e n Messungen d e r Eisdi cke, der
Gesch wi ndig keit, d er Schneeakkumula tion und d er D e format ion a n d er OberAach e he rangezogen. Die
Ana lyse li efe rt die Zunahmerate der Schelfe isdicke in A bha ngigkeit von A urfri erratc a n der U nterseite,
di e j edoch unbekan nt ist. I nd ire kte Schlilsse lasse n j edoch vermuten , d ass der MassenAuss a n d e r Unterseitc
z wischen e in em g eringen Au f'frie ren im Sliden und e in e m Schm elzbetrag vo n etwa I m Eis pro J a hr a n der
E isfron t li egt. W enn di ese W c rte ri chtig sind , d an n scheint d er Eisstro m a m Si.idost-Eck d es Sc helfeises urn
e inen Mittelwe rt von (34 ± 15) c m pro J a hr a n D ic ke z u zun ehmen. Ein e a nha ltendc Di ckcn z unahrn e in
d iesem Ausmass m uss zum A uf~ it ze n weiter Geb iete d es Schel feises am U n tergrund flihre n. D a m it wli rde die
Transportleistung d er E isst rome a us der West-Antarktis, welche dicsen T eil des Sch el fe ises ern a hren,
drosseln ; sie w lirden a n Di cke z un eh men und ihre Aufsitz lini e gege n cl as Schclfeis vorschi e ben. \"'eiter
nord li ch, a n d e r Stell e dcs RISP-Bo hrI oches, befind et sich d as Eis vermu t li ch im Gleichgew ich t. D er stii rkste
Eiss trom li cgl im Si.iden unci O ste n von R oosevelt Isla nd; er dlirfte sich e be nfalls im G lcich gew ichtsz ustand
b efind en, so fe rn dort betrach t li ch es Abschmelzen a n d e r Un terseitc d es Sc helfeises bis zu I11 ch!" a ls 100 km
Frontabstancl stattfindet.
I NTRODUCTI ON
T he W est Antarctic ice sheet is a marine ice sheet resting on rock that was b e low sea-level
b efore isostatic d ep ression. W eertm an (1974) has shown th at m a rine ice sheets a r e proba bly
unstabl e, existing usuall y in a state of growth or retreat, a nd r etreat may be very rapid .
M ercer ( 1968) suggested tha t complete coll apse o f the West Antarctic ice shee t co uld have
* Geoph ysical a nd
P ola r R esearch Ce ntcr Contributi on No . 347.
50 9
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JOURNAL
OF GLACIOLOGY
been responsible for the well-documented higher sea-level during the Sangamon Interglacial,
and H u ghes (1975) believes that the West Antarctic ice sheet may currently be collapsing.
Data from a network of stakes up-stream of "Byrd" station on the West Antarctic ice sheet
were interpreted by Whillans (1973) to indicate current thinning of the ice sheet, as was a lso
suggested by work on oxygen isotope ratios and temperatures in the bore hole at " Byl'd"
station (Robin, 1970; Johnsen and others, 1972 ). However, from a re-analysis of the " Byrd"
strain -network data, Whillans (1976) concluded that a large region near the ice crest of West
Antarctica has been stable for about 30 000 years. This view is supported by Mayewski 's
(1975) interpretation of glacial geology in the Transantarctic Mountains, indicating that the
Antarctic ice sheet has remained almost unchanged for more than 10 000 years. However,
other geological evidence suggests that the West Antarctic ice sheet has decreased in size
significantly during the last 12 000 years, and it may have retreated across the entire area
currently occupied by the Ross Ice Shelf since 6000 B.P . (Denton and Borns, 1974) ' Meanwhile, Bentley and others (in press) have concluded that it would be difficu lt to reconcile
isostatic gravity anomalies on the ice shelf with ice thicknesses substantiall y greater than at
present less than about 5 000 years ago.
o
100
200
k ''-m-'--''
1
' . .. . . . . . . . . . . . . . . . .
•
BASE CAMP
•
ROSETTE ( rem ea su re d )
{; ROSETTE ( planted )
o
PRECISE POSIT ION FI X
D DRill HOLE
Fig. [ . The Ross Ice Shelf, showing positions of RIGGS stations where measurements have been made of ice thickness, depth oj'
sea bed, local graviry, snow-accumulation rates, ice velociry and strain-rates. Sillce the measurement of ice velociry alld'
strain-rates requires two visits to a statioll, these data are available only for the stations where " rosettes" have been remeasured.
The remaining stations will be reoccupied during [977- 78.
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EQUILIB RI UM
OF THE
ROSS
ICE SHELF
5I
I
It may be possible to d evise a scenario that reconciles these apparently conflicting opinions,
but reconciliation is unlikely until there is more information on the pas-t and present equilibrium state of the West Antarctic ice sheet/Ross Ice Shelf system . T he acquisition of this
information is one of the main aims of the Ross Ice Shelf Project (RISP). This proj ect
represents a first attempt to compile a systematic data base for a large and well-defined
portion of the Antarctic ice sheet (Zumberge, 197 1). The program involves geophysical and
glaciological measurements at stations forming a 55 km grid over the entire surface of the
Ross Ice Shelf, with related investigations within and beneath the ice shelf by way of a drill
hole. The work on th e surface of the ice shelf has b een designated the " Ross I ce Shelf
Geophysical and Glaciological Survey" (RIGGS), and it includes measurements of ice velocity
and strain-rates, snow accumulation rates, surface-snow oxygen-isotope ratios, snow temperatures at 10 m depth , gravity values, ice thickness, sea-bed topography, and the seismic and
electrical properties of the ice. The field work was started in 1973- 74 and, by the end of the
1976- 77 season a lmost a ll of the planned grid stations (Fig. I) had been visited once for
geophysical m easurements and for the planting of stake patterns (strain rosettes) to m ea sure
ice-shelf strain-rates.
Stations in the eastern half of the ice shelf have b een reoccupied for remeasurem e nt of
strain rosettes and for precise relocation of some of the stations by satellite tracking . Comparison with initial positions gives absolute velocities at these stations, and velocities a t
neigh boring stations have been interpolated using th e strain-rate data. Where interpolated
ice velocities and measured values overlapped they gen erally showed agreement to within
25 m year- 1 (Thomas, 1976[aJ). At some of the stations firn cores down to 10 m depth were
taken for surface-snow oxygen-isotope ratios a nd for ide ntification of the maximum d e pth of
snow containing fall-out from nuclear bombs. This la tter m easurement gives average snowaccumulation rates (C lausen and Dansgaard, 1977 ) . Sea-bed topography and ice thi ckn ess
were d educed from seismic measurem ents and from radio-echo sounding (Cloug h a nd
Robertson, 1975) .
In this paper we shall use the RIGGS measurements to examine the present equilibrium
state of the eastern half of the Ross Ice Shelf.
ICE-SH E LF EQU ILIBRIUM
The equilibrium state of an ice shelf can be assessed by considering volume-continuity
requirem ents as the ice shelf passes through a stationary vertical column at a dista nce x a long
a flow line (Thomas , 1977 ) :
.
oH . .
ox = A+ F + Hi ,
H+ V-
it
wh er e A is snow acc umulation rate, the bottom freezing r ate, and if the ice-shelf thicke ning
rate, a ll expressed a s thickness of ice p er unit time. H is th e ice thickness, i the vertica l str ai nrate due to creep of th e ice (positive for ex tension), V the ice velocity a long the flow line, a nd
oH/ox the ice-thickness g ra dient along
th e flow line. All of these parameters are functions of x.
.
.
A steady state is represented by H = o. When H is positive the ice shelf is growing thicker
with time and vice versa.
Velocity vectors th a t are calculated from RIGGS d a ta give the routes of flow lines across
the ice shelf, and Thomas ( 1976[b] ) solved Equa tion ( I) to give (H - F ) along the flow line
that passes through the RISP drill-hole site. The resul ts are very sensitive to values of oH/ ox
a nd i and, since these were interpolated from meas ure m ents at nearby grid sta tions, they
possess an indeterminate error which may be large e nough to invalidate any conclusions
concerning the equilibrium state of the ice shelf. In a n a ttempt to doc ument errors a nd to
minimize them , we shall consider th e volume continuity of three fl ow bands of ice shelf (Fig. 2)
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JOURNAL OF GLACIOLOGY
ROil SEA~ \ ..~
.-. . . . . . . ~
,eeSEVEl-;'' (jP. ~~
ISLAND
o
••
. .
.
...,
'\
'.~.--
ICE SHElF
. o~~:"
CRAR~
iCE
'~S~"
~
H
,. '
A
TRANSANTAR CT IC
MOU NTAIN S
Fig.
The eastern side oJ the Ross Ice Shelf showing positions oJ RICCS stations where ice thickness, snow-accumulation rate,
ice velocity and strain-rates have been measured. Additional ice thickness data were obtained Jrom several thousand km oJ
aerial radio-echo sounding. The three bands oJ ice she!! ABeD, EFCH and MNOPQR are bounded on each side by flow
lines. AD and B e are the entry and exit gatesJor the band ABeD.
2.
that are bounded laterally by flow lines a nd that each include several of the RIGGS grid
stations.
The volumes of ice entering ((:Le) and leaving (Qo) a band in unit time were calculated
by integra ting th e prod uct of ice velocity and thickness across the entry and exit gates, a nd the
vol ume of ice added in unit time b y snow accumulation (Q a) is the integral of snow accumulation over the surface area (S) of the band. Snow accumulation rates are from the analysis
of 10 m firn cores and from repeated stake measurements. Where the two m e thods overlap
th e results show excellent agr eement.
For conservation of volum e (Fig. 3) we have
Q e+ Q ,,+ Q b
=
Qo + SH,
where Q b is th e volume of ice frozen to the base of the flow band in unit time (= SF ), and
.
.,
F and H represent values of F and H averaged over S. This equation can be rewritten as
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EQU ILIBRI U M
OF
TH E
RO SS
s=
0 e + 0 a+
Ob
=
°
0
I CE
S H E LF
s u rfa ce area
+ S H
Fig. 3. Volume continuity fo r a band of ice shelf that is bounded
011
each side by flo w lincs.
V a lues of ice velocity a nd ice thickn ess across each g a te are shown in Fig ure 4. Th ey were
interpola ted from m easured values a t th e grid sta tions a nd , for ice thic kness, from a irbo rne
ra dio-ech o-sounding d a ta . Random errors are t1H = ± 2 0 m for ice thickness, a nd for
velocity t1 V is based on the consistency of values th at a re interpola ted fro m different neig hboring grid sta tions (Thomas, 1976[a] ) . I ce thickness errors are probabl y less than ± 20 m
sin ce a irborne radio-echo sounding acr oss part of each gate prov ides excellent con trol.
Errors in 0.. e and 0.. 0 a r e calcula ted assuming that th e errors in each d a ta point i a ppl y over
the r egion of wid th W .; where W i is h a lf the distance from data point (i - I) to d a ta p o in t
(i I) a nd tha t errors a re consta nt within a bracketed r egion bu t ind epe nden t of erro rs in
oth er regions. Errors in o.. e and 0.. 0 a r e th en
+
t1o.. e or t1Q. o =
i =
tl
t =
I
±{~
( W;Vi Jt1HiJ)2 + (W; H;Jt1 ViJ)2 f ,
wh er e 11 is the number of d ata points w i thin the gate.
In a ddition to these ra ndom erro rs w e have ass umed tha t the thickness a nd velocity
m easurem ents include systematic errors of t1Hs = ± I 5 m a nd 6 Vs = ± 10 m yea r - I
respectively, which imply a n error in (Q. e- 0..0) of
t1o.. s
{[ t1 Vs(HeW e - Ro Wo )P + [t1Hs( VeWe- VoWo)]2P,
=
where t he ba rs imply ave rages taken across the appropria te ga te. Th e error in 0.. [; is 60.. [;
a nd it is calculated ass uming a ± 15 0/0 error in th e a ver age snow-accum.ul ation rate over the
ba nd .
F ina ll y th ere is error in the divergence of the flow lines th at define th e la tera l m argins o f a
band . T he flo w-line direction at a n y p o int is determined mainly by th e ice-flow directio n
at the nea rest grid point a nd this has a n error of ± ( 1. 5 to 2'5t . Thus, a la tera l fl ow line
consists of a series of linked segm ents each of leng th L j and with a random erro r of
!:!.D j = ±( I. 5 to 2.5 ) °. T he cumula ti ve effect of these errors is to impose a n error on th e
width Wo of the exit gate :
j = m
~ Wo =
±{~
j =
I
L
j' = k
(Ljsin Jt1D j J)2 +
j' =
(L j • sin !6Di' I) 2f
=
{t1 W t 2+ M V/ p,
1
wherej a nd }' refer to th e " left " a nd " rig ht" latera l m a r g ins, and
segm ents forming each of these margins.
In
a nd k a re the num be r of
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JO URNAL OF GLACIOLOGY
600 W
* W, * W3 *
* W5
4
W
., 400
'~500 ~ 900~
'-
c
u
- '.
~
g 406
:g!
D
"
\\
~
\
+-__
o
E 300
.....
~
/
\
~~
'-
I
__
~
____
40
Distance
~
~
A
__
Cl>
5 00
V1
o
,
'-
40
D istan c e
6 00
E
>,
-';~\ g~66G - j
E
70 0
.... --- ,
>,
--
.Q 300
~
C
B
~ ____4
200'+-__~____~__~____~~~
o
40
80 V
120
Di stance
km
',- 5 0 0
--- .......
>,
f-
80
km
'-
'=u
i'
E -
~-r 700
>,
E 4 00
E
'"
H
,
>"
,
"c
4 00t
>
80
km
.~
_... ,
52 200
800t
\
600
>,
>,
E
~
~O___ - - - - - - - -
.-
u
.Q
~
"
>
G
500
VI
:too
-'"
u
40
i'
f--
F
o
'"cCl>
80
Distance
km
800
.---
--
E
-
400
>,
./
.......
"-
/ , _/
'-
E
"-
7 00 :::
"-
Cl>
~
c
u
-'"
u
6 00E
5'.300
"
f-
>
N \
M
40
0
80
Di stanc e
12 0
km
600
500
,
't E
---
4 00
400
VI
VI
'-
>,
"
300~
E
u
i'
>,
I--
'60 200
q;
>
~
u
<f
R
0
0
40
80
DI s ta nce
12 0
o
i:: P
Q
0
40
80
km
Fig. 4. Ice velocity (solid line) and ice thickness (broken line) plotted against distance across the gates to the ice-shelfflow bands
that are shown in Figure 2 . The error bars on the velocity data include random errors only. The velocity curves were drawn
to COliform to measurements of both velocity and velocity gradient across the direction of flow . The velocity minima in sections
CB and RO represent the effects of local grounding by Crary Ice Rise and RooseveLt Islalld. A system of shear crevasses
extends for about 20 km to the south-west of Crary Ice Rise and so we have assumed that shear predominates over this section
of the velocity curve. On the other side of the ice rise the ice shelf suffers massive fracture along the north-east grounding line,
and shear crevasses are restricted to a narrow zone on the ice-shelf side of this fracture zone.
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EQUILIBRIUM
OF THE
ROS S IC E
S HELF
The pronounced curvature of flow line AB (Fig. 2) a nd the lack of grid stations along the
central part of its route introduce an additional uncertainty in the position of B. We have
attempted to quantify this error b y p lotting the flow line first using lateral strain-rates to
calculate divergen ce along the flow- line route and second by assuming that flow direction
varies linearly between grid stations. Individual attempts by both authors gave a maximum
difference of 8 km in the position of B along the gate BC. Here we adopt the central position
of B and we assign an additional error to Wo of ~ Wb = ± 5 km. Thus, for the flow band
A BCD
.2:
j' = k
~Wr2 = ~Wb2+
(Lj ' sin
I~Dj' 1) 2.
j' = I
For flow band MNOPQR in the north-east of the ice shelf, the m a rgins P and Q lie at the
grounding line b etween ice shelf and Roosevelt Island . I ce at Q , on the west side of the
isla nd , is assumed to have negligible seaward component of velocity , since there is no sign of
fracture at the grounding line. On the east side of the island at P , however, the ice shelf is
severel y fractured and we have assigned to P an ice velocity of iOo ± 70 m year - I. The
position errors for P a nd Q are assumed to be ~ W p = ~ W q = ± 8 km .
The error to be applied to (H - F ) can now be written
~
I
= ± -s
{ ML e2 + ~Q.0 2 + ~Q. s2 + ~pq 2 +( VIH1~ Wl ) 2 +( VrHr~Wr) 2p,
where subscripts I and r refer to the " left" and " rig ht" sides of the exit gate, and
exce pt for Aow b a nd M NOPQR, where
~ I)q2
=
~pq
=
0
( V pHp~ Wp ) 2 +( Vq Hq~Wq ) 2 .
For each fl ow b a nd the values of S, A, Q. ", Q. e a nd Q.o are give n in Table 1.
TABLE
i
Q.
Qe
Qo
1.
VALUES OF PARAMETERS FOR EAC H FLOW BAND
ABeD
Flow band
S
m'
( 148 ± 5) X 108
0.1 3
( 19 ± 3) X 108
(339 ± 7)X I0 8
(308 ± 20) X 108
m
m 3 year- I
m 3 year- I
m 3 year- I
For section ABCD in Figure
2
EFCfI
( 160 ± 3) X 108
0. 10
( 16 ± 3) X 10 8
( 142 ± 5) X 108
( 157 ± 10) X 108
M N OPQR
(550 ± 11 ) X 108
0. 165
(g l ± 14) X 10 8
(402 ± 1O) X 108
(412 ± 26) X 10 8
we then have
(H - F ) = +(34 ± 15) cm of ice per yea r,
for sec tion EFGH
(H - F ) = + ( 1± 7) cm of ice per year,
and fo r section M
OPQR
"7
(H - F ) = +( I5 ± 6) cm of ice per year .
T hus, for negligibl e basal freezing or melting, the ice sh elf a ppears to be thickening with time
in the a rea up-stream of Crary I ce Rise, but is a pproximately in equilibrium near the RISP
drill-hole site. Although no direct m easurement of th e basal freezin g rate has yet been made
at the RISP site, temperatures in the upper three-quarters of the ice shelf (personal communication from B. L. H a nsen and J. M . R a nd in 1976 ) a re full y consiste nt with a model b ased on
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JO U RN A L
OF
GLACIOLOGY
the analysis of Crary (196 1) taking F = 0 (Bentley, in press). Further south , in the zone of
intense fracture immediately north of Crary Ice Rise (Fig. 2), observations of slabs of p a rtiall y
overturned ice shelf r eveal layers of debris-laden ice that may have froz en onto the base of the
ice shelf as it approached the ice rise (Gaylord and Robertson, 1975) ' This would imply that
F is positive, so that up-stream of Crary Ice Rise H > (34 ± 15) cm of ice per year.
This value is larger than th e regional snow-accumul ation rate and if the ice shelf is
thickening at this rate then ice that flows into the region from W est Antarctic ice strea ms is
b eing dammed , probably by C rary I ce Rise. Our result gives no indication of where the
thickening rate reaches a maximum. Thickening may be concentrated over a fairl y small zone
immediately up-stream from C ra ry Ice Rise or, as concluded by Thomas (1976 [b] ), it may
increase from about zero near the drill-hole site to reach a maximum a t the grounding line
in the south-east corner of the ice shelf. In either case, within the zone of maximum thic kening,
the sea bed is separated from the ice shelf by a very narrow wedge of sea-water so that even a
small rate of thickening leads to grounding of large areas of ice sh elf. If the a ngl e b etween
sea bed and ice-shelf base is 1> and the local ice-shelf thickening rate is H , th e grounding line
a dvances at (piH ) I (pw sin 1», where Pi and pw are densities of ice and sea-water respectively.
Up-stream from Crary Ice Rise 1> ~ 10- 3 radians and near the grounding line in the southeas t corn er of the ice shelf, 1> ~ 5 X 10- 4 radians. Thus, for zero bottom melting, th e average
regional thickening rate implies g rounding-lin e a dvance rates of about 300 m yeat-- I upstream of Crary I ce Rise or a bout 600 m year- I for the south-east corn er of the ice shelf.
Such large adva nce rates can only b e sustained by continued rapid ice Row from the West
Antarctic ice streams . If the grounding lines of th ese ice streams are advancing into the ice
sh elf then we mig ht expect th e resultant a reas of grounded ice shelf to offer increased r esistance
to flow down the ice streams. This would act as a n egative-feedback mechanism and tend to
sta bilize the grounding-line position. If ice-shelf thickening is confirmed in the area immediately up-stream of Crary I ce Rise however, it could continue undiminished since icestr eam flow rates would not immediately be affected. U ltimately, however, the increased
size ofCrary I ce Rise would tend to restrict ice-stream flow rates. One of the authors (R.H .T. )
h as traveled exten sively over the surface of th e ice sh elf seeking stations in order to remeasure
strain rosettes. During these journeys ma ny small ice rises, where the ice shelf had locally
g ro unded, were encountered within the region extending 200 km up-stream of Crary I ce Rise
and some of these, although well m a rked by patterns of strand cracks, showed little of the
increase in surface elevation that gives ice rises their name. This m ay indicate that the ice
sh elf had but recently run agro und and that sufficient time had not yet elapsed to allow the
ice rise to ass ume its equilibrium surface profile.
Further north , near Roosevelt I sland, conditions m ay be favorable for bottom melting so
that F becomes n egative. If the ice shelf in this area is in equilibrium, then th e average
bottom-melting rate beneath the ice-shelf portion of Row band M NO PQR is ( I5 ± 6) cm
of ice p er year. This can be compared with estimates of bottom-melting rate near the seaward
ice front at Littl e America V of about one meter per year (Cra r y, 196 1).
SUMMARY
Bala nce calcul a tions for the eastern half of the R oss I ce Shelf indicate that the south-east
corner of the ice shelf may be growing thicker by more than 30 cm year- I. If this is so then
it is probably due to the damming effects of Crary Ice Rise which may h ave formed comparatively recently at a point where the ice shelf ran aground on a n isostatically-rising sea -bed
ridge. Our res ults do not indicate where thickening is greatest. It may be immediately
up-stream of the ice rise in which case the ice-rise grounding line is advancing about 300
m year-I into th e ice shelfin a south-easterly direction, or it may be along the grounding lin e
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EQUILIBRIUM
OF
THE
RO SS
ICE
HELF
of ,,'es t Antarctic ice streams that drain into this part of the ice shelf, and this would imply
loca l advance of the W es t Antarctic ice sheet in a north-westerly direction. In either case
large a l"eas of comparatively flat grounded ice will be formed a nd these must ultima tely offer
increased r esistance to th e flow of ice into the ice shelf, so that ice velocities d ecrease and ice
pil es up in the lower reac hes of the ice streams. In this way the a dvance would become
consolid ated a nd an equilibrium grounding -line position would finally be achieved. Sea-bed
topogra ph y suggests that, if advance is indeed taking place, it could continue until Crary I ce
Rise has been absorbed by th e W est Antarctic ice sheet, which event should signal a furore of
activity from the various Place-Names Committees. If for no other reason this problem
deserves further a ttention and the RICCS data provide excellent guidelines to where
additional measurements are required.
The ice shelf to the north of Crary I ce Rise, including the site of the RISP drill hole,
a ppears to be approximately in equilibrium and this a lso m ay be so for the ice shelf near
R oosevelt I sland, where our results indicate either thickening or bottom melting of approxima tely 15 c m of ice year- I.
H ug h es ( 1975) suggested th at the W es t Antarctic ice sheet currently may be collapsing,
but our r esults provide no support for this hypothesis ; ind eed the ice sheet appears to be
adva ncing into the so uth-east corner of the Ross Ice Shelf. However, we should note that
growth at th e edge of the W est Antarctic ice sheet m ay b e ta king place at the same time as
thinning of the central portions, which currently may be responding to earl ier retreat of the
ice-sheet margins (Thomas, 1976[b] ) . If this is the case then the W es t Antarctic ice sheet
cou ld be slumping to cover a larger area but with a lower summit elevation.
ACKNOWLEDGEMENTS
Th is work was supported by National Science Foundation grants DPP76-2 3047 a nd
OPP72-05802. W e are ind ebted to the numerous field assistants who helped us to gath er
da ta from the Ross I ce Shelf. W e a lso thank W . MacDona ld of the United States Geological
Survey, who provided th e precise position fixes on the ice shelf that were used to calculate ice
velocities, and 'vV. C hapma n of the U .S.C.S. , who allowed u s to use strain-rate measurem e nts
th at he had made at a station to the east of R oosevelt Island . An anonymous referee m a d e
suggestions th at have h e lped us to clarify t he text.
NIS. received
20
October 1.977 and in revised form 24 April 1978
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