Notes
602
ber), it is tempting to attribute the phenomenon to photoinhibition,
which is common, but not ubiquitous, among temperate
water bioluminescent dinoflagellates
(Tett
and Kelly 1973). But the absence of photoinhibition
on a daily basis in the spring
makes this assumption questionable.
The
summer disappearance of bioluminescence
may thus be due to a seasonal factor other
than sunlight.
James A. Raymond
Arthur L. DeVrks
Physiological Research Laboratory
Scripps Institution of Oceanography
La Jolla, California
92093
References
ANDRIYASHEV, A. P. 1962. Bathypelagic
fishes
of the Antarctic.
1. Family Myctophidae,
p.
216-300.
In E. P. Pavlovskii
[ed.], Biological reports of the Soviet antarctic expedition
1955-1958, v. 1. Israel Prog. Sci. Transl.
BALECH, E. 1968. Dinoflagellates,
p. 8-9.
In
V. C. Bushnell
[ed.], Antarctic
map folio
series, folio 10. Am. Geogr. Sot.
CLARKE, R. 1950. The bathypelagic
angler fish
Ceratias
holbolli
Kroyer.
Discovery
Rep.
26: l-32.
DEBENHAM,
F. [Ed.].
1945. The voyage
of
Field
determination
of the densities
Abstract-A
method
of calculating
the
mean density for a lake ice sheet and estimating the mean density of the white ice
component of such a sheet makes use of the
buoyancy
equation
for floating
ice in the
form
h’ wp’ w - h’qp’.
p’i =
h’i
’
where p’ and h’ are mean density and thickness respectively
and the subscripts are ice
(i), water (w),
and snow (s).
The technique requires the measurement of snow density on the lake. Mean ice sheet densities of
0.89 and 0.85 g cm-3 and mean white ice densities of 0.84-0.87
are reported
from two
lakes.
The major components of the winter
cover of lakes in temperate and subarctic
Captain Bellinghausen
to the antarctic
seas
1819-1821,
v. 1. Cambridge
Univ.
FAWEL,
P. 1936. Polychaetes,
p. 9. Voyage
de la Belgica, Rapp. Sci. Exped. Antarct.
Belg. 1897-99. Buschmann.
HARDY, A. 1956. The open sea, v. 1. Collins.
-.
1967. Great waters.
Harper and Row.
HARVEY, E. N. 1952. Bioluminescence.
Academic.
report of the
HODGSON, T. V. 1905. Preliminary
of the
“Discovery.”
biological
collection
Geogr. J. 25: 396-400.
of
IVANOV, B. G. 1969. On the luminescence
superba ) .
the antarctic
krill
(Euphausia
Okeanologiya
9 : 505-506.
investiLITTLEPAGE, J. L. 1965. Oceanographic
gations in McMurdo
Sound, Antarctica,
p. l37. In M. 0. Lee [ed.], Biology of the antarctic seas, v. 2. Am. Geophys. Union.
MARR, J. 1962. The natural history and geography of the antarctic
krill Euphausia
superba. Discovery
Rep. 32: 33-464.
NICOL, J. A. C. 1967. The biology of marine
animals.
Wiley.
TETT, P. B., AND M. G. KELLY.
1973. Marine
bioluminescence.
Oceanogr. Mar. Biol. Annu.
Rev. 11: 89-173.
exWILSON, E. 1966. Diary of the Discovery
pedition.
Blandford.
WILTON, D. W.
1907. Report of the scientific
results of the S.Y. Scotia, v. 4, pt. 1. Scot.
Oceanogr. Lab.
Submitted: 3 October
Accepted: 23 February
1975
1976
of lake ice sheets
areas that experience considerable snowfall
are illustrated in Fig. 1. The dimensions
shown are easily measured, although only
hi and h, are standard measurements in the
regular North American ice surveys. Each
of the components has a more or less important role in the biological, energetic,
and hydrologic regimes of a lake and in determining the strengths and trafficability
conditions of the cover. However, for most
such roles, properties other than thickness
are critical; a basic one is density, which is
important in determining
cover thermal
light transmissivity,
water
conductivity,
equivalent, strengths, and the like.
While the point measurements and areal
Notes
Maaswng
tape
and
b*,
h,z(h,+HWL+)
SNOWCOVER
WHITE
ICE
lml
BLACK
ICE
Fig. 1. Principal
components
of lake cover.
Black ice is directly frozen lake water and is columnar; white ice is slush refrozen on the ice sheet
surface and is granular.
HWL is the distance between the surface of the sheet and the level of
water after drilling; it is considered positive when
the water, as here, is higher than the ice. HWL
and total ice thickness (hi ) are used, as shown,
to calculate h,, h,, hwt, and hai (thickness of water, snow, white ice, and black ice ) .
samples necessary to calculate a mean density of a lake snow cover are easily acquired
with standard equipment and techniques
for snow surveys on land (e.g. UNESCO
1970), this is not so for ice sheet density.
Field measurement of the density of solid
ice is a relatively laborious process and the
collection and measurement of samples of
solid ice from a large number of points on a
lake are impracticable.
As a result, it is
usual to assume a density for a lake ice
sheet. Schindler et al. (1974) used 0.917 g
crnm3in their calculation of the gross energy
budget of a lake covered with black ice
( terminology in Fig. 1)) and Scott ( 1964)
used the same value for work on lakes with
a small proportion of white ice; Michel
( 1971) used 0.9 g cm-3 in calculations of
the equilibrium
of an ice sheet, Shaw
( 1964) 0.9 in his calculation of the density
of lake snow cover, and Jones (1969) 0.9
and 0.8 g cm-3 for black ice and white ice
in calculations of the displacement of water by an ice sheet.
I present here a method of obtaining a
603
more precise value for the mean density of
a floating lake ice sheet and a means of estimating the mean density of the white ice
component of the sheet.
I am grateful to D. Lasenby, S. J. Mathewson, C. H. Taylor, and J. Valverde for
their contributions to this note.
The maximum density of normal freshwater ice at 0°C is 0.91663 + 0.00001 g
cmm3; at -3.5”C the density is 0.917192 *
0.000006 g crne3 (Butkovitch
1954). Such
values refer to single crystals of pure ice;
the density of large pieces will be lower. It
would appear likely that the mean density
of a lake ice sheet, even where it is entirely
black ice, will be appreciably lower, given
that it subsumes interfaces between crystals, air bubbles, and flaws in the ice.
The density of small pieces of white ice
measured by Ager (1962) varied between
0.85 and 0.90 g crnw3, samples measured by
Butkovitch (1955) between 0.78 and 0.87
g cm-3. Pounder (1965) suggested that ice
containing air bubbles could easily have a
specific gravity as low as 0.86. The principal controls of this variation in density include the size and shape of the original
snow crystals incorporated in the ice, the
rate of spread of water on the floating ice
sheet and the rate of refreezing of slush.
However, generalization from such factors
to a probable density using, for example,
the appearance of the ice is not possible.
It would appear reasonable to assume, in
the case of white ice as in the case of black
ice, that mean densities for an entire sheet
will be lower than the density of small
pieces of ice taken from that sheet.
In March of 1970 and 1971, large random
sets of measurements were made of the
covers of Knob Lake, Quebec (50”48’N,
80”49’W, 530 m above sea level, area 1.870
x 10” m2, volume 10.826 X lo6 m3, maximum depth 17.1 m), and Gillies Lake, Ontario (45”12’N, 81”21’W, 246 m, 3.520 X
10” m2, 2.713 x 10” m3, and 33 m). The purpose was to study the major spatial variations of ice cover components (survey
method in Adams and Brunger 1972, 1975)
but as standard snow sampler-density mea-
604
Notes
Gill ies Lake, Ontario
X
measuring
@
site
center
sample,
water
over
4.5
m
deep
SCALE
500
Fig. 2.
500
0
Distribution
1000
of the random
samples used and the center and margin
surements were made at most ice measuring
sites and as both lakes experience substantial snowfall, the data provide an excellent
basis for the calculation of mean ice densities by the method presented below. The
distribution of sample points on Gillies is
shown, as an example, in Fig. 2.
Where measurements of snow density are
available, the buoyancy equation for a
floating ice sheet can be used to calculate
ice density. This equation can be written
in weight terms as
h’,p’,
- h’,p’, - h’p’i = 0,
(1)
where h’ is a mean of thickness, sampled
areally, of the layers of water ( w ), snow
(s), and total ice (i) shown in Fig. 1 and
where the p’ values are similar means of
the densities (g cm-3) of these layers. Rewritten for p’i, this becomes
pfi
=
method
of calculation.
h’ wp’w - h’,p’s
hfi
’
(2)
Inserting, as an example, the values from
the overall sample column for Gillies in Table 1 yields
pfi
(57.81 x 1) - (20.81 x 0.264)
61.44
= 0.851 g crnm3.
=
This is the mean density for the Gillies
Lake ice sheet on the date concerned, using
the entire sample shown in Fig. 2; the
equivalent value for Knob Lake is 0.891 g
crnm3.
The validity of the buoyancy relationships used in the above equations requires
a free-floating piece of ice in calm water.
Implicit assumptions include that there is
605
Notes
Table 1. Measured and calculated values for ice cover on Knob Lake (8-10
lies Lake ( 12 March 1971). Calculations
were made in inches and converted.
Knob Lake
center
sample
(sites
>4.6m
deep)
Measured
h'w
h's
Pls
h'i
h'bi
h'wi
% White
Gillies
margin
sample
(sites
<4.6m
deep)
center
sample
(sites
>4.6m
deep)
1970) and Gil-
Lake
overall
sample
margin
sample
(sites
<4.6m
deep)
n = 45
n = 118
n = 73
n = 22
n = 54
n = 32
96.52
40.79
0.324
93.19
52.40
40.79
94.46
41.37
0.316
91.33
49.22
42.11
93.19
41.73
0.310
90.19
47.24
42.95
57.17
19.55
0.267
59.91
27.58
32.30
57.81
20.81
3.264
51.44
24.94
36.47
58.24
21.74
0.263
62.45
23.13
39.31
0.891
0.889
0.867
0.851
0.841
values
cm
cm
(g cm-3)
cm
cm
cm
Calculated
p'i
P'bi
P'wi
overall
sample
March
values
(g crns3)
(g Cmm3)
(g cm-3)
0.893
See Table
See Table
ice
43.8
46.1
47.6
53.9
59.3
62.9
13.20
12.99
12.95
5.23
5.51
5.71
Snow cover
equivalent
as water
(cm water)
2
2
no water or slush in the ice cover, that the
effect of the weight of the observer is constant and that the ice is truly buoyant, unaffected, for example, by shoreline effects.
In both cases, the amount of slush was
slight (6 sites out of 60 in Gillies, 2 out of
118 in Knob) and the second assumption
seems reasonable; but the last, the truly
buoyant situation, presents a problem. The
fact that a lake cover is attached to the
shore and may be resting on the bottom of
the lake or perched on boulders in shallow
areas is a serious complication.
In such
cases, the ice sheet will not be depressed
by a given load of snow as much as it would
be in a free-floating case. As a result, the
hfu,pf, expression of Eq. 2 would be too
small and a calculated ice density would
therefore also be low.
To reduce this effect, the samples from
the two lakes were divided to produce, for
each, one set of values from measuring locations which had over 4.6-m depth of water below them (referred to here as the
center sample) and one set from locations
where the water was less than 4.6 m deep
(the margin sample). These two sets of
values together form the overall sample
(Table 1, Fig. 2). The 4.6-m depth is arbitrary (and probably high: J. Scott personal communication),
selected to eliminate all possible direct and indirect effects
of the shoreline and shallow water on the
buoyancy of the sheet. A higher proportion
(63%) of Gillies fell into the <4.6-m category than of Knob (46%). The characteristics of the six samples thus defined can be
seen from Table 1 and Fig. 3.
Contrasts between center and margin
tend to be greater on Gillies. Differences
of snow are slight in both cases. The pattern of differences is generally the same on
both lakes and is generally as might be expected: for example, the high proportion
of white ice in both margin cases, possibly
reflecting the effects of early season snow
on shorefast, incomplete ice cover, and the
lower snow depths but higher snow densities in the exposed centers etc. The fact
that Gillies has thinner ice in its center than
606
Notes
Knob Lake
center
sample
overall
sample
margin
sample
Hydrostatic
Water
Level
Gillies Lake
301
center
sample
overall
margln
sample
sample
15-
o-
-
Hydrostatic
-
Water
Level
15.
30-
Legend
‘,,::,i snow
:,..,.
: I’: . . .
m
4560751 cm
*.
,: ,.
l!!Ezl
white
ice
lsssi
ice
black
Fig. 3. Comparison of the main characteristics
of
thickness of each of the layers shown is known, as is
two solid ice components, which together determine
All plotting is with reference to the hydrostatic
water
at its margins while the reverse is true on
Knob probably reflects the persistence of
the effects of late freeze-up (owing to currents) in the short Gillies ice season (approx 130 days), as compared with the
dominance of heat loss at exposed center
locations during the long ice season (220
days) of Knob Lake.
Thus the broad patterns present seem
plausible, including the consistently lower
calculated mean ice densities in the Gillies
case where the proportion of white ice is
much greater. The low calculated ice den-
the samples from Knob and Gillies Lakes. The
the density of snow cover. The densities of the
the mean density ( p’c) of the sheet, are unknown.
level.
sities in both margin cases tend to support
the hypothesis that part of the margin ice
is not fully depressed although the higher
proportion of white ice around the margins,
in both cases, must be a contributing factor. In light of the very different characers of these two lake covers and their very
different states at the time of survey (a
markedly negative hydrostatic water level
in Gillies, positive on Knob), the relationships between the different components of
the buoyancy equation discussed here appear reasonable. It also seems likely that
Notes
Table 2. White ice densities
sumed black ice densities, center
(g cm4)
sample.
for as-
Assumed
0.900
0.910
0.917
Sillies
Lake
IKnob Lake
0.838
0.886
0.830
0.873
0.824
0.864
the center sample provides the most accurate indication of the free-floating conditions, especially in the case of Gillies Lake
where there is a large shallow area.
It should be noted that both the overall
and center samples are required for the
best estimate of the amount of water which
the ice sheet represents or its mass. The
overall data give the most accurate indication of the volumetric characteristics of the
whole cover, while the center data provide
the best estimate of the density of the
whole sheet. Thus the total water equivalent of the Gillies Lake ice sheet is 0.867
(Table 1: center sample) x 61.44 (Table
1: overall sample) x lake area + cubic m
of water.
Each of the p’i values discussed above
includes a considerable proportion of white
ice, which generally has a lower density
than black ice and has a considerably
greater normal range of density. If the
two center samples represent the freefloating case, they provide measured values that can be used to estimate white ice
densities for the whole lake.
As hipi = ( hwipwi + hbipbi), Eq. 2 can be
rewritten for the least easily estimated of
the two solid ice components, white ice, as
prwi =
h’ wp’w - h’,p’, - hfbiprbi
f&vi
,
(3)
where, as in Fig. 1, bi and wi refer to black
ice and white ice. The results of this calculation for assumed black ice densities of
0.90, 0.91, and 0.917 g cm-3 are shown in
Table 2.
The 0.917 g cm-3 values provide a lower
limit. It would appear from the literature
and from arguments presented above that
the mean density of a sheet of black ice will
be lower than both the maximum density
607
of ice (0.917 g cme3) and density values
derived from small pieces of it. Values in
the 0.90-0.91 range are probably common
(J. Scott found values close to 0.91 in his
1964 study of Wisconsin lakes: personal
communication).
Thus the data for Gillies
Lake (Table 2) suggest that the mean density of white ice sheets can be considerably
lower than Ager’s (1962) values although
not, here, as low as Butkovitch’s
(1954)
minimum values.
Thicknesses of ice and snow on a lake
can be measured to k1.3 cm, hydrostatic
water level to -10.6 cm. The error in snow
density measurements made with standard
samplers is, in the relatively simple lake
less than
surface situation, considerably
10%. The most critical of these measurements for the calculation
discussed are
those of solid ice thickness (see Shaw 1964),
but the use of very large, well designed
samples minimizes the effects of measuring
errors in the examples presented here.
The principal result presented here is
that diverse ice sheets, one including 45%
white ice, the other 60%, appeared to have
mean densities in the order of 0.89 and
0.85 g cm-3. This is appreciably lower than
is normally assumed, and the mean density
of sheets of white ice is even lower. Measurements of snow density and hydrostatic
water level, which are rapid and simple,
might well be made in conjunction with
standard ice survey measurements. They
provide, with the center calculation procedure described here, an apparently useful means of estimating ice sheet densities.
In the longer term, it would be worthwhile, perhaps on a regional basis, to accumulate good pfi values and develop
curves for percentage white ice vs. pfi. I
would be most interested to receive data
for this purpose on ice thickness, hydrostatic water level, and snow depth and density from free-floating situations.
W. P. A&m.s
Department of Geography
Trent University
Peterborough, Ontario
608
Notes
References
ADAMS, W. P., AND A. G. BRUNGER. 1972. Sampling a subarctic lake cover, p. 222-226.
In
International
Geography 1972 La Geographic
Internationale,
Univ. Toronto.
-,
AND -.
1975. Variations
in the
quality and thickness of the winter cover of
a subarctic
lake.
Rev.
Geogr.
Montreal
29( 4) : in press.
AGER, B. H. 1962. Studies on the density of
naturally
and artificially
formed fresh-water
ice. J. Glacial. 4: 207-214.
BUTKOVITCH, T. R. 1954. Ultimate
strength of
ice. USA Snow, Ice and Permafrost Res. Establ. Res. Pap. 11. 12 p.
-.
1955. Crushing
strengths of lake ice.
USA Snow, Ice and Permafrost Res. Establ.
Res. Pap. 15. 5 p.
JONES, J. A. A. 1969. The growth and significance of white ice at Knob Lake, Quebec.
Can. Geogr. 13: 354-372.
Lake Ontario
circulation
MICHEL, B. 1971. Winter regimes of rivers and
lakes.
U.S. Cold Regions Res. Eng. Monogr.
3-B. 131 p.
POUNDER, E. R. 1965. Physics of ice. Pergamon.
SCHINDLER, D. W., H. E. WELCH, J. KALFF, C. J.
BRUNSKILL, AND N. KRITSCH. 1974. Physical and chemical limnology
of Char Lake,
Cornwallis
Island (75”N latitude).
J. Fish.
Res. Bd. Can. 31: 585-607.
of the heat
SCOTT, J. T. 1964. A comparison
balance of lakes in winter.
Univ. Wisconsin,
Dep. Meteorol. Tech. Rep. 13. 138 p.
SHAW, J. B. 1964. Calculation
of the density of
a lake snowcover.
McGill
Subarctic
Res.
Pap. 18, p. 56-59.
UNESCO.
1970. Seasonal snowcover.
UNESCO/
IASH/WMO
Tech. Pap. Hydrol. 2.
Submitted:
Accepted:
24 July 1975
18 February 1976
in November
Abstract-A
Lake Ontario
current meter
study during November 1972 showed counterclockwise
circulation
with higher speeds in
the western portion of the lake. Results from
wind-driven
numerical models run for comparison agreed in the western section, but
showed a clockwise gyre in the eastern portion of the lake.
A current meter study of Lake Ontario
was conducted in 1972 as part of the International Field Year for the Great Lakes
(IFYGL ) . Measurements were taken from
U.S. and Canadian buoys and towers placed
throughout the lake. One object of the
study was to deduce mean circulation patterns for the whole lake for each month.
Data for July 1972, a month when the lake
was stratified, were analyzed first (Pickett
and Richards 1975). They showed two
counterclockwise gyres side-by-side in apparent geostrophic balance, with flow in
the same direction at all recorded depths.
One gyre occupied the western two-thirds
of the lake and the other the eastern third.
This note adds the analysis of the November 1972 data, a month quite different from
July because simultaneous temperature recordings showed the lake was isothermal.
From this analysis, the mean flow in November also seems to be counterclockwise.
The buoys and towers in Lake Ontario
were designed to record surface winds
within 1 m s-l and 5”, water temperatures
within 0.2”C, and currents within 2 cm s-l
and 5”. Sensors were sampled every 6 min
by the U.S. instruments, and every 10 min
by the Canadian instruments. Details on
equipment
and sampling are given in
IFYGL Project Office (1972). Data from
instruments recording less than 20% of the
full month’s record were discarded. The
remaining data were edited, and currents
vector-averaged (by scalar averaging each
component, then recombining)
for each
current meter at each depth for the entire
month.
The current meter results in Fig. 1 show
strong counterclockwise
circulation at all
recorded depths (-5 to -19 m) with higher
speeds (up to 12 cm s-l) toward the west.
Data from the multilevel station off Rochester suggest that flow is in similar directions at all depths. The circulation
appears to weaken toward the eastern portion
of the lake, but the general flow pattern