THERMODYNAMICS
RADOK, U., SCHWËRDTFF.GF.R, P., and WELLER, G.
165
1968.
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meteorological conditions at Plateau Station. Antarctic Journal of the United
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SHUMSKY, P. A. 1963. On the theory of glacier variations. 1UGG-IASH Bulletin
VIII Année No. 1,45-56.
UEDA, H. T., and GARFIELD, D. E. 1968. Deep core drilling program at Byrd
Station (1967-1968). Antarctic Journal of the United States, Vol. 3, No. 4,
p. 111-12.
WEERTMAN, J. 1968. Comparison between measured and theoretical temperature
profiles of the Camp Century, Greenland, borehole. J. Geophys. Res., Vol. 73,
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ZOTIKOV, I. A. 1963. On temperatures at depths in glaciers. "Antarctic",
Moscow. (Translated by the Israel Program for Scientific Translations,
Jerusalem.)
A study of 10m firn temperatures in central East Antarctica*
BY
H. SCOTT KANE
Institute of Polar Studies, The Ohio State University
Introduction
This paper is the result of a study to analyze certain relationships
between the mean annual air temperature and topographical features in
central East Antarctica. The attempt is to explain a phenomenon which
was first observed on the Queen Maud Land Traverse I (QMLT I) and
subsequently on Queen Maud Land Traverse II (QMLT 11), which was
at that time designated "an anomalously warm area" (Cameron et al.,
1968).
These traverses were carried out in November, December, and January
of the 1964-65 and 1965-66 summers respectively. QMLT I covered an
approximately 1500-km "Z"-shaped path between the South Pole (90°S)
and the Soviet station at the "Pole of Inaccessibility" (55°6'E, 82°7'S).
QMLT II was a traverse toward the Greenwich Meridian from the "Pole
of Inaccessibility" and then back to the newly-established U.S. Plateau
Station, over a distance of approximately 1340 km. These routes are
shown in Figs. 1, 2 and 3. Other traverse stations adjacent to this area
have been plotted to permit contours to be continued outside the QMLT III area.
All temperatures reported in this paper are derived from a series of
measurements in boreholes of approximately 40 m depth. The measurements were made from 15 to 40 m and extrapolated to 10 m depth. This
is so as to be in accord with the standard and accepted practice of interpreting the "10 m temperature" as an approximation of the mean average
* Contribution No. 143 of the Institute of Polar Studies, Ohio State University
Columbia, Ohio 43210.
166
ISAGE
annual air temperature at that location. The measurements were taken
with thermistors, thermohms, and a Hewlett-Packard quartz crystal
thermometer. The measurements, for the purpose of this study, are
considered accurate to ± 0-05°C.
Temperature distribution
The first two curves in Fig. 4 show the relationship between 10 m
temperature and elevation', the primary variables measured in this study,
along the two traverse routes. The two areas labelled as anomalously
SNOW
SURFACE ELEVATION
• CENTRAL ANTARCTICA
CCHTOUf
INTERVAL
>O0O METERS
• TRAVERSE STATIC«
FIG. 1. Snow surface elevation, central Antarctica.
THERMODYNAMICS
167
warm are bracketed. The temperature in these areas is seen to decrease
as elevation decreased, the reverse of the normally expected situation. A
lapse rate of l°C/100 m has been dotted in between "Pole of Inaccessibility"
and turning point 2 (T.P. 2) for the purpose of comparison. This is the
rate of adiabatic warming, and in other studies has been shown to hold
for certain polar regimes (Loewe, 1935).
All the curves in Fig. 4 are plots of 8th degree, two-dimensional trend
surfaces. This has been done to remove local variations (residuals) and
more clearly display the relationships among the variables. However,
IO-NEÏER
"EMPERATURES
CENTRAL ANTARCTICA
CONTOJR INTERVAL TC
• TRAVERSE STATWN
FIG. 2.
10 m temperatures, central Antarctica.
168
ISAGE
in the numerical analysis to follow, actual measured values have been used
throughout (no smoothing). The third and fourth curves in this figure
are the slope and slope gradient respectively. These are true vector
quantities, i.e., they represent the magnitude of a three-dimensional vector
and not simply the derivatives along the traverse line. They were derived
from elevation measurements in conjunction with the elevation and slope
contour maps (Figs. 1 and 3).
It can be seen that the temperature anomaly may be explained as a
function of the gradient of elevation (slope) and perhaps its gradient.
SJ3FACE SLOPE
CENIRAL ANTARC1:CA
J.
L
FIG. 3. Surface slope, central Antarctica.
«0.
THERMODYNAMICS
,-Q a u U T H POLE
TP.I
TP.2
POLE OF
169
INACCESSIBILITY
TR3
PLATEAU
|
38003500^
2S00J
'"I
2
it
2
-
2n
-2J
5 7 7»
15 a
20
QMLT I
TRAVERSE STATION
8th
DEGREE TREND
SMOOTHED
29 0
5
9 9
QMLT n
VARIABLES
ALONG
16
TRAV. STA.
TRAVERSE
ROUTE
FIG. 4. 8th degree trend smoothed variables along traverse route.
The inflection points in the temperature curve (station numbers 1-11,
1-21, II-6, and 11-11) have been indicated on the slope curve by small
arrows. In all four cases this point is one station downslope from the
point of maximum slope. This corresponds to a linear displacement of
approximately 65 km.
The overall relationship among these variables can also be seen in the
contour map. The temperature contours (Fig. 2) follow the elevation
contours (Fig. 1) in the high plateau areas, but more closely resemble the
slope contours in the low elevations—especially where the slope is low.
Returning to Fig. 4, it is clearly seen that (1) an area of high slope
corresponds to a warmer-than-expected temperature, and the corollary,
(2) an area of low slope corresponds to a colder-than-expected temperature, and that there is (3) a shift downslope of this relationship on the
170
ISAGE
order of 65 km which may be thought of as a lag factor or phase shift.
An attempt was made to analyze this shift in terms of the slope gradient
without success.
Analysis
The above results proved of great interest, but still remain too qualitative
to be of much use. Furthermore, there are other spatial variables which
were measured over the course of the two traverses which might also prove
to have an effect on the annual average temperature at a given location.
It was decided to pursue this analysis through the standard technique of
multiple regression; however, rather than utilizing a step-wise regression,
a method was adopted which promised to lend more physical insight into
the problem at hand.
As a first step, all cross correlation coefficients (R) between the variables
were calculated on a digital computer. This matrix is shown in Fig. 5.
TEMPERATURE
ELEVATION
SLOPE
1.000
-.845
.212
.273
-.608
-.449
.709
.427
.419
1.000
.242
-.434
.658
.161
-.734
-.557
-.616
1.000
-.252
.121
-.464
-.327
-.132
-.246
1.000
244
-.010
.085
-.015
.Oil
1.000
.210
-.575
-.774
-.506
1.000
-.065
-.183
.103
1.000
.351
.456
LATITUDE
LONGITUDE
ICE THICKNESS
CONTINENTALITY
SLOPE
DIRECTION
SLOPE
GRADIENT
1.000
.527
1.000
CORRELATION
COEFFICIENT
MATRIX
FIG. 5. Correlation coefficient matrix.
A minus sign is included to indicate an inverse relationship with temperature. The variables chosen in addition to the dependent variable of
temperature were elevation, slope, latitude, longitude, ice thickness,
"continentality", slope direction, and slope gradient ("continentality" is
defined as the distance from the centre of the continent which was defined
as the point farthest removed from open sea; this was determined for
the purposes of this study to be 64°E, 83°35'S). Some elements of this
matrix are expected, such as the strong correlation between temperature
and elevation (R = —845), and some elements are a little surprising,
such as the extremely low correlation between ice thickness and latitude.
171
THERMODYNAMICS
It is to be remembered, however, that these results are derived only for
the traverse area, which is limited when compared with the scope of the
continent as a whole.
The correlation coefficient matrix is otherwise difficult to interpret in
its present format since low coefficients are interspersed with high
coefficients. The dendro diagram (McCammon, 1968) is a means of
sorting out this matrix. All of the dependent variables are analyzed on
this diagram (Fig. 7). Those variables with the highest cross correlation
CORRELATION
.7
SLOPE
COEFFICIENT
.6
.5
.4
DIRECTION
LONGITUDE
CONT1NENTALITY
• 11
ELEVATION
SLOPE GRADIENT
LATITUDE
SLOPE
ICE
THICKNESS
-
DENDRO
FIG. 7.
DIAGRAM
Dendro diagram.
coefficient are placed at the top of the diagram, and connected at the
abscissa value equal to this coefficient. For this purpose the coefficient
is taken as an absolute value; direct ( + ) and inverse (—) relationships of
variables to temperature are treated alike. Composite coefficients are
calculated once two or more variables have been joined. All of the
variables combined at a coefficient of -304. The importance of this
diagram is that it provides a method of ranking the variables in terms of
their contribution to the dependent variable.
Once this ranking has been obtained a rearranged coefficient matrix
can be constructed, as in Fig. 6. It is now apparent that all eight variables
fall into two groups (or possibly three groups if one considers the standalone latitude variable as a, complete and separate group). Multiple
regressions have been run on a digital computer taking into account these
groupings. The results.are shown in the Table. As was expected, a
regression with elevation is the best with a single independent variable.
For the area covered by QMLTI and II, it can explain 71-4% (R 2 = -714)
of the surface.
172
ISAGE
SLOPE
1000 -.774
DIRECTION
.527
-.015
-.132
-.183
.658
-.506
.244
.121
.210
1.000 -.734
.456
.085
-.327
-.065
1.000 -.616
-.434
.242
.161
1.000
.011
-.246
.103
1.000 -.251
-.010
1.000 -.575
LONGITUDE
CONTINENTALITY
ELEVATION
SLOPE
-.557
.351
GRADIENT
LATITUDE
1.000 -.464
SLOPE
ICE
1.000
THICKNESS
CORRELATION COEFFICIENT MATRIX REARRANGED
FIG. 6. Correlation coefficient matrix rearranged.
TABLE
MULTIPLE REGRESSIONS RESULTS
R2
Residuals
No.
Variables
1.
2.
3.
4.
5.
6.
•714
•735
•899
•904
•903
•915
1-83°C
1-78
110
109
109
103
1
2
2
3
3
4
7.
•920
1-02
5
8.
•951
0-83
8
a
-26-45 -26-94 -16-41 5. T p = -25-34 6. T p = -7-31 1.
3.
4.
Tp
Tp
Tp
=
=
=
E Elevation
La Latitude
S Slope
F Test
Factors not
significant
at 0-1% Level
110 ( > 5 % )
6 0 ( < l % ) La—3%
191 (<1%)
132 (<1%) La—7%
131 ( < 1 %) SG—8%
111 (<1%) La—1 %,
SG—1-2%
92 ( < 1 %) S G - 2 % ,
SD—7 7
90 (<1 %) 1-13%,
SD—3%
Variables
E
E, La
E, S
E, S, La
E, S, SG
E, S, SG, La
La, E, S, SG, SD
La, Lo, E, I, S, SG,
SD, C
Examples of regression equations
0-792 (E) x 10~22 °C
0-893 (E) x 10~2 + 2-16 (S) °C
0-924 (E) x 10"2 + 2-10 (S) - 0-113 (La) °C
0-941 (E) x 10" -I- 2-12 (S) - 0-366 (SG) °C
1-024 (E) x 10- 2 + 1-99 (S) - 0-181 (La) - 0-614 (SG)°
Symbols for variables
SG Slope Gradient
SD Slope Direction
Lo Longitude
I
C
Ice Thickness
Continentality
THERMODYNAMICS
173
For two independent variables, the equation with elevation and latitude
does surprisingly poorly: with a poor F test of R and latitude failing the
student's T test at the 3 per cent level. The equation with elevation and
slope, however, provided the highest F test of any regression run and
succeeded in explaining 89-9 per cent of the surface—a very good result
for only two independent variables. Adding latitude as a third variable
did not significantly improve the result.
For this area of central Antarctica, one equation stands out as a clear
improvement over a simple equation with elevation as the only variable,
and that is the one including slope:
T p = -26-94 - 0-893 (E) x 10"2 + 2-16 (S) °C
where E = elevation in metres, S = slope in metres/km, and T p = the
predicted temperature.
The coefficient with respect to elevation agrees well with the adiabatic
lapse rate. The coefficient with respect to slope shows a strong warming
effect with increased slope. This is plausible if one considers a slopeinduced wind of sufficient strength to produce mixing of the warmer air
above the inversion with the colder air at the surface. Two types of
slope-related influence are possible: (1) katabatic air flow, and (2) air
flow modified by a thermal wind.
We shall follow the treatment of Dalrymple et al. (1963, p. 37) which
is based on the hypothesis that "air motion in the lower atmosphere is
controlled by surface friction, and by the geostrophic motion in the free
atmosphere above the inversion layer, modified by thermal winds due to
horizontal temperature gradients which result from the general slope of
the terrain". Evidence in favour of this approach is that the wind
erosional features measured on QMLT II (Orheim, 1968) are more closely
aligned parallel to the elevation contours than down slope.
The thermal wind velocity can be calculated from the following equation
(Dalrymple et ai, 1963, p. 36):
g = acceleration of gravity = 9-82 m/sec2
AT = difference in temperature over the inversion
T a = average absolute layer temperature in °K
f = Coriolis parameter = 1-458 X KH/sec
oc = surface slope (of large-scale features).
For the South Pole, AT = 11-4°C and Ta = 220°K, which gives a value
of C = 3-5 km/sec. At Plateau Station, AT = 28°C and Ta = 205°K,
which gives C = 11-8 km/sec. A value of C = 8 km/sec will serve as the
average for the traverse areas.
The thermal wind provides a mechanism for focusing the wind above
the inversion into the mono-directional wind of greater constancy at the
surface. As stated above, the surface wind is influenced by (1) the wind
above the inversion, (2) the thermal wind, and (3) surface frictional
where
174
ISAGE
effects. If we make the seemingly reasonable assumption that the thermal
wind is much stronger (about double) than the wind above the inversion,
the latter's effect on the surface wind will be negligible, i.e., the strength
of the surface wind will be more purely a function of the thermal wind.
Under these assumptions, the surface wind would vary from about
2 m/sec for a surface slope of 0-5 m/km to about 12 m/sec for a surface
slope of 3-0 m/km. The slower wind speed would not be enough to
provide mixing in the inversion layer, while the faster, resulting in turbulent
flow conditions, would. For complete mixing, the maximum temperature
possible at the surface would be about — 40cC, the temperature at the top
of the inversion (Sponholz, 1968). The highest temperature measured
on all traverses was —44-9°C at QMLT II station number 11.
Conclusion
It has been shown, for the traverse areas under consideration, that
surface slope does participate in the control of average annual temperature.
A multiple regression analysis on the data collected at 46 traverse stations
indicates that the temperature isoincreased 2-16°C for each metre/kilometre
increase in slope. The mechanism for this warming appears to be turbulent mixing of the inversion layer caused by slope-induced thermal
winds.
Ackno wledgmen ts
The author would like to acknowledge the support of NSF Grants
GA-236 and GA-1076 awarded to The Ohio State University Research
Foundation, and Task Force 43 of the U.S. Navy, who provided logistic
support in the Antarctic. J. Beitzel and J. Clough of the University of
Wisconsin kindly provided the reduced values for ice thickness and
elevation. N. Peddie and D. Elvers of the U.S. Coast and Geodetic
Survey provided the station positions for QMLT I and II respectively.
•Dr. Uwe Radok, of the University of Melbourne, contributed direction
and suggestions helpful to this study.
REFERENCES
CAMERON, R. L., PICCIOTTO, E., KANE, H. S., and GLIOZZI, J.
1968.
Glaciology
on the Queen Maud Land Traverse, 1964-1965, South Pole—Pole of Relative
Inaccessibility. Ohio State Univ. Res. Foundation, frist. Polar Stud. Rept.,
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DALRYMPLE, P. C , LETTAU, H. H., and WOLLASTON, S. H.
1963.
South Pole
micrometeorology program, part II: data analysis. Quartermaster Research
and Engineering Center, Earth Sciences Division, Natick, Mass., Technical Report
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LOEWE, F. 1935. Klimas des Grönländischen Inlandeises. In: Koppen, W., and
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MCCAMMON, R. B. 1968. The. Dendrograph: a new tool for correlation. Geol.
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ORHEIM, O. 1968. Surface snow metamorphosis on the Antarctic Plateau. Norsk
Polarinstitut, Ârbok 1966, p. 84-91.
SPONHOLZ, MARTIN P.
1968.
Meteorological studies on the Antarctic Plateau.
Antarctic Journal of the U.S., Vol. 3, No. 5, p. 189-90.