Thermal Conductivity of Sea Ice and Antarctic Permafrost

216 Pages·2005·11.92 MB·English

Thermal Conductivity of Sea Ice
and Antarctic Permafrost
Daniel James Pringle
A thesis submitted for the degree of
Doctor of Philosophy.
School of Chemical and Physical Sciences.
Victoria University of Wellington
Wellington, New Zealand
18 October 2004
Supervised by Prof. H.J. Trodahl
This thesis was typeset with LATEX2ε, using the American Geophysical
Union 2001 style files, and 2004 referencing convention.
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Abstract
We present results from measurements of the thermal conductivity of sea ice,
k , usingtwodifferenttechniques. Inthefirst, icetemperaturesweremeasured
si
at 10 cm and 30 minute intervals by automated thermistor arrays deployed in
land-fast first-year (FY) and multi-year (MY) ice in McMurdo Sound, Antarc-
tica, and in FY ice in the Chukchi Sea and shallow Elson Lagoon, near Point
Barrow, Alaska. Conductivity profiles through the ice were calculated from
the coupled time- and depth- dependence of the temperature variations using
a conservation of energy analysis, and a graphical finite difference method.
These profiles show a reduction in the conductivity of up to 25% over the
top ∼ 50 cm, consistent with similar previous measurements. From simula-
tions and a detailed analysis of this method, we have clearly identified this
reduction (for which physical explanations had previously been invoked) as an
analytical artifact, due to the presence of temperature variations with time
scales much less than the 30 min sampling interval. These variations have a
penetration depth that is small compared with the thermistor spacing, so the
effect is shallow. Between 50 cm and the depth at which the method becomes
noise-limited, we calculate average conductivities of 2.29 ± 0.07W/m◦C and
2.26 ± 0.11W/m◦C at the FY McMurdo Sound and Chukchi Sea sites, and
2.03±0.04W/m◦C at the MY site in McMurdo Sound.
Using a parallel conductance method, we measured the conductivity of small
(11×2.4cmdiameter)icecoresbyheatingoneendofasampleholder, andwith
the other end held at a fixed temperature, measuring the temperature gradient
with and without a sample loaded. From several different cores in each class,
we resolved no significant difference, and certainly no large reduction, in the
conductivity of FY surface (0-10 cm) and sub-surface (45-55 cm) ice, being
2.14±0.11W/m◦C and 2.09±0.12W/m◦C respectively. The conductivity of
less dense, bubbly MY ice was measured to be 1.88 ± 0.13W/m◦C. Within
measurement uncertainties of about ±6%, the values from our two methods
are consistent with each other and with predictions from our modification of
an existing theoretical model for k (ρ,S,T). Both our results and previous
si
measurementsgiveconductivityvaluesabout10%higherthanthosecommonly
usedinArcticandAntarcticseaicemodels. ForFYice, wetentativelypropose
a new empirical parameterisation, k = 2.09−0.011T +0.117S/T [W/m◦C],
si
where T is temperature [◦C] and S salinity [0/ ]. We expect this parameter-
00
isation to be revised as thermal array data from other researchers are made
available.
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We also report thermal array measurements in ice-cemented permafrost at
Table Mountain in the Antarctic Dry Valleys, between November 2001 - De-
cember 2003. From 13 months of temperature data with a sampling interval
reduced from 4 hours to 1 hour (November 2002 - December 2003), we have
modified some aspects of an already published initial analysis [Pringle et al.,
2003]. Using thermal diffusivity profiles calculated from measured tempera-
tures, and a heat capacity estimated from recovered cores, we have determined
thermal conductivity profiles at two sites that show depth- and seasonal- vari-
ations that correlate well with core compositions, and the expected under-
lying temperature dependence. The conductivity generally lies in the range
2.5±0.5W/m◦C, but is as high as 5.5±0.4W/m◦C in a quartz-rich unit at
one site. The wintertime diffusivity is 4 ± 7% higher than the summertime
value, which we understand to reflect the underlying temperature dependence.
In this analysis we find our graphical finite difference method more versatile
and more accurate than common ‘Fourier’ time-series methods.
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Acknowledgements
There are many people that I would like to thank for their part in what has
been a very rewarding and enjoyable project for me. I have learned scientific
and personal lessons from all of you. To Joe Trodahl, thank you so much for
everything from getting me on board, to helping me along with good humour
and gentle prodding. I know that I will continue to appreciate your signifi-
cant scientific and personal influence well beyond this work. To Hajo Eicken,
thank you for the fantastic opportunities to visit, work with, and learn about
sea ice from you and your group at the University of Alaska Fairbanks, for
making unpublished data and measurements available to me, and for the sup-
port during the completion of this dissertation. To Warren Dickinson, thank
you for the opportunity to become involved in the Table Mountain project,
and for the amazing opportunity of field work in the Dry Valleys. To Tim
Haskell, thank you for your organisational and experimental support, and for
your great company in Antarctica, 2002 and 2003.
Alan Rennie in particular, and Dave Gilmour, deserve special thanks for their
expert machining of the thermal arrays and vacuum chamber. Thanks to Eric
Broughton and Alex Pyne who assembled the Table Mountain arrays, to Alex
and Warren for installing them, and to Alex for discussions about equipment.
Thanks also to Mark McGuinness for helpful mathematical assistance and
discussions. I received fantastic scientific support from Scott Base technicians
Tim Kerr, Shane Thomson, Margaret Auger and Jamie Plowman, and winter-
over science staff Johno Leitch, Craig Purdie and Greg Leonard.
In the course of this study I was hosted three times by Hajo Eicken and his
sea ice group at UAF. Thank you to everyone involved in making these trips
scientifically exciting and stimulating, and for welcoming me into your lives in
Fairbanks. This group was shocked by the tragic death of Karoline Frey in
March 2002. I acknowledge with sadness but gratitude Karoline’s contribution
to my field work, her observations and insights, her unpublished data, and her
lasting personal influence. Thank you Andy Mahoney, Craig Zubris, Lars
Backstr¨om and Meg Smith for your help with my field work, and along with
Tina Tin, Alain Burgisser, Tanja Petersen, and the rest of the UAF crew, for
receiving me so warmly. Thanks also to Cliff Atkins, Paul Callaghan, Mark
Hunter, Ocean Mercier, and the friendly Scott Base ‘beakers’ and staff for your
parts in my Antarctic experience. Respect and good luck to Alex, Steve and
all the guys at Cornell Physics.
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For their administrative help over the last three years I am very grateful to
Margaret Brown, Barry Lewis, Maureen Penning and particularly Celia Simp-
son.
Special thanks to Gazza and Angela, DC and Ang, Paddy and Julz, Lloyd
and Briony, Buckey, and Bakie. Thank you Mum and Dad for your continued
support and love.
Above all, thank you so much Lisa for your continual support, love, patience,
encouragement, example and inspiration. Thanks so much for abiding my
trips, all the late nights, and my early-onset absent mindedness. It means the
world to me.
This work was funded through the New Zealand Public Good Science Fund,
and a Victoria University Targeted Postgraduate Scholarship. Antarctica New
Zealand provided logistic, and scientific support at Scott Base. NSF-funded
supportfurnishedbytheBarrowArcticScientificConsortium(BASC)isgrate-
fully acknowledged.
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With thanks to those who continue to provide inspiration.
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Contents
Abstract iii
Acknowledgements v
1 Introduction 1
1.1 Heat Flow near the Earth’s Surface . . . . . . . . . . . . . . . . 5
1.2 Effective Properties of Composite Materials . . . . . . . . . . . 7
1.3 Sea Ice Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4 Heat Flow in Sea Ice . . . . . . . . . . . . . . . . . . . . . . . . 12
1.5 Structure of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . 16
2 Background 17
2.1 Composition and Phase Relations . . . . . . . . . . . . . . . . . 17
2.2 Theoretical Thermal Conductivity of Sea Ice . . . . . . . . . . . 20
2.3 Theoretical Specific Heat of Sea Ice . . . . . . . . . . . . . . . . 24
2.4 Previous Experimental Results . . . . . . . . . . . . . . . . . . . 26
2.4.1 Stefan, 1873 . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4.2 Malmgren, 1927 . . . . . . . . . . . . . . . . . . . . . . . 27
2.4.3 Nazintsev, 1950-60s . . . . . . . . . . . . . . . . . . . . . 30
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2.4.4 Ono, 1960s . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.4.5 Schwerdtfeger, 1960s . . . . . . . . . . . . . . . . . . . . 32
2.4.6 Lewis, 1966 . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.4.7 Weller, 1965-68 . . . . . . . . . . . . . . . . . . . . . . . 37
2.4.8 Trodahl and co-workers, 1996- . . . . . . . . . . . . . . . 39
3 Thermal Array Measurements 43
3.1 Overview of Experiment . . . . . . . . . . . . . . . . . . . . . . 43
3.1.1 Array Construction . . . . . . . . . . . . . . . . . . . . . 45
3.1.2 Thermistors . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.1.3 Measurement Circuitry . . . . . . . . . . . . . . . . . . . 52
3.2 Data Loggers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.2.1 Campbell CR10X Loggers . . . . . . . . . . . . . . . . . 54
3.2.2 Custom Built Loggers . . . . . . . . . . . . . . . . . . . 54
3.3 Site Assembly and Installation . . . . . . . . . . . . . . . . . . . 55
3.4 Experimental Uncertainty in ∆z, ∆t . . . . . . . . . . . . . . . 56
4 Analysis of Temperature Array Data 57
4.1 Conductive Heat Flow in Sea Ice . . . . . . . . . . . . . . . . . 57
4.2 Overview of Graphical Finite Difference Analysis . . . . . . . . 60
4.3 Effect of Measurement Noise . . . . . . . . . . . . . . . . . . . . 61
4.3.1 Gaussian Noise and Data Distribution . . . . . . . . . . 62
4.3.2 Uniform Measurement Noise and Data Spread . . . . . . 65
4.4 Effect of Finite Sampling Intervals . . . . . . . . . . . . . . . . . 66
4.5 Simulations of Many-Component Driving . . . . . . . . . . . . . 70
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