In order to determine the thermal conductivity of first-year sea ice experimentally, measurements of temperature were performed every hour for five months using an array of thermistors. These were placed in a 25mm diameter hole on 12 June 1996, in fast sea ice about 1km offshore to the west of Arrival Heights in McMurdo Sound. The ice in the study area was quite flat, with almost no snow accumulation during the study. It was first year sea ice, grown from open sea, and it was fast to the land throughout the time that measurements were made.
The array
consisted of twenty thermistors 100 
2mm apart, inside a 6mm diameter
stainless steel tube, with a 0.15mm thick wall. The tube was filled
with a vegetable oil, which became a viscous grease below 0 
C,
to eliminate convection within the tube. Heat conduction along the
array was estimated to be equivalent to an ice plug with a diameter of
no more than 8mm. Conductive corrections associated with the array are
of the order of the square of the ratio of the radius (4mm) to the
wavelength of the thermal waves (>400mm), negligible at the 3%
uncertainty level achieved in the experiment.
The thermistors were Omega 44031 devices, calibrated to within 
C, with interchangeability 0.1 C and resolution
C. Resistance values were automatically recorded to a
similar accuracy. At each hour, an average of three resistance
measurements taken within a short time of each other is actually
recorded. A close look at the data and at first differences in time,
suggests that the truncation to C used in recording
the temperatures dominates any random fluctuations.
The temperature data obtained from the array is plotted in Fig. 1, as
temperature versus time at various depths. Each line represents the
temperature measured by a thermistor, with the thermistors placed
100mm apart. The sea temperature is -1.8 C, with colder temperatures
nearer the surface. Data from the upper five thermistors is plotted
separately for clarity.
It is clear from the data that the ice was about 700mm thick when the array was deployed, and thereafter grew to reach the twentieth (deepest) thermistor at 1900mm on day 120 (10 October). Note that day one is 12 June 1996. Both rising and falling temperatures are present, and the thermal conductivity may be determined directly by using the heat conduction equation
where k is
the thermal conductivity of the sea ice, U is the total specific
internal energy, 
the sea ice density (here taken to be
910 kg/m 
), and T is the temperature at depth z and time t.
The internal energy is given by integrating the effective heat
capacity C (Schwerdtfeger 1963; Ono, 1966; Yen, 1981), to give
where U is in J g 
, S is the average salinity of the sea ice
in parts per thousand ( 
), and 
is temperature in C. This
expression allows for the effect of latent heat as brine pockets
change volume to maintain thermodynamic equilibrium between
temperature and brine concentration.
Salinity measurements have been made from ice cores taken from the
area studied, at the time of the experiment and at various times over
the past ten years in the McMurdo Sound area. Average salinities fall
in the range 5 to 6 (except in the top 200mm of ice), so a
value of 5.5 was used to convert from temperature to internal
energy in the following. The fitted unbiased value of thermal
conductivity increased, by amounts varying from 2% near the top of
the ice to 9% near the bottom of the ice, when a salinity of 6.5
was used as a check on sensitivity.
The nonlinearity in C leads to a strong
temperature dependence in the thermal diffusivity 
, and
prevents using the more usual Fourier transform method for finding
k. It also prevents the substitution 
since this requires C to be
independent of T. The emphasis is shifted then, from finding the
diffusivity to finding the thermal conductivity.