<p>We present results from measurements of the thermal conductivity of sea ice, ksi, using two different techniques. In the first, ice temperatures were measured 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, Antarctica, 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 simulations 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 +/- 0.07 W/m degrees C and 2.26 +/- 0.11 W/m degrees C at the FY McMurdo Sound and Chukchi Sea sites, and 2.03 +/- 0.04 W/m degrees C at the MY site in McMurdo Sound. Using a parallel conductance method, we measured the conductivity of small (11 x 2.4 cm diameter) ice cores by heating one end of a sample holder, and with 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 +/- 0.11 W/m degrees C and 2.09 +/- 0.12 W/m degrees C respectively. The conductivity of less dense, bubbly MY ice was measured to be 1.88 +/- 0.13 W/m degrees 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 ksi(p, S, T). Both our results and previous measurements give conductivity values about 10% higher than those commonly used in Arctic and Antarctic sea ice models. For FY ice, we tentatively propose a new empirical parameterisation, ksi = 2.09 - 0.011T + 0.117S/T [W/m degrees C], where T is temperature [degrees C] and S salinity [0/00]. We expect this parameterisation to be revised as thermal array data from other researchers are made available. We also report thermal array measurements in ice-cemented permafrost at Table Mountain in the Antarctic Dry Valleys, between November 2001 - December 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 temperatures, and a heat capacity estimated from recovered cores, we have determined thermal conductivity profiles at two sites that show depth- and seasonal- variations that correlate well with core compositions, and the expected underlying temperature dependence. The conductivity generally lies in the range 2.5 +/- 0.5 W/m degrees C, but is as high as 5.5 +/- 0.4 W/m degrees 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.</p>
Numerical investigation for a hyperbolic annular fin with temperature dependent thermal conductivity
