Thermal conductivity of firn at Lomonosovfonna, Svalbard, derived from subsurface temperature measurements

Abstract

Accurate description of snow and firn processes is necessary for estimating the fraction of glacier surface melt that contributes to runoff. Most processes in snow and firn are to a great extent controlled by the temperature therein and in the absence of liquid water, the temperature evolution is dominated by the conductive heat exchange. The latter is controlled by the effective thermal conductivity k. Here we reconstruct the effective thermal conductivity of firn at Lomonosovfonna, Svalbard, using an optimization routine minimizing the misfit between simulated and measured subsurface temperatures and densities. The optimized k * values in the range from 0.2 to 1.6 W (m K) −1 increase downwards and over time. The results are supported by uncertainty quantification experiments, according to which k * is most sensitive to systematic errors in empirical temperature values and their estimated depths, particularly in the lower part of the vertical profile. Compared to commonly used density-based parameterizations, our k values are consistently larger, suggesting a faster conductive heat exchange in firn.

Thermal Conductivity of Snow, Firn, and Porous Ice From 3‐D Image‐Based Computations

“…We thus plotted here our results at −20°C, as the more relevant to be compared with. General trends are in agreement but data of Marchenko et al () shows more scatter and overall larger values than ours. As discussed by the authors, the scatter likely reflects uncertainties related to measurement deviations or vertical mismatches between density profiles and temperature profiles.…”

“…We compare now our values of thermal conductivity with the data of Marchenko et al () and Giese and Hawley () presented in section (Figure a). Authors reported temperatures fluctuating between −15 and −40°C at the Summit site (Giese & Hawley, ) and between 0 and −20°C at the Lomonosovfonna site (Marchenko et al, ). We thus plotted here our results at −20°C, as the more relevant to be compared with.…”

“…In both studies, thermal conductivity is obtained by best matching modeled temperature profiles to in situ measured ones. A linear correlation between density and conductivity is found but comes with a large scatter, which is attributed to measurement errors (Marchenko et al, ). The microstructure of firn and porous ice can be noticeably different at a given density because of the different thermomechanical constraints they underwent (Burr et al, , ; Lomonaco et al, ).…”

“…Because of the lack of data and dedicated predictive formulas, thermal conductivity of firn and porous ice is often estimated based on parameterizations actually designed for snow, that is, for densities between 100 and 550 kg/m 3 , without being able to evaluate their performances at higher densities. Marchenko et al () indicate that snow‐designed parameterizations may underestimate firn conductivity. As summarized in Table , some of the most commonly used formulas to model heat conduction in glaciers are the following: the average of the Van Dusen and the Swcherdtfeger formulas, often described as lower and upper limits, respectively (Paterson, ) (e.g., used in, Humphrey et al, ; Lüthi & Funk, ; Van Ommen et al, ) the Yen formula (e.g., used in, Arthern & Wingham, ; Cummings et al, ) the Sturm formula (e.g., used in, Reijmer & Hock, ; Zwinger et al, ) the Schwander formula (e.g., used in, Goujon et al, ) the Calonne formula (e.g., used in, Gilbert & Vincent, ; Gilbert et al, ) …”

“…Data on thermal conductivity of firn and porous ice are very scarce: Giese and Hawley (2015) provide a single bulk value of the top first 30 m of firn at Summit, Greenland, and Marchenko et al (2019) present eight vertical profiles of firn conductivity of 10 m depth and 1 m resolution at Lomonosovfonna, Svalbard. In both studies, thermal conductivity is obtained by best matching modeled temperature profiles to in situ measured ones.…”