Twenty-seven studies on the thermal conductivity of snow (k eff ) have been published since 1886. Combined, they comprise 354 values of k eff , and have been used to derive over 13 regression equations predicting k eff vs density. Due to large (and largely undocumented) differences in measurement methods and accuracy, sample temperature and snow type, it is not possible to know what part of the variability in this data set is the result of snow microstructure. We present a new data set containing 488 measurements for which the temperature, type and measurement accuracy are known. A quadratic equation, k eff = 0.138 - 1.01ρ + 3.233ρ 2 {0.156 ≤ ρ ≤ 0.6} k eff = 0.023 + 0.234ρ {ρ < 0.156}, where ρ is in g cm -3 and k eff is in W m -1 K -1 , can be fit to the new data (R 2 =0.79). A logarithmic expression, k eff = 10 (2.650ρ-1.652) {ρ ≤ 0.6}, can also be used. The first regression is better when estimating values beyond the limits of the data; the second when estimating values for low-density snow. Within the data set, snow types resulting from kinetic growth show density-independent behavior. Rounded-grain and wind-blown snow show strong density dependence. The new data set has a higher mean value of density but a lower mean value of thermal conductivity than the old set. This shift is attributed to differences in snow types and sample temperatures in the sets. Using both data sets, we show that there are well-defined limits to the geometric configurations that natural seasonal snow can take.

/pdf/the-thermal-conductivity-of-seasonal-snow-1han96i2jg.pdf

The thermal conductivity of seasonal snow

[1] Modeling the densification of polar firn is essential to estimate variations of close-off characteristics (density, close-off depth, delta age) in relation with past climate parameters (temperature and accumulation rates). Furthermore, the air composition in the firn is modified by gravitational and thermal fractionation, and stable isotope measurements of permanent gases like nitrogen or argon can provide information on the amplitude of these fractionations. In this work, we propose a new model coupling firn densification and heat diffusion. In addition to the determination of the firn thickness and gas-ice age differences, the model allows a reconstruction of the time evolution of the temperature for different sites in Antarctica (Vostok) and Greenland (GISP2) and therefore the evolution of gravitational and thermal isotopic fractionations in firn. Under present-day conditions, the modeled profiles are in good agreement with the available temperature measurements in firn. For sites with low accumulation rates such as Vostok, the results show the existence of temperature gradients in the firn column even when no rapid climatic changes occur. The comparison of the modeled δ15N results to measurements allows to better constrain the δ18O-temperature relationship, used to infer the surface temperature history, and for GISP2, the model validates the long-term borehole-based temperature.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2002JD003319

Modeling the densification of polar firn including heat diffusion: Application to close-off characteristics and gas isotopic fractionation for Antarctica and Greenland sites

. Air and water stable isotope measurements from four Greenland deep ice cores (GRIP, GISP2, NGRIP and NEEM) are investigated over a series of Dansgaard–Oeschger events (DO 8, 9 and 10), which are representative of glacial millennial scale variability. Combined with firn modeling, air isotope data allow us to quantify abrupt temperature increases for each drill site (1σ = 0.6 °C for NEEM, GRIP and GISP2, 1.5 °C for NGRIP). Our data show that the magnitude of stadial–interstadial temperature increase is up to 2 °C larger in central and North Greenland than in northwest Greenland: i.e., for DO 8, a magnitude of +8.8 °C is inferred, which is significantly smaller than the +11.1 °C inferred at GISP2. The same spatial pattern is seen for accumulation increases. This pattern is coherent with climate simulations in response to reduced sea-ice extent in the Nordic seas. The temporal water isotope (δ18O)–temperature relationship varies between 0.3 and 0.6 (±0.08) ‰ °C−1 and is systematically larger at NEEM, possibly due to limited changes in precipitation seasonality compared to GISP2, GRIP or NGRIP. The gas age−ice age difference of warming events represented in water and air isotopes can only be modeled when assuming a 26% (NGRIP) to 40% (GRIP) lower accumulation than that derived from a Dansgaard–Johnsen ice flow model.

https://cp.copernicus.org/articles/9/1029/2013/cp-9-1029-2013.pdf

Spatial gradients of temperature, accumulation and δ 18 O-ice in Greenland over a series of Dansgaard–Oeschger events

The temperature profile measured in the Vostok bore hole is analysed. The temperature distribution in polar ice sheets depends mainly on past surface temperature, geothermal flux, and accumulation rate. In the present work, the heat equation is solved both for ice and for the underlying bedrock. The Vostok ice core offers a 160 000 year climatic record which is used to define the past surface temperature, while accumulation-rate variations are assumed to be governed by the saturation vapour pressure. The model is run for a number of different sets of parameters in order to find the parameter associations giving a good fit between the observed and the computed temperature profiles. With this model, it is possible to simulate the measured temperature profile within 0.1°C. To obtain this good fit, geothermal flux has to be higher than 50 mW/m2 and present-day accumulation rate must be lower than 2.6 cm/year. Sensitivity of these results both to the amplitude of surface-temperature change and to the velocity profile with depth is also investigated. Finally, it is shown that ice is at the melting point at the base of the ice sheet, which is in agreement with the presence of a subglacial lake near Vostok Station.

/pdf/interpretation-of-the-temperature-profile-measured-at-vostok-2urxbwoo90.pdf

Interpretation of the temperature profile measured at Vostok, east Antarctica

We use a hybrid finite-element/finite-difference model of ice-shelf flow and heat transfer to investigate the effects of basal melting on the present observed flow of the Ross Ice Shelf, Two hypothetical basal melting scenarios are compared: (i) zero melting everywhere and (ii) melting sufficient to balance any large-scale patterns of ice-shelf thickening that would otherwise occur. As a result of the temperature-dependent flow law (which we idealize as having a constant activation energy of 120 kJ mol−1, a scaling coefficient of 1.3 N m−2 s1/3, and an exponent of 3), simulated ice-shelf velocities for the second scenario are reduced by up to 20% below those of the first. Our results support the hypothesis that melting patterns presently maintain ice thickness in steady state and conform to patterns of oceanic circulation presently thought to ventilate the sub-ice cavity. Differences between the simulated and observed velocities are too large in the extreme south-eastern quarter of the ice shelf to permit verification of either basal melting scenario. These differences highlight the need to improve model boundary conditions at points where ice streams feed the ice shelf and where the ice shelf meets stagnant grounded ice.

The Effects of Basal Melting on the Present Flow of the Ross Ice Shelf, Antarctica

The thermal conductivity and diffusivity of natural snow computed from Fourier-type analyses of annual snow temperature variations are shown to be strongly temperature dependent. The computed temperature coefficients of-0.007 and -0.012 deg-1 respectively, agree well with older laboratory experiments carried out on polycrystalline ice.

/pdf/short-notes-new-data-on-the-thermal-conductivity-of-natural-52zamwvh6d.pdf

Short Notes: New Data on the Thermal Conductivity of Natural Snow

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Short Notes: New Data on the Thermal Conductivity of Natural Snow