In the high Arctic, thermal bridging through frozen shrub branches has been demonstrated to cool the ground by up to 4°C during cold spells, affecting snow metamorphism and soil carbon and nutrients. ...In alpine conditions, the thermal conductivity contrast between shrub branches and snow is much less than in the Arctic, so that the importance of thermal bridging is uncertain. We explore this effect by monitoring ground temperature and liquid water content under green alders and under nearby alpine tundra in the Alps. During a January 2022 cold spell, the ground temperature at 5 cm depth under alders is 1.3°C colder than under alpine tundra. Ground water freezing under alders is complete, while water remains liquid under tundra. Finite element simulations reproduce the observed temperature difference between both sites, showing that thermal bridging does affect ground temperature also under Alpine conditions.
Plain Language Summary
With climate warming, shrubs are expanding in seasonally snow‐covered Arctic and alpine areas. In the Arctic, it has been shown that shrubs buried in snow act as thermal bridges between the ground and the atmosphere, so that the ground winter temperature is colder than if thermal effects due to snow only are considered. Thermal bridging is efficient in the Arctic because the thermal conductivity of shrub branches is 30–70 times as large as that of snow. In alpine areas, the difference in thermal conductivity between the shrub branches and the snow is much lower, so that the efficiency of thermal bridging by shrubs is uncertain, even though shrub branches are much thicker. We monitored the soil temperature at an Alpine site at a spot with green alders and a nearby spot with herbaceous vegetation. The ground was 1.3°C colder under alders during a cold spell. Using finite element simulations, we show that this is explained by thermal bridging through alder branches. Snow and land surface models must therefore include this process for adequate simulations of the soil temperature, soil freezing and carbon recycling, snow metamorphism and snow physical properties.
Key Points
The winter ground temperature in a snow‐covered alpine area during a cold spell is 1.3°C colder under alders than under nearby grass
Using finite element modeling, we demonstrate that this is due to thermal bridging through alder branches
Plane‐parallel snow layer geometry cannot be used to model ground temperature, soil freezing, and snow metamorphism if shrubs are present
Heated needle probes provide the most convenient method to measure snow thermal conductivity. Recent studies have suggested that this method underestimates snow thermal conductivity; however the ...reasons for this discrepancy have not been elucidated. We show that it originates from the fact that, while the theory behind the method assumes that the measurements reach a logarithmic regime, this regime is not reached within the standard measurement procedure. Using the needle probe without this logarithmic regime leads to thermal conductivity underestimations of tens of percents. Moreover, we show that the poor thermal contact between the probe and the snow due to insertion damages results in a further underestimation. Thus, we encourage the use of fixed needle probes, set up before the snow season and buried under snowfalls, rather than hand-inserted probes. Finally, we propose a method to correct the measurements performed with such fixed needle probes buried in snow. This correction is based on a lookup table, derived specifically for the Hukseflux TP02 needle probe model, frequently used in snow studies. Comparison between corrected measurements and independent estimations of snow thermal conductivity obtained with numerical simulations shows an overall improvement of the needle probe values after application of the correction.
Despite being one of the most fundamental microstructural parameters of snow, the specific surface area (SSA) dynamics during temperature gradient metamorphism (TGM) have so far been addressed only ...within empirical modeling. To surpass this limitation, we propose a rigorous modeling of SSA dynamics using an exact equation for the temporal evolution of the surface area, fed by pore-scale finite-element simulations of the water vapor field coupled with the temperature field on X-ray computed tomography images. The proposed methodology is derived from the first principles of physics and thus does not rely on any empirical parameter. Since the calculated evolution of the SSA is highly sensitive to fluctuations in the experimental data, we quantify the impact of these fluctuations within a stochastic error model. In our simulations, the only poorly constrained physical parameter is the condensation coefficient α. We address this problem by simulating the SSA evolution for a wide range of α values and estimate optimal values by minimizing the differences between simulations and experiments. This methodology suggests that α lies in the intermediate range 10-3<α<10-1 and slightly varies between experiments. Also, our results suggest a transition of the value of α in one TGM experiment, which can be explained by a transition in the underlying surface morphology. Overall, we are able to reproduce very subtle variations in the SSA evolution with correlations of R2=0.95 and 0.99, respectively, for the two TGM time series considered. Finally, our work highlights the necessity of including kinetic effects and of using realistic microstructures to comprehend the evolution of SSA during TGM.
Accurate models for the viscous densification of snow (understood here as a density below 550 kg m−3) and firn (a density above 550 kg m−3) under mechanical stress are of primary importance for ...various applications, including avalanche prediction and the interpretation of ice cores. Formulations of snow and firn compaction in models are still largely empirical instead of using microstructures from micro-computed tomography to numerically compute the mechanical behavior directly from the physics at the microscale. The main difficulty of the latter approach is the choice of the correct rheology/constitutive law governing the deformation of the ice matrix, which is still controversially discussed. Being aware of these uncertainties, we conducted a first systematic attempt of microstructure-based modeling of snow and firn compaction. We employed the finite element suite Elmer FEM using snow and firn microstructures from different sites in the Alps and Antarctica to explore which ice rheologies are able to reproduce observations. We thereby extended the ParStokes solver in Elmer FEM to facilitate parallel computing of transverse isotropic material laws for monocrystalline ice. We found that firn densification can be reasonably well simulated across different sites assuming a polycrystalline rheology (Glen's law) that is traditionally used in glacier or ice sheet modeling. In contrast, for snow, the observations are in contradiction with this rheology. To further comprehend this finding, we conducted a sensitivity study on different ice rheologies. None of the material models is able to explain the observed high compactive viscosity of depth hoar compared to rounded grains having the same density. While, on one hand, our results re-emphasize the limitations of our current mechanical understanding of the ice in snow, they constitute, on the other hand, a confirmation of the common picture of firn as a foam of polycrystalline ice through microstructure-based simulations.
Quantifying the link between microstructure and effective elastic properties of snow, firn, and bubbly ice is essential for many applications in cryospheric sciences. The microstructure of snow and ...ice can be characterized by different types of fabrics (crystallographic and geometrical), which give rise to macroscopically anisotropic elastic behavior. While the impact of the crystallographic fabric has been extensively studied in deep firn, the present work investigates the influence of the geometrical fabric over the entire range of possible volume fractions. To this end, we have computed the effective elasticity tensor of snow, firn, and ice by finite-element simulations based on 391 X-ray tomography images comprising samples from the laboratory, the Alps, Greenland, and Antarctica. We employed a variant of Eshelby's tensor that has been previously utilized for the parameterization of thermal and dielectric properties of snow and utilized Hashin–Shtrikman bounds to capture the nonlinear interplay between density and geometrical anisotropy. From that we derive a closed-form parameterization for all components of the (transverse isotropic) elasticity tensor for all volume fractions using two fit parameters per tensor component. Finally, we used the Thomsen parameter to compare the geometrical anisotropy to the maximal theoretical crystallographic anisotropy in bubbly ice. While the geometrical anisotropy clearly dominates up to ice volume fractions of ϕ≈0.7, a thorough understanding of elasticity in bubbly ice may require a coupled elastic theory that includes geometrical and crystallographic anisotropy.
Heat transport in snowpacks is understood to occur through the two processes of heat conduction and latent heat transport carried by water vapor, which are generally treated as decoupled from one ...another. This paper investigates the coupling between both these processes in snow, with an emphasis on the impacts of the kinetics of the sublimation and deposition of water vapor onto ice. In the case when kinetics is fast, latent heat exchanges at ice surfaces modify their temperature and therefore the thermal gradient within ice crystals and the heat conduction through the entire microstructure. Furthermore, in this case, the effective thermal conductivity of snow can be expressed by a purely conductive term complemented by a term directly proportional to the effective diffusion coefficient of water vapor in snow, which illustrates the inextricable coupling between heat conduction and water vapor transport. Numerical simulations on measured three-dimensional snow microstructures reveal that the effective thermal conductivity of snow can be significantly larger, by up to about 50 % for low-density snow, than if water vapor transport is neglected. A comparison of our numerical simulations with literature data suggests that the fast kinetics hypothesis could be a reasonable assumption for modeling heat and mass transport in snow. Lastly, we demonstrate that under the fast kinetics hypothesis the effective diffusion coefficient of water vapor is related to the effective thermal conductivity by a simple linear relationship. Under such a condition, the effective diffusion coefficient of water vapor is expected to lie in the narrow 100 % to about 80 % range of the value of the diffusion coefficient of water vapor in air for most seasonal snows. This may greatly facilitate the parameterization of water vapor diffusion of snow in models.
Water vapor transport in dry snowpacks plays a significant role for snow metamorphism and the mass and energy balance of snowpacks. The molecular diffusion of water vapor in the interstitial pores is ...usually considered to be the main or only transport mechanism, and current detailed snow physics models therefore rely on the knowledge of the effective diffusion coefficient of water vapor in snow. Numerous previous studies have concluded that water vapor diffusion in snow is enhanced relative to that in air. Various field observations also indicate that for vapor transport in snow to be explained by diffusion alone, the effective diffusion coefficient should be larger than that in air. Here we show using theory and numerical simulations of idealized and measured snow microstructures that, although sublimation and deposition of water vapor onto snow crystal surfaces do enhance microscopic diffusion in the pore space, this effect is more than countered by the restriction of diffusion space due to ice. The interaction of water vapor with the ice results in water vapor diffusing more than inert molecules in snow but still less than in free air, regardless of the value of the sticking coefficient of water molecules on ice. Our results imply that processes other than diffusion play a predominant role in water vapor transport in dry snowpacks.
The surface energy budget drives the melt of the snow cover and glacier ice and its computation is thus of crucial importance in numerical models. This surface energy budget is the result of various ...surface energy fluxes, which depend on the input meteorological variables and surface temperature; of heat conduction towards the interior of the snow/ice; and potentially of surface melting if the melt temperature is reached. The surface temperature and melt rate of a snowpack or ice are thus driven by coupled processes. In addition, these energy fluxes are non-linear with respect to the surface temperature, making their numerical treatment challenging. To handle this complexity, some of the current numerical models tend to rely on a sequential treatment of the involved physical processes, in which surface fluxes, heat conduction, and melting are treated with some degree of decoupling. Similarly, some models do not explicitly define a surface temperature and rather use the temperature of the internal point closest to the surface instead. While these kinds of approaches simplify the implementation and increase the modularity of models, they can also introduce several problems, such as instabilities and mesh sensitivity. Here, we present a numerical methodology to treat the surface and internal energy budgets of snowpacks and glaciers in a tightly coupled manner, including potential surface melting when the melt temperature is reached. Specific care is provided to ensure that the proposed numerical scheme is as fast and robust as classical numerical treatment of the surface energy budget. Comparisons based on simple test cases show that the proposed methodology yields smaller errors for almost all time steps and mesh sizes considered and does not suffer from numerical instabilities, contrary to some classical treatments.
Interpretation of greenhouse gas records in polar ice cores requires a good understanding of the mechanisms controlling gas trapping in polar ice, and therefore of the processes of densification and ...pore closure in firn (compacted snow). Current firn densification models are based on a macroscopic description of the firn and rely on empirical laws and/or idealized geometries to obtain the equations governing the densification and pore closure. Here, we propose a physically-based methodology explicitly representing the porous structure and its evolution over time. In order to handle the complex geometry and topological changes that occur during firn densification, we rely on a Level-Set representation of the interface between the ice and the pores. Two mechanisms are considered for the displacement of the interface: (i) mass surface diffusion driven by local pore curvature and (ii) ice dislocation creep. For the latter, ice is modeled as a viscous material and the flow velocities are solutions of the Stokes equations. First applications show that the model is able to densify firn and split pores. Using the model in cold and arid conditions of the Antarctic plateau, we show that gas trapping models do not have to consider the reduced compressibility of closed pores compared to open pores in the deepest part of firns. Our results also suggest that the mechanism of curvature-driven surface diffusion does not result in pore splitting, and that ice creep has to be taken into account for pores to close. Future applications of this type of model could help quantify the evolution and closure of firn porous networks for various accumulation and temperature conditions.
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