Impact of water vapor diffusion and latent heat on the effective thermal conductivity of snow

Abstract

Abstract. 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.

Thermal Bridging Through Branches of Snow-Covered Shrubs Cool Down Permafrost in Winter

“…The average density of the SALIX pits was 267 kg m -3 vs 317 kg m -3 at TUNDRA, 19% greater than SALIX, similar to earlier observations 18,19 . Since density and thermal conductivity are positively correlated [20][21][22][23] , the greater density observed at TUNDRA is consistent with monitored thermal conductivities. All pits had a basal depth hoar layer 10 to 25 cm thick, slightly denser and with smaller grains at TUNDRA than at SALIX.…”

Permafrost cooled in winter by thermal bridging through snow-covered shrub branches

“…This is similar to earlier observations at similar spots in 2017 (17% greater at TUNDRA 19 ) and in 2015 (19% greater at TUNDRA 7 ). Because density and thermal conductivity are positively correlated 20 – 23 , the greater density observed at TUNDRA is consistent with monitored thermal conductivities. All pits had a basal depth hoar layer 10–25 cm thick, slightly denser at TUNDRA than at SALIX.…”

On the use of heated needle probes for measuring snow thermal conductivity

“…For each sample, a tetrahedral mesh was first obtained using a sub-cube of the segmented μCT scan and the CGAL meshing library. A steady-state simulation of heat conduction under a thermal gradient was performed, by imposing the top and bottom temperatures of the snow sample and enforcing zero-flux conditions on the remaining sides (Riche and Schneebeli, 2013; Fourteau and others, 2021). As in Riche and Schneebeli (2013), the effective thermal conductivity was then obtained as the ratio of the resulting heat flux to the imposed gradient.…”

“…However, the motion of water vapor carrying latent heat, also leads to heat transport (Yosida and others, 1955; De Vries, 1987; Hansen and Foslien, 2015). The importance of these latent heat processes depends on the surface kinetics of water molecule sublimation and condensation (Fourteau and others, 2021). If water molecules are rapidly accommodated and sublimated, then heat transport occurs as if the air had an extra thermal conductivity of magnitude D 0 L (d c sat /d T ) (Yosida and others, 1955; De Vries, 1958, 1987; Moyne and others, 1988), where D 0 = 2 × 10 −5 m 2 s −1 is the diffusion coefficient of water vapor in the air (Calonne and others, 2014), L = 28 × 10 5 J kg −1 is the latent heat of sublimation of water (Lide, 2004), and d c sat /d T is the derivative of the saturation concentration of water vapor with respect to temperature, estimated to be 2.6 × 10 −4 kg m −3 K −1 at 268 K. On the contrary, if the surface kinetics of water molecules deposition is very slow, then latent effects can be neglected and snow behaves as an inert bi-phasic medium.…”