Snow at or close to the surface commonly undergoes temperature gradient metamorphism under advective flow, which alters its microstructure and physical properties. A functional understanding of this process is essential for many disciplines, from modeling the effects of snow on regional and global climate to assessing avalanche formation. Time‐lapse X‐ray microtomography was applied to investigate the structural dynamics of temperature gradient snow metamorphism exposed to an advective airflow in controlled laboratory conditions. Experiments specifically analyzed sublimation and deposition of water vapor on the ice structure. In addition, an analysis of the ice‐air interface dynamics was carried out using a macroscopic equivalent model of heat and water vapor transport through a snow layer. The results indicate that sublimation of the ice matrix dominated for flow rates < 10 −6 m 3 s −1 while during increased mass flow rates the water vapor deposition supplied by the advective flow counteracted sublimation. A flow rate dependence of water vapor deposition at the ice interface was observed, asymptotically approaching an average estimated maximum deposition rate on the whole sample of 1.05 · 10 −4 kg m −3 s −1 . The growth of microsized whisker‐like crystals on larger ice crystals was detected on microscope photographs, leading to an increase of the specific surface area and thus suggest a change of the physical and optical properties of the snow. The estimated values of the curvature effect of the ice crystals and the interface kinetic coefficient are in good agreement with previously published values.

1 Introduction Snow has a complex porous microstructure and consists of a continuous ice structure made of grains connected by bonds and interconnecting pores [Löwe et al., 2011]. It has a high permeability, and under appropriate conditions airflow through the snow structure can occur [Sturm and Johnson, 1991]. Variation in surface pressure resulting from strong wind associated with surface features like dunes and ripples leads to continuous airflow through the seasonal snowpack [Colbeck, 1989]. Simultaneous warming and cooling at different locations in a horizontal plane in the snow as well as measured temperature gradients of up to 16 K m−1 led to air movement in an arctic snow cover [Sturm and Johnson, 1991]. In addition, small pressure variations (>3 Pa) are sufficient to cause significant air movement in some arctic snowpacks, leading to an advective‐controlled heat transfer [Albert and Hardy, 1995]. Both diffusive and advective airflows affect heat and mass transport in snowpacks and have an influence on chemical concentrations [Gjessing, 1977] or a filtering effect [Waddington et al., 1996]. Under isothermal conditions, the pore space in snow is almost at saturation vapor pressure but undersaturation may occur in large pore spaces or in regions of rapid interstitial airflow [Neumann et al., 2008, 2009]. Furthermore, saturated advective airflow across a snow sample has been shown to have no significant disturbance of the vapor flux in the pores, and no dependence of various airflow velocities on the structural evolution was observed under isothermal condition [Ebner et al., 2015]. Adding a temperature gradient induces a water vapor concentration gradient in the pores. The absence of a flow rate has been shown to have no effect on heat transfer by water vapor diffusion [Yosida, 1955; Yen, 1963]. When inducing airflow, the vapor transport processes make a significant contribution to the process of heat transfer associated with a natural snow cover [Yen, 1962, 1963]. Numerical simulation combined with laboratory experiments demonstrated that heat transfer associated with vapor transport makes a significant contribution in the determination of the overall temperature profile for ventilated snow [Albert and McGilvary, 1992]. The growth of ice particles in dry seasonal snow is caused by vapor diffusion among particles due to temperature gradients imposed on the snow cover [Colbeck, 1983]. The whole ice matrix is continuously recrystallizing by sublimation and deposition, with vapor diffusion as the dominant transport process. The average residence time for an ice structure is between 2 and 3 days under typical temperature gradients [Pinzer et al., 2012]. The intensity of the recrystallization is dictated by the temperature gradient, temperature, and geometrical factors (porosity and specific surface area) also play a significant role [Pinzer and Schneebeli, 2009; Pinzer et al., 2012]. The change in shape of the snow crystals and ice matrix during metamorphism also affects the permeability of the snow. This further affects the airflow and the shape of the snow structure. The knowledge of the ice‐air interface dynamic is still limited, and neither experiments nor models were able to fully elucidate these processes, in particular the kinetic aspects. The fact that the surface dynamics of pure ice is complex and near the melting point makes experiments and also theoretical estimations difficult [Libbrecht, 2005; Kaempfer and Plapp, 2009]. Macroscopic equivalent modeling of heat and water vapor transfer through a snowpack is important to describe dry snow metamorphism of a snow layer [Calonne et al., 2014b]. Albert and McGilvary [1992] described the thermal effect due to airflow and vapor transport for different snow types and conditions by two coupled advection‐diffusion equations including a source term due to sublimation and deposition. The aim of this paper is to characterize and quantify the surface dynamic of snow metamorphism under an induced temperature gradient and saturated airflow in controlled laboratory experiments. In situ time‐lapse experimental runs were conducted with microcomputer tomography (micro‐CT) [Pinzer and Schneebeli, 2009; Chen and Baker, 2010; Pinzer et al., 2012; Wang and Baker, 2014; Ebner et al., 2014; Schleef et al., 2014b; Calonne et al., 2014a] to obtain the discrete‐scale geometry of snow. Morphological parameters, such as porosity, specific surface area, and the initial mean pore size, were extracted from the micro‐CT pictures to study the ice‐air interface dynamic, depending on the airflow velocity. An analytical solution from the macroscopic equivalent description of the vapor transport equation [Calonne, 2014] was formulated and averaged over the entire snow volume. Combined with the experimental results, the curvature effect (d 0 K) of the capillary length d 0 , and the interface curvature K, and the interface kinetic coefficient β were extracted. The experimental and analytical results allowed a qualitative evaluation of the ice‐air interface dynamic in a natural snowpack.

2 Time‐Lapse Tomography Experiments Vertical temperature gradient experiments of approximately 40 K m−1 and with fully saturated airflow across snow samples were performed in a cooled micro‐CT (Scanco Medical μ‐CT80) in a cold laboratory temperature of T lab = −15°C. A specifically designed sample holder [Ebner et al., 2014] was used to ensure controlled advective airflows, temperature gradients, and air humidity. Warm air at around −12°C was blown from the bottom into the snow samples and cooled down to around −13°C while flowing across the sample. We analyzed the following flow rates: a volume flow of 0 (no advection), 5 · 10−6, 1.7 · 10−5, and 3.0 · 10−5 m3 s−1. Higher flow rates were experimentally not possible as shear stresses by airflow destroyed the snow structure [Ebner et al., 2015]. Natural identical snow produced in a cold laboratory [Schleef et al., 2014a] was used for the snow sample preparation (water temperature: 30°C; air temperature: −20°C). The snow was sieved with a mesh size of 1.4 mm into a box and was sintered for 27 days at −5°C to increase the strength and to evaluate the structural change in the earlier stage of metamorphism of new snow. The sample holder (diameter: 53 mm; height: 30 mm) was filled by cutting out a cylinder from the sintered snow and pushing into the sample holder without mechanical disturbance of the core. The snow samples were measured with a voxel size of 18 µm over 108 h with time‐lapse micro‐CT measurements taken every 3 h, producing a sequence of 37 images. The reconstructed micro‐CT images were filtered by using a 3 × 3 × 3 median filter followed by a Gaussian filter (σ = 1.4, support = 3). The Otsu method [Otsu, 1979] was used to automatically perform clustering‐based image thresholding to segment the grey‐level images into ice and void phase. Morphological properties of the two‐phase system were determined based on the exact geometry obtained by the micro‐CT. Tetrahedrons corresponding to the enclosed volume of the triangulated ice matrix surface were applied on the segmented data to determine morphological parameters as porosity (ε) and specific surface area (SSA). An opening‐based morphological operation was applied to extract the initial mean pore size (d mean ) [Haussener et al., 2012]. Table 1 summarizes the initial snow characteristics and experimental conditions. Table 1. Morphological and Flow Characteristics of the Experiments Name (m3 s−1) u D,0 (m s−1) ρ 0 (kg m−3) ε 0 SSA 0 (m2 kg−1) d mean (mm) T in,ave (°C) T out,ave (°C) ∇T ave (K m−1) Re Pe mass Pe heat ta1 – – 284.3 0.69 26.7 0.32 −11.9 −13.2 42 – – – ta2 5.0 · 10−6 0.004 302.6 0.67 25.3 0.30 −12.5 −13.7 39 0.08 0.06 11.5 ta3 1.7 · 10−5 0.012 247.6 0.73 27.6 0.33 −12.5 −13.5 35 0.23 0.18 30.1 ta4 5.0 · 10−5 0.036 275.1 0.70 27.8 0.30 −11.8 −13.0 41 0.78 0.60 134.9

3 Physical Model w n [Kaempfer and Plapp, 2009 Bensoussan et al., 1978 Sanchez‐Palencia, 1980 Auriault, 1991 Auriault et al., 2009 (1) l and L are the characteristic lengths of the heterogeneities at the pore scale and of the macroscopic sample or excitation, respectively. The macroscopic sample size of 53 mm and the corresponding representative elementary volume (REV) of around 1 mm3 allowed to satisfy the condition of equation ρ v , modeled by the macroscopically equivalent description of the vapor transport equation for an incompressible flow field and moderate convection [Calonne, 2014 (2) (3) ε is the porosity, D is the water vapor diffusivity in air, u D is the advection velocity in the porous snow structure, and S m is the mass change at the ice‐fluid interface given by (4) ρ i is the density of ice, SSA V is the specific surface area per volume, and w n is the normal interface growth velocity w n = w · n i , which is given by the Hertz‐Knudsen equation (5) β is the interface kinetic coefficient, d 0 is the capillary length, and K is the interface mean curvature. The saturation water vapor density ρ vs is given by the Clausius‐Clapeyron equation (6) L sg is the latent heat of sublimation of ice, m the mass of a water molecule, ρ i the density of ice, and k B the Boltzmann's constant. The reference values Tref and are equal to 273 K and 2.173 × 10−3 kg m−3. The phenomena involved in the transport process of dry snow metamorphism are (i) water vapor diffusion and advection of air and (ii) sublimation of ice and deposition of vapor at the ice‐pore interface, which is characterized by the interfacial growth velocity]. Physical phenomena in the heterogeneous snow were homogenized by a continuous macroscopically equivalent description, such that the condition of separation of scales was satisfied [.,.,whereandare the characteristic lengths of the heterogeneities at the pore scale and of the macroscopic sample or excitation, respectively. The macroscopic sample size of 53 mm and the corresponding representative elementary volume (REV) of around 1 mmallowed to satisfy the condition of equation 1 . Figure 1 shows schematically the homogenization of the model. The steady state fluid transport of water vapor density, modeled by the macroscopically equivalent description of the vapor transport equation for an incompressible flow field and moderate convection [, equation (3.50)], is given bywith the boundary conditionwhereis the porosity,is the water vapor diffusivity in air,is the advection velocity in the porous snow structure, andis the mass change at the ice‐fluid interface given bywhereis the density of ice, SSAis the specific surface area per volume, andis the normal interface growth velocity, which is given by the Hertz‐Knudsen equationwhereis the interface kinetic coefficient,is the capillary length, andis the interface mean curvature. The saturation water vapor densityis given by the Clausius‐Clapeyron equationwhereis the latent heat of sublimation of ice,the mass of a water molecule,the density of ice, andthe Boltzmann's constant. The reference valuesandare equal to 273 K and 2.173 × 10kg m Figure 1 Open in figure viewer PowerPoint Pinzer et al. [ 2012 Illustration of the 2‐D model and the homogenization of a microscopic physical description given by the representative elementary volume (REV) to an equivalent macroscopic physical description. Sublimation and deposition are also illustrated in the movie by. [, supplement]. 3.1 Analytical Solution The following assumptions and boundary conditions were introduced: (i) the system is isobaric at the total pressure p 0 = 101,325 Pa; (ii) a constant temperature gradient of 38 K m−1; (iii) inlet temperature of T in = −12°C and outlet temperature of T out = −13.1°C; (iv) constant physical properties along the z direction; (v) open system; (vi) mass transfer only in z direction; (vii) an average saturation density ρ vs at T ave = ½(T in + T out ); (viii) the concentration in the pores and the outlet concentration are unknown; (ix) perfect saturation of the airflow at the inlet; (x) temporal change in SSA and porosity is neglected; (xi) uniform temporal change of the ice grain; (xii) d 0 K and β are constant and isotropic; and (xiii) the properties of air and ice are isotropic. The above assumptions, in particular (ii), (iv), and (vi)–(xiii), allow for considerable simplifications of the complex interface dynamic process. V tot . Thus, (7) L is the length of the sample and A is the inlet area. Rearranging equation ρ v,z = L = f (d 0 K, β) expressed by (8) (9) (10) A 1‐D finite volume method was applied to discretize equation 2 in space and was integrated and subsequently averaged over the total volume. Thus,whereis the length of the sample andis the inlet area. Rearranging equation 7 , the outlet concentration is given as a function of(d) expressed byFinally, the analytic solution of the mass source rate at the ice‐fluid interface inside the snow can be expressed asand the interfacial growth velocity of the ice‐fluid interface is given by On the basis of equations 9 and 10, S m,model and w n,model are positive when the ice surface grows and negative when the ice surface sublimates. The baseline parameters used in the analyses are summarized in Table 2. Table 2. Baseline Simulation Parameters Parameter Value Unit A 0.0022 m2 D 2.036 · 10−5 m2 s−1 k B 1.38066 · 10−23 J K−1 L 0.03 m L sg 2.6 · 109 J m−3 m 2.992 · 10−26 kg SSA V 2.35 · 104 m−1 T in −12.0 °C T out −13.1 °C ∇T 38.0 K m−1 Tref 273 K ε 0.69 – ρ ice 917 kg m−3 2.173 · 10−3 kg m−3

5 Discussion The deposition rate due to the nonuniform airflow velocity was too small to see an influence in the vertical density gradient in the scanned area. In the experiments, no spatial change of the porosity with time was observed. Densification and mass redistribution occurred uniformly along the snow height. However, in long‐term experiments (e.g., several months) the observed spatial density gradient will cause a nonuniform airflow velocity across the sample height changing the deposition rate (see Figure 10) and the thermal properties such as thermal conductivity [Riche and Schneebeli, 2013]. This would lead to a change of the ice matrix and a change of the velocity again causing a nonuniform densification. The cooling of the saturated airflow along the snow sample height caused deposition of water molecules on the ice surface causing a decrease in porosity and hence an increase in density of the ice structure. The rate of porosity decrease was strongly dependent on the airflow velocity. Increasing the mass flow rate caused higher water molecule deposition on the ice surface. After a flow rate of ≈ 1.5 · 10−5 m3 s−1, mass transfer at the ice‐fluid interface by deposition started to become the limiting factor, asymptotically approaching a maximum rate of 1.05 · 10−4 kg m−3 s−1. The observed process could be relevant for the creation of a wind crust, which is not yet well understood. The work by Seligman [1936] concluded that the combination of high wind speed above the surface and humid conditions is a relevant factor for the creation of wind crust. High wind speed leads to a destruction of the surface snow, and the fragile structures accumulate in the pores and sinter together under humid conditions [Seligman, 1936]. In addition, a temperature gradient along an airflow in the snowpack enhances water deposition in the pores leading to a fast densification of the surface snow, as observed in the experiments. To validate this assumption, additional experiments with airflow above the snow surface and an induced temperature gradient are necessary. The creation of whisker‐like crystals alters the SSA evolution, leading to an increase of SSA for high mass flow rates and hence to an increase of the albedo. Although the observation of the whisker‐like crystal for ta4 was quite challenging because these structures are brittle and sensitive to outer interactions, the observation of whisker‐like crystal for ta3 is a strong evidence that the formation of such crystals increases with increasing flow rate. SSA can only increase if new surface structures are created, which was the case for higher flow rate. The observed SSA evolution would change the snow albedo and, therefore, has an influence on the snow albedo feedback [Hall, 2004]. In most cases, the natural evolution of snow is to reduce its surface energy, and therefore, SSA almost always decreases with time [Taillandier et al., 2007]. However, there are several cases in nature where the SSA of snow increased over time [Domine et al., 2009]. These are (1) the transformation of a melt‐freeze crust into depth hoar; (2) the mobilization of surface snow by wind, which reduces the size of snow crystals by sublimation and fragmented them; (3) the sieving of blowing snow by a snow layer, which allows the smallest crystals to penetrate into open spaces in the snow; and (4) high‐temperature gradient snow metamorphism also showing an increase of the SSA [Wang and Baker, 2014]. Our observed results showed another possible natural process to increase the SSA and therefore the snow albedo. Adams et al. [ 2008 Rango et al. [ 1996 Wergin et al. [ 2002 Adams et al., 2008 Chen and Baker, 2010 Furukawa and Wettlaufer, 2007 Continuous sublimation and deposition of water molecules occurs at the ice surface [Pinzer and Schneebeli, 2009 Kessler et al., 1988 The growth is determined by the crystallographic orientation of the nucleation grain. Furukawa and Wettlaufer [ 2007 Adams et al. [ 2008 The growth of whisker‐like crystals is due to density variations of water vapor caused by convective flow. It is a result from the combined action of temperature and concentration, also called double‐diffusive convection. Heat and water vapor diffuse at different rates, resulting in a complex flow structures called mushy zone [Song and Viskanta, 1994 Huppert and Turner, 1981 Chen and Johnson, 1984 2) (15) d mean is the average pore diameter, u D is the airflow velocity in the pores, α therm is the thermal diffusivity, and D is the diffusion coefficient of water in air. This phenomenon has already been observed in solidifications of alloys [Song and Viskanta, 1994 Sparrow et al. [ 1979 The creation of whisker‐like crystal is not well understood and was rarely observed in previous studies.. [] observed small ice dendrites similar to ours in a study of disaggregated snow particles in a temperature‐controlled microscope stage. Small structures deposited locally on specific regions of the surface of ice grains but not uniformly over the whole surface. Surface microstructures have also been reported on natural snow by. [] and. [], who presented scanning electron microscopy images of rimed precipitation particles and irregular snow crystals, respectively. The formation of whisker‐like crystals is anecdotally mentioned to develop in snowpacks [.,]. While the effect is well known for atmospheric snow [], the formation in a snowpack is much less clear. Our experiments show that advection is one cause, which can lead to the formation of whiskers, and therefore, the following consideration becomes apparent:whereis the average pore diameter,is the airflow velocity in the pores,is the thermal diffusivity, andis the diffusion coefficient of water in air. This phenomenon has already been observed in solidifications of alloys []. Additionally, experiments by. [] showed the presence of whisker‐like crystals on a controlled freezing surface by natural convection. The calculated Peclet numbers are expressing a macroscopic phenomenon; however, locally higher numbers can occur. The combination of the experimental results and the analytical solution allowed us to extract important ice‐air interface dynamic parameters and is an appropriate procedure for further studies on ice‐air interaction. The small value of the d 0 K = 1.2 · 10−9 obtained in this study implies that the influence of interface curvature on the water pressure and chemical potential is very small for snow grains, which are expected to have radii of 0.02 mm. Nevertheless, the difference of local curvatures between different parts of the interface provides a driving force for sublimation and deposition known as Kelvin effect. The extracted kinetic coefficient β = 9.7 · 109 s m−1 in this study is within the range from the most recent ice crystal growth rate experiments by Libbrecht [2005], who found values from 104 to 109 s m−1. Calonne et al. [2014b] computed a value of β (using equation 13) around 109 s m−1 to be in good agreement with the experimental data of Neumann et al. [2008] for a mass transfer coefficient h m ≈ 10−2–10−4 m s−1. Our estimated β is an order of magnitude higher, and therefore, the estimated mass transfer coefficient is an order of magnitude lower than that estimated by the experimental data of Neumann et al. [2009]. However, the study by Neumann et al. [2009] considered only sublimation of the ice matrix, whereas in this study both sublimation and deposition were analyzed, which interacted, leading to a lower overall mass transfer at the ice interface. Comparing our result with previous work, our estimated normal growth velocity w n = 4.87 · 10−12 m s−1 is in the same order of magnitude proposed by other studies. Numerical studies by Kaempfer and Plapp [2009] and experimental results by Fukuzawa and Akitaya [1993] calculated a normal growth velocity w n in the order of 10−9 m s−1 for a temperature gradient of ∇T > 100 K m−1 as well as for lower ∇T [Pinzer et al., 2012]. Simulations by Calonne et al. [2014b] estimated a normal growth velocity w n for ice spheres, which increases with increasing temperature gradient. The values typically ranged from 10−15 to 10−9 m s−1 for a temperature gradient within the range 0 to 250 K m−1. Neglecting advective transport processes (u D = 0 m s−1) and only considering diffusion processes, our estimated interface growth velocity w n = 7.94 · 10−14 m s−1 is in good agreement with the average value w n ≈ 9 · 10−14 m s−1, deduced from the macroscopic equivalent model of Calonne et al. [2014b] for a temperature gradient of ∇T = 38 K m−1. However, the proposed simulations by Calonne et al. [2014b] only considered vapor diffusion; the additional transport process by advection showed significant influence on the growth velocity w n . Including advective transport process our estimated interface growth velocity w n showed a good agreement with the macroscopic equivalent model of Calonne [2014] assuming an average value.

6 Summary and Conclusion Four experiments of temperature gradient metamorphism of snow under saturated advective airflow with duration of 108 h were performed. The temperature gradient varied between 35 and 42 K m−1, and the snow microstructure was observed by X‐ray microtomography every 3 h. The micro‐CT scans were segmented, and porosity and specific surface area were calculated. Microscopic pictures were taken to analyze the structural changes of ice crystals. An analytical model was formulated to calculate the mass change rate at the ice‐air interface. Finally, a macroscopic treatment of the interface dynamics was carried out. In contrast to temperature gradient snow metamorphism without advection [Pinzer et al., 2012], the applied advective airflow caused an additional change of the snow microstructure. A flow rate dependence of water vapor deposition at the ice interface was observed, asymptotically approaching a maximum rate. Creation of small whisker‐like dendrites and therefore an increase of the SSA were observed. These dendrites are potentially relevant to ice‐air interaction within and above snowpacks. The microstructures change the total surface area available for trace gas adsorption and chemical reactions, and alter albedo. However, no documented observation in Nature are known. The mechanism of whisker‐like crystals formation is complex, and various processes are involved: (1) the interaction of continuous sublimation and deposition and the irregularity of the flow field in the snow sample induce a roughening of the ice surface; (2) crystallographic orientation of the nucleation grain; and (3) diffusive convection alters the combined action of temperature and concentration. In summary, we carried out a first detailed analysis of the interface dynamic under temperature gradient and advective flow, combined with experimental results and a numerical model. The interface kinetic, coupling diffusion and advective mass transfer, was estimated by a curvature effect of d 0 K = 1.2 · 10−9 and an interfacial kinetic coefficient of β = 9.7 · 109 s m−1 which are in the range of literature values. Although these dynamic parameters were surface averaged, they can be applied in numerical models of snow metamorphism to simulate the evolution of a snowpack.

Notation A area, m2. d 0 capillary length, m. d diameter, m. D water vapor diffusivity in air, m2 s−1. h m mass transfer coefficient, m s−1. k B Boltzmann's constant, 1.38066 · 10−23 J K−1. K interface mean curvature, m−1. l length of the heterogeneities at the pore scale, m. L length of the macroscopic sample, m. L sg latent heat of sublimation, J m−3. m mass of water molecule, kg. p pressure, Pa. S m mass change at the ice‐fluid interface, kg m−3 s−1. SSA specific surface area, m2 kg−1. SSA V specific surface area per volume, m−1. t time, s. T temperature, K. u D superficial velocity, m s−1. V volume, m3. volume flow, L min−1. w interface growth velocity. Greek symbols α thermal diffusivity, m2 s−1. β interface kinetic coefficient, s m−1. ε porosity. ρ density, kg m−3. Subscripts ave average. exp experimental. i ice. in inlet. lab laboratory. max maximum. model model. n normal. out outlet. p pore. s snow. therm thermal. tot total. v water vapor. vs saturation water vapor. Abbreviations Pe Peclet number.

Acknowledgments Swiss National Science Foundation granted financial support under project 200020–146540. The authors thank an anonymous reviewer and F. Flin for the suggestions and critical review and M. Jaggi, S. Grimm, and H. Löwe for the technical and modeling support. The data for this paper are available by contacting the corresponding author.