Tomography-based observation of sublimation and snow metamorphism under temperature gradient and advective flow

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Introduction
Snow has a complex porous microstructure and consists of a continuous ice structure made of grains connected by bonds and inter-connecting pores (Löwe et al., 2011).It has a high permeability (Calonne et al., 2012) and under appropriate conditions airflow through the snow structure can occur (Sturm and Johnson, 1991) due to variation of surface pressure (Colbeck, 1989;Albert and Hardy, 1995), simultaneous warming and cooling, and induced temperature gradients (Sturm and Johnson, 1991).Both diffusive and advective airflows affect heat and mass transport in the snowpack and influence chemical concentrations (Gjessing, 1977;Waddington et al., 1996).Various airflow conditions in a snow sample occur, namely: isothermal airflow, temperature gradient along the flow direction, and temperature gradient opposite to the airflow (Fig. 1).Under isothermal condition, the continuous sublimation and deposition of ice due to the Introduction

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Full Kelvin-effect leads to a saturation of the pore space in the snow (Neumann et al., 2008;Ebner et al., 2014).However, applying a fully isothermal saturated airflow across a snow sample has been shown to have no influence on the coarsening rate that is typical for isothermal snow metamorphism independently of the transport regime in the pores (Ebner et al., 2015a).When applying a temperature gradient, the effect of sublimation and deposition in the snow results from interaction between snow temperature and the local relative humidity in the pores.If vapor is advected from a warmer zone into a colder zone, the air becomes supersaturated, and some water vapor deposits onto the surrounding ice grains.This leads to a change in the microstructure creating whistler-like crystals (Ebner et al., 2015b).The flow rate dependence on the deposition rate of water vapor on the ice matrix was observed, reaching asymptotically a maximum rate of 1.05 × 10 −4 kg m −3 s −1 (Ebner et al., 2015b).Contrarily, if the temperature gradient acts in the opposite direction of the airflow, the airflow through the snow brings cold and relatively dry air into a warmer area, causing that the pore space air becomes undersaturated, and surrounding ice sublimates.Here, we investigate specifically this last effect.Sublimation of snow is a fundamental process that affects its crystal structure (Sturm and Benson, 1997), and thus is important for ice core interpretation (Stichler et al., 2001), as well as calculation of surface energy balance (Box and Steffen, 2001) and mass balance (Déry and Yau, 2002).Albert (2002) suggest that condensation of water vapor will have a noticeable effect on the microstructure of snow using airflow velocities, vapor transport and sublimation rates calculated using a two-dimensional finiteelement model.Neumann et al. (2009) determined that there is no energy barrier to be overcome during sublimation, and suggest that snow sublimation is limited by vapor diffusion into pore space, rather than by sublimation at crystal surface.
In the present work, we studied the surface dynamic of snow metamorphism under an induced temperature gradient and saturated airflow in a controlled laboratory experiments.Sublimation of ice was analyzed by in-situ time-lapse experiments with microcomputer tomography (micro-CT) (Pinzer and Schneebeli, 2009;Chen and Baker, Introduction Conclusions References Tables Figures

Time-lapse tomography experiments
Temperature gradient experiments with fully saturated airflow across snow samples (Ebner et al., 2014) were performed in a cooled micro-CT (Scanco Medical µ-CT80) in a cold laboratory temperature of T lab = −15 • C. Cold saturated air was blown into the snow samples and warmed up while flowing across the sample.Aluminum foam including a heating wire was used to generate the warm site of the snow, opposite to the entering airflow.We analyzed the following flow rates: a volume flow of 0 (no advection), 0.3, 1.0, and 3.0 L min −1 .Higher flow rates were experimentally not possible as shear stresses by airflow destroyed the snow structure (Ebner et al., 2015a).Natural identical snow produced in a cold laboratory (Schleef et al., 2014) 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 analyzed 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.The segmented data were used to calculate a triangulated ice matrix surface and tetrahedrons inscribed into the ice structure.Morphological parameters such as porosity (ε) and specific surface area (SSA) were then calculated.Introduction

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Full Opening size distribution was applied to extract the mean pore size of each micro-CT scan (d mean ) (Haussener et al., 2012).The influence of structural changes on the heat transfer in the snow is analyzed by the effective conductivity k e (Kaempfer et al., 2005;Petrasch et al., 2008;Calonne et al., 2011).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.As additional physical and structural parameter, the thermal conductivity was determined by direct pore-level simulations (DPLS) to determine the influence of changing microstructure (Kaempfer et al., 2005;Petrasch et al., 2008;Calonne et al., 2011;Löwe et al., 2012) 3 Results Time-lapse tomographic scans were performed with temperature gradients between 43-53 K m −1 (Table 1).Small fluctuations of the measured inlet and outlet temperature were due to temperature regulation both inside the cold chamber and inside the micro-CT (Ebner et al., 2014).A shift of ∆t < 10 min between inlet and outlet temperature indicated that a fast equilibrium between the temperature of the snow and the airflow was reached (Albert and Hardy, 1995;Ebner et al., 2015b).The morphological evolution was similar between all four experiments and only a slight rounding and coarsening was visually observed, shown in Fig. 2, indicating that the initial ice grain did not change with time.Only coarsening processes of the ice grain were observed for example, Fig. 3 shows the locations of sublimation and deposition for "ota3" and "ota4".Sublimation of 7.7 and 7.6 % of the ice matrix and deposition of 6.0 and 9.6 % on the ice matrix were observed.The data were extracted by superposition of vertical crosssections at 0 and 108 h with an uncertainty of 6 %.The mass sublimated preferentially at locations of the ice grain with low radii and was relocated leading to a smoothing of the ice grain and to an increase in the size of pores (Fig. 4a).The pore size increased by 3.4, 3.6, 5.4 and 6.5 % for "ota1", "ota2", "ota3", and "ota4", respectively.Introduction

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Full Loss of ice of the snow due to sublimation could not be detected by the micro-CT scans and no flow rate dependence was observed during any of the four experiments.The temporal porosity distribution, shown in Fig. 4b, did not change with time and the influence of sublimation of water vapor was not observed.Only "ota2" showed a slight drop in the temporal evolution of the porosity until 18 h into the experiment but kept constant afterwards.This slight drop (≈ 0.5 %) was probably caused by settling of the snow.A coarsening was observed for each experiment but the influence of changing airflow was not visible, confirmed by the temporal SSA evolution, shown in Fig. 4c.
Although the repositioning of water molecules led to a smoothing of the ice grains, it did not affect the heat transfer in the snow.The thermal conductivity slightly increased after applying airflow to the temperature gradient, shown in Fig. 4d, but no flow rate dependence was observed.Every third scan was used to extract the thermal conductivity and a change of −2.6, 3.6, 2.2, and 2.7 % for "ota1", "ota2", "ota3", and "ota4" was detected.

Discussion
The kinetic phase-change from gas to solid is preferable over solid to gas as energy is released rather than consumed leading to more ice deposition rather than ice sublimation.The rate of deposition onto the ice surface depends on the flow rate where warm saturated air cooled down while flowing through the sample, as shown in previous experiments (Ebner et al., 2015b).Its deposition rate asymptotically reached a maximum of 1.05 × 10 −4 kg m −3 s −1 .In this study, changing the flow direction lead to a warming up of a cold saturated flow, and resulted in a sublimation rate too small for the analyzed period of the experiment to measure a flow rate dependence by the micro-CT and an influence on the temporal density gradient.A smoothing of ice grains and an increase of the pore space was measured but the airflow velocity did not affect the relocation process of water molecules.Introduction

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Full A structural change of the ice grains and repositions of water molecules was observed but the total net flux of the snow was not affected.The superposition of vertical cross-section in Fig. 3 shows a big effect on reposition of water molecules on the ice structure.However, the temporal porosity (Fig. 4b) was not affected and the total water vapor net flux was negligible for the analyze volume.Continued sublimation and deposition of water molecules due the Kelvin-effect led to a saturation of the pore space.However, the uptake of water molecules and their transport due to the undersaturated airflow was counteracted by diffusion of water molecules due to the temperature gradient.As thermally induced diffusion was opposite to the airflow gradient, a backflow of water vapor occurred and the two opposite fluxes cancelled each other out.The Peclet numbers, describing the ratio of mass transfer between diffusion and advection, measured during each experiment, showed that diffusion was still dominant (Table 1), thus indicating that water molecules were transported back and forth due to diffusive and advective transport.
As a Peclet higher than 1 is not possible in nature (Ebner et al., 2015a), sublimation inside a snowpack has a significant influence not on the total net mass change but on the structural orientation of the ice grains due to redistribution of water vapor on the ice matrix.Also the increasing pore size has an influence on the flow field leading to a deceleration of the flow and therefore the interaction of an air-parcel with the ice matrix in the pores increases.In addition, the diffusive transport rises whereas the advective transport decreases changing the mass transport in the pores.Our results support the hypothesis of Neumann et al. (2009) that sublimation is limited by vapor diffusion into the pore space rather than sublimation at crystals faces.This is also supported by the temporal evolution of the porosity (Fig. 4b) and the SSA (Fig. 4c), as no velocity dependence was observed and the structural changes were too small to be detected by the micro-CT.
The influence of diffusion of water vapor in the direction of the temperature gradient and the influence of the residence time of an air-parcel in the pores were also confirmed by a low mass change at the ice-air interface.Overlapping two consecutive 3-D

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Full images, the order of magnitude of freshly sublimated ice was detected.The absolute mass change at the ice-air interface (kg m −3 s −1 ) estimated by the experimental results is defined as where ∆(1 − ε) is the change in the porosity between two images separated by the time step ∆t, and ρ i is the density of ice.Albert and McGilvary (1992) and Neumann et al. (2009) presented a model to calculate sublimation rates directly in an aggregate snow sample where SA V is the specific surface area per volume of snow, and h m is the mass-transfer coefficient (m s −1 ) given by (Neumann et al., 2009) h m = (0.566 × Re + 0.075) × 10 −3 (3) assuming that the sublimation occurs within the first few mm of the sample.Re is the corresponding Reynolds-number of the flow.The absolute sublimation rate is driven by the difference between the local vapor density (ρ v ) and the saturation vapor density (ρ sat ) (Neumann et al., 2009;Thorpe and Mason, 1966).Table 2 shows the estimated absolute sublimation rate by the experiment (Eq. 1) and the model (Eq.2).The very small change in porosity due to densification during the first 18 h for "ota2" was not taken into account.The estimated sublimation rates by the experiment were two orders of magnitude lower than the modelled values and also two orders of magnitude lower than for the temperature gradient along an airflow experiment (Ebner et al., 2015b).As the air in the pore spaces are always saturated (Neumann et al., 2009), the back diffusion of water vapor in the direction of the temperature gradient led to a lower mass transfer rate of sublimation.The flow rate dependence for the model described Introduction

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Full is shown by the mass-transfer coefficient (Eq.3), increasing with higher airflow.However, the values calculated from the experiment showed a different trend.Increasing the flow rate led to a lower mass transfer rate due to a lower residence time of the air in the pores.Transfer of heat toward and water vapor away from the sublimating interface may also limit the sublimation rate.In general, the results of the model by Neumann et al. (2009) have to be interpreted with care, as the model was set up to saturate dry air under isothermal conditions.Ice crystals sublimated as dry air enters the snow sample; water vapor was advected throughout the pore space by airflow until saturation vapor pressure was reached, preventing further sublimation.The model by Neumann et al. (2009) does not consider the influence of a temperature gradient and the additional vapor pressure gradient was not analyzed.
In the experiments by Neumann et al. (2009), sublimation of snow using dry air under isothermal condition showed a temperature drop for approximately the first 15 min after sublimation began and stayed constant because the latent heat absorption of sublimation for a given flow rate and heat exchange with the sample chamber equalized each other.Such a temperature drop was not observed in our experiments.In the experiments by Neumann et al. (2009) the amount of energy used for sublimation was between −10 and −40 J min −1 for saturation of dry air.Using the expected mass change at the ice-air interface S m, exp (Eq. 1) and the latent heat of sublimation (L sub ≈ 2834.1×10 3 J kg −1 ) the energy needed for sublimation ranged between −2 and −12 J min −1 for our experiments.Our estimated values are a factor up to five lower than the estimated numbers of Neumann et al. (2009), because the entering air was already saturated (with reference to the cold temperature) at the inlet.The needed energy for sublimation could be balanced between the sensible heat carried into and out of the sample, and the exchange of the snow sample with the air stream and the surrounding prevented a temperature drop.Thermal conductivity changed insignificantly in these experiments.This indicates that advective cold airflow opposite to a temperature gradient reduces or suppresses

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Full the increase in thermal conductivity usually observed by temperature gradient metamorphism (Riche and Schneebeli, 2013).

Summary and conclusion
We performed four experiments of temperature-gradient metamorphism of snow under saturated advective airflow during 108 h.Cold saturated air was blown into the snow samples and warmed up while flowing across the sample.The temperature gradient varied between 43 and 53 K m −1 and the snow microstructure was observed by X-ray micro-tomography every 3 h.The micro-CT scans were segmented, and porosity, specific surface area, and the mean pore-size were calculated.Effective thermal conductivity was calculated in direct pore-level simulations (DPLS).
Compared to deposition (shown in Ebner et al., 2015b), sublimation showed a small effect on the structural change of the ice matrix.A change in the pore size was most likely due to sublimation of ice crystal with low radii but a significant loss of water molecules of the snow sample and mass transfer away from the ice interface due to sublimation and advective transport could not be detected by the micro-CT scans and no flow rate dependence was observed.The interaction of mass transport of advection and diffusion of water vapor in the direction of the temperature gradient and the influence of the residence time of an air-parcel in the pores led to a negligible total mass change of the ice.However, a strong reposition of water molecules on the ice grains was observed.
The kinetic phase-change from gas to solid is preferable as energy is released compared to solid to gas where energy is required, thus leading to more water molecule deposition than water molecule sublimation.The energy needed for sublimation was too low to see a significant temperature drop because the needed energy was balanced between the sensible heat carried into and out of the sample, and the exchange of the snow sample with the air stream and the surrounding.Introduction

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Full This is the third paper of a series analyzing an advective airflow in a snowpack.Previous work showed that: (1) under isothermal conditions Kelvin-effect leads to a saturation of the pore space in the snow but did not affect the structural change (Ebner et al., 2015a), (2) applying a temperature gradient along the flow direction leads to a change in the microstructure and creation of whistler-like structures due to deposition of water molecules on the ice matrix (Ebner et al., 2015b), and (3) a temperature gradient opposed to the flow had a negligible total mass change of the ice but a strong reposition effect of water molecules on the ice grains, shown in this paper.Conditions (1) and ( 3) showed that they have a negligible effect on the structural changes of the ice matrix and can be neglected to improve models for firn compaction and evolution.In contrast, conditions (2) showed a significant impact on the structural evolution and seem to be essential for such snowpack models and other numerical simulations.Nevertheless, the strong reposition of water molecules on the ice grains observed for all conditions (1)-( 3) can have a significant impact on atmospheric chemistry.Full

The
Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Thorpe, A. D. and Mason, B. J.: The evaporation of ice spheres and ice crystals, Brit.J. Appl.Phys., 17, 541-548, 1966.Waddington, E. D., Cunningham, J., and Harder, S. L.: The effects of snow ventilation on chemical concentrations, in: Chemical Exchange Between the Atmosphere and Polar Snow, NATO ASI Series 43, edited by: Wolff, E. W. and Bales, R. C., Springer, Berlin, 403-452, 1996Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Figure 1 .Figure 2 .
Figure 1.Schematic of the ice-air interface transport processes: (a) under isothermal conditions Kelvin-effect leads to a saturation of the pore space in the snow but did not affect the structural change (Ebner et al., 2015a); (b) temperature gradient along the flow direction leads to a change in the microstructure due to deposition (Ebner et al., 2015b); (c) temperature gradient opposite to the flow has a negligible total mass change of the ice but a strong reposition effect of water molecules on the ice grains, shown in this paper.

Table 1 .
Morphological and flow characteristics of the experiments: volume flow ( V ), initial superficial velocity in snow (u D,0 ), initial snow density (ρ 0 ), initial porosity (ε 0 ), specific surface area (SSA 0 ), initial mean pore size (d mean ), average inlet (T in, ave ) and outlet temperature (T out, ave ), and the average temperature gradient (∇T ave ), corresponding Reynolds number (Re) and Peclet number (P e).

Table 2 .
Neumann et al. (2009) rate S m using the mass transfer coefficient h m determined byNeumann et al. (2009)and the corresponding average surface area per volume SA V,ave .S m can be compared with the measured sublimation rate of the experiment S m, exp (Eq.1).