Laboratory-based observations of capillary barriers and preferential flow in layered snow

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Introduction
Around one century has passed since Horton noted that "there is a marked lag between the melting of snow and the appearance of the resulting water as run-off in the Figures

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Full streams" (Horton, 1915).Liquid water in snow is originated by rain events and/or by melting (Techel and Pielmeier, 2011;De Michele et al., 2013).The modeling and/or measuring of its flow through the snow porous matrix have interested hydrologists as well as avalanche forecasters for decades.In fact, within snow-dominated catchments, the process of water transmission in snow rules streamflow timing and amount (Lundquist and Dettinger, 2005;Lehning et al., 2006;Wever et al., 2014), while wet snow instabilities due to water movement are considered a serious hazard for mountain environments (Baggi and Schweizer, 2008;Mitterer et al., 2011bMitterer et al., , 2013;;Mitterer and Schweizer, 2013;Schmid et al., 2015).Harper et al. (2012) report that meltwater storage capacity of snow and firn (and associated percolation dynamics) may play an important role even in arctic environments by buffering sea-level rise (see also Gascon et al., 2014 on this point), while Zawierucha et al. (2015) note that some water-filled holes on glaciers called cryoconite holes are a valuable ecological hotspot.
Starting from the first observations by, e.g., Horton (1915), Hughes and Seligman (1938) or Gerdel (1945), the flow of liquid water in snow has been often assimilated to the process occurring in other porous materials, like soils (Wankiewicz, 1978).In particular, a collection of papers by Colbeck and others in the 70s (Colbeck, 1972(Colbeck, , 1974b(Colbeck, , 1976;;Colbeck and Davidson, 1972;Dunne et al., 1976;Wankiewicz, 1978) propose the use of a Darcy-based theory to describe water movement in snow.Within this framework, a frequent hypothesis is that capillary gradients in snow are negligible.
Consequently, water flux at a point is assumed as driven by gravity alone (Colbeck, 1972(Colbeck, , 1974a;;DeWalle and Rango, 2011).In this perspective, Wankiewicz (1978) reports examples of suction profiles in snow, showing that expected suction gradients are usually much lower than gravitational potential gradients.This assumption has been largely used within the field of snow hydrology (Avanzi et al., 2015), and even simplified in many complex one-dimensional models, such as CROCUS (Brun et al., 1989(Brun et al., , 1992;;Vionnet et al., 2012), or the first version of SNOWPACK (Bartelt and Lehning, 2002), that consider a bucket-type approach for water percolation.However, increasing evidences show how liquid water percolation in snow is a very complex, and multi-dimensional, problem (Hirashima et al., 2014;Wever et al., 2014).As an example, Marsh and Woo (1985) observed spatial heterogeneity in the percolation process (also known as preferential flow).Schneebeli (1995) notes that heterogeneity seems to be the prevalent process involved in water flow in snow, and that fingers (i.e., preferential channels) seem to migrate from one position to another during a snow season.By means of laboratory experiments, Waldner et al. (2004) observe that a finer-over-coarser transition in snow layering constitutes a capillary barrier.This is a textural discontinuity that causes water ponding, hence a delay in the expected arrival time of water at the snow base.Moreover, they observe that fingers seem to be stable in their position in time.Recently, Wever et al. (2014) report that solving Richards equation accounting for suction gradients improves run-off estimations at different temporal resolutions with respect to a simple bucket-type approach, although the latter seems to return a better agreement with observed snow microstructure profiles (Wever et al., 2015).As an additional complication, percolation in snow usually starts while most of the snowpack is still at sub-freezing conditions (Pfeffer and Humphrey, 1996).This causes a strict coupling between hydraulic and energetic processes (Illangasekare et al., 1990).Moreover, wet snow structure evolves quickly once it has come in contact with liquid water (Wakahama, 1968;Colbeck, 1986;Brun, 1989).
As a result, it is nowadays argued that the impact of capillary effects on water flow in snow may have been generally underestimated (Wever et al., 2014).As a result, the degree of quantitative characterization of several associated processes, such as capillary barriers, is still limited (Eiriksson et al., 2013).This is also partially due to difficulties in measuring liquid water distribution (Colbeck, 1978;Techel and Pielmeier, 2011;Avanzi et al., 2014) and to the fact that running experiments with wet snow is sometimes cumbersome due to water redistribution and wet snow metamorphism (Brun, 1989).
Examples of previous attempts include Jordan (1995), who observed capillary barriers in the field throughout a snow season.Similar observations are reported by Waldner et al. (2004); Peitzsch et al. (2008).In soil science, capillary barriers have been often Figures

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Full associated with the occurrence of instability in the wetting front at the textural boundary and onset of preferential flow, or fingering (Hill and Parlange, 1972;Hillel and Baker, 1988;Baker and Hillel, 1990;Liu et al., 1994;de Rooij, 2000;DiCarlo, 2007DiCarlo, , 2013)).On the contrary, these two processes have been rarely investigated together in snow (see e.g.Marsh and Woo, 1984).
Here, we focus on investigating capillary barriers development and associated preferential flow patterns in snow using laboratory experiments.We collected systematic observations of dyed water infiltration in layered snow samples with different grain size combinations and different water input rates.We measured, for each sample, the thickness of the ponding layer at the textural boundary, liquid water distribution, wet snow fraction at different levels and the time of arrival of liquid water at sample base.Such a wide data-set allows a characterization of capillary barriers properties that is more exhaustive than before.The focus on preferential flow allows also to investigate how these two processes combine in snow.Similar analyses have been recently performed by Katsushima et al. (2013), who note that the fraction of snow involved in water flow seems to depend on both snow grain size and infiltration rate.Their analysis focuses on homogeneous snow, while here we focus the investigation on stratified snow.In addition, all the laboratory experiments were reproduced numerically by using the SNOW-PACK model.

Capillarity in snow
In melting snow covers, liquid water occupies a variable amount of pores volume.We define as saturation degree S r (-) the ratio between the volume occupied by liquid water (V W ) and the volume of pores V P , at a given point, S r = V W /V P .We define as volumetric liquid water content (LWC, or θ) the ratio V W /V , where V is the total volume Figures

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Full of the mixture, at a given point (Fierz et al., 2009).We measure this quantity in vol.%, or simply %.
In unsaturated snow, liquid water is usually under tension.Under equilibrium, the pressure drop across the interface between the phases, ∆P = P A − P W , with P A the pressure of air and P W the pressure of water, is given by Laplace equation (see Jordan, 1995;Jordan et al., 1999 for details).∆P depends on the surface tension T and the mean radius of curvature of the interface γ. Accordingly, ∆P increases with increasing T and with decreasing γ. ∆P can be easily related with the height reached by water in capillary tubes.In fact, capillary rise is caused by the need for balancing water weight and the pressure drop across the meniscus (Jordan et al., 1999): the narrower the tube is, the higher the elevation reached by water.Accordingly, ∆P is usually referred to as capillary pressure, or suction ψ (DiCarlo, 2007), and is usually measured in m.
Natural snow is formed by a great variety of pores with different dimensions.In this context, a capillary bundle model (i.e., a collection of capillary tubes with different diameters, see Millington and Quirk, 1959) can be employed to establish an intuitive relation between θ and ψ.This calls Water Retention Curve (WRC) and is nowadays usually modeled using the approach by van Genuchten (1980), which depends on a number of parameters, including θ r (residual volumetric liquid water content), θ s (saturated volumetric liquid water content), α and n (shapes parameters).As a rule of thumb, the lower is LWC, the higher is ψ, but this relation is strongly dependent on pores shape and, in general, medium structure.Although first experimental examples of WRC in snow date back to the 70s (Colbeck, 1974a), Yamaguchi et al. (2010) and Yamaguchi et al. (2012) have been the first ones, to our knowledge, to provide a systematic parametrization of α and n basing on snow density and grain size as predictors.These expand the preliminary results reported, e.g., in Colbeck (1974a); Jordan (1983); Daanen and Nieber (2009).Following additional experiments, Adachi et al. (2012) note that snow WRCs seem to be hysteretic.This means that the relation between ψ and θ is not univocal, since it depends on the process considered (wetting or drainage, see Jordan et al., 1999).Usually, at a given θ, ψ is higher during a drying process than during a wet-Figures

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Full ting process, if snow structure keeps constant (Jordan et al., 1999).The relationship between ψ and the height reached by water in snow allows for a straightforward derivation of these curves in the laboratory (Yamaguchi et al., 2010(Yamaguchi et al., , 2012)).Suction gradients and gravity rule water movement in a porous material.In particular, the combination of the Darcy-Buckingham equation and mass conservation returns the well-known Richards equation (Richards, 1931).According to this equation, water movement in snow is related to the hydraulic conductivity (K W ) and to the gradient in water head (H), which is defined as the algebraic sum of elevation z and suction ψ.In unsaturated conditions, K W depends on S r (DeWalle and Rango, 2011;Wever et al., 2014) and saturated hydraulic conductivity (K S ).The latter depends on dynamic viscosity ν, liquid water density ρ W , acceleration due to gravity g and intrinsic permeability K , which has been initially related with snow density and grain size (Shimizu, 1970;Sommerfeld and Rocchio, 1993;Jordan et al., 1999).However, a number of works are now available that relate this quantity with density and equivalent sphere radius (hence, Specific Surface Area SSA, see Carmagnola et al., 2014).Examples include Calonne et al. (2012) and Zermatten et al. (2014).

Ponding and water flow instability
Typically, vertical water movement in an uniform porous medium like soils obeys to a stable infiltration profile, with no lateral heterogeneity in the front position in time.However, both laboratory and field observations have shown that sometimes infiltration is prone to instability, namely to the development of preferential channels that break the uniform infiltration front in fingers (DiCarlo, 2013).As already mentioned, this behavior has been largely observed in snow, too (DeWalle and Rango, 2011;Schneebeli, 1995;Katsushima et al., 2013).
A number of factors can trigger water flow instability in soils (de Rooij, 2000).Among these, one (historical) case is the fingering associated with an initially dry fine-overcoarse profile in layering.First attempts to explain instability under such conditions were made by Hill and Parlange (1972); Baker and Hillel (1990) 1988).Accordingly, when the wetting front arrives at the layer boundary, it is still marked by a high ψ.As a result, water cannot enter the lower (coarser) layer, so that it starts ponding.This causes an increase in LWC, hence a decrease in ψ at the boundary.This process continues until suction reaches a value that allows water to enter in the smallest pores of the coarser layer that are interconnected.At this stage, water starts entering at various locations.This process continues until suction at the interlayer plane reaches a value permitting massive entering of water in the lower layer (the so-called effective water entry suction ψ WE ).According to the stability criterion developed by Hillel and Baker (1988); Baker and Hillel (1990), subsequent flow should be marked by fingers if, in steady conditions, the hydraulic conductivity of the lower layer at ψ WE is greater than the flux through the top layer q.In fact, in those conditions, only a fraction of the lower medium can convey water (due to mass conservation).Such a process (together with ponding time) has clear implications in determining the time of arrival of water at a given location.This is one of the reasons why soil scientists have been largely interested in the prediction and modeling of these phenomena.
During recent years, additional observations have shown that, in soils, an unstable infiltration profile is marked by an overshoot profile in terms of S r (DiCarlo, 2004).Accordingly, "unstable fronts dry out, while stable fronts wet up behind the wetting front" (Baver et al., 2014).This process is clearly related with a capillary pressure overshoot, since these two variables are linked by the water retention curve (DiCarlo, 2007).Although "the exact physics for the creation of pressure and saturation overshoot at the wetting front remains in debate" (DiCarlo, 2007), saturation and pressure overshoots in soils are nowadays considered the cause of gravitational flow instability, rather than an effect.Examples of pressure overshoots have been also observed in homogeneous snow samples during preferential infiltration by Katsushima et al. (2013), thus suggesting that a similar process may have parallels within an ice porous matrix.Introduction

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Full 3 Laboratory experiments

Preparation of samples and experiments run
To observe capillary barriers development and associated preferential flow patterns in snow, three combinations of grain sizes g S and three different water inputs W were considered.Grain size combinations are (1) FC, i.e. fine-over-coarse snow; (2) FM, i.e. fine-over-medium snow; (3) MC, i.e. medium-over-coarse snow.We consider snow with 0.25 ≤ g S ≤ 0.5 mm as fine, snow with 1 ≤ g S ≤ 1.4 mm as medium, and snow with 2 ≤ g S ≤ 2.8 mm as coarse.Note that we adopt such a nomenclature because it is convenient for the scopes of this paper, although it is not consistent with the International Classification proposed by Fierz et al. (2009) that, e.g., defines medium snow grain size as as 0.5 mm ≤ g S ≤ 1 mm.The water input rates considered are 10, 30 and 100 mm h −1 .As a results, nine samples were prepared (3g S combinations for each W ). Samples were prepared in a cold room at −20 • C using refrozen melt forms.Fragmented snow particles were firstly partitioned in several grain size classes.Afterwards, the three g S chosen were sieved a second time to prepare the samples.Snow was packed in a cylindrical container.No tamping was applied.The container was composed by a number of acrylic rings (height equal to 20 mm, diameter equal to 50 mm) that were previously taped on the external side.After sieving the lower layer, its dry density (ρ D,L ) was measured by gravimetry.The dry density of the upper layer (ρ D,U ) was measured by gravimetry at the end of sieving operations (by considering the difference between sample total weight and sample weight before sieving the upper layer).
After preparation, each sample was moved to a second cold room at 0 • C, where it was stored for at least 12 h to guarantee that initial conditions of snow during the experiments were dry and isothermal at 0 We report in Table 1 the details of each experiment.W is reported both in mm h −1 (that is the unit of measurements we will use in the paper) and in g min −1 , which is the original unit of measurements of the data.The conversion can be done by calculating Introduction

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Full sample area from sample diameter (5 cm).The coefficient of variation of ρ D,U and ρ D,L is equal to 0.06 and 0.03, respectively.Consequently, this work investigates how ponding and associated preferential flow vary as a function of the grain size combination, and not density.Future investigations should focus on the generalization of this work to layers of different density.Due to operational reasons, some samples (namely, FC2, FM2 and MC2) have a different total height from the others.However, the thickness of the upper layer (the one that is affected by ponding) was kept constant throughout all the experiments.At the beginning of each experiment, dye tracer supplying at the top of each sample was started using a micro-tube pump.The dye used was blue ink, diluted by a factor of 10 times in water, at 0 • C. We placed a thin cotton ring on the top of each sample, to let the point source of the tracer to spread over the surface of the upper layer.By automatically registering the weight of the tracer reservoir (1 min resolution), we estimated W .As visible in Table 1, experimental values of W are slightly different from those chosen at the beginning of this paragraph (mainly due to operational reasons).

Data collection
When the tracer reached the base of each sample, tracer supply was stopped.The time needed by the tracer to reach the base (t t ) was registered with a manual chronometer watch by visually inspecting samples during the experiments.Since samples have different total heights, we will consider a specific travel time τ = t t /h in what follows, with h equal to sample height.Pictures of the external sides of the samples were taken to estimate the approximate thickness of the ponding layer (p, in cm), i.e. the volume of the upper layer marked by horizontal spreading of the tracer and tracer accumulation (see Sect. 2.2 for details).Soon afterwards, we took pictures of the top section of each acrylic ring (by gradually removing them from the column, snow included).At the same time, the liquid water mass w, in grams, in each of the rings was measured using a portable calorimeter (Kawashima et al., 1998).Starting from these information, profiles of volumetric liquid water content were obtained by converting w to θ.By using Introduction

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Full the ImageJ software (Abramoff et al., 2004), fractions of wetted areas over total area (f ) were estimated for each section using the pictures taken.

The comparison with the SNOWPACK model
We replicated the dynamics of each sample during the experiment using the wellknown 1-D model SNOWPACK (Bartelt and Lehning, 2002).In this way, it is possible to compare observations with predictions by a multi-layer physically-based model.Particular attention is paid to the following variables: (1) capillary barriers development, (2) ponding layer thickness, (3) LWC distribution.On the contrary, the model cannot reproduce spatial heterogeneity, hence preferential flow patterns, due to the 1-D geometry used (Hill and Parlange, 1972).
The model discretizes the snow medium using a FEM grid and simulates the evolution in time of a wide set of variables along a vertical profile of snow, subjected to known external forcings (Bavay and Egger, 2014).Examples are snow density, temperature, grain size and shape or liquid water content.A number of papers are available in the literature where it is possible to find exhaustive details about SNOWPACK Here, the temporal resolutions of simulations was set to 1 min, while the initial spatial resolution was set to 2 cm.We set input data to replicate experiments conditions, i.e. a constant precipitation flux (equal to the measured water input flux W , see  and a fixed (positive) air temperature of +1.51 • C, so that this incoming flux is classified as liquid and not as new snow.According to laboratory conditions, wind speed and solar radiation were set to zero, while incoming longwave radiation was determined to balance with upward long wave radiation from a 0 • C snow surface.At the base of the sample, we considered as a boundary condition a clay soil, with parameters given by Carsel and Parrish (1988).As snow initial conditions, we considered a replication of samples granulometry, density (Table 1), wetness (initially dry) and temperature (0 • C).
Using the same sieves we used here, Katsushima et al. (2013) obtained a mean grain size (hereinafter, g S ) for the class 0.25-0.5 mm and the class 1-1.4 mm equal to 0.421 and 1.439 mm, respectively.The fact that g S for medium snow is greater than the upper boundary of the sieve is probably caused by snow grains not being perfectly spherical.
In the simulation, we therefore set g S = 0.421 mm for fine snow, g S = 1.439 mm for medium snow and g S = 2.926 mm for coarse snow (by assuming this last value as two times the average medium grain size).Bond size was assumed equal to one third of grain radius.As for the water transport simulation, we chose the approach introduced  2011b) that this approach is able to reproduce capillary barriers, and this is the main target of this evaluation.These measurements could allow an exhaustive evaluation of this modeling scheme, that simplifies the explicit solution of the Richards equation.

Results
We report in Fig. 1 the horizontal sections of the samples at the end of the experiments (i.e., when dyed water arrived at sample base).Dyed water is visible as blue areas.As a rule of thumb, the darker the blue is, the higher is local LWC.In Table 2 reports the results in terms of observed thickness of the ponding layer (p), time of arrival of liquid water at the base of each sample, t t , and specific travel time τ.In Figs. 3 and 4, profiles of wet snow fractions f and LWC for the different samples are reported.For LWC, each point represents an average θ in the underlying 2 cm.As an example, any value reported at a depth equal to 8 cm is an average value between 8 and 10 cm.These represent the LWC registered immediately over the textural boundary.
Figure 5 compares observed and SNOWPACK-based profiles of volumetric LWC for each sample.As described in Sect.3, observed profiles were obtained at the end of each experiment.Accordingly, SNOWPACK-based data refer to the predictions by the model at the same instant.As an example, Fig. 5a compares the LWC profile observed in sample FC1 with the SNOWPACK prediction obtained 92 min after the beginning of the simulation (see Table 2).

The ponding process
Observations confirm that liquid water movement within a finer-over-coarser snow texture is subjected to ponding when water comes to a textural boundary.Such a behavior is systematic in FC and FM samples (irrespective to W ), while MC samples report no definitive results.In fact, all FC and FM samples are characterized by horizontal spreading of water at 10 cm (Fig. 1).This creates a clear transition between finer and coarser layers (see Fig. 2).In 4/6 samples of these two classes, a homogeneously blue area develops at a depth equal to 8 cm as well.On the contrary, MC samples show a more variable behavior: water spreading is minimum for MC1, while a marked ponding layer is visible in MC3.In terms of p, MC samples show again a small or absent ponding layer, while FC and FM samples show from 2 to 4 cm of ponding.In FC-FM samples, infiltrating water is under a high suction when it initially arrives at the textural bound-Introduction

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Full ary.The higher the initial ψ is, the longer is the duration of the ponding process at the same W .As a result, the larger is the mass of water accumulated.When considering MC samples, differences in ψ between the upper and the lower layer are smaller than in FC-FM samples.Thus, p is reduced.FC and FM samples are characterized by similar LWC profiles.In particular, LWC increases with depth in the upper layer and presents a peak at the textural boundary.Below this boundary, LWC decreases again.All FC-FM samples report a similar LWC at the boundary.In particular, at that position LWC is ∼ 33 vol.% in FC samples, while it spans between 34 and 36 vol.% for FM samples.At the boundary, water accumulates until suction at the interlayer plane becomes equal to the water entry suction ψ WE (Baker and Hillel, 1990).ψ WE is driven by LWC through the Water Retention Curve (specifically, by the primary imbibition curve in conditions of hysteresis, see DiCarlo, 2007).It follows that 34-36 vol.% may be seen as the threshold LWC that allows massive transportation of water across the boundary between the fine snow layer (which is the same in all these six samples) and a coarse or medium snow layer.No variability in this process as a function of W was detected.On the contrary, MC samples show a much smaller peak in LWC at the boundary, here again attesting that this type of texture seems prone to limited ponding.The occurrence of ponding in snow has been already reported in the literature.As an example, Jordan (1995) reported that a newer over older snow transition can cause horizontal spreading and capillary barriers development.A similar conclusion is also reported by Waldner et al. (2004).During a laboratory experiment, they subjected a layered sample to artificially induced melting and measured LWC dynamics by means of TDRs (Schneebeli et al., 1998).However, a restricted variety of g S combinations were considered by both works (g S < 1 mm in the first paper, and a 1.5 mm over 2.5 mm transition in the second one).In this perspective, our analysis enlarge these conclusions by (1) including the case of a fine (i.e., 0.25-0.5 mm) over medium (i.e., 1-1.4 mm), or coarse (i.e.2-2.8 mm) stratigraphy and (2) considering different (controlled) water input rates.A comparison between the LWC profiles measured by Waldner et al. (2004)

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Full those reported in Fig. 4c (i.e., those experiments that show a comparable g S transition) shows that the LWC peak at the inter-layer boundary measured by Waldner et al. (2004) (i.e. 13 %) is not far from the one measured during our experiments for faster input rates (∼ 9 %).

Preferential flow patterns and travel time of water in snow
Liquid water transmission in samples is marked by a high degree of heterogeneity.We measure this using the variable f .This is higher in fine snow layers than in medium or coarse snow layers and, in general, it increases with depth over the boundary (where f = 1 for all FC and FM samples), while it decreases below it.This is expected since horizontal suctions gradients in fine layers are higher than in coarser layers.As a result, one-dimensional gravitational movement is easier in coarser snow than in finer snow.
The external source of water was punctual and this may represent a limitation to this analysis.However, we used cotton rings to limit this problem, while deeper sections (i.e., depth ≥ 2 cm) show that water is also able to spread horizontally and change the position of fingers (compare e.g. the positions of the blue area at 0 and 2 cm in Fig. 1).
As a result, this problem is probably restricted to sample surface, only.
A similar analysis has been recently conducted by Katsushima et al. (2013) using samples made by vertically homogeneous snow.They observe that heterogeneity in water flux increases with grain size but decreases with increasing input flux.We also observe an increase in heterogeneity with g S , while no clear decrease of heterogeneity with W is found.Note that an increase in heterogeneity means that f decreases, and vice versa.Fingering behavior is clearly sensitive to snow microstructure heterogeneity.Sieving snow samples that are homogeneous at the particles scale is very difficult since some variations will occur at random locations.As a result, outcomes of different samples on this point are probably difficult to be compared.Additional investigations are clearly needed on this point.
During recent years, it has been sometimes debated if preferential flow paths in snow are stable in their positions in time, or not (Schneebeli, 1995;Waldner et al., 2004) though we observed here that new paths create during the percolation, and that sometimes fingers stop their vertical percolation at some locations but continued to develop at others (hence showing that the process of preferential flow development is dynamic in time), experiments duration did not allow to investigate this problem extensively.τ increases with decreasing W , as widely expected (Table 2).No clear difference between FC and FM samples is visible, thus confirming the general agreement between these experiments.In the case of FM2 (fine over medium snow, W = 27.7 mm h −1 ), we can compare the τ measured during our experiment (2.2 min cm −1 ) with the τ observed during the experiments by Katsushima et al. (2013), since this is the only g S -W combination that these two works share.The τ measured by Katsushima et al. (2013) for fine snow and W = 22.3 mm h −1 is equal to 1.7 min cm −1 , while the τ for medium snow and W = 21.7 mm h −1 is equal to 0.7 min cm −1 .It follows that, if samples are subjected to a comparable W , τ for a FM snow sample is not only higher than the τ observed in a sample composed by snow with the same grain size as the coarser snow layer of the layered sample (as expectable), but this is even higher than the τ observed in a sample made by snow with the same grain size of the finer snow layer.This difference shows the strong effect of ponding on liquid water travel time in snow.

The comparison with SNOWPACK
Results in Fig. 5 show that the considered version of SNOWPACK is able to predict the occurrence of a capillary barrier at different grain sizes and W combinations.A similar Clearly, these conclusions are limited to the grain sizes combinations and the water input rates used in these experiments.
In the case of FC and FM samples, the SNOWPACK-based profile usually overestimates θ in the upper layer due to the fact that the simulated velocity of water is slower than observed.The model predicts correctly the decrease in LWC below the boundary.
Predictions and observations of LWC at the boundary are very close for FC1 and FM1 (i.e., when W is small), since their difference is equal to ∼ 2 vol.% (as absolute value).In the case of FC2 and FM2, the absolute difference is equal to ∼ 4.8 and 0.43 vol.%, respectively, while it is equal to ∼ 12 and 8.3 vol.% for FC3 and FM3.In some cases, the predicted LWC at the boundary is higher than the observed one: this may be a hint that the observed LWC at that location is smaller than the actual peak reached by LWC during the ponding process.
Results are much more variegated when looking at MC samples.As an example, the simulated wetting front in MC1 has not reached the textural boundary at the end of the physical experiment.On the contrary, for MC3 (Fig. 5i) data and SNOWPACK return the same time of arrival of water at sample base and a similar LWC profile.Simulated profiles in MC1 and MC2 resemble a typical Richards-based infiltration profile where S r increases behind the front (DiCarlo, 2004).
At this stage, SNOWPACK cannot model a horizontal heterogeneity of flow due to its 1-D nature, and this process has a dramatic impact on this problem since water concentrates in fingers that are characterized by a higher-than-average unsaturated hydraulic conductivity (due to a higher-than-average LWC).Accordingly, it should come as no surprise that (1) the modeled velocity of the wetting front is slower than observed and (2) that these phenomena are paramount in case of MC samples, where fingering is particularly evident.However, observations and simulations agree very well in MC3.
This suggests that measuring and modeling liquid water flow in snow are still marked by high uncertainties.The approach used by Hirashima et al. (2010)  itself and on a parametrization of retention that bases, for instance, on grain size and density (Yamaguchi et al., 2012), unsaturated conductivity depends on a given relation with LWC (Hirashima et al., 2010) and on a suitable parametrization of intrinsic permeability (hence on grain size or equivalent sphere radius and density).Clearly, such a heavy parametrization can play an important role in the success of these predictions.

Experiments limitations
There is still room for improvements of this analysis.In particular, while comparing simulated and observed LWC profiles in Fig. 5, observed profiles suggest that the total mass of liquid water in each sample is different from the total mass supplied.A mass balance between supplied and measured liquid water mass shows that the measured mass ranges between 93 and 176 % of supplied mass in 8/9 samples, while in MC1 measured mass is 434 % of supplied mass.Note that in this last sample the total mass supplied is very low, due to a short experiment duration.A first explanation may be that the initial LWC was not equal to zero.An initial LWC > 0 may help explaining the peculiar behavior of MC1: as an example, its τ is the same observed in MC2 (Table 2), which is unexpected given that W for MC1 and MC2 are 11 and 27.3 mm h −1 , respectively.However, any undesired melting was avoided, as samples were all prepared at −20 • C and brought to 0 • C within a cold chamber where also dyed water was stored before using it in the experiment.Another explanation may be instrumental noise.LWC measurements by gravimetry depend on a set of temperature and density measurements and Kawashima et al. (1998) noted that this device returns alternatively higher or lower LWC if compared with high and low readings by a dielectric device.Sample dimensions make it challenging to use dielectric devices for similar experiments, while a highly fingered flow may be missed and/or disturbed.Fierz and Föhn (1995) report that the absolute error in measuring water content using dielectric methods spans between 0.2 and 0.9 vol.%, while Techel and Pielmeier (2011) note that 1 vol.% is the expected difference between mea-Introduction

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Full  (2015).Most of these works stem from two general impressions: on the one hand, as Fierz and Föhn said in 1995, "reliable measurements on wet snow are difficult to perform and therefore our understanding relies mostly on qualitative observations".On the other hand, "there is a strong need for a better understanding and improved models to describe the complex water flow in natural snow covers" (Wever et al., 2014).
In this paper, we focused on the systematic observation of capillary barriers development and associated preferential flow using laboratory experiments in a cold chamber.We considered three different textures and three water input rates.Nine samples were prepared and subjected to controlled infiltration of dyed water until water reached sample base.By means of visual inspection, LWC measurements and horizontal sectioning, the processes of ponding and preferential flow development were characterized.Results were also compared with SNOWPACK simulations.
We confirm that a fine-over-coarse/medium snow layering can cause ponding of water when this comes at the textural boundary.However, the process seems more variable when passing to a medium-over-coarse texture.Peaks in LWC over the boundary can reach ∼ 33 vol.% in FC samples and ∼ 34-36 vol.% in FM samples.Horizontal sectioning of samples confirmed that preferential flow seems the dominant process in water transmission in snow.Heterogeneity is observed to increase with grain size, while no explicit relation with W has been observed.The comparison with SNOWPACK showed that, in general terms, the water transport scheme that we considered here re-Introduction

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Full  Full  Full 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 | formulation and examples of previous applications.Examples areBartelt and Lehning (2002);Lehning et al. (2002);Hirashima et al. (2004);Yamaguchi et al. (2004);Mitterer et al. (2011b).The original version of SNOWPACK considers a simple buckettype approach to describe liquid water percolation in snow.Accordingly, liquid water is retained at a given position in the profile until it exceeds a threshold.After exceeding, excess water is transmitted to the lower layer.Hirashima et al. (2010) modifies this scheme, introducing a water transport model based on the van Genuchten equation(van Genuchten, 1980) and on gravity drainage experiments byYamaguchi et al. (2010).Recently,Wever et al. (2014) has also introduced a discretization of Richards equation.
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Hirashima et al. (2010) and the WRC parametrization byYamaguchi et al. (2012).It has been reported inHirashima et al. (2010);Mitterer et al. ( Fig. 2, we report three examples of samples at the end of the experiment.These are FC2 (as an example of FC tests), FM2 (as an example of FM experiments) and MC1 (as an example of MC experiments)Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | result was already shown byHirashima et al. (2010);Mitterer et al. (2011b), but, in this case, we considered a wide set of laboratory experiments, where different snow textures were subjected to various water input rates.This comparison shows also that, generally, this water transport scheme underestimates observed water speed.In fact, in 8/9 samples the simulated front has not reached the base of the sample at the end of the associated laboratory experiment.A similar conclusion has been reported recently byWever et al. (2014), who compare the performances by this scheme with an explicit resolution of Richards equation in SNOWPACK and with field observations.Discussion Paper | Discussion Paper | Discussion Paper | to model water velocity in snow needs the prediction of a wide set of variables, which includes, among others, suction and unsaturated conductivity.While ψ can be predicted basing on LWC Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | surements taken using a Denoth meter and a Snow Fork.This suggests that, generally, measuring low LWCs is very challenging for existing techniques.6 Conclusions In the recent past, the problem of measuring and modeling wet snow dynamics has emerged as a living topic in snow research.Examples of recent works on this topic include Mitterer et al. (2011a); Eiriksson et al. (2013); Mitterer and Schweizer (2013); Avanzi et al. (2014); Hirashima et al. (2014); Wever et al. (2014, 2015); Schmid et al.
Discussion Paper | Discussion Paper | Discussion Paper | produces LWC distribution over a capillary barrier, but underestimates the velocity of water in snow.Implications and limitations of these results in view of existing theory and technology within this field were discussed.Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Figure 1 .Figure 2 .Figure 3 .Figure 4 .Figure 5 .
Figure1.Sections of all the samples considered (2 cm vertical resolution) at the end of the experiment.Each column refers to a different sample (as indicated in the last row), while each row refers to the same depth from sample top surface (depth indicated by the number on the right side of each row).For all the samples, the texture boundary between different grain sizes is located at a depth equal to 10 cm.

Table 2 .
Results of the experiments: observed ponding layer thickness p, experiment duration t t , specific travel time τ.As for p, approximated lower and upper values are reported due to spatial heterogeneity in this variable.