Drivers of Flow Channel Formation on the Snow Surface: Rain Versus Meltwater—A Case Study in the Austrian Alps

1. Introduction

Visual observations of snow cover features reported to avalanche warning, hydrological, or meteorological services by field observers are essential for snow cover assessment, avalanche forecasting, or verification of weather forecasts. These observations provide real-time information on snowpack and meteorological conditions unavailable from automated measurements alone. Importantly, observational data can be communicated to avalanche warning, hydrological, or meteorological services by individuals with varying levels of expertise, including non-experts or less trained personnel, thereby adding to the overall information available. To accurately interpret field observations and assess the consequences of the observations for snowpack stability, water availability, or weather conditions as well as their spatial variability, a profound understanding of the underlying physical processes is essential. The understanding of the processes is an important precondition for the correct integration of observations into forecasting routines and models.

Flow channels on the snow surface (Figure 1) are among the surface features frequently reported from the field. As described by La Chapelle (2001), flow channels result from the percolation of liquid water through the snowpack, which subsequently concentrates in subsurface flow channels [1]. Those flow channels (or "snow dimples") were already described by Nohguchi (1984) in Nagaoka, Japan, where the formation of a "dimple pattern" can be observed several times every winter [2,3]. In situ observation of the formation of snow dimples on artificial snow layers were performed by Shimada et al. (2017), who found that the "dimples" form due to a concentration of water movement within the snow, depending on the amount of liquid water and the original properties ot the dry snow [4]. The international classification for seasonal snow on the ground [5] shortly mention roughness elements of the snow surface attributed to deposition, ablation, rain, melt, or sublimation processes.

The formation of flow channels on the snow surface is commonly attributed mainly to rain-on-snow (ROS) events [6]. Tremper (2008) states that flow channels on the snow surface are usually taken as an indicator that it rained on the snow surface, "Prolonged or hard rain on new snow forms drainage channels (also called "rill marks") down in fall line and makes a corrugated pattern in the surface snow" [7], p. 124, while Harvey et al. (2012) show a photo of a "typical snow surface with flow channel after a period of rain" [8], p. 49.

The origin of the water causing the flow-channels is important for the spatial distribution of wet-snow. In case of rain on snow, all slopes below the elevation where snow turns to rain are effected [9]. Whereas when water infiltration is due to melting, wet-snow is expected to be more pronounced for sunny slopes (higher solar radiation) and lower elevations (higher air temperature).

Thus, in particular for avalanche forecasting, the flow channels are used as indicators for several key factors: the elevation of the snowfall level (altitude above sea level at which precipitation falls as snow which is deposited on the ground), wet-snow [10] or glide-snow [11] avalanche conditions, the formation of crusts within the snowpack, crust-related weak layers within the snowpack, and generally the overall stability of the snowpack. In short, knowing the source of the liquid water forming the observed flow channels is important for drawing the right conclusions for forecasting routines and modeling.

Within this paper we study a wide-spread flow channel formation event in the Austrian Alps in December 2023. We compare the liquid water input from melt processes with that from rain during the formation of the flow channels. By combining field observations, measurements as well as model simulations, we seek to enhance the understanding of the processes driving surface flow-channel development.

2. Materials and Methods

2.1. Field Site Overview and Meteorological Data

A map of Austria with an overview of all observation and measurement sites is shown in Figure 2. As a basis for the calculations and the modeling within this study, meteorological data from Automatic Weather Stations (AWS) in the Präbichl and Brunnalm/Hohe Veitsch skiing areas (Figure 3) were utilized. To complement these observations with snow cover and meteorological measurements from the broader region, precipitation and temperature data from the AWSs at Rudolfshütte and Obertauern is also shown (Figure 4).

The AWS Präbichl and Hohe Veitsch are situated along the main Alpine divide in the Eastern Austrian Alps, approximately 40 km apart in a straight-line distance, sharing similar topographic settings and elevation ranges. Meteorologically, both sites are characterized by their susceptibility to northerly to north-westerly orographic precipitation events, which frequently impact the region during winter. Their proximity suggests that meteorological conditions at the two AWS are likely to be broadly similar, making them a suitable pair for further analysis of the atmospheric conditions preceding flow channel formation in the Eastern Austrian Apls. The Rudolfsütte is located at 2317 m and approximately 250 km to the West of Präbichl, providing data from the westernmost part of our observation areas. Observational data from the AWS Obertauern Pass located at 1772 m in the Central Austrian Alps is used to close the gap between Eastern and Western Austrian Alps. The temporal resolution of observational data on weather stations was 10 min. The meteorological data spans the early winter period up to 31 December 2023, allowing for a comprehensive review of meteorological conditions leading up to the observed phenomena.

At Präbichl, the dense AWS network provides a range of measurements across different elevations, from which the following were utilized in this study:

• precipitation and air pressure at 1214 m
• snow height, air temperature, relative humidity, incoming short-wave radiation, snow surface temperature and wind measurements at 1731 m
• wind measurements at 1907 m

AWS Hohe Veitsch contributed the following data:

• snow height, air temperature, relative humidity, snow surface temperature and net radiation at 1323 m
• wind measurements at 1973 m

and AWS Obertauern and Rudolfshütte contributed:

• precipitation and air temperature at 1772 m and 2317 m, respectively.

2.2. Weather Conditions

Following initial snowfall events at alpine elevations (> 2000 m) in early November, a continuous snow cover formed above mid-elevations (around 1500 m) from mid-November onward. Variable weather conditions, characterized by repeated precipitation and occasional ROS events at alpine elevations, followed by cold periods with snowfall and wind, resulted in a rather heterogeneous early-winter snowpack structure.

From mid-December onward (Figure 3), the onset of a pronounced Azores High brought several days of mild and sunny weather to the Eastern Alps, with temperatures reaching up to +8 °C at 2000 m (Figure 3 uppermost panel – air temperatures at 1323 m at AWS Veitsch reached a maximum of 15 °C on 18 and 19 December 2023. This warm period caused the snowpack to settle and by 21 December 2023 a compact snow base had developed, primarily composed of multiple melt-freeze crusts interspersed with various stages of partly moist decomposed or fragmented particles.

Beginning on 22 December 2023, a shift to a stormy north-west weather pattern led to significant snowfall, particularly along the northern flanks of the Alps where orographic precipitation frequently contributes to large precipitation amounts. We see measured snowfall accumulations of 60 cm to 100 cm within approximately 48 h (22 to 24 December 2023, Figure 3 lowermost panel). The snowfall occurred at relatively high temperatures, around or slightly above 0 °C resulting in a warm layer of fresh snow (Figure 3, uppermost panel). The snowstorm ended on 24 December 2023 and was immediately followed by an influx of warm air masses into the Eastern Alps. Due to the warm conditions, the new snow stabilized rapidly, becoming compact and free of significant weak layers, even at higher elevations.

2.3. Snow Cover Observations

Manually observed snow profiles from the latter half of December 2023 (see Figure 5 and Figure 6) provide information on snowpack stratigraphy at this time. Both profiles feature a thick basal layer of compact and hard melt forms or melt-freeze crusts. Above this layer, differences in the middle snowpack structure are evident, that can be attributed to differences in elevation and local conditions. The two sites are separated by approximately 400 m in elevation, which likely marked the boundary between rain and snow during repeated early winter precipitation events. The profile from Radmer (Figure 5) shows alternating melt-freeze crusts and degrading faceted crystals, whereas the profile at Vordernberger Griesmauer (Figure 6) reveals a relatively uniform layer of compact rounded grains. Additionally, the snow depth at the Vordernberger Griesmauer site was approximately twice as high, suggesting frequent loading with wind-transported snow. The south-facing orientation of this site leading to increased solar radiation likely resulted in lower temperature gradients, reduced constructive metamorphism and enhanced snowpack settling, explaining the presence of the compact layer of rounded grains. The top layers of both profiles reflect the fresh snow from the snowfall event between 22 and 24 December 2023. On 23 December 2023, the Radmer profile shows loose new snow particles in the upper layers. However, slightly moist conditions were already observed within these fresh snow layers, likely due to air temperatures near 0 °C during the snowfall. By the morning of 25 December 2023, the Griesmauer profile indicated that the uppermost layers had already transitioned to moist or wet snow, with crystals transforming into melt forms or fragmented new snow particles. These observations highlight the significant changes experienced by the snowpack’s upper layers within this short period.

2.4. Field Observations of Flow Channels

Wide-spread flow channels on the snow surface were observed by avalanche forecasters from the Styrian and Lower Austrian Avalanche Warning Services during a field campaign near the Präbichl skiing area on 25 December 2023 [12]. To evaluate the extent of the flow channels on a larger scale, additional sources of snow observations, including webcam imagery, were analyzed. The observations and webcam images revealed widespread flow channel development across the Austrian Alps, spanning from regions such as Göller (Figure 1) and Veitsch (Figure 7), along the main Alpine divide towards the west, including Obertauern (Figure 8) and extending as far as the western Hohe Tauern, such as Wildgerlostal (Figure 9). The spacial distribution covers approximately 263 km in straight-line distance.

2.5. Surface Energy Balance Calculations

To determine the factors influencing the formation of the observed flow channels, we calculated the available energy for snow-melt per unit area based on the surface energy balance of the snowpack. Assuming the snow surface behaves as an infinitesimally thin layer with no heat capacity, the principle of energy conservation dictates that the energy fluxes into the surface must balance those leaving it. Following Wallace and Hobbs (2006) [13], the surface energy flux is therefore expressed as:

$$Q_{\mathrm{surf}}=Q_{\mathrm{SW}}+Q_{\mathrm{LW}}+H+E+Q_A$$

(1)

where:

$Q_{\mathrm{surf}}$=energy flux at the snow surface $Q_{\mathrm{LW}}$=net long-wave radiative flux (measured) $Q_{\mathrm{SW}}$=net short-wave radiative flux (measured) E=latent heat flux H=sensible heat flux $Q_A$=advective heat flux (e.g., by rain)

$\left[{\displaystyle \frac{\mathrm{W}}{{\mathrm{m}}^2}}\right]$

The ground heat flux $Q_{\mathrm{G}}$ is neglected in this surface energy balance approach, assuming that the snowpack provides sufficient thermal insulation to decouple the snow surface from the underlying ground. $Q_{\mathrm{A}}$ is determined by

$$Q_{\mathrm{A}}=m_{\mathrm{rain}}·c_{\mathrm{water}}·(T_{\mathrm{air}}-T_{\mathrm{surf}})$$

(2)

where:

$m_{\mathrm{rain}}$	=	rain mass flux per unit area (measured) $[{\displaystyle \frac{\mathrm{mm}}{\mathrm{s}}}={\displaystyle \frac{\ell }{{\mathrm{m}}^{2}s}}={\displaystyle \frac{\mathrm{kg}}{{\mathrm{m}}^{2}s}}]$
$c_{\mathrm{water}}$	=	specific heat capacity of water = 4186 $\left[{\displaystyle \frac{\mathrm{J}}{\mathrm{kg}\mathrm{K}}}\right]$
$T_{\mathrm{air}},T_{\mathrm{surf}}$		= temperatures of the rain (assumed equal to air temperature)
		and the snow surface (measured) $\left[\mathrm{K}\right]$

Applying the bulk aerodynamic approach [13] the sensible heat flux H and the latent heat flux E can be calculated by

$$H={\rho }_{\mathrm{air}}·c_{\mathrm{p},\mathrm{air}}·VW·C_{\mathrm{H}}·(T_{\mathrm{air}}-T_{\mathrm{surf}})$$

(3)

$$E={\rho }_{\mathrm{air}}·L_{\mathrm{s}}·VW·C_{\mathrm{E}}·\left(q_{\mathrm{air}}-q_{\mathrm{surf}}\right)$$

(4)

where:

${\rho }_{\mathrm{air}}$	=	density of the air, assumed constant = 1.225 $\left[{\displaystyle \frac{\mathrm{kg}}{{\mathrm{m}}^3}}\right]$
$c_{\mathrm{p},\mathrm{air}}$	=	specific heat capacity of air = 1004 $\left[{\displaystyle \frac{\mathrm{J}}{\mathrm{kg}\mathrm{K}}}\right]$
$L_{\mathrm{s}}$	=	latent heat of sublimation = $2.5\times {10}^6$ $\left[{\displaystyle \frac{\mathrm{J}}{\mathrm{kg}}}\right]$
$VW$	=	wind velocity (measured) $\left[{\displaystyle \frac{\mathrm{m}}{\mathrm{s}}}\right]$
$C_{\mathrm{H}},C_{\mathrm{E}}$	=	dimensionless bulk transfer coefficients for heat and water vapor $\left[-\right]$
$T_{\mathrm{air}},T_{\mathrm{surf}}$	=	temperatures of the air and the snow surface (measured) $\left[\mathrm{K}\right]$
$q_{\mathrm{air}},q_{\mathrm{surf}}$	=	specific humidities of air and the snow surface $\left[{\displaystyle \frac{k{g}_{\mathrm{water}}\mathrm{vapor}}{k{g}_{\mathrm{snow}}}}\right]$

We used conservative $C_{\mathrm{H}}=0.002$ and $C_{\mathrm{E}}=0.0021$ for heat and water vapor transfer, respectively, as suggested in literature, assuming a flat snow surface under statically neutral conditions [13,14]. $q_{\mathrm{surf}}$ is the specific humidity of the snow surface (uppermost layer), for which we assume saturation. This means that the relative humidity at the surface is RH=1 and the vapor pressure at the snow surface equals the saturation vapor pressure over ice, i.e., $e=e_{\mathrm{sat},\mathrm{ice}}\left(T_{\mathrm{surf}}\right)$, where $e_{\mathrm{sat},\mathrm{ice}}$ is calculated using the surface temperature $T_{\mathrm{surf}}$ measured at the AWS (Equation 7).

Specific humidities are determined by

$$q={\displaystyle \frac{0.622\times e}{p-e}}$$

(5)

where:

p	=	air pressure $\left[\mathrm{Pa}\right]$
e	=	water vapor pressure $\left[\mathrm{Pa}\right]$ using the water vapor pressure

$$e=RH\times e_{\mathrm{sat}}$$

(6)

where:

$e_{\mathrm{sat}}$	=	saturated vapor pressure $\left[\mathrm{Pa}\right]$
$RH$	=	relative humidity (measured) $\left[-\right]$. $e_{\mathrm{sat}}$ is determined via

$$e_{\mathrm{sat}}=6.112\times exp\left(17.67\times {\displaystyle \frac{T-273.15}{T-29.65}}\right).$$

(7)

and the air pressure $p_{\mathrm{Veitsch}}$ is calculated by the barometric equation:

$$p_{\mathrm{Veitsch}}=p_{\mathrm{Pr}\text{ä}\mathrm{bichl}}·{\left({\displaystyle \frac{T_{\mathrm{air},\mathrm{Veitsch}}}{T_{\mathrm{air},\mathrm{Pr}\text{ä}\mathrm{bichl}}}}\right)}^{{\displaystyle \frac{g}{R·L}}}$$

(8)

where:

p	=	air pressure at Veitsch and Präbichl $\left[\mathrm{Pa}\right]$
$T_{\mathrm{air}}$	=	air temperature at Veitsch resp. Präbichl (measured) $\left[\mathrm{K}\right]$
g	=	gravitational acceleration = 9.81$\left[{\displaystyle \frac{m}{s^2}}\right]$
R	=	specific gas constant for dry air = 287.05 $\left[{\displaystyle \frac{J}{kgK}}\right]$
L	=	temperature lapse rate = $6.5\times {10}^{-3}$ $\left[{\displaystyle \frac{K}{m}}\right]$

Ultimately, $Q_{\mathrm{surf}}$ (Equation 2) represents a 10 min averaged energy flux per unit area, based on the 10 min measurements of the AWS. To determine the total energy available over a 10 min period, the mean flux is integrated over the averaging period (in this case 10 min):

$$E{B}_{\mathrm{surf}}=Q_{\mathrm{surf}}\times 600s$$

(9)

where $E{B}_{\mathrm{surf}}$ represents the total energy available $\left[{\displaystyle \frac{J}{{\mathrm{m}}^2}}\right]$ per unit area over a 10-minute interval.

2.6. Estimation of Potential Meltwater Production

The potential meltwater production $M_{\mathrm{melt}}$ based on the surface energy balance $E{B}_{\mathrm{surf}}$ was then estimated by

$$M_{\mathrm{melt}}={\displaystyle \frac{E_{\mathrm{melt}}}{L_{\mathrm{f}}}}$$

(10)

where:

$M_{\mathrm{melt}}$	=	potential amount of meltwater per time interval (10 min) $\left[{\displaystyle \frac{kg}{{\mathrm{m}}^2}}\mathrm{or}\mathrm{mm}\right]$
$E_{\mathrm{melt}}$	=	energy available for snowmelt per unit area $\left[{\displaystyle \frac{J}{{\mathrm{m}}^2}}\right]$
$L_{\mathrm{f}}$	=	latent heat of fusion $=3.34\times {10}^5\left[{\displaystyle \frac{\mathrm{J}}{\mathrm{kg}}}\right]$

The energy per unit area available for snowmelt $E_{\mathrm{melt}}$ is determined by

$$E_{\mathrm{melt}}=E{B}_{\mathrm{surf}}-E_{\mathrm{heat}}$$

(11)

where the energy needed to heat the upper 1 cm of the snow to the melting point 0 °C, $E_{\mathrm{heat}}$, is estimated by:

$$E_{\mathrm{heat}}=c_{\mathrm{p},}\mathrm{snow}\times m_{\mathrm{snow}}\times (273.15-T_{\mathrm{surf}})$$

(12)

with:

$E_{\mathrm{heat}}$	=	heat energy per unit area $\left[{\displaystyle \frac{J}{{\mathrm{m}}^2}}\right]$
$c_{\mathrm{p},}\mathrm{snow}$	=	specific heat capacity of ice and snow $=2100\left[{\displaystyle \frac{\mathrm{J}}{\mathrm{kg}\mathrm{K}}}\right]$
$m_{\mathrm{snow}}$	=	mass of snow to heat to 0 °C$\left[{\mathrm{m}}^3\right]$
$T_{\mathrm{surf}}$	=	snow surface temperature $\left[K\right]$

with the snow volume $V_{\mathrm{snow}}=0.01{\mathrm{m}}^3$ and ${\rho }_{\mathrm{snow}}=150{\displaystyle \frac{\mathrm{kg}}{{\mathrm{m}}^3}}$ the assumed density of the fresh snow layer.

The energy available for snow-melt is strongly influenced by $Q_{\mathrm{heat}}$. In this study, we assume that only the uppermost 1 cm of snow is heated to the melting point within each 10-minute interval, with no energy lost to other processes. To minimize the impact of this assumption, calculations have been restricted to periods when the snow surface temperature was generally at 0 °C. However, a minor effect remains for periods when the measured snow surface temperature temporarily drops below 0 °C.

Data used for this study was quality-controlled and preprocessed to remove erroneous values and fill data gaps. Additionally, corrections for sensor biases and inconsistencies were applied to ensure the reliability of the dataset.

2.7. SNOWPACK Modeling

We conducted snow cover simulations using the physically-based SNOWPACK model [15,16], driven by meteorological measurements from AWS Präbichl (1731 m). As a water transport scheme we used the traditional bucket model [15]. Our simulations provide detailed insights into the evolution of snowpack stratigraphy, as well as the presence and transport of liquid water within the snowpack.

3. Results

On the morning of 25 December 2023, avalanche forecasters from the Styrian Avalanche Warning Service reported extensive formation of flow channels, observed at least up to 1900 m. Hourly webcam imagery from Brunnalm/Hohe Veitsch, covering elevation ranges between 1400 m and 1700 m (Figure 7), as well as from the Obertauern skiing area further west, corroborates this observation and documents the overnight formation of flow channels despite minimal liquid precipitation (Figure 4). The following section presents the results of the investigation conducted in this study to address this phenomenon.

3.1. Surface Energy Balance Calculations

Surface energy balance components, along with estimated snowmelt and measured precipitation rates for the period from 24 December 2023, 12 CET, to 25 December 2023, 12 CET, are presented in Figure 10. To compensate for missing wind measurements caused by frozen instruments, wind data from AWS Veitsch were supplemented with measurements from AWS Präbichl to obtain these results.

Figure 3 shows that the main phase of precipitation concluded around midnight on 23 December 2023. Thereafter, only 1.3 mm of precipitation was recorded between 24 December 2023 at noon and midnight, as presented by the precipitation rates in Figure 10. During this period, air temperatures at the AWS locations (1731 m and 1323 m) had already risen to or slightly above 0 °C, suggesting that precipitation likely occurred in liquid or mixed form (Figure 3, upper panel), resulting in an initial but minor liquid water input into the fresh snow. However, in the subsequent hours, potential meltwater production was estimated and modeled to be roughly two orders of magnitude greater than the recorded liquid precipitation in the afternoon of 24 December 2023 (Table 1). Based on this calculation, the measured precipitation accounted for only about 1.7 % of the total liquid water input (precipitation plus potential snowmelt), underscoring the dominant role of melt processes in the formation of surface flow channels rather than direct liquid precipitation input.

3.2. SNOWPACK Modeling Results

Figure 11 shows the results of the SNOWPACK modeling. Simulated snow grain types indicate that the fresh snow from the main snowfall event accumulated on an older, well-compacted snowpack, primarily composed of rounded grains and melt-freeze crusts, as corroborated by manual snow profiles presented earlier. The freshly deposited snow consisted predominantly of defragmented particles, likely resulting from wind transport and mechanical fragmentation of new snow. These particles rapidly underwent sintering and settling processes, transitioning toward rounded grains.

Regarding snow temperature evolution, prior to the precipitation event, the upper approximately 50 cm of the snowpack exhibited a pronounced diurnal temperature gradient, leading to cooling during clear nights and subsequent warming during the day, although temperatures mostly remained below the melting point. In contrast, the fresh snow layer following the snowfall event was rather "warm" in terms of snow temperatures and therefore had a significantly lower cold reserve.

In terms of snow density, the fresh snow was substantially less dense than the pre-existing, well-settled snowpack, particularly when compared to the dense melt-freeze crust at the old snow surface. This difference in density and structural characteristics likely played a role in controlling the rate of water percolation.

The model results further indicate that snowpack wetting began during the afternoon and evening of 24 December 2023, coinciding with the onset of liquid precipitation, as simulated by SNOWPACK and measured at our automatic weather stations. However, despite the presence of liquid precipitation, full percolation of liquid water beyond the uppermost snow layers did not occur immediately but progressed gradually throughout the night. Notably, even in the absence of additional precipitation, SNOWPACK simulations indicate a continuous increase in liquid water content within the snowpack, suggesting that meltwater production from surface energy fluxes played a significant role in enhancing water infiltration and redistribution.

Consistent with observational data, the model results indicate that precipitation accounted for only approximately 2.5% of the total liquid water input, with meltwater production contributing the remaining fraction. By the night and morning of 25 December 2023, the snowpack had become fully isothermal, coinciding with liquid water percolation throughout the entire snow column.

4. Discussion

4.1. Choice of Data

This study primarily utilizes data from the automatic weather stations at Präbichl, which are located near the original observation site of the flow channels and provide measurements from relevant elevation ranges. These observations are complemented by surface energy balance data from AWS Veitsch. While this approach introduces some limitations compared to a fully localized dataset, the proximity of the stations and the similarity of their meteorological conditions ensure that these limitations remain minimal relative to the benefits of the combined dataset.

Surface energy balance calculations were primarily based on data from AWS Veitsch. However, due to sensor freezing, wind measurements at Veitsch were unavailable from 22 to 24 December 2023, necessitating the use of wind data from AWS Präbichl to fill this gap. Wind speeds at Präbichl were measured at two locations, both providing continuous and consistent recordings, with values generally slightly lower than those recorded at AWS Veitsch. Consequently, the calculated snowmelt rates based on Präbichl wind data were lower compared to those derived from Veitsch wind data.

Generally, it is important to acknowledge that wind measurement stations are typically positioned in exposed locations, where wind speeds tend to be higher than in more sheltered areas. As a result, these measurements may not fully represent conditions at the snow height and radiation balance measurement site at AWS Veitsch (1323 m), which is more sheltered. This discrepancy can influence the estimation of turbulent fluxes and energy balance calculations, potentially leading to an overestimation of wind-driven processes such as turbulent heat exchange and sublimation.

4.2. Energy Used for Warming vs. Snowmelt

To simplify the analysis, it was assumed that all available energy was used exclusively for snowmelt. However, Harpold and Brooks (2018) demonstrated that the actual partitioning of energy between snowmelt and sublimation is strongly influenced by atmospheric conditions [17]. Under very dry conditions, particularly those characterized by low relative humidity, a larger proportion of the available energy is allocated to sublimation rather than melting. This effect is especially pronounced during Föhn storm events in the Alps, where warm and dry air is advected over the snow surface. In such cases, a significant fraction of the available energy is expended on sublimation, leading to notably reduced snowmelt and liquid water percolation. Such a situation was evident on the morning of 25 December 2023, when cloud cover diminished and relative humidity dropped. However, the effect of energy partitioning between snowmelt and sublimation is not explicitly considered in our calculations, as all available energy is assumed to be used for snowmelt, leading to a potential overestimation. In contrast, the model simulations accounted for evaporation, resulting in lower snowmelt estimates.

The calculation is further based on the assumption that only the uppermost 1 cm of the snow cover is raised to 0 °C before meltwater production starts, which strongly influences the amount of energy available for melting. The penetration depth of radiation into snow depends on multiple factors, including the wavelength of incoming radiation, the physical properties of the snow and the duration of radiation exposure. Snow behaves approximately as a black body in the long-wave spectrum, absorbing most of the radiation at the surface, which is then conducted downward over time [18]. In contrast, a significant portion of short-wave radiation is reflected at the surface due to the high albedo of snow, while the remaining portion is refracted and absorbed within the of the snowpack [19]. Given our 10 min calculation steps, we assume that energy losses to deeper snow layers are minimal and that most of the available energy remains confined within the uppermost 1 cm of snow.

To minimize the effect of this assumption, we confined our calculation periods to times, when the measured snow surface temperature was already at 0 °C. Consequently, only a small amount of energy was required to raise the snowpack temperature to 0 °C if it had temporarily fallen below this threshold. Once this initial energy input was met, any additional available energy was directed toward melting.

4.3. Energy-Driven Snow-Melt and Snowpack Response to Atmospheric Conditions

The estimated potential meltwater production during the morning of 25 December 2023 was significantly greater than the accumulated liquid water from rainfall during the evening of 24 December 2023. While only 1.3 mm of rain was recorded, the estimated potential snowmelt from the positive surface energy balance reached 75.2 mm in the calculations and 50.8 mm in the SNOWPACK model. This indicates that energy-driven snow-melt was the predominant source of liquid water input into the snowpack during this period, far exceeding the contribution from direct precipitation. It underscores the crucial role of snow cover properties and atmospheric conditions in determining whether meltwater production or direct precipitation serves as the dominant source of liquid water input into the snowpack. Key factors such as snow density and temperature, as well as air temperature, relative humidity and net radiation, influence the availability and transport of liquid water, ultimately controlling the extent and dynamics of water infiltration within the snowpack.

The modeled snow temperatures suggest that the fresh snow had minimal cold content, allowing the snowpack to quickly respond to energy input, leading to accelerated warming and subsequent wetting. In contrast, prior to the snowfall event, the hard snow surface was able to accumulate a substantial cold reserve during cloudless nights with low relative humidity, which slowed or even prevented the formation of meltwater. Additionally, low relative humidity during the earlier period likely enhanced sublimation losses, further reducing the available liquid water [17,20].

Overall, the modeled and calculated snow-melt correspond well to the observed snow height reductions measured at the stations during this period. In Figure 3, both stations show a snow height reduction of over 50 cm between 24 and 25 December 2023. For fresh snow at moderate temperatures, a common rule of thumb is that 1 mm of precipitation corresponds to approximately 1 cm of snow accumulation. Applying this in reverse, melting 50 cm of fresh snow would yield approximately 50 mm of snow water equivalent. For more densely packed snow, an even higher snow water equivalent would be expected. The calculated and modeled values fall within this range, indicating plausible magnitudes of snowmelt.

5. Conclusions

Our study challenges the widely held assumption that flow channels are formed exclusively by rain-on-snow (ROS) events, revealing that meltwater generated from a positive surface energy balance can also lead to the development of flow channels. By analyzing snowpack characteristics, meteorological data, energy balance calculations, and model simulations, we demonstrate that energy-driven snow-melt can exceed liquid precipitation input and dominate liquid water production. Specifically, during the morning of 25 December 2023 in Styria, Austria, estimated meltwater production reached 75.2 mm based on energy balance calculations, while SNOWPACK simulations indicated 50.8 mm of total snow-melt. In contrast, measured precipitation during the preceding evening amounted to only 1.3 mm, contributing just roughly 2 % of the total liquid water input in the energy balance and SNOWPACK simulations, respectively. This highlights the significant role of a positive energy balance in generating a significant amount of meltwater, which can lead to flow channel formation even in the absence of substantial rainfall. Our findings underscore the importance of considering both ROS events and energy-driven snow-melt in interpreting meltwater channel formation. Atmospheric and snowpack conditions are pivotal in this process, challenging the traditional view that ROS events are the sole contributors.

Despite the conservative approach and assumptions taken in our analysis, the findings clearly indicate that liquid water generated from a positive energy balance, rather than solely from liquid precipitation, plays a crucial role in the formation of these channels. The SNOWPACK simulations further corroborate this conclusion, demonstrating that liquid water content within the snowpack increased continuously even in the absence of additional precipitation.

Our case study therefore highlights the necessity of accounting for multiple sources of liquid water in the analysis of flow channel formation, emphasizing that a comprehensive understanding requires consideration of both ROS events and energy-driven meltwater production.