Originally developed for seasonal snow cover in alpine environments, SURFEX/ISBA-Crocus (hereafter referred as Crocus, ) is a physically based, model designed to simulate the microstructural evolution of snowpacks using a multilayer approach. Crocus is a one-dimensional column model and is used at the point scale. For spatial applications, the model is run at multiple independent grid points (i.e. without lateral transfers). In this study, the simulations are limited to a single-point configuration. The snowpack is discretized on a vertical grid, and using a Lagrangian approach, the model dynamically adjusts the vertical layering (number and size of layers, with a maximum of 50 layers) to represent changes in snowpack stratigraphy over time. Each layer represents snow with specific physical state variables, including mass, density, temperature, liquid water content, and microstructure properties (optical diameter and sphericity). The snowpack thermodynamical evolution is simulated by solving the energy and mass conservation equations at a 15 min time step (denoted as Δt in s). Key processes such as heat transfer, melting, sublimation, water percolation and refreezing are explicitly represented .This computation of the liquid water and temperature fields in the snowpack is then used to simulate snow metamorphism, i.e. the evolution of the microstructural properties of snow.

Crocus has already been used to simulate glacier surface mass balance in the Alps and also in other mountainous regions such as the Andes or the Himalayas in a modified version that accounted for rock debris on ice:. Crocus simulates glacier ice by treating it as a highly compacted, non-porous form of snow e.g., with adjusted physical properties (such as the albedo, aerodynamical roughness length, or thermal conductivity). In this configuration, layers are classified as ice when their density exceeds 850 kg m⁻³, a threshold that can be adjusted if needed. Pure ice has a maximum density of 917 kg m⁻³.

Crocus requires atmospheric forcing variables including air temperature, relative and specific humidity, wind speed and direction, incoming shortwave and longwave radiation, and precipitation (solid and liquid). These inputs are used at an hourly resolution in the model, and an interpolation is realized for all atmospheric variables except for rainfall and snowfall where a mean rate is applied. Additionally, we assume no geothermal heat flux at the base of the snowpack (ground flux set to zero), thus excluding any basal melt contribution. We use the Crocus version within the SURFEX plateform .

In Crocus, liquid water percolation follows a conceptual bucket model , where each layer retains water up to a defined threshold. This threshold, known as the liquid water holding capacity, is expressed as a percentage of the layer’s pore space. Layers act as stacked reservoirs that fill up until reaching this limit, which depends on their porosity. The excess water then drains into the underlying layer. By default, the maximum water holding capacity is set to 5 % of a layer’s pore space , consistently with the experiments from on snow.

However, the standard implementation of Crocus was not designed to properly handle the presence of non-porous and impermeable layers such as ice. Indeed, up-to-now these layers were treated as having zero holding capacity but remained permeable. Consequently, liquid water is allowed to pass through pure ice, without any retention or barrier to percolation. Specifically, it means that in the case of a temperate ice column, all liquid water percolates without any storage or refreezing, causing all rain and meltwater to convert directly to runoff without surface retention. Conversely, if the ice column temperature falls below the triple point (273.15 K), refreezing can occur within sufficiently cold layers during percolation. Consequently, potential water retention mechanisms observed on glaciers, such as ponding, refreezing, or temporary storage of liquid water within surface irregularities, cannot be represented in the Crocus current version.

Surface water retention is modeled using a virtual surface layer called a buffer, that holds liquid water between time steps, representing water accumulated in surface ice rugosity (Fig. ). This buffer explicitly accounts for liquid water at the surface only, without representing percolation into or water storage within the underlying ice layers. The buffer is implemented as a scalar variable rather than as an additional physical layer in the model structure. This choice avoids unnecessary complexity in the definition and treatment of layers within the model routines, while still capturing the key processes associated with surface water storage. The model workflow, which provides information on the state of routine modifications and their order of use, can be found in the Supplement, Sect. S1.

The buffer layer is implemented as an optional parameterization within Crocus that can be activated or deactivated through model configuration. When activated, it allows explicit consideration of the thermal influence of liquid water on the underlying ice, its effects on surface albedo, and its contribution to the surface mass balance. This implementation introduces a feedback between the surface energy balance and the thermal profile of the underlying layers at each time step. When deactivated, the model runs in its basic configuration.

The buffer exists only when the three following conditions are met: (i) the entire column is ice (i.e. density greater than 850 kg m⁻³) ; (ii) there is no snowfall during the time step and (iii) no freezing rain. Otherwise the buffer is completely drained to the runoff and the model reverts to its default configuration with no surface water storage. These conditions are necessary to avoid overly complex situations such as snowfall accumulating on a surface already covered by stored liquid water. Although such events do occur in reality, the treatment of these specific cases is beyond the scope of this study.

The mass of the buffer is updated at each time step, accounting for rain and melted ice added to it, any refreezing, and the rate of decay. The mass balance equation for the buffer is given by: 1∂Mbuff∂t=Rmelt+Rrain-Rrefrz-MbuffτD where Mbuff(t) (in kg m⁻²) is the mass of liquid water in the buffer, Rmelt, Rrain and Rrefrz (in kg m⁻² s⁻¹) are the rates of melt, rain and refreezing respectively and τD is the characteristic time of drainage linked to the so-called drainage coefficient D by Eq. (). 2D=exp-ΔtτD

A maximum threshold, zmax,buff (in m), is set for the buffer to prevent unrealistic water storage. Once the water content in Mbuff exceeds this threshold, any additional meltwater or rainfall is transferred directly to the runoff variable exiting the glacier without further interaction with the ice surface. By default, zmax,buff is set to 1 cm but can be adjusted by the user. On the other end, when Mbuff equals zero, the buffer's thermal and radiative effects are deactivated by setting the fraction parameter x to zero (see Sect.  for details on the energetic impact), while the mass remains in the buffer.

At the end of each time step, the drainage coefficient D is applied to Mbuff to partially empty the buffer, mimicking the natural downward flow of water on a glacier. As for the excess water storage, the drained water goes directly to the runoff. This gradual drainage occurs as long as water is present in the buffer, even without additional water from melt or rainfall, ensuring that the buffer empties over multiple time steps. D is an empirical variable fixed by the user, ranging from 0 (complete drainage at each time step) to 1 (no drainage) and is arbitrarily set to 0.995. The impact of this choice will be tested and discussed in Sect. . Note that D is linked to τD via Δt, the time step duration (in s), to ensure the simulation remains independent of the chosen time step.

For the rest of this section, variables are expressed as v+ or v-, where + and - denote the variable (v for the example) before and after the process described in the subsection.

The top layer's thermal profile is adjusted to account for the presence of water. In the model, the heat diffusion equation is solved to determine the column thermal profile. When liquid water is present at the ice surface, an additional term Kbuff+ (in W m⁻²) is included to the heat diffusion equation to account for the conductive fluxes between the liquid water (with a fixed temperature of 273.15 K ) and the top layer of ice. 3Kbuff+=2xλbT0-T1+Δz where x is the fraction of a representative surface area of the grid point which is impacted by the buffer (i.e. the fraction of ice covered by water on Fig. c), λb the thermal conductivity of liquid water (in W m⁻¹ K⁻¹), T1+ the temperature (in K) of the top of the first layer, T0 the temperature of the buffer which is at the triple point (273.15 K) and Δz the thickness of the first layer (in m). λb is fixed at 0.6 W m⁻¹ K⁻¹, an empirical value recommended by for water at 273.15 K.

The fraction x was introduced to modulate the buffer's influence on the thermal profile and albedo, since water only covers part of the surface. When the buffer scheme is activated and liquid water is present (Mbuff>0 kg m⁻²), x is set by the user to a constant value in the range x∈]0,1]. This user-defined value represents the fraction of the representative surface area affected by the buffer and must be greater than zero to ensure that the buffer's thermal contribution is integrated into the heat diffusion equation's conduction term and its radiative effects are included in albedo calculations. When the buffer scheme is deactivated (either through model configuration or when buffer conditions are not met) or when Mbuff equals 0, x is effectively set to zero in the calculations, decoupling any thermal and radiative effects. In this study, x is set by default to 0.2 when the buffer is active, a value chosen to allow significant thermal contribution while keeping ice as the dominant surface component. This choice and its impact are discussed in Sect. .

The heat equation for the first layer, using a formalism adapted from , with the additional conductive term is: 4cIρ1z1T1+-T1-Δt=G0+-G1++R0-R1+Kbuff+ where G1+ (in W m⁻²) is the heat flux between layers 1 and 2. cI (2106 J kg⁻¹ K⁻¹) is the ice specific heat capacity, ρ1 (in kg m⁻³) and z1 (in m) are respectively the volumic mass and the thickness of layer 1. T1+ and T1- (in K) are temperatures for layer 1. R0 and R1 are the radiative fluxes (in W m⁻²) entering and passing through the layer, respectively. The heat flux between the atmosphere and the surface, G0, is the sum of all the energy fluxes at the surface: 5G0=ϵ(LW↓-σT14)-H-LE+PrcWΔt(Ta-T0) where ϵLW↓ (in W m⁻²) is the incoming longwave radiation, ϵσT14 (in W m⁻²) is the emitted longwave radiation expressed with Stefan-Boltzmann law and PrcWΔt(Ta-T0) (in W m⁻²) is the energy carried by the liquid precipitations with Pr (in kg m⁻² s⁻¹) the rainfall flux, cW the liquid water specific heat capacity (4218 J kg⁻¹ K⁻¹), Ta (in K) is air temperature.

Note that over the ice, the radiative components of Eq. () are calculated without considering liquid water and the turbulent fluxes remain unchanged. This choice is made based on the assumption that the exchange between the atmosphere and the surface primarily occurs with ice, since water covers only a small fraction of the surface (x=0.2). As mentioned above, it is assumed that liquid water on the ice only affects the ice by conduction. In addition, albedo parameters are set accounting for the presence of liquid water at the surface (see Sect. ).

When the heat diffusion equation provides a temperature Ti+ above T0, melting occurs. The amount of melted mass, Mmelt,i, is limited either by the available energy (related to Ti+) or by the solid mass present in the layer before melting, denoted as Ms,i (in J m⁻²): 6Mmelt,i=min⁡(cIρi(Ti+-T0);Ms,i)

Equation () is evaluated for all layers to determine if a layer melts completely within a time step. If multiple layers are melting, multiple iterations are performed.

In our implementation, the melt calculation (Eq. ) remains unchanged, but the fate of the melted mass Mmelt,i is modified as Mmelt,i is stored in Mbuff. Meltwater from all layers in the ice column is accumulated in this buffer, regardless of depth. As melting is confined to the uppermost layers (typically the first few centimeters in our simulations) due to the absence of basal flux and attenuation of penetrating shortwave radiation, this approach avoids the need to define an arbitrary depth threshold in the code.

Then, the total mass of layer i is defined after melting (including both solid and liquid fractions) as Mi (in J m⁻²). After melting, the depth and total density are updated based on the change in solid mass: 7zi+=zi-Ms,i-Mmelt,iMs,i8ρi+=Mi-Mmeltzi+ ρi accounts for both the solid and liquid fractions of the layer. In contrast, the model also defines a “dry density”, denoted as ρdry,i (kg m⁻³), which represents only the solid fraction. As the melt is stored within the buffer outside the layering system, it is considered in the total density calculation which includes the liquid fraction.

Finally, the layer temperature, Ti, is updated to account for the cooling effect of the phase change: 9Ti+=Ti--MmeltcIρdry,izi-

Refreezing depends on the availability of stored liquid water in the buffer and the energy deficit of the first layer. The refrozen mass, Mrefrz (in J m⁻²) is expressed in Eq. (): 10Mrefrz=min⁡(Kbuff+Δt,MbuffLm) where Lm is the latent heat of ice fusion (3.337 × 10⁵ J kg⁻¹).

A positive Kbuff+ indicates that heat is conducted from the buffer to the first layer, meaning the first layer is sufficiently cold and/or the buffer is thin enough for a phase change to occur. If the energy deficit in the first layer exceeds the available liquid water, the excess energy is redirected to the first ice layer. This ensures that any heat not used for refreezing in the buffer contributes to cooling the ice column, thereby affecting the energy state of the glacier surface layer. The temperature of the first layer is then updated as follows: 11T1+=T1--min⁡(0,Kbuff+Δt-Mrefrz)cIρizi

When refreezing occurs, the liquid water in the buffer is converted to refrozen ice. This process increases the surface mass of the glacier, directly impacting its mass balance, and alters energy exchanges.

The model determines whether to create a new surface layer or aggregate the refrozen mass with the existing surface layer. If the refrozen mass Mrefrz is thick enough (greater than 1/10 of the first layer thickness), a new refrozen ice layer is created at temperature T0 with a density of 917 kg m⁻³. Otherwise, Mrefrz is aggregated into the existing surface layer at its temperature.

To track the proportion of refrozen ice within the upper layers and properly compute albedo, a refreezing fraction variable rfrac,i is introduced for layers i∈[1,2]. This variable ranges between 0 (bare ice) and 1 (fully refrozen ice) and is calculated differently depending on the refreezing scenario: when a new layer is created, the new surface layer receives rfrac,1 = 1, while when refrozen mass is aggregated with an existing layer, rfrac,1 is calculated as a weighted average based on the relative thicknesses of the refrozen and existing ice. The variable rfrac,i remains stored between time steps, allowing the albedo calculation to account for the presence of refrozen ice in the surface layers. When melting occurs in layer i, rfrac,i is reset to 0, assuming the refrozen layer melts first.

A detailed description of the layer management strategy, numerical thresholds, and the mathematical formulation of rfrac,i can be found in the Supplement, Sect. S3.

In the default version of Crocus, ice surface albedo is handled by dividing incoming solar radiation into three distinct spectral bands ([0.3–0.8], [0.8–1.5], and [1.5–2.8] µm), with a constant albedo value prescribed for each band. The spectral albedo is used to attenuate incoming radiation in each band, and the remaining energy penetrates into the ice and is gradually absorbed, following an exponential decay with depth. Originally, ice albedo in Crocus was treated as a fixed value, independent of depth or surface conditions. However, the model architecture allows for albedo computation across the top two layers of the surface. Building on this, the present study introduces a modified scheme that enables the prescription of distinct albedo values for each of these layers, depending on surface conditions (bare ice, refrozen ice, or ice with liquid water). In this modified configuration, albedo is computed based on the properties of the first two layers, allowing for a more realistic representation of varying ice surface states.

The albedo calculation is updated to also consider the presence of liquid water and refreezing ice. When surface liquid water is present (as indicated by a non-zero Mbuff), the first layer albedo follows Eq. (). 12α1=xαwat+(1-x)(rfrac,iαrefrz+(1-rfrac,i)αice) where i∈[1,2] refers to layers 1 or 2. Without liquid water, the first layer's albedo is determined using Eq. (). The albedo of the second layer, meanwhile, always follows Eq. (). 13αi=rfrac,iαrefrz+(1-rfrac,i)αice For snow-covered surfaces, the classic albedo parameterization is maintained, with values dependent on optical diameters and layer age .

Due to the lack of observational albedo data for liquid water over ice surfaces and for superimposed ice on mountain glaciers, as well as the potentially high spatial variability, no fixed values can be prescribed. As a result, the choice of albedo values is fully user-defined. The specific albedo values adopted in this study are presented in Sect. . Given the critical influence of albedo on energy balance, sensitivity tests are conducted (Sect. ), and this aspect is further discussed in Sect. .

Crocus was run at a point scale, at the AWS located on the ablation area of Mera Glacier, for the years 2016–2017, 2019–2020, 2020–2021 and 2021–2022. Model runs with a 15 min temporal resolution, using default parameters and scheme processes as presented in . Simulations ran from 1 November to 1 November each year and used two distinct configurations: an unmodified base version (R18 as described in ) and our updated version incorporating buffer implementation (BV). A 60 m column of temperate ice (7 layers at 273.15 K) with a density of 917 kg m⁻³ was used as initial conditions. In order to illustrate the diurnal cycle of the buffer, results are presented at first over four days (from 1 to 5 April 2022), during which bare ice is exposed. Then, other periods are considered for the impact at annual scale.

The parameter values used for all simulations are summarized in Table . The ice albedo value is set based on available observations and is consistent with the findings of (Fig. S2 in the Supplement). However, due to the lack of observational albedo data for the specific surfaces, two sets of simulations are performed. In the first setup (simulation named BV_default), a fixed albedo value was applied to all three surface states: bare ice, refrozen ice, and liquid water over ice. This approach was chosen to limit their differentiated impact in order to better explore the effect of the other parameters (Sect. ). In the second setup (simulation BV_albedo), distinct albedo values were prescribed for each surface type, and analysed over the 2021–2022 period. Values have been chosen in agreement with literature. Supraglacial water reduces the albedo by about -20 % e.g.,, and thus the albedo of liquid water over ice is decreased to 0.28 in the model. On the contrary, superimposed ice generally leads to an increase in albedo and is set to 0.43 (i.e. an increase of 23 %, following ). The other variables have been arbitrarily chosen and sensitivity tests are performed as described in the following section.

The default simulation (BV_default) is compared to observations (see Fig. S3 and Table S1 in the Supplement). While some biases are observed in simulated mass balance, the surface temperature at the AWS shows very good agreement with observations, with a mean bias of 0.34 °C without systematic bias. In particular, the model accurately captures the timing of temperate ice conditions, which is critical for assessing surface energy processes. All details regarding model calibration and evaluation, including a thorough discussion of their implications for this study, are provided in the Supplement, Sect. S2.

To assess parameter sensitivity (Sect. ), tests were conducted on fraction x, drainage coefficient, maximum buffer thickness, and surface state albedo (see Table ) for the 2021–2022 period. Note that fraction x excludes 0, as the presence of a buffer without any impact on the thermal profile is not physically meaningful. The drainage coefficient was tested across its full range, with a finer resolution between 0.9 and 1 to better capture its influence on water retention and drainage. The sensitivity to the maximum buffer thickness was explored up to 50 cm to define the limits of the model's applicability. Albedo of liquid water over ice varies up to 70 % following and albedo of the refrozen ice up to 60 %, to explore a broad range of possible surface conditions, accounting for the high uncertainty in these values.

When comparing the mass balance simulated with BV_default and with R18, at the AWS of Mera Glacier over the four studied years (Fig. ) we find that, on average, incorporating the buffer leads to a less negative annual mass balance, with a mean difference of 0.16 m w.e., corresponding to approximately 4 % of the annual mass balance. This impact varies by year, ranging from 0.1 m w.e. (3 %) to 0.20 m w.e. (6 %) of the annual mass balance (see Table ). If the albedo of liquid water over ice and refrozen ice are different from the albedo of the ice, the BV_albedo version will not lead to a significant difference (less than 1 %, see Fig. S4 in the Supplement S4). Sensitivity tests will provide further explanation in Sect. .

The influence of the buffer implementation on mass balance exhibits strong seasonal dependence. During the pre-monsoon period (March to June, before the transition), simulations with BV_default version results in a more negative mass balance than R18, with a mean difference of 0.07 m w.e. as the buffer increases energy absorption and accelerates melt rates. However, at the onset of the monsoon season (June–July), this trend reverses, with BV_default consistently showing a less negative mass balance. The buffer's capacity to retain and refreeze water becomes increasingly influential, particularly during nocturnal cooling periods. The refreezing process effectively restores mass to the system, counteracting daytime ablation. Our results show that in BV_default refreezing accounts for approximately 25 %–40 % of the daily melt volume during typical monsoon periods. This cumulative effect ultimately leads to a lower annual mass loss when simulated with BV_default compared to R18.

The thermal structure of the glacier explains these seasonal differences in mass balance between models. The temperature profiles at 6 p.m. (Fig. ) reveal contrasting behavior between pre-monsoon and monsoon periods. During pre-monsoon (24 March 2022), BV_default (purple thick line) maintains a temperate surface that rapidly cools to 266 K at 3 m depth before warming to 271 K at 8 m. In contrast, R18 (purple dashed line) exhibits a colder surface (267 K) that quickly warms to 273.15 K at 0.7 m depth before converging with temperature simulated by BV_default, at greater depths (8 m).

During pre-monsoon periods, R18 handles the warming of the ice column differently than BV_default. In R18, meltwater refreezes immediately in the deeper cold ice layers until the entire column becomes temperate. This process effectively traps heat within the ice column through latent heat release at depth. In contrast, BV_default confines water to the surface where it refreezes only during nighttime cooling periods. This fundamental difference in thermal energy distribution causes BV_default to maintain a warmer surface temperature while limiting heat transfer to deeper layers. This warming effect dominates early in the season, primarily because the thermal profile of the glacier still reflects cold winter conditions.

During monsoon (7 July 2022, green lines), both model versions show nearly identical thermal profiles, with R18 maintaining 273.15 K throughout, while BV_default shows only minor cooling to 272.08 K between 0.6–0.8 m. This thermal homogeneity eliminates R18's ability to refreeze meltwater at depth, while BV_default continues to benefit from nocturnal surface cooling. As the monsoon progresses, the buffer's role shifts as its refreezing capacity becomes increasingly influential, counteracting daytime ablation and reducing overall annual mass loss by 0.1–0.2 m w.e. depending on meteorological conditions. This seasonal transition from a “melt-dominated” regime to a “refreeze-dominated” regime explains the reversal in mass balance trends between the two model versions.

Figure  shows the seasonal evolution of the mass balance over the different periods of the hydrological year 2021–2022. Each subfigure corresponds to a representative 7-days period for the winter, pre-monsoon, monsoon, and post-monsoon seasons, highlighting the key differences between the model versions (BV_default and R18).

Winter period

During the winter period (December to March), the buffer remains inactive as the surface is entirely covered by snow throughout the sub-period (hatched area). Additionally, the consistently low temperatures (mean daily surface temperature: -10 °C) prevent melting, and the absence of rainfall results in no significant mass fluxes. As a consequence, no differences are observed between model versions during this season (Fig. a).

The drainage coefficient significantly influences liquid water retention and associated mass balance components. Figure a shows how drainage values affect the buffer water content, with higher retention (coefficient near 1) maintaining maximum water content of 10 mm w.e., while lower retention (coefficient of 0.3) reduces maximum content to 0.5 mm w.e.

The drainage coefficient regulates the balance between refreezing and melt volumes (Fig. b). A high coefficient (0.995) increases refreezing by 98 % compared to a low coefficient (0.5) due to greater liquid water retention in the buffer. During this period, R18 exhibits total melt of 0.27 m w.e., while BV_tests shows reduced melt between 0.22–0.23 m w.e., demonstrating the buffer's protective role.

The combined effects of additional refreezing and reduced melt directly impact mass balance outcomes. Lower drainage coefficients produce more negative mass balances (-0.22 m w.e. for coefficient 0.3 versus -0.15 m w.e. for coefficient 0.995). Under high drainage conditions (coefficients 0.3 to 0.8), the final mass balance becomes nearly identical between models (-0.22 m w.e. for both). However, under low drainage conditions, BV_tests produces a significantly less negative mass balance (-0.15 m w.e.) compared to R18 (-0.22 m w.e., 31 % difference), highlighting how low drainage enhances refreezing and mitigates mass loss.

We tested the sensitivity of the mass balance to variations in the maximum buffer capacity (zmax,buff) and the drainage coefficient (D). Across all tested values, the maximum difference in annual mass balance was 0.84 m w.e., representing 17 % of the annual mass balance (Fig. ).

Drainage coefficient sensitivity shows a threshold-dependent response. For values below 0.8, the influence on mass balance remains limited (differences < 0.1 m w.e. across simulations). However, for coefficients exceeding 0.8, the mass balance becomes progressively less negative as D approaches 1. At D=0.95 and zmax,buff > 3 mm, the reduction in mass loss reaches -4.16 m w.e. compared to -4.64 m w.e. in R18 or -4.04 m w.e. in BV_default with D=0.995.

The sensitivity to zmax,buff is more pronounced for values between 10⁻³ and 3×10-2 m, where an increase of 0.01 m w.e. in the maximum capacity results in a 10 % less negative mass balance.

Beyond zmax,buff=0.01 m and D=0.9, the mass balance stabilizes around -4.0 m w.e., indicating a saturation point where further parameter increases have negligible effect. This suggests physical limits on water storage and drainage efficiency.

We systematically evaluated mass balance sensitivity across albedo values for both refrozen ice and liquid water on ice. The results obtained demonstrate that the albedo of liquid water on ice exerts a dominant influence on annual mass balance, with higher albedo values resulting in significantly less negative mass balances (ranging from -4.71 to -4.17 m w.e.; Fig. a). This represents a 11 % variation in annual mass balance across the tested range. Conversely, variations in refrozen ice albedo produce minimal impact (<0.1 m w.e., less than 2 % variation) across the same albedo range. This sensitivity difference stems from contrasting surface exposure durations: refrozen ice persists for only 2-3 h before melting and is mainly a thin layer, while liquid water-covered ice remains exposed for approximately 80 % of the surface time from March to October (see the Supplement, Sect. S5). However, the albedo effect of liquid water is moderated by the fraction x, which weights the relative contributions of ice albedo and liquid water albedo in the overall albedo calculation.

The influence of albedo is contingent on surface state, and thus season. By selecting a period in which the majority of the surface is composed of refrozen ice, as illustrated in Fig. b, a significant influence of the refrozen ice albedo can be observed (up to 4 % variation during this period). During that period, liquid water over ice exerts a similar influence (up to a 4 % variation). During periods when liquid water over ice dominates (Fig. c), which means that liquid water over ice occurs for more than 60 % of the of the time during this subperiod, the variation is similar to the annual graph, with liquid water albedo showing an even more dominant influence (up to 18 % variation over the period).

The annual scale sensitivity test is particularly influenced by periods of significant mass balance changes. In March, the albedo effect of refrozen ice may be a contributing factor to mass balance variations; however, the magnitude of these variations is comparatively negligible in relation to those observed during pre-monsoon or monsoon periods, when liquid water becomes the predominant surface state.

The buffer implementation models surface water retention on glaciers while balancing realism with computational feasibility. Built on the Crocus framework within a 1D approach, this implementation offers key advantages for numerical modeling, particularly maintaining scheme stability through end-of-timestep heat flux calculations and representing inherently sub-grid processes. The approach captures surface water heterogeneity within individual grid cells while preserving computational efficiency and numerical robustness.

For energy balance calculations, our implementation assumes that ice remains the dominant surface material, even when liquid water is present. We treat the surface as ice for all energy balance processes except albedo and thermal conduction. This approach avoids significant changes to the model, since water coverage remains minor relative to ice coverage (i.e. <20 % in this study). However, it introduces limitations when large amounts of water accumulate in the buffer layer that could invalidate our energy balance assumptions. Water substantially alters surface energy fluxes by changing surface roughness, turbulence patterns and radiation properties . These changes would imply that the surface should be treated as water-dominated rather than ice-dominated. In order to maintain the validity of our ice-dominated assumption, we deliberately limit the maximum reservoir capacity to 0.01 m w.e., ensuring that ice characteristics dominate the surface energy balance. The fraction x further modulates water storage to maintain a reasonable ice-surface assumption. The sensitivity to these parameters will be further discussed in Sect. . In order for the hypothesis to remain true, users must be careful about the choice of parameter values. For example, the model is not adapted for an x over 0.5.

The buffer response to snowfall and freezing rain presents a minor limitation due to the small volumes of liquid water involved. Our current implementation assumes that snowfall and freezing rain immediately empties the buffer, preventing mixed phase interactions. While reasonable for heavy snowfall, this assumption may not hold for light snowfall where liquid water could warm and partially melt new snow. At Mera Glacier, freezing rain occurs infrequently (25 events, draining 0.01 m w.e.), but snowfall-driven buffer drainage is more common (53 events, draining 0.15 m w.e.), particularly during the monsoon. The potential impact of incorporating energy exchanges would depend on precipitation, temperature and intensity, with outcomes ranging from additional liquid water refreezing to partial snow melting. However, given the relatively small buffer volumes involved (maximum capacity of 0.01 m w.e. by default), it is likely that this refinement would produce only minor adjustments to annual mass balance calculations without altering fundamental melt patterns.

Our model currently uses constant parameter values throughout the season, but temporal evolution would improve realism for glacier-scale hydrological studies. Both D and zmax,buff could be parameterized as functions of seasonal conditions rather than constant values. This approach would better capture the natural evolution of glacial drainage systems. Observational studies support the importance of seasonal drainage evolution. documented seasonal drainage system evolution in the Alps and found that drainage efficiency increases as the ablation season progresses. observed distinct seasonal phases in supraglacial hydrology on debris-covered Nepalese glaciers. They found inefficient early-season drainage that evolves into well-developed channel networks later in summer. Our model does not yet capture such temporal dynamics. However, it is not necessary to take this temporal dynamic into account, since we are studying surface processes where water percolation is not considered. Future studies using this implementation for detailed hydrological analysis or glacier-wide applications might need to incorporate seasonal parameter evolution.

While Crocus is primarily designed for snowpack modeling, this work advances its generalization to represent the snowpack-glacier continuum within a single framework. A typical challenge when representing snowpack and glacier as a single column involves treating liquid water percolation, which fundamentally differs between porous, permeable snow and dense, impermeable ice. Due to their specific focus and temporal scope, previous Crocus glacier studies, such as those focusing on snowpack processes (e.g., in the Andes) or covering short periods and glacier-wide (e.g., at Saint-Sorlin glacier), are likely only negligibly impacted by this implementation. However, longer-term studies focusing on the Saint-Sorlin glacier over extended periods, such as , may increasingly experience impacts from this process. Specifically, discussed the importance of liquid water at the ice surface for the energy balance. These earlier studies ended in the 2000s or 2010s when melt rates were lower and ablation zones are bigger, resulting in more ice surface exposed . There was therefore less surface water and a reduced need for this implementation. However, most current snow-ice models lack proper representation of surface water storage on ice. This limitation may significantly impact recent and future studies of glacial ice under current and projected climate conditions. Future mass balance modelisation studies should include this process, especially in long-term projections, which, to the best of our knowledge, are not currently taken into account.

This analysis focuses on an important surface process that occurs on a fine scale, affecting only a small proportion of the grid cell (the fraction x). However, it has an annual impact up to 6 % on a single point on Mera Glacier. Future work would be to scale up this implementation both spatially and temporally across entire glaciers. This phenomenon might have a greater impact in regions with more rain or in zones of ablation with longer ice exposure during the year. Applying this buffer approach to any mountain glacier would provide insight into the potential for significant impacts under future climate scenarios, particularly given the evolving rain-snow limit and its effect on the precipitation phase . However, such large-scale applications require thorough observations of the processes involved, particularly albedo measurements, in order to properly constrain and validate implementation in diverse glacial environments.

x is constrained to ensure physical consistency in the surface energy balance. Most surface energy fluxes are computed assuming an ice-covered surface, except for albedo and thermal conduction. However, when the liquid water fraction becomes too large, this assumption no longer holds. To prevent this inconsistency, we advice limiting x to values below 0.5, which ensures that ice remains the dominant phase in each grid cell. Sensitivity tests were performed on x, but with x lower than 0.5 and for D=0.995 (not shown), the sensitivity is lower than 2 % and is largely dependent on the albedo values chosen for the different surfaces.

This limit is in agreement with some existing observations. For example, melt pond fractions above 0.5 are rarely reported during the Arctic melt season . provide specific measurements of pond fractions (related to the parameter x described in Sect. ) from Greenland. Given that these observations originate from Arctic regions (typically flatter than mountain glacier environments) the derived thresholds may be overestimated in the context of our study. Nevertheless, such values are expected to be strongly site-specific and not readily transferable, underscoring the need for local observations to ensure accurate calibration.

The sensitivity to D is particularly influential, controlling the residence time of liquid water and subsequently affecting both energy absorption and refreezing. Variations in D by 10 % alter annual mass balance by up to 10 % in our simulations (see Sect. ), aligning with findings from or who identified drainage parameters as critical factors in melt pond evolution on sea ice.

In Greenland ice sheet models, similar drainage coefficients typically range from 0.8 to 0.995 , with MAR commonly using values close to 0.995 combined with a maximum residence time of 18 h (version 3.14) to ensure that liquid water does not remain longer than one night. However, glacier environments differ substantially from ice sheets in their surface roughness, slope, and drainage networks. documented highly variable drainage efficiencies in mountain glaciers, suggesting that a single static drainage coefficient may oversimplify actual conditions.

Due to the high sensitivity and possible significant spatial variability of this coefficient, which make it site-dependent, we recommend careful selection of its value and conducting sensitivity tests to ensure its relevance for the specific study site.

zmax,buff establishes critical thresholds for water retention with clear implications for model sensitivity. Values exceeding 0.01 m lead to limited additional impact on mass balance (Fig. ), providing useful constraints for future model implementations. To our knowledge, no direct field observations of surface water pond heights exist for temperate mountain glaciers similar to our study site, highlighting a knowledge gap that our findings could help address. Existing literature on surface water depths provides context but from very different glaciological settings. report depths of 0.2–3 m of supraglacial melt ponds, while suggest approximately 15 cm of meltwater storage in porous ice in Greenland. Similarly, studies by in Svalbard and on debris-covered glaciers examine different water systems that differ substantially from our temperate mountain glacier context. Although region-specific observations would help to refine estimates of buffer capacity, the results of the sensitivity tests suggest that constraining water storage to 0.01 m is a justifiable and practical assumption in the absence of additional observations.

Albedo is the most sensitive parameter requiring observations for accurate calibration. While the parameter D shows the strongest influence across the full tested range, this effect becomes less dominant when D is restricted to more realistic values (i.e. >0.95). In that case, albedo variations have the greatest impact, leading to up to 18 % change in mass balance. This is consistent with numerous studies identifying solar radiation as the primary energy source controlling glacial melt rates e.g.,. Our results specifically show that changes in the albedo of the three surface types we model – bare ice, liquid water on ice, and refrozen ice – can significantly alter annual mass balance, with variations in liquid water albedo alone changing mass balance by up to 18 % (Fig. c). This sensitivity emphasizes the importance of accurately representing the optical properties of these different ice surface conditions, as current observational gaps contribute to limited understanding.

Bare ice albedo has been characterized using both satellite-based observations and in situ measurements. While remote sensing enables large-scale monitoring of ice albedo e.g.,, it struggles with liquid water on ice or refrozen ice surfaces due to constraints in spatial resolution and spectral signature. Conversely, in situ broadband measurements provide precise point-scale data, yet they are inadequate to represent the pronounced spatial and temporal heterogeneity observed on glacier surfaces . Additional observations aimed at characterizing the albedo of liquid water and refrozen ice surfaces would require dedicated field campaigns and careful methodological design.

The optical properties of ice surfaces with or without liquid water are highly complex and dynamic. Field measurements by and more recent work by demonstrate that liquid water on ice surfaces can reduce albedo by 20 %–70 %, depending on water depth, substrate characteristics, and impurity content. Our sensitivity testing range of 0.1–0.35 for liquid water albedo encompasses these observations but highlights the need for site-specific measurements to constrain this parameter. The albedo reduction occurs because water fills surface irregularities, creating a smoother surface that reduces light scattering and increases absorption . The refrozen ice presents additional complexity in albedo representation. Our simulations test refrozen ice albedo values from 0.35–0.55, based on observations by who found that refrozen ice can increase albedo by up to 23 % compared to bare ice.

However, the impact of refrozen ice albedo is limited, in our model, as these surfaces persist for only 2–3 h before re-melting and mainly represent a thin layer with a very low rfrac,i on average (see Fig. S5 in the Supplement, Sect. S5). Under different meteorological conditions, this effect might be more significant. It is also important to note that sensitivity tests are performed on Mera Glacier, which exhibits a relatively high bare ice albedo (0.35) compared to many other glaciers (e.g., 0.15–0.2 at Saint-Sorlin Glacier ). As a result, the sensitivity observed in this study may be underestimated, underscoring the importance of careful calibration of albedo values in model applications.

Additionally, other surface characteristics, such as surface roughness, introduce complexity in accurately measuring and interpreting albedo. For instance, , , and showed that micro-scale surface roughness can alter albedo independently of water content by changing the effective angle of incidence for solar radiation. Crocus currently uses a constant roughness parameter, which limits its ability to capture temporal and spatial variations in surface characteristics. Furthermore, the effect of impurity content and biological activity linked to surface liquid water conditions would deserve dedicated study. Light absorbing impurities such as mineral dust and black carbon significantly reduce ice albedo e.g.,, yet their interactions with liquid water at the ice surface remain poorly documented. Liquid water potentially facilitates both impurity accumulation through ponding and biological growth . Our model does not currently account for these processes, potentially underestimating albedo reduction in certain scenarios.

Finally, the temporal evolution of surface conditions also challenges albedo parameterization in glacier models. documented substantial diurnal and seasonal variations in ice albedo related to changing surface conditions, while and emphasized measurement biases related to solar zenith angle and surface slope. Our model applies fixed albedo values for each surface state, neglecting these temporal dynamics. Future improvements could incorporate time-dependent albedo evolution to better capture these processes.

Whether to improve the parameterization of albedo values for different surface types in the model or to advance the albedo scheme for better representation of spatial and temporal variability, targeted and dedicated field measurements are essential.

The buffer layer implementation is based on physical representations of water retention at the ice surface (water accumulation, thermal exchange, albedo modification, drainage, and refreezing) and was developed without region-specific calibration to remain broadly transferable. However, buffer parameters still require site-specific tuning, as they depend on local conditions (e.g. glacier geometry, surface topography, climate conditions). For instance zmax varies with surface roughness and microtopography, D reflects local drainage efficiency influenced by crevasse density or channel development, x adjusts for surface water coverage (constrained to x<0.5 to maintain ice dominance), and albedo values depend on sediment concentration, ice crystal structure, and impurity content e.g.. Additional care may be needed for instance for polar regions due to the prevalence of superimposed ice formation and the potential for seasonal meltwater storage within ice layers , which differ from the surface-only water storage represented by the buffer. Consequently, parameter calibration requires careful tuning to ensure reliable model performance and parameters are intentionally left free for users to adjust, preferably calibrated with local observations to ensure the proper functioning of the buffer approach.

More generally, the question of model transferability applies to Crocus beyond its original alpine context . Although built on a robust physical basis, Crocus still requires calibration when applied in contrasting climatic environments. Previous studies have demonstrated its use in regions such as the tropical Andes e.g. and the Arctic e.g. where adjustments to some key processes (e.g. fresh-snow density or thermal-conductivity parameterizations) were necessary. In the present study, however, only the ice surface is considered, which makes the approach more easily transferable for the specific case of surface meltwater retention.

Our results demonstrate that buffer physics reduce annual mass loss of Mera Glacier by 0.1–0.2 m w.e. under current climate conditions, with implications that will intensify under future warming scenarios. As global temperatures rise, high mountain regions will experience increased melting and shifts in the snow-rain limit . The frequency and intensity of precipitation events at glacier elevations are expected to increase , potentially enhancing liquid water availability for surface water retention processes.

Climate warming will significantly increase the importance of surface water processes on mountain glacier mass balance. indicate that a 2 °C temperature increase will likely result in mass losses between 49 %–64 % in the Himalayan region, consequently increasing supraglacial water accumulation due to enhanced melt rates. Under such conditions, buffer effects could substantially modify mass balance responses, with prolonged meltwater retention potentially mitigating short-term ablation through refreezing processes.

The increased presence of liquid water on glacier surfaces creates a complex competition between opposing processes affecting mass balance, as shown in this study. On one hand, liquid water accelerates melting through reduced albedo and enhanced conduction during “melt-dominated” regimes when surface temperatures remain consistently above freezing. On the other hand, refreezing processes add mass through buffer formation during “refreeze-dominated” regimes when diurnal or seasonal temperature cycles promote ice formation. This competition between melt enhancement and mass addition through refreezing represents a fundamental control on glacier response to warming. This new implementation is essential for a better understanding of this phenomenon and for constraining it for future projections.

Regional variations in accumulation patterns will significantly influence how buffer processes respond to climate change. Summer accumulation glaciers, such as those found in the Andes or the Himalayas , receive most of their snowfall during the warm and wet season, when melting also occurs. This means that snow can fall while the glacier is already melting. In contrast, winter accumulation glaciers like those in the Alps get most of their snowfall during the cold season, when limited melt occurs. Warming trends may progressively shorten the duration of refreezing phases during ablation seasons, as already observed on low-elevation Alpine glaciers , while simultaneously increasing the frequency and persistence of surface water. This shift would enhance melt through feedback associated with water's lower albedo compared to bare ice, potentially reducing the net mass-conserving effect of buffer processes.

The net impact of these competing processes likely varies substantially with regional climate and topographic context, making buffer effects difficult to predict without site-specific analysis. This variability underlines the need for comparative, multi-site studies to better constrain the role of surface water retention in glacier mass balance evolution under different climate scenarios and to determine whether buffer processes will serve as a significant feedback mechanism in future glacier response to warming.