The physics of snow is very complex. The snow layer in SAMSIM is intended to simulate only the most basic aspects of snow on sea ice. In contrast to the widely used 1-D thermodynamic sea-ice model of , which is implemented in both the Los Alamos (CICE) and the Louvain-la-Neuve sea-ice models, snow does not turn directly into meltwater in SAMSIM. Instead, melted snow from the snow surface percolates downward and accumulates on the sea-ice surface, forming a slush layer of depth B as illustrated in Fig. . This snow-to-slush conversion in SAMSIM is based on two core assumptions. The first assumption is that the snow can only retain a maximum liquid mass fraction (ψl,max) which is a function of the snow solid mass fraction. The function we use is ψl,max=0.057(1-ψssnow)ψssnow+0.017, which we take from the laboratory study of . In Fig.  the volume fractions are shown instead of the mass fractions because the volume fractions are proportional to the area depicted.

The second core assumption is that when the liquid water content surpasses the retainable amount, the excess water pools at the bottom of the snow layer, forming a layer of slush. At each time step the depth of the slush layer is determined and then the slush layer is added to the top ice layer. Since the slush layer is merged with the top ice layer as soon as it forms, there is never a slush layer present at the beginning of the following time step. As such, the slush layer is not a physical representation of any physical material but instead a means to transform the model definition of snow into the model definition of sea ice. However, as the model definition of sea ice does not limit the liquid fraction, the sea ice can be in a condition which could be referred to as slush.

Two additional assumptions are required to determine the slush depth which is marked as B in Fig. : the gas fraction of the slush ϕg,melt and the solid fraction of the slush layer and remaining snow layer. We assume that the solid volume fraction equals the solid fraction of the previous time step and that ϕg,melt is a constant. In this paper we set ϕg,melt to 20 %, which we base on the measured surface sea-ice densities of .

Following these assumptions, when the liquid volume fraction of the snow layer exceeds ϕl,max, the slush depth B is calculated from the snow solid fraction of the last time step (ϕssnow) and the gas content as B=△zϕlsnow-ϕl,max1-ϕl,max-ϕssnow-ϕg,melt.

As a result, the top ice layer grows thicker by B, and mass and enthalpy are transferred according to the composition of the slush layer. To maintain the solid fraction of the last time step, the snow needs to be reduced in thickness by A as illustrated in Fig. . In total, the snow-to-slush conversion shrinks the snow layer by A+B, the total snow and ice column shrinks by A, the top ice layer grows by B, and the snow layer retains its density.

To our current knowledge, the approach of converting snow into slush before it can run off as meltwater is unique. Compared to the standard approach, in which snow melts at the top of the snow layer and immediately runs of as meltwater, our approach leads to a slight delay in the onset of flushing. This delay is because our approach requires the whole snow layer to convert to the model definition of sea-ice via slush formation before runoff occurs.

In reality, sea ice has a varying surface height, which causes the meltwater in the slush to flow into melt ponds. In SAMSIM, by the time the snow layer has melted away, the top model layers that were formed by snow-to-slush conversion are predominantly liquid and salt free but also contain the solid fraction of the meltwater-soaked snow. These top ice layers can be interpreted as a spatial average over melt ponds and snow remnants. As a result the snow melt stage of SAMSIM is shorter than the first melt stage of because not all of the latent heat which resided in the snow layer before the onset of melt needs to be released before the snow layer disappears in the model. Although the implemented snow-to-slush conversion neglects many of the finer aspects of snow physics, our approach, by having some interaction between the meltwater which forms at the snow surface with the underlying snow, captures snow melt somewhat more realistically than the standard approach of turning snow directly into meltwater.

Two additional processes also convert snow to slush: flooding as introduced in Sect.  and meltwater wicking. Wicking occurs when the top ice layer is so liquid that excess brine seeps into the snow. This process is incorporated into the model as introduced in the following subsection.

Surface ablation in general refers to an ice-thickness decrease at the surface. Surface ablation is by necessity linked to a flux of melted ice away from the ice surface. In SAMSIM, surface ablation occurs when liquid from the top ice layer is removed via flushing. In this subsection we describe how SAMSIM determines how much liquid is available to be removed from the top layer, what the properties of this liquid is, and how this liquid interacts with the snow layer and the top ice layer.

To describe this clearly we must first clarify how meltwater is defined in SAMSIM. The model definition of meltwater is the liquid in the top layer with the ability to leave the top layer. This ability distinguishes meltwater from the rest of the liquid in the top layer. Otherwise meltwater is identical to the remaining liquid in the top layer (i.e. temperature, salinity, density). Meltwater is assumed to be located on the ice surface in the top sea-ice layer as a thin film. The meltwater film is a part of the top layer, and its thickness is △zmelt as shown in Figs.  and .

The amount of meltwater which is present in the top layer is a diagnostic variable which is computed at each time step independently of the amount of meltwater in the previous time step. As the amount of meltwater determines the meltwater film thickness, the thickness is also calculated anew at each time step.

Meltwater can leave the top layer via two processes. The first process is via parametrized flushing, which is detailed in Sect.  and . Flushing leads to surface ablation because the thickness of the top layer is reduced by the thickness of the meltwater film when the water flushes away. The second process by which meltwater can leave the top layer is via wicking into the snow layer, as explained at the end of Sect. .

SAMSIM relies on three assumptions to diagnose meltwater amount and thickness. The first is that ice melted at the surface of the top sea-ice layer instantly turns into meltwater. The second is that if the solid fraction of the top ice layer sinks below a minimal low value, excess brine turns into meltwater. The third is that over time the gas fraction increases until it reaches the value of ϕg,melt. The first two assumptions determine how much meltwater is available in the top layer, while the third assumption influences how thick the melt film is.

SAMSIM determines if melting occurs at the ice surface by analyzing the heat fluxes at the surface. As soon as the surface temperature surpasses the freezing temperature given by the bulk salinity of the top ice layer, meltwater can form. The amount of meltwater formed is determined by the amount of latent heat release necessary to balance the energy difference between the atmospheric heat flux to the surface and the flux from the surface into the top ice layer (depicted in Fig. ). This approach is commonly used in sea-ice thermodynamic models e.g. but needs to be adapted to incorporate the varying density and gas fraction of SAMSIM. The discretized diffusive heat flux from the ice surface into the top ice layer is q1=-k12Tfreeze-T1△z1.

The thermal conductivity of the top ice layer k1 is a linear combination of the liquid and solid phases, while the gas phase is treated as an insulator. The depth of the meltwater film for a given atmospheric energy flux qatmos is then △zmelt=qatmos-q1ϕs1ρsL.

The second way meltwater can form is when the solid fraction of the top ice layer ϕs1 falls below a minimal low value ϕs,melt. When this occurs the solid fraction ϕs1 is rearranged by △zmelt until ϕs1 reaches ϕs,melt, as shown in Fig. . From volume conservation it follows that △zmelt=△z11-ϕs1ϕs,melt.

This second way of forming meltwater ensures that meltwater forms before the top ice layer is fully liquid. Not shown in the Fig.  is that a similar limit exists on the gas fraction which arises from our third assumption that the gas fraction increases to a specific value over time. If the gas fraction exceeds ϕg,melt then the top ice layer is compacted to reduce ϕg1 to ϕg,melt, which also slightly increases the density of the top layer. ϕg,melt is the same parameter which determines the amount of air captured in the slush during snow melt and is set to 0.2 based on density measurements at the surface of . To our knowledge there are no measurements from which to estimate ϕs,melt. As first guess we assume a value of 0.4, which is slightly above the solid fraction assigned to fresh snow in SAMSIM. If meltwater forms primarily due to low solid fractions, the top ice layer will approach the given values of ϕg,melt and ϕs,melt over time.

If the meltwater forms due to a low solid fraction while snow is present, the meltwater is assumed to wick up into the snow and creates a slush layer which is then added to the top ice layer again. We refer to this as wicking, and it is similar to snow melt (Fig. ). The difference between wicking and snow melt is that in wicking the amount of water available to form slush is given by the amount of meltwater present in the top ice layer, while in snow melt the amount is given by how far the liquid fraction of snow exceeds the threshold limit.

The first and only published flushing parametrization incorporated in a full thermodynamic sea-ice model by assumes that once the ice reaches a certain permeability, a fraction of the meltwater flows downward through the sea ice and into the ocean below. Although this approach neglects many aspects of flushing, it is able to reproduce field measurements of salinity . In this subsection we will introduce two parametrizations. The complex parametrization attempts to model flushing as a physically consistent hydraulic system, and the simple parametrization is a numerically cheap alternative based on the assumption that the liquid fraction increases towards the surface during surface melt.

It is known from the field observations of that much of the brine movement during flushing occurs horizontally in the upper layers. Once the horizontally flowing meltwater reaches a flaw or crack it drains below the sea ice, which can lead to underwater ice formation . These cracks can also be situated below melt ponds as discussed by , who refer to them with the term macroscopic holes. The parametrization of has no explicit treatment of horizontal fluxes. Our goal is to design a flushing parametrization which is as physically consistent as possible in a 1-D model and includes horizontal brine fluxes which are highest when close to the ice surface. Additionally the parametrization should have as few free parameters as possible. The resulting parametrization (sketched in Fig. ) treats sea ice as a hydraulic network in which each model layer has a vertical and a horizontal hydraulic resistance (Rv and Rh). The assumptions on which the parametrization is based are as follows:

Cracks always exist in the ice.

The resulting parametrization has only a single free parameter β which determines the average distance x to the next crack for a given ice thickness h through x=β⋅h.

The Darcy flow in a porous medium with a hydraulic resistance of R leads to a mass flux f of f=△p⋅ARρ for the pressure difference △p and liquid density ρ. In SAMSIM, for each layer i the vertical hydraulic resistance Rvi=μΠ(ϕli)A△zi is defined by the permeability Π, which is a function of the layer's liquid fraction ϕli, the brine viscosity μ, the column area A, and the layer thickness △z. SAMSIM uses the permeability function of , which was derived from measurements of vertical flows. We use it here for both horizontal and vertical permeability. This simplification should not adversely affect our results, since the major simplification lies in the underlying assumption that the permeability is only a function of solid fraction.

To define the horizontal hydraulic resistance we take the average distance to the next crack from our assumptions, resulting in Rhi=μΠ(ϕli)Ahix.

In contrast to the vertical flow area A, which is always 1 m2 in the column model, the horizontal flow area Ahi varies with layer thickness as well as with the geometry of the cracks and resulting flow field. We take Ahi to be equal to the vertical layer surface with an area of △zi⋅1 m.

The resulting horizontal and vertical brine fluxes (fh and fv as shown in Fig. ) are then computed from hydraulic head and resistance. The total resistance over multiple layers is calculated as a sum of parallel and serial resistances, the same method used in resistor ladder circuits. To illustrate how the layers interact, refer to the sketch with six layers shown in Fig.  as an example. The lowest layer 6 has by definition no hydraulic resistance. The total resistance of the second lowest layer 5 (Rtotal5) is Rtotal5=Rv5Rh5Rh5+Rh5 because Rv5 and Rh5 are connected in parallel. The total resistance over layers 4 and 5 (Rtotal4) is the parallel resistance of Rv4 with the serially connected Rh4 and Rtotal5, resulting in Rtotal4=(Rtotal5+Rv4)Rh4Rtotal5+Rv4+Rh5.

Generalizing this for all layers results in Rtotali=(Rtotali+1+Rvi)RhiRtotali+1+Rvi+Rhi, which is true for any number of layers. The total amount of flushing brine through the whole ladder circuit shown in Fig.  is accordingly fv5+∑15fh=△p⋅ARtotal1ρ. The total amount of flushing brine can not exceed the amount of meltwater present in the top ice layer.

The calculated vertical fluxes advect salt and heat from layer to layer using the upstream method, while horizontal fluxes transport both salt and heat directly to the lowest model layer, i.e. the ice–ocean interface. As the thermal profile in melting ice is almost uniform and the brine salinity is linked to temperature, the vertical fluxes lead to a smaller desalination than the horizontal fluxes.

Although the top ice layer can accumulate meltwater faster than it can flush it away, a fully liquid top layer in the model is impossible with the complex flushing parametrization. As the top ice layer becomes more and more liquid, the permeability increases and the horizontal hydraulic resistance of the top ice layer decreases, resulting in a strong horizontal flushing in the top ice layer. This strong flushing removes water from the top layer and prevents the top layer from ever becoming fully liquid.

To illustrate the fluxes which result from the complex flushing parametrization, we apply some numbers to a specific example with six layers as shown in Fig. . For this simple thought experiment, layers 1 through 5 are identical with the same permeability and 20 cm thick. Accordingly, the vertical and horizontal resistances of each layer are equal to each other: Rh1=Rh2=…=Rh and Rv1=Rv2=…=Rv. The ratio of Rh and Rv is determined by the free parameter β, the layer thickness △z, and the total ice thickness h. In our example we chose △z=0.2 m, which results in h=1 m because we have five layers of ice. Combined, these result in Rh=Rvβ/0.22=25Rvβ. We can now calculate the ratios of the resulting fluxes for a given value of β, which are shown in Table .

For the default value of β=1, 60 % of the flushing brine would penetrate vertically through all five layers of the ice while 40 % of the flushing brine would flow horizontally until falling through cracks and flaws (row (a) of Table ). The horizontal fluxes are strongest in the top layer and decrease with depth. A lower value of β would favour horizontal fluxes. Reducing β to 0.2 results in only 18 % of the brine flushing vertically through all five layers, while over 50 % flushes horizontally in the three top layers (row (b) of Table ).

In the previous example all layers have the same permeability. To illustrate how the complex flushing layer reacts if the lower ice is less permeable, we repeat the same scenario with a higher permeability close to the surface. Specifically, let us assume that the top two layers are 20 times more permeable than the lower three. This reduces the percentage of brine that flushes vertically through the whole ice layer from 60 to 15 %, while over 80 % leaves the ice in the top two layers horizontally (compare row (c) to (a) in Table ). Meanwhile, the horizontal flushing in layers three to five is very small. Less than 5 % of the total brine leaves the ice through cracks and flaws in the lower three layers. If the third layer were impermeable, all flushing would occur horizontally through the top two layers.

The scenario of higher permeable upper layers is slightly more realistic than the uniform permeability scenario; however, SAMSIM is run with many more layers and a correspondingly detailed vertical permeability profile. Idealized simulations illustrating how the complex flushing interacts with salinity and thermodynamics are discussed in Sect. .

We propose a second, numerically cheaper, parametrization which we will refer to as the simple flushing parametrization. In contrast to the complex parametrization, which calculates brine fluxes that affect salinity via advection, the simple parametrization directly modifies the salinity to fulfill a stability criterion. This stability criterion is based on the simple assumption that the liquid fraction is highest in the top ice layer during melt and decreases into the ice. If this were not the case, the ice below the top layer could become fully liquid. Indeed, fully liquid pools inside the ice have, to our knowledge, never been observed, although rotten ice and slush layers seem to be common during the melt period. This stability criterion is only applied when surface melt occurs and has no affect on the rest of the year when solid fraction is high enough to prohibit liquid from running off as meltwater.

The implementation is as follows. At each time step the meltwater which forms in the top ice layer as explained in Sect.  is removed. The salinity of the meltwater is higher than the bulk salinity over the total layer because the solid fraction of the ice is salt free. Accordingly, meltwater removal leads to a reduction of the bulk salinity in the top ice layer. Over time this ensures that the top layer becomes less saline than the second layer. Given that the temperature difference between the top layers is small during surface melt, the second, saltier layer will gradually become more liquid than the fresher top layer.

To ensure that our assumption is fulfilled and the liquid fraction is highest in the top layer, SAMSIM checks each time step if ϕl1>ϕl2. When this occurs, the salinity of the second layer is simply reduced by a fixed fraction ϵ. This increases the solid fraction while raising the temperature.

The same procedure is then applied to the third layer, to ensure that the second layer is not less liquid than the third layer, and after that to the fourth, fifth etc. until a layer is reached which is less liquid. As long as ϕli>ϕli+1, the salinity of layer i+1 will be reduced by the factor ϵ. For example if ϕl1<ϕl2<ϕl3>ϕl4<ϕl5, the salinity of the second and third layer are reduced while the fourth and fifth remain untouched.

Flooding can occur when the weight of snow pushes the ice below the ocean surface, causing ocean water to well up and flood the snow. The resulting frozen mix of snow and ocean water, called snow ice, can be identified by various means in ice cores, from which we know that flooding occurs mainly in the Antarctic and contributes up to 25 % of ice production in certain areas . We base our understanding and treatment of flooding on the work of and . To readers interested in flooding we recommend the PhD thesis of .

Although at first glance flooding seems to be the same process as flushing but with a reversed pressure gradient, there are a number of additional uncertainties. Field measurements have shown that a negative freeboard does not automatically lead to flooding although the lower the freeboard, the higher the chance of flooding is. Additionally, very little is known about what happens to the flooded brine once it reaches the ice surface. As flooding occurs at the bottom of the snow mantel, direct observations of flooding are extremely difficult to obtain. Snow metamorphism is in itself a complex process, but the interactions between flooding brine and snow are even more complex and little research has been devoted to this specific issue. Brine movement must occur at the ice surface after or during flooding, because otherwise snow–ice salinities would be higher than the measured values.

As for flushing and gravity drainage, we again developed two separate parametrizations for flooding. However, the two flooding parametrizations are rather similar. We will simply refer to the slightly more sophisticated parametrization as the complex parametrization and the simpler one as the simple flooding parametrization.

The complex parametrization assumes that during flooding ocean water passes through cracks and channels in the ice to flood the snow layer. The flooding ocean water is assumed not to interact with the brine in the sea ice: showed that if flooding resulted in an upward brine displacement through the whole ice, the resulting desalination would quickly turn the ice impermeable. Experiments with SAMSIM reached the same conclusion as that upward brine displacement would quickly turn the ice impermeable (experiments not shown). Although the complex flushing parametrization consists partially of vertical flows that displace brine, these only seldom cause the ice to become impermeable for three reasons. Firstly, as a layer becomes less permeable the flushing brine is increasingly diverted horizontally. Secondly, the temperature gradients are much smaller in melting ice so that brine advection leads to less desalination. And thirdly, the ice is usually cooled by the atmosphere during flooding which can compensate the latent heat released during desalination.

The flux of ocean water to the surface is calculated as a Darcy flow driven by the negative freeboard and limited by the permeability of the least permeable model layer. Here we assume that the permeability function of provides a useful estimation regardless of the detailed pathways that the ocean water takes through the ice. Although this is a simplification, the major uncertainty stems from the uncertainty in permeability itself and the poor physical understanding of flooding.

Our approach of using the ice permeability to regulate the strength of flooding can lead to a large negative freeboard if the ice layer is impermeable. To avoid this a maximum negative freeboard ζmax is defined. If the freeboard sinks below this threshold, the flux of ocean water necessary to raise the freeboard to the threshold is determined and applied.

The ocean water transported to the ice surface forms a slush layer which is immediately added to the top ice layer at each time step. This is the same approach SAMSIM uses to imitate snow melt and meltwater wicking into the snow layer (described in Sects.  and ). However, given a snow solid volume fraction of approximately 30–40 %, this approach would result in the flooded slush layer having a very high salinity of roughly 20 g kg-1, which is inconsistent with measurements. To avoid this high salinity, we assume that the ocean water which floods the snow simultaneously wicks upward and dissolves additional snow into the slush which leads to a freshening of the slush. The ratio of dissolved to flooded snow is assumed to be constant and is defined by an additional free parameter δ.

In this paper we use a value of 5 cm for ζmax, which is based on the freeboard measurements analyzed in , and we use a value of 0.5 for δ as a preliminary best guess.

The simple parametrization is the complex parametrization stripped of the permeability-dependent flooding speed and without snow dissolving into the slush layer. The simple parametrization is identical to the complex parametrization if the free parameters are set to ζmax=0 m and δ=0. This means that as soon as a negative freeboard develops, flooding sets in right away and no snow is dissolved into the forming slush.

The first trait we selected is the link between salinity and thickness which was studied by and . For the single growth season studied in the model results agreed well with the fit of for first-year ice up to 2 m.

We separate first-year from multiyear ice before comparing the bulk salinity against thickness (Fig. ). One simulation was singled out and highlighted, allowing the reader to track the progress over 4 years as the first-year ice turns into multiyear ice and becomes less saline over time. The simulation which was singled out is the same simulation as shown in Fig. .

Both first-year and multiyear ice show a distinctly different behaviour during growth and melt. The gradual transition from growth to melt is visible as a drop in bulk salinity at a constant thickness. A closer examination reveals that a slight thickness increase is visible in many simulations before ablation sets in. This bump in ice thickness arises from SAMSIM's definition of sea ice, which includes melting snow that has turned into slush (for details see Sect. ). That this little bump appears at the end of the downward drop signals that until then no flushing has occurred. From that we can conclude that gravity drainage causes the drop in salinity.

Ice thinner than 20 cm has a wide spread in bulk salinity caused by melting and flooding at the onset of the growth season. The simulated first-year ice thicker than 20 cm agrees well with the empirical results of and during growth, with the model having only a slightly higher salinity. This bias is especially high for ice thinner than 0.5 m, which may be partially due to the fact that the underestimation of bulk salinity due to brine loss is higher for thin cores. After the onset of melt the bulk salinities are comparable to the estimates of , which were based on a limited amount of cores that were at least 1 m thick.

As expected, multiyear sea ice shows a much smaller range of bulk salinities (Fig. b). During growth the bulk salinities show no coherent dependence on thickness, but during melt there appears to be a slight linear dependence on thickness. This is not far off from the estimation of .

Both the modelled first-year and multiyear profiles are almost completely salt free at the end of the melt season. Neither or included ice cores of such thin ice during melt, so we can not conclude from our comparison if this model behaviour agrees with reality. However, it is plausible that the 1-D nature of SAMSIM, which is built on the assumption that ice layers are totally homogeneous and all brine pockets are connected, would lead to an overestimation of desalination during flushing.

In conclusion, the modelled thickness–salinity relationship of growing first-year ice agrees well with the empirical fits to measurements of both and . For growing multiyear ice there is no one-to-one relationship between thickness and salinity, though growing multiyear ice tends to to be less salty the thicker it gets. The transition from growing to melting ice leads to a loss in bulk salinity at a constant thickness which is caused by gravity drainage in the warming ice. Both melting first-year and multiyear ice show a weak linear dependence of salinity on thickness. In our simulations, the ice loses almost all its salt during melting; hence its mean salinity after the re-onset of growth is strongly affected by the salinity evolution of the newly forming ice.

The second trait of the modelled salinity we evaluate with core data is the evolution of first-year ice salinity from January until June. A longer time frame was not possible due to data availability; the period nonetheless allows us to study the salinity changes after gravity drainage is mostly restricted to the lower layers. We use the ice-core data taken as part of the Seasonal Ice Zone Observing Network and the Alaska Ocean Observing System by the sea-ice research group at the Geophysical Institute at the University of Fairbanks from 1999 to 2011 . The great advantage of these measurements, other than the sheer number of cores taken, is that by measuring repeatedly over a decade a large spread of conditions were captured. After rejecting all cores which did not include an ice thickness measurement or contained gaps in the salinity profile, a total of 86 first-year profiles remained between January and June.

The comparison of the model salinity with the Barrow cores is not ideal because SAMSIM is forced with conditions from throughout the Arctic, while the cores were all taken close to the Alaskan coast as part of an ongoing effort to understand and alleviate the impact of changing sea-ice on the human settlements along the coast . Ideally we would force our model with the forcing experienced by the ice measured at Barrow. This is not possible for a number of reasons. Firstly, we have no measurements of the oceanic heat flux. Secondly, although the ice was measured in Barrow we do not know where it was before the core was extracted. Most of the ice will likely have formed near the extraction points, but as illustrated by the multiyear ice cores taken in a region which is ice free in summer, there is a substantial amount of drift. Thirdly, we do not know when the ice was formed. The ice could have been formed during the initial freeze-up in fall, or later on in a lead or polynya. And lastly, due to the uncertainty in reanalysis data and the high variability in snow depth, we could not be certain that applying reanalysis forcing taken from the exact point where the cores grew would be correct. However, we do have a number of reasons to believe that the model-data comparison is useful. Firstly, the cores are taken over 12 years. This means that interannual variability will ensure that ice grown under a range of conditions was measured. Secondly, we show in the subsection on interannual salinity variability that the salinity variations resulting from atmospheric conditions are strongest in the uppermost 20 cm (Sect. ). Because of this, we believe that the comparison should work well for the lower 80 % of the ice.

To compare the core profiles against the model profiles, both are first normalized to a depth of 0 to 1 before averaging over time. Often the salinity measurements did not extend all the way to the bottom of the ice, in which case the lowest measurement was extrapolated downwards. This extrapolation will contribute to the underestimation of salinity at the ice–ocean interface common to ice cores. We group the 86 core measurements into three bins of similar size based on the dates they were taken. The first bin spans from January to March (27 cores), the second from April to May (29 cores), and the final bin contains the remaining 29 cores taken in June.

As expected, even though the core profiles have a sharp increase of salinity at the ice–ocean interface they are still less saline at the ice–ocean boundary than SAMSIM (Fig. ). Other than the top and bottom 10 % of the ice thickness, the simulated salinity profiles and the Barrow cores never differ by more than 2 g kg-1, which is in itself a mentionable model feat.

Other than the general agreement, this comparison highlights some limitations of SAMSIM's complex salinity approach. One of these limitations is that flushing and snow melt by design lead to a zero salinity at the surface once surface melt commences. Accordingly, the June SAMSIM profile is completely salt free at the surface while the core data show a salinity of roughly 1 g kg-1 at the surface (Fig. ).

This total desalination at the surface is rooted in two of SAMSIM's design choices. The first design choice is that the snow layer in SAMSIM has zero salinity and that melting snow forms slush which is treated as sea ice. Accordingly, when snow melts the top ice layer will consist of melted snow slush and be absolutely salt free. The second design choice which leads to zero salinity at the surface is the implementation of flushing in SAMSIM. One of the core assumptions of the complex flushing parametrization is that the meltwater leaving the top ice layer has a brine salinity determined by the liquidus relationship. Accordingly, as the brine salinity of the top ice layer is by definition always higher than the bulk salinity of the top ice layer, flushing always results in a salinity decrease at the surface. This desalination quickly desalinates the surface once flushing commences as shown by the idealized flushing experiments (Sect. ). While the freshly desalinated ice can freeze solid and thus inhibit any further flushing, this can only occur in the ice if the underlying ice is sufficiently cold as in the idealized example. At the surface this could also occur but only if there were a negative atmospheric heat flux to remove sufficient energy from the top layer to overcome the latent heat released during freezing.

The second distinct difference between model and core salinity is that SAMSIM has a high surface salinity with a very strong salinity gradient before the onset of melt (profiles from January to May, Fig. b). The sharp salinity gradient which occurs in the top few model layers could be a numerical artifact arising from SAMSIM's semi-adaptive grid. No matter which resolution is used, the initial ice growth occurs when only a few layers are active. This issue was investigated in our previous paper when comparing to freezing plate experiments conducted in the lab, but available data were insufficient to make any conclusions . A different explanation is snow wicking, a process which transfers some of the surface salinity into the snow layer. In the model wicking only occurs when meltwater forms in the top ice layer beneath snow. The discrepancy between model and data at the surface could also arise from the neglect of frazil or pancake ice formation in SAMSIM. In frazil and pancake ice the wave motion and turbulence cause brine motion not captured by the gravity drainage parametrization which could desalinate the initial ice before it freezes into a static structure.

The third discrepancy between the cores and SAMSIM is that the bulk salinity in the upper 40 % does not change substantially from the period of January–March to that of April–May in the model. There are many possible explanations for this discrepancy, such as the non-ideal comparison itself (see second paragraph Sect. ), insufficient simulations or core measurements, and errors of the core-salinity measurements. Another explanation is that the model is unable to simulate the salinity evolution correctly close to the surface during winter. A likely candidate to explain that the salinity remains constant near the surface is that the gravity drainage parametrization desalinates too quickly during growth. The modelled salinity is quickly reduced to 5 g kg-1 after which it stabilizes, instead of a weaker initial desalination followed by a gradual desalination over time (Fig. ). The neglect of frazil and pancake ice formation in SAMSIM could again be an issue since turbulent conditions during the initial freeze-up would influence both the microstructure and permeability of the surface ice. It is also possible that the freeboard plays an important role, and that brine from above the waterline drains away by an unknown mixture of gravity drainage or flushing. The differences between the cores and SAMSIM as well as our poor understanding of what happens during flooding indicate that unknown, yet relevant, brine movements may occur at the ice–snow interface. It is also possible that the gravity drainage parametrization has some limitations. Despite the indirect model-to-data comparison and the three discrepancies in the salinity evolution discussed, SAMSIM successfully captures the general shape and magnitude of the three core-derived salinity profiles.

The final and best-documented trait we select to compare is the mean multiyear salinity profile. The most widely used multiyear profile in the sea-ice modelling community is based on 40 ice cores taken at the drifting ice station A in 1958 from May to September. Although later studies have incorporated additional measurements e.g., the basic shape has remained similar. The fitted bulk salinity profile of on a normalized vertical coordinate z from zero to one, Sbu(z)=1.6(1-cos⁡)(πz0.4070.573+z), is used in the 1-D models of and . As the Schwarzacher cores were all taken from May to September, and the eight multiyear cores from Barrow were also taken in summer, we compare the normalized Barrow cores and Schwarzacher profile against the mean of SAMSIM from May to September. We did not compare directly to the Schwarzacher data as they were not easily available and the data displayed in were not regularized before averaging. Although the fitted Schwarzacher profile has a 3.2 g kg-1 salinity at the ice–ocean interface (Fig. ), an increase is clearly visible in the measurements, similar to the salinity increase of the eight multiyear salinity cores taken at Barrow. Due to this ignored increase and the repeatedly mentioned salinity loss in cores, we only compare to the upper 90 % the Schwarzacher profile. Although this comparison of SAMSIM to field data is far from perfect, it is the closest we can come to evaluating the flushing parametrization until controlled laboratory measurements are available.

We compare the May-to-September mean of all normalized multiyear SAMSIM profiles to the profile of and the Barrow cores, which all share a similar magnitude and shape in the upper 90 % (Fig. ). Both SAMSIM and the Barrow cores have a slight maximum at a depth of 40 %, which indicates that the complex flushing parametrization predicts the desalination depth reasonably correctly. The good agreement between SAMSIM and ice-core data is a very positive result given that the complex flushing parametrization contains large parameter uncertainties and was developed from scratch without any data available to tune the free parameter β.

Between the depth fractions of 0.5 and 0.8, SAMSIM and the Barrow cores show a slight salinity decrease with depth while the Schwarzacher profile has a slight increase (Fig. ). The differences between the model and the ice-core data are of similar magnitude to the differences caused by different values of α and Rcrit obtained from the optimization process mentioned in Sect. . The Barrow cores and SAMSIM both have a sharp salinity increase in the lowest 10 %. That the model is saltier at the ice–ocean boundary is expected due to brine loss during coring and a lower spatial resolution of the measurements compared to the model.

According to SAMSIM there is a clear link between ice thickness and bulk salinity in growing first-year ice as described by . However, after the ice stops growing, gravity drainage in the warming ice causes a thickness independent desalination. Both melting first-year and multiyear ice show an approximately linear dependence of bulk salinity on ice thickness as suggested by . The modelled ice loses almost all its salinity, a feature against which we do not have any core data to evaluate. The mean multiyear salinity profile of SAMSIM from May to September agrees well with the core data of and from Barrow. The salinity evolution in first-year ice in SAMSIM is comparable to ice-core measurements at Barrow . However, in contrast to the Barrow core data, the modelled salinity close to the ice surface remains constant from the period of January–March to that of April–May, indicating that in reality, brine fluxes occur close to the surface and are poorly captured by the complex set of parametrizations.

All comparisons between SAMSIM and ice-core data show that SAMSIM captures the general salinity evolution well, both qualitatively and quantitatively. Keep in mind that no tuning was used to reach these results and that all parametrizations were developed without any field data. Additionally, all parametrizations were developed separately, with no regard to possible interactions.

So far we have only evaluated characteristics of the Arctic simulations that we could compare against ice cores. From the comparison to ice cores we conclude that our parametrizations and understanding of desalination processes are sufficient to use SAMSIM as a tool to study Arctic sea ice beyond reproducing ice-core salinity.