The rate of sea-ice growth strongly depends on the energy fluxes at the ice or ocean surface. If the total atmospheric heat flux is negative, the ocean loses heat either directly to the atmosphere or via conduction through an existing sea-ice cover. In the former case frazil ice forms, which aggregates subsequently to a new thin-ice layer under calm conditions. In the latter case basal freezing occurs to balance this heat loss. Most of the heat loss from the ocean occurs over open water or thin-ice areas, such as leads and polynyas, within an otherwise compact sea-ice cover . Although the fraction of such areas in polar oceans is relatively small during winter, they are of major importance for the heat budget of the atmospheric boundary layer (ABL) and the ocean circulation, such as the Arctic circumpolar boundary current e.g..

The Laptev Sea (Siberia) is a very shallow shelf sea with water depths between 15 and 200 m and comprises an area of about 500 × 103 km2 . It is one of the most significant regions where a considerable amount of the total Arctic sea ice is produced . The newly formed sea ice is subsequently transported by the Transpolar Drift Stream and accounts for about 20 % of the total ice export through Fram Strait . The Laptev Sea thus plays a key role for future Arctic sea-ice development .

Quasi-stationary latent-heat or flaw polynyas reoccur frequently along the Siberian coast and along the fast-ice edge due to offshore wind stress . These polynyas are narrow, long bands of open water and/or thin ice, which separate landfast ice from seaward drifting ice on the Siberian continental shelves during winter , predominantly from October until June . In general, the ice cover in the Laptev Sea can be divided into three regimes: fast ice, pack ice, and flaw polynyas in between .

Particularly in winter, sea water at the freezing point is directly exposed to a cold atmosphere, resulting in intense ice formation . Due to this strong surface heat loss within coastal polynyas frazil ice forms, which is subsequently transported toward the downwind edge of the polynyas . This process creates a spatial gradient of thin-ice thickness (TIT) increasing from open-water conditions at the windward polynya edge to thicker ice at the downwind side. Here, at the polynya edge, the advected frazil ice accumulates to a thin layer , which thickens and consolidates before it drifts further offshore. During the ice formation, salt is excluded from the ice matrix and is drained as brine from the sea ice . This salt input induces haline convection and erodes the density stratification of the underlying water column and, if penetrative, dense bottom water forms . The long-term mean probability for convective mixing down to the seafloor is only about 20 % in the western and about 70 % in the eastern Laptev Sea , which is owed to the general preservation of the stratification throughout the winter caused by freshwater input from the Lena River during summer . The cold, dense bottom water contributes to the Arctic halocline and thermohaline structure in the Eurasian Basin .

The horizontal resolution of regional climate models is generally too coarse to represent leads and small polynyas explicitly. Therefore, they have to be treated as inhomogeneities of momentum and energy fluxes on a subgrid scale. investigated three approaches to account for such subgrid-scale inhomogeneities within a model grid box: the (i) aggregation, (ii) mosaic, and (iii) tile approach (TA). In the aggregation approach the parameters for the fluxes (such as roughness length or albedo) are weight-averaged over different surface types within a grid box and then the fluxes are calculated from these grid-scale means. In contrast, in the mosaic approach the fluxes are explicitly calculated on a sub-scale grid and averaged afterwards. In the standard version (v5.0_clm1) of the regional climate model COnsortium for Small-scale MOdel – Climate Limited area Mode (COSMO-CLM or CCLM; ), which is the climate version of the numerical weather prediction model COSMO of the German Meteorological Service , a model grid box is assumed to be either completely covered with sea ice or completely ice free. However, if neglecting subgrid-scale energy fluxes or heat loss from open-water or thin-ice areas, the energy transfer is underestimated and subsequently also the sea-ice production (IP). This underestimation affects the sea-ice budget and associated processes connected to the ocean, such as salt release and deep water formation . Although the ocean processes are not represented in CCLM, the quantification of IP can be seen as a proxy for dense water formation.

In other regional climate models, such as the Polar Weather Research and Forecasting (Polar-WRF) model, fractional sea ice is already a default option with the assumption of subgrid-scale open water and with fixed sea-ice concentrations (SIC) and ocean temperatures during a 48 h simulation . However, assumptions have to be made for the subgrid-scale thin-ice thickness, since particularly in winter leads and polynyas are rarely ice free .

In the following we quantify the sea-ice production in the Laptev Sea polynyas (Siberia) and investigate its sensitivity on the assumptions of thin-ice thickness associated with the tile approach. The sea-ice module of was already successfully applied in the Laptev Sea by , who could show that polynyas significantly affect the ABL. More recently, calculated sea-ice production rates for this region based on COSMO simulations with an assumed thin-ice thickness of 10 cm (B10) or open water (B00) within polynyas. Their model results showed that the presence of grid-scale thin ice affects the IP considerably.

The implementation of a TA for subgrid-scale energy fluxes constitutes, from a physical point of view, an improvement to the representation of polynyas in regional climate models. However, it is unclear how sensitive the energy fluxes, the resulting IP, and the ABL are to the choice of grid-scale and subgrid-scale ice thickness. By varying the thin-ice thickness in a sensitivity experiment, we aim to quantify these uncertainties. As a benchmark for our study we use the IP estimations of . We further comprise model results of and derived IP from Moderate Resolution Imaging Spectroradiometer (MODIS) data.

This paper is structured as follows: in Sect. 2, a short overview of the model configuration and the study region is given; in Sect. 3 the basics of the sea-ice module are described (see details in Appendices  and ). The model is validated with in situ data in Sect. 4 and the effects on the atmospheric boundary layer and on ice production rates are presented in Sects. 5 and 6 and discussed with respect to remote sensing estimates in Sect. 7. Finally, we conclude in Sect. 8.

The domain of CCLM (Fig. ) covers the whole Arctic at a horizontal resolution of 15 km (C15). CCLM was run on 450 × 350 grid boxes and with 42 vertical layers, of which 16 are below 2 km height. Nested within, we performed simulations for the Laptev Sea (Fig.  and Table ) at 5 km resolution (C05) with 260 × 260 grid boxes and 60 vertical levels, of which 24 levels are below 2 km height. We subdivided this domain into four polynya regions, which have been already used in previous studies, e.g. by : the north-eastern Taimyr polynya (NET), the Taimyr polynya (T), the Anabar–Lena polynya (AL), and the western New Siberian polynya (WNS). The total area of the masks is 26.19 × 104 km2.

The C15 model is forced by ERA-Interim data with updates to the lateral boundaries every 6 h. The C05 models are then forced by the output of C15 with an update frequency of 1 h. The models were run in a forecasting procedure for the winter period November 2007 to April 2008 (182 days in total). They were restarted every simulation day at 18:00 UTC and simulated the following 30 h. Thereby the initial sea-ice conditions (see Sect. 3.2) were prescribed to the sea-ice concentration and thickness of the following day. The first 6 h were cut off as spin-up. The simulation output (00:00–23:00 UTC) was stored at a temporal resolution of 1 h.

Surface fluxes were calculated by a bulk transfer scheme with a stability dependence (see Appendix ). The vertical diffusion was parameterized by a level-2.5 closure scheme based on a prognostic equation for turbulent kinetic energy (TKE). Radiation processes were calculated hourly using the scheme extended for ice clouds. We applied a Runge–Kutta scheme of third order . Additionally, a fast-wave solver for sound and gravity waves was used . All simulations were run without spectral nudging.

To improve the simulation of heat loss over fractional sea ice in CCLM, we modified the standard version with regard to the following points: (i) we implemented the thermodynamic two-layer sea-ice module of , (ii) we used daily sea-ice thickness (SIT) fields from the Pan-Arctic Ice-Ocean Modeling and Assimilation System (PIOMAS) data set as initial data, (iii) we implemented a new albedo scheme for sea ice based on , and (iv) we implemented a tile approach for the energy balance over fractional sea ice. The TA is a simplification of the mosaic approach, considering only the percentage of different surface types but not their exact location. According to the TA provides similarly good results as the mosaic approach, but with distinctly less computation time. Thus, we decided to implement this variant. First steps in the direction of a tile approach in CCLM were made by . However, their adjustments were limited to area-weighted albedo values and to surface roughness values within a grid box that is covered with fractional sea ice. Although points (ii)–(iii) represent new modifications to CCLM as well, we accept them as the default option for our simulations.

The C15 simulation was performed without a TA in order to introduce effects from the TA only through the 5 km simulations. In case of C05, we performed a reference simulation in the Laptev Sea area without a TA (C05-ref) and five sensitivity simulations with the TA. The configuration of the reference simulation is similar (as far as possible) to the configuration of the previous studies of , where no TA was available. However, they used an older model version, which causes differences. C05-ref is thus comparable to the simulations of and further the reference without TA for our sensitivity simulations.

While the sea-ice thickness outside the polynyas was specified as explained in Sect. , the ice thickness within the polynya areas has to be prescribed. For C15 and C05-ref the ice thickness in polynyas areas is generally 10 cm, but we assume 1 cm thin ice at polynya grid boxes in C05-ref, where the sea-ice concentration is 0 %. Such areas particularly produce new ice and consist of a mixture of open water, grease and frazil ice, and thin solid ice. However, in winter open-water areas occur mostly at the windward side of polynyas, which is only a small fraction of the entire polynya area.

For three of the five sensitivity simulations we assumed also a grid-scale ice thickness of 10 cm for polynyas and assumed either subgrid-scale open water (C05-10/0) or a subgrid-scale TIT of 1 cm (C05-10/1) and 10 cm (C05-10/10). The fourth and fifth sensitivity simulations were configured with a grid-scale ice thickness of 50 cm and a subgrid-scale TIT of 5 cm (C05-50/5) or 1 cm (C05-50/1). See Table  for an overview of the simulations. The assumption of 10 cm TIT originates from the fact that the mean TIT below 20 cm, derived from MODIS data, is of the order of ≈ 10 cm. derived a mean thin-ice thickness of 11.6 cm for November to April (1979–2008), while from the MODIS TIT histogram in Fig.  a mean thin-ice thickness of 13.5 cm for November to March in the period 2002/2003–2014/2015 and of 14 cm for the winter 2007/2008 results, respectively. In a previous study by 10 cm was thus assumed to be a realistic value for the thin-ice thickness within Laptev Sea polynyas. For better comparisons we assumed 10 cm as well in our reference simulation (and in two sensitivity runs).

The first three sensitivity simulations investigate the effect of the TA, if even thinner subgrid-scale ice is assumed. The C05-50/5 and C05-50/1 runs are motivated by the fact that the sea-ice cover in the marginal ice zone consists of thicker ice floes (> 20 cm) (detected by microwave satellite sensors) and thin ice (here the assumed 5 or 1 cm), which is not detected by microwave sensors. Thus we denote C05-50/1 as the simulation with “realistic” assumptions based on MODIS TIT.

Although this is a crude simplification to the real sea-ice thickness, it is suited for our purpose to investigate the impact on the magnitude of ice production and on the modification of the ABL. We intended to consider sea ice in a computational cheap approach that still incorporates realistic thermodynamical processes. For a more sophisticated approach, a full dynamic–thermodynamic sea-ice model needs to be coupled to CCLM.

The model output of the reference and the five sensitivity simulations were first evaluated with in situ data. During the Transdrift XIII-2 expedition from 11 to 29 April 2008 four automatic weather stations (AWS, Table ) were deployed on the fast ice of WNS (see Fig. ) . The AWS measured wind speed and direction at 3 m height with an accuracy of 2 % in speed and 3∘ in direction, air temperature and relative humidity at 2 m height with and accuracy of 0.5 K and 4 %, and pressure with an accuracy of 1 hPa. Furthermore, net radiation was measured by a net radiometer with an accuracy of 5 W m-2.

Here, we compared hourly C05 data with the AWS data. In order to judge whether the simulations deviate significantly from the AWS data two-sided t tests were performed (α = 95 %). The statistical comparisons were only performed for data pairs without missing values and only for days when the SIC was > 95 %. This limitation is necessary because the time series of CCLM represent spatial averages of a grid box, whereas the AWS time series are point data on a solid ice cover. If the SIC of CCLM is < 100 % then the grid average automatically differs from the station time series, which always represent conditions at 100 % SIC.

Table  shows the results for the reference simulation (C05-ref) and two sensitivity simulations: C05-10/0 (subgrid-scale open water) and C05-50/1 (realistic assumptions). In the remainder of the paper, we concentrate on the comparison of these three simulations. Since the comparison was made only over a solid sea-ice cover, the other simulations showed very similar results (not shown).

In general, the inter-model differences are minor for all variables. The comparison for the 2 m temperature shows that the C05 simulations are generally able to reproduce the observed temperatures during the measurement period. The temporal correlation is about r = 0.8, except for the comparison with AWS4. The bias is about -1 ∘C for AWS2–3, less for AWS1, and about -3 ∘C for AWS4. Except for the latter, C05 underestimates the variability of the 2 m temperature. This might be caused by the assumptions made on snow properties in C05. Although the t tests are significant for differences of about 1 ∘C, this difference is sufficient for our analysis keeping in mind that grid-box averages were compared with point data.

In case of wind speed there is a good agreement (r ≥ 0.7), although we compared 10 m wind speed of CCLM with measurements at 3 m height. The mean and standard variance are both in accordance with the AWS data, although significant for differences ≥ 0.4 m s-1. Inversely, this agreement implies that CCLM underestimates wind speeds at 10 m, although we do not have reference data at 10 m for a evaluation. Significant differences were found for the comparison of the net radiation. Although the temporal correlation is high (r ≥ 0.7), the mean of C05 is about 13–22 W m-2 lower than observed, meaning a slightly too-high heat flux through the sea-ice cover. This difference might be caused by the assumption on the sea-ice properties (e.g. a constant temperature at the ice–ocean interface) or by the slight cold bias of the ABL above the sea ice.

Albeit some deviations CCLM is able to reproduce the basic conditions of the near-surface variables during this period with our chosen configurations. However, the reasons for these deviations need further investigation with longer time series.

The daily sea-ice production rates were calculated for the individual polynyas as described in Sect. . Here we compared the ice production of the C05 simulations to the remote sensing estimations of , to estimates based on MODIS2km (Sect. ), and to model results of .

The time series of daily IP (km3 day-1) are shown in Fig.  and the total ice production for the whole winter are shown in Table . The total IP in the winter 2007/2008 is about 29.1 km3 in the reference simulation (C05-ref), which is not significantly different from the 33.0 km3 estimated by . The temporal correlation is r = 0.65, which is sufficiently high, but some differences are visible (Fig. ). This result agrees well with the remote sensing estimates, although used a constant CH for calculating the heat fluxes and much coarser atmospheric data.

The strongest, significant increase (p < 0.01) in IP was estimated from C05-10/0 with 65.2 km3 (+125 %), where subgrid-scale open water was assumed. For realistic assumptions (C05-50/1) the IP increases to 38.3 km3 (+39 %), which is not significant at the 95 % level. The increase of IP is caused by the higher heat fluxes from the ocean into the overlying atmosphere as presented above. Compared to the results based on MODIS2km, where we estimated about 49.1 km3 due to the large polynya area, most of the simulations produced much less ice. Exceptions are C05-10/0 and C05-10/1, which reach or even exceed this estimate. These results show that there are large differences not only between the models but also between remote sensing approaches. For instance, the time of polynya openings and IP also differ (r = 0.45). Although such high IP could be reproduced in the Laptev Sea, the question remains of which remote sensing data set should be used for calibrating the models.

The IP based on an older reference COSMO simulation by with 10 cm ice within polynyas (B10) is slightly less compared to our reference run (C05-ref), but significantly lower compared to . Although the open-water sensitivity run of  (B00) produces higher IP, it is considerably less compared to our C05-10/0 run. B10 and B00 show a slightly higher correlation with the IP time series of . The differences of B10/B00 with respect to our C05 simulations can be explained by differences in the model version, configuration, and nesting chain (GME vs. ERA-Interim, different model domains). However, we cannot quantify the individual contributions to the deviations. All C05 sensitivity simulations show a higher daily standard deviation compared to the data from , which increases with decreasing subgrid-scale thin ice. This is logical, because if a polynya opens then more heat is released compared to the reference simulation and thus the IP is higher.

Spatial maps of the total IP within polynyas in the winter 2007/2008 are shown in Fig. . In all simulations the highest IP occurs in the NET polynyas, with rates > 2 m/winter in C05-ref and > 5 m/winter in C05-10/0. Further, with considering the subgrid-scale thin ice or open water the spatial gradient of ice production is much better represented, with higher rates at the windward edge of the polynyas. Overall, we think that the assumptions made in C05-50/1 are realistic. Although we are aware that open-water areas may occur at the windward site of polynyas, the area of open water is much smaller compared to the entire polynya area (see Fig. ). Thus, the heat flux and IP would be overestimated if open water were assumed in every grid box with fractional sea ice.

The simulation results of our study showed that there is a high sensitivity of the ice production to the assumptions on subgrid-scale thin-ice distribution, with considerable effects on the atmospheric boundary layer. The ABL receives more heat the thinner the ice is and warmed by up to +3 ∘C in our subgrid-scale open-water configuration. However, the warmer ABL did not prevent further heat release from the ocean due to a weakened vertical temperature gradient. The simulations showed that the vertical temperature gradients remain or even exceed the gradients of the reference simulations. Two effects are responsible for this: (i) as the ice becomes thinner the surface temperature increases stronger than the heating of the ABL, which increases the vertical gradient; and (ii) the near-surface wind speed is enhanced due to increased local pressure gradients, which increases the wind-shear and thus the sensible heat fluxes. Further, the warm plumes over the polynyas are efficiently advected over the pack ice. Thus heat is removed from above the polynyas and a strong temperature gradient is maintained, which enhances the ice production.

Constraining the assumptions on subgrid-scale thin ice was found to be difficult. The comparison of model-based IP with remote sensing estimates revealed large discrepancies. Further, large differences were found between the two remote sensing approaches. The usage of higher resolved MODIS data and ERA-Interim, compared to the approach of in which NCEP and AMSR-E data were used, nearly produced +50 % more ice. The configuration of C05-50/1, in which we assumed 50 cm thick grid-scale and 1 cm subgrid-scale thin ice, seems to be a realistic assumption in the marginal ice zone of the polynyas.

The resulting IP is close to the estimates of , which we defined as a baseline for our sensitivity experiment. However, if for instance the results of MODIS2km were defined as a baseline, then even thinner ice might be considered. We are aware that our sea-ice module is simplified compared to more sophisticated sea-ice models, where the thin-ice thickness might be a prognostic variable and not a constant. However, despite our simple assumption, the results are promising and satisfactory in order to represent sea ice in a regional climate model in a computationally cheap approach. We further argue, based on our results, that assuming subgrid-scale open water within fractional sea ice, such as in Polar-WRF , leads to too-high heat fluxes from the ocean into the atmosphere.

However, even if more sophisticated sea-ice models were used to estimate the IP, the issues remain of how to constrain parameters and to which data set to compare. It is not our intention to disentangle all factors controlling the estimation of sea-ice production based on different approaches, data sets, or models, but several issues are important in a general sense:

Polynya area is affected by the definition of polynyas (e.g. SIC ≤ 70 % or hi < 0.2 m) and the horizontal resolution of the model and the satellite products.

The complexity of these factors make a comparison of model and remote sensing studies difficult. It further indicates that some assumptions in the remote sensing approaches, such as a constant value for CH, might be oversimplified. Furthermore, a problematic issue is the usage of coarse atmospheric data sets, such as NCEP or ERA-Interim, for remote sensing approaches, if not combined with high-resolution satellite products. The horizontal resolution of such atmospheric reanalysis data sets is not sufficient to represent polynyas adequately. Thus subsequent errors, such as wrong simulations of the atmospheric boundary layer over polynyas, are the consequence. These errors are then transferred to the remote sensing approach and might result in wrong sea-ice production estimates. From a modelling point of view the question arises of what reference for IP estimates should be used. This question is not easily answered and is still an open issue. A strategy might be a simultaneous application of both modelling and remote sensing approaches in order to compensate for weaknesses. This issue directly impedes the decision of an optimal model configuration.

According to our study, the approach of constitutes the closest reference because of the same satellite data that were used to derive polynya area at a comparable horizontal resolution. Although the definitions of polynyas are different, the assumption of 0.1 m thin ice in areas of SIC ≤ 70 % is similar to the definition of ≤ 0.2 m as in . Larger differences evolve from the assumptions made on CH (Fig. ) and the horizontal resolution of the atmospheric data. Given these deviations, the IP based on C05-ref and C05-50/1 is still close to the results of . Although the use of MODIS, i.e. higher resolved satellite products, results in higher IP estimates, the reason for this is the higher horizontal resolution that causes larger polynya areas and not the representation of subgrid-scale energy fluxes within polynyas in ERA-Interim, which is still too coarse. For thicker ice the CH values converge to ≤ 1.5 × 10-3, a value also reported by .

Given these issues, the decision of which TIT should be used with the TA is another degree of freedom and cannot sufficiently be answered from our study. A justified assumption is to rely on MODIS TIT (Fig. ). The mean derived TIT for the winter periods (November–March) 2002/2003–2014/2015 is 13.5 ± 0.5 cm, which is slightly thicker than our assumed TIT in CCLM. Unfortunately, the MODIS TIT distribution for the polynya areas shows no maximum at a specific ice thickness, which gives no preference for the choice of the subgrid TIT for the tile approach.

In this study we quantified the ice production in the Laptev Sea polynyas for the winter 2007/2008 based on simulations with a regional atmospheric model (CCLM) and remote sensing data. A new tile approach for fractional sea ice, considering subgrid-scale thin ice, was implemented into CCLM. Besides a reference run, five sensitivity simulations with different assumptions on grid-scale and subgrid-scale ice within polynyas were performed. We further investigated the impact on the atmospheric boundary layer above polynyas.

The results show that the ice production is highly sensitive to the assumptions made on the ice thickness within polynyas. Compared to the estimated total winter ice production of 29.1 km3 of the reference simulation, the ice production more than doubled when subgrid-scale open water was assumed and increased by about (+39 %) for the most realistic assumptions based on remote sensing of ice thickness. The increase of the ice production is caused by a larger heat loss from the ocean, whose magnitude is proportional to the thin-ice thickness. Although the atmospheric boundary layer is heated by up to +3 ∘C in the open-water configuration, strong vertical temperature gradients and associated high sensible heat fluxes at the surface were maintained. On one hand, the tile approach improves the physical representation of polynyas in CCLM because fractional sea ice is considered; on the other hand, a new degree of freedom is introduced to constrain the thin-ice thickness. The derivation of an optimal configuration for CCLM or other regional climate models remains difficult because of sparse observed ice thickness distributions within polynyas. We used remote sensing data as a baseline to constrain our configuration, but several issues were found which hamper such comparisons. At this point coupled atmosphere–ice–ocean models are needed to fully simulate feedback processes.

In summary, realistic ice production estimates could be retrieved from our simulations. Neglecting subgrid-scale energy fluxes might considerably underestimate the ice production in coastal polynyas, such as in the Laptev Sea, with possible consequence on the Arctic sea-ice budget.

The data used in this study are available on request from the authors (gutjahr@uni-trier.de or heinemann@uni-trier.de).