Impact of lateral melting on Arctic sea ice simulation in a coupled climate model

Lateral melting is an important process driving the sea ice decay, yet it is not well represented in many Coupled Model Intercomparison Project Phase 6 (CMIP6) models. This study explores the impact of lateral melting on Arctic sea ice simulation by implementing lateral melting and floe size parameterization schemes in the medium resolution version of the Beijing Climate Center Climate System Model. Results from a series of CMIP6 historical-type experiments indicate that inclusion of lateral melting results in a reduction in both the Arctic sea ice concentration and thickness, thus improving the sea ice extent and volume simulation. Lateral melting increases open waters, leading to an enhanced net sea surface heat flux into the ocean and further increased lateral and bottom melting. This positive feedback is intensified from 1982 to 2014, particularly when the floe size parameterization scheme is introduced. This accelerates the Arctic sea ice decline from 1982 to 2014 in the model, which is more consistent with observations. Further analysis indicates that the enhancement of this feedback is associated with accelerated lateral melting due to the increased (decreased) trend of the sea surface temperature (floe size) from 1982 to 2014. This study highlights that sea ice lateral melting is an important factor affecting the simulation of Arctic sea ice decline and needs to be better represented in current climate models.


Introduction
It is well known that the melting of polar sea ice occurs mainly at the surface and bottom.In summer, the absorption of solar shortwave radiation by sea ice promotes the surface melting, whereas the absorption of solar radiation by seawater is conductive to the bottom melting.However, as the polar sea-ice cover is composed of floes with various sizes and shapes (WMO 2014), the melting in the lateral interface between floes and seawater should not be neglected.Results from observations and numerical simulations suggest that lateral melting can account for about 5%-29% of the total sea ice melting in the Arctic region (Perovich et al 2003, Tsamados et al 2015).Moreover, the surface and bottom melting of sea ice would result in open water formation only when the ice is very thin, but lateral melting promotes the formation of open water directly regardless of ice thickness.Given this, realistic representation of the lateral melting is crucial for accurate sea ice simulation and prediction, especially under the condition that the proportion of seasonal sea ice becomes larger due to the global warming.However, Keen et al (2021) found that the lateral melting process was not considered in 7 out of 15 Coupled Model Intercomparison Project Phase 6 (CMIP6) global climate models (GCMs).Moreover, the proportion of lateral melting is profoundly underestimated, only accounting for approximately 4% of total melting in the models.
The fact that the lateral melting of floes can accelerate sea ice retreat was first discovered by Zubov (1945), who derived a simple equation to describe this process.However, the assumption in this equation that all the solar radiation absorbed by the water is immediately and exclusively used for lateral melting is contrary to observations, especially when the waterway is wide (Doronin and Kheisin 1975).Parkinson and Washington (1979) used a simple lead parameterization scheme to calculate the proportion of heat absorbed by lead for lateral melting.However, the impact of sea surface temperature (SST) on lateral melting was not considered in this scheme.To improve this, Josberger and Martin (1981) established an empirical relationship between the SST and lateral melt rate based on the results of laboratory experiments.Perovich (1983), Maykut and Perovich (1987) further improved this empirical relationship by using the observation data from static leads in the Canadian archipelago, and the impact of the advection process of ocean currents on the lateral melt rate was also considered.Based on this, Steele (1992) further introduced the parameters of floe geometric shape and size into the lateral melting parameterization scheme, a scheme currently commonly used worldwide.
The lateral melting of sea ice is highly sensitive to the floe size.With the melting of floes, the effective perimeter of sea ice cover per unit area increases, enhancing the lateral melt rate and further increasing the open ocean surface area.The wider open seawater allows the absorption of more solar radiation, which further strengthens the lateral melting (Roach et al 2018).Numerical simulations have suggested that the floe size has non-negligible impact on the extent and volume of sea ice, especially in the marginal ice zone with the sea ice concentrations between 15% and 80%, where the interactions among oceansea ice-atmosphere-wave are complex (Bateson et al 2022).The scheme developed by Steele (1992) has considered the impact of floe diameter, where it is assumed that the floes in areas covered by sea ice have a constant size.However, it has been observed that the floe size varies from several meters to tens of kilometers (Rothrock andThorndike 1984, Stern et al 2018).Lüpkes et al (2012) established an empirical relationship between sea ice concentration and floe diameter in the marginal ice zone by using aircraft observation data in the Fram Strait.This scheme makes a great progress compared with default constant floe size.Moreover, owing to the accessibility of the sea ice concentration in the GCMs, this scheme is more convenient for application in large-scale sea ice simulations.A previous study showed that this scheme has a substantial impact on the surface roughness of sea ice in the model (Martin et al 2016), but further research is needed to investigate its impact on the lateral sea ice melt.
In view of this, this study introduces lateral melting and floe size distribution parameterization schemes into the medium resolution version of the Beijing Climate Center Climate System Model (BCC-CSM2-MR).The main objective is to improve the performance of the BCC-CSM2-MR in simulating the Arctic sea ice and explore the impact of varying floe size on the lateral melting of the Arctic sea ice.The remainder of this paper is organized as follows.A brief introduction to the lateral melting and the floe size parameterization schemes is given in section 2. Section 3 deals with the simulation results, and section 4 displays the conclusions and discussions.In this study, a modified thermodynamic seaice module developed by Fang et al (2022) is adopted as the thermodynamic module in SIS.The module is based on the Winton's three-layer thermodynamic sea ice model (Winton 2000), but the vertical resolution is increased to four layers.The effect of snow heat capacity is considered as well.Besides, parameterization schemes for vertical salinity profile and heat conductivity of sea ice are also introduced.The modified model has greatly improved the Arctic sea ice simulation, especially the sea ice thickness (Fang et al 2022).In addition, Sea ice dynamics is based on an elastic-viscosity-plastic rheology (Hunke and Dukowicz 1997).Sea ice is divided into five categories according to the thickness.The redistribution between different sea ice types is based on a simple enthalpy conservation principle.The sea ice (snow) albedo adopts the scheme from the Community Climate System Model version 3 (CCSM3, Briegleb et al 2004).(3) and (4).

The parameterization schemes for lateral melting and floe size
In this study, the lateral melting scheme developed by Steele (1992) is adopted, by which the variation of sea ice concentration (sea ice area) caused by lateral melting can be expressed as follows: ( dA dt where A is the sea ice concentration of each ice category, dt is the time step of the sea ice model, and M r is the lateral melt rate which is determined by the empirical relationship between the SST and the freezing temperature (Josberger andMartin 1981, Maykuat andPerovich 1987), T w is the seawater temperature over lead (usually expressed by the SST), and T f is the freezing temperature of seawater.m 1 = 1.6 × 10 −6 and m 2 = 1.36 are empirical values estimated by Perovich (1983) based on the observation of a single static lead in the Canadian Archipelago.L D represents the floe diameter, which has a constant value of 300 m.Lupkes et al (2012) further parameterized the floe diameter L D as a function of sea ice concentration based on the aircraft observation data in the Fram Strait, Here D min = 10 m and D max = 300 m are the minimum and maximum floe diameters, respectively.β [0.8-1.2] is constant with the value being 1.1 in this study.Figure 1 shows the variation curve of floe diameter with sea ice concentration calculated based on equations ( 3) and ( 4).It can be seen that the decreasing sea ice concentration corresponds to an increase in the marginal ice zone and a nonlinear decrease in the floe diameter, which are consistent with the observation (Lupkes et al 2012).
In addition, it should be pointed out that the salinity, heat and water fluxes between sea ice and ocean in the BCC-CSM2-MR need to be adjusted when the lateral melting occurs, since the energy for lateral melting is from the ocean.

Experimental design and data
A series of CMIP6 historical-type experiments are conducted using the BCC-CSM2-MR.The external forcings (including greenhouse gas concentrations, ozone concentrations, stratospheric aerosols, solar radiation, land-use types, and anthropogenic aerosol emissions based on simple plume parameterization) are derived from the CMIP6 webpage (https:// esgf-node.llnl.gov/search/input4mips/).The detailed experiment design is listed in table 1. Exp_ctr is the control experiment conducted by the BCC-CSM2-MR without considering the lateral melting.The other two experiments take the lateral melting into consideration, but the floe diameter is constant in Exp_d300 and calculated using the scheme from Lüpkes et al (2012)

Results
As is well known, the melting period of Arctic sea ice is mainly in the summer, resulting in the minimum ice cover in September.Figure 2 shows the distributions of the simulated and observed sea ice concentration in September.It can be seen that the observed sea ice in September is mainly located on the Arctic Basin and the north of the Canadian Arctic Archipelago.The Exp_ctr overestimates marginal ice zones for the entire Arctic Ocean, especially for the Greenland/Iceland/Norwegian (GIN) and the Barents Seas (figure 2(b)).Exp_d300 shows the similar biases, but with a slightly improved magnitude (figures 2(c) and (f)).In contrast, the sea ice concentration simulated by Exp_new has notably decreased in all marginal ice zones of Arctic Ocean compared with those in Exp_ctr and Exp_d300, and the area with the sea ice concentration above 80% is obviously smaller, comparing better with observation (figures 2(d) and (g)).This is due to the enhanced lateral melting in Exp_new, which is associated with the reduced average floe diameter when compared with the Exp_d300 as shown in figure 1.
Figure 3 shows the spatial distributions of the simulated and observed Arctic sea ice thickness in September.It is found that the maximum of observed sea ice thickness in September is located over the north of Canadian Archipelago and Greenland, which gradually decreases towards the Eurasian Continent.These features are generally captured by the Exp_ctr, but the sea ice thickness is apparently underestimated over the Beaufort Sea, Chukchi Sea and central Arctic and overestimated along the North Atlantic sector including the Kara Sea, Barents Sea and GIN Seas (figure 3(a)).Inclusion of lateral melt parameterization within BCC-CSM2-MR results in a reduction of sea ice thickness over the whole Arctic region especially when the varying floe size scheme is considered (figures 3(b) and (c) and (g)).This indicates that lateral melting process aggravates the deterioration of sea ice thickness simulation over the central Arctic and the marginal ice areas along the Pacific sector, although the marginal ice thickness along the North Atlantic sector is slightly improved.
Figure 4(a) exhibits the seasonal variations of Arctic sea ice extent (SIE) and volume.It is note that all three experiments well simulate the seasonal variations of SIE which is featured by a maximum in March and a minimum in September, consistent with the observation.However, the Arctic SIE in all months are overestimated by the three experiments, with the largest bias in Exp_ctr, followed by Exp_d300.By contrast, Exp_new has the smallest SIE bias, especially in summer and autumn.Similarly, the seasonal variations of sea ice volume in all experiments are comparable to the observations (figure 4(b)).However, the sea ice volumes in all months are overestimated by Exp_ctr.This bias in Exp_d300 is slightly reduced but still exists, similar to the model behavior in simulating the SIE.In contrast, the sea ice volume in Exp_new is in better agreement with the observation, although the magnitude is slightly underestimated probably due to the thinner sea ice in this experiment as shown in figure 3(d).
The time series of Arctic SIE and sea ice volume in September from 1982 to 2014 are further analyzed.Similar to figure 4(a), the SIE is overestimated by all experiments in all years, among which Exp_new is most close to the observation.In addition, the observed SIE shows a decreasing trend from 1982 to 2014 with a value of −0.069 × 10 6 km 2 yr −1 .This trend is captured by all experiments, especially for Exp_new with a value of −0.071 × 10 6 km 2 yr −1 showing the best, followed by Exp_d300 and Exp_ctr with values of −0.055 and −0.042 × 10 6 km 2 yr −1 respectively (table 2).Furthermore, although the sea ice volume is underestimated by Exp_new in most years (figure 4(d)), the decreasing trend is better reproduced with a value of −0.235 × 10 6 km 3 yr −1 in Exp_new versus −0.347 × 10 6 km 3 yr −1 in observation, whereas those in Exp_ctr and Exp_d300 are −0.137 and −0.194 × 10 6 km 3 yr −1 respectively (table 2).These results indicate that the sea ice lateral melting scheme with varying floe size can substantially improve the model performance in simulating the declining trend of Arctic sea ice over the past 30 years.
To further explore the reason for the improvement on the Arctic sea ice simulation especially for its decreasing trend after considering the lateral melting, figure 5 shows the seasonal and summer time series of total melting, surface melting, bottom melting, and lateral melting averaged over the Arctic basin (area north of 70 • N) in the three experiments.It is illustrated that all melting processes occur mainly in summer, and the total melting in summer simulated by Exp_new is notably larger than the other two experiments (figure 5(g)).Considering that the differences in surface and bottom melting among the three experiments are negligible (figures 5(c) and (e)), the differences in total melting mainly result from the larger lateral melting owing to the relatively smaller average floe diameter in Exp_new (figure 5(g)).Further analyses reveal that there is no significant trend for the summer total melting from 1982 to 2014 in Exp_ctr with the linear trend of 0.015 W m −2 yr −1 , whereas Exp_d300 and Exp_new show significant increasing trend at rates of 0.285 and 0.442 W m −2 yr −1 , respectively (figure 5(b)).Table 2 implies that both the bottom and lateral melting contribute to this change of total melting in Exp_d300 and Exp_new, as illustrated by their larger linear trends.It should be noted that although the linear trends of lateral melting in Exp_d300 and Exp_new are small in terms of the magnitude (table 2), they may still play an essential role in the increased total melting because of the continuously reduction of total sea ice volume from 1982 to 2014.
Here, a possible positive feedback mechanism is proposed.When the lateral melting of sea ice is considered, the increasing open water caused by lateral melting leads to the absorption of more solar radiation and increased net heat flux into the ocean, which can further enhance the bottom and lateral melting and reduce the sea ice area and volume finally.It seems that this positive feedback enhances from 1982 to 2014 especially when the varying floe size is considered in Exp_new as can be shown in table 2. This may be the main reason for the improvements in the simulation of the declining trend of Arctic sea ice in recent 30 years by Exp_new as shown in figures 4(c) and (d).The enhancements of positive feedback in the Exp_d300 and Exp_new may be associated with the strengthening of lateral melting from 1982 to 2014.From figures 6(b) and (c), it can be seen that the average SST in the polar region increases and the sea ice concentration decreases with the global warming in all experiments, among which Exp_new shows the largest linear trend (0.016 • C yr −1 for SST and −0.248% yr −1 for sea ice concentration), followed by the Exp_d300 (0.012 • C yr −1 for SST and −0.191% yr −1 for sea ice concentration).According

Conclusions and discussions
Lateral melting is an important component of the sea ice melting processes, but is excluded in most CMIP6 models.Accurate modeling of this process is important to understand the mechanisms for the rapid decline in summer Arctic sea ice during the last decades.By coupling the lateral melting and floe size parameterization schemes into the BCC-CSM2-MR model, the impact of the lateral melting process on Arctic sea ice simulation was explored, and the influence of floe size on lateral melting process was also analyzed.The main conclusions are summarized as follows: Similar to the surface and bottom melting of sea ice, the lateral ice melt process mainly occurs in the summer.The experiment results by using BCC-CSM2-MR show that lateral melting can remarkably improve the Arctic sea ice area simulation in September especially when the varying floe diameter scheme is introduced.This is associated with the enhanced lateral melting effect due to the decrease in average floe diameter.However, lateral melting also results in an underestimation of sea ice thickness, although it makes the simulated sea ice volume closer to the observations.Since many CMIP6 models systematically overestimate the Arctic sea ice thickness and volume (Langehaug et al 2013, Long et al 2021), the introduction of the lateral melting process may have a positive effect on improving the sea ice simulation of current GCMs.
Our results show that the increased open water area caused by the lateral melting absorbs more solar radiation, further enhancing the bottom and lateral melting and reducing the sea ice area and volume finally.This positive feedback process has strengthened from 1982 to 2014, resulting in a better simulation of the rapid decline of Arctic sea ice cover and volume in BCC-CSM2-MR, which remains a considerable challenge for most CMIP6 GCMs (Shu et al 2020).Further analysis indicates that, with the reduction of sea ice concentration, the average SST in the polar region increases and the floe diameter decreases from 1982 to 2014.These changes accelerate the lateral melt rate from 1982 to 2014, which is the main reason for the enhancement of this positive feedback.
It should be noted that although the scheme proposed by Lüpkes et al (2012) well characterizes the relationship between the sea ice concentration and floe diameter in the marginal ice zone, there are still some limitations in this scheme.The variation of floe diameter is not only related to the sea ice concentration, but also to the low-level wind field, ocean current and waves (Perovich and Jones 2014, Boutin et al 2021), especially under the condition of global warming when sea ice becomes thinner (Rae et al 2014).Therefore, such factors need to be considered and optimized by using the latest polar observational data to further improve the lateral ice melt parameterization scheme.Finally, figure 5 indicates that lateral melting can account for above 30% of the total melting, which is higher than the findings of some previous studies (Perovich et al 2003, Tsamados et al 2015).This may be partly due to the overestimation of marginal ice zone as shown in figure 2 in BCC-CSM2-MR, which can exaggerate the lateral melt rate through reducing floe diameter.Implementations of lateral melting scheme on more GCMs are needed to further test its effect and dependence on model performance in the future.
The BCC-CSM2-MR is a fully-coupled GCM participating in CMIP6 (Wu et al 2019), which was developed by the Center for Earth System Modeling and Prediction of the China Meteorological Administration.There are four components in BCC-CSM2-MR: the atmospheric component is the BCC Atmospheric General Circulation Model version 3.0 (Wu et al 2010), the land component is the BCC Atmosphere Vegetation Interaction Model 2.0 (Li et al 2019), the oceanic component is the Modular Ocean Model version 4 (MOM4; Griffies et al 2005), and the sea-ice component is the sea ice simulator (SIS; Winton 2000).All components are dynamically coupled by the commonly used coupler CPL5.0 from the National Center for Atmospheric Research.The atmospheric and land components have a horizontal resolution of T106 (1.125 • × 1.125 • ), and 46 layers in the vertical direction.The MOM4 has 40 vertical layers with a horizontal resolution of 1 • × 1 • poleward of 30 • N and 30 • S gradually descending to 0.33 • between 30 • N and 30 • S. The SIS has the same horizontal resolution with the MOM4.These are the main configurations of BCC-CSM2-MR for CMIP6.Preliminary validation of BCC-CSM2-MR indicates that it can moderately capture the declining trend of Arctic sea ice, but larger positive biases exist in climatology especially for the sea ice concentration, which is similar to most CMIP6 models (Wu et al 2019, Long et al 2021).
in Exp_new.All experiments are run from 1972 to 2014.The atmosphere, land, and ocean is initialized by the state of 1 January 1972 from the BCC-CSM2-MR CMIP6 historical simulation.The initial thickness and temperature of each sea ice layer are prescribed to 1 m and −5 • C, respectively.In this study, the simulation results of all the experiments from 1982 to 2014 are analyzed.Besides, the datasets of sea-ice concentration and SST from the Met Office Hadley Centre (Rayner et al 2003) and the sea-ice thickness output by the Pan-Arctic Ice Ocean Modeling and Assimilation System (Zhang and Rothrock 2003) are used to validate the simulation results.

Figure
Figure Same as figure 1, but for the Arctic sea ice thickness.

Figure 4 .
Figure 4. Seasonal cycles and September time series of Arctic sea ice (a), (c) extent and (b), (d) volume over the period 1982-2014.

Figure 6 .
Figure 6.Summer time series of (a) net sea surface heat flux (downward is positive), (b) sea surface temperature, and (d) sea ice concentration over the Arctic basin for the period 1982-2014.
D = 300 m Exp_new Parameterization of lateral melting is used with effective floe diameter L D parameterized by Lüpkes et al (2012)

Table 2 .
Linear trend of September Arctic sea ice extent and volume, and summer mean total melting, top melting, bottom melting, lateral melting, sea surface net heat flux, sea surface temperature, and sea ice concentration over the Arctic basin.