Arctic sea ice sensitivity to lateral melting representation in a coupled climate model

The melting of sea ice floes from the edges (lateral melting) results in open water formation and subsequently increases absorption of solar shortwave energy. However, lateral melt plays a small role in the sea ice mass budget in both hemispheres in most climate models. This is likely influenced by the simple parameterization of lateral melting in sea ice models that are constrained by limited observations. Here we use a coupled climate model (CESM2.0) to assess the sensitivity of modeled sea ice state to the lateral melt parameterization in pre-industrial and 2xCO2 runs. The runs explore the implications 5 of how lateral melting is parameterized, and structural changes in how it is applied. The results show that sea ice is sensitive both to the parameters determining the effective lateral melt rate, as well as the nuances in how lateral melting is applied to the ice pack. Increasing the lateral melt rate is largely compensated by decreases in the basal melt rate, but still results in a significant decrease in sea ice concentration and thickness, particularly in the marginal ice zone. Our analysis suggests that this is tied to the increased efficiency of lateral melting at forming open water during the summer melt season, which drives the 10 majority of the ice-albedo feedback. The more seasonal Southern Hemisphere ice cover undergoes larger relative reductions in sea ice concentration and thickness for the same relative increase in lateral melt rate, likely due to the hemispheric differences in the role of the sea ice-upper ocean coupling. Additionally, increasing the lateral melt rate under a 2xCO2 forcing, where sea ice is thinner, results in a smaller relative change in sea ice mean state, but suggests that open water formation feedbacks are likely to steepen the decline to ice-free summer conditions. Overall, melt processes are more efficient at forming open water in 15 thinner ice scenarios (as we are likely to see in the future), suggesting the importance of accurately representing thermodynamic evolution. Revisiting model parameterizations of lateral melting with observations will require finding new ways to represent salient physical processes.

diameter on the order of 30 m or less, while another study suggests that lateral melt is sensitive to floe size with diameters 100 m or less (Tsamados et al., 2015). Hunke (2014) found that in a coupled climate model, lateral melting may be important, 60 despite being a small term in the mass budget, because of the sensitivity of sea ice to thermodynamic processes, especially in thin ice categories. Model experiments showed that although lateral and basal melt are both driven by heat in the ocean, they may respond to model changes in different ways. Skyllingstad et al. (2005) developed an large-eddy simulation model for leads which showed that freshwater stratification in leads plays a major role in controlling lateral melting. It is clear that further field data are required to illuminate the relationships of physical controls with lateral and basal melt rates, as existing empirical relationships (Perovich, 1983) have large uncertainties as a result of limited observations. The lateral melt rate has been suggested to be particularly sensitive to floe sizes (Steele, 1992;Roach et al., 2018Roach et al., , 2019Boutin et al., 2020;Bateson et al., 2020). With recent model developments to include a floe size distribution (e.g., Zhang et al., 2015;Roach et al., 2018Roach et al., , 2019Boutin et al., 2020Boutin et al., , 2021Bateson et al., 2020), there has been renewed interest in the modeling community to properly describe lateral melt. However, all sea ice models incorporating floe size still utilize the 70 empirical relationship for lateral melting introduced by Perovich (1983). There is a notable disconnect in the evolution of models to include more complex and realistic physics and the progress of our physical understanding of lateral processes that drive these changes. Roach et al. (2018Roach et al. ( , 2019 and Bateson et al. (2020) explored the sensitivity of sea ice to higher lateral melting by incorporating a floe size distribution with smaller floe sizes. They found that increased lateral melting was largely compensated for by decreased basal melting in standalone sea ice models, but the reduction in basal melt was smaller than the 75 increase in lateral melt in a coupled sea ice-ocean setup . Even further differences might be expected in a model with a coupled atmosphere that allows feedbacks related to the formation of open water.
Previous studies have explored the importance of open water for sea ice mean state by using what was defined by Holland et al. (2006b) as the open water formation efficiency: the area of open water formed in a region as a result of a unit reduction in sea ice volume. The mean sea ice thickness and volume are strongly related to the total summer open water formation 80 efficiency in models, as the open water formation is important for sea ice volume evolution (Holland et al., 2006b;Massonnet et al., 2018). The open water formation efficiency has since been used to understand the trajectory of the Arctic towards an icefree summer, indicating the importance of melt processes on the ice-albedo feedback in capturing sea ice response to forcings (i.e., Massonnet et al., 2018;Lindsay et al., 2009;Merryfield et al., 2008). While the efficiency of different melt processes at forming open water has not been explored, we expect that the relative magnitude will play a role in determining the resulting 85 sea ice state.
In the present paper, we modify the lateral melt parameterization in a coupled global climate model, CESM2.0. The main objective of this study is to investigate to what extent lateral melting can affect the simulation of sea ice in a coupled climate model as a result of factors driving sea ice change associated with open water formation, including the ice-albedo feedback.

CESM2.0
Sensitivity tests were completed with CESM2.0 (Danabasoglu et al., 2020) using a constant pre-industrial forcing, over a global model domain with nominal horizontal resolution of 1 • . Runs were branched from year 880 of the CESM2.0 CMIP6 preindustrial control run (Danabasoglu et al., 2020), providing fully initialized states for all model components. CMIP6 preindustrial control runs are forced by interannually invariant atmospheric conditions appropriate for the year 1850. 95 The model runs completed here have fully coupled atmosphere, sea ice, and land models, and a simplified slab ocean model (SOM). The SOM replaces the standard full-depth ocean model with a surface ocean mixed layer governed by the equation (Eq. (1) from Bitz et al., 2012): where ρ o is the density of seawater, c p is the ocean heat capacity, h and Q f lx are respectively the mixed layer depth (MLD) 100 and ocean heat flux convergence (associated with advection and mixing) obtained from a fully coupled CESM2.0 run, and F net is the net heat flux to the ocean. The prescribed MLD h varies spatially based on climatological conditions simulated by CESM2.0 coupled runs with an active ocean component. However, it is constant over time (i.e., doesn't vary seasonally or inter-annually), and has a minimum depth of 10 m. The prescribed ocean heat flux Q f lx varies both spatially and seasonally.
The mixed layer temperature (here defined as equivalent to the sea surface temperature, SST) evolves with surface heat fluxes 105 determined by the coupled climate model; thus ice-albedo feedbacks are permitted. A result of the prescribed MLD and Q f lx is that feedbacks associated with ocean dynamics and mixing are not present, and there is no ability for variability in ocean dynamics to drive changes in ocean heat content.
The use of the SOM requires significantly less computational time as a result of not running a full ocean model, and because it allows the model to converge much faster -around 30 years vs. 100s of years for the fully coupled model. Nonetheless, runs 110 with a SOM reproduce the climate of the fully coupled model quite well (Bitz et al., 2012); it has been particularly used to assess climate sensitivity Gettelman et al., 2019)   , which uses mushy-layer thermodynamics by default Bailey et al., 2020). Other key features include the elastic-viscous-plastic rheology and sub-grid ice thickness distribution, with a default of five categories, as standard in prior versions of the CICE model ( Fig. 1). Sea ice 120 simulated by CESM2.0 over the historical period has reasonable mean state and variability in both hemispheres (DeRepentigny et al., 2020). The version used here uses tuned albedos for a more realistic simulation of ice thickness (Kay et al., in review). Specifically, the albedo of snow on sea ice was increased by decreasing the snow grain radius (with an increase of the parameter r snw from 1.25 to 1.5), and the temperature at which snow grain growth is permitted to occur (due to melting conditions) was increased by 0.5 • C from 1.0 to 1.5 • C.

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Each run was at least 60 years long, and averaging was typically done over the last 25 years (simulation years 35-60) after the system has equilibrated and to minimize the contribution from internal variability. Monthly-averaged outputs are used to examine changes in mean state of the sea ice for computation efficiency and for better comparison with other studies (which typically use monthly averages), while daily averages are required to examine efficiency of melt processes.

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The CICE model includes an ice thickness distribution, which is common across most modern global sea ice models (Keen et al., 2021). Sea ice is discretized into a set number of categories, which occupy an evolving fraction of the grid cell. Sea ice volume and area are transferred between categories as a result of sea ice melt and growth, as well as dynamic processes. Lipscomb (2001) introduced a linear remapping scheme to transfer ice between categories, which has faster convergence and is less diffusive than prior schemes.

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Based on the results of Bitz et al. (2001), a majority of global climate models with a sea ice component use five thickness categories as the default (Keen et al., 2021), where all are assumed equally in contact with open water (Fig. 1). Runs in a coupled climate model showed that this number struck a balance of capturing the features of runs with higher numbers of categories, while still keeping computational load low. However, there are a number of different schemes for determining the boundaries of the discretized ice thickness categories. The original discretization scheme, used here, follows the definition of 140 category boundaries from Eq. (22) in Lipscomb (2001) which gives more widely spaced boundaries for thicker ice. The higher resolution for thin ice is beneficial to minimize diffusion, as well as to better resolve the evolving mass budget. The mass budget has a non-linear sensitivity to ice thickness because of the inverse relationship with congelation growth, where thick ice grows slowly and thin ice grows rapidly (e.g., Massonnet et al., 2019).

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The lateral melt rate is determined based on an empirical relationship with the difference of the SST from freezing (∆T ) giving a uniform melt rate around the perimeter of the floe: where the constants are based on empirical estimates from a single static lead in the Canadian Arctic by Perovich (1983), m 1 = 1.6 × 10 −6 (units m s −1 deg −m2 ), and m 2 = 1.36 (unitless).

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This is then used to calculate the change in ice concentration (a) for each thickness category as a result of lateral melt over a given time-step, dt (Steele, 1992). Effective floe diameter (D) is a constant value of 300 m by default that does not evolve with melting. α is a floe shape parameter representing the non-circularity of floes set at a default of 0.66 (Rothrock and Thorndike, 1984). Note that the change in area in each category over a timestep da dt lat,n is referred to as r side in the model.

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This lateral melting parameterization is commonly used throughout coupled climate models. For example, six of the eleven CMIP6 models examined by Keen et al. (2021) include a lateral melt parameterization, and all of these use the sea ice model CICE with the same lateral melt parameterization described here. We note again here that while there are recent model developments to include an evolving floe size distribution based on coupled processes (e.g., Zhang et al., 2015;Roach et al., 2018Roach et al., , 2019Boutin et al., 2020Boutin et al., , 2021Bateson et al., 2020), most models do not currently have the capability to have a variable floe 160 size or include the necessary couplings (such as surface waves).
Finally, the lateral melt rate, (dV /dt) lat , is calculated as where V ice,n is the volume of ice in each thickness category, n.
The sum of ocean flux terms is not allowed to exceed the heat content in the ocean surface layer. If the sum of lateral and 165 basal heat flux represents a larger flux than that available, the lateral and basal heat fluxes are both reduced by the scalar factor necessary such that all ocean heat content is lost to the ice.
For a selected part of the historical period , CESM2 predicted 0.4 Gt×10 3 mass loss per year associated with lateral melting, which is about 4.2-4.8% of the total mass loss per year associated with vertical melting (with the range representing configurations with different atmospheric models; Keen et al., 2021). With the pre-industrial forcing and configuration of CESM2 used in this study, the average annual volume loss from lateral melting is similarly about 4.5% of the volume loss associated with vertical melting (Fig. 5).

Sensitivity experiments
The control run using default parameterizations of lateral melting as described above (i.e., floe diameter = 300 m) was run using a constant pre-industrial forcing for sixty years, and three additional experiments of 60-year duration were performed. To 175 test the impact of increased lateral melting, we completed two runs where the constant floe diameter D was decreased to 30 m and 3 m, where floe size is used as a convenient approximation for lateral melt rate in the context of this study. These decreases in floe size effectively increase the lateral melt rate by 10x and 100x, respectively. Observations of floe size distribution are limited, and do not have sufficient spatial or temporal coverage to determine what floe size is most representative for icecovered regions; the most complete coverage is provided by satellite products such as CryoSat-2 , but the 180 relevance for lateral melt is significantly limited by the footprint of 300 m. Notably, our sensitivity simulations are not designed to assess the influence of a more realistic floe diameter, but instead to investigate the cumulative influence of uncertainties in the magnitude of lateral melting and to explore the physical processes that govern the sea ice response. As such, changes to the floe size are used as a catchall for factors impacting the sensitivity of the lateral melt rate. Other parameters controlling the rate of lateral melting as a function of temperature difference, m 1 and m 2 , were kept the same, but it is noted that the effect of 185 increasing m 1 is the same as decreasing the diameter D (Fig. 2) such that the 10x and 100x sensitivity runs can alternatively be thought of as m 1 = 1.6 × 10 −5 and m 1 = 1.6 × 10 −4 , respectively. There is substantial uncertainty in the default m 1 and m 2 parameter values, which were derived from a single set of observations (Perovich, 1983). Therefore, these large perturbations are justified by the uncertainties in the functional form of this parameterization and allow us to examine how they impact the sea ice and climate system. As the lateral melt already comprises a small fraction of the mass budget in the control run (Fig. 190 5), sensitivity runs with decreased lateral melting were not completed.
For the control and increased lateral melt rate (10x and 100x) runs, Eq. (4) suggests that lateral melt occurs equally in all thickness categories such that all decrease by the same percent each time step. However, we can imagine a number of physical reasons why lateral melt rate might be unequally distributed across the ice thickness categories, including: (i) the possibility that the upper ocean is stratified as a result of heating during the melt season (i.e., Holland, 2003), (ii) the potential for a 195 relationship between ice thickness and floe size, (iii) cases where the open water area (leads) that result in lateral melting are unequally distributed across the ice thicknesses. While we can not yet explicitly test the impact of these processes in the model, we can explore the impact of the non-uniform lateral melt they may result in. Although there are not yet large-scale observations of floe size or lead distribution with respect to ice thickness, we hypothesize that thinner ice will have smaller floe sizes on average, and that open water is more likely to be adjacent to thinner ice categories due to the lower ice strength.

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Therefore, we perform an additional sensitivity test of the model distribution of lateral melting by increasing the melt rate in thin classes and decreasing it in thick classes. Eq. (4) is altered to include an ITD re-distribution factor (r n ) over the n ice categories: The schematic in Fig. 2 summarizes the effective changes to lateral melt rate in each of these runs compared to the control.
The changes to the effective lateral melt rate scale are larger for the 10x and 100x runs (blue and purple, respectively) than for the redistribution run (light red), but remain evenly applied across all thickness distribution categories (delineated by the grey dashed lines).
This permits the examination of the contribution of melt processes to the albedo feedback, regardless of the total volume of melt that they currently result in within the model. We look only at grid cells from daily outputs with non-zero melt rates and zero total growth rates in order to isolate the influence of melt processes. The OWFE of lateral melt is specifically defined as: In general, the calculation of change in concentration from lateral melt is calculated as: With the default model configurations, where lateral melt as defined in Eq. (4) is applied to all thickness categories equally, this simplifies to: Thus, the area of open water formed from lateral melting is directly proportional to the average ice thickness in the grid cell in 230 the control and sensitivity runs with increased lateral melt rate. For the run with lateral melt redistribution, the OWFE of lateral melt will additionally include the redistribution factor: Vertical melt is a result of both basal and surface melt. The efficiency of vertical melt processes (OWFE vert ) is calculated using the difference between the total change in concentration due to thermodynamic processes (output daily from the model 235 as (da/dt) thermo ) and the change in concentration due to lateral melt: The open water formation efficiency of vertical processes is then: The schematic in Fig. 1 Figure 3 shows the seasonal cycle of sea ice area, volume, average thickness, average fractional coverage (calculated as the ratio of sea ice area to extent), and thick ice area in the Northern Hemisphere with a constant pre-industrial forcing. As is The most notable effect on sea ice state in sensitivity runs is that increasing the lateral melt rate reduces sea ice volume (Fig.   3b). However, there is a minor response to the 10x increase in lateral melting, while the 100x increase drastically reduces sea ice volume (by approximately 5×10 12 m 3 during all months), and moderately reduces sea ice area (Fig. 3a). In fact, the average 255 thickness is somewhat higher July to October in the 10x run compared to the control, while it is significantly reduced in the 100x run (Fig. 3c). Redistribution of lateral melt to thin categories reduces the sea ice volume across all months. Contrary to intuition, substantial increases in the lateral melt rate do not necessarily result in reductions of sea ice area and volume of a comparable magnitude. The ratio of sea ice area to sea ice extent is approximately equal to the average fractional coverage (Fig. 3d). All runs atmosphere-ocean interactions in ice-covered areas when the lateral melt rate is higher. Increasing the lateral melt rate primarily reduces the sea ice concentration around the margins (Fig. 4b-c), where the sea ice is relatively thin and has low concentration 265 during the summer (Fig. 4a). For example, there is a substantial decline (∼20-30% in July) in Hudson Bay in the 100x run compared to the control (Fig. 4c). Here, the ice is relatively thin and increasing the efficiency of formation of open water can contribute to an albedo feedback. The changes in spatial patterns with the redistribution of lateral melt (Fig. 4d) results from the patterns in ice thickness distribution, where the relatively high proportion of thick ice to thin ice in summer in the Barents Sea results in an increase in concentration.

Changes in mass budget
The average volume of sea ice grown and melted annually is comparable across all runs, as shown by mass budgets in Fig.   5. This agrees with the consistent amplitude of the sea ice volume seasonal cycle seen in Fig. 3b. This is primarily because the increase in total lateral melting (when lateral melt rate is increased) is largely compensated by a decrease in basal melting, such that the change in total sea ice melted is small. Both lateral and basal melting are driven by heat in the slab ocean model.

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As there is a finite amount of heat available in this layer, increasing the heat used for lateral melting reduces the heat available for basal melting. The change in the sea ice area also contributes to the observed basal melt decrease. Following the analysis by Bateson et al. (2020, Fig . 5), we find a partial contribution from loss of ice area; for example, in July it accounts for 33% in the 10x run and 48% in the 100x run, compared to the nearly complete attribution in their standalone sea ice model runs.
More rapid lateral melt increases the total melt rate early in the season, when more heat is available, but decreases it later 280 in the summer as more heat has already been used for melting and solar insolation is lower. We note that although the total Although there is a similar magnitude change in the volume of lateral melt from the control run to the 10x and 100x sensitivity runs (Fig. 5), there is a significantly more drastic decrease in sea ice area and volume in the 100x lateral melt run 285 compared to the 10x lateral melt run (Fig. 3). This suggests that the feedbacks associated with increased lateral melting are initially small, such that the increase associated with the 10x run results in little change in total sea ice. As the lateral melt rate becomes much larger, there is more open water formed in ice covered areas over the melt season (Fig. 3c) and the feedbacks are significant enough to result in substantial changes in sea ice mean state. This likely includes the ice-albedo feedback, as well as other processes related to dynamic and thermodynamic changes in the ice.

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The portion of the mass budget accounted for by lateral melting is decreased in the lateral melt redistribution run, despite the intention to keep the total lateral melt approximately the same. This is likely a result of the adjustments to the lateral melt parameterization (Fig. 2) and the unequal distribution of sea ice between categories; the redistribution results in more rapid melt of thin ice, which results in less thin ice to melt, and there is less lateral melting in the thick ice that remains. The seasonal cycle of the mass budget (not shown) shows that total melt is in fact increased early in the melt season, but approximately 295 unchanged in mid-late summer.  When the lateral melt rate is increased, it not only comprises a larger portion of the total ice volume melted (Fig. 5), but also forms open water more efficiently for the same volume melted (Fig. 6). The OWFE of lateral melting is more drastically increased for the 100x run, to 0.47 m 2 /m 3 . As the lateral melt OWFE is closely tied to the average sea ice thickness, it is clear to see that this is a result of the thinner ice and reduction in thick ice area (Fig. 3c,e). However, it is less clear why there is still 305 an increase in lateral OWFE for the 10x run, where average sea ice thickness is actually higher. Here, the importance of thick ice in different melt processes is underscored. The thick ice area in the 10x lateral melt run is lower than in the control run, especially during the peak of the melt season (Fig. 3e). This results in an increase in the fraction of moderate thickness ice, in the range at which lateral melting is relatively efficient at forming open water.

Open water formation efficiencies
The OWFE of vertical melting is significantly reduced to 0.25 m 2 /m 3 for the 100x run because lateral melting more effi- Interestingly, the total OWFE remains approximately constant across all sensitivity runs. This is most surprising for the 100x lateral melt run, where we may expect a higher total OWFE as a result of thinner ice on average. Massonnet et al. (2018) showed that across a range of climate models, runs with less ice volume have higher OWFE. (Though, it is worth noting that their definition of OWFE varies from that used here in that it is defined as the linear fit between annual summer area loss and volume loss, such that it may be more related to inter-annual variability.) This suggests that for a single model, the mean state 320 of the sea ice is more a result of the distribution of thermodynamic processes, rather than just the total OWFE. Altering the lateral melt parameterization changes the open water formation in a way that is not fully reflected in the average thickness or sea ice mass budget.

Redistributing lateral melt towards thin categories results in large increases in OWFE of lateral melting as thin ice is more
rapidly converted to open water (Fig. 6), but the vertical and total OWFE remain essentially unchanged. Both of these are 325 a result of changes in the distribution of ice thickness. Basal melt transitions sea ice between categories, while lateral melt does not, such that an unintended consequence of reducing lateral melt in the thick categories is increasing basal melt in these categories. This results in overall less thick ice (Fig. 3e). So, the lateral OWFE increases in the redistribution sensitivity run not only because the alterations to the parameterization form open water more efficiently, but also because there is thinner ice on average, which inherently forms open water from lateral melting more efficiently. However, changes to average thickness is on average thinner due to the inclusion of thin first-year ice in the marginal ice zone (Fig. 7). The OWFE of lateral melt remains high throughout the melt season, and is higher than vertical melt after June 1.
The changes in basin-averaged sea ice thickness in Fig. 7b delineate two melt regimes that correspond to the temporal importance of melt processes. From April until early June, the average thickness over the entire Northern Hemisphere ice pack is increasing. This indicates that mass loss is dominated by the melt of thin ice. In mid-June, the average thickness begins

Sensitivity in the Southern Hemisphere
Here, we have focused on the sensitivity of modeled Arctic sea ice thickness and volume to lateral melting parameterizations.
The majority of observations of lateral melting have been made in the Arctic, where the sea ice area and volume are under- going the most drastic changes. We expect the sensitivity to melt parameterizations to be somewhat different in the Southern Hemisphere, where sea ice is typically thinner and more seasonal, and there is more ocean heat availability.
355 Figure 8 shows the seasonal cycle of sea ice area and volume in the Southern Hemisphere. Sea ice area and volume are significantly lower year-round for all sensitivity runs. In particular, the area and volume of sea ice is approximately 50% lower during the summer months in the 100x lateral melt rate run compared to the control. The relative reductions in the 10x and 100x runs indicate a more linear response of sea ice to the lateral melt rate compared to the Arctic. Here, the 10x lateral melt and redistribution runs result in nearly the same reduction in sea ice area and volume. The redistribution of lateral melt to thin 360 ice categories has an even larger impact than in the Arctic, likely due to the larger proportion of thin ice. It is notable that redistribution results in a comparable decrease in ice to the 10x run, despite negligible change in the lateral melt (Fig. 10).
The reduction in Southern Hemisphere summer sea ice concentration is well-distributed across the ice-covered area (Fig. 9), in comparison to the changes in the Northern Hemisphere which were focused around the marginal ice zone.
As in the Arctic, the increase in total lateral melt in the Southern Hemisphere sea ice results in a decrease in total basal melt 365 (Fig. 10). However, the total melt in the mass budgets here are lower when lateral melt is increased and there is less ice (Fig.   8b), whereas the total melt volume remained comparable across runs in the Arctic (Fig. 3b). In fact, nearly all of the decrease in basal melt can be attributed to the loss of sea ice area to melt (following the methods of Bateson et al. (2020)). This suggests that the limiting factor in total melt in the Southern Hemisphere is likely the amount of sea ice, rather than the available heat in the ocean. This is consistent with the larger ocean heat flux convergence (Q f lx ) prescribed in the model for the Southern Ocean 370 compared to the Arctic. Increasing the lateral melt rate results in similar rates of heat flux from the ocean to the ice in most areas of the Antarctic, but over the smaller resulting ice-covered area (Fig. 9). This results in a relatively uniform observed decrease in sea ice concentration across the ice-covered area (Fig. 9b-c). In contrast, in the Arctic, increasing lateral melt 100x increases the rates of heat flux from the ocean to the ice in the summer, but over a smaller area. The limiting factor in melt in   the Arctic Ocean is the available ocean heat, and the reduction in ice area compensates for the increased ice-ocean heat flux to 375 result in a similar total annual melt.
The OWFE of lateral melting in the Antarctic is higher early in the melt season, when open water likely contributes to larger ice-albedo feedback (Fig. 11). The OWFE of vertical melting for the control run peaks in early January, when it becomes more efficient than lateral melting. During January to February, the thin ice is melting more rapidly and the average thickness of the ice is increasing. The OWFE of lateral melting and vertical melting diverge more strongly in the 100x run (magenta lines in 380 Fig. 11). Here, lateral melting has a higher efficiency at forming open water than vertical melting through nearly the entirety of the melt season. As the average ice thickness peaks in mid-February, and the average ice thickness begins to decline due to the formation of new ice in some regions, the vertical melt OWFE increases again. Similar shapes are seen across the other runs. The increased absorption of shortwave radiation due to an ice-albedo feedback is likely to play a role in delaying the ice growth during freeze-up. The differences observed in the role of lateral melting in the Antarctic compared to the Arctic may 385 be indicative of what we might expect to see for Arctic sea ice in the future, when an ice-free summer is common and sea ice is even more seasonal.

Sensitivity in a 2xCO 2 scenario
We expect melt processes to be different in other climate conditions with less overall sea ice, particularly in the Arctic where there is more often multi-year ice. We completed sensitivity runs with control and 100x lateral melt rate settings in a 2xCO 2 390 scenario. Runs were branched from an experiment with atmospheric carbon dioxide abruptly increased to 2x pre-industrial levels that has been run to steady state.
There is lower sea ice area and volume from November to July in a 2xCO 2 scenario with 100x the default lateral melt rate (Fig. 12). Both the control and 100x runs experience an "ice-free summer", with effectively no sea ice from July through October (Fig. 12a). Compared to the runs with a pre-industrial forcing, there is less total and percent change from increasing the lateral melt 100x as the sea ice is already substantially less extensive and thinner. Maximum sea ice area similarly occurs in March, but is approximately 50% lower than in pre-industrial conditions. Most notably, the increased lateral melt rate steepens the decline to ice-free summer conditions during the melt season (Fig. 12).
Both total and process OWFEs are significantly higher for both runs; while total OWFE was below 0.4 for all pre-industrial runs, it is approximately 0.8 for both in the 2xCO 2 runs (Fig. 13a). Separating it out into lateral and vertical melt shows that 400 the 100x lateral melt rate significantly increases the OWFE of lateral melt and decreases the OWFE of vertical melt processes.
Interestingly, the OWFE is higher for vertical melt than lateral for the control run. The low average ice thickness allows vertical melt processes to be very efficient at forming open water, and so lateral melt is relatively inefficient.
In 2xCO 2 runs, lateral melt dominates open water formation early in the summer (regardless of the lateral melt rate). OWFE of vertical melt peaks just before the Arctic becomes essentially ice-free, when ice is very thin (Fig. 13b). The difference 405 between lateral and vertical melt during early summer melt is enhanced by increased lateral melt rates. This suggests that in thinner ice scenarios, lateral melt is more critical to open water formation feedbacks driving ice-free Arctic conditions. In particular, as Arctic sea ice becomes thinner on average over the 21st century, increasing the parameterized lateral melt rate may result in earlier ice-free conditions as a result of an earlier peak in open water formation efficiency.  Arctic ice in the current climate. However, we might expect that the resolution of thin ice categories will have more impact in a fully coupled climate model, where ice-albedo feedbacks are likely more realistic as the atmosphere can respond to changes in the ocean and sea ice. More work to understand the role of the number of ITD categories and remapping scheme in a fullycoupled context is needed. Particularly, it will be informative to investigate how the ITD controls feedbacks related to melt 430 processes.

Implications for future parameterization development
Putting the magnitude of the sensitivity to lateral melting in the context of model sensitivity to other sea ice parameterizations is instructive in understanding the relative importance of this process. For example, small changes to the sea ice albedo have large impacts on the sea ice mean state. Here we used tuned albedo values that were determined to produce a more realistic 435 historical sea ice state (Kay et al., in review). The small changes to albedo of snow on sea ice (detailed in Sect. 2.1) resulted in an increase in sea ice volume that is quite comparable to the reduction in volume associated with increasing lateral melt rate 100x. In other words, the loss of sea ice volume resulting from 100x increase in lateral melt rate is approximately the same as that resulting from increased surface melt with a small decrease in snow albedo. Additionally, a similar magnitude of reduction in sea ice volume is achieved by reducing the magnitude of snow on sea ice by half (Holland et al., 2021). The role of lateral 440 melting in achieving a realistic sea ice cover with the appropriate feedbacks will clearly depend on reasonable sea ice albedo and snow cover.
As the results suggest that nuances of parameterizations can impact the sea ice state, we encourage revisiting model representations of how ocean heat drives sea ice melt using observations. Other factors beyond those currently included are likely to contribute. Modeling work (Skyllingstad et al., 2005) has suggested that lead width and wind speed are likely to influence 445 the melt rates. Forthcoming observations from MOSAiC (Nicolaus and et al., 2021 in review) and other summer field campaigns will be useful to better constrain the controls on melt processes. For example, Richter-Menge et al. (2001) presented observations from the SHEBA campaign in 1998 that showed the accumulation of significant heat content in the upper meter of a lead. This led to accelerated lateral melt, and rapid basal melt associated with the delayed mixing of this layer. We saw a similar evolution in leads during the summer on the MOSAiC expedition in 2020, with a warmer and fresher layer on the 450 order of 0.1 to 1 m thick spanning more than a month during the melt season. This suggests that small-scale stratification is a common occurrence in summer leads that should be considered in modeling. Currently, the minimum 10 m ocean surface layer in CESM2 prevents simulating the nuances of how much heat is captured specifically in leads. One possible way forward is to explicitly represent aspects of leads within the sea ice component of the model, such that finer-scale processes can be represented.

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Another potentially important simplification in the model representation is that it assumes a uniform distribution of vertical and lateral melt locally, as sea ice is represented as a rectangle for thermodynamic and radiative transfer calculations (Fig.   1). In reality, lateral melt rates are often higher near the surface, resulting in a sub-surface shelf. The formation of the shelf, which appears light like a melt pond (e.g., Perovich et al., 2003, Fig. 13), results in a higher albedo locally and likely reduced heat accumulation. In addition, the results suggest that basal and lateral melt rates are closely linked. It could be important to 460 resolve uncertainties in basal melt transfer coefficients, which is beyond the scope of the current sensitivity study. Revisiting lateral melt parameterizations will require finding new ways to capture the important physical controls. For example, it will be possible to explicitly represent the relationship of thickness and floe size in CICE using the joint floe size-thickness distribution developed by Roach et al. (2018) fully coupled with wave, atmosphere, and ocean models. There are a number of additional efforts currently underway to include floe size distributions in sea ice models (e.g., Zhang et al., 2015;Roach et al., 2018Roach et al., , 2019Boutin et al., 2020Boutin et al., , 2021Bateson et al., 2020). Thus, the redistribution of lateral melt towards 470 thinner categories as tested in this study may be able to be explicitly represented in future versions of the model.
We have assessed the sensitivity of sea ice to the lateral melting parameterization in a coupled climate model. Our sensitivity runs in pre-industrial and 2xCO 2 climates confirm the importance of a physically based parameterization for lateral melting through a few key conclusions:

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-Higher lateral melt rates increase the efficiency of lateral melting at forming open water, which decreases local ice concentrations during the summer. Due to the interconnected nature of lateral and basal melting, this does not uniformly result in less ice. Feedbacks related to open water formation result in a notably thinner and less extensive ice cover in the Arctic (particularly at high lateral melt rates) and in the Antarctic.
-The details of how lateral melting is represented and distributed matter. The assumption that lateral melting occurs at 480 the same rate across all ice thicknesses is particularly called into question, as it is unlikely to capture the complexity of feedbacks associated with melt. Higher lateral melt rates (or smaller floes) in areas of thin ice reduce sea ice volume in both hemispheres. Observational constraints on the lateral melt rates are particularly necessary to constrain the possible impact of increased lateral melt rate on thinning ice throughout the 21st century.
-While the lateral melt may play a relatively small role in the mass budget, these results suggest that this does not tell the 485 full story of how sea ice evolves thermodynamically. Lateral melt can have an impact on the mean state due to its role in open water formation which is key to the ice-albedo feedback.
The applicability of the results presented here may be limited by the sophistication of the model used. The use of the slab ocean model may result in the inability to represent some complexities in feedbacks due to the lack of seasonally and interannually varying MLD, and prognostic dynamic ocean heat transport. As a result, we may miss additional feedbacks associated 490 with thermodynamic changes, such as shifts in brine rejection during freeze-up, and changes in ocean dynamics. In the future, a fully coupled dynamic ocean model could be run to understand and isolate the role of such factors. Additionally, there is a great deal of uncertainty in the current functional form of the lateral melt parameterization. Some of the suggested conclusions may require revision due to the future incorporation of a floe size model, which will more accurately capture the complexity of feedbacks with changes in open water formation.

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Author contributions. MH and BL developed the concept and obtained funding for this work. MS and MH designed and ran experiments.
MS led preparation of the manuscript, with feedback from MH and BL.
Competing interests. The authors declare that no competing interests are present.