A Sensitivity Study of Arctic Ice-Ocean Heat Exchange to the Three-Equation Boundary Condition Parametrization in CICE6

Lei YU, Jiping LIU, Yongqi GAO, and Qi SHU

1Climate Changes Research Center, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China

2Department of Atmospheric and Environmental Sciences, University at Albany,State University of New York, Albany, New York 12222, USA

3Nansen Environmental and Remote Sensing Center/Bjerknes Center for Climate Research, Bergen N-5007, Norway

4Nansen-Zhu International Research Centre, Institute of Atmospheric Physics,Chinese Academy of Sciences, Beijing 100029, China

5First Institute of Oceanography, Ministry of Natural Resources, Qingdao 266061, China

ABSTRACT In this study, we perform a stand-alone sensitivity study using the Los Alamos Sea ice model version 6 (CICE6) to investigate the model sensitivity to two Ice-Ocean (IO) boundary condition approaches. One is the two-equation approach that treats the freezing temperature as a function of the ocean mixed layer (ML) salinity, using two equations to parametrize the IO heat exchanges. Another approach uses the salinity of the IO interface to define the actual freezing temperature, so an equation describing the salt flux at the IO interface is added to the two-equation approach, forming the so-called threeequation approach. We focus on the impact of the three-equation boundary condition on the IO heat exchange and associated basal melt/growth of the sea ice in the Arctic Ocean. Compared with the two-equation simulation, our threeequation simulation shows a reduced oceanic turbulent heat flux, weakened basal melt, increased ice thickness, and reduced sea surface temperature (SST) in the Arctic. These impacts occur mainly at the ice edge regions and manifest themselves in summer. Furthermore, in August, we observed a downward turbulent heat flux from the ice to the ocean ML in two of our three-equation sensitivity runs with a constant heat transfer coefficient (0.006), which caused heat divergence and congelation at the ice bottom. Additionally, the influence of different combinations of heat/salt transfer coefficients and thermal conductivity in the three-equation approach on the model simulated results is assessed. The results presented in this study can provide insight into sea ice model sensitivity to the three-equation IO boundary condition for coupling the CICE6 to climate models.

Key words:Arctic ice-ocean heat exchange,three-equation boundary condition,reduced oceanic turbulent heat flux,CICE6

1.Introduction

Sea ice basal growth and melt/ablation play significant roles in balancing the Arctic Sea ice mass budget. Observations between 2000 and 2013 (Perovich et al., 2014) showed surface and basal melt to be of similar magnitudes in the average summer Arctic sea ice mass balance, and the basal melt doubled over the period from 2008 to 2013 compared to its value in the period 2000–05; additionally, there was a satellite record of a sharp decrease in Arctic sea ice cover in recent decades. The important contributions from ice basal growth and melt have been represented in modeling efforts. An intercomparison among the CMIP6 models (Keen et al., 2021)showed that basal growth and melt were the main processes in the modeled annual circle of the Arctic sea ice mass budget, where the amounts of annual mean ice mass increasing from basal growth were ten times as large as those from frazil ice formation, and summer basal melt contributed comparable amounts to the top melt for the ice mass lost. In a stand-alone model sensitivity study by Tsamados et al.(2015), basal melt accounted for more than two-thirds of the total ice melt, followed by top melt, while lateral melt accounted for less than 10%.

Locally, ice basal growth or melt/ablation is determined by the energy balance between the heat conduction ( fcondbot)and oceanic heat flux ( fw) at the ice-ocean (IO) interface.This IO energy balance can be written as the Stefan condition:

where ρiis the sea ice density, L is the latent heat of fusion,(t)≡?h/?t is the rate of growth (<0) or ablation (>0)in m s–1, ρiLh˙(t) denotes the sea ice energy changes, fwis the oceanic heat flux, λ is the thermal conductivity, T is the temperature, z is the vertical coordinate, andis the parametrization of heat conduction fcondbot. This IO boundary condition (IOBC) describes the constraint that any heat imbalance between heat conduction and oceanic heat flux will cause sea ice phase changes (i.e., melt or growth). As introduced above, basal growth and melt make substantial contributions to the sea ice mass budgets, so proper parametrization of the Stefan condition to describe the IO heat balance is important in Arctic Sea ice modeling. Substantial efforts have been made to develop this boundary parameterization scheme (e.g., Mellor et al., 1986; Perovich and Maykut,1990; Scheduikat and Olbers, 1990; Wettlaufer et al., 1990;Wettlaufer, 1991; Maykut and McPhee, 1995; Holland and Jenkins, 1999; Schmidt et al., 2004; McPhee et al., 2008; Malyarenko et al., 2020). Currently, the obtained schemes treat the oceanic heat flux (fw) as either momentum or turbulent flux. Moreover, the double diffusion condition is used to parametrize the relatively faster heat and slower salt flux at the IO interface during ice ablation conditions (e.g., Notz et al., 2003). In the next section, we describe these IOBC methods.

The remainder of this paper is structured as follows: Section 2 describes several IOBC parametrization approaches with formulations forming these approaches, the CICE6 model configuration and setup of the sensitivity runs in this

study, section 3 presents the main results in this study, and finally, discussion and concluding remarks are given in section 4.

2.IOBC approaches, CICE6 model configurations, and setup of the sensitivity experiments

2.1.IOBC approaches

2.1.1.Momentum model of fw

Earlier IOBC approaches treated fwanalogous to momentum flux

where ρwis the seawater density, cwis the specific heat capacity of liquid water, Tfmixis the ocean freezing point, hmixis the mixed layer (ML) depth, and Tmixis the ML temperature.Here, Tfmixis taken as a linear function of the ML salinity Smix:

where μ=0.054 is an empirical coefficient for salinity and ocean freezing temperature. The momentum model assumes that any excess heat absorbed in seawater of an ice-covered ML is almost instantaneously used by sea ice melt. Such an IO system is often referred to as an “ice bath” (e.g., Josberger, 1983; Mellor et al., 1986). The ice-bath paradigm leads to rapid ocean heat loss from the ML to the sea ice above (e.g., R?ed, 1984, Fichefet et al., 1997); thus, little heat energy can be stored in the ML below sea ice for extended periods.

However, direct measurements from the Marginal Ice Zone Experiments (MIZE) in 1984 (McPhee et al., 1987)and observation-based studies (Krishfield and Perovich,2005) have reported that the ice-covered upper Arctic Ocean stores significant amounts of heat for extended periods during the summer months when Tmixis greater than Tfmix.Such heat storage has also been observed in earlier laboratory studies (e.g., Yaglom and Kader, 1974). This evidence demonstrated that, IO heat exchanges are more likely governed by the turbulent heat flux or heat/salt molecular diffusion occurring in a very thin viscous sublayer below the sea ice bottom, within which the turbulent heat process or heat/salt molecular diffusion played a significant role. This is different from the momentum flux at the ocean ML. This view was further bolstered from the one-year-long Arctic Ice Dynamic Joint Experiment (AIDJEX, Maykut and McPhee, 1995),the Surface Heat Budget of the Arctic-SHEBA (Uttal et al.,2002), and short summer projects (McPhee, 2002). Motivated by these studies, turbulent heat flux and molecular diffusion models have been proposed (e.g., McPhee, 1992; Maykut and McPhee, 1995; Notz et al., 2003; Schmidt et al., 2004)to parametrize the heat budget at the IO interface.

2.1.2.Turbulent model of fw

In the turbulent model, fwis parametrized based on the Reynolds averaged turbulent heat flux: fw=ρwcww′T′.Using dimensional analysis, the basic formulation of the turbulent model can be written as follows:

where αtis the turbulent heat transfer coefficient; u?is the friction velocity; Tfiois the freezing temperature of seawater.Tfio?Tmixis the temperature difference between the IO interface and the ML ocean. Compared with the momentum “ice bath” model, the amount of heat exchange at the IO is reduced because the value is scaled by u?and αt. Applying the turbulent heat flux model given by Eq. (4) to the Stefan condition [Eq. (1)], we obtain the following equation:

Depending on the definition of the seawater freezing point, Tfio, the turbulent model can appear as a one-, two- or three-equation approach.

In the 1-equation approach, Tfiois simply set to a constant value (i.e., –1.8°C). In the two-equation approach, Tfiois defined by Eq. (3), which forms the two-equation approach together with Eq. (5). The two-equation approach has been used to estimate the oceanic heat flux in observational studies(e.g., McPhee, 1992; Maykut and McPhee, 1995; Krishfield and Perovich, 2005), and because of its simplicity for computation, it is the default IO parametrization scheme in several sea ice models, i.e., CICE6, the Global Sea Ice Component(GSI8.1) or the Louvain-la-Neuve Sea Ice Model (LIM2,LIM3). Using Eq. (3) to define Tfioresults in fast salt flux exchanges, identical to the turbulent heat exchanges between the IO interface and the ML. However, both theoretical studies and observations have shown that the opposite is true: the transfer rate of salt is much slower than that of heat(e.g., Woods, 1992; Notz et al., 2003; McPhee et al., 2008).To realistically represent the salinity effects in the models,Tfmixand Smixin Eq. (3) are replaced with Tfioand actual interfacial salinity Sio, respectively:

To solve for Sio, an equation describing the IO boundary salt flux balance is added to the two-equation scheme:

where Siis the salinity of the bottom sea ice, and αsis the turbulent salt transfer coefficient. The above Eqs. (5), (6), and(7) constitute the three-equation boundary approach (e.g.,Holland and Jenkins, 1999). In the three-equation approach,Tfiocan be greater than the Tmixunder a relatively small Sio,in this case a downward heat flux from the sea ice bottom to the ocean ML can happen (e.g., Notz et al., 2003; McPhee et al., 2008; Shi et al., 2021). Considering the IO brine energy balance during sea ice melt or freezing, Schmidt et al. (2004) replaced the latent heat of fusion, L in Eq. (5),with energy changes ?E′during the sea ice melt or growth process:

where, ?E′=E0′(Tfio,Sio)?Ei′(Tib,Sib), E0′is the energy of the seawater, Ei′is the internal energy of sea ice, and Tiband Sibare the temperature and salinity of the volume transferred at the IO interface. Replacing the Siin Eq. (7) with Sib, we obtain:

and the values of Tiband Sibdepend on ice melt (>0) or new ice formation (<0):

where fsis the fraction of the boundary salinity initially retained within the ice. In this study, we used the three-equation system by Eqs. (6), (8), (9), and (10) to parametrize the IO boundary condition to examine the impacts of a three-equation approach on IO heat budgets in CICE. Note that the energy is defined by per mass (J kg–1) and melt rate is in units of kg m–2s–1as in Schmidt et al. (2004), while in CICE, the energy is defined by per volume (J m–3) and the unit of melt ratehas unit of m s–1.

To our knowledge, in the CMIP6 (Coupled Model Intercomparison Project Phase 6) models, the three-equation approach is the IO boundary condition parametrization in the Goddard Institute for Space Studies (GISS) ModelE and the two-equation approach is used in models that treat the sea ice component with CICE5 (i.e., CESM2-CAM, the CESM2-WACCAM, the NorESM-LL, and the NorESMMM), the GSI8.1 (i.e., UKESM1-0-LL, HadGEM3-GC31-LL, HadGEM3-GC31-MM, ACCESS-CM2,) or the LIM (i.e., AEMET_EC-Earth3, SMHI_EC-Earth3-Veg, IPSLCM6A-LR, and CanESM5).

2.1.3.Double molecular diffusions

Finally, we provide a short description of double molecular diffusion. As demonstrated above, the three-equation boundary condition induces a much fresher IO interface;because of this, double-diffusive convection of heat and salt occurs between the fresh IO water and underlying saltwater.Previous studies (i.e., Notz et al., 2003; McPhee et al.,2008; Tsamados et al., 2015; Shi et al., 2021) showed that the choice of the ratio R (= αt/αs), where αtand αsare the heat and salt flux diffusion rate, respectively, has important effects on the sea ice states. Considering that αtis faster than αsin the sea ice melting process, Notz et al. (2003)used an R =35 to model the observed summer false bottom persistence (Jeffries et al., 1995; Eicken et al., 2002; Perovich et al., 2003). McPhee et al. (2008) pointed out that an R used under melting conditions is inappropriate for the ice growth process. In some previous studies based on CICE, R was set to 35 (Shi et al., 2021) or 50 (Tsamados et al., 2015)for the melt condition and was set to 1 (αt= αs) under ice growth conditions. In this study, following Tsamados et al.(2015), we set the ratio R = 50 for melt and R = 1 for growth conditions.

2.2.Model configurations

The sea ice model used in this study is the CICE6.There are many physical parameterization schemes in CICE6 for users to turn on and off according to specific configurations, and detailed descriptions can be found in Hunke et al. (2013); Craig et al. (2018). A brief description follows. We use mushy thermodynamics in both the twoequation and the three-equation runs in this study because the three-equation scheme needs to operate with a mushy sea ice layer (Feltham et al., 2006), where the mush enthalpy is the combination of the brine and pure ice enthalpy according to the brine fraction. The model uses multiple ice thickness categories compatible with the ice thickness redistribution scheme (ITD) of Lipscomb et al. (2007),and we chose five ice thickness categories in this study. The level-ice formulation pond scheme is used for melt pond parametrizations, by which the ponds are carried as tracers on the level ice area of each thickness category. For the dynamics option, we chose the elastic-viscous-plastic (EVP)rheology in all model runs, as described in Hunke and Dukowicz (2002).

We ran the CICE6 in stand-alone mode and coupled the ML that forms part of the CICE6 package. The ML depth is fixed at 10 m in summer and 20 m in winter, the ML salinity had a fixed seasonal circle obtained from climatology data, and the SST evolved through the IO heat exchange. We apply a slow (15 days) temperature restoration of the ML temperature toward the monthly climatology of the reanalysis SSTs in our model runs. The climatology of the monthly atmospheric dataset from the Modern-Era Retrospective analysis for Research and Applications version 2(Gelaro et al., 2017) and monthly reanalysis ocean data from ECMWF-ORAS5 (Zuo et al., 2019) are used to force the model. The input field consists of the 10 m wind velocity, 10 m specific humidity, incoming shortwave/long radiation, snowfall/rainfall rate, air density, sea level pressure(SLP), and SST. The model integrations reach equilibrium after ～20 model years and run continuously for 100 years.The results presented in this paper are the mean values over the last 50 model years.

2.3.Set-up of the sensitivity experiments

In our reference run (REF), the IO boundary condition is parameterized by the two-equation scheme [Eqs. (2) and(3)]. We set αtto a constant value of 0.006 and parametrized the thermal conductivity according to Maykut and Untersteiner [1971, hereafter, we refer to this conductivity method as (MU71)].

We take the three-equation runs as our sensitivity runs,in which the IO boundary condition was parametrized using the three-equation scheme [Eqs. (6) to (10)] with several combinations of coefficient αtand ice conductivity λ . For the αt, we used the constant (= 0.006) and form-drag-based αtby switching the form drag parametrization off/on (Tsama dos et al., 2014) in CICE6, where the form-drag-based αtis accounted for by half of the ocean form drag coefficient under melt conditions (Tsamados et al., 2015). Then we combined the two kinds of αtto the MU71 and the conductivity of Pringle et al. (2007, hereafter, we refer to this conductivity method as P07) in our three-equation sensitivity runs.Table 1 lists the name and coefficient combination for each model run used in this study. The oceanic heat fluxfwhas a linear dependency on the friction velocityu?, it can be calculated by(where τwis the IO drag) in CICE6.To exclude the effects of constant and form drag parametrization onu?, we fixedu?at 0.002 (Notz et al., 2003) in all our model runs. Finally, we ran our model experiments using a grid resolution of 1oon the global domain and focused our analysis on the Arctic region.

Table 1. The name, IO boundary condition approaches, heat (αt ), salt (as ) transfer coefficient, and ice conductivity (λ) for each model run.

3.Results

3.1.The seasonal cycles in the two-equation REF run and three-equation runs

This section describes the impact of the two-equation and three-equation approaches. In CICE6, all heat fluxes are positive (negative) downwards (upwards). To avoid confusing “increase” and “decrease” of negative values, we refer to the upward oceanic heat flux as ?fw(positive, Figs. 1–4,6–9). Accordingly, we use the temperature difference ?Tobetween the ocean ML (sea surface temperature, SST) and the freezing temperature (Tf, ?To= SST?Tf) to explain the simulated upward oceanic heat flux ?fw. Note thatTfis taken as theTfmixin the REF, while it is defined asTfioin the three-equation runs. We look first at the general responses of the main results to the two approaches. Figure 1shows the seasonal cycles of several thermodynamic processes at the IO interface in each run, including the basal melt, interfacial salinity Sioand freezing temperature, temperature difference ? To, upward oceanic heat flux (? fw), temperature difference ? Tb(between the sea ice temperature of the bottom layer (Tib) and the freezing temperature (Tf): ? Tb=Tib?Tf, downward bottom heat conduction fcondbot, the net IO heat exchange by fcondbot– fw, congelation, and sea ice thickness. We start with the responses of basal melt (Fig. 1a)and interfacial salinity (Fig. 1b). In all our model runs, the basal melt speeds up beginning in June, reaches a maximum in July, and remains high until August. The acceleration of the basal melt leads to a large release of freshwater, freshening the IO interface directly below the sea ice bottom in each three-equation run. From Fig. 1a, we can see the significant reduction in the interfacial salinity Sioduring the summer months (June?July?August, JJA). Note that the maximum melt rate is in July, but the minimum Siooccurs in August.This reflects an accumulated freshening process at the IO interface from June until August. For the two-equation REF run, there is no interfacial freshening process since the interfacial salinity Siois used as the salinity of the ML (Sio= Smix)in the two-equation approach.

Fig. 1. Impacts of the two-equation (REF) and three-equation approach on (a) basal melt, (b) interfacial salinity(S io) , (c) interfacial temperature (T fio) , (d) temperature difference between SST and IO interface (? To), (e) upward heat flux (? fw) , (f) temperature difference between ice bottom and IO (? Tb) , (g) bottom heat conduction ( fcondbot),(h) net IO heat flux ( fcondbot – fw), (i) congelation, (j) top melt, (k) lateral melt, and (l) sea ice thickness. Units are shown on the y-axis.

In each three-equation run, a common lower Sioresults in a common greater IO freezing temperature Tfioabove the oceanic freezing temperature Tfmix(Fig. 1c). This greater Tfioimpacts the heat balance by changing the temperature differences at the IO interface. First, the increase in Tfioreduces the temperature differences (? To; Fig. 1d), and thus reduces the upward oceanic heat flux (? fw; Fig. 1e). Meanwhile, it leads to a reduced temperature difference between the ice bottom and the Tfio(? Tb; Fig. 1f), and hence reduces the downward heat conduction ( fcondbot; Fig. 1g). Both the decrease in downward fcondbotand upward heat flux (? fw)then resulted in a weakened heat energy convergence( fcondbot?fw; Fig. 1h) at the IO interface and consequently,slowed the basal melt rate (Fig. 1a). Furthermore, ice congelation occurs in August in CST_DRAG_MU71 and CST_DRAG_P07 (Fig. 1i), indicating a heat divergence at the IO interface (Fig. 3g), while no ice congelation is found in other experiments.

Finally, the sea ice thickness (Fig. 1l) increased in each three-equation run compared with the REF in summer (JJA).Comparison among the bottom (Fig. 1a), top (Fig. 1j), and lateral (Fig. 1k) melt rates show that the decrease in the basal melt is the major contributor to the increase in the sea ice thickness: the mean anomaly of bottom melt is ～ –0.5 cm d–1(1.2–1.5 cm d–1in three-equation runs against ～1.8 cm d–1in REF), while that for top melt is ～ –0.2 cm d–1(1.3–1.4 cm d–1against ～1.5 cm d–1), and no pronounced differences are observed for the lateral melt.

The above results show a common lower Sioin all the three-equation runs in comparison to that in the REF run.This increases the IO freezing temperature and thus reduces oceanic turbulent heat flux and slows basal melt rate.Finally, we find a common increase in the sea ice thickness during summer compared with the two-equation REF run.

After analyzing the general differences among the seasonal cycles between the three-equation and two-equation approaches, we now compare the differences among the three-equation runs. The results show that the most significant differences among the three-equation runs occur in the summer months (JJA) since the heat absorption from the incoming solar shortwave radiation in the ocean ML is significantly increased, which, in turn, causes more significant changes in the upward oceanic heat flux (Fig. 1e). First, for the differences between the constant and form-drag-based αtruns(CST-DRAG-MU71 vs. FORM-DRAG-MU71, CSTDRAG-P07 vs. FORM-DRAG-P07), we can see that the basal melt rate is faster in the constant αtruns than that in the form-drag-based αtmodel runs (Fig. 1a). The mean basal melt rates during JJA are ～1.5 cm d–1and ～1.3 cm d–1in the CST-DRAG-MU71 and CST-DRAG-P07, faster than the melt rate of ～1.25 cm d–1and ～1.20 cm d–1in the FORM_DRAG_MU71 and FORM_DRAG_P07, respectively. This faster basal melt rate can be attributed to the fact that the constant αt(0.006) is larger than the form-dragbased αtin most regions of the Arctic basin except for the heavily ridged regions north of Greenland. It amplifies the upward oceanic heat flux (? fw; Fig. 1e) in the constant αtrun in comparison to that in the form-drag-based αtand, therefore, causes a faster basal melt rate. As a result, the Siois lower, and hence the Tfiois greater in the constant αtruns as compared with those in the form-drag-based αtmodel runs(Fig. 1b). The relative faster bottom rate and greater upward oceanic heat flux result in the thinner sea ice thickness in the constant αtruns (Fig. 1l). Again, from Fig. 1i, the ice congelation in August occurs only in the constant αtruns (CSTDRAG-MU71 and CST-DRAG-P07) are most notable. Further analysis in section 3.5 shows that this ice congelation in August lies in the region of downward heat flux from the ice to the ocean (Fig. 8), which causes a heat divergence at the IO interface and leads to the congelation as a consequence. This important difference will be addressed by detailed analysis based on the spatial pattern maps in section 3.5. For the differences between the conductivity in the MU71 and P07 runs, we can see that the upward heat flux(? fw) is less in the P07 runs (Fig. 1e) than that in the conductivity MU71 runs, it is associated with relatively slower basal melt rates (Fig. 1a), greater Sio(Fig. 1b), and lower Tfio(Fig. 1c), and hence leads to a greater thickness (Fig.1l)in each P07 run (CST-DRAG-P07 vs. CST-DRAG-MU71,FORM-DRAG-P07 vs. CST-DRAG-MU71). A previous study (Hunke, 2010), based on the two-equation approach,reported that the conductivity P07 decreases the e-folding scale of the ice thickness redistribution function, reduces the ocean heating on the sea ice, and adjusts the albedo upward,each of which tends to increase the sea ice thickness. In this study, the increased sea ice thickness is also be found in our three-equation runs by the conductivity P07, as discussed above. Further analysis will be given in section 3.5.

The above results indicate that August has the largest differences between the two approaches, such as the interfacial salinity, interfacial freezing temperature, and IO heat exchanges. This can be attributed to the insolation effect in that more background insolation leads to more pronounced changes in the IO heat flux between the two approaches. During the summer months (JJA), less surface ablation due to reduced sea ice concentration (SIC) and thinner sea ice thickness allow more incoming shortwave radiation to penetrate through the sea ice. Meanwhile, the ocean ML is also absorbing more shortwave radiation. This insolation effect increases both the upward oceanic heat flux (? fw) and the downward heat conduction ( fcondbot), where the upward oceanic heat flux ? fwdetermines the net heat flux at the IO interface (～50 W m?2of the ? fwvs. ～4 W m?2of the fcondboton average, see Fig. 1e, Fig. 1g, and Fig. 1h). In August, the?fwreaches the greatest magnitude (Fig. 1e), causing the largest changes in the related bottom process among our model runs for this month. In the next section, we focus our study on the August spatial maps of the absolute values from the REF and CST-DRAG-MU71 (the run of the lowest Sio, the greatest Tfioand the summer bottom congelation) to study how the two approaches impact the IO heat exchanges and associated basal melt/growth. Then, we will compare the differences among our three-equation runs to assess how different results were obtained by different combinations of αtand thermal conductivities.

3.2.The IO heat exchanges and basal melt/growth in the two-equation REF run

Figure 2 shows the spatial maps of the August ML salinity, thermal differences, basal melt, and congelation in the REF. From Figs. 2a and 2b, we see an opposite linear dependency of Tfmixon Smix: a greater (lower) salinity results in a lower (greater) ocean Tfmix. In the REF, the minimal Tfmixis～ –1.8°C and located in the eastern Arctic Ocean. It increases to ～ –1.6°C to –1.4°C in the central Arctic Ocean and to ～ –1°C in the coastline regions of the East Siberian Sea and the Beaufort Sea (ESB). This freezing temperature Tfmixresults in an overall positive temperature difference between the ocean ML layer and IO interface (? To; Fig.2d), which is relatively greater (～1.0°C) along the sea ice edge (defined as the 15% SIC contour) regions than that in the central Arctic Ocean, the heavily ridged regions north of Greenland, and in some parts of the Canadian Archipelago(hereafter, we refer to this region as NGCA). Consequently,the positive ? Tobetween the ocean ML and the IO interface leads to an overall upward heat flux (– fw; Fig. 2f) to the ice bottom, with magnitudes of 20–60 W m–2and 2–10 W m–2in the ice edge regions and the Arctic basin, respectively.Meanwhile, the Tfmixresults in an overall positive temperature difference between the ice bottom and IO interface (? Tb;Fig. 2c), causing downward heat conduction fcondbotin most of the Arctic Ocean (Fig. 2e).

The upward oceanic heat flux (? fw) and downward fcondbotresult in heat convergence ( fcondbot?fw> 0; Fig. 2g)in the whole Arctic basin during summer in the REF. Accordingly, the basal melt is faster than 2.0 cm d?1in the ice edge regions (Fig. 2i). Over the Arctic basin, the basal melt is ～0.7 cm d?1, on average, and less than 0.2 cm d?1in the NGCA. No bottom growth occurred in August in the REF(Fig. 2h). Comparison between the magnitude of the upward oceanic heat flux (? fw) and downward fcondbotshows that the upward oceanic heat flux (? fw) is the primary heat contributor to the basal melt in August.

3.3.The IO heat exchanges and basal melt/growth in a three-equation run

Section 3.2 described how the two-equation boundary condition influences the IO heat exchanges and the associated basal melt/growth in CICE6. Different from the two-equation approach, the three-equation approach treats the freezing temperature as the interfacial temperature Tfio(rather than the Tfmix) , which is dependent on the interfacial salinity Sio(Eq.6). Following the algorithm by Schmidt et al. (2004), the Siovalues were solved by the Newton-Raphson iteration method. We calculated those physical variables in Eqs. (6)–(10) for each ice thickness category and used their mean values at the IO boundary for our analysis. We have shown in Fig. 1 that the three-equation boundary condition results, on average, in a much lower Siocompared with Smix, indicating an IO freshening process induced by the three-equation approach. Here, the spatial map (Fig. 3a) shows that IO freshening mainly occurs in the ice edge regions where fast basal melt occurs (Fig. 3i), while in the central Arctic Ocean, Siois nearly identical to Smix(～30 PSU), showing a relatively weaker IO freshening process in this region. This can be attributed to the fact that the much higher SIC in the center Arctic Ocean reduces the change in the radiative heat flux absorbed by the seawater. Hence, the changes in both oceanic heat flux and the basal melt rate are relatively smaller than the changes in the sea ice edge regions.

Compared with the REF, the lower Sioin the ice edge regions results in a greater Tfio(Fig. 3b), which changes the heat exchanges at the IO interface. (1) For the upward oceanic turbulent heat flux (? fw; Fig. 3f), the increased Tfioreduces the ?To(Fig. 3d), causes an average decrease of ～25 W m?2in upward oceanic heat flux (? fw) in the ice edge regions (Fig. 4a), which demonstrates the heat-reducing role of the three-equation condition in the IO heat exchange. Furthermore, the increased Tfioresults in a negative ? To(SST

Fig. 2. The simulated bottom thermal process in August in the twoequation run (REF). (a) ML salinity (S mix, PSU), (b) ocean freezing temperature (T fmix, °C ), (c) temperature difference (? Tb,°C) between ice bottom and Tfmix, (d) temperature difference (? To, °C) between SST and Tfmix, (e) bottom heat conduction ( fcondbot, W m–2), (f)upward oceanic heat flux(? fw, W m–2), (g) net IO heat exchanges ( fcondbot – fw, W m–2), (h) congelation (cm d–1) and (i) basal melt rate (cm d–1). The black line in panel (d) denotes the 15% SIC contour.

Fig. 3. The simulated bottom thermal process in August in the threeequation sensitivity run (CST-DRAG-MU71). (a) Interfacial salinity(S io, PSU), (b) interfacial temperature (T fio,°C), (c) temperature difference (? Tb, °C) between ice bottom and Tfio, (d) temperature difference (? To, °C) between SST and T fio, (e) bottom heat conduction ( fcondbot, W m–2), (f) upward oceanic heat flux (? fw, W m–2),(g) net IO heat exchanges ( fcondbot ?fw, W m–2), (h) congelation (cm d–1) and (i) basal melt rate (cm d–1). The black line in panels (d),(f), and (h) denotes the 15% SIC contour.

The above studies detected a heat-reducing impact of the three-equation boundary condition on the IO heat exchanges in the CST-DARG-MU71. The differences between the other sensitivity runs and the REF run show also a common decrease in the upward oceanic heat flux along the ice edge regions (Fig. 4a), which is associated with a decrease in basal melt (Fig. 4b) and an increase in sea ice thickness in each three-equation run (Fig. 4c).

Fig. 4. The difference in (a) upward oceanic heat flux (? fw, W m–2), (b) basal melt rate (cm d–1), (c) sea ice thickness (m), and (d) SST (°C) in August between each of the three-equation sensitivity runs and the REF in August. In each panel, (1) denotes CST-DRAG-MU71 minus REF, (2) FORM-DRAG-MU71 minus REF (3)CST-DRAG-P07 minus REF, and (4) FORM-DRAG-P07 minus REF.

3.4.The SST responses to the three-equation boundary condition

Figure 4d shows the impact of the three-equation condition on the SST. Because of the absence of the changes in feedback between the ML and deep ocean in our standalone sensitivity runs with a prescribed ML depth, the SST changes are dependent mainly on the heat balance among the net atmospheric heat flux ( fsurf) on the sea surface, the solar shortwave radiation that penetrates through the sea ice to the ocean ML ( fswthru) and the available oceanic heat flux( focn) (accounted for as the available heat flux in the ocean ML after the energy consumption during the melt/sublimation process). From Fig. 4d, our results show that the SST is lower in the sea ice edge regions but close to or warmer in the central Arctic compared with the values observed in the REF (Fig. 4d). According to this SST anomaly (SSTA) spatial pattern, we calculated the mean values of the fsurf, fswthruand focnin the ice edge regions (SIC less than 15%) and central Arctic Ocean (SIC greater than 30%). The results are presented in Fig. 5 and Table 2 (Table 3) for the ice edge (central Arctic) regions. Note that all heat fluxes are positive downwards, so the downward (upward) anomalies tend to enhance (reduce) the SST. Now we study how the heat balance anomaly causes these SSTAs. First, we study the absolute values in the REF (Figs. 5a, b). In the ice edge regions,there are an upward (negative) focnof ～ –23.6 W m–2on average from the ocean ML, a downward atmospheric heat flux of fsurf(～28.9 W m–2on average) and fswthru(～9.2 W m–2on average). Accordingly, there is a downward (positive)net heat flux of 14.5 W m–2, heating the ocean ML in summer. For the central Arctic Ocean, due to the relative higher SIC, greater sea ice thickness, and reduced oceanic heat flux(Fig. 2f), all the three heat fluxes are much smaller (from–23.6 to –6.9 W m–2in the focn, from 28.9 to 6.1 W m–2in the fsurf, and from 9.2 to 4.5 W m–2in the fswthru) in comparison to those in the ice edge regions. As a result, the downward(positive) net heat flux is reduced to 3.6 W m–2on average.The difference in the heat flux balance between the ice edge regions and the central Arctic Ocean shows that the summer heating on the SST by the three heat fluxes is greater in the ice edge regions than in the central Arctic Ocean.

Fig. 5. The August heat flux balance among the available oceanic heat flux ( focn), the net atmospheric heat flux ( fsurf) and the shortwave radiation penetrated to the ocean ML through the sea ice ( fswthru). All heat fluxes are positive downwards and have units of W m–2. Absolute values in the REF in (a) the ice edge regions and(b) the central Arctic, and anomalies in the ice edge regions in (c) CST-DRAG-MU71, (d) FORM-DRAGMU71, (e) CST-DRAG-P07, and (f) FORM-DRAG-P07. (g)–(j) as (c)–(f) but for the central Arctic.

Now we move to the anomalies in our three-equation sensitivity runs. We start with the heat balance in the ice edge regions, where we have found a common cooling (Fig. 4d)in all our three-equation sensitivity runs (～ –0.16oC on average, Table 2). First for thefocn, we can see a common anomalous downward (positive)focn(～ 4.8 W m–2on average) in these sensitivity runs (Figs. 5c–f). This can be explained by the fact that in our three-equation sensitivity runs, the slower basal melt processes in the ice edge regions (Fig. 4b)consumes less upward oceanic heat flux (?fw; Fig. 4a), leading to more available heat energy retained in the ocean ML,as indicated by anomalous downward (positive)focnto the ocean ML. The anomalous positivefocntends to enhance the SST. However, the increased sea ice thickness in the ice edge regions (Fig. 4c) leads to simultaneous decreases in bothfsurfandfswthruas shown by Fig. 5 and Table 2. As a result, there is a common anomalous upward (negative) atmospheric heat flux (～ –14.0 W m–2on average), and thus it tends to decrease the SST in each three-equation run. The–14.0 W m–2anomalous atmospheric heat flux and the 4.8 W m–2anomaly in thefocnresult in an anomalous upward (negative) net heat flux (～ –9.2 W m–2), explaining the common cooling in the ice edge regions in the sensitivity runs, as shown by Fig. 4d. Further looking at net heat flux and SSTA in each sensitivity run in Table 2, we see that the negative SSTA matches well with the anomalous net upward (negative) heat flux: –0.17°C and –8.8 W m–2in the CST-DRAG-MU71, –0.13°C and –7.2 W m–2in the FORMDRAG-MU71, –0.18°C and –10.6 W m–2in the CSTDRAG-P07, –0.18°C and –10.1 W m–2in the FORMDRAG-P07. On the contrary, in the central Arctic, there is a slight positive SSTA (～0.027°C on average) in three of our sensitivity runs (CST-DRAG-MU71, FORM-DRAG-MU71,and the FORM-DRAG-P07), and there is no clear SSTA(anomaly close to 0°C ) in the CST-DRAG-P07 in this region (Fig. 4d and Table 3). The relatively smaller positive SSTAs in the central Arctic can be explained by the relatively smaller anomalous positive net heat flux among thefocn,fsurfandfswthruin this region. Compared with the total anomalies (–1.9 W m–2) in the atmospheric heat flux (～ –1.1 W m–2of thefsurfanomalies plus ～ –0.8 W m–2of thefswthruanomalies, averaged among the three runs of positive SSTA,see Table 3), the anomalous positivefocn(2.7 W m–2on average) (Figs. 5g–j) is greater in the three sensitivity runs. Consequently, there is an anomalous positive net heat flux(～ 0.8 W m–2, 2.7 W m–2vs. –1.9 W m–2), leading to the slight positive SSTA (less than 0.05°C) in the three sensitivity runs.

The above results show the influences of heat balance among thefocn,fsurfandfswthruon the SSTA and, the influencing magnitude is dependent on the changing in sea ice thickness. From Fig. 4c, the increase in ice thickness is much higher along the ice edge regions than in the central Arctic(0.5 m vs. 0.07 m on average, see Table 2 and Table 3). The 0.5 m increase in sea ice thickness in the ice edge regions leads to a greater reduction infsurfandfswthruthan in the increased downward (positive)focn(Figs. 5c–f and Table 2),causing the cooling in the ice edge regions, as discussed above. While for the central Arctic (Figs. 5g–j and Table 3),the 0.07 m increase in sea ice thickness is insufficient(Fig. 4c) to cause great decreases in atmospheric heat fluxes,therefore the relatively greater increase in the retained heat flux of the ocean ML (focn) dominates the heat balance among these heat fluxes in the central Arctic. Consequently,the SST is either increased slightly in the CST-DRAG-MU71, FORM-DRAG-MU71, and FORM-DRAG-P07 or comparable in the FORM-DRAG-P07. Finally, the comparison between the ice edge regions and the central Arctic shows that the cooling in the ice edge region is much greater than the warming in the central Arctic Ocean. The degree of the differences is small among the three-equation runs (less than 0.04oC on average); therefore, these will not be addressed further.

Table 2. The absolute mean values in REF and anomalies in the three-equation sensitivity runs of simulated SST, sea ice thickness(SIT), and the heat flux balance among the available oceanic heat flux ( focn) , the net atmospheric heat flux ( fsurf) and the shortwave ra diation that penetrated through the sea ice ( fswthru ) in the ice edge regions in August.

Table 3. Same as Table 2 but for the central Arctic.

It should be pointed out that the SSTAs presented here need to be further examined in sea ice-ocean or fully coupled models because the feedbacks between the sea ice and ocean, between the sea ice and atmosphere, and between the ocean ML and deep ocean can influence the heat balance and thus cause SST changes. Nevertheless, the stand-alone model experiments can help us to directly assess the sensitivity of the SST to the three-equation approach.

3.5.The differences among the three-equation coefficient sensitivity runs

Sections 3.2–3.3 demonstrated how the two-equation and three-equation approaches influence the IO heat exchanges and related basal melt/growth processes in August differently. In this section, we assess the sensitivity of the bottom heat flux, basal melt, and sea ice thickness to different combinations of αt, αs, and λ used in the threeequation approach (the coefficient combinations are listed in Table 1 and explained in section 2.3).

First, by comparing the differences between the formdrag-based and constant αt(= 0.006) runs in Fig. 6, we find a general spatially bimodal impact of from-drag-based αton the oceanic heat flux (Figs. 6a, d). The upward oceanic heat flux is increased (decreased) in the NGCA (Russian continental shelf) region in each form drag run, which is associated with enhanced (reduced) basal melt (Figs. 6b, e) and decreased (increased) sea ice thickness (Figs. 6c, f). The spatial distributions of these positive/negative differences match the distribution of higher/lower values of the formdrag-based αt(with respect to 0.006; Fig. 7), indicating that a larger (smaller) form-drag-based αtincreases (decreases)the upward oceanic heat flux and increases (decreases) the basal melt. The impact of the form-drag-based αtis consistent with the results of Tsamados et al. (2015).

Moreover, compared with the form-drag-based αt, a constant αt(0.006) seems to play an important role in creating the condition for a reversed (downward) fw(Fig. 8). We found a downward oceanic heat flux in the CST-DRAGMU71 (Fig. 3f). Figure 8b also shows a similar downward oceanic heat flux in the CES region in the CST-DRAG-P07.In contrast, there are no downward oceanic heat fluxes in the two form-drag-based αtruns (Figs. 8a, c). To study the influences of the summer IO freshening process beginning in June (Fig. 1) on the reversed oceanic heat flux in the CES region, we calculated the mean changes in this region from June to August. The results are listed in Table 4 (Table 5)for the CST-DRAG-MU71 and FORM-DRAG-MU71 (for CST-DRAG-P07 and FORM-DRAG-P07). First, for the CST-DRAG-MU71, the mean value of the upward oceanic heat flux (? fw) in June in the CES region is ～5.6 W m–2,this is associated with the ～0.60 cm d–1of basal melt rate, ～23.7 PSU of interfacial salinity, and ～ –1.28°C of interfacial temperature in this region. As the oceanic heating continues on the sea ice during the summer season (Fig. 1e), the basal melt rate increases by ～0.27 cm d–1(from 0.60 in June to 0.87 in August, cm d–1). Accordingly, there is a decrease of ～3.6 PSU in the interfacial salinity (from 23.7 PSU in June to 20.1 PSU in August), indicating a significant IO freshening process. Given the reduced interfacial salinity, the interfacial temperature is enhanced by ～0.2°C (from –1.28°C in June to ～ –1.08°C in August). As a result, there is a negative temperature difference (～ –0.2oC; Fig. 3f) between the SST(–1.25°C ) and Tfio(–1.08°C ), which leads to a reversed heat flux (from the ice to the ocean ML) of ～5.2 W m–2in the CES region in August.

After analyzing the results of CST-DRAG-MU71, we now look at how different changes in the CES region can affect FORM-DRAG-MU71. Our results show that by the smaller form-drag-based αtin the CES region (< 0.006;Fig. 7) in FORM-DRAG-MU71, the upward oceanic heat flux in June (3.4 W m–2) in the FORM-DRAG-MU7 is less than that in the CST-DRAG-MU71 run (5.6 W m–2). Accordingly, the basal melt rate is relatively slower (0.38 cm d–1)compared with that of 0.60 cm d–1in the CST-DRAGMU71. Associated with the slower basal melt rate, the decrease in the interfacial salinity from June to August (～–0.1 PSU) is less than that (–3.6 PSU) in the CST-DRAGMU71 run, indicating a relatively weaker IO freshening process in the FORM-DRAG-MU71 in comparison to the CSTDRAG-MU71. Therefore, although the IO freshening also causes an increase of 0.05°C for the interfacial temperature(from –1.32°C in June to –1.27°C in August), the interfacial temperature –1.27°C is still lower than the SST (～ –1.22°C ),and hence the heat exchange at the IO interface is still from the ocean ML to the ice (upward) in the FORM-DRAGMU71 run.

Fig. 6. The difference of (a) upward oceanic heat flux (? fw, W m–2), (b) basal melt rate (cm d–1), and (c) sea ice thickness (m) in August between the CST-DRAG-MU71 and FORMDRAG-MU71. (d)–(f) as (a)–(c) but for CST-DRAG-P07 minus FORM-DRAG-P07.

Fig. 7. Spatial distribution of the form-drag-based heat coefficient αt in (a) FORM-DRAGMU71 and (b) FORM-DRAG-P07. In each plot, the 6×10?3 form drag contour is shown by the dashed black line, and the region (CES) of downward heat flux in the CST-DRAG-MU71 and CST-DRAG-P07 is shown by the red contour line in (a) and (b), respectively.

Fig. 8. The simulated upward oceanic heat flux (? fw, W m–2) in (a) FORM-DRAG-MU71, (b) CST-DRAG-P07, and (c)FORM-DRAG-P07. Note that the negative values in (b) denote the downward oceanic heat flux.

Similar differences in the CES region can be seen between the runs of a larger constant and smaller form-dragbased αtcombined with P07 conductivity (CST-DRAG-P07 and FORM-DRAG-P07, Table 5). We can see that there is also a relatively greater (smaller) oceanic heat flux, a relatively greater (smaller) decrease in the interfacial salinity, a relatively greater (lower) interfacial temperature than the SST, and thus a downward (upward) oceanic heat flux associated with a larger (smaller) constant (form-drag-based) αtin the CES region in the CST-DRAG-P07 (FORM-DRAGP07).

Table 4. The simulated mean values of the upward oceanic heat flux (? fw), the basal melt rate (Meltb), the interfacial salinity (S io)and the interfacial temperature (T io) in June and August, and the changes (August–June) in the CES region in the CST-DRAGMU71 and FORM-DRAG-MU71.

In summary, the above results suggest a coupled mechanism in the three-equation IO boundary approach for a downward heat flux from the ice to the ocean ML in summer. It involves the increased oceanic heat flux since the early period of summer, the continuously strong IO freshening process during JJA, the reduced interfacial salinity, the increased interfacial temperature above the SST, and the final downward heat flux from the ice to the ocean in the later summer, where the parametrization method applied to the αtplays an important role in amplifying the magnitude of the oceanic heat flux to the IO interface in early summer.The latter can cause a greater freshening effect at the IO interface.

Finally, we describe the impacts of the conductivity on the model simulations. Hunke (2010) demonstrated that the conductivity P07 decreases the e-folding scale of the ice thickness redistribution function, reduces the ocean heating on the sea ice, and adjusts the upward albedo, each of which acts to thicken the ice. In this study, we also observe an increase in the sea ice thickness in our P07 runs compared to our MU71 runs (Fig. 9a). Additionally, we find that the impacts of the P07 conductivity reported by Hunke (2010)can be strengthened by the three-equation boundary condition, which can be demonstrated as follows. In Fig. 1g, we see that the positive heat conduction fcondbotis increased in the P07 runs compared with the MU71 runs. According to the three-equation scheme, the increased fcondbottends to be associated with a reduced oceanic heat flux to avoid overestimating the heat convergence under a given melt condition(see Eq. 10). Ultimately, this process, controlling the IO energy balance, results in a decreased upward oceanic heat flux (Fig. 9b) and a reduced basal melt (Fig. 9c) in the P07 runs, contributing to the increase in the sea ice thickness(Fig. 9a).

4.Discussion and conclusion

We have presented a stand-alone sea ice model sensitivity study that focuses on the impacts of the two-equation and three-equation approaches on summer (August) bottom heat exchanges and basal melt processes in the state-of-the-art Los Alamos community sea ice model CICE6. The influences of combinations of form-drag-based/constant heat transfer coefficients and two kinds of conductivity are also studied.

Compared with the two-equation boundary condition,our results show that the three-equation boundary condition resulted in a much fresher IO interface mainly in the sea ice edge regions, where the salinity effects increase the IO freezing temperature, reducing the oceanic turbulent heat flux,slowing the basal melt rate, and increasing the sea ice thickness. By comparing the seasonal cycles of these processes,we found that the above impacts of the three-equation approach are more pronounced in the summer months (JJA)than in other months.

Furthermore, we found a reverse (downward) turbulent heat flux at the IO interface in our three-equation runs with constant αt. This downward oceanic turbulent heat flux is conditioned by a significant IO freshening process to increase the interfacial temperatures. Our results show that such a condition could be achieved in the areas along the sea ice edges; in this study, the suspect area lies in the Chukchi Sea and the East Siberian Sea. It should be noted that the downward IO heat flux in summer obtained in our stand-alone experiments should be further examined in a coupled iceocean model or a fully coupled climate model, and this will be addressed in our future work. Nevertheless, this study shows a potential possibility for a reverse oceanic turbulent heat flux by the three-equation boundary condition, which will change the heat balance, causing bottom ice formation in summer. Also, the strong flushing process through the surface melt ponds can also cause bottom ice formation in summer, known as the summer false bottom (Notz et al., 2003).In our model runs, most pond fractions are found in June,with wider and more center-extending coverages than the area of the congelation in August (Fig. 1i). Thus, it is hard to attribute the bottom ice formation in August to the false bottom mechanism.

The results presented in this study suggest that the sea ice edge is important due to its great sensitivity to the threeequation approach in summer, which is evidenced in the relatively more pronounced anomalies in the IO heat flux, the bottom melt rate, the sea ice thickness, and the SSTA. Additionally, congelation near the sea ice edge regions does occur.This ice-edge sensitivity reveals an important effect of the open water on the sea ice properties. Previous studies have shown that in the open-water area, sea ice growth and melt have had a direct impact on water mass formation (i.e., Haapala et al., 2005). By performing sensitivity experiments using a climate model and an idealized 1-D thermodynamic model, Shi and Lohmann (2017) reported that in the Arctic winter, a reduced horizontal-to-vertical aspect ratio of the open water in models can lead to significant decreases in the SIC, which reduces the surface albedo and enhance the heat release from the ocean to the atmosphere, in turn creating the conditions for sea ice formation. In this study, along the ice edge regions, the larger fractions of open water tend to amplify the influence of the three-equation approach on the oceanic heat flux (Fig. 4a) in summer since more openwater fractions allow more incoming shortwave radiation,causing the more evident changes in the bottom melt rate and sea ice thickness in this region. Also, we have discussed in section 3.4 that the greater anomalies of the surface heat balance in the ice edge regions are related to the larger anomalies in the sea ice thickness in the open-water area as compared with those anomalies in the central Arctic, the former causing more evident SSTA in our three-equation boundary condition.

Fig. 9. The difference of (a) sea ice thickness (m), (b) upward oceanic heat flux (? fw, W m–2) and (c) basal melt rate (cm d–1) between the CST-DRAG-MU71 and CST-DRAG-P07.(d)–(f) as (a)–(c) but for FORM-DRAG-MU71 minus FORM-DRAG-P07.

The results of our three-equation model runs with different combinations of heat/salt coefficients and thermal conductivity show that (1) compared with the form-drag-based αt, the constant αtleads to more oceanic heat flux and a stronger IO freshening process in the CES region, creating favorable conditions for the downward heat flux to occur in this region, (2) the P07 conductivity reduces the oceanic heat flux and increases sea ice thickness, and (3) the combination of the constant αtand the conductivity MU71 results in the strongest IO freshening process and greatest interfacial temperatures. The combination of the constant αtand conductivity P07 conductivity results in the slowest basal melt rate and greatest ice thickness.

In this study, the CICE6 is used to assess the model sensitivity to the two-equation and three-equation boundary parameterization based on stand-alone sensitivity runs forced by the climatological ocean and atmospheric data. Compared with previous studies on this subject, similar results include the increased sea ice thickness, the increased interfacial temperature and IO freshening in the ice edge regions in summer(i.e., Shi et al., 2021), and the bi-modal pattern of the differences in sea ice thicknesses between the constant and formdrag-based αtruns (i.e., Tsamados et al., 2015). Additionally, this study analyzes the response of the heat balance to the three-equation condition in greater detail, and we have found a reversed oceanic heat flux in August and an associated congelation in the ice edge region, which was not reported in previous studies based on CICE.

There are, however, some limitations to this study. The results presented here are based on stand-alone sensitivity runs with a fixed ML depth (10 m during summer and 20 m during winter). In summer, as the ML becomes shallower,the upper ocean can significantly warm and significantly increase the heat flux to the ice bottom, potentially influencing the results presented in this study. However, a previous stand-alone run, including a prognostic ML in CICE, also resulted in an increased IO freezing temperature and a decrease in basal melt by the three-equation boundary condition. For example, the modeled minimum 10 m ML depth and reduced basal melt in Tsamados et al. (2015; see Fig. 6 in their paper).

Finally, a comparison between the simulation results and observations is not the ambition of this study. Rather,our goal is to study the sensitivity of the Arctic summer IO heat balance and associated ice basal process to the threeequation parametrizations employing a stand-alone sensitivity experiment. Also, the impacts of the three-equation approach on the basal process presented in this study could be compromised by the interactions between the ocean ML and deep ocean in a coupled sea ice-ocean model, or could be changed by the feedback from the atmosphere to the sea ice in a coupled climate model (e.g., Shi et al., 2021). Nevertheless, the stand-alone approach has an advantage in that it excludes model uncertainty from the internal variability inherent to a fully coupled model. Thus, this study can serve as a stand-alone model sensitivity study providing an insight into the CICE6 sensitivity to the three-equation boundary condition, which is helpful for coupling CICE6 using the threeequation approach to a climate model.

Acknowledgements.This research is supported by the National Key R&D Program of China (Grant No.2018YFA0605901), by the National Natural Science Foundation of China (GrantNo. 41775089), by the National Key R&D Program of China (GrantNo. 2017YFC1502304), and by the Partnership for Education and Cooperation in Operational Oceanography(PECO2) project awarded by the Research Council of Norway(111280). The authors thank anonymous reviewers for their helpful comments.