Large-eddy simulation of the ice shelf-ocean boundary layer and heterogeneous refreezing rate by sub-ice shelf plume

The role of the refreezing effect in the ice shelf–ocean boundary layer (IOBL) flow with a super-cooled, plume beneath the ice shelf is investigated using the large-eddy simulation. To reveal the detailed physical processes and characteristics of the IOBL flow, a model domain is initialized and forced by in situ observations and a comparison is made 10 between two simulations, one with the refreezing effect and one without. The simulated velocity, potential temperature, and salinity field are validated with in situ observations performed in Terra Nova Bay in the western Ross Sea in 2016/2017, confirming that the vertical structures in the simulation results agree well with observations. In particular, it is evident that, when the refreezing effect is considered, the IOBL flow can be more realistically resolved, especially upward advection from the sub-ice shelf plume and the ice front eddy. Beneath the ice shelf, two district regions (the inner and outer regions) are 15 identified based on flow characteristics and the refreezing pattern. In the inner region, stratification and stable conditions are observed with negative momentum flux and low refreezing rates. Meanwhile, in the outer region, high shear impact and unstable conditions with a heat flux of –9 to –52 W m–2 are observed, demonstrating the high refreezing rate and the entrainment of super-cooled water from the sub-ice shelf plume. A total of 94% of the refreezing events occur in the outer region, with a maximum refreezing rate of 1.86 m yr-1 at the ice front. 20

through basal melting is thought to be greater than that (Gwyther et al., 2016). The basal melt rate of ice shelves is mainly determined by the heat exchange at the boundary layer between the ocean and ice, which is known as the ice shelf-ocean boundary layer (IOBL). The nature of the IOBL is highly complex and depends on the stratification of the ambient water column, the level of turbulence, the strength of tidal currents, and the roughness and slope of the ice base, among other factors (Holland et al., 2020). 45 In the cold-water cavity where both melting and freezing take place, positively buoyant sub-ice shelf meltwater plumes created near the grounding zone can modify the stratification and heat entrainments within the IOBL through the shear impact of its momentum near the grounding zone and the ice shelf front, resulting in the change of the melting and refreezing rates (Dutrieux et al., 2013;Sansiviero et al., 2017). The stratified water column formed by the potential density difference (or salinity difference) between glacial meltwater-rich water and denser continental shelf water near the grounding zone is likely 50 responsible for preventing the heat entrainment (Begeman et al., 2018). As the sub-ice shelf plume modulates the IOBL characteristics with shear mixing, the basal melt rate can be increased by weakening a stratification and enhancing the entrainment of seawater from the outer region. At the ice shelf bottom near the ice front, increased turbulent mixing can increase the IOBL thickness, leading to changes in heat exchange and entrainment with a modification of the refreezing rate (Jenkins, 2011). 55 Flow structure and its quantity within the IOBL beneath the ice shelf is closely related to the basal melting and refreezing rate since the IOBL is the interface linking the ice shelf and ocean, in terms of heat transfer, salt flux, and momentum change (Holland and Jenkins, 1999;Jenkins, 2016;Rees Jones and Wells, 2018). However, the flow physics and detailed mechanisms for the melting and refreezing processes within the IOBL remain unclear. The challenges in elucidating the aforementioned primarily come from technical difficulties in accessing and observing the sub-ice shelf ocean cavity, more specifically the 60 IOBL and the complexity of the flow itself, which has highly turbulent and buoyant characteristics with various spatial and temporal scales (Nicholls et al., 2006;Everett et al., 2018). Nevertheless, there are growing demands to deal with this highly https://doi.org/10.5194/tc-2020-166 Preprint. Discussion started: 20 July 2020 c Author(s) 2020. CC BY 4.0 License. complex physics, which has led researchers to introduce high-resolution turbulence models such as the large-eddy simulation (LES) which have more realistic boundary conditions constrained by in situ observations (Gayen et al., 2016).
The LES has been successfully applied to investigate the role of turbulence in the ice-ocean interaction within the IOBL 65 for cases in Greenland (Carsey and Garwood, 1993;Denbo and Skyllingstad, 1996) and the Arctic Sea (Glendening and Burk, 1992;Glendening, 1995;Skyllingstad and Denbo, 2001;Matsumura and Ohshima, 2015;Ramudu et al. 2018;Li et al. 2018).
Additionally, the LES has been used to explore the detailed processes of ice-ocean-atmosphere interaction in the vicinity of Arctic leads (Glendening and Burk, 1992;Weinbrecht and Raasch, 2001;Esau, 2007;Lupkes et al. 2008). However, applications of the LES to the sub-ice shelf interface are quite limited. 70 In this study, we performed large-eddy simulation experiments for the IOBL flow including the refreezing process and validated the results with in situ observation data-namely Conductivity-Temperature-Depth (CTD) and Lowered Acoustic Doppler Current Profiler (LACDP) data-collected in front of the Nansen Ice Shelf (NIS; cold-water cavity) during the Antarctic Expedition led by the Korea Polar Research Institute in January and February 2017. The main objectives of this study are to examine flow characteristics within the IOBL in this region and to determine its impacts on the refreezing rate at 75 the bottom of the ice shelf. Given validated outputs, we were able to account for refreezing patterns, detailed flow structures including turbulent characteristics, fluxes and the relationship between the refreezing and entrainment of super-cooled water from sub-ice shelf plume within the IOBL. Section 2 of this paper presents the governing equations (i.e., the Navier-Stokes equation and liquidus condition) for the oceanic flow with refreezing along with a detailed explanation of the simulations. Section 3 provides an overall analysis of the 80 simulations in order to validate the LES results and determine the characteristics within the IOBL-flow velocity, potential temperature, salinity, fluxes, and turbulence statistics. Primary findings, future works, and implications of this study are summarized in Sections 4 and 5.

Numerical model
To simulate the oceanic flow with refreezing, the Parallelized Large-Eddy Simulation Model (PALM) developed by Leibniz University was employed (Maronga et al., 2015;Noh et al., 2009;Raasch et al., 2001). This model solves the nonhydrostatic, Boussinesq-approximated, filtered Navier-Stokes equations with buoyancy force, Coriolis force, and subgridscale (SGS) turbulent closure. The Boussinesq approximation can be applied to flows with negligible density variation. In the 90 time integration, the time-difference formulas were computed using the third-order Runge-Kutta method. The 5 th order upwind scheme was used to solve the flow advection (Wicker and Skamarock, 2002). The pressure was modeled by a Poisson equation, while the mass, momentum, potential temperature, and salinity conservations were governed by Eqs. (1)-(4), respectively. https://doi.org/10.5194/tc-2020-166 Preprint. Discussion started: 20 July 2020 c Author(s) 2020. CC BY 4.0 License.
where u k is the flow velocity, ρ is the seawater density, π * is the dynamic pressure, ε ijk is the Levi-Civita symbol, f is the Coriolis force, δ ij is the Kronecker delta function, g is the gravitational acceleration, ρ θ is the potential density, T is the absolute 100 temperature, ν is the dynamic viscosity, τ r kj is the Reynolds stress, θ is the potential temperature, p is the hydrostatic water pressure, p 0 is the reference pressure, and Sa is the salinity. Q θ and Q sa are the external forcing of the source/sink terms of T and Sa, respectively. Overbars denote that the values have been filtered over the grid volume. Combining these equations, the SGS turbulent kinetic energy (e) equation [Eq. (5)] is derived as follows: , and ε is the SGS dissipation rate.
The SGS stresses for the momentum, potential temperature, and salinity are parameterized as follows: where l is the turbulent mixing length scale and Δ is the length scale of the filter.
To resolve thermal and salt changes by the refreezing effect at the ice-ocean boundary, it is necessary to determine ambient 115 variables (θ f and S f ) within the IOBL and interfacial variables (θ b and S b ) near the ice-ocean boundary. In this study, we determined the ambient variables based on in-situ CTD observations. To obtain interfacial variables, we solved the conservation equations of heat and salt, along with the liquidus condition and turbulent exchange velocities for heat and salt (Beckmann and Goosse, 2003;Vreugdenhil and Taylor, 2019). https://doi.org/10.5194/tc-2020-166 Preprint. Discussion started: 20 July 2020 c Author(s) 2020. CC BY 4.0 License. 120 where r is the refreezing rate, the subscript w refers to parameters for water, the subscript i refers to parameters for ice. The specific heat capacity of water (c w ) = 3974 J kg -1 o C -1 , the latent heat of fusion (Li) = 3.35 ⅹ 10 5 J kg -1 , and λ = 0.054 o C psu −1 125 (UNESCO, 1981). The molecular diffusivities of heat k θ and salt k S are 1.3 ⅹ 10 -7 m 2 s -1 and 7.2 x 10 -10 m 2 s -1 , respectively (based on Prandtl number = 14, Schmidt number = 2,500 in Antarctic). Grid size used in this study cannot resolve the gradients of temperature and salinity at the interface near the ice-ocean boundary, and therefore we used the turbulent exchange velocity of heat (γ θ ) which have value of 10 -4 m s -1 .
The fluxes for temperature and salinity, q θ * and q S * at ice shelf bottom are formulated by Monin-Obukhov similarity and 130 interfacial values, θ b and S b obtained by resulting equation, Eq (13) (McPhee et al., 1987;Ramudu et al. 2018) 135

Simulation description
In this study, we conducted two LES simulations, one with the refreezing effect and one without this effect, to reveal the role of the refreezing on IOBL characteristics. Idealized experiments were designed to resolve the IOBL flow with sub-ice shelf plume beneath the NIS with turbulence structures of various scales. The simulation dimensions were 3072 m × 3072 m × 864 m in the x, y, and z directions, respectively. For the simulations, a grid of 384 × 384 × 288 cells was used with an 8 m 140 horizontal grid and a 3 m vertical grid with a surface roughness of 0.07 m. The used grid size and surface roughness were based on a numerical study of high shear plume flow and observation of surface roughness in the marginal ice zone in Greenland (McPhee et al., 1987;Gao et al., 2019). An idealized ice shelf with a depth of 280 m was located in the upper-left part of the simulation domain, referring to the ice shelf depth near the ice front of the NIS study (Stevens et al., 2017). For the velocity, the potential temperature, and the salinity, the inlet boundary condition was set to the Dirichlet boundary condition 145 with constant vertical profiles which was the same as the initial profiles. At the start of the simulation, initial profiles were imposed on the whole domain. Initial profiles were set in the variation range of vertical profiles of our 24 CTD and 23 LADCP observations conducted near the ice front of the NIS. The outlet boundary condition was determined to match the radiation boundary condition, which prevented numerical errors without rapid change of velocity and scalars. The cyclic boundary condition was applied to lateral boundaries, while a Dirichlet boundary condition (U top = -0.075 m s -1 ) was imposed on the top 150 layer. A random generator for small velocity perturbation was applied at depths from 15 to 800 m to quickly spin up the turbulence. The total simulation time required to reach the quasi-steady state was 86 hours. Detailed information about the simulation domain and boundary conditions is summarized in Fig. 1. This figure shows the target research region, observation points, and simulation domain with a schematic diagram for the oceanic flow with a sub-ice shelf plume. In the oceanic region, the simulated ocean velocity, potential temperature, and salinity of the LES results were validated with CTD and LADCP 155 observations. After this validation, detailed flow characteristics of the IOBL flow beneath the ice shelf were analyzed.

CTD, LADCP observations
During the hydrographic survey conducted from 26 January to 15 February 2017 by the icebreaking research vessel ARAON operated by the Korea Polar Research Institute, full-depth CTD and LADCP profiles were obtained with one-hour 160 intervals from 14 February 2017 13:00 UTC to 15 February 2017 11:55 UTC at a single site in the Terra Nova Bay in front of the NIS in order to examine the vertical structures of the super-cooled, sub-ice shelf plume with temporal variations. The exact location of the observations is 75.008 °S, 163.617 °E (Fig. 1b). Because the LADCP data was incorrectly observed at the final casting, 24 CTD profiles and 23 LADCP profiles were used in this study. The CTD data were processed following the SBE recommended procedure (Sea-Bird Electronics, Inc., Bellevue, Washington, USA; 2014) and the LADCP data were processed 165 using the methods introduced in Thurnherr (2004). The detailed shipboard information and processing methods for the hydrographic data are described in Yoon et al. (2020). showing there are a large-scale eddies beneath the ice shelf. In 3-h moving average results, a convergence trend appears clearly 175 after 17 t * . Friction velocities in cases without and with refreezing are 0.00219 and 0.00283 m s -1 , respectively. This difference is induced by high momentum exchange by refreezing and its brine rejection. To observe the averaged features of the flow without temporal variance in two simulation cases, we used the time-averaged results within 1 t * period in the later analysis. https://doi.org/10.5194/tc-2020-166 Preprint. Discussion started: 20 July 2020 c Author(s) 2020. CC BY 4.0 License. Figure 3 illustrates vertical sections (y = 1536 m, domain center) of velocity, potential temperature, and salinity which are time-averaged in 1 t * period to examine the spatial distributions of flow structures and variables in the case with refreezing 180 effect. In Fig. 3a, vortical structures that are identified by the swirling strength criterion (s = 2 ⅹ 10 -7 ) to observe the structures of overturning eddies clearly (Na et al., 2019). Due to neutral buoyancy, sub-ice shelf plume is about 100 m apart from the ice shelf and has a high velocity (0.05~0.08 m s -1 ). In the IOBL beneath the ice shelf, there are various coherent structures induced by the shear impact of the sub-ice shelf plume and momentum entrainment from the upper mixed layer. Near the ice front, a large-scale eddy structure with negative mean velocity is observed. In this study, we refer to this large-scale eddy as the "ice 185 front eddy". This eddy is induced by strong flow shear near the ice front and unstable conditions by refreezing. The occurrence of the ice front eddy enhances the entrainment of super-cooled water from the sub-ice shelf plume, which leads to vigorous refreezing. Subsequently, the latent heat release and brine rejection caused by this vigorous refreezing affect the upper mixed layer region. This brine rejection produces a downward force which prevents the upward advection of super-cooled water from the sub-ice shelf plume in the oceanic region. In the vertical distribution of potential temperature (Fig. 3b), the sub-ice shelf 190 plume layer and its stratified features are clearly visible, at depths from 400 to 600 m. The active interaction between the subice shelf plume and the IOBL is focused in the upper region (> 430 m) of the plume, where salinity stratification is not strongly formed. In both the ice shelf and oceanic regions, the temperature in the depth range from 280 to 400 m ranges from -1.95 to -1.90 °C, due to latent heat release and weak upward advection from sub-ice shelf plume. This demonstrates that the stratification is more dominant than flow shear near the ice front and play a major role in preventing flow advection from sub-195 ice shelf plume. In the LES model, the filtered Navier-Stokes equation is solved with the modelled effect of small-scale eddies to reduce computational cost. Therefore, the criteria for "small-scale" are important; these criteria are determined by grid size. To 205 evaluate grid size and modelling of small-scale eddies in this study, it is necessary to confirm that the turbulence characteristics of the LES result are similar to the turbulence characteristics of inertial subrange in which energy cascading occurred with few dissipations. Figure 5 shows plots of the one-dimensional energy spectra at different depths where flow shear is strong in the LES results with and without the refreezing effect. In the overall range of wavenumbers, in cases with and without refreezing, energy spectra follow the -5/3 slope of the Kolmogorov scale in the inertial subrange. At high wavenumbers, at similar 210 magnitude of the energy spectra is observed in cases with and without the refreezing effect with a slight underestimation of turbulence energy in SGS turbulence. At low wavenumbers, the energy spectra in the case without refreezing are higher than https://doi.org/10.5194/tc-2020-166 Preprint. Discussion started: 20 July 2020 c Author(s) 2020. CC BY 4.0 License. those in the case with refreezing, showing that strong turbulence energy is developed with expanded upper region of sub-ice shelf plume in the case without the refreezing effect. Figure 6 plots the vertical profiles of the stream-wise zonal velocity, potential temperature, and salinity in the LES results 215 and CTD and LADCP observations to quantitatively compare the vertical distribution of the momentum and variables related to potential density. The initial profiles of observed velocity, potential temperature, and salinity used for domain initialization and the inlet boundary condition are compared with the LES results to observe how the LES results are adjusted under the geometrical effect of the ice shelf and boundary conditions. In the velocity profiles, the LES results with and without the refreezing effect agree well with the 23 LADCP profiles, except for slight difference in the velocity magnitude and the depth 220 of the peak induced by the difference in upward advection and downward force caused by brine rejection. Due to this difference, the magnitudes of potential temperature in the upper mixed layer in the cases with and without refreezing are quite different:

Validation of simulation results
in the upper mixed layer, the potential temperature in the case without refreezing is about -1.97 °C, whereas that in the case with refreezing is about -1.94 °C, which is closer to the CTD observation results. This difference is due to the latent heat of refreezing at the ice shelf bottom and the weak upward advection in the case with the refreezing effect, which is close to reality. 225 Regarding the salinity profiles, the two LES results agree with the 24 CTD profiles. However, the multi-layered stratified characteristics of the salinity profile at depth of ice shelf bottom and IOBL top are observed in the case with refreezing effect.
Through the comparison of quantity and its characteristics, we conclude that the LES results with the refreezing effect are similar to in situ observations of oceanic environments. However, it should be noted that, since this is an idealized model, some differences can be expected between the simulated results and observations, in terms of ice shelf bathymetry and surface 230 roughness, the temporal variability of the sub-ice water plume, the drag effect of frazil ice, etc.

IOBL characteristics in the sub-ice environment
Through the afore-mentioned analysis, it is shown that the LES model adequately resolves the oceanic flow beneath the ice shelf with the proper refreezing effect beneath the ice shelf. Next, we explores the flow characteristics of the IOBL beneath 235 the ice shelf using the validated LES results. Within the IOBL, there are the shear forces caused by the momentum of the subice shelf plume and the buoyancy force (stratification) caused by the vertical gradient of potential density. In this section, we analyze the detailed flow physics within the IOBL to reveal the relationship between the flow physics and refreezing patterns within the IOBL beneath the ice shelf.  observed in the inner region. Meanwhile, a high negative heat flux is observed near the ice front, which causes the refreezing rate in the outer region to increase rapidly; the results show that 94% of the total refreezing rate occurred in the outer region.
The maximum refreezing rate (rmax) which is observed at the ice front is 1.86 m yr -1 . The main factors that determine the magnitude and distribution of the refreezing rate are the ice front eddy and the entrainment of super-cooled water. Figure 9 plots vertical profiles of the mean velocity and turbulence intensity in the inner and outer regions to obtain insight 255 into the stochastic characteristics of the ice front eddy and negative heat flux in the IOBL. Near the ice shelf bottom, there is negative zonal velocity in the outer region due to refreezing and the strong shear force near the ice front, having a steep velocity gradient. In contrast, the zonal velocity in the inner region has almost zero magnitude. Turbulence intensity is the second moment of velocity and represents the magnitude of the mixing by the advective motion of the flow. Owing to a steep velocity gradient, the IOBL turbulence intensity in the outer region is almost twice as high as that in the inner region. This means that 260 the IOBL in the outer region is an effective environment to elevate super-cooled water from the sub-ice shelf plume to the IOBL.  Fig. 7a) are developed, having the negative heat flux which represents negative heat transfer from the IOBL to the ice shelf for refreezing. In the depth range from 280 to 320 m, negative heat fluxes vary from -9 to -52 W m -2 . This range is 270 comparable with the order of the negative heat flux in frazil ice formations beneath sea ice near the Ross Sea (Langhomrne et al., 2017). This suggests that there is a frazil ice layer and refreezing between depths of 280 and 320 m in the outer region.
From depths of 390 to 440 m, another negative heat flux is developed by the ice front eddy, which causes the entrainment of super-cooled water from sub-ice shelf plume to IOBL the flow. where the peak flatness occur. The flatness factor is the fourth moment of velocity and represents the possibility and frequency of high magnitude events. The spatial distribution of the velocity magnitude is almost homogeneous, showing flatness factors within the IOBL in the inner region is in the range of 2.6-3.8, which corresponds to a Gaussian distribution. However, within the IOBL in the outer region, the flatness factor is in the range of 4.4-5.6 and its peak occurs at a depth of 416 m, close to the top of the IOBL. As shown in the inset graph of Fig. 11, the fluctuation of vertical velocity at a depth of 416 m in the inner 280 region has 3σ, which corresponds to moderate magnitude events, while that in the outer region has 6-10σ, which corresponds to high magnitude events. These high magnitude events are also induced by the ice front eddy and large-scale advection near the ice front.

LES simulation for IOBL flow
The main processes of the ice-ocean interactions related with ice mass balance in cold-water cavity are basal melting near the grounding zone and refreezing near the ice front Jacob et al., 1992;Petty et al., 2013). One of these processes is triggered by the intrusion of the High Salinity Shelf Water (HSSW). When this dense seawater intrudes into the ocean-filled cavity beneath the ice shelf, the base of the deep ice shelf is melted because the temperature of the HSSW is higher 290 than the freezing temperature at this depth. Then, super-cooled, less-dense water is formed at the base of the deep ice shelf and rise, creating the sub-ice shelf plume with high momentum and buoyancy. This water plume refreezes in the outer cavity region or near the ice front with increased freezing temperature and forms platelet ice (Galton-Fenzi et al., 2012;Robinson et al., 2014).
During these processes, the IOBL flow and its turbulence structures have a crucial role in mass and energy transport in 295 Antarctic oceanic flow. Additionally, these are key to explaining and evaluating the complex phenomenon of ice-ocean interaction beneath the ice shelf. Therefore, it is necessary to investigate the detailed structures and their physical processes to follow the trajectory of mass and energy. Understanding the flow physics and structures using only the one-dimensional profile obtained by CTD and LADCP has many limitations. Moreover, the observational approach is difficult in sub-ice shelf environments. As shown in previous LES studies of ice-ocean boundary (Ramudu et al. 2018;Vreugdenhil and Taylor, 2019), 300 the LES model is a powerful tool for resolving the flow and its three-dimensional structures with the change of mass and energy, with high accuracy and low computational cost. Therefore, when employing the numerical approach including the LES, a regional ocean model is one of the solutions for resolving the three-dimensional structures in the oceanic flow. In this study, we used the LES model to expand the one-dimensional observation profile in oceanic region to the three-dimensional flow-field in oceanic region and the sub-ice shelf region. Additionally, we set to ambient values (θf, S f ) by using the CTD 305 results to obtain the interfacial values (θ b , S b ) in the liquidus condition. We assumed that the LES results for the sub-ice shelf region are validated if the LES results for the oceanic region are validated. Via an evaluation of the refreezing effect, we obtained a successful validation for the oceanic region (Fig. 6). In future work, this methodology will be validated using multidimensional sub-ice shelf observation methods such as autonomous underwater vehicle (AUV), glider instruments, etc.

IOBL characteristics in the sub-ice environment
The characteristics of the IOBL are more complex than the oceanic characteristics in the upper mixed layer since brine rejection and latent heat release by refreezing at the ice shelf bottom affect the density inversion and advection magnitude within the IOBL. In this study, our main findings were the heterogeneous distribution of the refreezing rate and its causes within the sub-ice shelf environment. Moreover, we quantified important values such as the scale of ice front eddy, the IOBL 315 depth, negative heat transfer, and the refreezing distribution. The results of this study will be used to interpret an insufficient amount of information obtained by limited observation of the sub-ice shelf cavity. If direct observation for IOBL flow structures and turbulence characteristics in sub-ice shelf environment is available, this study can be improved by comparing LES results with observations and its feedback. Other important factors which were not included in this study should be addressed and investigated in future studies-e.g., the effect of ice shelf bathymetry and surface roughness on shear 320 characteristics, the temporal variability of the sub-ice water plume, and the drag effect of frazil ice. If a database for flow physics in various parameters is completed, these studies can be used for the improvement of parameterizations (e.g. vertical mixing within the IOBL, sea-ice formation and behavior) in the regional ocean model.

Conclusions 325
We successfully simulated the IOBL flow with a super-cooled, sub-ice shelf plume and the refreezing effect beneath the NIS using a large-eddy simulation and boundary conditions based on in-situ observations. The flow performed for 86 h (23 t*) reaches a quasi-steady state after 17 t*, showing the convergence trend in temporal variance. To validate the LES results with and without the refreezing effect, the simulated velocity, potential temperature, and salinity are compared with 24-hour CTD and LADCP observations obtained near the NIS in Terra Nova Bay of the western Ross Sea in a 2016/2017 shipboard survey. 330 The simulation results agree well with the observations in terms of magnitude and the slope and the depth of peak values, except for the temperature difference in the upper mixed layer. Based on this validation, we conclude that the LES results with the refreezing effect better resolve the Antarctic environment in the NIS, especially the upward advection from the sub-ice shelf plume. In the one-dimensional energy spectra, the slope of the energy spectra in the overall wavenumber range follows the -5/3 slope which corresponds to the Kolmogorov scale in the inertial subrange, except that SGS turbulence energy is 335 underestimated in the low wavenumber range. In the IOBL flow beneath the ice shelf, two distinct regions (an inner region and an outer region) can be identified based on the refreezing rate and flow physics. Stratification and stable conditions caused by refreezing and weak upward advection from the sub-ice shelf plume are observed within the IOBL in the inner region.
These features are identified by negative momentum flux within the IOBL and a moderate magnitude event (3σ) of vertical velocity at the top of the IOBL. However, unstable features by strong shear of ice front eddy and refreezing are observed within 340 the IOBL in the outer region, showing the occurrence of high magnitude event (> 6σ) of vertical velocity caused by the entrainment of super-cooled water from sub-ice shelf plume. These different features in the two regions yield the heterogeneous distribution of the refreezing rate. A total of 94% of the total refreezing is concentrated in the outer region, having a maximum refreezing rate of 1.86 m yr -1 at the ice front.    https://doi.org/10.5194/tc-2020-166 Preprint. Discussion started: 20 July 2020 c Author(s) 2020. CC BY 4.0 License.       https://doi.org/10.5194/tc-2020-166 Preprint. Discussion started: 20 July 2020 c Author(s) 2020. CC BY 4.0 License.