A daily basin-wide sea ice thickness retrieval methodology: Stefan’s Law Integrated Conducted Energy (SLICE)

As changes to Earth’s polar climate accelerate, the need for robust, long–term sea ice thickness observation datasets for monitoring those changes and for verification of global climate models is clear. By coupling a recently developed algorithm for retrieving snow–ice interface temperature from passive microwave satellite data to a thermodynamic sea ice energy balance relation known as Stefan’s Law, we have developed a new retrieval method for estimating thermodynamic sea ice thickness growth from space: Stefan’s Law Integrated Conducted Energy (SLICE). The advantages of the SLICE retrieval method include 5 daily basin-wide coverage and a potential for use beginning in 1987. The method requires an initial condition at the beginning of the sea ice growth season in order to produce absolute sea ice thickness and cannot as yet capture dynamic sea ice thickness changes. Validation of the method against ten ice mass balance buoys using the ice mass balance buoy thickness as the initial condition show a mean correlation of 0.991 and a mean bias of 0.008 m over the course of an entire sea ice growth season. Estimated Arctic basin-wide sea ice thickness from SLICE for the sea ice growth seasons beginning between 2012 through 1

temperatures yields the snow-ice interface temperature. We have replicated the procedure from Lee and Sohn (2015) for use in the retrieval method described here.
Assuming the absorption by snow and the atmosphere is negligible, the snow-ice interface temperature can be related to satellite observed brightness temperature from a channel with a weighting function peak at the snow ice interface through (1) 70 where T H (ν) is satellite observed horizontally polarized spectral brightness temperature, ϵ H (ν) is local snow-ice interface spectral emissivity for horizontal polarized emission and T si is snow-ice interface temperature. This relationship also holds for vertically polarized satellite observed spectral brightness temperature and spectral emissivity T V (ν) and ϵ V (ν). As such, the following relationship also holds: 75 where r H (ν) and r V (ν) are horizontal and vertical spectral reflectance, respectively. A combined Fresnel relationship closes Equation 2 and allows solving for one of the emissivities (Sohn and Lee, 2013): where θ is satellite viewing angle. The resultant emissivity can be inserted into Equation 1 to solve for T si . Additional detail can be found in Lee and Sohn (2015).

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The AMSR-E and AMSR2 6.9 GHz channels were used to calculate snow-ice interface temperature here as in Lee and Sohn (2015). The resultant snow-ice interface temperatures were found to require a bias correction of 5 K in order to match buoy snow-ice interface temperatures and in order to produce the best sea ice thickness retrieval method results. This bias correction may address atmospheric absorption and snow absorption to the extent that they cannot be assumed negligible. Figure 1 shows snow-ice interface temperatures on 1 January 2013 calculated from AMSR2 radiances.

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The AMSR-E and AMSR2 brightness temperatures available from the National Snow and Ice Data Center (NSIDC) were used in this study (https://nsidc.org/data/AE_SI25/versions/3; https://nsidc.org/data/AU_SI25/versions/1; Cavalieri et al., 2014;Markus et al., 2018). The AMSR-E data is available for June 2002 through October 2011 and the AMSR2 data is available for July 2012 to the present. The AMSR2 data has been intercalibrated with the AMSR-E data and the brightness temperatures between these two instruments are treated here as a continuous dataset (Markus et al., 2018). The data is provided on a 25 km 90 polar stereographic grid but when needed on a basin-wide scale for use with the sea ice thickness retrieval method described here, the data were linearly interpolated to a 25 km Equal-Area Scalable Earth (EASE) 2.0 grid. In Lee et al. (2018), the method is adapted for use with the SSM/I 19.35 GHz channel to allow for retrieval of snow-ice interface temperature beginning in 1987.
Liquid water at the emitting layer in the form of open ocean or melt ponds interferes with the snow-ice interface temperature algorithm (Lee and Sohn, 2015). As such and in line with Lee and Sohn (2015), the snow-ice interface is only calculated here 95 in grid cells with greater than 95% sea ice concentration. A method for calculating snow-ice interface temperature for grid cells with under 95% sea ice concentration is described in the appendix of Lee and Sohn (2015) but is not implemented here pending further investigation. The snow-ice interface temperature retrieval is also subject to the polar data gap associated with AMSR-E/2 data. For basin-wide analysis, the polar data gap is filled using two-dimensional linear interpolation.

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In order to statistically characterize the sea ice thickness retrieval method described herein, ice mass balance buoy data served as the reference. The ice mass balance buoys were deployed and maintained by the United States Army Corps of Engineers Cold Regions Research and Engineering Laboratory (CRREL) (Perovich et al., 2021). Undeformed ice floes are chosen for buoy sites to ensure the buoy is representative of the surrounding ice (Polashenski et al., 2011). travels with the ice pack rather than remaining geospatially stationary. The retrieval method calculates ice thickness change and requires Lagrangian tracking of ice thickness making buoy data a good match for validation.
Data fields used from the buoys were sea ice thickness and geolocation in latitude and longitude. Ice thickness is observed using two acoustic rangefinder sounders, one positioned above and one positioned below the ice. Efforts to compare satellite based records of sea ice thickness with ground truth are hampered by the scale of the question.
Ground truth measurements of sea ice are necessarily taken from a single point while satellites observe sea ice thickness on the scale of kilometers. The variability of sea ice across those kilometers leads to uncertainty in the comparison. It has been shown, however, that while variability in absolute ice thickness may be significant on the scale of a satellite observation, sea ice growth 120 and melt is relatively uniform on the satellite length scale (Polashenski et al., 2011). Therefore, while absolute comparisons of sea ice thickness between a ground truth and satellite observation may be tenuous, comparisons of growth over a winter season between single point ground truth and satellite based observations are more robust.

AWI CS2SMOS
CryoSat-2 is a currently operational radar altimeter (Wingham et al., 2006;Laxon et al., 2013) launched by the European Space 125 Agency (ESA) in 2010. Similar to other satellite altimeters, ice thickness is determined from CryoSat-2 data by first calculating the thickness of the sea ice above sea level-known as the freeboard-and then assuming a snow loading and hydrostatic balance to determine sea ice mass which in turn is converted to thickness using an assumed density (Laxon et al., 2013). Gridded ice thickness products derived from ESA CryoSat-2 Level 1b data are provided by the ESA Centre for Polar Observation and Modelling (CPOM) (Tilling et al., 2018), the National Aeronautics and Space Agency (NASA) Goddard Space Flight Center 130 (GSFC) (Kurtz et al., 2014), the Alfred Wegener Institute (Ricker et al., 2014;Hendricks and Ricker, 2020;Ricker et al., 2017a), the NASA Jet Propulsion Laboratory (Kwok and Cunningham, 2015), the ESA Climate Change Initiative (Hendricks et al., 2018) and the Laboratoire d'Études en Géophysique et Océanographie Spatiales Center for Topographic studies of the Ocean and Hydrosphere (Guerreiro et al., 2017). The primary differences between these datasets relate to averaging period, grid sizing and radar response waveform retracking.

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The ESA Soil Moisture and Ocean Salinity (SMOS) satellite carries the Microwave Imaging Radiometer using Aperture Synthesis (MIRAS) instrument which measures 1.4 GHz passive microwave brightness temperatures at 35 to 50+ km resolution (Mecklenburg et al., 2012). While originally intended for measuring soil moisture and ocean salinity, the high penetration depth of the 1.4 GHz channel into sea ice allows for retrieval of an ice temperature that when incorporated into a radiative transfer model yields a sea ice thickness estimate (Tian-Kunze et al., 2014). This approach has associated uncertainties in sea ice below 140 0.5 m thick that are lower than those of satellite altimeters.
Sea ice thickness observations from SMOS and CryoSat-2 have complimenting uncertainties. SMOS has high uncertainties when measuring thick ice and CryoSat-2 has high uncertainties when measuring thin ice (Ricker et al., 2017b). This creates an opportunity for synergy between the instruments. The AWI CS2SMOS dataset takes advantage of this synergy. By combining the datasets through a weighted averaging scheme, root mean squared errors are reduced from 76 cm with CryoSat-2 alone to 145 66 cm and the squared correlation coefficient is increased from 0.47 with CryoSat-2 to 0.61 when compared against NASA Operation Ice Bridge data (Ricker et al., 2017b). The AWI CS2SMOS dataset is available at a weekly time resolution and on a 25 km EASE-Grid 2.0 and was used with the method demonstrated here due to the high spatial coverage.

PIOMAS
The Pan-Arctic Ice-Ocean Modeling and Assimilation System (PIOMAS) is a numerical model reanalysis product that cou-150 ples the Parallel Ocean Program (POP) model developed at Los Alamos National Laboratory with a thickness and enthalpy distribution (TED) model (Zhang and Rothrock, 2003). The TED model includes a viscous-plastic sea ice rheology (Hibler, 1979) and a sea ice thickness distribution scheme that accounts for redistribution due to ridging (Thorndike et al., 1975).

AMSR SIC
The NASA Team 2 algorithm is a passive microwave brightness temperature based sea ice concentration algorithm (Markus and Cavalieri, 2000). It as an enhancement to the original NASA Team algorithm (Cavalieri et al., 1984;Gloersen and Cavalieri, 1986) in that it adds 85 GHz frequency brightness temperatures to the original algorithm, which used only 19 GHz and 37 160 GHz data, in order to better account for interference from surface effects. The algorithm utilizes open ocean and 100% ice concentration tie points in polarization ratio and spectral gradient ratios to determine sea ice concentration. While originally developed for use with SSM/I data (Markus and Cavalieri, 2000), the algorithm was planned to be and is now in use with AMSR-E and AMSR2 data. Here we use this AMSR-E and AMSR2 sea ice concentration data which is available from the NSIDC as a part of the same dataset that contains the brightness temperatures used to calculate snow-ice interface temperature 165 (https://nsidc.org/data/AE_SI25/versions/3; https://nsidc.org/data/AU_SI25/versions/1; Cavalieri et al., 2014;Markus et al., 2018).

Methodology
Sea ice grows thicker through two primary physical mechanisms: thermodynamic phase change and dynamic changes due to the relative motion of the ice pack. The governing equation for sea ice thickness can be written as where H is plane slab sea ice thickness, t is time, f is a function of time, thickness and position vector x describing thermodynamic sea ice thickness increase and u is the ice motion vector. This equation is analogous to Equation 3 in (Thorndike et al., 1975), but does not include the redistribution term in that equation because here we use a plane slab thickness H rather than a thickness distribution. The second term on the right hand side of Equation 4 captures dynamic thickness changes. The focus in 175 the remainder of this section will be on the first term on the right hand side of Equation 4.
By coupling the conductive heat equation to a latent heat of freezing term, Stefan's Law relates the rate of thermodynamic sea ice thickness increase to the temperature difference between the snow-ice interface and bottom of the ice layer, the later of which is at or very near to the freezing temperature of sea ice (Stefan, 1891;Lepparanta, 1993). The physical explanation for this relationship is that the latent heat of freezing at the bottom of the ice is conducted up to and through the snow-ice interface.

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When the snow-ice interface temperature drops below the temperature at the bottom of the ice, heat provided by the latent heat of freezing is pulled to the snow-ice interface. In the method described here, a new satellite observation of snow-ice interface temperature (Lee and Sohn, 2015) drives the analytical solution to the Stefan's Law relationship in order to determine sea ice thickness growth.
Just as fluid flows across a pressure difference and electricity flows across a voltage difference, all heat transfer occurs across 185 a temperature difference. Conduction is the transfer of heat across a solid medium and is always accompanied by a temperature difference across that medium. The equation governing one dimensional, steady state conduction iṡ whereq is heat per unit area or heat flux, κ is the thermal conductivity of the medium, T 1 and T 2 are the boundary temperatures and D is the distance between the boundaries.

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A change in the phase of a material must either release or accept energy as the molecular bonds and motion within the material change. In the case of a phase change from liquid to solid, energy is released as the molecular motion is reduced with the introduction of molecular bonds. The equation describing the one dimensional, latent heat release in this scenario iṡ whereq is heat per unit area or heat flux, ρ s is the density of the solid phase of the material, L is the latent heat of fusion and dD dt is the one dimensional change in solid material size per unit time. In Stefan's Law, Equations 5 and 6 are combined via the common heat flux term,q to form where ρ i is the density of sea ice, L is the latent heat of fusion of sea ice, ∂H ∂t is the change in sea ice thickness per unit time, κ i is the thermal conductivity of sea ice, T f is the freezing point of sea water, T si is the snow-ice interface temperature and H is 200 sea ice thickness (Lepparanta, 1993). There are a number of assumptions inherent to this relationship (Lepparanta, 1993). First, heat conduction in the horizontal direction is assumed to be negligible. Second, it is assumed that there is no thermal inertia present in the ice. This means that the local derivative of temperature with respect to sea ice depth is constant throughout the sea ice layer and the system is in equilibrium. The spatial derivative of temperature found in a typical heat equation reduces to the temperature difference between the snow-ice interface temperature and the freezing point of water due to these first two 205 assumptions. Next, it is assumed that there is no internal heat source, such as the absorption of short wave radiation. This is valid during polar winter and times of the year when solar incidence angles are very shallow. Last, heat flux from the sea water to the sea ice is assumed negligible. A more detailed mathematical development of Stefan's Law than the following can be found in Lepparanta (1993).
Equation 7 defines the thermodynamic growth function, f , found in Equation 4 and is equivalent to Equation 4 when dynamic 210 growth is neglected. Equation 7 is a differential equation with the following analytical solution (Lepparanta, 1993) where a is defined as H 0 is the initial sea ice thickness and S is the sum of negative degree-days and is defined as The time interval t chosen for the results shown herein is one day based on the daily availability of snow-ice interface temperature. The value for a is taken to be 3.3 cm ( • C −1 d −1 ) 1/2 (Lepparanta, 1993). This equates to a density of 900 kg m −2 , a latent heat of fusion of 3.35 x 10 5 J kg −1 and a thermal conductivity of 1.9 W m −1 K −1 . The freezing point of sea water is taken to be -2 • C.

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At each time step, the sea ice thickness after thermodynamic growth is determined by solving Equation (4) for H given an H 0 using the snow-ice interface temperature calculated at the nearest AMSR-E or AMSR2 grid cell. Because both H and H 0 are squared in Equation (4) while the other terms are not, the change in sea ice thickness at each time step is dependent on initial sea ice thickness. This necessitates this retrieval method be applied in a Lagrangian sense as the sea ice thickness must be tracked and stored in order to accurately calculate the change at the next time step. Fortunately, this mathematical 225 characteristic also means this method is self correcting. In equation (4), thicker sea ice grows slower than thinner sea ice and thinner sea ice grows faster than thicker ice with a given snow-ice interface temperature. This means sea ice that is too thick or too thin will correct towards the true thickness. This relationship replicates the phenomenon described in Bitz and Roe (2004), whereby thick ice grows slower than thin ice and vice versa.

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The SLICE sea ice thickness retrieval methodology can be applied on a single one-dimensional profile basis or across a large area. Here we present results comparing one-dimensional profiles to ice mass balance buoy thicknesses and Arctic basin-wide results compared to AWI CS2SMOS and PIOMAS data.

One-dimensional Profiles
The SLICE retrieval method results were compared to sea ice thickness from ice mass balance buoys. The retrieval method 235 was initialized with the buoy observed sea ice thickness on the day when the 14 d rolling average sea ice growth exceeded 1 mm d −1 . From this time step forward, the retrieval method is dependent only on the satellite based snow-ice interface temperature. The snow-ice interface temperature used on a given day is taken from the nearest AMSR-E or AMSR2 grid cell to the buoy location. The resultant sea ice thickness profiles and buoy profiles are plotted in Figure 2. It is clear from Figure 2 that the SLICE profiles agree well with the buoy sea ice thickness when initialized with an accurate initial ice thickness. The The initial condition is very important for the accuracy of sea ice thickness SLICE retrieval method. At the same time, due 245 to the dependency of sea ice growth on initial thickness shown in Equation 7, an initial condition that is biased high will lead to a lower growth rate and an initial thickness that is biased low will lead to a higher growth rate. In this way, SLICE is self correcting. In Figure 3, the retrieval method is initialized with sea ice thickness that is 0.25 m both higher and lower than the buoy thickness. The profiles follow the same smooth thermodynamic growth exhibited in Figure 2 and both approach the buoy sea ice thickness over time.

Arctic Basin-wide Comparisons
Next, the SLICE retrieval method was applied on a Arctic basin-wide scale. Using the AWI CS2SMOS data for the first week of November as the initial state for one set of integration and the PIOMAS data from 1 November as the initial state for another  Monthly basin-wide sea ice thickness plots for the sea ice growth season beginning in fall 2012 using AWI CS2SMOS as the initial state are shown in Figure 4. The sea ice thickness data from SLICE is available daily. The data from the first of every month is plotted. The sea ice thickness on 30 April 2013 is higher but shows similar spatial distribution to that on 2 November 265 2012. The sea ice is growing thermodynamically but there is no dynamics to rearrange the thickness distribution.
The cumulative effects of this lack of dynamics are depicted in Figures    April. Their differences represent dynamic changes and are in areas expected by climatology.

Discussion
The SLICE retrieval method captures thermodynamic sea ice thickness accretion very well. Figure 2 shows a comparison between ice mass balance buoy sea ice thickness measurements and the retrieval method initialized with the buoy data for 10 buoys within the years 2003-2016. The mean correlation coefficient of 0.991 between the buoy measurements and the method 295 is high. The bias values are also very encouraging with a mean of 0.008 m. Additionally, SLICE has a self-correcting quality by nature of Equation 7 whereby sea ice thicknesses that are biased in either direction approach the correct sea ice thickness over time as shown in Figure 3. These points suggest the retrieval method is viable as a basis for estimating sea ice thickness but is highly dependent on an initial condition, as it calculates thermodynamic sea ice thickness increase rather than absolute thickness.

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While SLICE is capable of retrieving thermodynamic sea ice growth, it is unable to detect dynamic effects-i.e., thickness changes due to ice motion. Figure 4 shows monthly basin-wide plots of sea ice thickness for the sea ice growth season beginning on 1 November 2012 created using the retrieval method with an initial condition provided by the AWI CS2SMOS dataset. The sea ice thickness values are greater but the spatial distribution is similar from month to month as parcels are not moving, rather only growing thermodynamically. The consequences of this lack of dynamic sea ice thickness change are explored in 305 Figures 5 and 6 showing basin-wide comparisons of sea ice thickness from SLICE to that from AWI CS2SMOS and PIOMAS, respectively. The AWI CS2SMOS and PIOMAS products both have thicker ice in regions where dynamic sea ice effects are expected to increase ice thickness, notably north of the Canadian Archipelago and east of Greenland, and thinner ice in the marginal seas from where ice is exported. The difference plots between SLICE and these reference datasets look similar in each year. These plots are integrated to a volume perspective in Tables 2 and 3. In all cases, SLICE is within 20% volumetric growth 310 of the reference dataset. Interestingly, the retrieval method shows greater volumetric growth than CS2SMOS in all years and less volumetric growth than PIOMAS in all years.
These results are encouraging for the capability of SLICE to capture volumetric sea ice changes changes on a basin-wide scale. Per the model described by Equation 4, sea ice volume is only added through thermodynamic processes-dynamic processes only serve to rearrange the volume already present. Though this statement does invoke the false assumption that 315 dynamic processes do not change the density of the ice, it seems to be a factor in explaining the volumetric results described in Tables 2 and 3 indeed shows that H impacts ∂H ∂t . In regions where dynamic processes increase sea ice thickness, SLICE will overestimate sea ice thickness increase and in regions where dynamics decrease sea ice thickness, it will underestimate sea ice 320 thickness increase. These phenomena, along with any phenomena inherent to either reference dataset, may explain volumetric differences between SLICE and the reference datasets.
Another potential factor explaining differences in volumetric growth of SLICE versus the reference datasets is the choice of sea ice growth start and end dates. Figure 2 shows that most buoys experience sea ice thickness growth beginning around 1 November. November first is also the start date for the basin-wide growth examples shown in Figures 4, 5 and 6 but this is 325 undoubtedly inaccurate for some of the Arctic basin, regions of which begin ice accretion at varying start dates based on local conditions. Additionally, SLICE is incapable of capturing ice melt. If at any time during the growth season a region were to experience melting, the associated ice thickness decrease would not be captured. SLICE results are dependent on the values provided for the freezing point of sea water, thermal conductivity, density and latent heat, all of which are not constant values across the Arctic as we have treated them here. An additional value that is influential for the retrieval method is the initial 0.05 330 m ice given to grid cells where the SIC dataset shows new ice. A more rigorous treatment of these constants and their variation across the basin may improve the results.
There are a number of assumptions inherent to Stefan's Law (Lepparanta, 1993) that must be considered in relation to SLICE. In order to characterize conduction through the ice layer with only the snow-ice interface temperature and an assumed freezing point temperature at the bottom of the ice layer, it must be assumed that heat conduction in the horizontal is negligible 335 and that the local vertical derivative of temperature throughout the ice layer is constant. These assumptions are reasonable.
The remaining two assumptions are more salient. The first is that there is no internal heat source. This is untrue when there is significant short wave radiation absorbed within the sea ice. The final assumption is that there is no heat exchange between the sea ice and the ocean, which is likely to be invalid in some regions. Another source of uncertainty in SLICE ice thickness is the constraint that it is limited to areas with sea ice concentration greater than 95%. There is significant growth in areas 340 where the sea ice concentration is low, such as the marginal ice zone (MIZ). This constraint would likely cause underestimated sea ice growth over those areas. In a supplement to the body of the paper, Lee and Sohn (2015) suggest a procedure for calculating snow-ice interface temperature in areas with less than 95% but that has not been implemented here, pending further investigation. Further validation of SLICE, particularly in regions other than the Beaufort Sea and Central Arctic, where all ten buoys used here were located, as well as investigation of the impacts of these assumptions and full characterization of 345 uncertainties is warranted.
The SLICE retrieval method uses passive microwave brightness temperatures from the AMSR-E and AMSR2 instruments and a snow-ice interface temperature retrieval algorithm (Lee and Sohn, 2015) to drive a sea ice thickness growth equation.
Gridded brightness temperature data from these instruments are available at daily temporal resolution in the polar regions (Cavalieri et al., 2014;Markus et al., 2018), meaning daily sea ice thickness growth is available basin-wide. Lee et al. (2018) 350 provides a method for retrieving snow-ice interface temperatures using passive microwave brightness temperatures from the SSM/I and SSMIS instruments, allowing for the application of SLICE to sea ice growth seasons beginning in 1987. Current state of the art sea ice thickness observations from space, though capable of observing sea ice growth whether from thermodynamic or dynamic effects, are not capable of this spatial and temporal coverage. They also do not discriminate between dynamic and thermodynamic effects. For these reasons, a sea ice thickness dataset based on SLICE will be especially qualified 355 for investigating thermodynamic and dynamic sea ice phenomena that are small scale in space and time. SLICE need not be initialized the beginning of the growth season and applied for an entire growth season but can be initialized at any time during the growth season and applied to any interval of time, allowing for use with case studies or other small time and space scale events. Additionally, the high temporal resolution retrieval of thermodynamic effects will allow for creation of useful datasets sea ice or freshwater bodies.
With the availability of sea ice motion observation datasets from NSIDC  and the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) Ocean and Sea Ice Satellite Application Facility (OSISAF) (Lavergne et al., 2010), there is potential to add a dynamic component to SLICE by solving the second term of Equation 4.
Much effort has gone into discretizing this term for use with numerical techniques. A discussion of solution schemes for this 365 type of equation as it relates to sea ice transport is found in Lipscomb and Hunke (2004). An ideal scheme must conserve volume, must be stable, must be second-order accurate in space in order to avoid excessive diffusion, preserve monotonicity and be efficient. Early climate models utilized the multidimensional positive-definite advection transport algorithm (MPDATA) introduced in Smolarkiewicz (1984). The current iteration of the Los Alamos sea ice model (CICE) solves these types of transport equations using an incremental remapping scheme (Hunke and Lipscomb, 2010;Lipscomb and Hunke, 2004). Numerical 370 solution schemes such as these for solving the second term in Equation 4 are under consideration for use with this retrieval method but are beyond the scope of this present work. If a suitable dynamic component can be developed, a climatology of both thermodynamic and dynamic sea ice thickness growth will be created.

Conclusions
New methods for observing snow-ice interface temperature (Lee and Sohn, 2015) have made possible a new strategy for 375 observing sea ice thickness from space during the winter growth season: Stefan's Law Integrated Conducted Energy (SLICE).
The new strategy involves coupling observed satellite retrieved snow-ice interface temperature with Stefan's Law (Stefan, 1891;Lepparanta, 1993). In the Stefan's Law relationship, latent heat of fusion is conducted from the bottom of the ice layer where new ice forms to the snow-ice interface and this rate of conduction and accretion is calculated using the snow-ice interface temperature and an assumed freezing point temperature at the bottom of the ice layer. An initial value is required as 380 SLICE calculates sea ice thickness growth rather than absolute thickness and does not capture melting. Four assumptions make this relationship possible, including (1) negligible horizontal conduction, (2) no thermal inertia in the ice, (3) no internal heat sources and (4) no heat flux from the sea water.
When SLICE is initialized with an ice mass balance buoy thickness and compared against that buoy's ice thickness profiles during the ice growth season, the retrieval method compares extremely well with the buoy observed sea ice thickness growth.

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Using ten buoys from 2003 to 2016, the mean linear correlation value is 0.991 and the mean bias is 0.008 m. Two sets of basin-wide integrations were also performed for the winter growth seasons beginning in the years 2012-2020 using an initial state from the AWI CS2SMOS and PIOMAS datasets. SLICE underestimated volumetric growth in all years when compared to PIOMAS with a mean of 8.1% in relative difference and overestimated volumetric growth in all years when compared to AWI CS2SMOS with a mean of 11.9% in relative difference. The differences between ice thickness estimated with SLICE, a 390 thermodynamic method, and the reference data follow a pattern expected from the dynamic motion of the ice pack.