Linking sea ice deformation to ice thickness redistribution using high-resolution satellite and airborne observations

An unusual, large, ::::::::: latent-heat polynya opened and then closed by freezing and convergence north of the coast of Greenland :::::::::: Greenland’s :::: coast : in late winter 2018. The closing corresponded to a natural , but well-constrained, full-scale ice deformation experiment. We have observed the closing of and deformation within the polynya with satellite synthetic-aperture radar (SAR) imagery , and measured the accumulated effects of dynamic and thermodynamic ice growth with an airborne electromagnetic (AEM) ice 5 thickness survey one month after the closing began. During that time : , strong ice convergence decreased the area of the former ::::::: refrozen polynya by a factor of 2.5. The AEM survey showed mean and modal thicknesses of the one-month old :::::::::::: one-month-old ice of 1.96 ±1.5mand 0.95, ::: and ::: 1.1m, respectively. We show that this is in close agreement with the modeled thermodynamic growth and with the dynamic thickening expected from the polynya area decrease during that time. In addition, we found characteristic ::: We ::::: found ::::::::: significant : differences in the shapes of ice thickness distributions ::::: (ITDs) : in different regions of the 10 closing ::::::: refrozen : polynya. These closely corresponded to different deformation histories of the surveyed ice that were derived from the :: we ::::::: derived :::: from :::::::::: Lagrangian ::: ice :::: drift :::::::::: trajectories :::::::: backward :: in ::::: time. ::: We :::::::::: constructed ::: the ::: ice ::::: drift ::::::::: trajectories ::::: from ::::::: regularly ::::::: gridded, : high-resolution SAR imagery by drift tracking along Lagrangian backward :::: drift :::: fields ::::::::: calculated :::: from ::::: SAR ::::::: imagery ::: and :::::::: extracted :::::::::: deformation ::::::: derived ::::: from ::: the ::::::::: drift-fields ::::: along ::: the : trajectories. Results show a linear proportionality between convergence and thickness change that agrees well with ::: the ice thickness redistribution theory. In addition, ::: We ::::: found 15 : a :::::::::::: proportionality :::::::: between the e-folding of the tails of the different ice thickness distributions is proportional to the magnitude of the ::::: ITDs’ :::: tails ::: and ::: the : total deformation experienced by the ice. Lastly, we developed a simple, : volume-conserving model to derive dynamic ice thickness change from :: the ::::::::::: combination :: of :::::::::: Lagrangian ::::::::: trajectories ::: and : high-resolution SAR deformation tracking ::: drift :::: and :::::::::: deformation ::::: fields. The model has a spatial resolution of 1.4 km and reconstructs thickness profiles in reasonable agreement with the AEM observations. The computed ice thickness distribution resembles main characteristics like 20 ::::::: modeled :::: ITD :::::::: resembles :::: the :::: main :::::::::::: characteristics :: of :::: the ::::::: observed ::::: ITD, :::::::: including : mode, e-folding, and width of the observed distribution. This demonstrates ::: full ::::: width :: at ::: half ::::::::: maximum. ::::: Thus, ::: we :::::::::: demonstrate that high-resolution SAR deformation observations are capable of producing realistic ice thickness distributions. The MYI surrounding the polynya had a mean and modal total thickness (snow + ice) of 2.1 ±1.4m and 2.0m, respectively. The similar firstand multi-year ice mean thicknesses elude to the large amount of deformation experienced by the closing polynya. 25


Thermodynamic ice thickness growth
To separate the dynamic and thermodynamic contributions to the observed and computed ITDs we need a reliable estimate of the thermodynamic growth. Here we estimated accumulated thermodynamic growth from the observed modal thickness and the thickness of levelice, and the temporal evolution of thermodynamic growth from a thermodynamic model run.
(4) We performed the backward Lagrangian deformation analysis ::::::: tracking from March 30/31 until March 1. We have chosen :: 1, :::: 2018. ::: We ::::: chose : March 1as , ::::: 2018, :: as ::: the last day of the backtracking because, : before this date, : the new ice in the polynya was not consolidated enough to :: and :::: did ::: not reveal recognizable backscatter patterns on two consecutive days. Thus, the tracking In short, we reconstructed for each of the 715 derived trajectories a time series of the deformation events that the surveyed patches of ice had experienced during March 2018.

Uncertainty of deformation estimates along the ice drift trajectories
Uncertainties of the drift fields arise from a lack of recognizable radar signature variations that may be due to local ice and 280 weather conditions, sensor parameters, and strong changes of the signatures due to deformation. The error in the initial ice velocity fields propagates :::::::: propagate into the deformation estimates along the trajectories in three different ways.

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Applying this procedure to every time step of the ice drift trajectories starting at the consolidation of the ice, we thus obtained a Lagrangian time series of thermodynamic and dynamic thickness change from the deformation grid cells located along each trajectory from March 1 to March 31 by calculating the ::::: Based ::: on ::::::: equation ::: (4) ::: we ::::: obtain ::: the : mean thickness at time step + Δ :::: each :::: time by:

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::::: where : :::: runs :::: from :::::: March :: 1 :: to ::::: March ::: 31, ::::: 2018. : To account for the tracking uncertainty, we created for each trajectory random combinations of the potentially experienced divergence that were given by the tracking and statistical uncertainty. For each time step, we randomly choose one of the observed divergence states that were found in the uncertainty circles described in Sect. 2.5.1. We calculated thickness change along each trajectory with 10.000 combinations for the 30 time steps. Mean thickness converged to the first decimal after approximately 380 1000 iterations.
For completeness, here we also summarize the thickness observations of the MYI that gave way for and then surrounded the polynya ( Fig. 3b; see flight tracks in Fig. 1) Fig. 4 and in the ITD of the closing polynya (Fig. 1d, 2a), respectively. Interestingly, the modal thickness of the MYI was 2.0 m, and therefore quite similar to the mean (Fig. 3 b). This is due to the presence of larger fractions of ice thinner than 2 m, but also due to a less pronounced tail of deformed ice. We 445 speculate that this could show that large ridges have been smoothed by the previous summer's melt. We note that the mean thickness of the FYI in the closing polynya is almost as large as the one of the surrounding MYI, but that they differ strongly in their modal thicknesses.

Trajectories
The previous section was concerned with the average, large-scale, ::::: mean : dynamic thickness change in the closing polynya.
In short, we were able to identify four zones across the closing polynya with :::: FYI :::: with :::::: clearly differently shaped ITDs and 555 clearly different deformation histories. In contrast, modal thicknesses were similar in all zones and in agreement with the result of a thermodynamic model, indicating that thermodynamic ice growth was uniform throughout the polynya. Therefore ::::: Since ::::::::::::: thermodynamic :::::: growth :::: was ::::: rather ::::::: uniform, we conclude that the observed spatial thickness variability is fully linked to the deformation history of the ice. In the following section, : we will further explore this link on a more quantitative base :::: basis.

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ITDs of the four FYI zones on March 30/31. The ITDs differ in a. FWHM that characterizes the dominance of the mode, b.
mean and -folding of the exponential tail. The ITD of the complete measurements (all FYI) is displayed in gray.

Relationship between mean deformation and ITD key parameters in the four polynya zones. The standard deviations
of means and deformation are displayed as error bars. Thickness change and mean deformation is given for March 1-31. Note, convergence is negative divergence.

(3) Spatial agreement between modeled and observed thickness profiles
Lastly, we compared the modeled and observed thicknesses along the three AEM profiles (Fig. 10). The modeled thickness profiles resulted from the model grid cells of each trajectory that were all properly placed along the profiles at the end :::::::: represent :: the ::::::::: thickness :: at ::: the ::: last :::: time :::: step : of each trajectory's drift track, corresponding to their position at the first instance of the backward tracking. : , :: on :::::: March ::::: 30/31. : For the results shown in Fig. 10 : , the observed and modeled thicknesses were averaged with 625 a running mean to a common resolution of 2.5 km along the profiles. The figure shows that the modeled thicknesses generally reproduce the characteristic variability of the four zones (Table 1). However, they underestimate the observed thickness at most points of the profiles. The mean modeled ice thickness in the Fast Ice zone is steadily increasing away from the coast as observed.
Based on the good linear fit (Fig. 8c), we attribute the large range in the -folding to the magnitude of the deformation rate in agreement with Rabenstein et al. (2010) who related differences ::: the ::::::::: differences :: in :::: ITD ::::: shape in ITDs in the Arctic Trans Polar Drift to varying amount of convergence. Hence, we suggest to chose ::::::: choosing the parameter as a function of the deformation 705 rate. Since Ungermann and Losch (2018) showed in a sensitivity study with the MITgcm that is an important parameter in shaping the modeled ITD, we expect this to improve the fit between modeled and observed ITDs.
We identified two processes that change the -folding and potentially link it to the deformation rate.
(1) Ridge formation models from Hopkins (1998) and Hopkins et al. (1991Hopkins et al. ( , 1999 showed that ridges first reach a maximum ::::::: dynamic thickness and then continue to grow laterally. This lateral growth widens the ridge and therefore increases the relative 710 occurrence of deformed ice with the maximum thickness, and thereby reduces ::::::: dynamic :::::::: thickness, :::::::: reducing the -folding. When a ridge begins to form, the balance of the force needed to push ice farther up or down and the force needed to fracture the ice is decisive for redistributing the ice. In this process, ice thickness and friction play major roles. When the maximum ::::::: dynamic thickness is reached, the ridge grows laterally in proportion to the ongoing deformation. In this stage, larger deformation rates result in wider ridges with the maximum thickness and hence with smaller -folding. Applying the maximum keel draft criterion 715 of Amundrud et al. (2004), we identified several ridges in the measured thickness profiles in the Shear Zone that had reached the maximum ice thickness. However, the relationship between -folding and deformation rate might only be applicable in regions that experience strong deformation, e.g., : coastal regions, because Hopkins (1998) and Amundrud et al. (2004) pointed out that ridges in the central Arctic rarely reach the maximum thickness as the critical stresses do often not last long enough to complete the ridge building process.

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(2) Rafting leads to a different -folding than ridging. Riding distributes more ice into a few thicker ice thickness categories, while rafting leads to deformed ice with a rather ::::::: relatively : uniform thickness of only double the original one. If the occurrence of rafting and ridging depends on the magnitude of deformation, this could establish a link between -folding and deformation rate. Hopkins et al. (1999) identified that the relative likelihood of rafting increases with increasing homogeneity of the ice floes. thickness might have a higher portion of rafted ice, and thus a different -folding than regions that experienced more ridging.
Consequently, the -folding could also depend on the initial composition of thin and thick ice and on the deformation history.
Lastly, we acknowledge other aspects, for example the : : :::: The creation of rubble fields, hammocks :::::::: hummocks, or the ratio of shear and convergence, could influence the -folding. The shear to convergence ratio varied among the four zones in the polynya, but we were not able to ::::: could ::: not draw any conclusion due to too few data points. Since we do not have more frequent 730 thickness observations during the polynya closing period :::::: closing :: of ::: the ::::::: polynya, : we can only evaluate the impact of deformation integrated over 30 days. Therefore, we also miss information about potentially contrasting effects like, e.g., ridge consolidation and collapse.

Modeled vs observed thickness: Limitations of the model
Based on a simple volume-conserving model, we derived thickness change along ice drift trajectories and calculated ITDs from 735 the final thickness at the end of each trajectory.
Second, in the simplemodel , :::::::::::::::: volume-conserving :::::: model, the thermodynamic growth was modeled based on the growth of an undeformed layer of ice, regardless of the actual mean thickness of each grid cell. Hence, the model overestimates thermodynamic growth in all cells that experienced strong convergence and weretherefore , :::::::: therefore, : thicker than the thermodynamic thickness. At the same time, our approach underestimates ice growth in all cells that experienced divergence , because thermo-775 dynamic growth is stronger in leads than in adjacent consolidated ice. We carried out a sensitivity study to estimate the impact of unaccounted new ice formation in leads. If there was divergence, we replaced the ice leaving the grid cell with new ice of the thickness that could form within one day. Integrated over 30 days and all profiles, this resulted in an additional 0.3 m of ice, i.e., : a mean thickness of 2 m. Since the dominating deformation type in our :: this : study was convergence and shear, this effect is less important than it might be in a different deformation regime. For future work, we suggest to couple the SAR deformation retrievals 780 ::: We :::::: suggest :::::::: coupling ::: the :::::::::: deformation :::::: history :::::::: retrieved :::: from :::: SAR ::::::: analysis : with a fully developed sea ice model that considers those interdependencies :: for :::::: future :::: work. For example, the single-column model ICEPACKincludes :::::::: ICEPACK ::::::: includes : full solutions for thermodynamic growth and melting and mechanical redistribution due to ridging (see CICE Consortium Icepack, 2020). SAR derived :::::::::: SAR-derived deformation rates can be used to force the mechanical redistribution of ice in the ICEPACK model.

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Both those shortcomings can explain the observed differences in the mean thicknesses. However, there are additional possible reasons for deviations of observed and modeled thickness which we shortly discuss :::::: shortly :::::::: discussed below.
(1) Due to challenging conditions for SAR tracking over very young ice we could only begin the thickness modeling on March 1 and assumed an initial, uniform thickness of 0.49 m corresponding to the thermodynamic ice growth in the first days of the closing polynya. However, early deformation before March 1 might already have created an inhomogeneous ice thickness field.

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This concern is mitigated by the fact that we observed almost no polynya area decrease between February 25 to March 1.
(2) We did not consider additional opening and closing of ice due to shear on subgrid scales that can be observed in similar situations (e.g. Stern et al. (1995) and Kwok and Cunningham (2016)). However, the effects of divergence and convergence on mean thickness compensate each other on a subgrid scale in our simple model, apart from the effect of divergence on new ice formation (see above, main sources of uncertainty).

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(3) The daily imaging of the polynya by SAR images cannot account for deformation caused by tides. Tides and inertial motion can cause recurrent opening and closing with associated sub-daily new ice formation and subsequent deformation.
These processes can contribute 10-20 ::::: 10-20 % of the Arctic wide seasonal ice growth (Kwok et al., 2003;Heil and Hibler, 2002;Hutchings and Hibler, 2008). Due to the polynya's location across the continental slope, tidal currents in this region exceed the ones in the central Arctic that are in the order of 0.5-1 :: -1 cm s −1 (Baumann et al., 2020). In the polynya region over 800 the continental slope (83.2°N 22.9°W) the Oregan :::::: Oregon : State University tide model (Egbert and Erofeeva, 2002) states tidal currents of up to 5-6 :: 5-6 cm s −1 and oceanographic measurements under the Fast Ice close to Station Nord indicated semidiurnal tidal currents in the order of 2 cm s −1 (Kirillov et al., 2017). Assuming a contribution of tides to sea ice formation of at least a similar order as in the central Arctic, tides could have contributed, : in our case, : an additional new ice growth of 0.14-0.28 :::: -0.28 m.
This study provides evidence of the high relevance of deformation dynamics in creating and maintaining a thick ice coverage.
Trajectories on :: of : deformation grid. Grid cells as sketched in a and b are defined by the deformation grid. Divergence and convergence is extracted from the grid cell in which the trajectory is located. For the uncertainty estimate divergence is extracted in all grid cells whose center points (gray dots :: b,c)are located in the uncertainty range given by the tracking uncertainty (dashed circle).
Thickness ( Note different x-axis scales based on different lengths of profiles (see Fig. 1).