*5.4. Applicability of the L-band SIT Retrieval Methodology*

Assuming that L-band technology is only sensitive to thin ice conditions, the coverage of potentially useful L-band SIT retrievals is analyzed in this section.

Figure 9a shows the sea ice extent for all sea ice cells (i.e., SIC above 15%) and for those cells with specific ice conditions (red curve) and retrievable thin ice (green curve), while Figure 9b shows the latter as percentages with respect to the total sea ice extent. Figure 9b shows that relative percentages of retrievable thickness are highest at the beginning of the freeze-up period (i.e., October–November). Furthermore, when considering the optimal retrievable thickness range (i.e., below 0.5 m), this part of the year has also the largest share of observable ice thickness. Interestingly, as the freezing period progresses, the respective shares of observable thickness drop, but between them, the optimal retrievable thickness presents a further drop below 5% of the total sea ice extent (see Figure 9b).

**Figure 8.** Comparison between the modeled CFDD SIT and the UB ice thickness. (**a**) SIC is between 70% and 90%. (**b**) SIC is between 30% and 50%. SMOS thickness uncertainty and saturation ratio are always below 1 m and 90% respectively. The mean and standard deviations are depicted with a blue and red lines respectively. (**c**) PDFs of CFDD and UB SIT for case a. (**d**) PDFs of CFDD and UB SIT for case b.

It is also relevant to stress the limited temporal coverage of the L-band based SIT products, mainly valid during the freeze-up period and in regions of high SIC values (e.g., during October–November in the Northern Hemisphere). These optimally observable regions are typically located outside the multi-year ice holding half-ringed shape (i.e., a partial ring spanning from the northern coasts of Canada and Russia); eventually, this ring-shaped structure closes when reaching the Bering Strait. These regions shrink in size as the winter progresses (see Figure 9b), thus leading to poor-quality SIT retrievals due to the relatively low spatial resolution of the SMOS satellite. Therefore, optimal retrievable values are expected to be mainly located in these temporally and spatially-varying regions.

**Figure 9.** (**a**) Sea ice extent during the freeze-up period of 2011. The blue line depicts the full sea ice extent. The red line for ice that has <90% saturation, <1 m uncertainty and >90% SIC. The green line represents the same conditions as the red line but only for SIT below 0.5 m. (**b**) Same red and green lines as in (**a**) but shown as percentage of the total (blue line).

#### **6. Conclusions**

We have characterized the brightness temperature response to SIT using the processed upward looking sonar ground truth during the freeze-up period between October and January from BGEP from WHOI. TB shows a larger dispersion for thin sea ice, increases with SIT and saturates for ice thicker than 0.6 m at approximately 240 Kelvins where the effect of SMOS radiometric uncertainty (radiometric noise) is visible. PD intersects the ordinates axis between 70 and 80 Kelvins and saturates for ice thicker than 0.6 m at approximately 30 Kelvins. The observed dispersion of the TB propagates into the ice thickness estimation with a standard deviation that increases with ice thickness. The analysis of the attenuation parameter of the empirical retrieval reveals the lack of response of the TB to SIT thicker than 0.6 m.

The year-round, cost-effective, accurate record of ULS SIT and the lack of validation data stresses the strong need of deploying and maintaining more measuring units at appropriate locations of the Arctic Ocean. This approach would probably improve the quality and usefulness of validation data with respect to current costly ship-based campaigns performed so far for gathering SIT ground truth with EM [14,22,23], that are also very limited as they can only be done during late winter–early spring months due to the need of helicopter which entails measuring a fully developed ice pack therefore skewing the reference dataset.

The detailed comparison between CFDD-model SIT and ULS ground truth evidenced their strong correlation during the freeze-up period. We have taken advantage of this correlation to use the estimated CFDD SIT as a reference dataset during the freeze-up periods. Furthermore, we saw the similarity of the scatter plots between CFDD and ULS against UH and UB SIT products revealing again the strength of the proposed homogeneity hypothesis. The extension of the ground truth with the model-based thickness allowed characterizing the L-band ice thickness products in different scenarios. The analysis showed that L-band SIT present a clear dependency on SIC while this parameter is not considered in current SIT estimations [12,13].

The comparison between the CFDD SIT and UH SIT product at 90% SIC shows that their modes are coincident during the whole freeze-up period and also partially at other periods. UH SIT slightly underestimates for thicknesses below 0.3 and overestimates for thicker ice. However, the shapes of the PDFs of CFDD SIT and UH SIT, while being similar for the whole winter, becomes notoriously different at specific months. On the other hand, as the freezing period advances UH SIT mode corresponds to the CFDD SIT mode. This change in the shape of the distribution is probably needed to accommodate thickness values outside the L-band observational range and probably relates to the lognormal distribution [12]. As SIC is gradually lowered in the comparison, there is a trend of

increasing bias and the UH distribution becomes concentrated at low thicknesses. The shape of both distributions are very similar when the SIC is between 70% and 90%, an encouraging starting point for improving the already visible bias at this concentration range.

The comparison between the CFDD SIT and UB SIT product at 90% SIC indicates that UB SIT fits the ground truth very closely for thickness below 0.4 m. For thicker ice, UB SIT has a tendency to give a saturated response. This saturation stems from the fact that many CFDD thickness values (around 50%) over half a meter are wrongly classified by UB. However, the thickness distribution for October presents a shape very close to that of CFDD distribution. The latter comes as no surprise since [13] product is trained using the CFDD SIT model as a reference. Nonetheless, as the freeze-up period continues, the CFDD SIT distribution displaces to larger thickness outside the empirical retrieval observable range. In these cases UB SIT saturation is more pronounced. As SIC is decreased in the comparison, UB SIT presents an increasing negative bias and its distribution peaks at lower thickness (following exactly the same behavior as the UH product).

The former analysis permits us to understand the current limitations of SMOS-based ice thickness products. These limitations are not only related to the retrieval methodology but also to the geographical extent where L-band based SIT is applicable. There are specific periods of the year when optimal retrieval conditions are only reached for 5% or less of the whole sea ice Arctic coverage. This scarce coverage challenges the consideration of L-band-based SIT as an Arctic wide product. Regarding the methodological limitations, we indicate a minimum of ∼90% SIC for a successful thickness retrieval during the freeze-up period when the ice pack thickness remains below half a meter.

The observed limitations of the retrieval methodologies strongly suggest future lines of improvement. Considering the daily temporal resolution of the satellites, a temporally enhanced SIT retrieval would be a step ahead. This temporal adjustment would allow to present a temporally consistent SIT product with no variations in its behavior during the winter. The second line of improvement stems from the need of considering SIC as a required variable for SIT retrieval. This would permit adjusting the thickness inversion depending on the considered SIC. If the latter is not possible, indicating at least the ice concentration for the specific retrieved values as a quality flag is an absolute must. This would give the user fundamental information about the quality of the estimated ice thickness.

**Author Contributions:** P.S.-G. processed the data, wrote the manuscript and designed the research. C.G., M.P. and A.T. design the research and provide feedback and advice on the paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** L-BAND project, funded by Spanish R+D Plan (ESP2017-89463-C3-1-R).

**Acknowledgments:** The data of SIT from ULS were collected and made available by the Beaufort Gyre Exploration Program based at the Woods Hole Oceanographic Institution (https://www.whoi.edu/beaufortgyre) in collaboration with researchers from Fisheries and Oceans Canada at the Institute of Ocean Sciences. Sea ice concentration product of the EUMETSAT Ocean and Sea Ice Satellite Application Facility (OSI SAF, www.osi-saf.org).

**Conflicts of Interest:** The authors declare no conflict of interest.
