A Weekly Arctic Sea-Ice Thickness Data Record from merged CryoSat-2 and SMOS Satellite Data

Sea-ice thickness on a global scale is derived from different satellite sensors using independent retrieval methods. Due to the sensor and orbit characteristics, such satellite retrievals differ in spatial and temporal resolution as well as in the sensitivity to certain sea-ice types and thickness ranges. Satellite altimeters, such as CryoSat-2 (CS2), sense the height of the ice surface above the sea level, which can be converted into sea-ice thickness. Relative uncertainties associated with this method are large over thin ice regimes. Another retrieval method is based on the evaluation of surface brightness temperature in L-Band 5 microwave frequencies (1.4 GHz) with a thickness-dependent emission model, as measured by the Soil Moisture and Ocean Salinity (SMOS) satellite. While the radiometer based method looses sensitivity for thick sea ice (> 1m), relative uncertainties over thin ice are significantly smaller than for the altimetry-based retrievals. In addition, the SMOS product provides global sea-ice coverage on a daily basis unlike the altimeter data. This study presents the first merged product of complementary weekly Arctic sea-ice thickness data records from the CS2 altimeter and SMOS radiometer. We use two merging approaches: 10 a weighted mean and an optimal interpolation scheme (OI). While the weighted mean leaves gaps between CS2 orbits, OI is used to produce weekly Arctic-wide sea-ice thickness fields. The benefit of the data merging is shown by a comparison with airborne electromagnetic induction sounding measurements. When compared to airborne thickness data in the Barents Sea, the merged product has a root mean square deviation of about 0.7 m less than the CS2 product and therefore demonstrates the capability to enhance the CS2 product in thin ice regimes. However, in mixed first-year/multiyear ice regimes as in the 15 Beaufort Sea, the CS2 retrieval shows the lowest bias.

* Currently the authors use statistical uncertainties only for CryoSat-2 to highlight the complementary nature of the two measurement techniques. This is not sufficient. That CryoSat-2 measurements are unreliable over thinner ice, where they are associated with larger uncertainties, forms the major justification of this work. Therefore, the authors need to consider the spatial variations in the actual measurement uncertainty (not just statistical uncertainty) and show that they are larger over thinner ice. Are such uncertainty maps available? If not, can the authors produce them?
Then Figure 1 (measurement error not statistical error) and Figure 2 could be combined, and the reader has all the justification for the work in one place.
We thank the reviewer for these thoughtful and constructive comments. We tried to improve the structure of the paper in order to meet your suggestions. We have streamlined the introduction and shifted the part about the product uncertainties and complementarity to section 2. Now, product uncertainties and complementarity are only described briefly in the introduction, and then in more detail in section 2, where we inserted a new subsection: "2.1.3 Complementarity of CryoSat-2 and SMOS Sea-Ice Thickness Products". We have chosen this way in order to avoid introducing another subsection level (2.1.1.2 and 2.1.1.1).
Regarding the comment about the statistical uncertainties: we agree that the term "statistical" is misleading here, since it might also mean an uncertainty in the sense of standard deviation of observations or similar. Therefore, we decided to use the term "observational" uncertainty instead, throughout the manuscript. Indeed, CryoSat-2 uncertainties are derived by quantifying different sources of uncertainty in each single measurement, as speckle noise, uncertainty in sea-surface height determination, ice and snow densities, etc.. An observational thickness uncertainty is then found by gaussian error propagation. More details can be found in Ricker et al. (2014). We added a paragraph for further explanation. Therefore, to be more specific, the maps in Figure 1 (original version) are already the requested CryoSat-2 actual measurement uncertainty maps. There are different reasons why uncertainty over thin ice is higher in the CryoSat-2 product: 1. Thinner ice rather occurs in lower latitudes where, due to the CryoSat-2 orbit inclination, the density of measurements is lower than closer to the pole where ice is thicker. This is important as, by gridding, measurement uncertainties are reduced by spatial averaging and the uncertainty reduction depends on the number of available measurements within a grid cell.
In the following we briefly list major changes in the document: -We shifted the discussion about the complementarity of both thickness products from the Introduction to Data and Methods and inserted a new subsection there: 2.1.3 Complementarity of CryoSat-2 and SMOS Sea-Ice Thickness Products. Therefore, also the order of Figure 1 and Figure 2 has switched.
- Figure 1 has been updated, we accidentally plotted the SMOS relative uncertainty of March also for November. This has been fixed.
-For the background field, we now also included SMOS retrievals from the week after the target week in order to avoid a potential bias. As a consequence, also Figures 5 and 6 have been updated. However, the effect is minimal as shown by the changes of statistics in Tables 2 and 3.
- Figure 12 has been updated, since we found a bug in the plotting routine. Therefore, values have slightly changed.
NOTE: All tracked changes in the manuscript are attached to this response letter.
Specific comments: P1 L9: The authors and most readers will know that "narrow-swath altimeter" refers to CryoSat-2 data. However, this is not explained in the manuscript so should not be included here. Just refer to "radar altimeter data" or similar.
P1 L17: "Essential climate variable" is somewhat an ESA tag-phrase and adds nothing to the sentence. Suggest simply changing to "Sea ice affects many climate related processes. . ." We removed "Essential climate variable" as suggested.
P2 L3-4: The authors should quantify what is meant by large uncertainties over thin ice regimes, although with improved manuscript structure they might refer straight to uncertainty maps. They reference a paper by Wingham et al (2006), which I don't feel adequately supports their statement. Indeed, the Wingham paper highlights the insensitivity of the ERS altimeters to thin sea ice but the actual discussion of errors only mentions a thickness dependent error when considering observation probability, and states that the magnitude and scale of that error are not easy to estimate before improved resolution measurements from SIRAL.
We added a quantification to this statement. Referring to Figure 1 (original version), the relative uncertainties over thin ice (< 1 m) are in the range of 100 % or above. We also added the reference Ricker et al. (2014), since it explicitly discusses uncertainties in the CS2 ice thickness product. P7 L9-10: The final two sentences are far too vague. How is the intensity "almost" independent of incidence angle? This paragraph would benefit from further explanation of the angular dependence of brightness temperature intensity over sea ice.
As can be seen in Figure 1 in this document (which is Fig. 3 in Tian-Kunze et al., 2014), the vertically polarized brightness temperature increases with increasing incidence angle, whereas horizontally polarized brightness temperature decreases. This counteract behavior results in that the intensity, which is the average of both polarizations, remains almost constant in the incidence angle range of 0-40 degree.
P8 L4-9: The justification for merging SMOS and Cryosat-2 thicknesses relies on the complementary nature of their uncertainties. Therefore, this paragraph needs expanding.
We added following text to the uncertainty estimation part in the revised version: "The SMOS uncertainty given in the v3 product is estimated based on the uncertainty in the input parameters in the thermodynamic and radiation model as well as in the thickness distribution function. At present, the estimation was carried out for each parameterbrightness temperature, ice temperature and ice salinity respectively, by keeping the other parameters constant. The uncertainty given in the product is then the sum of uncertainties caused by each parameter. In v3, we also varied the sigma in the lognormal ice thickness distribution function, which is used to convert plane layer ice thickness into heterogenous layer mean ice thickness in the retrieval. This uncertainty is then added to the overall uncertainties caused by the brightness temperature, ice temperature and ice salinity. Errors caused by the assumptions about fluxes and snow thickness have not yet been included." In particular, how can a 100% ice coverage assumption cause underestimation of ice thickness if the condition is not met, and by how much?
This is discussed in detail in Tian-Kunze et al., 2014 (see section 4.1). Brightness temperature over ice-sea water mixed areas can be described as where IC is the ice concentration, TBwater and TBice are the brightness temperatures over sea water and sea ice respectively. TBice is about 100 K higher than TBwater, which means that under 100 % ice coverage assumption, we underestimate the TBice, leading to lower ice thickness. In Tian-Kunze et al., 2014, we showed that by using eq. 1 and the radiation model, the underestimation of ice thickness increases exponentially with decreasing ice concentration. However, a comparison with MODIS-derived ice thickness in the Kara Sea has shown that observational uncertainty of SMOS ice thickness under low ice concentration condition is as low as 10 cm (see SMOS + Sea Ice final report). A more deliberate estimation of SMOS ice thickness bias and uncertainty remains as future work.
The 100% ice coverage assumption is used because the accuracy of the ice concentration product is limited and by using the product ice concentration, one will introduce larger errors than with the 100 % assumption. Moreover, this issue only accounts for a minor area, while during winter, most of the ice covered area in the Arctic has ice concentrations (IC) higher than 90 % (Andersen et al., 2007).
The OSI SAF ice type is defined "ambiguous" when their Multi sensor ice type analysis approach has problems to differ between FYI and MYI. This is mostly the case in the transition zone between FYI and MYI regime where the ice type is mixed. For more details, we refer to the OSI SAF product manual: http://osisaf.met.no/docs/osisaf_cdop2_ss2_pum_sea-ice-edge-type.pdf P9 L11: How does OI minimize the total error of observations? This is a key justification for using the OI method to merge the thickness datasets, so needs further explanation.
The OI provides an estimate of sea ice thickness at a given location using a linear combination of arbitrarily distributed thickness observations. These observations are weighted so that the expected uncertainty of the thickness estimate is a minimum in the least squares sense. With Eq. 8, we calculate the weights K that are needed to minimize error variances. We added a sentence for clarification.
P10 L10-11: The assumption that ice thicknesses remain static through a week is highly simplified and unlikely. Whilst I appreciate the need to make such assumptions, the authors need to be more transparent about the unlikelihood of this, or provide reference to argue otherwise.
For many areas in the Arctic, ice motion during one week will be in the range of one or two grid cells (25-50 km), except Fram Strait and parts of the Beaufort Gyre. Considering the uncertainties of the satellite retrievals, we conclude that this assumption is acceptable, though including ice motion data in the optimal interpolation might still lead to improvements and should be investigated in future. Section 2.3.1: The development of the background field is the key aspect of the method that I am uncertain about. To ensure sufficient coverage, the authors create a background field from CryoSat-2 data extending two weeks before and after the target week.
They do not deem this necessary for SMOS data due to its improved coverage, so only use data from the previous week. What concerns me here is the lack of consistency in the background field time-frames, and the bias it may introduce in the final, interpolated thickness product. Indeed, the authors admit that their cross validation is impacted by the fact that the SMOS background is out of phase with observations (P19 L5) and I'm unconvinced by the authors claim that the negative bias should not affect the CS2SMOS sea ice thickness retrieval. Why do the authors not create temporally complementary CryoSat-2 and SMOS background fields? Have they investigated the impact on the merged product and its evaluation with airborne data of extending the SMOS background field?
Thank you for pointing on this issue. We are aware of this and now also included the SMOS retrieval from the week after the target week in order to generate the background field (see modified Figure 6). However, the effect is very small (in the range of few cm). We repeated the cross validation and still receive the negative bias. Moreover, we found a bug in the plotting routine of Figure 12. We fixed this, but the main results are the same. Reconsidering the negative bias in the cross validation, we found the following explanation: The CS2 and SMOS retrieval domains are not symmetric due to the fact that we have to truncate the SMOS retrieval for thick ice, since the methodical approach does not apply for thick ice. On the other hand, the CS2 retrieval is used over the entire thickness range, but with higher uncertainties over thin ice. Therefore, CS2 thickness over thin ice is mostly reduced by the SMOS retrieval, while in contrast this is barely the case for SMOS data over thick ice, because we truncate the retrieval. Hence, due to the optimal interpolation, there will be always a negative bias when doing the cross validation experiment with the original input data from CS2 and SMOS. We included an explanation to the manuscript.
Section 3.2: What week/month/year is the cross validation carried out for? Why? The date also needs to be stated in the caption for Figure 12.
We thank the reviewer for pointing on this. We added the date to the caption.
P21 L5: It would be interesting to know what fraction of AEM measurements exceed 5 m. It's not possible to tell from Figure 13 as colorbars are capped at 4 m and scatter-plots at 5 m, but just stating in the text would be sufficient.
We capped the ranges in the figures in order to improve the visibility of the differences between the AEM data and the satellite derived products. Indeed, one AEM (gridded) measurement point of 5.6 m ice thickness does not appear in the scatter plot. We added a note in the caption of Figure 13 that the reader is aware. Thanks for pointing on this. Although, CS2 measurements over these areas exist and by using other climatologies or even snow depth products, sea-ice thickness might be available with decent uncertainties in future. However, we added a comment in the "Notes and applicability" -column: "constraints in regions where snow climatologies are unavailable".
Due to the sensor and orbit characteristics, such satellite retrievals differ in spatial and temporal resolution as well as in the sensitivity to certain sea-ice types and thickness ranges. Satellite altimeters, such as CryoSat-2 (CS2), sense the height of the ice surface above the sea level, which can be converted into sea-ice thickness. However, relative :::::: Relative : uncertainties associated with this method are large over thin ice regimes. Another retrieval strategy is realized by :::::: method :: is ::::: based ::: on the evaluation 5 of surface brightness temperature in L-Band microwave frequencies (1.4 GHz) with a thickness-dependent emission model, as measured by the Soil Moisture and Ocean Salinity (SMOS) satellite. While the radiometer based method looses sensitivity for thick sea ice (> 1m), relative uncertainties over thin ice are significantly smaller than for the altimetry-based retrievals. In addition, the SMOS product provides global sea-ice coverage on a daily basis unlike the narrow-swath altimeter data. This study presents the first merged product of complementary weekly Arctic sea-ice thickness data records from the CS2 altimeter 10 and SMOS radiometer. We use two merging approaches: a weighted mean and an optimal interpolation scheme (OI). While the weighted mean leaves gaps between CS2 orbits, OI is used to produce weekly Arctic-wide sea-ice thickness fields. The benefit of the data merging is shown by a comparison with airborne electromagnetic induction sounding measurements. When compared to airborne thickness data in the Barents Sea, the merged products reveal a reduced :::::: product ::: has : a : root mean square deviation ::::: (rmsd) : of about 0.7 m compared to ::: less :::: than : the CS2 retrieval :::::: product : and therefore demonstrate the capability to enhance the CS2 retrieval ::::::: product in thin ice regimes. :::::::: However, :: in :::::: mixed :::::::::::::::: first-year/multiyear ::: ice ::::::: regimes :: as :: in ::: the :::::::: Beaufort ::: Sea, ::: the :::: CS2 ::::::: retrieval :::::: shows ::: the ::::: lowest ::::: bias.
Note that the CS2 uncertainties shown here represent statistical uncertainties only. Systematic errors as associated with the usage of a snow climatology or due to variable snow penetration will increase the uncertainty of altimetry based thicknesses 20 (Ricker et al., 2014;Kwok, 2014;Ricker et al., 2015;Armitage and Ridout, 2015).
input ice thickness data. Auxiliary data of ice concentration and ice type were obtained from the Ocean and Sea Ice Satellite Application Facility (OSI SAF).
We use ice densities of 916.7 kg/m 3 and 882.0 kg/m 3 for FYI and MYI (Alexandrov et al., 2010), and 1024 kg/m 3 for the sea water density. Z is calculated for each individual CS2 measurement along each orbit. All these retrievals are averaged on a 25 km EASE2 grid (Brodzik et al., 2012) within one calendar week (Figure 2 : 1a).

SMOS Weekly Sea-Ice Thickness Retrieval
Thin sea-ice thickness has been retrieved from the 1.4 GHz (L-band) brightness temperatures measured by SMOS for the winter seasons  Apr) from 2010 to present (Mecklenburg et al., 2016). The retrieval method consists of a thermodynamic sea-ice model and a one-ice-layer radiative transfer model (Tian-Kunze et al., 2014). The resulting plane layer thickness is 30 multiplied by a correction factor assuming a log-normal thickness distribution. The algorithm has been used for the operational production of a SMOS-based sea-ice thickness data set from 2010 on (Tian-Kunze et al., 2014). In this study we use the most up-to-date version (v3.1) of ice thickness data set, which has been produced operationally since October 2016. The v3.1 data for the previous winter seasons had been reprocessed using the same algorithm.
The v3.1 SMOS ice thickness data are based on v620 L1C brightness temperature data. Brightness temperatures (T B) used in the algorithm are the daily mean intensities averaged over incidence angles from 0 to 40 . The intensity is the average of horizontally and vertically polarized brightness temperatures, equal to 0.5 (T B h +T B v ). Over sea ice, the intensity is almost 5 independent of incidence angle. By using the whole incidence angle range of 0-40 , we can reduce the brightness temperature uncertainty to about 0.5 K.
SMOS measurements are strongly influenced by Radio Frequency Interference (RFI), especially in the first two years after its launch. In the previous processor RFI contaminated snapshots have been discarded using a threshold value of 300 K, applied either to T B h or T B v . The new quality flags given in the v620 L1C data have been implemented to identify the data 10 contaminated by RFI, by sun, or by geometric effects to improve the quality of the radiometric data used for the version 3.1.
For the merging, daily SMOS retrievals are averaged weekly and are projected on an EASE2 25 km grid to be co-located with the CS2 retrievals. Here, we only allow SMOS thickness values with a corresponding uncertainty < 1m which corresponds to a maximum theoretical thickness of about 1.1 m. Furthermore we expect strong biases for the SMOS ice thickness in thicker 15 MYI regimes. Therefore we use the OSI SAF ice type product (Eastwood, 2012) to discard any SMOS grid cells that are indicated as MYI. The weekly composites are shown in Figure 2 : 1b.

OSI SAF Ice Concentration and Type
We use the OSI SAF sea-ice concentration (OSI-401-b) and type (OSI-403-b) products (Eastwood, 2012) in order to identify grid cells that contain 15 % sea ice and to classify them as first-year (FYI ) or multiyear (MYI) sea ice :::: FYI :: or :::: MYI. The 20 products are delivered daily, projected on a 10 km polar stereographic grid. To combine these data with the CS2 and SMOS thickness grids, we calculate weekly means that are projected on the EASE2 25 km grid (Brodzik et al., 2012) to be co-located with the thickness retrievals. The original ice type product contains grid cells that are flagged as ambiguous. We apply an inverse-distance interpolation to those grid cells to obtain FYI or MYI flags for all ice-covered grid cells, because it is needed for further processing steps.

Weighted Mean
We compute the weighted mean sea-ice thickness Z using weekly CS2 and SMOS ice thickness grids during the target week: where represents the statistical :::::::::: observational : uncertainty of the individual products. Figure 4 shows the weighted means for weeks in November 2015 and March 2016. In contrast to the OI approach, presented in the next section, the weighted 30 mean only provides thickness estimates where observations are available during the target week, leaving data gaps in the CS2 domain. In the following we refer to the weekly weighted mean product as WM.

Optimal Interpolation
To achieve complete spatial coverage, we use an OI scheme similar to Böhme and Send (2005) and McIntosh (1990) that enables the merging of datasets from diverse sources on a predefined, so-called analysis grid. The input data are weighted based on their individual uncertainties and the modeled spatial covariances. OI minimizes the total error of observations and provides ideal weighting for the observations at each grid cell :: in :: the ::::: least ::::: square ::::: sense. In this section we present the processing methods, on which our OI approach is based. Figure 5 shows the processing scheme, which will be described in more detail in the following.
The OI scheme is used to get an objective estimate of values at observed or unobserved locations. The basic equation is: where the vector Z a is the analysis field, i.e. each element represents a grid cell of the merged CS2SMOS ice thickness retrieval to be produced. Z b is a background field vector and Z o the vector that contains all SMOS and CS2 observations. Here we use already gridded, weekly mean CS2 and SMOS thickness estimates as observations, as shown in Figure 2 : 1 and as described above. Using gridded data as observations reduces their statistical ::::::::::: observational uncertainties and provides equally distributed 10 observations, which improves the performance of the OI. In addition, gridding of raw data reduces the number of available observations used for the OI, increasing the efficiency of the OI routine. We assume that the observations are static, i.e. remain temporally coherent within a week and do not change due to ice deformation and motion. Therefore, we neglect any temporal correlations. H is an operator that transforms the background field into the observation space. To be more specific, this is realized by an inverse distance interpolation method. K represents a weight matrix and is derived from error covariances. We 15 aim to retrieve weekly analysis fields, based on calendar weeks from Monday to Sunday. Wet and warm snow or ice prevent the retrieval of summer sea-ice thickness estimates from CS2 or SMOS. Hence, the CS2SMOS product is limited to the period from October/November ::::::::::::: end-of-October to April.

The Background Field
The weekly CS2 ice thickness composite possesses large gaps resulting from the limited orbital coverage (Figure 2 : 1a). But 20 for the OI approach, an Arctic-wide coverage is required for the background field. Therefore, we use a composite of retrievals from adjacent weeks, to create a background field with nearly complete coverage for the Central Arctic at a certain target week ( Figure 6a). Here we combine data from the two weeks before and after the target week. Therefore, in contrast to CS2 near real-time sea-ice thickness retrievals (Tilling et al., 2016), products can only be released 2 weeks after data acquisition.
In order to ensure independence between observations and background field, CS2 data from the target week are not included 25 in the background field. For the same reason, we use a SMOS weekly mean from the previous ::: one :::: week :::::: before ::: and ::::: after ::: the ::::: target week. The initial background field is computed by a weighted mean using Eq. (4). Gaps in the weighted average are interpolated by using a nearest neighbor scheme. In order to reduce noise, the background field is low-pass filtered with a smoothing radius of 25 km, before it is applied in the OI algorithm (Figure 6b).
Since we use CS2 and SMOS retrievals for the background field beyond the target week and because the SMOS composite 30 contains artifacts in coastal regions, we additionally use a weekly mean of the daily OSI SAF ice concentration product to determine the ice coverage during the target week. Here, we apply a threshold of 15 % and only grid cells that exceed this value will be considered as ice covered, which corresponds to the ice extent products provided by OSI SAF and the National Snow and Ice Data Center (NSIDC).

Correlation Length Scale Estimation
The correlation length scale ⇠ controls the impact of a data point on the analysis grid point depending on their distance.
Considering the grid resolution of 25 km, correlation length here is used in the sense of large-scale thickness gradients. For 5 example, the correlation length scale estimate is large in the center of a certain ice type regime with similar ice thickness (i.e. level FYI). On the other hand, we expect a low ⇠ value at locations with strong thickness gradients, where distant observations are not representative for local conditions. Figure 7 illustrates the estimation of ⇠ for a certain grid cell Z 0 in the Lincoln Sea during a week in November. In order to estimate ⇠, we consider the unfiltered background field Z b (Figure 7a) and define a structure function ✏ 2 . The structure function can be used to assess the change of ice thickness with distance and is related to 10 13 the normalized auto correlation function R(d, Q) as follows (Böhme and Send, 2005): Quadrants Q are defined to accommodate the anisotropy of the spatial ice thickness distribution (Figure 7b). ✏ 2 (d, Q) represents the square differences between ice thickness of the grid cell and the ice thickness of the grid cells of binned 25 km distances 5 d in a quadrant Q. Z 0 Q,d is the background thickness, binned according to d and Q. Figure 7b reveals :::::::: illustrates the annuli of distance and the 4 Quadrants. 2 Z 0 are the corresponding mean variances of a certain quadrant. With Eq. (6) we then obtain the auto correlation function R(d, Q), which is computed up to radius of 750 km (30 bins). In the next step, we fit a function of the form: to R(d, Q), using a least squares scheme, and obtain an estimate for ⇠. Figure 7c shows the calculated auto correlation function R(d, Q) and the functional fit (Eq. (7)). A stronger decay of R(d, Q) occurs with rising deviation between Z 0 and the thickness at a certain distance in a certain quadrant. R(d, Q) can also become negative if ✏ 2 (d, Q)/2 2 Z 0 becomes >1. In order to improve the fitting performance, we set R(d, Q) = 0 if R(d, Q) becomes < 0. Furthermore, ⇠ is rejected if the computation fails. Finally, we average the ⇠ values from the 4 quadrants, as we do not use anisotropic weighting in the OI. In order to remove outliers 15 and noise, the derived ⇠ grid is low-pass filtered with a smoothing radius of 25 km. Grid cells with failed computation are interpolated by a nearest neighbor scheme afterwards. Figure 7d shows the spatial correlation length scales ⇠ for 3-9 November 2014. It highlights the sensitivity to changing thickness gradients as ⇠ decreases towards the coast of the Canadian Archipelago, where higher sea-ice thickness gradients likely occur due to increased deformation.
2. We assume that the influence of observations that are located far away from the analysis grid point can be neglected.
Therefore, instead of computing the entire covariance matrix, we only consider observations within a radius of influence.

10
This radius is set to 250 km to gather just enough observations in regions with large gaps, for example over MYI between two CS2 orbits where valid SMOS observations are not available.
3. To further reduce computation expense we limit the number of matched observations to 120, meaning that in the case of more matches, only the 120 closest observations are considered.
4. We generally assume that all observations are unbiased.

5
where I is the identity matrix. Since we consider variances exclusively, we only calculate the diagonal elements of 2 Za . Figure  8 illustrates how the analysis thickness is derived at a certain analysis grid point, considering distant grid cells with ice thickness estimates of CS2 and SMOS. The K weights decrease with increasing distance to the analysis grid point as a consequence of Eq. (9). In addition, the individual uncertainties affect the weighting according to Eq. (8). The considered grid cell is located at the boundary between the CS2 and SMOS domain. In the following, we use domain as the regions where CS2 or SMOS data 10 predominate. SMOS ice thicknesses of about 1 m reveal higher uncertainties than corresponding CS2 estimates (Figure 1 : 2) and hence the K weights of CS2 estimates exceed the SMOS weights for higher ice thicknesses. Figure 9 shows the innovation field, the merged CS2SMOS product and the analysis error field, which is the square root of the error variance (Eq. (11) Pole or over MYI. In this case the analysis depends on the accuracy of the background field, leading to increased uncertainties.

Evaluation of the Optimal Interpolation
In this section, we aim to evaluate the CS2SMOS product derived from the OI scheme by a comparison with the individual satellite products. In addition, we carry out a cross validation experiment by omission of random data to test the OI method.

Comparison with Input Products
20 Figure 10 illustrates the differences between CS2SMOS and the CS2 and SMOS retrievals from November 2015 to April 2016. The difference between CS2SMOS and SMOS weekly grids is shown in Figure 10a, limited to grid cells with SMOS observations in the target week. Positive anomalies of up to 1 m occur mostly in the transition zone between the SMOS and the CS2 domain where the thick ice in the CS2 retrieval leads to an increase of ice thickness in these grid cells with respect to the SMOS data ( Figure 10a). However, the general pattern remains the same during the season. Subtracting the CS2 monthly mean 25 sea-ice thickness from the CS2SMOS product, represented by one week within each month, reveals substantial scattering between -1 m and 1 m within the CS2 domain (Figure 10b). This is mainly caused by the fact that the monthly retrieval is compared with the weekly product. During the different time spans, the regional sea-ice thickness distribution is subject to ice drift, convergence and divergence, as well as thermodynamic ice growth. In addition, the OI algorithm evokes a low pass filtering of the spatial thickness distribution due to the impact of distant grid cells, reducing the noise compared to the original   Table   2 presents the corresponding statistics for the entire winter season including the mean and the standard deviation of each 5 month or week respectively. The CS2 retrieval lacks sensitivity for thin ice (< 0.5 m) over the entire season. The gap in this thickness range can be closed by the SMOS retrieval. While the mean thickness of the CS2 retrieval consistently grows from 1.46 m in November to 1.90 m in April, the SMOS thickness mean remains at about 0.5 m after an increase from November to December. Due to the increasing uncertainties of the SMOS product towards thick ice, the ::::::::: distribution frequency steeply drops at about 1 m for each month. Therefore, the SMOS mean thickness is mostly affected by the boundary condition at about 10 1 m in conjunction with thermodynamic ice growth and the newly formed ice (< 0.1 m). The thickness distributions show the capability of the CS2SMOS product to combine the complementary ice thickness ranges. As a consequence, the standard deviation of the merged product ranges between 0.8 m (December) and 0.99 m (April), and therefore exceed ::::::: exceeds the standard deviations of the individual products that reach maximum values of 0.78 (CS2) and 0.38 (SMOS) in April. The scatter diagrams in Figure 11b illustrate the thickness differences between CS2SMOS and the two individual products, with respect to CS2 retrieval. The comparison between CS2SMOS and SMOS shows increasing scattering with rising thickness. As shown in Figure 10, this originates from the transition zone between the CS2 and SMOS domain.
the difference between the satellite products and the corresponding mean and modal AEM thickness. Statistics resulting from Figure 13 are given in Table 3. Table 3. Statistics of the comparison of satellite retrievals with airborne EM thickness measurements (AEM), corresponding to Figure 13.
For each case we consider both the AEM modal thickness (AEM mode) and the AEM mean thickness (AEM mean On April 9 and 10, 2 AEM flights were carried out with a fixed wing DC3-T aircraft (Figure 13a). The AEM measurements indicate high mean ice thickness variability ranging between 0.2 m and more than 5 m. Comparing the mean (2.2 m) and modal thickness (1.2 m) of the entire data set indicates substantial deformation. Thickness distribution and OSI SAF ice type data suggest two ice types. First-year ice, reaching a modal thickness of up to 1 m, and multiyear ice with a modal thickness ranging 5 between 2 m and 4 m. The presence of two ice types and the drift along the Beaufort Gyre (Petty et al., 2016)  On the other hand, the modal ice thickness is slightly overestimated by up to 0.3 m (WM). It is important to note that WM and SMOS do not provide a full data coverage. The SMOS data, for example, usually only cover first-year ice. This is also the reason why SMOS exhibits the smallest rmsd for mean and modal thickness (1.16 m and 0.75 m). However, scatter diagrams show good agreement of AEM data and CS2SMOS, WM and SMOS retrievals within the first-year ice, up to about 1.2 m thick ice ( Figure 13). CS2 shows the lowest bias (-0.17 m) for the mean ice thickness, but the highest for the modal thickness. The scatter diagrams also indicate that CS2 is not able to capture high thickness gradients due to the presence of scattered heavily 5 deformed multiyear ice, which is transported along with the Beaufort Gyre. As discussed above, the usage of SMOS data in CS2SMOS and WM leads to a stronger underestimation of mean ice thickness of deformed multiyear sea ice, compared to CS2. But it substantially improves the representation of first-year ice thickness. The comparison between WM and CS2SMOS shows that in areas where weekly observations are available, both retrievals show similar agreement with AEM measurements. Moreover, the degree of deformation is lower, indicated by only 0.1 m difference between mean and modal thickness of the entire data set. For CS2, the rmsd is 0.97 m for the AEM mean thickness and 1.11 m for the AEM modal thickness, indicating a slightly better representation of the mean thickness in the CS2 product. However, scattering is high and the mean bias of 15 0.82 m with respect to the mean AEM thickness suggests a strong bias towards thicker ice. Such errors might originate from erroneous sea-surface height interpolation along the CS2 orbits : as :::: well :: as ::::: from ::::::: off-nadir :::: lead ::::::: ranging ::: and :::::::: retracker ::::::::: limitations :::::::::::::::: (Ricker et al., 2014). The SMOS and CS2SMOS retrievals are almost identical for that region, which is caused in part by the better coverage of the SMOS retrieval in that region. In addition, this area is dominated by thin ice, leading to a higher weighting of the SMOS retrieval due to the lower uncertainties (Figure 1 : 2). The scatter diagrams reveal a significantly better agreement 20 of the AEM mean thickness measurements with the CS2SMOS, WM and SMOS retrievals (rmsd = 0.27-0.30 :::: -0.31 : m, r = 0.65 ::: 0.61-0.73) than with the CS2 retrieval (rmsd = 0.97, r = -0.35). :::::: Hence, ::: the :::::::: reduction :: in ::::: rmsd :::::::::: considering ::::::::: CS2SMOS ::: or ::::

Barents
WM :::::::: compared :: to :::: CS2 :: is :::::: roughly ::: 0.7 ::: m. The observed bias with respect to the mean AEM thickness is -0.25 m for CS2SMOS, -0.17 for WM, and -0.24 m for SMOS, suggesting a bias towards thinner ice. The maps and scatter diagrams indicate that the CS2SMOS, WM and SMOS retrievals capture small thickness gradients visible in the AEM thickness data. This comparison 25 provides evidence that using SMOS data in areas with a thin ice regime will reduce the rmsd and the mean bias when compared to the CS2 product.

Conclusions
We presented methods to carry out the first joint data merging of CryoSat-2 (CS2) sea-ice thickness fields and thin ice thickness estimates obtained from the L-Band radiometer onboard the Soil Moisture and Ocean Salinity (SMOS) satellite. While CS2 30 lacks the capability to observe thin ice, SMOS is restricted to ice regimes thinner than about 1 m. We used two approaches for merging CS2 and SMOS ice thickness data: a weighted mean and an optimal interpolation scheme (OI) based on weekly CS2 and SMOS ice thickness grids. While the weighted mean product (WM) only provides estimates at grid cells where observations are available, the OI product (CS2SMOS) provides weekly Arctic-wide sea-ice thickness estimates with corresponding uncertainty estimates. We have shown that the merged products have the capability to allow for weekly thickness estimates that are sensitive to the entire thickness range, using the complementary sensitivity of the individual products to different thickness regimes. Moreover, the weekly merged products benefit from increased coverage at lower latitudes in conjunction with higher 5 temporal resolution compared to the CS2 retrieval, which is important for observing ice growth during the freeze-up. In particular, the usage of the combined product will improve thickness retrievals in all areas with thin ice, which we have demonstrated using case studies from the Barents Sea during spring 2014 and Beaufort Sea during spring 2016. Comparisons with airborne electromagnetic thickness measurements (AEM) reveal a reduced :::::::: reduction :: in : root mean square deviation of about 0.7 m for CS2SMOS and WM, compared to the CS2 thickness retrieval in the Barents Sea. Moreover, the comparison shows that re-10 trievals that use SMOS data seem to capture small thickness gradients in thin ice regimes, whereas the CS2 retrieval is very noisy. In the Barents Sea, the CS2 retrieval overestimates mean thin ice thickness by 0.8 m, while CS2SMOS, WM and SMOS underestimate by about 0.2 m. The comparison with the AEM data has also revealed that WM represents a good estimate in regions where weekly data of SMOS and CS2 are available. For the observation of thicker multiyear ice (> 1 m) , ::: and :::::: mixed :: ice ::::::: regimes : as in the Beaufort Sea 2016, ::: the CS2 provides the best estimates :::::: product ::: has ::: the :::::: lowest :::: bias, although limitations 15 in capturing high thickness gradients due to heavily deformed ice exist. CS2SMOS, however, exclusively provides weekly ice thickness estimates covering the entire Arctic and combining CS2 and SMOS data. The OI approach used in this study can be adopted to merge sea-ice thickness or freeboard data sets derived from other satellite missions, such as the recently launched European Space Agency mission Sentinel-3, which carries a Ku-band radar altimeter similar to SIRAL onboard CS2.
6 Data availability 20 The weekly updated CS2SMOS product, including the weighted means (WM), and the monthly updated CryoSat-2 product are provided at http://www.meereisportal.de. The SMOS ice thickness data are provided at http://icdc.cen.uni-hamburg.de.
Author contributions. Robert Ricker developed the optimal interpolation algorithm and conducted the processing. Stefan Hendricks processed the CryoSat-2 orbit files. Lars Kaleschke and Xiangshan Tian-Kunze were responsible for the SMOS processing. Jennifer King processed the AEM data in the Barents Sea. Christian Haas processed the AEM data in the Beaufort Sea. Robert Ricker wrote the paper and all Co-authors contributed to the discussion and gave input for writing.
Competing interests. The authors declare no conflict of interest.