First SMOS Sea Surface Salinity dedicated products over the Baltic Sea

. This paper presents the ﬁrst Soil Moisture and Ocean Salinity (SMOS) Sea Surface Salinity (SSS) dedicated products over the Baltic Sea. The SSS retrieval from L-band brightess temperature (TB) measurements over this basin is really challenging due to important technical issues, such as the land-sea and ice-sea contamination, the high contamination by Radio-Frequency Interferences (RFI) sources, the low sensitivity of L-band TB at SSS changes in cold waters and the poor characterization 5 of dielectric constant models for the low SSS and SST ranges in the basin. For these reasons, exploratory research in the algorithms used from the level 0 up to level 4 has been required to develop these dedicated products. This work has been performed in the framework of the European Space Agency regional initiative Baltic+ Salinity Dynamics. Two Baltic+ SSS products have been generated for the period 2011-2019 and are freely distributed: the Level 3 (L3) product (daily generated 9-day maps in a 0 . 25 ◦ grid, https://doi.org/10.20350/digitalCSIC/13859) (González-Gambau et 2021a) 10 and the Level 4 (L4) product (daily maps in a 0 . 05 ◦ grid, https://doi.org/10.20350/digitalCSIC/13860) (González-Gambau et al., 2021b)), that are computed by applying multifractal fusion to L3 SSS with Sea Surface Temperature (SST) maps. The accuracy of L3 SSS products is typically around 0.7-0.8 psu. The L4 product has an improved spatio-temporal resolution with respect to the L3 and the accuracy is typically around 0.4 psu. Regions with the highest errors and limited coverage are located in Arkona and Bornholm basins and Gulfs of Finland and Riga.

In this work, we present the dedicated algorithms used to develop the Baltic+ L3 and L4 SSS products and their quality 85 assessment. The article is structured as follows: Section 2 describes the datasets (section 2.1) and algorithms (section 2.2) used in the generation of the Baltic+ SSS products. Section 3 presents the quality assessment of the SSS products. Section 3.1 presents the different datasets used for comparison and validation, section 3.2 describes the methods, section 3.3 explains the quality metrics used in the validation and section 3.4 shows the validation results. The conclusions are summarized in Section 4.

2 Generation of Baltic+ SSS products
This section is devoted to explain the datasets and the main algorithms used in the generation of the Baltic+ L3 and L4 SSS products (see Figure 1). The processing starts from the SMOS L0 data distributed by ESA. The general algorithm encompasses several blocks (detailed in section 2.2): • Computation of brightness temperatures at antenna reference frame (ARF) from level 0 data by using the ALL-LICEF 95 calibration and applying the G kj correction to reduce ocean TB errors close to land and ice edges.
• Computation of the measured TB at the bottom of the atmosphere (BOA).
• Computation of the difference between SMOS TB and modeled TB and inversion to retrieve SSS.
• Correction of systematic biases on SSS by means of a SMOS-based climatological data.
• Generation of the Baltic L3 salinity maps.

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• Correction of temporal biases found in L3 SSS maps.
• Multifractal fusion of L3 SSS maps with an SST field to generate the L4 SSS maps.

SMOS Brightness Temperatures
We generate the TB dataset starting from the SMOS ESA Level 0 data (https://smos-diss.eo.esa.int/oads/access/). Level 0 is 105 the raw data containing both observation data and housekeeping telemetry.

Auxiliary data used in the salinity retrieval
The auxiliary data used for the SSS retrieval comes from the European Centre for Medium range Weather Forecast (ECMWF) (Sabater and De Rosnay, 2010). They can be accessed at https://smos-diss.eo.esa.int/oads/access/collection/AUX_Dynamic_ Open. ESA provides an ECMWF auxiliary file spatially and temporally colocated with each SMOS overpass. The following fields are used in the SSS retrieval: sea ice cover, rain rate, 10-meter wind speed, 10-meter neutral equivalent wind (zonal and meridional components), Significant Wave Height (SWH) of wind waves, 2-meter air temperature, surface pressure, and vertically integrated total water vapour (Zine et al., 2008).
We use a regional climatology as annual reference SSS field, which is added to the debiased SMOS SSS anomalies (see section 2.2.4). This regional climatology is distributed by SeaDataNet and provides temperature and salinity monthly clima-115 tologies computed from an historical dataset (mainly from CTD (Conductivity, Temperature and Depth) devices and discrete water samplers in the period 1900-2012) (SeaDataNet Baltic Climatology), with a spatial resolution of 0.11 • in longitude and 0.065 • in latitude. The salinity field at 0 m depth is used. Monthly climatologies are averaged to obtain an annual reference field. A nearest neighbour interpolation is used to compute the reference value at the grid of the debiased SMOS SSS anomalies.

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Since the SST is one important driver of the SSS errors, we analysed the errors of all the available SST datasets over the Baltic sea: i) ECMWF (Sabater and De Rosnay, 2010); ii) OSTIA (Donlon et al., 2012); iii) CMC (Canada Meteorological Center, 2012); iv) REMSS (Remote Sensing Systems, 2017); v) CCI (Merchant et al., 2019); and vi) CMEMS Baltic Sea reanalysis (Axell, 2019)). For this, we computed the differences with respect to the SeaDataNet in situ measurements (see section 3.1.3).
The ESA CCI SST combines data from both the Advanced Very High Resolution Radiometer (AVHRR) and Along Track Scanning Radiometer (ATSR) SST_CCI Climate Data Records, providing daily global SST on a 0.05 degree regular latitude-130 longitude grid.
The OSTIA dataset uses satellite data provided by international agencies via the Group for High Resolution SST (GHRSST).
These products include data from microwave and infrared satellite instruments. The OSTIA dataset has also daily global coverage on a 0.05 degree regular latitude-longitude grid.
These SST products are used in the SSS retrieval (section 2.2.4), in the correction of SMOS SSS systematic biases (section 135 2.2.4) and as a template in the fusion scheme to generate the L4 SSS product (section 2.2.8).

Sea Ice Fraction
A sea-ice mask is required to discard those SSS retrievals in ice-covered regions. This sea-ice mask is created from the sea ice fraction (SIF) information provided by OSTIA (product ID "OSTIA-UKMO-L4-GLOB-v2.0", (Donlon et al., 2012)). We generate an ice filtering flag (SSS are discarded when SIF>0) in order to discard those raw SSS retrievals acquired when sea 2.2 Algorithm developments for Baltic+ SSS products

Generation of SMOS brightness temperatures
Some of the corrections we propose to improve the quality of TBs over the Baltic Sea are not included in the current operational ESA L1B products. For this reason, we have used the MIRAS Testing Software (MTS) (Corbella et al., 2008), developed by 155 the Universitat Politècnica de Catalunya (UPC), that provides TBs at antenna reference frame from SMOS ESA level 0 data, to generate the TB dataset.
We use the ALL-LICEF mode as the calibration approach (Corbella et al., 2016). The main advantage of using this calibration mode is that the measurements of the zero-baseline visibility, and the rest of the visibility samples, are more consistent. The up-to-date methods developed by the UPC in the recent years for reducing image reconstruction errors are also included in the 160 MTS. Details on the used image reconstruction strategy can be found in Corbella et al. (2009Corbella et al. ( , 2019. Corbella et al. (2015) showed that the dominant contribution to both Land/Sea Contamination (LSC) and the Ice/Sea Contamination (ISC) is caused by a mismatch between the amplitude of the zero-baseline visibility (mean antenna noise temperature) and the rest of visibilities. In particular, it was found that the error comes from an overestimation of the MIRAS correlator 165 efficiencies (known as the G kj parameter) and proposed a 2% correction factor to the G kj parameter calibrated every 2 months during the long calibration sequences (Brown et al., 2008). This corrected G kj parameter is the one used in the denormalization of the calibrated visibilities (Corbella et al., 2005) previously to the TB image reconstruction.

Mitigation of errors in SMOS brightness temperatures
The application of this correction leads to an overall reduction of the TB contamination close to the coasts (Corbella et al., 2015). This enhancement is also reflected globally in the quality of the SSS retrievals from the corrected TBs (González- In the Baltic, the ALL-LICEF calibration approach and the G kj correction are crucial to reduce the LSC/ISC close to coasts and ice edges. As an indicator of the TB quality, the differences between the SMOS TB measurements and the theoretically modeled TBs at ocean surface (hereafter referred to TB anomaly) are analyzed. Details on the derivation of the modeled TBs can be found in González-Gambau et al. (2017).

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The impact of the G kj correction on the SMOS TB over the Baltic Sea is shown in Figure 2. A significant overall reduction of the systematic biases is observed in the whole basin (∼ 2 − 3 K), improving the quality of TBs. González-Gambau et al. (2015); González-Gambau et al. (2016) proposed a dedicated technique, the Nodal Sampling (NS), to mitigate the impact of RFI contamination. This technique has been successfully applied at a global scale (González-Gambau et al., 2017) and in the Black Sea . However, the application of the NS for the specific case of the

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The SSS retrieval is based on finding the appropriate value of raw SSS that makes the GMF (Geophysical Model Function) of TB closer to the actually measured TB. The GMF is derived from a dielectric constant model for sea water. All the dielectric constant models found in the literature are built by empirical fitting of laboratory measurements. The dielectric constant model Klein and Swift (1977) has been used until recently in the operational SMOS L2OS (Level 2 Ocean Salinity) processor. The dielectric constant model of Meissner and Wentz (M&W) (Meissner and Wentz, 2004;Meissner et al., 2018) is used in 190 Aquarius and SMAP salinity processors. The M&W model was reported as more suitable at low SST ranges (Meissner and Wentz, 2004;Zhou et al., 2017). Therefore, we propose to use the M&W dielectric constant model to retrieve SSS in the Baltic Sea.
In a first analysis of the retrieved raw SSS, a low number of retrievals was obtained in some regions of the Baltic, specially in regions where the SSS values are very low. Figure 3 (a) shows the difference between the SMOS and the modelled TB (i.e., 195 the TB associated to the retrieved raw SSS using the GMF) for all the measurements in 2013 under the following acquisition conditions (latitude, longitude, overpass direction, across-track distance, incidence angle): (ϕ = 56 • , λ = 19 • , Ascending, x = 0km, θ = 42.5 • ). Those values for which a salinity retrieval is obtained are marked with green circles.
It was found that raw SSS values were only retrieved if T B meas − T B mod ≤ 0. In the Baltic Sea, the values of SSS and SST are very low and the sensitivity of SSS to TB is also very low at cold waters. Thus, large biases on TB translate to large 200 biases on SSS, what typically leads to negative raw SSS values in the retrieval. These negative salinity values do not have any physical meaning; they just reflect the presence of instrumental biases that must be corrected.
The M&W dielectric constant model is reviewed for the SST and SSS conditions of the Baltic Sea. Figure 3   However, as shown in Figure 3 (b), MW model starts deviating considerably from the almost linear dependence on SSS at about 20 psu. Therefore, lacking of a better characterization of the dielectric constant at low SSS, we decided to perform a linear extension of M&W dielectric constant model for SSS lower than 20 psu.

Debiased non-Bayesian SSS retrieval
The debiased non-Bayesian (DNB) SSS retrieval  focuses on the correction of the residual systematic biases in SSS (produced by LSC and permanent RFI) and on the increase of coverage with respect to the standard (Bayesian) retrieval algorithm. The original debiased non-Bayesian approach has been fine-tuned for retrieving SSS in the Baltic Sea.
Major modifications are highlighted in this section.

Non-Bayesian salinity retrieval
A single SSS value is retrieved for each TB measurement at a given incidence angle, unlike the conventional Bayesian retrieval, where a single SSS is retrieved from the entire set of multi-angular TB. Details on the SSS retrieval (referred as raw SSS, since they need to be corrected from systematic biases and filtered) can be found in section 2.2 of Olmedo et al. (2017).
These raw SSS are then appropriately classified, filtered, and combined, to build global SSS maps.

Characterization and correction of SMOS SSS systematic errors
We want to characterize the systematic errors in SMOS SSS. This characterization is based on the hypothesis that systematic errors are the same for all those SSS acquired under the same conditions. Seven years of SMOS SSS retrievals (2013-2019, the cleanest period in terms of RFI contamination) are used for the characterization of those systematic biases on raw SSS that do not depend on time.

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The raw SSS are grouped together according to their geolocation in the same fixed grid of TB measurements (coordinated by the latitude and longitude), overpass direction (ascending or descending, denoted by d), across-track distance to the center of the swath (in 50-km bins, denoted by x) and incidence angle (in 5 • bins, denoted by θ). Then, for each group, we use the central estimator of the distribution for characterizing the systematic biases of this group. We call this central estimator the SMOS-based climatological data (see the original DNB method in Olmedo et al. (2017) for more details).

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When we applied the original DNB SSS retrieval to the Baltic Sea, we observed that seasonal variations were much higher than in the global ocean (Olmedo et al., 2020) and that high gradients not corresponding to geophysical gradients (they are not observed either in the reanalysis nor in the in situ measurements) appeared close to the coasts. These effects were evidenced when computing the monthly mean difference between SMOS SSS and CMEMS Baltic reanalysis salinity field ( Figure 4). Then, we analyzed the dependence of these differences on SST. SMOS SSS fields retrieved in 2013 were collocated with 240 the salinity and temperature outputs from the CMEMS Baltic reanalysis. Figure 5 shows the mean of the difference between the salinity, as observed by SMOS, and the reanalysis for each bin of 1 • C of SST. To mitigate these systematic spatial biases dependent on SST, we modify the original DNB to include the SST (T s ) as one more parameter in the classification of the SSS retrievals for the computation of the SMOS-based climatological data. Therefore, for each given 6-tuple (instead of the 5-tuple of the original DNB), c = (ϕ, λ, d, x, θ, T s ), all the raw SSS retrievals 245 SSS(ϕ, λ, d, x, θ, T s ) in the period 2013-2019 are accumulated. The introduction of the SST in the classification of SSS systematic errors leads to an important reduction in the number of measurements under given acquisition conditions. Therefore, to increase the number of measurements and have significant statistics, we use have extended the SST range when computing the SMOS-based climatological data. Seven bins of SST are defined (note that bin size varies depending on the SST range) with a certain overlap for the low ranges of SST (see Table 1). Examples of maps of the mean and the standard deviation of the SMOS-based climatological distributions are shown in 260 Figure 6 for two different bins of SST: bins 2 and 6 in Table 1. Note that the SMOS-based climatological values are very different for the two bins of SST and the distributions at colder temperatures are noisier, as expected, due to the low sensitivity of TB to SSS at cold waters (Yueh et al., 2001).

Generation of debiased non-Bayesian SMOS salinities
For the generation of the debiased non-Bayesian SMOS SSS values, each raw SSS acquired at a time t and at the given 265 acquisition condition (ϕ, λ, d, x, θ, T s ) is corrected with the corresponding SMOS-based climatological data, thus giving the SMOS-based anomalies.
Then, a time-independent SSS reference is added to the SMOS SSS anomalies to obtain the final debiased SSS values. The annual reference SSS field used is the Baltic regional climatology provided by SeaDataNet (see section 2.1.2).
We study now whether the multi-annual mean of the salinity (required for the bias mitigation) changes with SST. For this, the 270 impact of adding the regional climatology computed per bins of SST versus using a unique regional climatology as the annual reference field is analyzed. We use the salinity and temperature provided by CMEMS Baltic reanalysis in the period 2013-2019 to compute the averaged salinity for each bin of temperature. The mean error when using the single regional climatology as the annual reference field, instead of using the mean salinity value per bin of temperature (taking into account the frequency of each temperature value), is shown in Figure 7. The typical error is around 0.05 psu, except in the Danish straits, where can 275 reach up to 0.4 psu. Since this error is, in general, quite low in the basin, a single annual reference field is used to generate the debiased SMOS SSS.

Filtering criteria
Errors in SSS retrievals over the Baltic Sea are expected to be much larger than in the global ocean, due to the low sensitivity of SSS to TB at cold waters. Moreover, residual errors caused by land/sea and ice/sea contamination, as well as perturbations by 280 RFI sources, are also affecting the salinity retrievals. For this reason, the filtering criteria defined for the BEC global product  are not suitable for this basin. In this work, the filtering criteria are reviewed and made less restrictive while giving accurate enough values for the Baltic Sea.
The filtering criteria are the following: They reflect the instrumental biases and other systematic errors that need to be corrected.
• For a given 6-tuple, c = (ϕ, λ, d, x, θ, T s ), the SMOS-based climatological distribution under at least one of these conditions is discarded: -The histogram has less than 30 measurements.
-The standard deviation is greater than 35 psu.

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If the SMOS-based climatological distribution corresponding to a given 6-tuple has been discarded following the previous criteria, then all the associated raw SSS are discarded.
• Raw SSS are discarded if they deviate too much from the SMOS-based climatological data. That is, any raw SSS value Figure 6). Note that the standard deviation of the distributions is much higher than the expected geophysical variability of SSS. Therefore, 295 this criterion is not very restrictive.
• In order to improve the quality of L3 SSS maps, all SSS values with an associated SSS uncertainty (estimated as detailed in section 2.2.2 of Olmedo et al. (2021b)) larger than 2 psu are also discarded before the generation of the L3 maps.
These points mainly correspond to ice-covered areas during the cold season, such as the Bothnian Bay and the Gulf of Finland, as well as some grid points closest to the coast (see examples in Figure 8).

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• SSS retrievals in the Skagerrak and the Kattegat straits (grid points with longitudes lower than 14 • E) are also filtered out because of the large SSS uncertainties in the region, mainly during the cold season (see section 2.2.6).

Generation of SSS for a given satellite overpass and L3 maps
The Baltic+ L3 SSS data product is provided in a regular longitude-latitude grid of 0.25 • (final grid). All the debiased and filtered SSS obtained for a given grid point in one overpass are averaged using an area-weighted average. An extrapolated value 305 of SSS can be assigned to the cells of the final grid, by conveniently weighting the contributed values for each overlapping cell of the original grid (Lambert Azimuthal Equal Area grid of 25 km). We compute the L3 SSS maps by weight-averaging the SSS of the different overpasses in a 9-day period. Each contributing SSS is weighted by the inverse of its error variance.
An example of a L3 SSS map and its associated error are shown in Figure 8 for the cold (November to May) and warm (June to October) seasons. The estimated SSS error in the L3 product comes from the propagation of the errors in the debiased non-

Correction of time-dependent biases
SMOS measurements are affected not only by spatial biases, but also by biases that depend on time (Martín-Neira et al., 2016).

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In the debiased non-Bayesian retrieval, time-dependent biases are not corrected: the SMOS-based climatologies integrate a multi-year period, providing a reference that is constant in time (section 2.2.4). Therefore, an additional correction for the time-dependent biases is required.
In the BEC global product , the assumption used to mitigate these time-dependent biases is that the spatial average of SSS anomalies in the global ocean is zero at any instant. This hypothesis has been shown to hold well 320 with in situ SSS (Argo) in the global ocean. But this assumption is not suitable regionally, and even less in the Baltic Sea due to the net exchanges of salinity across region boundaries. In other BEC regional SSS products, such as the ones of the Mediterranean Sea (Olmedo et al., 2018b) and the Arctic Ocean (Olmedo et al., 2018a), time-dependent biases were corrected by using Argo measurements as reference. However, due to the scarce spatio-temporal coverage of Argo floats (restricted to Bothnian Sea, Gotland Deep and Bornholm Deep), this approach cannot be applied in the Baltic Sea. Instead, we assess the 325 temporal correction by using two different reference datasets: in situ measurements from SeaDataNet (section 3.1.3) and the CMEMS Baltic reanalysis (section 2.1.2). As it can be observed in Figure 9, both corrections are in agreement. However, due to the lack of in situ measurements and their spatio-temporal inhomogeneity, the temporal correction computed with in situ is much noisier and not always provides a value for the correction, what leads to data gaps. For these reasons, the CMEMS Baltic reanalysis is used for the temporal correction.
330 Figure 9. Temporal bias correction computed for the SSS product during 2013 by using the CMEMS Baltic reanalysis (red) and SDN in situ measurements (blue). Note that the peaks in the correction computed from SDN in situ measurements are due to the very scarce and fragmentary spatial distribution of collocated in situ data.

Multifractal fusion of SSS and SST
L4 SSS product has been generated by applying multifractal fusion techniques (Umbert et al., 2014;Olmedo et al., 2016), which allows to reduce the noise of the SSS maps (Turiel et al., 2014) without loosing effective spatial resolution . The application of this technique is aimed at improving the spatio-temporal resolutions of the Baltic+ L3 SSS maps to approach user requirements (Baltic+ team, 2019).

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The same SST data that is used as auxiliary data in the SSS retrieval, is used here as template in the fusion scheme. L4 SSS maps are produced with the same spatio-temporal resolutions as the template, i.e., daily maps at a spatial grid of 0.05 • × 0.05 • .
Before applying the fusion, the salinity field from CMEMS Baltic reanalysis is used to complete the coverage where SMOS L3 SSS is not available. Salinities from reanalysis are previously filtered by using the SIF information available in the OSTIA SST product. Figure 10 shows the number of times per year (as ratio to one) where the salinity reanalysis is used at each grid cell of 340 the L4 map. Overall, those regions with extrapolated values coming from the reanalysis are reduced to the gulfs, Bothnian Bay and in those cell grids closest to coast. As it can be observed, during the first period of the mission (mainly during 2011-2012), the reanalysis is also occasionally used in other regions when the maps are strongly affected by RFI contamination (Oliva et al., 2016). For filtering purposes, a flag included in the product indicates if the SSS provided at each pixel comes from an extrapolated reanalysis value.

Estimation of the L4 SSS error
To assess the inherent uncertainty of the L4 SSS product, the Correlated Triple Collocation (CTC) method is used (González-Gambau et al., 2020). When applying CTC, the data are assumed to represent similar spatio-temporal scales with two of the datasets possibly having correlated errors. Under these conditions, CTC can be used to obtain maps of error variances of triplets of remote sensing SSS maps. 350 We consider three sets of collocated SSS maps in the period 2016-2018: (i) Baltic+ L4 SSS product, (ii) CMEMS Baltic reanalysis product (Axell, 2019) and (iii) the BSIOM hindcast simulation (section 2.1.6). As it is shown in Figure 8, the L3 SSS error during the cold season is higher than in the warmer season. Since the expected errors are quite different between both seasons, we performed the CTC analysis for the warm and the cold seasons separately. This analysis is done with all the products reduced to the common resolution (that of Baltic+ L4, 0.05 degrees and daily frequency). Figure 11 shows the  The data collected from these vessels pass quality control checks before being distributed to the science community. All the ship routes available for the validation of Baltic+ SSS products are collected in Table 2. They are used for validation depending on data availability (i.e. each ship track has different operating time) and its quality check passed as "good data".

Collocation strategy of satellite-in situ data
The collocation strategy we follow for the comparison to in situ is the following: • Spatial collocation 405 -Ferrybox lines: These datasets provide SSS information at a very high temporal frequency. The location of in situ data are gridded to the nearest satellite grid cell, so, all the in situ measurements corresponding to the same cell grid in the satellite SSS product (0.25 • in the case of the L3 product and 0.05 • in the L4 product) are averaged.
-SeaDataNet: In this dataset the temporal sampling is quite sparse. Several measurements in depth are available at each station. We consider that the water in the upper 5 meters is homogeneously mixed and it is representative of 410 the surface water. Thus, we keep the shallowest measurement acquired between [1-5] meters depth, to be compared with the satellite SSS. The location of in situ data are referred to the nearest satellite grid cell and compared to the corresponding Baltic+SSS measurement. In this case, in contrast to the case of the Ferrybox measurements, almost no average of in situ in a single grid is expected.

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-For all the datasets, all the in situ available in the 9 days (for L3 product) of SMOS data used to generate the product, and in the same day (for L4 product) of the map are considered in the comparison.

Quality metrics for the comparison to in situ
The quality assessment of the SSS satellite retrievals results from the comparison against the reference datasets presented in sections 3.1.2 and 3.1.3. The validation metrics are based on statistical measurements of the difference between the two 420 quantities at the collocations (∆SSS = SSS sat − SSS insitu ).
The following metrics are computed both for Baltic+ L3 and L4 SSS products: • Global statistics of ∆SSS for the datasets per year.
• Analysis of the products performances in the cold and warm seasons separately. The separation in these two periods is based in the expected SST ranges for the different months and the expected SSS error due to those SST values. The cold 425 season ranges from November to May (average temperature of 3.9 • C) and the warm season refers to the period of June to October (average temperature of 13.4 • C). This analysis per seasons is devoted to assess if a quality improvement is observed during the warmer months, since the sensitivity increases and lower SSS errors than at colder temperatures are expected.
• Maps of the spatial distributions of ∆SSS statistics: the temporal mean and the temporal standard deviation of ∆SSS 430 are computed per each grid point in the map. This metric is devoted to track the possible origin of the errors (residual land sea contamination, sea-ice contamination, ice contamination itself, etc).

Correlated Triple Collocation
The three satellite SSS products with the best temporal and spatial coverage (see section 3.1.1) are inter-compared. It must be pointed out that the salinity values provided by each one of the three satellite products are very different between them. We 435 applied the CTC analysis using one year period (2016), which suffices to evaluate the performance of the datasets. Three sets of collocated SSS maps are considered: JPL SMAP v4.2 SSS, 8-day maps; REMSS SMAP v4.0 SSS, 8-day maps and Baltic+ L3 SSS, 9-day maps. We only consider Baltic+ L3 SSS here because it is the product with similar spatio-temporal resolutions as JPL and REMSS SMAPS maps, a condition needed to apply the CTC method. In this triplet, the two variables with correlated errors are the JPL and REMSS products, both from SMAP measurements. Time collocation is done by identifying the first 440 day of the three periods used in the generation of the corresponding maps. As JPL SMAP and REMSS SMAP maps are 1-day shorter, time collocation is not perfect but differences are considered to be negligible taking into account the orbital gaps in a 9-day period. Spatial collocation is straightforward, since the three products are provided in the same grid.

Baltic+ SSS variability and comparison to reanalysis and in situ data
The objective of this assessment is to analyse the SSS dynamics captured by Baltic+ SSS products and the CMEMS Baltic 445 reanalysis (Axell, 2019) and to compare them to the 22 in situ observation stations visited by research vessels (Figure 13).
Those stations are intended to cover different types of sea areas: from coastal regions to open sea. We choose the uppermost salinity observations, which means observations from 1 -1.5 meters depth.
Time-series of Baltic+ L3 and L4 SSS products are analysed and compared to the salinity provided by the CMEMS Baltic reanalysis and the in situ measurements. For that, we define boxes over given regions of interest where, both, the reanalysis 450 salinity and the Baltic+ L3 and L4 SSS products are averaged and compared to the in situ stations that are located in the region defined by each box. The boxes used for each region are shown in Figure 13.

Comparison to FerryBox lines salinity
All the in situ measurements from the different ferry routes are analyzed per year. The statistics are computed considering all 455 the collocations available for the Baltic+ L3 SSS product and FerryBox data (see Table 3, first row). Note that the number of match-ups corresponds to all the collocated measurements of SMOS and ferry data. In overall, similar statistics are obtained for all the years. In the year 2012 there is a significant reduction of the accuracy due to the strong RFI affectation in the North Atlantic for that period (Oliva et al., 2016). Slightly higher biases are found for years 2014 and 2015.  Table 3. Global statistics Baltic+ L3, L4 and filtered L4 (not considering extrapolated measurements from reanalysis) SSS products against FerryBox in situ data. Note the high variability in the number of match-ups is due to the different cruises operated each year.
To analyse the spatial distribution of the differences (∆SSS) between the Baltic+ L3 SSS product and the in situ provided 460 by ferry lines, we compute the mean of ∆SSS (Figure 14), and the standard deviation of ∆SSS (Figure 15), for all the measurements accumulated during one year, for each cell of the Baltic+ L3 SSS product grid. The number of match-ups is shown in Figure 16. Note that only grid cells with more than 10 accumulated measurements are considered. Higher standard deviation values are obtained for those cells closer to coast and ice edges, particularly close to Gotland, in the Arkona and Bornholm basins, and in the Bothnian Bay. Errors in these regions notably increase the standard deviation when computing the 465 statistics considering all the match-ups differences (see Table 3,first row).
To analyze the spatial distribution without the effect of the non-homogeneous spatial sampling, the histograms of the spatial distributions of the mean and the standard deviation of ∆SSS are computed (not shown). The most probable value of the mean  Global statistics are also computed considering all the collocations available for the Baltic+ L4 SSS product and FerryBox data (see Table 3, middle row). We can observe a clear reduction of the standard deviation and an increase of the correlation coefficient with respect to the statistics computed for L3 SSS product (see Table 3, first row). Similar biases to the ones for L3 product are found for the L4 product. This is expected because the fusion methodology aims at reducing the standard deviation of the error but not the biases present in the original L3 maps (Turiel et al., 2014). 475 We compute also global statistics of the collocations of Baltic+ L4 SSS and FerryBox data per year, considering only those Baltic+ L4 SSS that come from the L3 SSS (i.e., extrapolated data from reanalysis are filtered out) (see Table 3, last row). As it can be seen by comparing to the statistics considering all the measurements in the L4 product (Table 3, middle row), statistics have not significantly changed.
The spatial differences between the L4 SSS and the SSS provided by ferry data are computed in 0.05 • grid of the L4 480 product (not shown). However, due to the low number of accumulated measurements for each grid cell, measurements are accumulated in a coarser grid (0.25 • ) to have significant statistics (see Figures 17, 18, 19). Besides, grid cells with accumulated measurements lower than 10 are filtered out. The standard deviation is reduced in all the basin with respect to the L3 product (see Figure 18 in comparison to Figure 15). The histograms of the spatial distributions of the mean and the standard deviation

Comparison to SeaDataNet salinity
Global statistics are computed considering all the collocations available for the Baltic+ L3 SSS product and SeaDataNet data per year (see Table 4, first row). In overall, statistics are in agreement to the statistics of the comparison to the FerryBox data.
However, higher values of standard deviation are obtained. This is likely due to the fact that Arkona and Bornholm basins are 490 highly sampled with respect to the rest of the Baltic Sea and these regions present higher SSS errors.
The spatial distribution of the SeaDataNet in situ measurements allows us to analyse the performances of the Baltic+ L3 SSS product in the whole Baltic basin and the influence of the proximity to land and ice edges in the quality of the Baltic+ SSS products. We compute the mean of ∆SSS and the standard deviation of ∆SSS for all the measurements accumulated for each cell of the Baltic+ L3 SSS product grid. Measurements are accumulated in the original L3 grid (0.25 • ) for all the 9 years, 495 since there are not enough in situ observations to perform the analysis per year separately, as we do in the case of FerryBox data. Since the number of match-ups is still quite limited, we compute the same maps by accumulating the measurements in a 0.5 • . In this way, we increase the number of measurements in each cell to get significant statistics. In addition, all those grid cells with less than 10 measurements are discarded. Higher errors are detected in Arkona and Bornholm basins, which are highly sampled regions. We also repeat this spatial analysis for the cold and the warm seasons. In the warm season the standard  Table 4, middle row). Overall, statistics are in agreement to the statistics of the comparison to the ferry data.

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However, higher values of standard deviation have been obtained. This is likely due to the fact that Arkona and Bornholm basins are highly sampled with respect to the rest of the Baltic Sea basin and these regions present higher SSS errors. In any case, the improvement in terms of the standard deviation and correlation coefficient with respect to the L3 SSS product is very significant (see Table 4, first row).
Global statistics are also computed considering all the collocations available for the Baltic+ L4 SSS product when the 510 extrapolation of the reanalysis data is not considered and SeaDataNet data per year (see Table 4, last row). As it can be observed by comparing to the statistics when considering all the measurements in the L4 product, statistics have not significantly changed for most of the years. Higher differences are found for years 2011 and 2012, where the extrapolated data are not limited to the coastal pixels (see Figure 10).
The spatial distribution of the differences between the Baltic+ L4 SSS product (considering all the measurements) and the in 515 situ provided by SeaDataNet is also analyzed. For that, we compute the mean of ∆SSS and the standard deviation of ∆SSS for all the measurements accumulated in each cell of a 0.5 • grid (to get significant statistics) (see Figure 21). Measurements have been accumulated per all the 9 years since the match-ups are not enough to perform the analysis per year separately.
In agreement to the analysis of the L3 product, higher errors are detected in Arkona and Bornholm basins, which are highly sampled regions. We perform this spatial analysis for the cold and the warm seasons separately. Once again, for the warm 520 season the standard deviation is reduced with respect to the cold season, as expected. The most probable value of the mean ∆SSS for the L4 product is -0.25 in the cold season and -0.35 during the warm season. For the standard deviation of ∆SSS, the most probable value is around 0.47 in the warm season while during the cold season is around 0.53.

Estimated SSS uncertainty by CTC
Maps of the estimated error standard deviations per each SSS dataset are shown in Figure 22. Notice that the estimated errors 525 for the Baltic+ L3 SSS are in agreement with the differences found with respect to in situ measurements (see sections 3.4.1 and 3.4.2). Differences between both SMAP products and the Baltic+ L3 SSS are shown in Figure 23. As shown in the figure, the Baltic+ L3 SSS product has the smallest error in the whole basin, except in some grid points of the Bothnian Bay, where the SMAP REMSS product presents a lower error. The analysis of the Baltic+ L3 SSS product and the comparison with the other satellite products reveals that the Baltic+ L3 530 SSS product is currently the satellite-derived SSS product with the lowest salinity error among the currently available products, highlighting specially the improved spatial coverage and oceanographic resolution. Figure 24 shows the spatio-temporal collocations of the Baltic+ L3 and L4 SSS products and reanalysis with in situ measurements. It must be pointed out that the sampling frequency is too low to capture some relevant events in some in situ stations, but this work is hindered by the low temporal coverage of the data and lack of measurements from the eastern part of the Gulf of Finland. Same is also true for other sub-basins of the Baltic Sea and, especially, for the northern parts (Bothnian Sea and 545 Bothnian Bay), where monitoring data is still too sparse. Thus, the new products will foster model development and provide the possibility to assimilate SSS fields derived from space assets.  Table 4. Global statistics Baltic+ L3, L4 and filtered L4 (not considering extrapolated measurements from reanalysis) SSS products against SeaDataNet in situ data.

Conclusions
In this work, we present the first regional satellite-derived SSS maps over the Baltic Sea. To date, these are the unique dedicated remote sensed SSS products available over the region, mainly due to the technical difficulties for retrieving SSS from satellite and in the SSS retrieval from satellite L-band measurements in general.

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Baltic+ SSS products are proved to have a good spatio-temporal coverage with an accuracy of 0.7-0.8 psu for the L3 product (9-day, 0.25 • ) and around 0.4 psu in the case of the L4 product (daily, 0.05 • ). Regions with higher errors and limited coverage are located in Arkona and Bornholm basins and Gulfs of Finland and Riga (section 3). The impact assessment of Baltic+ SSS products reveals that they provide valuable information about the changes in the salinity gradients and about the temporal variability in the sea surface salinity. They also show a geophysically-consistent seasonal variability in surface salinity, which 560 results from the melting of sea ice in spring and increased run-off from land when snow cover melts after the winter.
For all the above, Baltic+ SSS products can help in understanding the salinity dynamics of the basin. On one hand, this EO SSS data can fill the temporal and spatial observational gaps in the region left by the very sparse in situ measurements. On the other hand, Baltic+ SSS products can also be useful for the validation and improvement of numerical models. Besides, the capability of the Baltic+ SSS product to map the horizontal gradients and their variability is of much value to evaluate the 565 performance of models, and provide the possibility to assimilate SSS fields.
Several scientific studies with Baltic+ SSS data are currently in progress, such as (i) the analysis of the consistency between the structures detected in the Baltic+ SSS products with the ones detected in the SST and in the DOT (Dynamic Ocean working in the Baltic, and in particular with Baltic Earth Working Group on Salinity Dynamics, has allowed to identify that Baltic+ SSS products can help in some knowledge gaps (Lehmann et al., 2021), such as (i) the determination of the SSS annual trends in the basin in the last decade, and (ii) the study of the inflow and outflow dynamics at the entrance of the North Sea.
For these potential applications, some additional technical developments in the product would be appropriated, mainly focused in applying a temporal correction of SSS maps without using external references, and applying fusion techniques at brightness 575 temperature level for improving their quality in terms of coverage and spatial scales.
integrating the seasonal averaged Baltic+ L4 SSS maps in HELCOM web map service. Last but not least, the authors want to acknowledge the anonymous reviewers and the editor for their valuable and helpful comments.