After more than 10 years in orbit, the Soil Moisture and Ocean Salinity (SMOS) European mission is still a unique, high-quality instrument for providing soil moisture over land and sea surface salinity (SSS) over the oceans. At the Barcelona Expert Center (BEC), a new reprocessing of 9 years (2011–2019) of global SMOS SSS maps has been generated. This work presents the algorithms used in the generation of BEC global SMOS SSS product v2.0, as well as an extensive quality assessment. Three SMOS SSS fields are distributed: a high-resolution level-3 product (with DOI

The European Space Agency (ESA) Soil Moisture and Ocean Salinity (SMOS) satellite was launched in November 2009, carrying the first orbiting radiometer that collects regular and global observations from space of two Essential Climate Variables (ECV) according to the Global Climate Observing System: sea surface salinity (SSS) and soil moisture (SM)

The Barcelona Expert Center (BEC) was created in 2007 to support the Spanish contribution to SMOS mission activities. Since the beginning, BEC’s goals have been to contribute to the quality assessment and the development of algorithms for the retrieval of geophysical variables from SMOS data as an ESA Level 2 Ocean Salinity Expert Support Laboratory and to the calibration and validation activities as a Level 1 Expert Support Laboratory. In recent years, BEC has developed a SMOS SSS internal processing chain that generates SSS maps from SMOS raw data (level 0) to levels 3 and 4 (L3 and L4 added-value SSS maps), thus allowing the integration of improvements in the different levels of the processing. The resulting products are freely distributed through a SFTP service (

In this work we present the new reprocessing of the BEC SMOS SSS global L3 and L4 products v2.0 for a 9-year period comprising 2011 to 2019, which comes with an improvement of the currently used methodology. This new reprocessing is focused on four aspects.

To assess the performance of the BEC SMOS SSS product v2.0, the complete 9-year time series of SSS maps is first compared with the salinity measurements provided by Argo. Secondly, an extensive battery of validation methods is applied to 1 year (2017) of data, and the results are compared with three other satellite and one reanalysis SSS products. Those methods are (i) statistics of the differences with Argo salinity match-ups; (ii) singularity analysis to assess the geophysical consistency of the data (

This paper is structured as follows. Section

The brightness temperatures (TBs) obtained from the SMOS MIRAS L1B v620 product provided by ESA are used as the input for the SMOS SSS retrieval. This data set is freely available at

The L1B v620 product contains the Fourier coefficients of the measured brightness temperatures. Starting from this product, using ESA's Earth Observation Customer Furnished Item (EOCFI) orbit propagation libraries

The Operational Sea Surface Temperature and Sea Ice Analysis (OSTIA) (see

The auxiliary data used for the SSS retrieval are provided by the European Centre for Medium-Range Weather Forecasts (ECMWF)

We have used as multiyear salinity reference the annual climatological salinity value provided by the World Ocean Atlas 2013 (WOA2013) at

The debiased non-Bayesian (DNB) retrieval approach proposed in

For the retrieval of raw SSS, the difference between the first Stokes TB measured and modeled is optimized as a function of the salinity value. A geophysical forward model links the modeled TB to the SSS. Besides the dielectric constant model proposed by

All the raw salinity retrievals over 9 years (

We have defined an estimator of the “typical value” or central estimator of the ensemble

Then, we have computed SMOS debiased SSS anomalies (

Finally, the debiased salinity value for the acquisition conditions

The retrieval algorithm proposed above effectively removes local biases, especially those produced by the land–sea contamination and artifacts produced by permanent radio frequency interference (RFI) sources.

Each value of raw salinity

Filtering out degraded measurements in the generation of the SMOS SSS maps is a key aspect. Without applying any filter, the error may become too large for many scientific applications; on the other hand, when the filtering criteria are too strict, the coverage of maps may be dramatically decreased, and part of the geophysical variability may be lost. In

We apply the following filtering criteria.

it contains more than 100 salinity retrievals,

the standard deviation of its distribution is lower than 10 psu,

the absolute value of the skewness of the distribution is lower than 1, and

the kurtosis of the distribution is greater than 2.

SMOS measurements are affected by biases that depend on time (see

The corrections applied so far aim at systematic biases which are time-independent or space-independent and therefore can be corrected separately. However, after applying both corrections, residual biases depending at the same time on time and on the geographical position are still present (see top panel in Fig.

We compute SMOS monthly climatologies

For each month

We fit

After computing the optimal polynomials

After applying all the above corrections, we make the last check. By construction, at each geographical location the average salinity of the full period should be equal to the multiyear reference introduced in Sect.

Difference between the 2011–2019 average of BEC SSS maps after applying corrections described in Sect.

We use the multifractal fusion techniques introduced in

By means of this multifractal fusion method, SMOS L4 SSS maps with the same spatial and temporal resolutions as the template (OSTIA SST), i.e., daily maps at a spatial grid of

The BEC SMOS SSS L3 global product v2.0 consists of 9 d SSS maps at a regular grid of

the BEC SMOS HR SSS product, where HR stands for high resolution and contains the binned salinity field

the BEC SMOS LR SSS product, where LR stands for low resolution and is a low-pass-filtered version of

The BEC SMOS L4 SSS product v2.0 (hereafter BEC L4) consists of daily SSS maps at a regular grid of

We have compared the performance of the new BEC products with that of other satellite SSS products. We have centered the validation in the year 2017 because there are not any large-scale geophysical phenomena (such as El Niño or La Niña events) and also because SSS products produced by the National Aeronautics and Space Administration (NASA) Soil Moisture Active Passive (SMAP) mission are available (this mission has been operating since early 2015;

For the purpose of direct comparison of values, we have used in situ salinity data obtained by Argo profilers

We are also interested in analyzing the strengths and weaknesses of the satellite products when compared with a reanalysis product. To this end and for completeness, we have used the SSS fields provided by near-real-time ARMOR3D

OSTIA SST is used as a reference to assess the spatial structure, geophysical consistency, and effective resolution of the SSS satellite products (see Sect.

Assuming that Argo values represent a ground truth (which is, we neglect representative errors that are however significant), we have used Argo SSS to assess the biases and the standard deviations of the errors of the different SSS products. To that goal, we temporally and spatially collocate the Argo SSS with the SSS maps as follows: every map is compared with the Argo SSS available during the same period (9 d in the case of BEC products) used in the generation of that map. We compare the Argo SSS with the value of the SSS product corresponding to the cell where the Argo is located. Before computing the match-ups between Argo and SSS products, we apply the following quality control over the values of Argo SSS.

The cut-off depth for Argo profiles is taken between 5 and 10 m.

Profiles from BioArgo and those included in the grey list (i.e., ﬂoats which may have problems with one or more sensors) are discarded.

We use WOA2013 as an indicator: Argo ﬂoat profiles with anomalies larger than 10

Only profiles having temperature between

Singularity analysis can be used for the assessment of the geophysical consistency among different products

SE for the 15 August 2017.

A way to assess the correspondence of SEs is to calculate conditioned histograms of one product SSS SE,

The histogram of a variable conditioned by the value of another variable serves to evidence any functional dependence between both. Conditioned histograms have been used to put in evidence the correspondence of singularity exponents of two variables

In the following, we detail the methodology employed in this work.

the most probable value of

the mean value of

the standard deviation of

Spectral analysis has been extensively used to analyze satellite observations, in situ data, and model outputs, in both the atmosphere and the ocean

Theoretical studies predicted that temperature and salinity should have the same spectral slopes

Therefore, both spectral methods are complementary from a validation point of view as PDS analysis gives information on the effective spatial resolution of the data, and the SPS method assesses the existing geophysical structures beyond the remaining sources of uncertainty in remote sensing products.

The spectral analysis approach that we have followed in this work is the following one.

We perform the spectral analysis over the same ocean regions proposed in

At each on of these regions, we compute the PDS from each SSS product and the OSTIA SST, as well as their corresponding SPS from their SE maps. Both spectra (PDS and SPS) are given as a function of wavenumber values per degree (latitude degrees for meridional regions and longitude degrees for zonal regions) and as wavelength values in kilometers. Recall that a wavelength contains a full oscillation from 0 to

For each region and product, we have computed the mean PDS and the mean SPS over the full year of 2017 to reduce the fluctuations of each individual spectrum.

We have computed and analyzed the slope of the averaged PDS and SPS, and we have compared them with the ones resulting from OSTIA SST.

Spatial distribution of Rossby radii of deformation, from

The triple collocation (TC) technique is a powerful tool to estimate the standard deviation of errors of three spatio-temporally collocated measurements of the same target. TC has been used to assess the quality of many remotely sensed variables, and in particular SSS

We have used a recently developed formulation of the triple collocation method, the correlated triple collocation (CTC), for the case of three data sets that resolve similar spatial scales from which two of them present correlated errors

The triplets used in this analysis are shown in Table

SSS triplets used in the analysis performed in Sect.

In order to estimate the SSS error of each product, we average the estimated errors resulting from each one of the triplets where the product is considered. We also compute the standard deviation of the estimated error in the different triplets as a metric of the uncertainty in the error estimation.

In the first part of this subsection, we present the comparison of the 9-year time series of the BEC SMOS SSS products with Argo SSS; then, in the second part, we extend the comparison to the rest of the SSS products (see Sect.

Ocean regions used in the statistics with respect to Argo SSS.

Statistics of the comparison of the BEC global SSS product v2.0 with Argo.

Table

In terms of mean differences with respect to Argo (which would account for biases in the products, if we consider Argo to be the ground truth), the three BEC products (HR, LR, and L4) provide very similar performances. The BEC SSS v2.0 products have a mean difference with respect to Argo below 0.02 and 0.06 psu, in GLO and in TRO, respectively. Those values are rather small and may be statistically non-significant.

Regarding the standard deviation of the differences with respect to Argo salinity, among the three salinity fields of the v2 product, BEC HR is the one with the largest standard deviation and L4 the one with the lowest (BEC LR is in between the other two). This is expected since BEC HR is known to have some high-spatial-frequency noise, while BEC LR is a smoothed version of the BEC HR salinity with a radius of 50 km, and therefore a reduction in the noise is expected. The fusion technique used in the generation of the L4 also leads to a reduction of the random noise of the salinity maps, and it is even better than a simple low-pass filtering as it preserves fine-scale structures. The standard deviations of the differences between BEC products and Argo salinity range between 0.34 and 0.26 psu in the case of L3 HR, 0.27 and 0.24 psu in the case of BEC LR, and 0.24 and 0.21 psu in the case of L4. There is a significant reduction of the standard deviation of the differences between SMOS and Argo since 2017, which is more significant in the case of the BEC HR product. We have analyzed several possible reasons for this reduction. One reason could be a reduction of RFI contamination, which has been observed at the global scale since 2017. Another reason could be a change in the spatial scales of the auxiliary data provided by ESA and what are used in the retrieval. Since 2017, the ECMWF auxiliary data (see Sect.

We have calculated the statistics of the comparison with Argo SSS in the regions defined in Table

Regional statistics of the differences between the SMOS and Argo SSS for the year 2017. For each product and ocean region the mean, standard deviation, root mean square of the difference, and coefficient of correlation

Regional statistics of the differences between the SMAP and Argo SSS for the year 2017. For each product and ocean region the mean, standard deviation, root mean square of the difference, and coefficient of correlation

Regional statistics of the differences between the satellite and Argo SSS for the year 2016. For each product and ocean region the mean, standard deviation, and root mean square of the difference are provided separated by a colon.

Figure

Spatial distribution of the mean differences with respect to Argo SSS. From left to right and top to bottom: BEC HR, BEC LR, JPL, REMSS, CATDS, and CMEMS.

Spatial distribution of the standard deviations of the differences with respect to Argo SSS. From left to right and top to bottom: BEC HR, BEC LR, JPL, REMSS, CATDS, and CMEMS.

We have also analyzed the spatial arrangement of the standard deviations of the differences between the gridded products and Argo SSS in

Figure

Hovmöller diagrams of the mean difference between salinity gridded products and the temporally and spatially collocated uppermost salinity measurement provided by Argo floats. The

We have also analyzed the temporal evolution of the difference with Argo statistics in Figs.

Regional statistics of the comparison with respect to Argo salinity. The numbers in the label plots correspond to the different products that are compared with Argo SSS: 1-BEC HR, 2-BEC LR, 3-CATDS, 4-JPL, 5-REMSS, 6-CMEMS, and 7-BEC L4.

Mean of the differences between the gridded SSS products and Argo salinity in different ocean regions for the year 2017.

Standard deviation of the differences between the gridded SSS products and Argo salinity in different ocean regions for the year 2017.

Regarding the temporal evolution of the standard deviation, there are some significant seasonal effects. For example, in the Northern Hemisphere, Arctic, and North Atlantic regions, the standard deviation is larger in winter than in spring–summer. This is expected because L-band TBs are less sensitive to the SSS in cold waters (wintertime) than in warm waters (summertime), which implies that the retrievals of SSS must be noisier in winter than in summer. However in the North Pacific, all the satellite products present the inverse behavior: a reduction of the standard deviation is present at the end of the year. The reason for this decrease is still under study. In the Amazon River region, the standard deviation increases in spring and summer. The reason for this increase could be related to the seasonal behavior of the North Brazil Current and the North Brazil Current retroflection that has a seasonal behavior which is manifested in the SSS

In this section we take the SE of OSTIA SST as a reference to assess the effective spatial resolution of the salinity products. The OSTIA SST product is not perfect and it also has some limitations in describing the small spatial gradients of SST, which could be reflected in the results of this comparison.

Figure

Histogram of SEs of SSS conditioned to the SEs of OSTIA SST. For each SST SE bin, the corresponding SSS SE distribution is normalized by the total number of SSS SEs. The black line corresponds to the mode of the SE SSS at each bin of SE SST (

All the conditioned histograms present three different well-defined ranges. The first part of the curve is unstructured and noisy: this is normal because there are very few points with those values, so the statistics are scarce and fluctuations are large; it is also affected by small mismatches in the positions of fronts, lack of accuracy of the sensors, and, very occasionally, different singularity-inducing effects acting on each variable. Then, we find a central part where the relation between

All the products present no correlation between

We observe that the value of the

Singularity analysis metrics of the SSS products over three different SST SE regimes:

Figures

From left to right in the following are shown: the most probable SSS SE value as a function of the SST SEs, the mean SSS SE value as a function of the SST SEs, and the standard deviation of the SSS SEs for each SST SE.

For a better comparison, Fig.

Power density spectra of the different SSS products.

Singularity spectral analysis of the different SSS products.

Slopes of the power density spectra

We observe a large diversity in the shapes of the SSS PDS (Fig.

BEC HR (in orange) presents the ﬂattest values of the PDS slopes, being higher than

The CMEMS product (in grey) presents the steepest PDS slope, becoming lower than

CATDS (in green) presents the ﬂattest PDS slope in the SPAC region (

BEC L4 (in red) presents the closest PDS to those of OSTIA SST. Its SPS slopes remain in the range of

Below 100 km, except for BEC HR, all spectral slope values get steeper (lack of signal variability into the data). REMSS (cyan line in Fig.

SSS error estimation by triple collocation, from top to bottom and left to right: BEC HR, BEC LR, BEC L4, JPL, REMSS, and CATDS.

Uncertainty in the SSS error estimation by triple collocation from top to bottom and left to right: BEC HR, BEC LR, BEC L4, JPL, REMSS, and CATDS.

Spatial distribution of the products with the minimum SSS estimated error.

Figure

We assign one number to each product to assess which is the product with the lowest estimated error standard deviation at each ocean location. We have not included the uncertainty associated with the estimation of the salinity error in this computation. This implies that, although we represent one map with a single product only at each grid point, after considering the uncertainty of each estimation, several products could provide a similar performance from a statistical point of view. In particular, the estimated error in regions of large salinity variability presents larger uncertainty than in regions of low salinity variability (see Fig.

The results obtained from triple collocation provide a complementary view to the comparisons with Argo floats (see Sect.

For sampling, the in situ measurements are provided over a few samples while the satellite data are synoptic. The dynamics displayed by the in situ measurement could be strongly conditioned by its sampling. Therefore, the results from the comparison could not be completely representative of the quality of the satellite product in the considered region.

The spatial and temporal scales of the in situ and satellite measurements are different. The in situ measurements provide punctual and instantaneous measurements while satellite measurements correspond to an integrated measure of several days and a footprint of several square kilometers.

The in situ measurements are typically given at several meters depth while the satellite data provide the salinity at a few centimeters depth.

The product is available for visualization purposes on the website of the

We have presented 9 years of the new release of SMOS SSS global products generated at the Barcelona Expert Center: the BEC SMOS SSS global L3 and L4 products v2.0. The methods used in their generation include several improvements with respect to the previous version of these products: (i) a new latitudinal–seasonal debiasing has been included; (ii) improved filtering criteria based on the salinity geophysical variability have been applied, which allows a better description of the salinity gradients without increasing the overall noise error in the maps; (iii) new interpolation schemes are proposed to allow better description of small-scale spatial features that are especially relevant in coastal regions; (iv) the fusion scheme used in the generation of the L4 product has been modified to preserve small-scale spatial features; and (v) an estimation of the salinity uncertainty is provided in the new products.

We have performed an extensive validation of the BEC SMOS SSS products v2.0. For doing this, we have compared the 9-year time series of the new BEC SMOS SSS with Argo uppermost salinity, and we have also compared the performance of BEC products with the other three satellite SSS products (the SMOS product produced at CATDS and two SMAP products generated by REMSS and JPL) and the reanalysis product distributed by CMEMS, but in this case restricted to the year 2017. The main conclusions of this comparisons are as follows.

The statistics of the comparisons with Argo salinity evidence a competitive performance in comparison with the statistics of the rest of the SSS products. This includes small mean and standard deviation of the differences with respect to Argo SSS (in the global and regional statistics, latitudinal biases, and stable differences in terms of temporal evolution). In this sense, the mean differences with respect to Argo SSS among the three BEC products (BEC L3 (HR and LR) and BEC L4) are very similar (being lower than 0.02 psu at a global scale), but the standard deviation is significantly different among them, with the BEC HR being the one with the largest standard deviation (lower than 0.34 psu at a global scale) and BEC L4 the one with the lowest deviation (lower than 0.27 psu).

In terms of effective spatial resolution and geophysical consistency, we have used two different metrics.

We have also computed an estimation of salinity errors by using triple collocation. Among the BEC products, BEC L4 provides the SSS field with the lowest error, but in regions strongly affected by rainfall and continental freshwater discharge, the L3 products (BEC HR and BEC LR) are better in terms of salinity error. When we compare all satellite products, BEC L4 remains as the product with the overall minimum salinity error.

EO is responsible for the development of the generation algorithms. She has generated the BEC product and is the main contributor to the writing of this paper. CG is responsible for the distribution of the products. The validation of the products has been carried out by CG, NH, MU, and EO. VG is the specialist for L1 data and calibration; she is also responsible for the triple collocation algorithm development and implementation. JM implemented all the algorithms for the correction of data at L2, as well as its georeference. CG is the specialist in high-latitude salinity and contributed to the discussion of the issues at polar regions, jointly with JM. AT is the head of the BEC. He has participated in the development of all the algorithms (both product generation and validation). He supervised the whole paper, improving the mathematical and oceanographic description of several sections. All the coauthors have contributed in the writing and revision of the paper.

The authors declare that they have no conflict of interest.

This work represents a contribution to the CSIC Thematic Interdisciplinary Platform PTI Teledetect. Argo data were collected and made freely available by the International Argo program and the national programs that contribute to it (

This work has been carried out as part of the Copernicus Marine Environment Monitoring Service (CMEMS) Land-Marine Boundary Development and Analysis (Lambda) project. This work was funded by the Ministry of Economy and Competitiveness, Spain, through the National R&D Plan under L-BAND project ESP2017-89463-C3-1-R and previous grants and by the European Space Agency through the contract CCI+ Salinity and SMOS ESL L2OS.

This paper was edited by Giuseppe M. R. Manzella and reviewed by two anonymous referees.