*2.4. Input Data Preparation: Simulating the SSS Observations*

Here, we discuss the generation of the synthetic in situ and CIMR SSS observations.



**Table 1.** CIMR instrument measurement frequencies.


**Table 2.** Variability range of the LUT quantities used in [19].

Based on the LUT estimates, we could generate a time series of daily L4 *σ*SSS. This was achieved relying on the daily SST-OWS-TCLW and TCWV observations provided by AMSR-2 [14] plus the daily MERCATOR SSS. In order to fill the gaps in the AMSR-2 observations, we used a linear interpolator, leading to a gap-free proxy of the *σ*SSS behaviour. However, in order to rely on higher quality data, the areas relying solely on interpolation were not taken into account when running the OI algorithm. This is further justified at the end of this section and schematically represented in Figures 4 and 5. Checking different SSS-SST-OWS-TCLW-TCWV combinations, we found that the local low SST and high OWS are primarily responsible for the *σ*SSS increase, consistently with [19]. An example of the *σ*SSS is provided in Figure 2.

**Figure 2.** *σ*SSS computed according to [19], example from 1 January 2016. The additional information in white are referenced in Section 3.2.1.

Based on these results, we added a white random Gaussian noise to the MERCATOR-SSS according to Equation (3):

$$\text{SSS}\_{\text{noise}} = \text{SS} + \text{WGN}(\sigma \text{SSS}), \tag{3}$$

where WGN(*σ*SSS) stands for a *σ*SSS dependent White Gaussian Noise. Figure 3 shows an example of the MERCATOR SSS after addition of the white noise. In the present work, only white noise has been taken into consideration. While actual errors would likely include instruments drift or other variations with time, these effects are still in evaluation [12]. For the moment, the error estimates (as also stated by [19]) are mostly based on the local ocean-atmosphere conditions at the measurement site. The impact of the CIMR radiometric and orbital stability on the global L4 SSS estimates maps is thus left for future investigations.

**Figure 3.** (**a**) MERCATOR SSS, 1 January 2016, Gulf Stream area; (**b**) MERCATOR SSS with addition of white noise according to Equation (3); 1 January 2016, Gulf Stream area.

In order to simulate the CIMR coverage, we used the 28-days cycle of the CIMR satellite overpasses over Earth provided by the European Space Agency, remapped onto a regular 1/4◦ grid. Such 28 days cycle was applied to our time series of MERCATOR SSS, arbitrarily assuming that the first day corresponds to 1 January 2016 and repeating the cycle throughout the year. The number of overpasses (NVIS) per day is between 0 (in a few small areas of the tropics) and 11 (in polar regions) (Figure 4a). In all the areas where NVIS exceeded 1, we used an averaged SSS obtained as follows: we oversampled the MERCATOR SSS according to NVIS (adding each time a different random Gaussian noise) and then computed the mean SSS in each grid box.

As a final step, in order to make the synthetic satellite-derived SSS more realistic, we derived a sea-ice mask, land mask and rainfall observations mask (i.e., a no observation mask) using the REMSS AMSR-2 SST L3U observations [14]. This is also schematically represented in Figure 4a–c. Except for extreme cases, L-band brightness temperatures are not significantly affected by precipitation, remaining within the CIMR radiometric accuracy [12,20]. In principle, this means a SSS retrieval is possible. However, in these cases, since higher frequency channels are significantly affected by precipitation, the retrieval would require ancillary information on relevant geophysical variables (e.g., SST and OWS). This would require an independent evaluation of the expected uncertainty on the SSS retrieval.

**Figure 4.** Simulating the CIMR observations from the MERCATOR SSS. (**a**) expected CIMR coverage; (**b**) daily mask for land, sea-ice and precipitation from AMSR-2 SST observations (blue and green respectively stand for available and unavailable observations); (**c**) synthetic CIMR observations obtained combining the information on the CIMR overpasses, the AMSR-2 observations and the noise. All of the figures are mapped onto a regular 1/4◦ grid (the same as the present-day CMEMS L4 SSS) and refer to 1 January 2016.

#### **3. Results**

In this section, we present the results of the OSSE described in Section 2.3 and summarized by Figure 1. Two different configurations of the CMEMS L4 SSS processing chain (including and not including the CIMR synthetic observations) are qualitatively and quantitatively validated against the

MERCATOR SSS, constituting the true SSS field. In the following, the L4 SSS given by the OI of in situ observations and the ones obtained combining in situ plus the CIMR estimates will be referred to as IL4 and CIL4, respectively.

#### *3.1. Qualitative Validation*

Observing the IL4 (Figure 5a) and the CIL4 (Figure 5c), a qualitative validation can be carried out using the original MERCATOR SSS as a benchmark (Figure 5e). We present a case study on one of the most dynamically active areas of the global ocean: the Gulf Stream (1 January 2016). In general, when the CIMR observations are not included, the resulting OI SSS misrepresents the salinity values as well as the mesoscale activity found in the benchmark salinity field. Indeed, the IL4 are given by a smooth field, close to a climatological estimate, with mesoscale activity appearing only in proximity of the in situ observations, where the multivariate algorithm can account for the spatial, temporal and thermal decorrelation (given by the L4 SST field) as indicated in Equation (2). This statement is confirmed by visual inspection of Figure 5a–f.

**Figure 5.** (**a**) L4 SSS from in situ observations (IL4); (**b**) extraction of in situ SSS from the MERCATOR SSS, squares and circles, respectively, stand for pseudo and in situ observations; (**c**) L4 SSS from the combination of in situ and CIMR observations (CIL4); (**d**) simulated CIMR L3 SSS; (**e**) MERCATOR SSS (benchmark); (**f**) MERCATOR SST. All figures refer to 1 January 2016, in the Gulf Stream Area.

Moreover, in Figure 5, we highlighted the basin south of Newfoundland and New Scotland using a black circle. Here, the IL4 underestimates the true SSS by about 1 to 1.5 PSU. When the CIMR observations are ingested in the OI processing, the salinity values are corrected and agree with the reference SSS. Finally, we discuss the CIMR performances in resolving the signature of two eddies located off New Jersey and in the Gulf of Mexico. In Figure 5a,c,e, these eddies are highlighted by two black squares. If the CIMR observations were not used in the OI processing, their signatures in the SSS field would either disappear or only partially be resolved.

## *3.2. Quantitative Validation*

The potential of the future CIMR SSS is here demonstrated through quantitative analyses. The metrics of the validation are based on the computation of the RMSE and PSD.

#### 3.2.1. Temporal Variability of the CIMR Impact in the CMEMS SSS

We computed the time series of the RMSE between the outputs of the CMEMS L4 processing chain and the true SSS field. Such statistics are based on weekly data for the year 2016. The main results of the validation are summarized by Figure 6a–c. The statistics have been computed in three latitudinal bands: 90◦S to 45◦S (referred to as Area S), 45◦S to 45◦N (referred to as Area M) and 45◦N to 90◦N (referred to as Area N). This choice is due to the behavior of the average *σ*SSS, whose map is well approximated by Figure 2, where these areas have been highlighted. The 45◦S/N latitudes correspond to the areas where the *σ*SSS reaches half of its maximum magnitude, i.e., 0.45 PSU, and then rapidly increases up to a maximum of 0.9 PSU moving towards the polar regions. On the other hand, in the 45◦S to 45◦N latitudinal band, the average *σ*SSS is mostly around 0.3 PSU.

As a general comment, the quantitative validations of the L4 SSS show that CIMR SSS will undoubtedly bring benefits for the CMEMS SSS operational products. The CIMR SSSs guarantee to reconstruct L4 salinity maps that systematically reduce the RMSE with respect to the true SSS, compared to products relying on in situ observations alone. In the Area M, the RMSE exhibits the largest improvements, whose magnitude is around 50% throughout the whole year 2016. The improvement is evaluated according to Equation (4) [21]:

$$\text{IMPROVE} = 100 \times \left[ 1 - \left( \frac{RMSE\_{CL4}}{RMSE\_{IL4}} \right)^2 \right]. \tag{4}$$

In the Area N, the improvements brought by CIMR vary between 20% and 40%, with the largest values observed during summertime. The RMSE time series of both the CIL4 and the IL4 exhibit a seasonal behaviour with enhanced values during summertime ( 3 PSU), which is a known behaviour for the CMEMS SSS, also discussed by Xie et al. 2019 [22]. The Area S is the only region exhibiting slight degradation using CIMR observations within CMEMS. Here, we could observe improvements reaching 30% during the austral Summer and Fall but from June to November, the CIL4 RMSE increases by about 10−<sup>2</sup> PSU compared to the IL4 reconstruction, mostly indicating that CIMR is not bringing a useful contribution to the SSS reconstruction in these areas during the austral Spring and Winter.

## 3.2.2. Spatial Variability of the CIMR Impact in the CMEMS SSS

In order to quantify the spatial variability of the CIMR improvements, we compared the local temporal RMSE between the CIL4 and the IL4. This was achieved by means of Equation (5), using the MERCATOR SSS as a reference:

$$
\Delta \text{RMSE} = \text{RMSE} (\text{SSS}^{\text{CLA}}) - \text{RMSE} (\text{SSS}^{\text{ILA}}).\tag{5}
$$

The negative ΔRMSE values indicate an RMSE reduction with respect to the true SSS, hence, an improved SSS retrieval given by CIMR. Figure 7a indicates that the CIMR observations improve the SSS retrieval in 63% of the world ocean, exhibiting better performances in the Area M (45◦S to 45◦N) and in coastal regions, which are characterized by the main upwelling systems and the larger river inputs. This is easily explained considering that the density of in situ observations is lower in coastal regions than in the open ocean, as confirmed by Figure 7b. In the figure, the white halo

located in correspondence of the coastal waters indicates the absence of in situ SSS estimates. Thus, progressively approaching the coastline, the relative contribution of the CIMR observations improve the SSS variability of the L4 interpolated fields. However, the CIMR sensor in itself is not expected to perform better in costal zones (because of a large measurement footprint). This is confirmed by the analyses reported in Figure 8, where both the RMSECIL4 and RMSEIL4 generally increase as the coastline is approached. In the future, provided the characteristics of the receiving antenna, an estimate of the expected land contamination will be possible. This will enable a more realistic evaluation of the CIMR performances within the CMEMS SSS in coastal areas.

**Figure 6.** (**a**) RMSE between the OI L4 SSS and the MERCATOR outputs. Blue and red, respectively, stand for IL4 and CIL4 reconstructions. The statistics are referred to the 45◦S to the 45◦N latitudinal band (Area M); (**b**) analyses referred to the the 45◦N to the 90◦N latitudinal band (Area N); (**c**) analyses referred to the 90◦S to the 45◦S latitudinal band (Area S).

**Figure 7.** (**a**) ΔRMSE based on weekly data, year 2016; (**b**) density of in situ SSS for the year 2016. The maximum number of in situ observations is 140 (in the North Atlantic). The colorbar is saturated to 5 in order to facilitate the visualization of the measurement sites at a global scale.

An overall CIL4 degradation is observed in the Area S and in the 60◦W–10◦W zone of Area N, where the RMSECIL4 exceeds the RMSEIL4 by 0.01 PSU on average, which is also confirmed by Figure 8a,b. This behaviour is discussed in Section 3.3 in more detail. As an additional analysis, we compared the SSS gradients magnitude found in the CIL4 and IL4 reconstructions. This was performed in a similar fashion as for the SSS fields, i.e., computing the ΔRMSE∇:

$$
\Delta \text{RMSE}\_{\nabla} = \text{RMSE}(|\nabla \text{SSE}^{\text{CLA}}|) - \text{RMSE}(|\nabla \text{SSE}^{\text{IL}}|) \tag{6}
$$

with |∇SSS| = (*∂*xSSS)<sup>2</sup> + (*∂*ySSS)2, where the quantities *∂<sup>x</sup>* and *∂<sup>y</sup>* are estimated via a centered finite differences numerical scheme and the subscripts "x,y" respectively stand for the zonal and meridional directions.

(**a**)

Accurate estimates of the SSS gradients in L4 products is crucial from a physical point of view. Combined with the information on SST, it gives access to the patterns of the surface density gradients, allowing for diagnosing the global ocean surface dynamics. In addition, the surface density gradients allow for predicting the subsurface circulation from surface observations [23], which justifies the interest in evaluating the CIMR contribution for the monitoring of this variable. CIMR itself will provide global SST fields at the same time as SSS based on the use of 6.9 GHz channel data where the real aperture of the CIMR channel is 15 km. According to Figure 9, CIMR improves the SSS gradients retrieval in 70% of the world ocean. This is more evident in the Area M and in coastal waters. As for the previous analysis, the Areas S and N show reduced performance, where the averaged RMSE(|∇SSSCIL4|) exceeds by about 0.04 PSU·m−<sup>1</sup> the one based on in situ observations alone. At latitudes exceeding 75◦N, the ΔRMSE<sup>∇</sup> shows alternating patterns of large improvement and degradation. This is not in agreement with the behavior of the ΔRMSE, where an overall improvement of the SSS values is observed. This indicates that, in this region, the CIMR SSS contributes to accurately

describe the temporal variability of the SSS but only locally improves the estimate of the SSS gradients with respect to a climatological field.

**Figure 9.** ΔRMSE<sup>∇</sup> based on weekly data, year 2016.

The statistical significance of the results shown in Figures 7–9 was evaluated via a bootstrap resampling technique. The analysis confirmed that both the ΔRMSE and ΔRMSE<sup>∇</sup> are in the 95% confidence interval.

#### *3.3. Further Insights on the Spatial-Temporal Variability of the CIMR Performances*

The spatial-temporal variability of the CIMR performances is consistent with the average physical conditions of the ocean surface throughout the year 2016. The evolution of the daily *σ*SSS, i.e., the CIMR spatially averaged measurement uncertainty confirms that the Area S exhibits the largest values throughout the year 2016 (Figure 10a). This is mostly due to the persistent low mean SST ( 5 ◦C) and high OWS ( 10.5 m·s<sup>−</sup>1) in this area [19] indicating a well mixed surface layer. This was obtained using weekly AMSR-2 observations. Moreover, during the austral Spring and Winter, the *σ*SSS exhibits a further increase which results in the degradation of the CIL4 estimates illustrated in Figure 6c.

Following the same logic, the fairly constant CIL4 improvements observed in the Area M are also explained. Indeed, in the 45◦S to 45◦N latitudinal band, the *σ*SSS is permanently around 0.35, guaranteeing an optimal SSS retrieval from CIMR. The CIMR measurement uncertainty of the Area N enables generally improving the CIL4 estimates compared to the IL4 reconstruction. Here, the *σ*SSS also exhibits a larger seasonal cycle than in the Area S, due to the enhanced SST and OWS variability of the northern hemisphere, in agreement with the results of Dunstan et al. 2018 [24]. This explains the time dependence of the CIL4 improvements found in the Area N, yielding a more precise reconstruction during the Summer.

The behaviour of the *σ*SSS also explains the spatial variability of the CIMR benefits within the CMEMS SSS operational products, summarized by Figures 7a and 9. These figures suggest that CIMR will improve the SSS and SSS gradients estimates in the 60% and 70% of the world ocean, respectively. Nevertheless, the Area S is the main degradation zone for both the CIL4-SSS and CIL4-SSS spatial gradients. The large values of *σ*SSS during April to November 2016 are most likely the responsible of this degradation, whose signature emerges in the ΔRMSE and ΔRMSE∇.

The present-day version of the CMEMS SSS processing chain may also be responsible for the partial degradation observed in the Area S. In future studies, we plan to further tune of the operational chain in this area. This will be achieved considering a different weighting of the CIMR SSS in the multivariate OI algorithm, given their decreased accuracy during the austral Spring and Winter.

**Figure 10.** (**a**) blue line: *σ*SSS in the 45◦S to 45◦N latitudinal band (Area M). Red line: *σ*SSS from 45◦N to 90◦N (Area N) and from 45◦S to 90◦S (Area S); (**b**) same analysis for the AMSR-2 derived OWS; (**c**) same analysis for the AMSR-2 derived SST.

#### *3.4. Spectral Content of IL4 and CIL4*

Here, we describe the capability of CIMR to retrieve the signatures of mesoscale activity in the CMEMS SSS. This will be assessed via a spectral analysis of the IL4 and CIL4 compared to the reference SSS provided by MERCATOR. We perform the spectral analyses in five land-free areas of the world ocean: the North and South Atlantic, the North and South Pacific and the Indian Ocean. The SSS power spectral density (PSD) computation is compliant with [11] and is based on Fast Fourier Transform with the Blackman–Harris window for the reduction of spectral leakage.

The spectra are computed over the entire 2016 using weekly data for both the L4 reconstructions. The time average of the mean zonal spectra is presented in Figure 11 as a function of the spatial wavenumber, indicating spectral properties of the IL4, CIL4 and MERCATOR SSS that agree in all the aforementioned investigation areas. Compared to the true SSS, the IL4 spectra (red lines of Figure 11) show a PSD drop around 0.1 degrees−1. On the other hand, the CIMR SSS allows for building interpolated SSS maps with spectral properties that follow the true SSS, except for the addition of noise at scales below 0.8 degrees−<sup>1</sup> (on average), where the CIL4 spectra begin to flatten.

**Figure 11.** Time average of the mean zonal spectra of the MERCATOR SSS (green line), the IL4 (red line) and the CIL4 (blue line). The time average is based on weekly data for the year 2016. The spectra are computed in five different areas of the global ocean, referenced in the top panel of the figure.

The spectral analysis presented here is not fully rigorous from a physical point of view. Indeed, our maps are presented over a regular 1/4◦ grid and we are computing the spectra over latitudinal extents exceeding 40◦, thus considering spatial grid separations ranging from approximately 27 to 14 km, e.g., going from the equator up to 60◦N/S. Nevertheless, the results presented here are still proving that the CIMR SSS are expected to enhance the effective spatial resolution of the CMEMS SSS with respect to reconstructions based on in situ observations. In order to quantify the spectral properties from a physical point of view, we performed the spectral analysis in a 20◦ box centered over the equator (±10◦ around the equator) in the Pacific and the Atlantic Oceans, i.e., guaranteeing grid separations around 27 km on average. The behaviour of the spectra are similar to the ones presented in Figure 11. The CIL4 reconstruction spectrum evolves in agreement with the one of the MERCATOR SSS until scales of 1.4 deg−<sup>1</sup> where the effect of noise becomes evident. This additional analysis indicates that the CIL4 are dynamically consistent with the MERCATOR fields until scales of approximately 70 km.

#### **4. Discussion and Conclusions**

The Copernicus Marine Environment Monitoring Service is presently serving a wide community of users with the distribution, amongst others, of global optimally interpolated L4 SSS (and sea-surface density) mapped on a 1/4◦ regular grid, updated weekly and based on a combination of in situ, satellite SSS and high-resolution SST data. The CMEMS SSS are obtained combining ARGO and CTD observations with SMOS SSS measurements [10,11,18]. After the SMOS era, the potential availability of the CIMR SSS could guarantee the accuracy and effective spatial resolution of the CMEMS SSS datasets. This was shown throughout this paper via a synthetic CMEMS SSS processing chain relying on simulated CIMR SSS retrievals. The core of our investigation was the CMEMS MERCATOR operational model, which was used to simulate the input SSS for the optimal interpolation processing as well as for assessing the accuracy of the CIMR-based L4 SSS. We focused on the year 2016. The main results of our evaluation study are summarized and discussed here.

CIMR will guarantee the retrieval of improved L4 SSS estimates (CIL4) with respect to optimally interpolated products based on in situ observations alone (IL4). Using the MERCATOR outputs as a benchmark, we obtained that the CIL4 RMSE is systematically reduced throughout the year in the latitudinal band 45◦S to 90◦N (Areas M and N), showing improvements up to 50% (based on Equation (4)) compared to the IL4 reconstructions. In the Area S, the CIMR benefits were confirmed during half of the year 2016, exhibiting a slight criticism during the austral Spring and Winter.

In past studies [11], the multivariate algorithm for the production of the L4 SSS was shown to perform much better in the open ocean. Offshore, the high pass filtered SST and SSS are generally more correlated and the assumptions made to derive the multidimensional covariance function are more strictly valid. This is more evident when SSS observations in coastal waters are too sparse, preventing an accurate mapping of the salinity changes related to groundwater fluxes or when the SST patterns are modified by localized heat fluxes (e.g., wind interactions with highly variable coastal orography). In the present study, we showed that the availability of remotely sensed CIMR SSS not only proves useful to monitor salinity changes associated with mesoscale-to-large scale processes in the open ocean, but also significantly improves our capability to describe salinity patterns in coastal areas.

Moreover, the use of the CIMR SSS will enable improving the effective spatial resolution of the global CMEMS L4 SSS, compared to L4 SSS obtained interpolating in situ observations alone. In our OSSE, the CIL4 reconstruction showed spectral properties in agreement with the true SSS, i.e., the MERCATOR model outputs. The optimal interpolation scheme only adds noise to scales smaller than 80 km, according to the tests performed in the Pacific and Atlantic equatorial bands.

These results indicate that the benefits of the potential SSS observations from CIMR will go even beyond the operational requirements within CMEMS. Their application to scientific and societal studies will be wide. The global L4 SSS obtained with CIMR will enable capturing the signatures of the major mesoscale dynamical features, e.g., the main Gulf Stream or Agulhas Rings [25], guaranteeing the monitoring of their spatial distribution and migration pathways. This will contribute to evaluating the global scale SSS distribution and budget. The monitoring of the global SSS is also a key element in studies of water cycle, oceanic water formation and ocean-atmosphere coupled dynamics [26]. For example, Ballabrera-Poy et al. 2002 [27] pointed out that SSS can be crucial in predicting the El Niño Southern Oscillation (ENSO) dynamics over time scales of 6 to 12 months. Indeed, the positive SSS anomalies in proximity of the Pacific equatorial band can modulate ENSO via their impact on the subsurface oceanic stratification. Quite interestingly, CIMR showed optimal measurement performances in the tropical Pacific area. Moreover, the accurate SSS estimate is useful for applications of three-dimensional fields reconstruction from surface information, as pointed out by [7,23,28] for the reconstruction of the three-dimensional horizontal and vertical oceanic motions and tracers. In conclusion, the expected performance of the CIMR mission confirmed the importance of ingesting the CIMR SSS within the framework of the CMEMS SSS data production. The future loss of the SMOS and SMAP missions fully justifies the high priority of the CIMR mission development within the framework of Copernicus.

**Author Contributions:** Conceptualization: D.C., B.B.N., R.S. and G.L.L. Formal analysis: D.C. and B.B.N. Funding acquisition: R.S. Investigation: D.C., B.B.N., G.L.L., and R.S. Supervision: B.B.N., G.L.L., R.S., C.P., and C.D. Validation: D.C. and B.B.N. Writing of original draft: D.C. and B.B.N. Writing—review and editing, B.B.N., C.D., G.L.L. and C.P.

**Funding:** This study was financed by the CIMR-Apps Mission Application Study, Contract 4000125189/18/NL/AI.

**Acknowledgments:** The authors wish to acknowledge the three anonymous Reviewers for providing constructive comments on the manuscript. Moreover, the authors thank the Barcelona Expert Center team and Kayla Jia for taking care of the reviewing process.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
