All ocean observations assimilated in the real-time forecasting system are assimilated in the same way in the OSEs presented here. Along-track sea level anomaly (SLA) observations distributed by Copernicus Marine Environment Monitoring Service (CMEMS) (http://marine.copernicus.eu/, last access: 18 April 2019) referenced to an unbiased mean dynamic topography (MDT) based on the CNES/CLS 2013 MDT are used. Gridded satellite SST Operational Sea Surface Temperature and Sea Ice Analysis (OSTIA) Level 4 (L4: SST analysis using optimal interpolation (OI) on a global 0.054∘ grid) are assimilated each week in addition to SST measurements from the in situ database delivered by the CORIOLIS center (http://www.coriolis.eu.org/, last access: 18 April 2019). Assimilation of in situ temperature and salinity profiles from this database is mostly from ARGO floats; expendable bathythermograph (XBT); conductivity, temperature, and depth measurements(CTDs); moorings; gliders; and sea mammals. The assimilation of those routine observations in the OSEs provides a realistic context for the global ocean observing system so that the experiments address the complementarity of the different data sets with satellite SSS. The only exception is the TAO mooring observations of salinity that are withheld from the analysis and kept as independent observations to evaluate the performance of the assimilation experiment and the impact of the SSS assimilation. The model SSS in the real-time system is only constrained at a large scale by in situ observations, mostly Argo floats that usually start to measure at 5 m depth.

In this study, we assimilate an SMOS Level 3 (L3: provided on a grid, but without infilling) SSS product at 0.25∘ resolution. L3 products are qualified (quality controlled) and processed at the Data Production Center (CPDC) of the Centre Aval de Traitement des Données SMOS (CATDS CEC-LOCEAN) (Boutin et al., 2017). Compared to Level 2 products (L2: SSS values at the native swath resolution), they benefit from additional corrections. These are 18-day products sampled at 25 km resolution provided every 4 days (the precise description of the time filtering is in the documentation at http://www.catds.fr/Products/Available-products-from-CEC-OS/L3-Debiased-Locean-v2, last access: 18 April 2019). We checked that this temporal resolution fits the model resolution and the weekly analysis window used in the assimilation scheme well; see the next section. In practice, the gridded SSS which is the closest to the analysis date (i.e., the fourth day of the week) provides the SSS data for the cycle. The model counterpart is the time average over the weekly cycle. Due to a low signal-to-noise ratio, the assimilation of the SSS data is limited in the latitudinal band between 40∘ S and 40∘ N.

The SAM2 system uses a background error covariance matrix with a reduced basis of a fixed collection of multivariate model anomalies. The model anomalies are computed from a previous simulation over an 8-year period with an in situ bias correction, detailed in Sect. 2.4. The forecast error covariances rely on a fixed basis, seasonally variable ensemble of anomalies calculated from this long experiment. A significant number of anomalies are kept from one analysis to the other, thus ensuring error covariance continuity. The aim is to obtain an ensemble of anomalies representative of the error covariance (Oke et al., 2008), which provide an estimate of the error in the ocean state at a given period of the year. The localization of the error covariance is performed assuming zero covariance beyond a distance defined as twice the local spatial correlation scale (Lellouche et al., 2013). These spatial correlation scales are also used to select the data around the analysis point. The model correction (analysis increment) is a linear combination of these anomalies. This correction is applied incrementally over the assimilation cycle temporal window using an incremental analysis update (Bloom et al., 1996; Benkiran and Greiner, 2008).

The observation errors specified in the assimilation scheme are assumed to be uncorrelated with each other. Observation errors include representativity errors specified as a fixed error map and an instrumental error. Representativity errors for in situ observations were calculated a posteriori from a reanalysis over the period 2008–2012. The applied statistic method (Desroziers et al., 2005) consists of the computation of a ratio, which is a function of observation errors, innovations and residuals. These estimated errors are constant throughout the year.

The instrumental errors of SLA, SST and in situ measurements are summarized in Table 1. Figure 2a shows the representativity error used for the in situ SSS and an example of the resulting salinity error (Fig. 2b) for in situ data for the week of 20–27 January 2016. The SSS error from space is estimated during the bias correction scheme procedure (see Sect. 2.5) and then used in SAM2.

Biases between model and data exist for subsurface quantities such as temperature and salinity. As with the time-varying error components, such biases can often be related to systematic errors in the forcing (Leeuwenburgh, 2007).

As written in Lellouche et al. (2013), a 3D-Var bias correction is applied for large-scale 3-D temperature and salinity fields. The aim of this bias correction is to correct the large-scale, slowly evolving errors of the model, whereas the SAM assimilation scheme is used to correct the smaller scales of the model forecast error.

This is applied separately to the model's prognostic T/S equations from in situ profile innovations calculated over the preceding month on a coarse grid (1∘×1∘). This bias (x) is the minimizer of the cost function given by Eq. (1). 1J(x)=1/2xTB-1x+1/2(d-Hx)TR-1(d-Hx), where d = 〈 Salinityin situ〉-〈 Salinitymodel〉 for the salinity field. Here, d is the innovation vector of T/S, i.e., the mean innovation of in situ T/S over 1 month in 1∘×1∘ grid boxes. Salinityin situ and Salinitymodel denote salinity values of in situ data and model and 〈⋅〉 indicates the mean. x is the temperature or salinity in situ bias to estimate, B denotes the background error covariance of the 3-D bias, H is the observation operator and R is the observation covariance error. The vertical grid is a coarse grid (only 23 levels) which is different to the model vertical grid (50 levels). For example, the in situ innovation at sea surface for T/S is calculated from the average of model and observations between 0 and 11 m depth.

Because temperature and salinity biases are not necessarily correlated at large scales, these two variables are processed separately. Spatial correlations in B are modeled by means of an anisotropic Gaussian recursive filter (Wu et al., 1992; Riishøjgaard, 1998; Purser et al., 2003). Finally, bias correction of T, S and dynamic height are computed and interpolated on the model grid and applied as tendencies in the model prognostic equations with a 1-month timescale.

Earlier attempts to assimilate SSS data have shown the importance of using unbiased satellite SSS data while implementing rigorous quality control in an upstream process (Tranchant et al., 2015). In this study, the bias control of satellite SSS has been modeled by modifying the current T/S bias (in situ) correction 3D-Var cost function (Eq. 1). Two extra terms to take into account biases in the satellite SSS data have been added in the following 3D-Var cost function (Eq. 2). The new SSS bias ξ is the minimizer of the cost function given by the Eq. (2). 2J(x,ξ)=+1/2xTB-1x+1/2(d-Hx)TR-1(d-Hx)+1/2ξTBξ-1ξ+1/2(dξ-Hξx)TRξ-1(dξ-Hξx), where dξ=(〈SSSSMOS〉-ξ)-〈 SSSmodel (0.5 m) 〉 Here, dξ is the innovation of SSS bias at surface, i.e., the mean innovation of satellite SSS over 1 month on a 1∘×1∘ grid. SSSSMOS denotes the original (non-debiased) SMOS SSS, SSSmodel (0.5 m) denotes the model SSS at 5 m depth and the first term (〈 SSSSMOS〉-ξ) corresponds to the unbiased SMOS SSS. Hξ is the linear operator which interpolates x to the positions of SMOS observations. Bξ denotes the background error covariance of the 2-D satellite SSS bias and Rξ is the estimated SMOS SSS observation covariance error.

To get an optimal set of parameters (weights, spatial scales and errors), several estimations were performed with data withdrawing. Figure 3a and c show examples of the model salinity bias x, near the surfacewithout Eq. (1) and with Eq. (2) the estimation of the bias of SMOS data, ξ. The patterns are similar except at the Equator where the estimated bias of SMOS data (Fig. 3b) influences the estimated model salinity bias (Fig. 3c) with smaller scales. In this example, a persistent large innovation at several depths (11, 41 and 79 m) (not shown here) induces a larger bias of salinity (negative anomaly) at the sea surface near 20∘ S, 120∘ W.

The REF and SMOSexp simulations differ only by assimilating satellite SSS data (Table 2). We first check the success of the assimilation procedure in reducing the misfit from the assimilated SSS observations within the prescribed error bar. We then look at the root mean square (rms) of in situ salinity observation innovations near 6 m depth in both simulations. The forecasted field is mostly independent of the reference data because those data have not been assimilated yet and the model forecast ranges from 1 to 7 days.

Figure 6 shows the time series of root-mean-square errors (RMSEs) of the model near-surface salinity at 6 m depth with respect to in situ observations (dotted lines) and of the model SSS (0.5 m depth) with respect to the bias-corrected SMOS SSS (solid lines) for both simulations (REF in black, SMOSexp in red). As expected, the SMOS SSS data assimilation clearly leads to a significant reduction in the innovations of the SMOS data (solid lines). When the SSS SMOS is assimilated, the time series of RMSE for the global, the tropical Pacific and the central Pacific (Niño3.4) domains present the same reduction with a higher variability for the smallest domain (Niño3.4). The global RMSE to SMOS data are around 0.28 pss (practical salinity scale) in the reference simulation and reduced to 0.21 pss when debiased SMOS data are assimilated, corresponding to an error reduction of 24 %. This shows that the combination of bias correction and data assimilation perform well.

Nevertheless, the essential issue is the salinity RMSE compared to in situ salinity observations (dotted lines). This error is slightly reduced from 0.20 to 0.19 pss in the global domain (5 %), but this reduction can reach 10 % in the northern tropical Pacific where the salinity anomaly is the strongest; see Table 3. This larger decrease in the near-surface salinity RMSE is consistent with that observed for the SSS SMOS RMSE (30 %). In addition, the reduction of the near-surface salinity RMSE is more important in the western part of the equatorial Pacific (Niño4). This shows that the assimilation of SMOS SSS observations does not introduce overall incoherent information and can even reduce the misfit with the in situ salinity observations. It also confirms that SSS errors estimated in the bias correction procedure and used in the assimilation scheme are well tuned and the data bring coherent information. Consequently, salinity large-scale biases are removed well. From Table 3, it should be mentioned that the number of in situ salinity observation per week is very small compared to the SMOS observations and is maybe not always sufficient to ensure robust statistics in small regions.

Time series and maps of the misfits between observation and model forecasts are complementary in the analysis of the temporal and spatial variability of the model–observation differences. Figure 7 shows the mean and root-mean-square differences of monthly mean SSS in the analysis fields in REF and SMOSexp compared to the original (non-debiased) SMOS data over the year 2015 for the tropical Pacific Ocean.

The mean SSS bias in REF exhibits large-scale patterns, coinciding with the 2015 SSS anomaly for the open ocean (Fig. 1). A large bias is also found in the Indonesian archipelago. In contrast, the bias is effectively reduced in SMOSexp as are the root-mean-square differences, which are reduced to less than 0.2 pss (black isohaline) in most of the tropical Pacific Ocean.

The mean RMSE and the percentage of RMSE difference in the salinity profiles (mainly from Argo floats) are computed over the entire period and the global domain (Fig. 8). There is a slight decrease in the first 30 m below the surface when SSS data are assimilated additionally to in situ salinity data. It shows that the additional information brought by the SSS is in agreement with the salinity in situ observations close to the surface. It can even help improve the global salinity representation in the first 30 m by better constraining the model forecast with the satellite SSS.

In situ temperature innovations in the global domain as well as in the tropical Pacific region do not show significant changes. The same is found for SLA (CMEMS/DUACS, Data Unification and Altimeter Combination System, along track) and SST innovations (OSTIA L4). SSS data assimilation has a quite neutral impact on the innovations associated with those observations.

We now look at the changes in the analyzed surface and subsurface fields due to the SSS data assimilation by comparing the 3-D analysis of the REF and SMOSexp experiments. At a basin scale, the REF simulation already agrees well with the 2015 mean deduced from the “unbiased” CATDS SMOS observations (Fig. 9). SMOS data assimilation induced changes on the order of 0.2 pss. It tends to weaken the salinity negative anomaly represented in the REF simulation within the ITCZ and SPCZ regions. This is in agreement with Kidd et al. (2013), who show an overestimation of the ECMWF precipitation in the tropics compared to satellite observations. Elsewhere, the SMOS data assimilation increases the salinity. Large changes also occurred in the coastal zones (Indonesian archipelago and Central America coast), even if the specified error in SSS data was larger in those regions than in the open ocean.

The associated vertical salinity changes brought by SMOS SSS data assimilation at the Equator are represented in Fig. 10. The largest high-salinity anomaly is found in the first 50 m depth and along the coastal bathymetry; elsewhere changes are very small (less than 0.05 pss). Overall, at the Equator (excepted in coastal areas), the data assimilation of SMOS SSS leads to fresher waters in the east and saltier waters in the west for the year 2015.

The highest variability of the surface salinity at a monthly scale during the year 2015 is found within the ITCZ, SPCZ and in the eastern Pacific fresh pool in both simulations and SMOS observations (not shown). SMOS assimilation decreases the intensity of the variability of the SSS, in agreement with the observed variability. In summary, the SSS assimilation acts to counteract the precipitation excess, with a visible result in the salinity both in terms of time mean but also in terms of variability.

During the El Niño 2015 event, a strong salinity anomaly pattern developed in the tropical Pacific (Gasparin et Roemmich, 2016); see also Fig. 1. This anomaly corresponds to the ITCZ and SPCZ areas. Figure 11 shows the time–longitude evolution of the SSS at 5∘ N, the latitude where the salinity anomaly is the largest (Hackert et al., 2014). Both the REF and SMOSexp simulations represent the decrease in the salinity in fall 2015 between 160∘ E and 120∘ W. Note that this salinity anomaly is smaller in the SMOS data (SMOS SSS is saltier) with a smaller extent. The eastern freshwater pool extended further west during 2015, but it was fresher in the REF simulation compared to the SMOSexp experiment.

While the impact of SSS assimilation is neutral on the other variables (temperature and sea surface height, SSH) in terms of data assimilation statistics (RMSE averaged in different areas), it is not the case when we look at the time evolution of model fields.

SST differences at 5∘ N and zonal velocity differences at the Equator are represented in Fig. 12. The differences are mainly associated with the wave propagation seen in all the surface fields. In the eastern freshwater pool, the SMOS data assimilation weakens the freshening and induces a slight warming of about 0.05 ∘C (Fig. 12b). At the Equator, the zonal eastward advection is enhanced (positive pattern at the east of the date line) from January to October 2015 (Fig. 12c) which could help the warm water pool migration to the east but this effect is very weak here. Note that the eastward warm water pool migration is known to promote the ocean–atmosphere coupling and thus the triggering of El Niño. In the eastern basin, there is also an increase in the westward propagation during fall 2015 that is possibly linked to the increase in tropical instability waves (TIWs), which will be shown later.

Another effect of SSS changes can be viewed on barrier layers which are quasi-permanent in the tropical Pacific. Barrier layer thickness (BLT) can influence the air–sea interaction, ocean heat budget, climate change and onset of El Niño–Southern Oscillation (ENSO) events (Maes et al., 2002, 2004). The barrier layer acts as a barrier to turbulent mixing of cooler thermocline waters into the mixed layer and thereby plays an important role in the ocean surface layer heat budget (Lukas and Lindstrom, 1991). The Hovmöller diagram of BLT at 5∘ N is shown in Fig. 13 for both experiments. It shows the occurrence of great BLT in the eastern Pacific (120–140∘ W) from September to November, which corresponds to measurements taken during strong El Niño events (Mignot et al., 2007). Note also that the eastward displacement of the thick barrier layer has already been observed during previous El Niño events (see Qu et al., 2014).

From Figs. 12a and 13, we show that the eastern and central Pacific are saltier in the SMOSexp experiment, which induces a decrease in the stratification and then a decreased BLT. A decrease in the stratification by SSS data assimilation can increase the convective mixing, on the one hand, and the TIWs can be modified by this change in stratification, on the other hand. From a long-term TAO mooring record at 0∘ N, 140∘ W, Moum et al. (2009) suggest that mixing may always be enhanced during the passage of TIWs both in and below the surface mixed layer. Lien et al. (2008) show that turbulence mixing was modulated strongly by the TIW. Consequently, even if TIWs are less active during an El Niño phase than in a La Niña phase, it was interesting to investigate the TIW propagation signature in SSH. Moreover, Yin et al. (2014) and Lee et al. (2012) also show the capability of monitoring TIWs by Aquarius and SMOS data. Lyman et al. (2007) show that TIWs, which have a 33-day period, are associated with the first meridional-mode Rossby wave. Hovmöller diagram of daily anomalies of SSH at 4∘ N filtered at 33 days are shown in Fig. 14. For both experiments, the westward propagation of TIW is shown in the eastern part of the basin. A reinforcement of the TIWs at the eastern edge of the western Pacific warm pool near 140∘ W (the slope is steeper) appears during the end of the second half of 2015 in the SMOSexp experiment (0.35 m s-1) compared to the REF experiment (0.20 m s-1). As mentioned above, this could be correlated to the decrease in BLT (see Fig. 13) which is associated with a mixing enhancement. By contrast, a weakening of TIWs appears during the August–September period in the eastern part of the basin for the SMOSexp experiment. The same kind of impact has been shown recently in Hackert et al. (2014) for the initialization of the coupled forecast, where a positive impact of SSS assimilation is provided on surface layer density changes via Rossby waves. They also show that these density perturbations provide the background state to amplify equatorial Kelvin waves and the ENSO signal.

TAO moorings deliver high-frequency measurements at fixed locations. Such platforms allow us to look at high-frequency variability that is not captured by drifting platforms. The hourly analyzed salinity is collocated at the TAO mooring positions for the REF and SMOSexp simulations. Figure 15 shows the time evolution of TAO salinity observations (valid at 1 m depth) at three mooring locations in the equatorial Pacific (warm pool, cold tongue and salt front) compared to the model (analysis) for the REF and SMOSexp OSE experiments at the first level (∼0.5 m depth). Assimilated SMOS data have also been added. In this example, the salinity evolution of the REF experiment (in green) appears less correlated with the TAO salinity mooring observations (black dots). The SMOSexp simulation shows a better agreement, except for some strongly variable events. The differences between the SMOSexp simulation and TAO non-assimilated observations are most of the time less than 0.1 pss. The high-frequency variability seen in the observations is also reproduced in the assimilative simulations, with a better agreement when SMOS data are assimilated, except during some specific periods. Tang et al. (2017) also found some disagreement among the TAO, SMAP/SMOS and Argo analysis during short periods. There is an improvement in the cold tongue during the end of summer, in fall 2015 and during the last 2 months of the SMOS simulation (Fig. 15a). The data assimilation of SMOS reduces the freshening in this region. Globally, an improvement occurs also in the warm pool (Fig. 15b) over the entire period. One interesting feature is that when TAO mooring data are missing during a long period near the salt front, the SSS from the SMOSexp experiment is different but closer to TAO mooring when measurements come back (Fig. 15c). Obviously, the time series of the assimilated SMOS data is smoother but is able to capture the large-scale variability. This also shows the level of accuracy we need to capture higher variability. The precipitation rate superimposed on the SSS proves that it is not the only process that plays a role in the salinity variability. Indeed, a high precipitation rate does not necessarily induce a strong freshening at the sea surface where advection, vertical mixing and SSS SMOS data assimilation can counteract its effect. This also shows that the observation error is not necessarily increased locally depending on the precipitation.

These three examples show a positive impact, but it is also interesting to have a global view of all TAO moorings over the 2015/2016 El Niño event. As in Martin et al. (2019), Fig. 16 shows the differences in root mean square difference (RMSD) from hourly TAO mooring salinity values at 1 m depth calculated over the period 1 January 2014 to 16 March 2016. The impact of the SMOS assimilation is contrasted by showing negative (positive) values, which indicates that it reduces (increases) the RMSD. The impact is positive and more significant in the western tropical Pacific near the dateline and in the western Pacific up to 5∘ N. The impact is quite neutral and even negative in the eastern tropical Pacific (140–110∘ W) between 2∘ S and 2∘ N, where generally (i) the SMOS bias is larger (Fig. 3b), (ii) there are few in situ SSS data (Fig. 2) and (iii) the observation error is larger (Fig. 5). Actually, the impact of SMOS SSS assimilation is larger in the ITCZ and SPCZ regions, as shown also in Fig. 9. This reflects the tendency for the SMOS data assimilation to reduce the low-salinity biases by mitigating the overestimation of E–P in the regions of large precipitation. Finally, during the El Niño 2015/2016 event, there is a small positive impact overall from the SMOS assimilation with a reduction in RMSD from 0.326 to 0.316 pss (about 3 %).

Post-processed TSG observations from the French SSS Observation Service (SSS-OS; (http://www.legos.obs-mip.fr/observations/sss, last access: 18 April 2019) were collected along the routes of voluntary merchant ships; see Alory et al., 2015. The SSS estimates have a ∼2.5 km resolution along the ship track with an estimated error close to 0.08 pss. Salinity analyzed fields from REF and SMOSexp simulations is collocated to the TSG observations. Salinity observations from vessel-mounted thermosalinographs allow the validation of the short timescales and space scales of near-surface salinity. Two ship routes (Fig. 17a) that cross the tropical Pacific Ocean in June 2015 are chosen to verify that salinity changes when SSS SMOS data are assimilated are in agreement with such observations.

Figure 17b and c (zoom) show the comparison between the TSG salinity observations (in red) along the Matisse ship route collocated with the REF (black dashed line) and SMOSexp (black line) salinity analyzed fields. The variability of the SSS measurements, lower than the daily frequency, is well represented in both simulations with only small differences of less than 0.2 pss except in the freshwater in the eastern part of the basin. In this region, the salinity dropped down to less than 34.0 pss. The REF simulation differs from the TSG data by more than 0.5 pss within the eastern freshwater pool, marked by a very sharp salinity front. The SMOSexp simulation shows a much better agreement with the SSS from the TSG observations: even if the differences remain large, the misfit is reduced. This confirms once again that the weakening of the freshening in the freshwater pool in the eastern Pacific induced by the SMOS data assimilation is realistic, as it is seen by different in situ observation platforms.