# Reconstructing monthly 20th century salinity fields using a data-driven method and Argo data

Erwan Oulhen, Nicolas Kolodziejczyk, Pierre Tandeo, Bruno Blanke, Florian Sévellec

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Erwan Oulhen, Nicolas Kolodziejczyk, Pierre Tandeo, Bruno Blanke, Florian Sévellec. Reconstructing monthly 20th century salinity fields using a data-driven method and Argo data. Ocean Dynamics, 2025, 75 (6), pp.47. 10.1007/s10236-025-01690-7. hal-05097260

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Distributed under a Creative Commons Attribution 4.0 International License
Reconstructing monthly 20th century salinity
fields using a data-driven method and Argo data

Erwan Oulhen¹*, Nicolas Kolodziejczyk¹, Pierre Tandeo²,³,⁴,
Bruno Blanke¹,², Florian Sévellec¹,³

¹Laboratoire d'Océanographie Physique et Spatiale (LOPS, UMR 6523),
Univ Brest, CNRS, IRD, Ifremer, Brest, 29200, France.

²Lab-STICC, UMR CNRS 6285, IMT Atlantique, Brest, 29238, France.

³Odyssey, Inria/IMT/CNRS, Rennes, 35042, Rennes.

⁴Cluster for Pioneering Research, RIKEN, Kobe, 650-0047, Japan.

*Corresponding author(s). E-mail(s): erwan.oulhen@univ-brest.fr;

Contributing authors: nicolas.kolodziejczyk@univ-brest.fr ;

pierre.tandeo@imt-atlantique.fr; bruno.blanke@univ-brest.fr ;

florian.sevellec@univ-brest.fr;

Abstract

The distribution of ocean salinity is influenced by factors such as ocean currents, freshwater exchanges with the atmosphere, continental inputs, and sea ice formation and melting. Salinity is a fundamental variable in the seawater's equation of state, influencing density, ocean dynamics, and stratification. To understand its distribution and impact, salinity variability must be accurately estimated from in situ observations. In the 20th century, temperature observations were scarce, but salinity data were even more limited, as many instruments measured only temperature. In 2002, the implementation of the Argo observing system improved sampling and reduced the disparity between both variables. Salinity variability can now be better assessed from the 20-year Argo period. In this study, information from the Argo period and estimates of salinity covariability with temperature are used to reconstruct monthly subsurface salinity fields. The reconstruction uses in situ measurements and employs the data-driven RedAnDA scheme, which combines Data Assimilation, Analog Prediction, and Reduced-space Interpolation, a method previously validated for temperature reconstruction. The coupling of temperature and salinity is achieved using density-weighted three-dimensional empirical orthogonal functions. The method is applied to the tropical Pacific to evaluate its ability to reconstruct variability at monthly, interannual and decadal timescales, with emphasis on ENSO-related variability, which is the primary mode

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of variability in the region. Compared to Optimal Interpolation results, salinity analysis by RedAnDA shows significant improvements. The results yield a salinity product that provides valuable insights into historical salinity variability, including fresh pool displacements and salinity-driven stratification changes. Changes in subsurface salinity associated with El Niño and La Niña events are estimated from 1930 to 2001.

**Keywords:** Salinity, tropical Pacific, ENSO, Analog, Data assimilation, multivariate EOFs

# 1 Introduction

The global distribution of ocean salinity reflects the balance between ocean diffusion, advection, and freshwater fluxes (precipitation, runoff, evaporation, and ice melting), providing insights into changes in the global freshwater cycle (Lagerloef, 2002). Salinity serves as a crucial indicator of variations in the hydrological cycle (Zika et al., 2015; Skliris et al., 2016; Cheng et al., 2020; Olmedo et al., 2022). Approximately 80% of Earth's surface freshwater fluxes occur over the ocean (Peixoto and Oort, 1992; Durack, 2015). At a broad scale, subtropical regions tend to be saltier due to intense evaporation, while high latitudes are fresher due to predominant precipitation. In recent decades, climate change has amplified this contrast by intensifying the hydrological cycle (Hosoda et al., 2009; Helm et al., 2010; Durack and Wijffels, 2010; Durack et al., 2012; Fox-Kemper, 2021; Basinski-Ferris and Zanna, 2023). However, the link between changes in freshwater fluxes and ocean salinity distribution is complex, as additional processes such as advection and mixing interfere. Some processes result from natural ocean variability (Delcroix and Hénin, 1991; Vinogradova and Ponte, 2017; Ge et al., 2023; Yu, 2023), while others are due to climate change-driven effects, such as ocean warming and ice melt (Zika et al., 2018).

Salinity influences temperature, marine ecosystems, and ocean dynamics by modulating water density, mixed layer depth, and stratification (Murtugudde and Busalacchi, 1998; Maes et al., 2002; Fedorov et al., 2004; Wang and Yin, 2021). For example, the barrier layer (BL), formed by salinity-driven stratification, significantly impacts ocean mixing and air-sea interactions (Miller, 1976; Lukas and Lindstrom, 1991; Sprintall and Tomczak, 1992; de Boyer Montégut et al., 2007; Qu et al., 2014). This process is particularly pronounced in the Pacific Ocean, where it favors upper-ocean heat uptake that can trigger an El Niño event (Cronin and McPhaden, 2002; Maes et al., 2005, 2006; Mignot et al., 2007; Maes, 2008; Yim et al., 2008; Bosc et al., 2009; Zhang et al., 2015, 2021; Guan et al., 2023). During El Niño, the increased eastward propagation of fresh anomalies strengthens the BL, intensifying El Niño's surface temperature signature (Zheng et al., 2014; Zheng and Zhang, 2015; Zhi et al., 2019; Zhang et al., 2021). Conversely, stratification destabilization due to negative freshwater fluxes can enhance La Niña events through vertical mixing and sea surface cooling (Zheng and Zhang, 2012).
<table>
  <tr>
    <td>Therefore, accurate analysis of the salinity field is crucial. Monitoring salinity using in situ measurements has undergone successive technological developments, improving sampling and observation quality. Before the Argo observing system (Wong et al, 2020), the quality of salinity measurements reached its peak during the World Ocean Circulation Experiment (WOCE, Thompson et al, 2001) in the 1980s and 1990s. Historically, ocean salinity observations have been sparse in both space and time. In the 20<sup>th</sup> century, most cruises occurred during the summer months due to unfavorable winter conditions (harsh weather and sea ice) and were primarily located in the Northern Hemisphere and coastal areas (Abraham et al, 2013; Durack, 2015; Cheng et al, 2020). Furthermore, high-quality salinity measurements were even scarcer than temperature data, as most Mechanical and Expendable Bathythermographs (MBTs & XBTs) did not measure salinity. Additionally, CTD (conductivity, temperature, depth) profilers are prone to drift in their salinity measurements, necessitating careful delayed-mode quality control and corrections (Romero et al, 2021; Wong et al, 2023; Tang et al, 2024).</td>
    <td>093</td>
  </tr>
  <tr>
    <td>Since the late 1990s, the Argo global observing system has been deployed, reaching its targeted quasi-global coverage of the upper 2000 m by 2006 (Roemmich et al, 2019). Over two decades, it has become the backbone of the Global Ocean Observing System and the main source of ocean temperature and salinity measurements in the upper 2000 m for many studies (see Johnson et al, 2022, for a recent review). It addresses the aforementioned biases in ocean observing systems, enabling more accurate estimations of changes in freshwater content, stratification, and oceanic heat content (Hosoda et al, 2009; Hansen et al, 2011; von Schuckmann et al, 2014; Roemmich et al, 2015; Riser, 2016; Li et al, 2020a).</td>
    <td>108</td>
  </tr>
  <tr>
    <td>In a previous study, we validated and applied RedAnDA, a data-driven mapping method (Oulhen et al, 2024) that combines the Analog forecasting method (Lorenz, 1969) and ensemble Data Assimilation techniques (Tandeo et al, 2015; Lguensat et al, 2017), adapted for in situ data processing following the Reduced-Space Interpolation framework (Kaplan et al, 1997). In Oulhen et al (2024), we aimed to reconstruct the three-dimensional temperature field in the tropical Pacific during the second half of the 20<sup>th</sup> century, leveraging dynamical knowledge from a learning period (i.e., Argo data) and recent advances in applied mathematics. Proper mapping of sparsely distributed data facilitates the study of regional and temporal physical patterns. RedAnDA successfully estimated the temperature field and provided an uncertainty estimate, accounting for observation sampling, unresolved scales, and system nonlinearity.</td>
    <td>117</td>
  </tr>
  <tr>
    <td>In the present study, RedAnDA is applied to reconstruct salinity maps between the surface and 500 m depth, from 1930 to 2001, using the Argo period as the learning period. Since Argo floats collect data every 10 days, we aim to produce monthly snapshots to capture seasonal-to-interannual variations.</td>
    <td>128</td>
  </tr>
  <tr>
    <td>A common approach is to exploit the relationship between salinity and temperature to compensate for the lack of salinity observations and generate oceanic T/S vertical profiles, for example, by using satellite observations (Maes and Behringer, 2000; Fujii and Kamachi, 2003; Chang et al, 2011; Goes et al, 2018; He et al, 2021; Tang et al, 2022). Fujii and Kamachi (2003) estimated the salinity field in the equatorial Pacific</td>
    <td>132</td>
  </tr>
</table>
from temperature observations using vertically coupled T/S empirical orthogonal func-
tions constructed from the World Ocean Database 2001 (WOD01). Goes et al (2018)
employed multivariate linear regression to obtain salinity from in situ observations
where only temperature was available, calibrating their parameters on Argo profiles
in the Atlantic Ocean from the surface to 2000 m depth. In the northern South China
Sea, Tang et al (2022) obtained the daily, high-resolution three-dimensional tempera-
ture field from Sea Surface Height and Sea Surface Temperature, using a polynomial
relationship calibrated to a monthly climatology derived from Argo and satellite data.
They determined the three-dimensional salinity distribution at the same scales using
their temperature estimate and its correlation with salinity.

Alternatively, salinity can be inferred directly from observational and simulated
data. For example, Good et al (2013) reconstructed the past variability of temperature
and salinity from 1900 onward, using an optimal interpolation method that combined
a priori climatology with local observational information limited in its spatio-temporal
extent, emphasizing the evaluation of observation quality. Li et al (2023) produced a
high-resolution salinity dataset from 1940 to the present, allowing long-term estimation
of salinity changes while capturing smaller-scale signals. To achieve this, they combined
in situ observations with several climate or Earth system model simulations (including
CMIP6) in an ensemble optimal interpolation procedure.

Here, we investigate inferring salinity by exporting temperature information
through the application of RedAnDA TS, the coupled version of the method. Both
variables are linked by seawater density through the thermodynamic equation of state
(McDougall et al, 2010). As temperature has been more extensively observed than
salinity, it is expected that salinity reconstruction will benefit from this procedure.

Our reconstruction focuses on the tropical Pacific Ocean, between 25°N and 25°S. In
this region, west of 160°W, lies the West Pacific fresh pool (WPFP), characterized by
salinity below 34.8 PSS and a permanent east-west haline gradient, often described as a
salinity front. This front shifts eastward to the dateline during El Niño events because
of anomalous surface currents and intensified rainfall caused by enhanced atmospheric
convection in the central Pacific (Picaut et al, 1996). In this region, salinity-driven
stratification in the BL allows heat accumulation and displacement toward the central
Pacific, potentially favoring extreme El Niño events (Maes et al, 2002; Zhang et al,
2021). In the central Pacific, the Argo observing system has provided valuable insights
into tropical BL variability (Bosc et al, 2009; Qu and Yu, 2014; Steffen and Bourassa,
2018). Therefore, using the Argo period to learn typical monthly salinity changes
enables a more accurate representation of past salinity-driven stratification in the
RedAnDA TS reconstructed product.

This paper is organized as follows: Section 2 describes the datasets used for
reconstruction and analysis. Section 3 outlines the RedAnDA method, explains the
temperature-salinity coupling via the EOFs, and presents the validation and imple-
mentation details. Section 4 presents validation results, first with an Observing System
Simulation Experiment (OSSE), then with real observations. Section 5 discusses the
results and Section 6 concludes with future research directions.
## 2 Data and products

In this section, we first describe the OCCIPUT model outputs used to validate our approach within an OSSE framework. Then we focus on real datasets: the EN.4.2.2 in situ observations, used to estimate the 20th century salinity field, followed by the ISAS20 temperature and salinity products from which the learning period catalog is constructed. Finally, we introduce the IAP and EN4 objective analysis products, which are used for comparison with different results obtained with RedAnDA.

### 2.1 Model outputs

The OCCIPUT (Penduff et al, 2014; Bessières et al, 2017) simulations correspond to an ensemble of 50 realizations of a global 1/4° ocean/sea-ice simulation, based on the NEMO 3.5 model. The simulations provide synthetic profiles, which are simulated in situ observations, extracted at specific times and locations corresponding to the historical database. They span the period from 1961 to 2015, employing the DFS atmospheric forcing over the same period (Dussin et al, 2016). The forcing updates heat, freshwater content and momentum of sea surface using the NEMO bulk formula. SSS is restored to Levitus et al's (1998) climatology with a piston velocity of 167 mm/day (Bessières et al, 2017)

### 2.2 In situ observations

The pre-Argo period is reconstructed by RedAnDA by assimilating profiles from the EN.4.2.2 dataset (Good et al, 2013). This dataset represents the latest version of the Met Office Hadley Centre's 'EN' dataset series, offering quality-controlled potential temperature and salinity profiles from 1900 to the present. Most profiles originate from the World Ocean Database 2018 (WOD18, Boyer et al, 2006), the Global Temperature and Salinity Profile Program (GTSPP, Sun et al, 2010), and Argo floats (Roemmich et al, 2012). For this study, in both the synthetic profiles of the OSSE and EN.4.2.2, only depths where temperature and salinity observations have a quality flag of 1 are used.

Observations are selected if sufficiently close to the target depth, without modification. The instrumental error is evaluated following Cowley et al (2021) and Atkinson et al (2014). It ranges from $5 \times 10^{-3}$ PSS for CTD and profiling floats to $2 \times 10^{-2}$ PSS for moored buoys. For temperature, it ranges from 0.3°C for MBTs and moorings to 0.002°C for the most accurate CTDs. These values are used to construct the observation error matrix employed in our analyses (see Section 3).

### 2.3 Learning period dataset

For the analysis of real data, the Argo period serves as the learning period from which the catalog and coupled EOFs are calculated. The ISAS20 (Gaillard et al, 2016, In Situ Analysis System) gridded product is used here to represent the Argo period. ISAS20 analysis focuses only on Argo measurements, preserving as much as possible the time and space sampling capabilities of the Argo network (Kolodziejczyk et al, 2023). It provides 0.5°×0.5° gridded temperature and salinity fields, constructed with

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an Optimal Interpolation method. It includes 187 standard levels distributed between 0 m and 5500 m. The product covers the period from 2002 to 2020, with monthly maps.

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## 2.4 Temperature and salinity products

RedAnDA's temperature reconstruction is compared to two state-of-the-art reanalysis products that use optimal interpolation techniques.

EN4: A gridded product from the Hadley Centre of the UK Meteorological Office, assimilating EN.4.2.2 in situ profiles. EN4 employs an optimal interpolation technique, using a smoothed 1971–2000 climatology from the EN2 version. It provides monthly temperature and salinity fields from 1900 to the present day over 42 depth levels.

IAP: An Ensemble Optimal Interpolation of the CODC-GOSD dataset (Cheng and Zhu, 2016; Cheng et al., 2017). This method utilizes an ensemble of CMIP5 models to reconstruct global and gridded temperature and salinity at a monthly resolution, from 1940 to the present, at a spatial resolution of 1°×1° in the upper 2000 m, over 41 levels for salinity and 119 levels down to 6000 meters for temperature (Cheng et al., 2020). Our study uses the sixth and standard versions of the IAP product for temperature and salinity, respectively.

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# 3 Method

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## 3.1 RedAnDA

RedAnDA extends AnDA (Analog Prediction Data Assimilation, Tandeo et al., 2015; Lguensat et al., 2017) by incorporating Reduced-Space Data Assimilation as introduced by Kaplan et al. (1997) to process observations that are sparse in time and three-dimensional space.

The model is based on the Analog forecast method (Lorenz, 1969), which was later adapted into the Analog backcast in Oulhen et al. (2024) to enable predictions backward in time. This data-driven approach requires a reference database (a catalog) of previously recorded system trajectories, consisting of state analogs and their temporal predecessors. For a new instance of the same system, its evolution toward an earlier time is predicted using a data-driven linear model statistically built by analyzing 170 analog situations and their temporal predecessors. For further details, we refer the reader to Oulhen et al. (2024). The catalog used in this study was built from the Argo period. The backward-in-time approach implies that the reconstruction starts at the most recent time step, with the model estimating trajectories toward preceding months. The method facilitates the propagation of information from periods with more observations to those with fewer observations.

In this study, RedAnDA is applied to reconstruct past temperature and salinity fields in the tropical Pacific, between 120°E and 70°W, 25°S and 25°N. Depth levels are restricted to 5, 10, 50, 100, 200, 300, 400, and 500 m. The final result consists of 3°×3° gridded temperature and salinity fields, representing several thousand spatial grid points. This high dimensionality challenges the identification of analogs, which justifies the use of a space reduction technique (Kaplan et al., 1997), here EOF decomposition.

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We construct the three-dimensional EOFs using the temperature and salinity covariance estimated from the maps of the learning period, retaining only the most significant EOFs. The number of EOFs selected for RedAnDA (see Section 4.1 for justification) is approximately $L = 15$.

In the context of historical reconstruction, EOF decomposition can be interpreted as a change of variables, where the new variables to be optimally estimated at each desired time step are the principal components at time $t$, i.e., PC($t$), of the retained EOFs (Kaplan et al, 1997; Emery and Thomson, 2001). Once PC($t$) for the 15 EOFs are obtained through a 250-member Ensemble Data Assimilation procedure, three-dimensional gridded temperature and salinity fields are reconstructed using:

$$X(t) \approx \text{PC}(t) \text{ EOF}, \quad (1)$$

where $X$ represents the target three-dimensional temperature or salinity field, and EOF contains the $L$ retained EOFs.

Ensemble Data Assimilation provides a robust mathematical framework that combines Analog Prediction and Reduced-Space Interpolation to assimilate sparse observations, using a Kalman smoother (Tandeo et al, 2015; Lguensat et al, 2017; Oulhen et al, 2024). An additional procedure automatically extends the temporal window for assimilation (Oulhen et al, 2024) to mitigate insufficient observational sampling in the early part of the time series.

Analysis uncertainty is estimated from the spread of a 250-member ensemble, reflecting chaos in the system, as well as sampling and instrumental errors in the observations. The variance of the unretained EOFs is included in the uncertainty estimate, providing insight into misrepresented scales.

Climatologies for salinity and temperature are calculated over the Argo period, using ISAS20 (In Situ Analysis System) temperature and salinity fields (Gaillard et al, 2016). The corresponding PC($t$) values from 2002 to 2020 are incorporated into the RedAnDA catalog.

The reconstruction covers the 1930-2001 period, assimilating EN.4.2.2 profiles (Good et al, 2013). In the following, RedAnDA salinity anomalies are compared with those from EN4 and IAP products, both estimated with optimal interpolation schemes. Their respective monthly climatologies were computed for the period 2002-2015. The final comparison examines the impact of salinity on stratification and its interannual variability.

## 3.2 RedAnDA TS

RedAnDA TS is the application of RedAnDA (Oulhen et al, 2024) to temperature and salinity simultaneously. It uses three-dimensional coupled EOFs that express main covariance patterns for salinity and temperature. This approach leverages in situ temperature observations to compensate for the lower availability of salinity data.

### 3.2.1 Coupled EOFs

To standardize temperature and salinity units, both variables must be weighted before the EOF calculation. To preserve the physical relationship, both variables are
transformed into their density contributions. We consider the linearized seawater equation of state (Bryan and Cox, 1972):

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$$
\begin{align*}
\rho(t) &= \rho_0 + \rho_0 \left[ \frac{1}{\rho_0} \frac{\partial \rho}{\partial T} \bigg|_S \Delta T(t) + \frac{1}{\rho_0} \frac{\partial \rho}{\partial S} \bigg|_T \Delta S(t) \right] \\
&= \rho_0 [1 - \alpha(t) \Delta T(t) + \beta(t) \Delta S(t)],
\end{align*}
$$

where $t$ is the time, $\rho$ is the density, $\rho_0$ is the reference mean density, $T$ is the potential temperature, $S$ is the practical salinity, $\Delta T$ the potential temperature anomaly (from the monthly climatology), $\Delta S$ the practical salinity anomaly (from the monthly climatology), $\alpha$ and $\beta$ are the first derivatives of density with respect to temperature and salinity, respectively, when the other variable is fixed (they are the thermal expansion coefficient and haline contraction coefficient, respectively, McDougall et al, 2010). The Python package gsw 3.4.0 (McDougall and Barker, 2011) is used to compute $-\alpha T$, $\beta S$, and density.

We express changes in temperature and salinity anomalies as their contributions to changes in density. The coupled EOFs are estimated from these thermodynamically normalized variables:

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$$
[-\bar{\alpha} T(t), \bar{\beta} S(t)] \approx \text{PC}(t) \text{ EOF}, \quad (2)
$$

where $\bar{x}$ designates the temporal average of $x$.

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3.2.2 Description of the EOFs

The EOFs are calculated from ISAS20 temperature and salinity fields, weighted as $-\bar{\alpha}\Delta T(t)$ and $\bar{\beta}\Delta S(t)$. Variables $\alpha(t)$ and $\beta(t)$ are first calculated at all time steps of the learning period, then temporally averaged.

The coupled EOF decomposition captures a substantial portion of both variables' variability while significantly reducing the dimensionality of the system. With $L = 15$, ~72% and ~66% of the total variances of the initial true temperature and salinity fields are explained, respectively. Temperature signals at 5, 10, 50, 100, 300, and 500 m depths are reconstructed up to ~75%, 75%, 73%, 75%, 65%, and 52%, respectively. For salinity signals, percentages are 67%, 67%, 68%, 57%, 56%, and 46%.

The EOF patterns show structures associated with ENSO variability in oceanic temperature and salinity (Fig. 1a-l). The first coupled EOF shows a temperature tongue extending from America to 140°E and a strong salinity anomaly around the dateline, in the ITCZ and South Pacific Convergence Zone (SPCZ), due to changes in precipitation and ocean dynamics (Fig. 1a, g). The ENSO signature in temperature penetrates deeper than it does for salinity. Salinity variability is confined to the surface (Fig. 1b and h).

The second EOF (Fig. 1c, d and i, j) is associated with changes (positive in the figure) concentrated in the center of the basin around the dateline and extending poleward in a horseshoe shape (Fig. 1c), while changes of opposite signs occur in the
<figure><img src="image_2.png" /><figcaption>**Fig. 1** The potential temperature component of the first three coupled EOFs at 5 m depth and as a zonal section along the equator is shown in panels (a, b), (c, d), and (e, f), with each pair associated with the first, second, and third mode, respectively. Panels (g, h), (i, j), and (k, l) display practical salinity anomalies associated with the coupled EOFs. Temperature and salinity panels use different colormaps. Associated colorbars are found on each side of panel m. Panel m shows the percentage of explained variance in the initial temperature and salinity time series as a function of the number of EOFs used for their approximation. Solid lines represent the explained variance in the coupled EOF decomposition, while dotted lines are associated with univariate EOFs. In this panel, the x-axis increases logarithmically.</figcaption></figure>

eastern part, along the equator, associated with upwelling (Fig. 1c and d). Salinity changes are more widespread over the basin, and the contrast between regions of opposite changes is stronger (Fig. 1i). The third EOF (Fig. 1e, f and k, l) is associated with a significant increase in the subsurface below 50 m (Fig. 1f), SST decrease east of the dateline, and well-marked salinity changes, with a western salinity decrease and its augmentation along the equator and east of the SPCZ region.

It is important to note that the structures of these EOFs only determine the spatial distribution of changes in salinity and temperature. Temporally, the changes are modulated by the coefficients $PC(t)$, notably with changes in sign. For the first EOF, $PC(t)$ would be positive during El Niño and negative during La Niña.

However, relating the EOFs to specific dynamics in the tropical Pacific is likely not straightforward; instead, several modes may be needed to represent them. Therefore, ENSO variability may be expressed by a combination of the first, second, and other EOFs. Eastern and Central Pacific El Niño events (Kao and Yu, 2009; Chi et al., 2022) represent two types of spatial distributions for SST anomalies. In the literature, they were found to be well represented by their respective combinations of the first and second surface temperature EOFs (Takahashi et al., 2011). How the variability is shared among three-dimensional EOFs is more uncertain. The influence of the thermocline and halocline variability may spread ENSO-related changes over more modes, as subsurface heat content and SST do not evolve simultaneously (Zhao et al., 2021).

The third, fourth, and higher EOFs are thus important to consider, as they add degrees of freedom when expressing the system's state. Also, the EOF space reduction applied to a nonlinear system may preserve long-living structures but neglect the
stochastic components that modulate them if the truncation is too severe (Farrell and Ioannou, 2001; Wang and Scott, 2005).

Each additional mode contributes progressively less to the explained variance (Fig. 1m), which is a characteristic feature of EOF decomposition. The first EOFs for temperature explain a greater amount of the initial variance than they do for salinity. Coupled EOFs explain less salinity variance than the univariate version. Conversely, the differences between the two EOF versions for temperature are minimal. For salinity, the coupled EOFs express about 5-8% less of the initial signal variance than univariate EOFs.

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## 3.3 OSSE

To validate salinity reconstruction by RedAnDA TS, its efficiency is first assessed through an OSSE (Masutani et al, 2010), using OCCIPUT data (Penduff et al, 2014; Bessières et al, 2017), as in Oulhen et al (2024). Analogs and predecessors are evaluated during the 1995-2015 learning period (red 1, Figure 2). The period spanning 1961-1994 is reconstructed at a monthly resolution, based on in situ synthetic observations, using RedAnDA (red 2, Figure 2). The results are expressed as PC(t), which are projected back into real space to reconstruct both temperature and salinity anomalies (red 3, Figure 2).

The target truth is represented by the full-grid maps. To simplify the calculations and focus on large spatial scales, the OSSE reconstruction grids are coarsened to 3°×3° through horizontal averaging, with depth levels limited to 5, 10, 50, 100, 300, and 500 m.

In the OSSE experiment, the optimal value of *L* is determined through an initial application of RedAnDA TS using a relatively high number of EOFs. The effective contributions of each reconstructed PC(t) are then evaluated based on their temporal and spatial correlation with the reference truth, helping to identify the required number of useful EOFs (see Section 4.1). This optimal number, *L*, is selected for a second RedAnDA TS analysis. If the results remain robust, i.e., if the temporal and spatial correlation scores are still maximized for *L* EOFs, the configuration is adopted and the same number of EOFs is used for real data reconstruction.

Within the OSSE framework, the RedAnDA TS method is compared with the previous version of RedAnDA (Oulhen et al, 2024), referred to as UnivarS when applied to salinity reconstruction and UnivarT for temperature (Fig. 2).

UnivarS uses only salinity data from the learning period to derive its EOFs and catalog (blue 1, Figure 2). RedAnDA is then applied (blue 2, Figure 2), and the analyzed PC(t) are projected onto the univariate EOFs to obtain the gridded salinity analysis (blue 3, Figure 2).

To explore the potential of leveraging temperature information for salinity estimation, an S-from-T approach is also implemented. This method relies on UnivarT analyses (green 1, Figure 2). The full-grid temperature results are projected onto the temperature component of the coupled EOFs (green 2, Figure 2), then transformed back into full-grid space using the salinity component (green 3, Figure 2).

As in Oulhen et al (2024), an Optimal Interpolation (OI) method is implemented, following Good et al's 2013 methodology. This approach performs a sequential analysis
<figure><img src="image_3.png" /><figcaption>Fig. 2 Summary of data sources (lighter gray), types of EOFs and catalogs (intermediate gray), and final outputs (darker gray) for different RedAnDA approaches: UnivarT for temperature (light blue), UnivarS for salinity (dark blue), RedAnDA TS (red), and S-from-T (green). The numbers enumerate the steps in each approach.</figcaption></figure>

of temperature or salinity anomalies relative to a monthly climatology, derived from in situ profiles. Two horizontal correlation radii (300 km and 400 km) and two vertical correlation radii (100 m and 200 m) are used. Temporal persistence propagates forward ~82% of the analysis from time $t - dt$ and incorporates it into the background field at time $t$.

Correlation is used to quantify the performance of the reconstructions. It is defined as follows:

$$ \text{Correlation}(\mathbf{T}, \mathbf{T}^{\text{true}}) = \frac{\overline{\mathbf{T}(t) \times \mathbf{T}^{\text{true}}(t)}}{\sqrt{\overline{\mathbf{T}(t)^2} \times \overline{\mathbf{T}^{\text{true}}(t)^2}}}, \quad (3) $$

where $\mathbf{T}(t)$ and $\mathbf{T}^{\text{true}}(t)$ are the anomalies at time $t$, respectively, from the reconstructed signal and from the truth; and $\overline{\mathbf{T}(t)}$ designates the temporal average of $\mathbf{T}(t)$. The correlation score ranges from -1 to 1, where -1 indicates opposite phase variations, 1 indicates similar variations, and 0 indicates there is no consistency between the signals.

# 4 Results

## 4.1 OSSE – Selection of the number of EOFs

Within the OSSE framework, temperature and salinity fields are reconstructed from 1961 to 1994 using synthetic in situ measurements and compared with the truth, i.e.,
the model outputs. We construct the catalog for the different RedAnDA approaches using model outputs from 1995 to 2015 to mimic the length of the Argo period (20 years) (Oulhen et al., 2024).

The OSSE allows estimation of the best tuning for RedAnDA, notably the optimal number of EOFs ($L$). This optimum is set by considering two criteria: the ability to accurately represent temporal fluctuations in salinity and the spatial distribution of the variability. The first criterion is the spatially averaged temporal correlation between the reconstructed anomalies and the true values. The second is the spatial correlation of the interannual standard deviation with that of the truth. RedAnDA TS, UnivarS, and S-from-T are applied with $L = 40$ EOFs, and we examine the evolution of these correlation scores (Fig 3) depending on the number of EOFs used when reconstructing the gridded field (we have the analyses for the 40 temporal coefficients, but the gridded fields are evaluated by combining the temporal coefficients with their respective EOFs). This enables us to determine which $L$ optimizes the reconstruction for each RedAnDA configuration.

Increasing the number of EOFs generally improves the spatial distribution of variability, following a logarithmic evolution. However, the temporal correlation increases sharply with the first three EOFs, then grows more gradually for $L$ values in the $\sim 3-15$ interval. Beyond this range, adding more modes degrades the quality of the reconstruction for salinity anomalies.

Based on these results, we set two conditions for choosing $L$: the spatial correlation must exceed 0.9, and the temporal correlation must be maximized. The 0.9 threshold

<figure><img src="image_4.png" /><figcaption>**Fig. 3** (a) The spatially averaged temporal correlation between the anomalies of the true salinity field (1961–1994) and these from S-from-T (blue dots), RedAnDA TS (black triangles), and UnivarS (red squares) analyses, as a function of the number of EOFs used to reconstruct the gridded field. (b) The spatial correlation of the temporal standard deviation of the analyses with the true standard deviation. Monthly anomalies are used when estimating the standard deviations. The horizontal black line indicates the 0.9 threshold. Markers appear duller and smaller when the spatial correlation of the standard deviation falls below 0.9, highlighting when this threshold is reached.</figcaption></figure>
(horizontal bar in Fig 3 b) is arbitrary but allows reaching the higher correlations when L is between 10 and 20 (Fig 3a). Beyond L = 20, the correlation diminishes, likely due to the inadequacy of the EOFs to represent the changes over the reconstruction period.

For RedAnDA TS and S-from-T, we set L = 15 and for UnivarS L = 14. The values of the correlations for RedAnDA TS are 0.23 and 0.91 for temporal and spatial correlations, respectively. For UnivarS, they are 0.2 and 0.92, and for S-from-T, they are 0.23 and 0.93.

## 4.2 OSSE – Validation

We then compare the true salinity field with reconstructions by the Optimal Interpolation (OI) method and the three RedAnDA configurations (i.e., TS, UnivarS, S-from-T) applied with the selected L values.

Table 1 presents spatially averaged temporal correlation scores of the different reconstructions for three timescales: decadal, interannual, and seasonal.

Correlation scores at interannual scales indicate the superiority of RedAnDA TS (0.27) and S-from-T (0.27) over UnivarS (0.2) and OI (0.12). Regarding the decadal anomalies, the correlation scores are lower for all products (around 0.05). The ranking differs, with UnivarS having the highest score (0.11) and OI the lowest (0.01). The monthly climatology estimated over the reconstruction period remains similar to that of the learning period, with high correlation scores (about 0.85 for RedAnDA TS and 0.87 for other analyses).

To better assess the reasons for the rankings in Table 1, we study our various reconstructions from different perspectives, including structures and dynamics at depth, ENSO representation, and interannual variability in stratification.

The different salinity reconstructions at 300-m depth during the La Niña event of 1973-74 are shown in Figure 4, for October 1973, January 1974, and April 1974.

Between 10°N and 20°N and 120°E and 170°W, near Box A (northern boxed region), an intense high-salinity anomaly of about 0.15 PSS persisted throughout the three displayed months. The OI method fails to adequately reconstruct this structure (Fig. 4d, e, and f). Overall, at 300 m depth, the OI interannual anomalies barely compare with the truth due to the lack of observations in most of the basin. Even with observations along the dateline in October 1973, around 15°S and 170°W in January 1974, and along

<table><caption>**Table 1** Spatially averaged temporal correlations with the detrended truth for, from left to right, RedAnDA TS, UnivarS, S-from-T, and OI. Three lines of scores indicate the scores obtained when comparing the interannual anomalies (salinity anomalies with removal of the decadal signal), the decadal signal (10-year running-mean filtered anomalies) between 1966 and 1990, and the monthly climatology of the reconstructions.</caption><thead><tr><th></th><th>RedAnDA TS</th><th>UnivarS</th><th>S-from-T</th><th>OI</th></tr></thead><tbody><tr><td>Interannual</td><td>0.3</td><td>0.27</td><td>0.31</td><td>0.12</td></tr><tr><td>Decadal</td><td>0.09</td><td>0.11</td><td>0.09</td><td>0.03</td></tr><tr><td>Seasonal</td><td>0.85</td><td>0.88</td><td>0.87</td><td>0.87</td></tr></tbody></table>
20°N between 150°E and 160°W in April 1974, the reconstructed field displays anomalies that neither capture the zonally extended structures of the truth nor maintain consistent signs, as evidenced by the band of fresh anomaly (–0.15 PSS) located along 15-20°S (Fig. 4a-f). In situ observations may capture small-scale variability, which can alias the large-scale salinity reconstruction without sufficient additional observations to correct these spurious deviations.

RedAnDA TS, UnivarS, and S-from-T reconstruct the high-salinity anomaly near Box A, though with a reduced intensity of ~0.1 PSS (Fig. 4g-o), likely due to variance loss from spatial compression.

In the southern part of the basin, in Box B, the true salinity field shows zonal strips of strong anomalies with alternating signs (with absolute values exceeding 0.15 PSS), featuring a northern salty strip and a fresh southern strip. This structure is associated with the Southern Equatorial Current (SEC), and its interannual variability relates to ENSO variability (Kessler and Cravatte, 2013). In October 1973, while this strip is not well reconstructed by RedAnDA TS and S-from-T, it is more accurately estimated by UnivarS (Fig. 4g, j, and m). In January and April 1974, the warm side of the anomaly strip is satisfactorily reconstructed by all three methods (Fig. 4b, c, h, i, k, l, n, and

<figure><img src="image_5.png" /><figcaption>**Fig. 4** Salinity anomaly snapshots at 300-m depth in October 1973, January 1974, and April 1974. From the first row to the fifth, displayed salinity fields are the OCCIPUT output (considered the truth, detrended in this figure to better highlight interannual anomalies), OI (implemented for comparison), RedAnDA TS, UnivarS, and S-from-T, respectively. Black dots represent available observations at the current depth (larger dots) and at other depth levels (smaller dots). The black boxes in a, b, and c represent two areas of high variance, referred to as “Box A” and “Box B”. Salinity variability in these regions is associated with the Northern and Southern Equatorial Currents (Li et al, 2020b).</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>**Fig. 5** (a) and (b): averaged salinity anomalies at 300 m depth within “Box A” and “Box B” from Fig. 4a-c. The RedAnDA TS average is shown as a solid blue line, UnivarS as a dashed purple line, OI as a red line, and S-from-T as a green line. The detrended signals of the truth are shown in black. The vertical blue line indicates the selected month in Fig. 4b, e, h, k, and n.</figcaption></figure>

o). However, around 120°W and along 20°S, UnivarS reconstructs a spurious southern salty anomaly instead of the fresh extension (Fig. 4g-o).

Between October 1973 and April 1974, at the equator between 170°W and 100°W, a fresh anomaly appears and propagates westward (Fig. 4a, b, and c). This event is not captured by the OI method (Fig. 4d, e, and f). RedAnDA approaches show more skill in reconstructing this change, particularly UnivarS, which more accurately reproduces the contrast between the central fresh anomaly and the salty patch eastward (about 0.1 PSS difference) (Fig. 4a-c, g-o). Again, the intensity of the anomalies is slightly underestimated by RedAnDA approaches by about ~0.05 PSS.

The temporal evolution of salinity in “Box A” (Fig. 4a, b, and c) is presented in Figure 5a. It is strongly related to the interannual variability of the NEC, which carries saltier or fresher waters from the subtropics. The most intense events, occurring in 1970-1972, 1973-1976, 1984-1986, and 1988-1989, corresponded to La Niña events. They are accurately captured by the different reconstructions, although underestimated by about 0.05 PSS, except for the 1973-1976 and 1988-1989 events. Overall, S-from-T and RedAnDA TS yield very similar results, with S-from-T being smoother than RedAnDA TS, and their correlations with the truth are 0.59 and 0.61, respectively. Despite fewer salinity observations compared to the temperature, the results from UnivarS are accurate, with a correlation reaching 0.63. The OI method fails to reconstruct the variability between 1976 and 1983. Most of the time the OI fluctuations are noisy, resulting in a relatively low correlation score of 0.1.

The temporal variability of “Box B” (150°E-110°W, 10°S-20°S, Fig 4 a, b, and c) is associated with the SEC (Fig. 5b). Salinity fluctuations are more intense in this region than in the northern part of the basin (up to twice the greatest amplitude, as in 1983). Additionally, decadal variability appears significant, with a roughly positive
<figure><img src="image_7.png" /><figcaption>**Fig. 6** (a) The filtered temporal evolution of Niño 3.4 indices obtained with temperature anomalies from OCCIPUT (thick black lines), OI (red), RedAnDA TS (blue), and UnivarS (magenta) with time on the y-axis. (b), (c), (d), and (e) Salinity anomalies averaged between 5°S and 5°N at 5 m depth over time from OCCIPUT, OI, RedAnDA TS, and UnivarS, respectively. A third-order low-pass Butterworth filter is used to remove the annual signals from Niño 3.4 indices to facilitate their interpretation and readability. All anomalies are calculated relative to the 1995-2015 period.</figcaption></figure>

phase between 1961 and 1974, a negative phase between 1976 and 1987, and a positive phase again from 1988 onward. RedAnDA TS and S-from-T fail to capture the decadal variability, despite seeming to capture the interannual fluctuations. Their correlation scores are 0.42 for RedAnDA TS and 0.44 for S-from-T, higher than OI's score (0.3). UnivarS achieves the highest score of 0.46 though it does not efficiently capture certain changes, such as those in 1964 and 1983. Its higher score may be due to its consistent positive sign during the positive phases of decadal variability. However, since UnivarS fails to reconstruct the negative phase, it likely does not accurately estimate this variability.

We now assess the ENSO variability at the surface, with Figure 6 showing SST Niño 3.4 indices and SSS anomalies in a longitude-time system. First, SST estimated by all the reconstructions satisfactorily represents the ENSO events (Fig. 6a).

The relationship between the western Pacific fresh pool position and ENSO is clear, as the Niño 3.4 index aligns well with the zonal displacements of the fresh anomalies throughout the period (Fig. 6a, b). The development of El Niño is accompanied by an eastward displacement of the fresh pool, as trade winds weaken, allowing warm waters to extend further eastward, inducing changes in oceanic currents and enhanced precipitation in the central Pacific around 180°E. During La Niña events, saltier anomalies appear near the dateline, associated with the opposite behavior. This is consistent with Maes et al. (2005).

In the central tropical Pacific (around 140°W), the OI reconstruction fails to reconstruct salinity sufficiently, as most of the in situ data along the equator are located near the coasts of the tropical Pacific Ocean, west of 150°E and east of 110°W (Fig. 6c).
Consequently, anomalies are mostly found west of the dateline and the easternmost part of the basin, and between 160°W and 110°W, no signal is satisfactorily reconstructed (Fig. 6b and c). The western anomalies roughly correspond between the truth and the OI, but the zonal distribution of the changes is underestimated in the latter. Eastern anomalies are poorly resolved. The OI fails to reconstruct most of the other annual salty events, such as those in 1988-1993 (Fig. 6b and c). However, events in 1983 and 1994 are captured.

Both RedAnDA TS and UnivarS approaches provide more robust reconstructions of surface salinity (spatially averaged temporal correlation scores reaching 0.43 and 0.41, respectively, and 0.41 for S-from-T against 0.26 for OI). Most of the fresh pool displacements associated with ENSO, west of 160°W, are reconstructed, e.g., in 1963, 1966, 1969, 1972, 1976, 1983, and 1988 (Fig. 6b, d, and e). In 1983, the displacement was strong enough to create an intensified fresh signature in the eastern Pacific. This event was reconstructed successfully, though the saltier anomalies west of 150°E appear overestimated. A similar overestimation is also found during the 1972 El Niño event (Fig. 6b, d, and e). UnivarS shows a tendency toward persistence, which may mask some La Niña events, such as before 1970 (Fig. 6b and e). The persistence issue is also noticeable between 1976 and 1980, hiding more subtle salinity fluctuations west of the dateline.

East of 160°W, the true salinity exhibits annual salty events, some of which are particularly intense, such as in 1972 (Fig. 6b). Some short-lived and less frequent fresh events also occur, notably in 1973, 1974, and 1975. Neither OI nor UnivarS successfully reconstructs this variability (Fig 6 c and e). RedAnDA TS captures some of it, but with underestimated intensity as in 1972 (Fig 6 d). In the western Pacific, correlations between the true equatorial SSSA values and the reconstructions are approximately 0.54, 0.5, 0.53, and 0.32, for RedAnDA TS, UnivarS, S-from-T, and OI, respectively. In contrast, east of 160°W, the correlations are around 0.29, 0.30, 0.27, and 0.21.

RedAnDA TS and UnivarS tend to propagate strong western anomalies eastward (Fig. 6b, d, and e), which can introduce spurious changes, such as a non-existent fresh anomaly in 1992-1993, around 110°W (Fig. 6d and e).

Reconstructions of temperature and salinity allow for the assessment of density and ocean stratification. Here, stratification is quantified by the Brunt-Väisälä frequency $N^2(T, S)$. It is calculated as follows:

$$N^2(T, S) = -\frac{g}{\rho} \frac{\partial \rho}{\partial z} \approx g \left( \bar{\alpha} \frac{\partial T}{\partial z} - \bar{\beta} \frac{\partial S}{\partial z} \right), \quad (4)$$

where $g$ is the gravitational constant, $\rho$ is the density, $z$ is the depth oriented upward, $\bar{\alpha}$ and $\bar{\beta}$ are the temporally averaged thermal expansion coefficient and haline contraction coefficient, respectively. We compute $N^2(T, S)$ using absolute temperature ($T$) and salinity ($S$) values from all reconstructions. Anomalies are derived by subtracting the corresponding monthly climatology for 1961-1994. UnivarT temperature product was used for S-from-T and UnivarS. The skill of the reconstruction with respect to stratification is estimated through their correlations with the truth (Fig. 7).

Surface (5 m and 10 m) and 500-m depth stratification are the most poorly reconstructed levels by the four methods, with OI showing the lowest correlations: 0.08, 0.21, and 0.20 on average, respectively (Fig. 7a-e). Between 50 and 300-m depth, the
<figure><img src="image_8.png" /><figcaption>Fig. 7 (a) Meridionally (25°S-25°N) averaged correlation of the true N² anomaly with N² anomalies estimated from the UnivarS, OI, S-from-T, and RedAnDA TS products, with depth. (b) to (e) Meridionally averaged correlations of the true N² to N² estimated from OI, RedAnDA TS, UnivarS, and S-from-T, respectively, with depth.</figcaption></figure>

correlations are higher (0.3-0.5), with the 300-m level being the best reconstruction for all products (~ 0.46) (Fig. 7a-e). S-from-T, UnivarS, and RedAnDA TS share similar correlation scores.

Two regions are better evaluated (correlations between 0.3-0.6 against 0.1-0.3 around 135°W) (Fig. 7b-e). These correspond to regions where the regional observational sampling is higher.

To further assess the accuracy of reconstructed stratification at the interannual timescale and to visualize the salinity contribution, the stabilizing and destabilizing effects of Ocean Salinity Stratification (OSS) in the upper 500 m layers are determined following Maes and O'Kane (2014) and O'Kane et al (2016). We consider $N_T^2(T, S)$ and $N_S^2(T, S)$, the respective contributions of temperature and salinity to the overall stratification. We approximate them as:

$$N_T^2(T, S) \approx g\bar{\alpha}\frac{\partial T}{\partial z}, \qquad (5)$$

$$N_S^2(T, S) \approx N^2(T, S) - N_T^2(T, S). \qquad (6)$$

The stabilizing impact of salinity on water masses, with amplification of N², denoted OSS+, is determined as the average over the upper 500 m of the positive values of $N_S^2(T, S)$. The destabilizing part is OSS- and is the average over the upper 500 m of the negative values of $N_S^2(T, S)$. Temporal means and interannual standard deviations of OSS+ and OSS- for the different products are shown in Figure 8.

In the model truth, in the Southern Hemisphere, the average OSS- distribution has a greater amplitude: lower than $-8 \times 10^{-6} \text{ s}^{-2}$ (Fig. 8a). Along 10°N, it is lower: around $-4 \times 10^{-6} \text{ s}^{-2}$. This global distribution is reconstructed by OI, RedAnDA TS, and UnivarS, partly due to a priori seasonal climatology (Fig. 8c, e, and g). However, along the equator, east of 180°E, the reconstructions overestimate the OSS-.

Regarding the mean OSS+ true distribution (Fig. 8b), two regions with values exceeding $1.5 \times 10^5 \text{ s}^{-2}$ are found, corresponding to the Western Pacific Fresh Pool
(west of 180°E), the SPCZ (along 10°S), and the Eastern Pacific Fresh Pool (east of 120°W, north of 5°S). A local minimum is found on the equator, between 180°E and 120°W. The mean OSS+ distribution in OI, RedAnDA TS, and UnivarS reconstructions correlates well with the true OSS+, exhibiting no significant differences (Fig. 8).

Areas of high interannual variability (shading in Fig. 8) for OSS− and OSS+ roughly align with regions where salinity significantly affects the upper 500 m stratification (Fig. 8a and b). For OSS−, south of 10°S and north of 8°N between 180°E and 120°W, the RedAnDA TS and UnivarS OSS− standard deviation distributions match the truth, with similar values: up to $5 \times 10^{-6} \text{ s}^{-2}$ (Fig. 8a, e, and g). The OI reconstructs only partially the OSS− variability (Fig. 8a and c). East of 120°W, both RedAnDA reconstructions and, to a lesser extent, the OI reconstruction, express significant spurious OSS− variability (Fig. 8a, c, e, and g). The spatial correlation of OSS− standard deviation is higher for RedAnDA TS (0.43) than for OI (-0.13) and UnivarS (0.33). The negative correlation observed in OI is primarily due to spurious results north of Australia at 10°S.

<figure><img src="image_9.png" /><figcaption>**Fig. 8** (a, c, e, g) OSS− averaged values (contours) and interannual standard deviations (shading) estimated from true salinity and temperature, OI T/S products, RedAnDA TS, and UnivarT/UnivarS, respectively. Dash-dot lines, dashed lines, and solid lines correspond to $[-4 \times 10^{-6}, -6 \times 10^{-6}] \text{ s}^{-2}$. (b, d, f, h) OSS+ averaged values (contours) and interannual standard deviations (shading) estimated from true salinity and temperature, OI T/S products, RedAnDA TS, and UnivarT/UnivarS, respectively. Dash-dot lines, dashed lines, and solid lines correspond to $[5 \times 10^{-6}, 1 \times 10^{-5}, 1.5 \times 10^{-5}] \text{ s}^{-2}$.</figcaption></figure>

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<figure><img src="image_10.png" /><figcaption>**Fig. 9** (a) Annual histogram of in situ salinity observations in the tropical Pacific between 5 and 500-m depth. (b), (c), (d), and (e) Absolute salinity averaged between 5°S and 5°N at 5-m depth over time from RedAnDA TS assembled with ISAS, IAP, EN4, and UnivarS assembled with ISAS, respectively. The thick black line highlights the 34.8 PSS isohaline, an ENSO index used by Qu and Yu (2014). The horizontal black line separates ISAS reconstructed salinity from that of RedAnDA TS (b) and UnivarS (e).</figcaption></figure>

For OSS+, in the Western Pacific Fresh Pool, Eastern Pacific Fresh Pool and SPCZ regions, interannual standard deviations in the OI reconstruction appear underestimated compared to RedAnDA TS and UnivarS (Fig. 8b, d, f, and h). The correlation scores for OI, RedAnDA TS and UnivarS are 0.73, 0.92, and 0.92, respectively.

## 4.3 Application to real data

We apply RedAnDA TS and UnivarT/UnivarS to real oceanographic data, maintaining the same number of EOFs as in their OSSE versions. We reconstruct salinity and temperature for 1930-2001. The IAP and EN4 products are used for intercomparison. First, we compare the three different SSS results in terms of absolute salinity. Their respective climatologies are calculated for 2002-2020. This period aligns with the ISAS20 product, which serves as the catalog (learning period) in our experiment. We calculate salinity-based ENSO indices and compare them to the Niño 3.4 index and the Southern Oscillation Index (SOI) from the National Oceanic and Atmospheric Administration (NOAA, Ropelewski and Jones, 1987; Rayner et al, 2003). The impact of salinity on stratification is then assessed for each product and the results are compared with results from O’Kane et al (2016).

Surface salinity variations in the Pacific are shown for the different products in Figure 9 in a longitude-time coordinate system, alongside the histogram of salinity
observations over time. Between 180°E and 110°W, IAP shows higher absolute salinity on average (by approximately 0.16 PSS) than RedAnDA TS, which in turn is moderately saltier than EN4 (around 0.02 PSS). Similar values are found for UnivarS biases (Fig. 9b-e). This difference in salinity magnitude results in smaller fresh pools in the western and eastern Pacific for the IAP product (Fig. 9c). After 2002, the bias between IAP and ISAS is approximately 0.18 PSS, while it is 0.05 PSS between ISAS and EN4 and 0.23 PSS between IAP and EN4.

EN4's relaxation to climatology in the absence of observations is apparent, notably before 1960 (Fig. 9a and d). During this period, EN4's salinity field exhibits mostly the seasonal cycle related to the first guess climatology.

Following Qu and Yu (2014), we define the separation of the WPFP from the central Pacific salinity as the 34.8 isohaline front (Fig. 9b, c, d, and e). In their study, they defined the Niño S34.8 index, i.e., the longitude of the front, to express ENSO variability in terms of sea surface salinity (from SST and SSS analyses of satellite and in situ observations). For the IAP product, which has higher average SSS than other products, the 34.8 isohaline is located around 159°E, while it lies between 167°E and 165°E for EN4, UnivarS, and RedAnDA TS. UnivarS shows greater variability east of 120°W than RedAnDA TS. For example, in 1962, it captures a fresh event reaching 34 PSS that is absent in RedAnDA TS. Similarly, UnivarS reconstructs more persistent high-salinity events (reaching 34.8 PSS) in 1973, 1988, 1989, 1992, 1993, 1994, and 1998 (Fig. 9b and e).

We observe larger extensions of the fresh pool during the major El Niño events of 1965, 1972, 1987, and 1997. The associated retraction of the pool during major La Niña events is observed in 1954, 1975, 1988, and 1998. Disagreements between the salinity reconstructions, highlighted by the 34.8 isohalines, are unsurprisingly intensified during poorly observed periods, such as before 1965 (Fig. 9a, b, c, d, and e). During these periods, RedAnDA TS and UnivarS still reconstruct interannual variability.

To assess the ENSO-related variability of the 34.8 isohaline, we compare correlations of the different Niño S34.8 indices with the Niño 3.4 index from Rayner et al (2003) (Table 2). A second salinity-based ENSO index complements the comparison. It is calculated as $C - (A + B)$, where A is the surface salinity anomaly averaged over 2°S-2°N and 150°E-170°E, B over 2°S-2°N and 170°E - 170°W, and C over 160°E - 160°W and 25°S-10°S (Singh et al, 2011). In their study, they used Delcroix et al's 2011 salinity analysis from in situ observations (Voluntary Observing Ships, TAO/TRITON moorings, CTD and Argo profiles), which was representative of 5 m depth variability. The correlation of their index with the Southern Oscillation Index (SOI) monthly anomalies from Ropelewski and Jones (1987) is analyzed.

To validate this approach, we calculate correlation scores (Table 2) in a way similar to Singh et al (2011); Qu and Yu (2014), with equivalent indices, temporal windows and lags, enabling direct comparison with their former results (Ref. Value in Table 2). Correlation scores of the RedAnDA products concatenated with ISAS, IAP and EN4 are calculated in running temporal windows (31 and 8 years long for the indices from Singh et al (2011) and Qu and Yu (2014), respectively). The results show increasing correlation scores from the 1930s to 2020 (not shown), suggesting an expected improvement in surface salinity reconstruction over time. The standard deviations
reveal how correlation scores vary over time, with high standard deviations indicating a deterioration of correlation in the past.

<table><caption>**Table 2** First row: Temporal mean and standard deviation of 8-year running correlations between Qu and Yu's 2014 salinity-based ENSO index, with Niño 3.4 leading by 1 month, for RedAnDA TS-ISAS20 (1930-2020), IAP (1940-2021), EN4 (1930-2019), and UnivarS-ISAS20 (1930-2020). Second row: Mean and standard deviation of 31-year running correlations between Singh et al's 2011 salinity-based ENSO index with the SOI index leading by 2 months. The first column (Ref. Value) shows the scores obtained in both reference studies during their respective periods: 2005-2013 for Qu and Yu (2014) and 1977-2008 for Singh et al (2011).</caption><thead><tr><th></th><th>Ref. Value</th><th>RedAnDA TS</th><th>IAP</th><th>EN4</th><th>UnivarS</th></tr></thead><tbody><tr><td>Qu & Yu, 2014</td><td>0.75</td><td>0.74 ± 0.17</td><td>0.48 ± 0.22</td><td>0.46 ± 0.28</td><td>0.64 ± 0.28</td></tr><tr><td>Singh et al., 2011</td><td>-0.88</td><td>-0.56 ± 0.09</td><td>-0.53 ± 0.06</td><td>-0.51 ± 0.11</td><td>-0.55 ± 0.15</td></tr></tbody></table>

RedAnDA TS indices show the highest correlations of about 0.74 and -0.56, with relatively low standard deviations. These values are close to the reference values from Singh et al (2011) and Qu and Yu (2014), respectively, suggesting good reconstruction skill of RedAnDA TS compared to other methods. Standard deviations for EN4 and UnivarS are high, indicating discrepancies between the correlation scores during the mid-20th century and the 21st century. On average, IAP scores are lower than those of RedAnDA TS and UnivarS. While UnivarS correlation scores are satisfactory, poor observational sampling significantly impacts the reconstruction. The difference between RedAnDA TS scores and those from Singh et al (2011) may result from differences in their respective analysis methods.

The estimates of salinity control on stratification (OSS- and OSS+) by RedAnDA TS, EN4, IAP, and UnivarT/UnivarS are compared in Fig. 10. The results are compared with those of O'Kane et al (2016), whose Fig. 9 shows the upper 500 m averaged OSS+ and OSS- fields, estimated from the CSIRO reanalysis dataset Oke et al (2013), an EnOI scheme, using the ACCESS-O model, and in situ and remote sensing observations.

The averaged distributions (contours) for OSS- and OSS+ from RedAnDA TS and UnivarS resemble those obtained in the OSSE (Fig. 8) and the results of O'Kane et al (2016, Fig. 9). RedAnDA products and EN4 fields show similar patterns, particularly for OSS+, while IAP's absolute salinity appears notably intense.

The OSS- and OSS+ interannual variability (color shades) estimated by RedAnDA TS and UnivarS follows the areas of pronounced salinity effects on stratification, a previously observed tendency. Both products reproduce the variations observed in O'Kane et al (2016) (Fig. 10a, b, g and h). In the EN4 and IAP products, the reconstructed variability differs from the analysis of O'Kane et al (2016) (Fig. 10c, d, e and f).

# 5 Discussion

Using the OSSE, we calculate RedAnDA's performance compared to the classical OI approach. RedAnDA variations (RedAnDA TS, S-from-T, UnivarS) can estimate the interannual changes in salinity anomalies more accurately than a classical OI approach.
<figure><img src="image_11.png" /><figcaption>**Fig. 10** (a, c, e, g) OSS- averaged values (contours) and interannual standard deviations (colors) estimated from RedAnDA TS, EN4, IAP, and UnivarS, respectively. Dashed and dotted lines, dashed lines, and solid lines correspond to [-0.5 x 10⁻⁵, -1 x 10⁻⁵, -1.5 x 10⁻⁵] s⁻². (b, d, f, h) OSS+ averaged values (contours) and interannual standard deviations (colors) estimated from RedAnDA TS, EN4, IAP, and UnivarS, respectively. Dashed and dotted lines, dashed lines, and solid lines correspond to [1 x 10⁻⁵, 2 x 10⁻⁵, 3 x 10⁻⁵] s⁻².</figcaption></figure>

Applied to real data, RedAnDA TS and UnivarS are compared with IAP and EN4 products. The interannual scale is better represented by the RedAnDA approaches (Tab. 1,2, Figures 6,8,9,10). Notably, RedAnDA better estimates the complexity of the spatial distribution of these anomalies through the use of EOFs. The vertical structure of salinity in RedAnDA products is more consistent with its description in O’Kane et al.’s (2016) dedicated study.

ENSO-related surface salinity variability is particularly well represented in coupled EOFs approaches (RedAnDA TS, S-from-T). This type of space-reduction captures temperature and salinity interannual covariability and filters out some salinity small-scale features, likely intensifying the ENSO-related signature in salinity reconstruction.

The interannual variability of SSS derived from RedAnDA TS shows a stronger correlation with ENSO-related temperature indices than UnivarS, IAP, and EN4. This correlation value is consistent with reference values from other studies Singh et al. (2011); Qu and Yu (2014).

S-from-T’s satisfactory results demonstrate the accuracy of coupled EOFs approach in representing interannual changes. Its results are close to those of RedAnDA TS. This likely occurs because salinity observations are significantly fewer than temperature observations, thus attenuating their impact when assimilated in RedAnDA TS.
1059 The choice of space-reduction and variable coupling techniques is essential in deter-
1060 mining the final result. In this study, the retained component of TS covariability
1061 favors the reconstruction of ENSO-related changes at the expense of reconstructing
1062 variability in the Eastern Pacific and at depth. Future work should explore different
1063 approaches to estimate rotated EOFs (Lian and Chen, 2012) and other space-reduction
1064 techniques like Dynamical Modes (Gavrilov et al, 2019).

1065 The seasonal scale is well estimated in all different products of the OSSE (OI,
1066 RedAnDA TS, UnivarS and S-from-T). The climatology is well estimated over the
1067 learning period. However, all methods struggle to resolve decadal variability. This low-
1068 frequency variability is likely associated with changes in the North and South Pacific
1069 gyres, and the tropical Pacific EOF decomposition for RedAnDA may not include
1070 them. Additionally, the length of the learning period may limit the extent to which
1071 decadal variance can be incorporated into EOFs. Considering EOFs for the whole
1072 Pacific could help capture this aspect of variability.

1073 A 20-year learning period limits the EOFs' ability to capture long-term variability.
1074 Compared to IAP and EN4, RedAnDA TS trends in salinity differ, with increasing
1075 SSS west of 170°E, north of 5°N. A limited catalog might not adequately represent the
1076 diversity of system dynamics and its long-term variability. Investigating the sensitivity
1077 of temperature and salinity reconstruction quality to the size of the catalog is necessary
1078 to fully understand these implications.

1079 The RedAnDA approaches effectively capture the (de)stabilizing effects of salinity
1080 on stratification on average. At the interannual scale, these effects were well recon-
1081 structed, though with an overestimation of the destabilizing effect OSS⁻ and an
1082 underestimation of the stabilizing effect OSS⁺ in the Eastern Pacific fresh pool in the
1083 OSSE.

1084 The better reconstructed interannual variations in stratification by UnivarS and
1085 S-from-T stem from the inclusion of UnivarT, which should be more thoroughly com-
1086 pared with the temperature component of RedAnDA TS in future work. UnivarT was
1087 studied in a previous study (Oulhen et al, 2024) and showed promising results.

1088 From the salinity reconstructions by RedAnDA TS, the interannual changes appear
1089 more similar to EN4 results than to IAP. As IAP uses CMIP5 outputs to calculate
1090 the background and covariance used in its analysis, this may indicate the limitations
1091 of using model-based information when reconstructing interannual patterns of salinity
1092 variability with real data.

1093

1094 6 Conclusion
1095

1095

1096 RedAnDA was used to reconstruct monthly salinity (and temperature) in the upper
1097 500 m of the tropical Pacific during the 20th century, assimilating data from Ocean
1098 Stations, CTDs, moored, and drifting buoys. It has also been extended to the cou-
1099 pled reconstruction of temperature and salinity (RedAnDA TS), leveraging the greater
1100 abundance of temperature observations (MBTs, XBTs) during this period and the
1101 common dynamics governing their distribution. To exploit this mutual relationship,
1102 their covariance was calculated over the Argo period, from 2002 to 2020, and employed
1103

1104
to construct Empirical Orthogonal Functions (EOFs) that optimally reduce the dimensionality of the system while preserving the main features of temperature and salinity covariability.

In an Observing System Simulation Experiment (OSSE), the performance of the reconstructions was assessed and compared, notably with a state-of-the-art Optimal Interpolation product following Good et al.'s (2013) methodology. The results showed that for reconstructing ENSO-related salinity variability, RedAnDA TS (salinity reconstruction coupled with temperature) is more effective than the OI and UnivarS, particularly during periods with fewer in situ observations. Including temperature information when reconstructing salinity gives satisfactory results, as evidenced by a better representation of major ENSO events in the western tropical Pacific. The S-from-T approach was also implemented, corresponding to the projection of UnivarT reconstruction onto coupled EOFs to determine the salinity field through correlation-based equivalence. The vertical structure of salinity is also enhanced, showing better correlation scores in stratification reconstruction. However, decadal variability may still be poorly estimated in our products, and caution should be exercised when using them to study long-term changes.

RedAnDA TS and UnivarS were applied to real data, enabling the reconstruction of regional temperature and salinity patterns and time series since 1930. Salinity results were compared with EN4 and IAP data, showing notable differences in salinity mean state, stratification mean state, and fluctuations.

The new TS product spanning 1930-2001, combined with its learning period (ISAS20), constitutes an unprecedented 90-year super-product for assessing the modulation of ENSO by longer components of variability and vice versa (Power et al, 2021; Hu et al, 2022). As ENSO patterns evolve in a warming climate, precipitation may intensify and shift eastward (Cai et al, 2021), potentially freshening salinity in the western equatorial Pacific and SPCZ (Singh et al, 2011). The combination of RedAnDA TS and ISAS20 could provide a valuable database for studying such shifts in ENSO regimes, provided low-frequency variability is improved.

**Acknowledgments.** ISAS temperature and salinity monthly gridded field products are made freely available by SNO Argo France at LOPS Laboratory (supported by UBO/CNRS/Ifremer/IRD) and IUEM Observatoire des Sciences de l'Univers (UBO/CNRS/IRD) at https://doi.org/10.17882/52367. The authors express gratitude to Thierry Penduff and Jean-Marc Molines for providing OCCIPUT outputs and their invaluable assistance. Appreciation is extended to Gaël Alory, Aida Alvera Azcárate, Laurent Bertino, Sophie Cravatte, Christophe Maes, Anne-Marie Tréguier, Jérôme Vialard, and Pascal Yiou for their constructive discussions and their suggestions.

## Declarations section

## Ethical Approval and Consent to participate

Not applicable.
1151 Human Ethics

1152 Not applicable.

1153 Not applicable.

1154 Consent for publication
1155

1156 All authors consent for publication.

1157

1158 Funding
1159

1160 Erwan Oulhen was funded by the Région Bretagne and the Université de Bretagne

1161 Occidentale. This study was conducted within the framework of the LEFE-GMMC

1162 OASIS project (CNRS-INSU/GMMC).

1163

1164 Author's contributions
1165

1165 E.O designed the study, conducted the analyse and wrote the main manuscript text.

1166 All other authors (N.K, P.T, B.B, and F.S) have participated to design the study, 1167 have edited the manuscript, and have looked for funding.

1168

1169 Availability of supporting data
1170

1171 ISAS20 data are available through 10.17882/52367; EN.4.2.2 profiles and objec-

1172 tive analyses are available through https://www.metoffice.gov.uk/hadobs/en4/

1173 download-en4-2-2.html; OCCIPUT data are available upon demand; IAP data are

1174 available through http://www.ocean.iap.ac.cn/; NOAA Niño 3.4 and SOI indices are

1175 available through https://psl.noaa.gov/; RedAnDA codes are available through https:

1176 //github.com/eoulhen/RedAnDA. RedAnDA TS, UnivarS and UnivarT products, as

1177 well as other datasets from our experiments are available through 10.17882/102598.

1178

1179 Competing interests
1180

1180 All authors declare that they have no conflicts of interest.

1182

1183 Clinical Trial Number in the manuscript

1184 Not applicable.

1185 Not applicable.

1186

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