Recent studies have shown significant sea surface salinity (SSS) changes at scales ranging from regional to global. In this study, we estimate global salinity means and trends using historical (1950–2014) SSS data from the UK Met. Office Hadley Centre objectively analyzed monthly fields and recent data from the SMOS satellite (2010–2014). We separate the different components (regimes) of the global surface salinity by fitting a Gaussian Mixture Model to the data and using Expectation–Maximization to distinguish the means and trends of the data. The procedure uses a non-subjective method (Bayesian Information Criterion) to extract the optimal number of means and trends. The results show the presence of three separate regimes: Regime A (1950–1990) is characterized by small trend magnitudes; Regime B (1990–2009) exhibited enhanced trends; and Regime C (2009–2014) with significantly larger trend magnitudes. The salinity differences between regime means were around 0.01. The trend acceleration could be related to an enhanced global hydrological cycle or to a change in the sampling methodology.

Global sea surface salinity (SSS) is changing at scales ranging from
regional to global

Recently,

The SSS spatial pattern has been associated with the “rich get
richer” mechanism for evaporation-precipitation

The determination of a single SSS trend by DW10 highlighted
significant challenges (e.g., data deficiencies in some regions and
times), but it represented only a first step toward a characterization
of the time evolution of global salinity. The results of recent
analyses of other ocean parameters, such as water level

The question we are trying to address in this study is whether the SSS changes are due to: (1) a regime shift in which the SSS has moved from one equilibrium state to another (maybe even several regime shifts), (2) a constant SSS trend (no new equilibrium has been achieved), (3) a varying SSS trend (not only is SSS changing, but the rate of change varies); or (4) a combination of the above.

In this study, we separate the different regimes (components with
substantially different characteristics) of the global SSS
(1950–2014) by fitting Gaussian Mixture Models (GMM) with and without
trends to the SSS data to characterize, not only the means, but also
the trends. The GMMs are estimated using an Expectation–Maximization
algorithm with the number of components determined non-subjectively by
the Bayesian Information Criterion to extract the optimal number of
means and trends. The long-term global SSS dataset from the UK
Met. Office Hadley Centre

The Met Office Hadley Centre provides global quality controlled ocean
temperature and salinity profiles and monthly long-term objectively
analyzed global fields with a one degree spatial resolution

In this work, the surface salinity field (top layer of the dataset)
from 1950 to 2014 is used. The 1950 cutoff was chosen to match
previous trend studies

The recently available SMOS (Soil Moisture and Ocean Salinity)
satellite

The SMOS satellite data exhibited deficiencies near coastal areas and
in high latitudes

A Gaussian Mixture Model (GMM) is a probabilistic model for which the
probability density function is a combination of two or more Gaussian
distributions. The Expectation–Maximization (EM) algorithm is an
iterative procedure to find a Maximum Likelihood Estimate (MLE) of the
parameters of a GMM. In the past, the EM algorithm was used to
separate the regimes of a spatial time series

In this implementation, we introduce the possibility of defining the
GMM by both a mean and a linear temporal trend. After we have found
the number of components (representing probability density functions),

Let

The two steps of the EM iterative procedure are:

We enforced that the time series is an autoregressive process of order
one (AR(1)) to avoid rapid switching between regimes. Thus, the
salinity at time

An EOF analysis can be conducted based on the component distributions
covariances,

Our approach is related to the multivariate adaptive regression
splines (MARS) method

To determine the optimal number of components (regimes) in the GMM, we
use the Bayesian Information Criterion (BIC,

The penalty term preventing over-fitting,

There are a number of potential combinations of means and trends
(Fig.

The Hadley Centre EN4 surface salinity interpolated fields
incorporated quality controlled observations in a similar manner as
the database used by

When the global SSS monthly data from the Hadley Centre EN4 were
analyzed, the EM method distinguished three separate regimes. These
regimes are characterized by different means but also different trends
(Figs.

The global surface salinity means for the three regimes
(Fig.

The trend for Regime A (1950–1990, Fig.

The salinity time evolution showed the changing temporal pattern
during the full record and the potential distinction between regimes
(Fig.

As described in Sect.

The recent availability of global surface salinity fields from
satellites (SMOS and Aquarius) provided the possibility of using
alternative data that were not included as part of the

The inclusion of the available 5

The means and differences of the two first regimes
(Fig.

As was the case with the means, the trends of the two first regimes
(A' and B') of the combined time series (Fig.

While the study focuses on the near-surface salinity, the vertical
extent of the changes can be much larger.

The described salinity change acceleration is likely the result of
global hydrological cycle intensification as was suggested by

While our most recent period (2009–2014) might be too short to be
considered a robust regime change, the differences in mean and trend
between the two early regimes (A: 1950–1990; and B: 1990–2009) are
consistent with the idea of salinity change acceleration caused by
enhanced hydrological cycle. The water cycle has been shown to be
farther increased in the period 1979–2010 due to accelerated warming

As the sampling methodology and number of observations have evolved in
time, the trend acceleration in recent times might not be a completely
realistic feature.

High quality global surface salinity fields that consider multiple
instrument sources, measurement error and instrument quality are
currently being developed

In this study, we have analyzed global salinity datasets to identify a series of regimes characterized by fluctuations around a changing average and temporal tendency (trend). The separation between regimes is achieved through the analysis of global features fitting a Gaussian Mixture Model to the data and using an Expectation–Maximization algorithm to determine the parameters that best describe the spatial salinity time series. The datasets used include global monthly fields from 1950 to 2014 with a global resolution of one degree.

The EM method allows for the separation of regimes based on their averages and trends assuming the spatial time series is a combination of Gaussians (GMM). The method uses Bayesian Information Criterion to choose the appropriate number of means/trends by penalizing excessive overfitting. The resulting fit represents the Maximum Likelihood Estimate (MLE) chosen using a non-arbitrary separation.

The method distinguished between three regimes characterized by
distinct mean and trend. Regime A (1950–1990) was similar to the
long-term average and trend described in several recent studies

A future goal is to use satellite data from SMOS and Aquarius to determine if the estimated means and trends are realistic. The combination of densely distributed in-situ observations (Argo profilers) and remotely sensed satellite data will provide a better approximation to the evolving global salinity field.

The historical time series was obtained from the UK Met Office Hadley
Centre (