*Highlights (for review)
Research highlights

Statistical approaches to analyzing Arctic Ocean salinity were developed.

Six classes of typical patterns in the surface salinity fields were identified.

Abrupt changes in the salinity of the Arctic Ocean surface layer were detected.

Three leading modes of salinity decomposition describe >70% of the total dispersion.

Interannual and quasidecadal oscillations linked to atmospheric and oceanic variability.
*Manuscript
Click here to download Manuscript: Paper_Ocean Modelling_resubmission_March_2015.docx
Click here to view linked References
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Surface salinity fields in the Arctic Ocean and statistical approaches to predicting large-
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scale anomalies and patterns
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Ekaterina A. Cherniavskaia1, Ivan Sudakov2,*, Kenneth M. Golden3, Leonid A. Timokhov1,
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and Courtenay Strong4
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Petersburg, 199397 Russia.
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45469-2314 USA
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3
Department of Oceanography, Arctic and Antarctic Research Institute, Bering str. 38, St.
Department of Physics, 300 College Park, SC 111, University of Dayton, Dayton, OH
Department of Mathematics, University of Utah, 155 S 1400 E, Room 233, Salt Lake City,
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UT 84112-0090 USA.
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Lake City, UT 84112-0090 USA.
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* corresponding author:
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email: isudakov1@udayton.edu
Department of Atmospheric Sciences, University of Utah, 135 S 1460 E, Room 819, Salt
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Abstract
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Significant salinity anomalies have been observed in the Arctic Ocean surface layer during
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the last decade. Using gridded data of winter salinity in the upper 50 m layer of the Arctic
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Ocean for the period 1950-1993 and 2007-2012, we investigated the inter-annual variability
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of the salinity fields, identified predominant anomaly patterns and leading modes of
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variability, and developed a statistical model for the prediction of surface layer salinity. The
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statistical model is based on linear regression equations linking the principal components
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with environmental factors, such as atmospheric circulation, river runoff, ice processes, and
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water exchange with neighboring oceans. Using this model, we obtained prognostic fields of
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the surface layer salinity for the winter period 2013-2014. The prognostic fields generated by
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the model were consistent with previously observed tendencies of surface layer freshening.
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Cluster analysis of the salinity fields exhibits a dramatic shift in behavior of the 2007-2012
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data in comparison to earlier observations.
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Keywords: Arctic Basin, surface layer, patterns, salinity anomalies, empirical orthogonal
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functions, gridding.
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1. Introduction
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The Arctic Ocean is very sensitive to changing environmental conditions. Its surface
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layer is a key component of the Arctic climate system, which serves as the dynamic and
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thermodynamic link between the atmosphere and the underlying waters (Carmack, 2000).
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Thermohaline characteristics of the surface layer fully reflect the effects of atmospheric and
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ice processes, as the water most directly exposed to the atmosphere and ice lies within the
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mixed layer (Cronin and Sprintall, 2001). The stability and development of the ice cover are
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associated with mixed layer thickness, as well as salinity and halocline structure in the upper
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layer, which influence the geographic distribution of sea ice and its variability. In this
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context, the Arctic Ocean surface layer is a critical indicator of climate change (Toole et al.,
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2010).
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The thermohaline structure of the Arctic Ocean surface layer has undergone
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significant changes in recent years. Of particular interest is the great freshening of the
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Amerasian Basin surface layer that had not been observed since 1950 until the early 1990s
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(Figure 1). In Jackson et al. (2012) it was emphasized that processes related to warming and
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freshening the surface layer in this region had transformed the water mass structure of the
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upper 100 m.
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In addition, there have been observations of significant salinification of the upper
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Eurasian Basin that began around 1989. One hypothesis for this is that the increase of Arctic
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atmospheric cyclone activity in the 1990s led to a large change in the salinity in the Eurasian
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Basin through changes in river inflow, and increased brine formation due to changes in Arctic
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sea ice formation. The other reason for salinification is the influence of Atlantic waters (AW),
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which by 2007 became warmer by about 0.24˚C than they were in the 1990s. Observations
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show that increases in Arctic Ocean salinity have accompanied this warming. This led to
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significant shoaling of the upper AW boundary and weakening of the upper-ocean
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stratification in the Eurasian Basin as well (Polyakov et al., 2010). However, current
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observations also show that the upper ocean of the Eurasian Basin was appreciably fresher in
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2010 than it was in 2007 and 2008 (Timmermans et al., 2011).
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Generally speaking, the problem of variability of Arctic Ocean salinity is challenging
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from a theoretical perspective. There are two main approaches to this problem. The first
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approach is to study variability of liquid freshwater export. For example, in (Lique et al.,
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2009) there is an analysis of the variability of Arctic freshwater content informed by a global
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ocean/sea-ice model. The authors showed that contrast in the interannual variability of the
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freshwater fluxes can be defined through flux velocity and salinity variations. They conclude
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that variations of salinity (controlling part of the Fram freshwater export) arise from the sea
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ice formation and melting north of Greenland. In (Jahn et al., 2012), simulations from ten
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global ocean-sea ice models of Arctic freshwater have been compared. The authors conclude
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that improved simulations of salinity variability are required to advance understanding of
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liquid freshwater export.
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The second approach is to model Arctic salinity stratification. It is known that for the
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Arctic Ocean, water density depends more on water salinity than on water temperature, and
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hence the thermohaline circulation is mainly determined by salinity distribution. This
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conclusion comes easily from an analysis of a linear equation for the state of sea water:
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(1)
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where ρ0, T0, and S0 are some initial values of water density, temperature, and salinity; and
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εT = 7·10-5 g/(cm3·K), εS = 8·10-4 g/(cm3·‰) (Fofonoff, 1985).
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Vertical variations of temperature and salinity in the upper layer (5-200 m) can reach
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0.5˚C and 1‰ respectively. If we put these numbers into equation (1) we obtain the
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contributions of variations in temperature and salinity to changes in water density, which are
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about 4% and 96%, respectively. Thus, salinity was chosen as the main characteristic of
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thermohaline structure variations of the Arctic Ocean surface layer.
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Improving the representation of the salinity distribution is crucial, however inclusion,
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representation, and parametrization of a number of processes is required (Steele et al., 2001,
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and Komuro, 2014). For example, in global ocean-sea ice models, salt is rejected in the first
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ocean model level during ice formation, while in reality, the salt is distributed in the mixed
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layer and below (Nguyen et al., 2009).
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Recently, Sea Surface Salinity maps at high latitudes have been developed at the
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SMOS Barcelona Expert Centre on Radiometric Calibration and Ocean Salinity (SMOS-
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BEC). The maps are computed by means of an objective analysis scheme and they are
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distributed in a spatial grid at 25km. However, the spatial coverage includes Arctic Ocean
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open water regions only. Also, it covers only 2011-2013 years.
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The transfer from the Arctic Ocean to the North Atlantic of briny water from sea ice
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formation and sea ice itself are significant components of global ocean circulation. Thus, the
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investigation of the variability of the surface layer can make a significant contribution to
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understanding ocean-climate feedback. In particular, abrupt changes in surface layer salinity
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may lead to critical transitions in patterns of global ocean circulation. A robust conceptual
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statistical model may help to describe features of anomalies in salinification of the Arctic
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Ocean, which are key players in the formation of surface salinity patterns. In this case,
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investigation of the structure of patterns and quality of anomalies leads to a better
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understanding of possible critical transitions in the patterns of global ocean circulation.
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Variations of Arctic Ocean surface salinity have complex spatial and temporal structures,
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which are affected by many external factors. Our aim is to distinguish the most significant
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factors that lead to recent changes in upper layer salinity patterns.
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We propose to develop a statistical (multiple linear regression) model for Arctic
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Ocean salinity fields building on ideas presented in, for example, Timokhov et al. (2012).
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This statistical model of variability of the Arctic Ocean winter salinity in the 5–50 m layer is
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used as a method for reconstruction of the winter salinity fields, which have been presented in
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Pokrovsky and Timokhov (2002). The model (see Appendix Figure A2 for a schematic of the
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model) is based on equations of multiple correlations for the time series - principal
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components (PC) associated with the first three leading modes from Empirical Orthogonal
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Function (EOF) analysis. We apply this type of spectral analysis to the salinity fields. The
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contribution of atmospheric factors and hydrological processes to variations in salinity can be
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interpreted by determining the structure of the multiple correlation equations. The variability
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patterns and relationships identified through the statistical analysis and modeling inform a
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conceptual model for principal drivers of Arctic salinity.
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Cluster analysis of the surface salinity allowed identification of six types of patterns in
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the salinity fields, which differ from each other by the position of the fresh water core, the
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position of the Transpolar Drift frontal zone, and the value of the horizontal salinity gradient.
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It has been shown that the structure of the salinity fields of 1990-1993 and 2007-2012
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differed greatly from previous years. The uniqueness of the haline structure (during 2007-
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2012) was also confirmed by the results of decomposing the surface salinity fields into EOFs.
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Analysis of the equations for the first three PCs showed that surface salinity fields
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were influenced most by hydrological processes. Using the PCs calculated by the model, we
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obtained forecast fields of Arctic Ocean surface layer salinity for the winter period 2013-
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2014. Prognostic fields demonstrate the same tendencies of surface layer freshening that were
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previously observed.
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2. Methods
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2.1. Data Set
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This study is based on a collection of more than 9800 instantaneous temperature and salinity
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profiles, with data available at the standard horizons (5, 10, 25, 50, 75, 100, 150, 200, 250,
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300, 400, 500, 750, 1000 and so on every 500 meters), collected between 1950-1993. The
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data were obtained from the Russian Arctic and Antarctic Research Institute (AARI) database
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which was also used in the creation of the joint U.S. Russian Atlas of the Arctic Ocean for
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winter (Timokhov and Tanis, 1997). This is complemented by data made available over the
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period 2007-2012 from the expeditions of the International Polar Year (IPY) and afterward,
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which consisted of Conductivity Temperature Depth (CTD) and eXpendable Conductivity
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Temperature Depth (XCTD) data, as well as data from the Ice-Tethered Profiler (ITP)-buoys
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(more than 14600 stations in total). The average vertical resolution of these profiles was 1 m.
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The first database was introduced by Lebedev et al. (2008). In areas where observations were
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missing, temperature and salinity data were reconstructed in a regular grid for the period of
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1950 to 1989 as detailed in the next subsection. Also, some data was found in the joint U.S.
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Russian Atlas of the Arctic Ocean for winter (Timokhov and Tanis, 1997). Thus, the working
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database is represented by grids with 200-km horizontal spacing, covering a deep part of the
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Arctic Ocean (with depths of more than 200 m). According to Treshnikov (1959), Rudels et
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al. (1996, 2004) and Korhonen et al. (2013), the average thickness of the Arctic Ocean mixed
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layer for the winter season is about 50 m. Also, a description of the data sources for other
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physical parameters can be found in Table 1.
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Table A1 lists the expeditions and number of stations that were used for
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reconstruction and gridding of salinity fields. Figure A1 shows the overall observation
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density and the year associated with each observation. The data exhibit a spatiotemporal non-
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uniformity that is undesirable but expected given the challenges associated with recovering
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long-term observations of Arctic salinity. Acknowledging its limitations, the data set still
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provides the most spatiotemporally detailed observational resource for studying multidecadal
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variations in basin-wide Arctic salinity, and there is community value in the identification,
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dissemination, and modeling of its principal modes of variability. To test for artifacts from
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the data gaps and the interpolation procedure (reviewed in the next subsection), we make
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several comparisons across methods and to independent data sets in the subsections to follow.
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For example, we note that our full-record cluster analysis yields dendograms similar to those
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found by Koltyshev et al. (2008) without using the 2007-2012 period. We further performed
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the EOF analysis with and without the additional 2007-2012 period, and report only modest
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change to the resulting modes of variability (Section 3.2). In Section 3.2, we also show that
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analogous EOF analysis on salinity fields from an independent, data-assimilated coupled
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ocean-ice model forced by atmospheric observations yields leading modes similar to the
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patterns found in our merged salinity data sets.
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2.2. Field reconstruction and interpolation
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To provide temporal and spatial continuity, we have unified existing data sets using
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reconstruction and gridding. The technique of computation of gridded fields for the period
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from 1950-1993 was described by Lebedev et al. (2008), and is summarized here.
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These techniques are based on the method of ocean field reconstruction, proposed by
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Pokrovsky and Timokhov (2002). This method projects the data onto EOFs and then recovers
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spatially continuous fields by interpolating the EOFs onto regular grids. This involves an
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eigen decomposition of the covariance matrix as widely performed in geostatistical analysis
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(e.g., Hannachi et al., 2007). The proposed method, which was used to obtain gridded
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salinity fields, is described as
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zi=zi(r )+e, zi z j =σ x x , zi ei =0,
i j
(2)
ei =0, ei e j =δij σe2.
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Here z(t, x) is the measured value of an oceanographic variable (e.g. temperature or salinity)
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and is a random function of time t and spatial coordinates x; i and j are the nodes of the
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irregular data grid; the notation <…> indicates the ensemble average of a value. We can
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reproduce the observed value of z(t, x) as the sum of a true value z(r)(t, x) of the
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oceanographic variable and an observational error e(t, x). The mean values of z(t, x) are
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derived by time averaging and space smoothing. We also propose that zi(r) has spatial
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correlations to the p variables; that a systematic error is not identified; a standard deviation of
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error (σe2) does exist, and  ij  
0 if i  j
is the Kronecker delta.
1 if i  j
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Biorthogonal decomposition of the oceanographic variable can help to identify the
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connections between spatial and temporal distributions within the data:
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z (t j , xi ) =  ckj f k ( xi ) + e(t j , xi ) ,
(3)
k
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where fk(xi) – is the spatial empirical orthogonal function (EOF); ckj – the calculated
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coefficient, so-called k-th principal component.
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The main goal of this spectral analysis method is to estimate the coefficients of
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j
spectral decomposition c k . In this case, we rewrite formula (3) in the following matrix
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form:
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Z  F C  e ,
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here  is the sign of the matrix multiplication.
 
(4)
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The system of linear equations (4) with respect to the unknown coefficients c kj can be
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solved on the basis of the a priori statistical information (2) with the use of the methods of
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statistical estimation. A formula for the estimation of the matrix of the unknown coefficients
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C was obtained in (Pokrovsky and Timokhov, 2002)
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Cˆ  ( F T  K e1  F  K c1 ) 1 F T  K e1  Z  ,
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where X 1 and X T are the inverse and transposed matrixes with respect to X, respectively.
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We use the following notation for the covariance matrices:
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K z   z2ij , K e   e2ij , (i, j  1,...., N ). The covariance matrix of errors of the expansion
ij
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(5)
coefficients
ij
is a diagonal matrix composed of eigenvalues of the covariance matrix
.
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The matrix F is formed by the values of the EOF, and the matrix Z is composed of
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the totality of the measurement data at the points of the observation net x i . In order to obtain
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an estimate of the unknown variables at the nodes of the regular grid ~
xi , it is necessary to
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interpolate the EOF into the corresponding nodes of the grid and obtain a new matrix F of
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the EOF. Using the matrix F obtained in this way and the estimates of the coefficients Ĉ
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from formula (5), we obtain from the matrix relationship
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~ ~ ~
Z  F  C  e~ ,
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an estimate of the unknown parameters at the nodes of a regular grid. Simultaneously with
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the salinity fields in the nodes of a regular grid, we can also calculate the covariance matrices
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of the errors of estimations obtained from the following equations:
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~
~
~
K cˆ  ( I  ( K  ( F T  K e1  F ))) 1  K c ,
~
~
K zˆ  F  K z  F T ,
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~
where K e is the covariance matrix of the observation error expanded over the regular grid
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~
xi .
~
~
(6)
(7)
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The approach detailed above is a combination of singular value decomposition and
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statistical regularization. These coefficients (modes) can be linked to the real physical
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processes that influence salinity (see Table 1). Preparation of the average salinity field data
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for 2007-2012 has consisted of several stages (see Appendix). First, we checked the data for
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random errors. Further, we used bilinear spatial interpolation. Next, we constructed an
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interpolation via a grid of nodes, and gaps in the data for uncovered sites were filled with
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climatic values from the Joint U.S.-Russian Atlas of the Arctic Ocean (Timokhov and Tanis,
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1997).
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2.3. Statistical approach
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Here we describe the approaches to data analysis which were used for physical
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interpretation of our statistical model. Polyakov et al. (2010), Rabe et al. (2011), and Morison
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et al. (2012) have emphasized that the thermohaline structure of the surface layer has
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undergone significant change over the last decade. However, it is not clear what physical
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processes led to these changes or what future trends may be.
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The analysis of the variability of the surface layer (including salinity fields) of the
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Arctic Ocean may be based on the decomposition using EOFs. This approach is useful in our
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case because this decomposition gives us EOF modes and principal components (PCs),
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respectively providing spatial and temporal views of variations in salinity. Each mode
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accounts for a certain fraction of the total variance of the initial data. The EOFs are
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conventionally ranked so that the first mode explains the largest fraction of total variance, the
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second mode explains the largest fraction of the remaining variance, and so on (Hannachi et
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al., 2007). The first 3-5 modes describe most of the variance of the analyzed salinity fields,
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which allows significant compressing of the information contained in the original data
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(Hannachi et al., 2007; Borzelli and Ligi, 1998). The EOF decomposition was carried out for
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the average salinity fields for the layer 5-50 m, as well as obtaining time series of PCs for the
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periods of 1950-1993 and 2007-2012.
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We applied our statistical model to interpret the physical processes through PCs. We
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used multiple linear regression to model the time series of principal components to identify
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predictors that determined variability of the salinity fields. The regression equations can give
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projections of future changes because the predictors lead the salinity field by various
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temporal lags. The statistical model is characterized by a system of linear regression
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equations constructed for the first three PCs, as the first three EOFs yield more than 72% of
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the total variance of the salinity data. The PCs were associated with the following factors:
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winter (October-March) and summer (July-September) atmospheric circulation indexes (AO
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and AD; Table 1), river runoff, the area of the ice-free surface in Arctic seas in September,
253
and water exchanges with the Pacific and Atlantic Oceans. For the latter two indices
254
representing water exchanges, we used the PDO and AMO indices as respective proxies
255
because of their influence on the temperature and salinity of water entering through the
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Bering Strait and the Faeroe-Shetland Strait to the Arctic Ocean (Zhang et al., 2010; Dima
257
and Lohmann, 2007). Atmospheric indexes were averaged by different time periods within
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indicated winter and summer seasons. The optimal periods of averaging for a particular index
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were chosen to maximize correlation with the PCs.
260
2.4. Cluster analysis
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The cluster analysis suggested by Ward (1963) was used to analyze the trajectories of
262
the evolution of winter salinity. Ward’s method is a hierarchical method based on
263
minimization of the sum of squares of any two clusters that form at each step. This method
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was chosen as it is regarded as very efficient and yields unique and exact hierarchy (Scheibler
265
and Schneider, 1985). Analysis was performed using the “Multivariate Exploratory
266
Techniques” toolkit in the STATISTICA 8.0 software package (Hill and Lewicki, 2007).
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According to this approach, we represented the salinity fields as a matrix (50×129)
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with years in columns and grid nodes in rows. Each of these nodes contained information
269
about salinity in the region. The measure of the distance between two years was introduced
270
through the Euclidean metric:
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Dij = ( (S i  S j ) )
2
1
2
(8)
ij
272
where Si and Sj are the salinity fields for the years i and j respectively
273
Consequently, this analysis allowed us to obtain the hierarchical salinity fields with a
274
feature of statistical identity (Figure 2). The figure shows that the salinity fields have
275
structural differences and thus are grouped in clusters for consecutive years. Based on the
276
tree ties, we have identified six of the largest groups in a temporal scale as well as the six
277
basic patterns in salinity fields. The first cluster includes the field for the years: 1950-59,
278
1976-77 and 1989; the second cluster includes 1960-1965; the third cluster includes 1966-
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1975; the fourth cluster includes 1981-1988; the fifth cluster includes 1978-1980; and the
280
sixth cluster includes 1990-93 and 2007-2012.
281
Similar results were obtained using other methods of cluster analysis (e.g., complete
282
linkage, and weighted pair-group average). This indicates that the chosen division into
283
clusters is stable and proper. In addition, a similar dendrogram was found in the work of
284
Koltyshev et al. (2008), where cluster analysis was completed for the data series of an
285
average salinity at a depth of 5-25 m for the period of 1950-1989. It also confirms the
286
robustness of our classification. Within the framework of our classification, the pattern may
287
persist for two to nine years.
288
289
3. Results
290
3.1 Cluster Analysis
13
291
Beginning with results from the cluster analysis, we calculated the average salinity
292
anomalies for each of the cluster time periods. This allowed us to find the differences (from
293
cluster to cluster) (Figure 3) in the structure of salinity fields (Table 2). In general, if we
294
compare the variability of salinity in the Eurasian and Amerasian basins, we may conclude
295
that the main difference in salinity fields for 2007-2012 (included in pattern 6) are in the
296
value of the salinity in the Canada basin (which is a part of the Amerasian basin). During this
297
period its values were 1.4 ‰ less compared with average values. This means there has been a
298
significant freshening of the surface layer, which had apparently not happened in at least the
299
past 50 years of available observations (Figure 1).
300
In addition, we note that pattern 6 has a separate branch with the largest Euclidean
301
distance on the dendrogram. Thus it can be assumed, that since 1990 the structure of the
302
salinity fields has undergone significant changes, which were most pronounced in 2007-2012.
303
These years can be isolated in a separate sub-branch.
304
3.2. Decomposition of surface salinity fields by EOF
305
Considering the results of cluster analysis, as a result of EOF decomposition of the
306
salinity fields for the 5-50 m layer, we obtained two sets of modes and PCs for the period of
307
1950-1993 (series 1), and for the same period adding the years 2007-2012 (series 2). Based
308
on North’s Rule of Thumb (North et al., 1982) the first three modes were accepted for further
309
analysis as physically significant. In summary, the first three modes obtained by the
310
decomposition of series 1 describe more than 60% of the total dispersion of the initial fields,
311
the first three modes of series 2 describe more than 70% of the total dispersion, and the
312
results from these two decompositions are quite similar. The only significant difference is an
313
additional core in the Canada Basin that appears in the first mode of series 2 (Figure 4b). We
314
assume that the modes obtained by decomposition in series 1 cannot take into account the
315
essential features of the distribution of surface salinity fields associated with the freshening of
14
316
the Canada Basin. Therefore, for further analysis we used the PCs and modes obtained upon
317
decomposition in series 2.
318
To enhance confidence in the robustness of these modes, Appendix Figure A3
319
presents a similar EOF analysis using model output from the Pan-Arctic Ice-Ocean Modeling
320
and Assimilation System (PIOMAS; Zhang and Rothrock, 2003, Lindsay and Zhang, 2006).
321
PIOMAS is a coupled ice-ocean model that uses data assimilation methods for ice
322
concentration and ice velocity. Forced by atmospheric observations, its output available for
323
1978-2005 is widely used as the best possible estimate of Arctic fields with limited long-term
324
observations including salinity and sea ice thickness. The spatial pattern of PIOMAS mean
325
salinity (Figure A3a) closely resembles the pattern shown for our data in Figure 4a. Without
326
detrending, the freshening trend in the Canada Basin (Jackson et al., 2012) dominates the
327
leading EOF of PIOMAS salinity (not shown) because the data begin in 1978. EOFs of
328
PIOMAS salinity after detrending (Figure A3b-d) compare favorably with corresponding
329
results in Figure 4b-d, despite incomplete overlap over the analysis periods. In particular, for
330
both data sets, the leading EOF of salinity features a prominent dipole between the Canada
331
Basin and Eurasian Basin (Figures 4b and A3b), and the second EOF of salinity features a
332
positive center of action elongated along the Lomonosov Ridge surrounded by negative
333
loading strongest near Svalbard (Figures 4c and A3c). Less agreement is seen for the third
334
EOF (Figures 4d and A3d), which is perhaps unsurprising moving toward modes accounting
335
for less variance.
336
3.3. The linear regression equation for the principal components
337
We present here a statistical model of inter-annual variability of the Arctic Ocean
338
surface layer salinity. This research builds on established approaches used by Pokroivsky and
339
Timokhov (2002) (specifically, their reconstruction of salinity fields applying modified EOF
340
methods).
15
341
We suggest some additions to improve the ideas presented in previous research. For
342
example, the analysis presented is based on a dataset updated for the period 2007-2012,
343
which is quite important for understanding the physical processes during the dramatic current
344
changes in Arctic sea ice. Also, in contrast to our previous study (Timokhov et al., 2012), we
345
do not use the preceding values of the principal components (history) as predictors for linear
346
regression, thus simplifying the physical interpretation of the equations obtained.
347
A set of external factors having the most correlation with salinity values have been
348
defined based on the results of correlation analysis. As a result of linear regression analysis,
349
we obtained empirical equations for the first three principal components (see Table A2 in
350
Appendix).
351
The structure of these equations can be explained through the sets of factors
352
representing the effects of both atmospheric and hydrological processes. Thus, the predictors
353
used can be divided into two groups: the first group includes atmospheric circulation indices
354
and reflects the influence of atmospheric processes; the second group reflects hydrological
355
processes captured by river runoff for Arctic seas, inflows through the Bering Strait and the
356
Faeroe-Shetland Strait (characterized by the PDO and AMO indices), and the areas of open
357
water in the Arctic seas in September. Predictors were included in the equations with
358
different time shifts so that the predictors may lead the PCs. The value of the time shifts was
359
1–10 years and was chosen on the basis of crosscorrelations of predictors with PCs in order to
360
maximize explained variance.
361
The contribution of each group to explained variance in PC1 – PC3 can be calculated
362
based on the magnitude and sign of the regression coefficients of correspondent predictors
363
included in that particular group. In this case, hydrological processes have a dominant
364
contribution to explained variance in PC1. Atmospheric factors (i.e. AO and AD) contribute
16
365
70% of the explained variance of PC2 and PC3 with the remainder falling on hydrological
366
processes.
367
368
4. Discussion and Summary
369
The first mode of surface salinity decomposition (EOF1) displays an out-of-phase
370
relationship between salinity anomalies in Canada Basin and Eurasian Basin (which includes
371
Nansen and Amundsen Basins) and Makarov Basin (Figure 4b). This opposition closely
372
resembles pattern 6, which features positive salinity anomalies in Eurasian Basin and
373
negative anomalies in Canada Basin (Figure 3f).
374
In the late 1980s, the atmospheric circulation regime began to change (Steele and
375
Boyd, 1998; Proshutinsky et al., 2009; Morison et al., 2012). Degradation of the Arctic
376
anticyclone is an key example. Some changes in the structure of the surface pressure field
377
were observed in association with a frequent recurrence of large values of the AD indices.
378
According to Wang et al. (2009), this could be a main reason for the local minima of sea ice
379
extent in the summers of 1995, 1999, 2002, 2005 and 2007. In addition, in the late 1980s the
380
inflow of warm and high salinity Atlantic water into the Arctic Basin increased (Morison et
381
al., 2000; Polyakov et al., 2010). At the beginning of this century, the heat flow of Pacific
382
waters through the Bering Strait to the Chukchi Sea increased as well (Woodgate et al.,
383
2010).
384
These observations allow us to suggest that pattern 6 of the dendrogram is the
385
consequence of these processes. Our suggestion is supported by the regression equation for
386
PC1 (Appendix) from which we see that PC1 is a function of AMO, PDO, and open water area
387
in East Siberian and Chukchi seas (the latter can be considered as an indirect indicator of
388
fresh water inflow form these seas to the Arctic). The time lags should be related to the time
17
389
that it takes for Atlantic and Pacific waters to reach the Arctic Basins and become involved in
390
circulation (Shauer et al., 2002; Bourgain and Gascard, 2012).
391
EOF2 exhibits opposite polarity of salinity anomalies in the central Arctic Ocean and
392
near-slope areas (Figure 4c). Spectral analysis of the associated PC2 revealed an 8-year cycle,
393
which we associate with shifts between cyclonic and anticyclonic circulation regimes
394
(Proshutinsky and Johnson, 1997; Rigor et al., 2002). The regression equation for PC2
395
indicates its dependence on summer AO and AD indices. PDO and river runoff from Laptev,
396
East Siberian and Chukchi seas make the largest contribution to variability of PC2 (28.8% and
397
25.9%, respectively) with slightly weaker effects from AO and AD (24.4% and 20.9%,
398
respectively). Cluster pattern 2 (Figure 3b) resembles the EOF2 (Figure 4c) spatial pattern.
399
For the averaging period 1960-1965, summer AO indices (and PC2) were negative. During
400
the anti-cyclonic regime of atmospheric circulation, fresh surface waters tend to flow to the
401
center of the Arctic basin and negative salinity anomalies form there. At the same time, along
402
the slopes there is upwelling of Atlantic waters and positive salinity anomalies occur
403
(Proshutinsky and Johnson, 1997). Positive PC2 (i.e. cyclonic circulation regime) indicates
404
the opposite conditions.
405
EOF3 is represented by two elongated bands of loading (Figure 4d). The “Eurasian”
406
band has two distinct centers located over Chukchi Plateau and over Lomonosov Ridge. The
407
“Canadian” band has one core over the North Pole. This pattern of variation is consistent with
408
the Arctic Dipole (Wu et al., 2006). The winter AD index is the leading predictor of PC3 with
409
a contribution of over 30%. Two centers of the “Eurasian” band are associated with influence
410
of river runoff from Kara and Laptev seas and Pacific water inflow. Corresponding predictors
411
account for 28.5 %and 22.5 % of the variability of PC3 (Appendix).
412
Time series of PC1-3 show a mixture of interannual and quasidecadal oscillations
413
(Figure 5). We may conclude that large-scale surface layer salinity anomalies (with period of
18
414
over 20 years) are the result of water exchange effects. The more short-period (8-9 years)
415
variations are determined by atmospheric circulation processes. Also interannual variations
416
occur due to interannual variability of both atmospheric and hydrological processes.
417
The derived equations in the Appendix (Table A2) describe the first three principal
418
components for the period 1950-2012; calculated with these equations the PCs have good
419
agreement with the values of PCs directly derived from the decomposition of salinity fields
420
via EOF analysis (Figure 5).
421
Theoretically, the salinity fields for 1994-2006 can be reconstructed using this
422
statistical model. We noted above that this period had gaps in observational data. In practice
423
they may lead to inaccuracies due to the higher-frequency variability of the calculated PCs.
424
This model cannot reproduce exact principal components for short-term time series, although
425
the trend in variability of all three PCs is reproduced correctly. Therefore, the model can be
426
used for tracking long-term processes of the structure transformation of salinity fields.
427
Validation of the model was carried out by calculating an error of reconstruction for
428
the surface salinity fields. The difference between the actual and reconstructed salinity fields
429
(ε) was determined as a percentage by the following formula:
430
 = ( ( S f  S c )  ( S f ))  100% ,
431
where σ is the standard deviation, Sf is the actual salinity, and Sc is the calculated salinity.
(9)
432
On the basis of 13 reconstructed salinity fields the average error of reconstruction
433
obtained was 31.2%. As the first three EOF modes describe more than 72% of the variability
434
of the initial fields, the error obtained exceeds by a small amount the rest of the dispersion
435
that is not covered by the first three EOFs. Thus we have a system of regression equations
436
(statistical model) that may reproduce long-term salinity anomalies relatively well.
437
The rest of the surface salinity dispersion captured by higher order EOFs (about 28%)
438
is likely explained through the short-term, and probably local, processes such as ice
19
439
formation and cascading in polynya regions (Ivanov and Watanabe, 2013), deep convection,
440
or mixing with Atlantic water upper boundary (Ivanov et al., 2012).
441
We applied our statistical model to the reconstruction of salinity fields for 2013-2014.
442
As a result, we obtained the salinity fields that correspond to the trends observed in recent
443
years. The dendrogram obtained via cluster analysis with the 2013-2014 fields added, showed
444
that reconstructed fields also fall into cluster 6 (not shown). This has preserved the significant
445
freshening in the Canada Basin as well as large spatial gradients between the Eurasian and
446
Amerasian Basins, though in 2014 these gradients appear to be smaller (Figure 6). According
447
to our projections for 2013-2014, freshened water from the Beaufort Gyre moves westward
448
along the Canadian Continental Slope. As a result, average salinity of the Eurasian basin will
449
decrease.
450
Recently, Sea Surface Salinity maps at high latitudes have been developed at the
451
SMOS Barcelona Expert Centre on Radiometric Calibration and Ocean Salinity (SMOS-
452
BEC) available from http://cp34-bec.cmima.csic.es/. The maps are computed by means of an
453
objective analysis scheme. However, it lacks the spatial coverage of our data because it is for
454
Arctic Ocean open water regions only. Also, it covers only 2011-2013 years.
455
Thus we have identified various patterns in Arctic Ocean surface salinity fields using
456
a reliable statistical model. In addition, we have found anomalies in the salinity fields, which
457
have occurred in the past and conclude that more than 70% of surface salinity variability is
458
constituted by long-term processes and only 30% are due to short-term and local processes.
459
Our findings again raise questions about nonlinearities in global ocean circulation,
460
particularly in the Arctic Ocean, which is strongly connected with Earth’s climate system. In
461
the future, information obtained about these anomalies may be helpful in determining
462
whether the Arctic Ocean salinity, and related oceanographic phenomena, have undergone
463
regime shifts or changes in response to climate forcing.
20
464
465
Acknowledgments
The authors thank the big data sources, which are mentioned below.
466
The detailed algorithm of the salinity data gridding procedure is available at the AARI web-
467
site:http://www.aari.ru/resources/a0013_17/kara/Atlas_Kara_Sea_Winter/text/tehnik_report.h
468
tm#p2. Indexes of atmospheric circulation are available at NOAA’s Data Base. The area of
469
ice-free
470
http://www.aari.ru/projects/ECIMO/index.php?im=100. River runoff data were obtained from
471
the Joint US-Russian Atlas of the Arctic Ocean and Arctic RIMS Data Server. We thank M.
472
Janout for providing AD indices north of 600N.
surface
in
the
Arctic
seas
was
calculated
from
data
sited
at
473
The authors are grateful for financial support from the Otto Schmidt Laboratory for
474
Polar and Marine Research (Grant No. OSL-13-05), and from the Russian Foundation for
475
Basic Research (Grants No. 16-34-00733_mol_a and 16-31-60070_mol_a_dk). Also, we
476
gratefully acknowledge support from the Division of Mathematical Sciences and the Division
477
of Polar Programs at the U.S. National Science Foundation (NSF) through Grants ARC-
478
0934721, DMS-0940249, and DMS-1413454. We are also grateful for support from the
479
Office of Naval Research (ONR) through Grant N00014-13-10291. We would like to thank
480
the NSF Math Climate Research Network (MCRN) as well for their support of this work. We
481
thank N. Lebedev and V. Karpy for help with data processing. In preparing this text, we have
482
benefited from discussions with Jessica R. Houf. Finally, the authors acknowledge helpful
483
comments from three anonymous reviewers.
484
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27
621
Table 1. Predictors used for the approximation of PCs.
Physical
Physical value
Description
processes and its
Data sources (references and
the web sources)
notation
Arctic oscillation
First EOF-mode of Sea-
When the AO index is positive, surface pressure is low in the
Thompson and Wallace (1998).
index (AO)
level pressure north of 60N
polar region.
NOAA Center for Weather and
latitude
When the AO index is negative, there tends to be high pressure
Climate Prediction (NCWCP)
in the polar region.
http://www.esrl.noaa.gov/psd/d
The lower case in Table A1 indicates the months of an average
ata/gridded/
period.
Arctic Dipole
Second EOF-mode of Sea-
When the AD index is positive, sea-level pressure has positive
Overland and Wang (2010).
Anomaly index
level pressure north of 60N
anomaly over the Canadian Archipelago and negative anomaly
NOAA Center for Weather and
(AD)
latitude
over the Barents Sea.
Climate Prediction (NCWCP)
When the AD index is negative, SLP anomalies show an
http://www.esrl.noaa.gov/psd/d
opposite scenario, with the center of negative SLP anomalies
ata/gridded/
over the Nordic seas. (Wu et al., 2006; Wang et al., 2009;
28
Overland & Wang, 2010).
Atlantic Multi
Variations of sea surface
Index has cool and warm phases that may last for 20-40 years at Enfield et al.(2001).
decadal oscillation
temperature in the North
a time and a difference of about 0.5˚C. It reflects changes of sea
ESRL Physical Sciences
index (AMO)
Atlantic Ocean
surface temperature in the Atlantic Ocean between the equator
Division (PSD)
and Greenland.
http://www.esrl.noaa.gov/psd/d
Was used as a substitute for processes of water exchange with
ata/timeseries/AMO/
the Atlantic Ocean.
The Pacific
North Pacific sea surface
When the PDO index is positive, the west Pacific becomes cool
Trenberth and Hurrell (1994).
Decadal
temperature variability
and part of the eastern ocean warms. When the PDO index is
Joint Institute for the Study of
Oscillation index
negative, the opposite pattern occurs. It shifts phases on at least
the Atmosphere and Ocean
(PDO)
the inter-decadal time scale, usually about 20 to 30 years.
(JISAO)
http://jisao.washington.edu/pdo/
River runoff
(RIV)
Water flows
Average annual runoff of the main Siberian rivers. It was used
Timokhov and Tanis (1997).
as total runoff in the Kara Sea (K), Laptev Sea (L), East-
Joint US-Russian Atlas of the
Siberian Sea (E) and Chukchi Sea (C). The lower case in Table
Arctic Ocean.
A1 indicates the first letters of the sea name.
http://rims.unh.edu/data/station/
29
list.cgi?col=4
Area of open water Area
Total ice-free area in the Kara Sea (K), Laptev Sea (L), East-
Russian Arctic and Antarctic
in Arctic seas
Siberian Sea (E) and Chukchi Sea (C) in September. The lower
Research Institute (AARI)
(OW)
case in Table A1 indicates the first letter of the sea name.
http://www.aari.ru/projects/ECI
MO/index.php?im=100
622
623
Table 2. Patterns of the salinity fields.
Pattern
Pattern 1
Structure of salinity fields
Our analysis for these years shows that a desalination zone occupies the Canada Basin and spread along the Canadian shelf till the Fram Strait
(Figure 3a). The salt-frontal zone lies along the Lomonosov Ridge.
Pattern 2
Here the distribution of salinity fields looks more like a freshening zone with multiple cores, which extend from the Beaufort Sea toward the Barents
Sea through to the North Pole (Figure 3b), while along the slope there were positive salinity anomalies. This kind of distribution of salinity fields
may be formed under the dominance of an anti-cyclonic mode of atmospheric circulation (Proshutinsky and Johnson, 1997), which is probably
reflected by dominant negative principal component (PC2) (see histogram).
Pattern 3
The main feature of the salinity distribution is an extensive area of freshening which occupies the entire Amerasian Basin, Eurasian and Greenland
slopes. As a result, the salinity frontal zone was shifted to the region of the Gakkel Ridge (Figure 3c). This structure of the salinity spatial distribution
may be formed at the cyclonic mode of the atmospheric circulation (Proshutinsky and Johnson, 1997).
Pattern 4
This cluster is opposite to cluster 3. Slight salinization was observed in Canada and Makarov Basins (Figure 3d).
Pattern 5
The core of freshening has a displacement to the region of the Makarov Basin to the Northeast from the slope of the Laptev Sea shelf. The freshening
zone extends from west to east (Figure 3e). This cluster is opposite to clusters 1 and 6 in terms of signs of PCs and location of salinity anomalies.
30
Pattern 6
This cluster is similar to cluster 1 as both have dominant negative PC1, but salinity anomalies are much more extreme. The zone of maximum
freshening is located in the southern part of the Canada Basin and spreading along the slope till the Lomonosov Ridge. The salt-frontal zone is at the
extreme eastern position and occupies the whole Eurasian Basin area up to Mendeleev Ridge (Figure 3f).
624
31
625
Figure Caption List:
626
Figure 1. Temporal changes in salinity averaged over the depth range 5-50 m.
627
Figure 2. Dendrogram of winter salinity fields for the layer 5-50 m in the Arctic Basin.
628
Figure 3. Winter salinity anomalies for the layer 5-50 m averaged over six periods to patterns:
629
a – pattern 1, 1950-59, 1976-77 and 1989; b – pattern 2, 1960-1965; c – pattern 3, 1966-1975;
630
d – pattern 4, 1981-1988; e – pattern 5, 1978-1980; f – pattern 6, 1990-93 and 2007-2012.
631
The histograms illustrates the differences between patterns in terms of PCs. Anomalies were
632
calculated relative to averaged surface salinity for 1961-1990.
633
Figure 4. The average salinity field (a) and first three modes of the average salinity field
634
decomposition for the layer 5-50 m: (b), (c), (d) - 1st, 2nd and 3rd modes, respectively, for the
635
period 1950-1993 and 2007-2012.
636
Figure 5. The actual (black line) principal components and calculated principal components
637
(red dashed line) with the help of the equations of linear regression. Correlation coefficients
638
between the calculated time series of PCs and actual PCs are: r(PC1)=0.87; r(PC2)=0.67;
639
r(PC3)=0.66.
640
Figure 6. There are reconstructed salinity fields for the layer of 5-50 m in 2013 (a) and 2014
641
(b) and their anomalies (c, d) comparatively averaged surface salinity for 1961-1990.
642
Figure A1.Observation density. Color bar indicate the last number of year in each decade.
643
Figure A2. Schematic of the conceptual statistical model.
644
Figure A3. Same as Figure 4, but for salinity averaged annually over the upper ten layers of
645
PIOMAS data for 1979-2005: a) mean salinity and (b-d) are respectively EOFs 1, 2, and 3 of
646
salinity.
32
647
648
649
650
651
652
Figure 1. Temporal changes in salinity averaged over the depth range 5-50 m.
33
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
Figure 2. Dendrogram of winter salinity fields for the layer 5-50 m in the Arctic Basin.
34
668
669
Figure 3. Winter salinity anomalies for the layer 5-50 m averaged over six periods
670
representing objectively determined clusters: a – pattern 1, 1950-59, 1976-77 and 1989; b –
671
pattern 2, 1960-1965; c – pattern 3, 1966-1975; d – pattern 4, 1981-1988; e – pattern 5, 1978-
672
1980; f – pattern 6, 1990-93 and 2007-2012. The inset histograms illustrate the differences
673
between patterns in terms of PCs. Anomalies were calculated relative to averaged surface
674
salinity for 1961-1990.
675
676
677
678
679
680
681
682
35
683
684
685
Figure 4. The average salinity field (a) and first three modes of the average salinity field
686
decomposition for the layer 5-50 m: (b), (c), (d) - 1st, 2nd and 3rd modes, respectively, for the
687
period 1950-1993 and 2007-2012.
36
688
689
Figure 5. The actual (black line) principal components and calculated principal components
690
(red dashed line) with the help of the equations of linear regression. Correlation coefficients
691
between the calculated time series of PCs and actual PCs are: r(PC1)=0.87; r(PC2)=0.67;
692
r(PC3)=0.66.
693
694
695
37
696
697
Figure 6. There are reconstructed salinity fields for the layer of 5-50 m in 2013 (a) and 2014
698
(b) and their anomalies (c, d) comparatively averaged surface salinity for 1961-1990.
699
700
701
702
703
704
705
38
706
Appendix:
707
Data and observation density
708
Table A1. Datasets used for reconstruction and gridding of surface layer salinity fields.
Expedition (cruise) or code of
expedition (cruise)
Regions, water areas
Date of station
performance
first
Number of stations
last
SEVER05
ArB,ChS,EsS
03/31/1950 04/02/1951
51
Toros1951
KrS,LpS
04/08/1951 04/24/1951
9
SEVER07
ArB, KrS,LpS
04/16/1955 05/15/1955
105
NP05
ArB
05/20/1955 03/20/1956
14
SEVER08
ArB, ChS,EsS
04/04/1956 05/16/1956
48
SEVER09
ArB
03/1957
11
Lena1958
GrS
03/11/1958 03/25/1958
28
SEVER10
ArB
03/1958
18
WOD98_31_3272
ArB
03/29/1958 04/14/1958
3
SEVER11
ArB
03/1959
30
Storm1959
GrS
04/26/1959 06/12/1959
59
NP08
ArB
06/30/1959 02/15/1962
52
27
05/1957
06/1958
05/1959
SEVER12
ArB
03/1960
WOD98_18_11445
ArB
04/18/1960 05/30/1960
05/1960
6
WOD98_31_672
ArB
12/29/1960 12/29/1960
1
SEVER13
ArB
03/1961
05/1961
27
SEVER14
ArB
03/1962
05/1962
29
SEVER15
ArB
02/1963
05/1963
58
SEVER16
ArB,ChS,EsS,KrS,LpS
03/23/1964 05/13/1964
43
SEVER17
ArB,ChS,EsS,KrS,LpS
03/17/1965 05/11/1965
44
NP14
ChS,EsS
05/30/1965 01/24/1966
16
SEVER18
ArB,ChS,EsS,KrS,LpS
03/12/1966 05/07/1966
42
SEVER19
ArB,ChS,EsS,KrS,LpS
03/19/1967 04/26/1967
32
OBTAZ1967
KrS
04/06/1967 08/21/1967
26
NP15
ArB
04/30/1967 03/14/1968
18
SEVER20
ArB,ChS,EsS,KrS,LpS
03/19/1968 05/03/1968
60
WOD98_31_2170
ArB
03/29/1968 04/06/1968
3
AUGMS1968
KrS
04/09/1968 05/03/1968
45
NP17
ArB
06/25/1968 09/26/1969
45
SEVER21
ArB,ChS,EsS,KrS,LpS
03/18/1969 05/14/1969
95
NP16
ArB
04/22/1969 03/15/1972
83
Tiksi1969
LpS
04/25/1969 12/08/1969
51
DUGMS1970
KrS
01/06/1970 12/18/1970
73
SEVER22
ArB,ChS,EsS,KrS,LpS
03/30/1970 05/11/1970
90
AUGMS1970
KrS
04/12/1970 05/01/1970
70
NP18
ArB
05/19/1970 03/15/1971
20
NP20
ArB,EsS
05/20/1970 04/15/1972
49
NP19
ArB,EsS
11/14/1970 03/26/1973
43
DUGMS1971
KrS
01/07/1971 12/23/1971
73
Tiksi1971
LpS
01/10/1971 11/30/1971
106
39
SEVER23
ArB,ChS,EsS,KrS,LpS
02/28/1971 05/10/1971
81
AUGMS1971
KrS
04/19/1971 08/07/1971
112
DUGMS1972
KrS
01/06/1972 12/27/1972
95
Tiksi1972
LpS
01/10/1972 06/20/1972
54
SEVER24
ArB,ChS,EsS,KrS,LpS
02/29/1972 05/07/1972
51
AUGMS1972
KrS
04/20/1972 05/30/1972
80
NP21
ArB,EsS
05/30/1972 03/21/1974
30
SEVER25
ArB,BfS,ChS,EsS,KrS,LpS
03/19/1973 05/10/1973
178
Liman1973
KrS,ObR
03/20/1973 09/23/1973
18
Tiksi1973
LpS
05/04/1973 11/16/1973
109
Tiksi1974
LpS
12/14/1973 12/15/1974
119
DUGMS1974
KrS
01/08/1974 12/27/1974
62
SEVER26
ArB,BfS,ChS,EsS,KrS,LpS
03/11/1974 05/10/1974
166
NP22
ArB,BfS,ChS,EsS
03/23/1974 03/03/1982
117
DUGMS1975
KrS
01/04/1975 09/23/1975
145
Tiksi1975
LpS
01/15/1975 12/15/1975
55
SEVER27
ArB,BfS,ChS,EsS,GrS,KrS,LpS
03/13/1975 04/30/1975
188
DUGMS1976
KrS
01/07/1976 12/16/1977
312
AUGMS1976
KrS,ObR
02/24/1976 09/24/1976
249
SEVER28
ArB,BfS,ChS,EsS,GrS,KrS,LpS
03/11/1976 05/09/1976
155
NP23
ArB,EsS
05/30/1976 10/17/1978
83
SEVER29
ArB,BfS,ChS,EsS,KrS,LpS
03/01/1977 04/29/1977
150
AUGMS1977
KrS,ObR
03/03/1977 05/27/1977
101
WOD98_31_10614
BeS
03/31/1977 04/03/1977
16
VegaDUGMS1978
KrS
01/19/1978 12/22/1978
10
SEVER30
ArB,BaS,ChS,EsS,KrS,LpS
03/08/1978 05/10/1978
185
WOD98_31_13021
BfS
04/04/1978 07/29/1978
46
NP24
ArB
12/19/1978 09/30/1980
31
KrS
01/09/1979 11/21/1979
22
ArB,BaS,BfS,ChS,EsS,GrS,KrS,LpS 03/02/1979 05/19/1979
205
VegaDUGMS1979
SEVER31
WOD98_18_8924
BeS,ChS
04/19/1979 04/28/1979
8
VegaDUGMS1980
KrS
01/17/1980 09/26/1980
17
SEVER32
ArB,BaS,ChS,EsS,KrS,LpS
02/15/1980 05/15/1980
138
WOD98_31_10726
BfS
03/05/1980 07/02/1980
62
VegaDUGMS1981
KrS
01/06/1981 12/23/1981
32
DUGMS1981
KrS
03/17/1981 10/01/1981
344
SEVER33
ArB,ChS,EsS,KrS,LpS
03/18/1981 05/18/1981
112
VegaDUGMS1982
KrS
01/06/1982 12/29/1982
14
SEVER34
ArB,ChS,EsS,KrS,LpS
02/17/1982 05/19/1982
117
DUGMS1982
KrS
03/20/1982 05/07/1982
155
AUGMS1982
KrS
03/27/1982 06/07/1982
190
NP25
ArB
05/27/1982 03/11/1984
25
VegaDUGMS1983
KrS
01/05/1983 12/06/1983
20
SEVER35
ArB,ChS,EsS,KrS,LpS
02/25/1983 05/14/1983
235
DUGMS1983
KrS
03/22/1983 05/02/1983
67
NP26
ArB
07/01/1983 02/21/1986
35
VegaDUGMS1984
KrS
01/05/1984 11/26/1984
24
AUGMS1984
KrS
01/06/1984 12/24/1984
175
40
TUGKS1984
LpS
01/15/1984 12/27/1984
112
SEVER36
ArB,ChS,EsS,KrS,LpS
02/27/1984 05/13/1984
247
TUGMS1984
EsS,LpS
03/23/1984 05/22/1984
20
DUGMS1984
KrS
04/01/1984 05/18/1984
36
Pevek1984
EsS
04/10/1984 12/29/1984
37
NP27
ArB,EsS
06/26/1984 03/10/1987
35
TUGKS1985
EsS,LpS
01/03/1985 09/24/1985
213
VegaDUGMS1985
KrS
01/03/1985 12/24/1985
20
Pevek1985
EsS
01/10/1985 03/29/1985
17
SEVER37
ArB,ChS,EsS,KrS,LpS
02/25/1985 05/10/1985
296
TUGMS1985
EsS,LpS
03/21/1985 05/04/1985
39
WOD98_31_12556
BfS
04/01/1985 04/18/1985
7
DUGMS1985
KrS
04/02/1985 09/20/1985
209
AUGMS1985
KrS
04/05/1985 07/01/1985
38
VegaDUGMS1986
KrS
01/06/1986 12/26/1986
22
SEVER38
ArB,ChS,EsS,KrS,LpS
02/26/1986 06/06/1986
196
DUGMS1986
KrS
04/03/1986 08/24/1986
96
SEVER39
ArB,ChS,EsS,KrS,LpS
02/25/1987 06/08/1987
284
NP28
ArB,GrS
05/07/1987 01/17/1989
34
SEVER40
ArB,BeS,ChS,EsS,LpS
03/09/1988 05/19/1988
282
AUGE1988
HtR,LpS
05/06/1988 09/19/1988
100
SEVER41
ArB,BeS,ChS,EsS,LpS
02/27/1989 06/02/1989
262
NP31
ArB,BfS
06/29/1989 03/26/1990
10
SEVER42
BeS,ChS,EsS
01/19/1990 08/11/1990
150
SEVER43
KrS
04/25/1991 05/24/1991
20
SEVER44
ArB,BeS,ChS,EsS,LpS
02/27/1992 06/02/1992
206
SEVER45
BaS,KrS,WhS
04/08/1993 06/14/1993
180
CELTIC VOYAGER
NoS
04/07/2007 04/07/2007
1
CLUPEA
NoS
05/10/2007 05/12/2007
57
LLZG (G.O. SARS)
NoS, BaS
02/07/2007 11/26/2009
350
HAKON MOSBY
NoS, GrS
01/10/2007 12/05/2009
989
HERWIG, W. (JAN.73)
NoS
02/07/2007 01/10/2007
14
ITP01
Bfs
01/01/2007 01/08/2007
32
ITP04
ArB
01/01/2007 05/31/2007
302
ITP05
ArB
01/01/2007 05/31/2007
453
ITP06
ArB
01/01/2007 05/31/2008
580
ITP07
ArB
04/28/2007 11/01/2007
134
LDGJ (JOHAN HJORT)
BaS, GrS, NoS
01/15/2007 12/04/2009
1178
MAGNUS HEINASON (OW2252)
NoS
02/15/2007 11/10/2008
364
Transarctica_2007
ArB, LpS, KrS
05/15/2007 05/31/2007
49
SCOTIA
NoS
01/29/2007 02/14/2010
288
Tara
ArB
01/13/2007 12/10/2007
35
Twin Otter
ArB
04/21/2007 05/07/2007
10
CELTIC EXPLORER
NoS
05/21/2008 05/21/2008
3
TRANSDRIFT XIII (Polynya)
LpS
04/10/2008 05/05/2008
17
ITP08
ArB
01/01/2008 05/31/2008
303
ITP09
ArB
01/01/2008 02/27/2009
408
ITP10
ArB
01/01/2008 05/25/2008
293
41
709
710
711
712
713
ITP11
ArB
01/01/2008 05/31/2009
630
ITP13
ArB
01/01/2008 05/31/2008
317
ITP16
ArB
01/01/2008 04/03/2008
140
ITP18
BrS
01/01/2008 05/31/2008
317
ITP19
ArB, GrS
04/08/2008 11/21/2008
216
LAHV (JAN MAYEN)
BaS
02/07/2008 03/06/2009
304
NP35
ArB
01/01/2008 12/31/2008
152
NPEO_2008 (Twin Otter)
ArB, BfS
03/21/2008 04/20/2008
43
TRANSDRIFT XV (Polynya)
LpS
03/24/2009 04/23/2009
15
HERWIG, W. (JAN.73)
NoS
02/10/2009 02/15/2009
16
NP36
ArB
01/01/2009 12/31/2009
151
ITP21
ArB
01/01/2009 05/31/2009
288
ITP23
ArB
01/01/2009 05/31/2010
599
ITP24
ArB
01/01/2009 05/31/2009
299
ITP25
ArB
01/01/2009 05/31/2009
298
ITP26
ArB
01/01/2009 02/26/2009
114
ITP27
ArB
01/01/2009 01/20/2009
40
ITP29
ArB
01/01/2009 05/31/2010
589
ITP33
BfS, ArB
01/01/2010 01/25/2011
351
ITP34
BfS, ArB
01/01/2010 05/31/2010
298
ITP37
ArB
01/01/2010 12/24/2010
301
ITP38
ArB, GrS
04/19/2010 12/28/2010
170
NP37
ArB
01/01/2010 12/30/2010
112
NPEO_2010 (Hercules)
BfS
05/25/2010 05/26/2010
4
NPEO_2011(Twin Otter)
ArB
04/28/2011 05/08/2011
25
ITP41
ArB
01/01/2011 05/31/2012
607
ITP42
BfS, ArB
01/01/2011 04/15/2011
201
ITP43
BfS
01/01/2011 02/11/2011
83
ITP47
ArB
04/11/2011 02/28/2012
434
PALEX 2011
ArB
04/10/2011 04/20/2011
20
NP38
ArB
01/01/2011 11/01/2011
147
BARNEO2012
ArB
04/06/2012 04/17/2012
24
ITP48
ArB
01/01/2012 11/16/2012
446
ITP53
BfS
01/01/2012 05/31/2012
304
ITP55
ChS
01/01/2012 05/08/2012
257
ITP56
ArB, GrS
04/15/2012 12/31/2012
185
ITP63
ArB
04/21/2012 12/31/2012
161
NP39
ArB
01/01/2012 12/31/2012
143
SWITCHYARD2012
ArB, NrS
05/03/2012 05/21/2012
23
TRANSDRIFT XX
LpS
03/26/2012 04/19/2012
7
All expeditions
All regions
03/31/1950 12/31/2012
24557
Note: Conventional names of regions and water areas in column 2: ArB - Arctic Basin, BaS Barents Sea, BeS - Bering Sea, BfS - Beaufort Sea, ChS - Chukchi Sea, EsS - East Siberian
Sea, GrS - Greenland Sea, HtR - Khatanga river mouth zone JpS - Japan Sea, KrS - Kara Sea,
LpS - Laptev Sea, NoS – Norwegian Sea, NrS – Nares Strait, ObR - Ob estuary zone, WhS White Sea.
42
714
715
716
Figure A1.Observation density. The color bar indicates the last number of year in each
decade.
43
717
718
The empirical equations for the first three principal components
The equations are derived from a simple formula of multiple linear regressions:
719
yi =  aij xij  bi
720
where yi – the principal components PCi; xij– the independent variables of yi (the different
721
environmental factors), aij – regression coefficients, bi – intercept. To determine which
722
predictors to include in each regression model, we used “forward stepwise” method.
723
Calculations were made using “Multiple Linear Regression” toolbar of the STATISTICA 8.0
724
software package.
725
Each predictor leads the salinity EOF by some number of years, and these temporal lags were
726
determined by cross correlations.
(A1)
727
The values of the correlation coefficients (R), coefficients of determination (R2) and
728
F-criteria (Hill and Lewicki, 2007) are shown in Table A2. The values of all F-criteria exceed
729
the threshold indicating that the variables used are statistically significant. The correlation
730
coefficients for all PCs were statistically significant and varied from 0.66 (R3) to 0.87 (R1).
731
732
733
734
735
736
737
738
739
740
741
44
742
Table A2. The empirical statistical model developed for each of the first three PCs.
PCi
PC1
Statistical Equations
PC1  10.88  AMO (7) *  0.009  OWEC (1)  1.18  PDO (10)  8.6
Multiple
Multiple
Adjusted
F-
R
R²
R²
criteria
0.87
0.76
0.74
48.48
(3;46)**
PC2
PC2  1.12  AOVII  IX (1)  0.98  ADVII IX (1)  0.73  PDO(6)  0.005  RIVLEC (4)  5.69
0.67
0.45
0.40
9.21
(4;45)
PC3
PC3  0.85  DA IIII (1)  0.64  AO X-III (1)  0.6  PDO(4)  0.003  RIVKL (3)  6.39
0.66
0.43
0.38
8.62
(4;45)
743
* – time shift for every predictor is indicated in parentheses (minus means that predictor leads the dependent variable).
744
** – numbers of degrees of freedom are indicated in parentheses.
45
745
746
747
Figure A2. Schematic of the conceptual statistical model.
46
748
749
Figure A3. Same as Figure 4, but for salinity averaged annually over the upper ten layers of
750
PIOMAS data for 1979-2005: a) mean salinity and (b-d) are respectively EOFs 1, 2, and 3 of
751
salinity.
Figure
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Figure
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Figure
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Figure
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Figure
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Figure
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