1. Introduction
The Arctic Ocean—the smallest of the world’s oceans—provides a direct link between the Pacific and Atlantic Oceans. It is also a region of extreme climatic conditions leading to strong water mass modification of the inflowing water. The water masses of the Arctic Ocean are primarily of Atlantic origin, entering the Arctic Ocean both via the deeper Fram Strait and the shallower Barents Sea. During its northward transit the uppermost part (~200 m) of the Atlantic water experiences considerable water mass transformation via cooling and freshwater input subsequently forming cold, near-freezing polar surface and halocline waters (e.g., Rudels et al. 1996). The main sources of freshwater input that drive the haline transformation are river runoff and net precipitation. In addition, the low-saline Pacific water (which is slightly fresher than Atlantic water) acts to further freshen the uppermost water masses primarily on the North American side. Sea ice processes also contribute significantly to water mass transformation through the seasonal melt–freeze cycle, though the long-term net effect in the Arctic Ocean is a salinification because of the net growth and export of sea ice.
Below the fresh and cold surface water a warmer (T ~ 0–2°C), saline, and less transformed variety of the Atlantic water resides at intermediate depths followed by cold and saline deep water in the abyss. The fresh and cold on top of warm and salty hydrographic structure is stable primarily because of the large freshwater input creating a sharp salinity gradient. In addition, the low temperatures reduce the thermal expansion coefficient, making the stratification less determined by the temperature gradient. This vertical structure, which effectively inhibits the heat stored in the Atlantic water to penetrate upward, is characteristic for the central Arctic and allows for a perennial ice cover to persist (e.g., Martinson and Steele 2001). Many studies of the Arctic Ocean have aimed to understand how this hydrographic structure is formed and maintained, and the present understanding is that both surface and internal (mixing) processes contribute (e.g., Aagaard et al. 1981; Steele et al. 1995; Rudels et al. 1996, 2004).
The water masses entering the Arctic Ocean eventually return to the North Atlantic Ocean (mainly through the Canadian Arctic Archipelago and the Fram Strait) and thus connect the Arctic Ocean to the Atlantic and global circulation. The flow of Atlantic water across the Arctic Mediterranean (the Arctic Ocean and the Nordic Seas) has by several authors been described as a double estuary (e.g., Stigebrandt 1985; Carmack 2007; Rudels 2010; Eldevik and Nilsen 2013) with Atlantic water transforming into either a denser water mass by cooling (negative estuary) or a lighter water mass by mixing with the freshwater input (positive estuary).
The distributions of the conservative ocean tracers temperature1 T and salinity S have long been used in oceanography to identify water masses and their transformations (e.g., Worthington 1981). Through their relation to the density of seawater, the spatial distributions of these tracers contain information on the large-scale ocean circulation. In two pioneering papers, Walin (1977, 1982) demonstrated how water mass transformations, and aspects of the large-scale circulation, can be deduced from surface fluxes and interior mixing if conservation equations are formulated in tracer coordinates rather than in geographical coordinates. Focusing on estuarine circulations, Walin (1977) used salinity as the independent tracer coordinate and derived a relation between the volume flow across isohaline surfaces and the haline forcing due to surface fluxes and mixing. In a study with a global perspective, Walin (1982) formulated volume and heat conservation relations in temperature coordinates. Based on this framework, he provided an illuminating discussion of the ocean circulation viewed in temperature space using observationally based computations of the net ocean surface heat flux as a function of the sea surface temperature compiled by Andersson et al. (1982). Many investigators have subsequently used and extended the ideas of Walin (1977, 1982) to examine the transformation of water masses in the context of both observational- and model-based studies. These investigations include analyses of water mass transformation between density classes (Tziperman 1986; Speer and Tziperman 1992; Iudicone et al. 2008); transformations due to wind-induced near-surface mixing (Nilsson 1996); abyssal transformations due to geothermal heating (Emile-Geay and Madec 2008); studies of how mixed layer processes, eddies, and seasonality affect water mass transformations (Marshall 1997; Marshall et al. 1999); and methods to map water mass transformation and formation back to geographical locations (Brambilla et al. 2008; Maze et al. 2009).
In studies of the Arctic Ocean, the ideas of Walin have mainly been used to compute the net volume transport as a function of salinity across specific sections such as the Fram Strait and the Eurasian shelf edge (Rudels 1987, 1989; Nilsson et al. 2008). An advantage of representing the transport as a function of the salinity is that it provides direct information on the associated salt or freshwater transport. However, a description of the Arctic Ocean in terms of only salinity or temperature fails to capture some of the key water mass transformations in the region. A drawback with a description in temperature is that inflowing Atlantic and Pacific waters occupy similar temperature ranges, making geographical divisions necessary for distinguishing how these two inflows are modified in temperature. A salinity description is able to separate the inflowing waters reasonably well and has the advantage of giving the approximate density of the water masses. However, over a broad range of salinities there are counteracting transformation tendencies because of the freshwater input from rivers and the atmosphere and freshwater extraction from sea ice formation. Thus, a S–T description of Arctic water mass transformations would for many purposes be advantageous, and it has the virtue of better resolving sea ice–related transformations, occurring near the freezing line in S–T space.
In fact, a S–T framework for studying water mass transformations now exists in the literature, which is the result of the work of several researchers. Speer (1993) generalized the ideas of Walin to describe water mass transformations in both S and T coordinates. Specifically, he showed how knowledge of surface fluxes of heat and freshwater can be translated to a transformation vector that describes the strength and direction of the associated water mass transformation in S–T space. Speer (1993) used these ideas to study water mass transformations due to air–sea fluxes in the North Atlantic based on observations. Several researches have also decomposed the volume transports across specific geographical sections in T and S classes (e.g., Marsh et al. 2005; Rudels et al. 2008; Zika et al. 2013). By decomposing the volume transport into an ocean region in this way, aspects of the water mass transformations occurring in the region can be diagnosed. In an Arctic Ocean application, Rudels et al. (2008) used observations to decompose the volume transport through the Fram Strait into T and S classes.
Recently, Döös et al. (2012) and Zika et al. (2012) introduced a thermohaline streamfunction that describes the time-mean global ocean circulation in S–T coordinates. This streamfunction is related to Speer’s vector-based description of water mass transformations. If the global ocean is in a steady state, then there is no net formation of water in any S–T class, implying that the vector field describing the net water mass transformation has to be nondivergent. Thus, in a steady state, the net transformation vector can be described by a streamfunction in S–T coordinates. In principle, the net transformation vector, and thus the thermohaline streamfunction, could be identical to zero. Interestingly, the global thermohaline streamfunction turns out to be nonzero, and it captures aspects of circulation patterns in geographical coordinates, including the interocean conveyor circulation (Döös et al. 2012). Groeskamp et al. (2014a) showed that the streamfunction introduced by Döös et al. (2012) and Zika et al. (2012), computed as a time mean of the instantaneous velocity components perpendicular to isothermal and isohaline surfaces, does not represent the total water mass transformation; there is an additional contribution arising from the seasonal movement of the isothermal and isohaline surfaces. Groeskamp et al. (2014a) denoted the total streamfunction due to the velocity field and the movements of the property surfaces, the diathermohaline function. Furthermore, they pointed out that this streamfunction is directly related to the thermohaline forcing due to surface fluxes and mixing (see also Groeskamp et al. 2014b).
Following the original ideas of Walin (1977, 1982), Hieronymus et al. (2014) formulated volume, heat, and salt budgets in S–T coordinates from which the relations between the volume flows across isothermal and isohaline surfaces and mixing, and surface fluxes are obtained. This provides a more formal derivation of the transformation vector due to Speer (1993) that now includes also the contribution from mixing in the ocean, illuminating the connection between the transformation vector and the diathermohaline streamfunction. Based on results from a global ocean circulation model, Hieronymus et al. (2014) used the generalized Walin formulae to investigate the role of surface fluxes and various parameterized mixing processes in creating the global diathermohaline streamfunction.
The framework developed by Hieronymus et al. (2014) is a useful tool for studying the processes responsible for the global water mass transformations. In addition, the framework can easily be extended to study water mass transformations in a specific oceanic region by including the volume, heat, and salt transports across the lateral boundaries of the region. In this context, the Arctic Ocean is an especially interesting region because of its characteristic settings where inflowing Atlantic and Pacific waters mix and strong water mass transformation occurs. Thus, the aim of the present study is to use and extend the results of Hieronymus et al. (2014) to examine water mass transformations in the Arctic Ocean. For this purpose, we analyze the results from a global ocean model, which allow us to identify the key processes in the model that transform the S–T characteristics of the Arctic Ocean water masses and the role of the heat and salt exchange with the North Pacific and North Atlantic.
The article is organized as follows: In section 2, we briefly present the theory of how water mass transformation can be studied in S–T coordinates. In section 3, we apply the method to the Arctic Ocean using a global ocean model. First, we analyze water mass transformations in salinity- or temperature-only coordinates; this is followed by analysis of transformations in S–T coordinates. Then the effect of model deficiencies is discussed in light of the simulated water mass transformations. In the final section, we summarize and conclude the main findings of our work. In addition, appendixes providing a more extensive explanation of the basic relations in the S–T framework are included.
2. The S–T framework
a. Basic equations
Here, we present the key equations that describe water mass transformations in the S–T coordinates. We closely follow the derivation of Hieronymus et al. (2014) and the details are presented in appendixes A, B, and C.
Sketch showing the region 
Citation: Journal of Physical Oceanography 45, 4; 10.1175/JPO-D-14-0197.1
Here, the right-hand sides are the volume transports across the boundaries of R; 
Here, E and Q are the net fluxes out of the ocean of freshwater and heat, respectively, across the parts of the sea surface where the salinity is less than S and the temperature is less than T; c is the heat capacity per unit volume; and 
b. The water mass transformation vector
3. Application
a. Model setup
As our diagnostic tool to study water mass transformation in the Arctic Ocean, we use the coupled ocean sea ice modeling framework NEMO version 3.2 (Madec 2008), including the Louvain-la-Neuve Sea Ice Model, version 2 (LIM2), sea ice model (Fichefet and Maqueda 1997). The model is run in a global configuration using the tripolar grid ORCA1 with a base resolution of 1°. Despite the relatively coarse resolution, the displaced poles over the Northern Hemisphere allow for a grid spacing of 30–60 km over the Arctic Ocean with the Canadian Arctic Archipelago represented by two gateways: the Barrow Strait and the Nares Strait. The vertical discretization uses 64 z levels starting at 6 m with a gradual increase to 204 m at the bottom; bottom topography is represented by the partial step approach. The model uses a linear free-surface formulation following Roullet and Madec (2000) and is thus only approximately salt and heat conserving.
In the model, unresolved mesoscale eddy effects are represented by isoneutral mixing (Redi 1982) and isoneutral advection (Gent and McWilliams 1990). Vertical mixing coefficients are solved using the TKE turbulent closure (Gaspar et al. 1990; Madec et al. 1998) with convection handled by locally enhanced background diffusivity. In addition, parameterizations for tidal mixing (Simmons et al. 2004) and unresolved bottom boundary flows (Beckmann and Döscher 1997) are used.
Air–sea fluxes for heat and freshwater are calculated using bulk formulations, and penetrative shortwave radiation uses a simple two-band scheme (Paulson and Simpson 1977). The sea ice–ocean fluxes assume a levitated ice model, and ice salt fluxes use a constant salinity of 6 g kg−1. The sea surface salinity is restored toward the WOA05 value by way of a restoring freshwater flux. The time scale of this restoration is approximately 40 days. The model is forced by the DRAKKAR forcing set, version 4.3 (DFS4.3), which includes a blend of the ERA-40 reanalysis, ECMWF operational analysis, and satellite products (Brodeau et al. 2010).
b. Simulation
The simulation starts from an ocean at rest with temperature and salinity drawn from the World Ocean Atlas 2005 (WOA05). Using a repeated 26-yr forcing cycle (years 1958–83), the model is run for 1500 yr to reach a near steady-state solution where the model drift is small. Then an additional cycle of 26 yr is run where the processes needed for calculating the water mass transformations are diagnosed from the model. The diagnostics are done online to fully resolve temporal variations, and the discretization of the fluxes follows Hieronymus et al. (2014), with the exception that the analysis is only done for the Arctic region (see Fig. 2). This means that additional terms for the boundary exchange flows 
Map showing the model bathymetry with geographical locations mentioned in this study: Barrow Strait (BaS), Bering Strait (BeS), Barents Sea Opening (BSO), Fram Strait (FS), Nares Strait (NS), and St. Anna Trough (SAT). The black lines show the gateways to the Arctic Ocean where boundary exchange flows M(S, T) have been calculated and together with the coast lines define the Arctic Ocean region used in this study.
Citation: Journal of Physical Oceanography 45, 4; 10.1175/JPO-D-14-0197.1
Figure 3 shows the time-mean freshwater content (referenced to 34.8 g kg−1) of the upper 254 m and the temperature maximum of the Atlantic layer. The model clearly captures the characteristic freshwater pool (Fig. 3a) over the Canada basin and a sharp gradient toward the Amundsen and Nansen basins. The inflow of warm Atlantic water across the Nansen basin is also evident (Fig. 3b); however, the downstream spreading along the basin boundary is not well simulated, making the Canadian side too cold. The inability to produce a realistic Arctic Ocean boundary current is a common problem among ocean circulation models (Holloway et al. 2007), and at the present model resolution, a well-simulated boundary current is not expected. However, the vertical water mass structure with a cold and fresh surface layer above a warm, salty Atlantic layer is generally well captured (Fig. 4). This makes the simulation suitable for studying the broad features of water mass transformations in the Arctic Ocean, which is the purpose of the present work.
(a) Time-mean freshwater content in m relative to a reference salinity of 34.8 g kg−1 integrated over the upper 254 m. (b) Potential temperature maximum (°C) in the Atlantic layer (200–1000 m). The dashed line shows the location of the transect in Fig. 4.
Citation: Journal of Physical Oceanography 45, 4; 10.1175/JPO-D-14-0197.1
Arctic-wide time-mean potential temperature (°C) along the transect in Fig. 3b (filled contours) and salinity (g kg−1) for a selected number of isohalines marking the surface, halocline, and Atlantic waters (white lines).
Citation: Journal of Physical Oceanography 45, 4; 10.1175/JPO-D-14-0197.1
The time-mean annual surface freshwater and heat fluxes are shown in Fig. 5. Over the Arctic region, the net freshwater flux shows an input of freshwater in the proximity of the river mouths as well as over most parts of the Barents Sea, Kara Sea, East Siberian Sea, Chukchi Sea, and the Canada basin. A net loss of freshwater is seen along the Siberian coast in the Kara and Laptev Seas, around large islands in the Arctic, as well as over the Nansen and Amundsen basins and along the Alaskan coast in the Chukchi region. The net freshwater extraction along the coasts and islands is mainly because of the sea ice process (not shown). The dipole pattern across the central Arctic with a net input of freshwater over the Canada basin and extraction of freshwater over the Nansen and Amundsen basins is mainly because of the surface salinity restoring flux, which acts to maintain the sharp salinity front across the basins. The net heat flux over the Arctic region shows an overall heat loss with the strongest signals in the Barents Sea and west of Svalbard where the warm Atlantic water enters the Arctic as well as in the Chukchi Sea where warm Pacific water enters. A small net input of heat is seen in some regions that are seasonally ice free.
(a) Time-mean net freshwater flux (mSv) counted positive when leaving the ocean. The freshwater flux includes the sea ice salt flux that has been converted into an equivalent water flux by scaling with the local salinity. (b) Net downward heat flux (W m−2).
Citation: Journal of Physical Oceanography 45, 4; 10.1175/JPO-D-14-0197.1
It should be noted that the present model has deficiencies in processes important for water mass transformations and uses the restoration of the sea surface salinity field. Thus, there are biases in the model-simulated hydrography and transformations, which will be further discussed in relation to observations in section 3g. However, to begin with, we describe and analyze the Arctic Ocean water mass transformations as they occur in the model.
c. Water mass distribution of the Arctic Ocean
Figure 6 shows the time-mean volumetric and surface area distributions for the Arctic Ocean. Many different water classes are usually identified for surface and subsurface waters of the Arctic Ocean [see, e.g., Rudels (2009), Aksenov et al. (2010), and references therein for a full presentation of the different classes]. As the model in this study has a relatively coarse resolution, we only use the most basic definition of water masses characterizing the broad-scale features of the region. Here, we distinguish between the following:
The Polar Surface Water, which comprises the fresh and cold polar mixed layer and the halocline. Here, we define the polar mixed layer as the water mass where
The Atlantic water, which is usually defined as the subsurface layer below and above the T = 0°C isotherm and
The Pacific water, which has a large temperature range centered around a narrow salinity range; here, we use
The Polar Deep Water, which is the cold and salty water mass with T < 0°C and
The time-mean volumetric S–T distribution υ(S, T) {log10 [m3 (°C S)−1]} and the surface S–T distribution a(S, T) {log10 [m2 (°C S)−1]} calculated over the Arctic Ocean region, defined in Fig. 3. The left column shows υ(S, T) for (a) PHC, (c) WOA05, and (e) model simulation. The right column shows a(S, T) for (b) PHC, (d) WOA05, and (f) model simulation. For the distributions based on the two climatologies, monthly values are used, and for the model distributions, calculations are done at the model time step. In (a), a selected number of σ0 isopycnals (thin black) as well as the Arctic water masses, polar mixed layer (PML), halocline layer (HL), Pacific water (PW), and Atlantic water (AW), are marked out (black dashed boundaries). The insets in (a),(c), and (e) show the υ(S, T) below 1000 m, roughly corresponding to the Polar Deep Water (PDW).
Citation: Journal of Physical Oceanography 45, 4; 10.1175/JPO-D-14-0197.1
In Fig. 6, the 
d. Exchange and transformation in temperature- or salinity-only coordinates
It is illuminating to first study the water mass exchange and transformation in a salinity- or temperature-only coordinate framework: the 1D frameworks of Walin (1977, 1982). How to recover the 1D frameworks from the S–T framework is described in appendix C. In what follows, we will discuss the volume exchange between the Arctic Ocean and the exterior as well as the water mass transformation within the Arctic, as described by the 1D frameworks. The fluxes are diagnosed from our model simulation and represent a steady-state situation.
Figure 7 shows the net total volume exchange 
Cumulative volume exchange M across the interior boundaries B and the net freshwater exchange E, both in Sv for (a) salinity less than S and (b) temperature less than T. The fluxes are calculated across the interior boundaries and sea surface area defined in Fig. 2.
Citation: Journal of Physical Oceanography 45, 4; 10.1175/JPO-D-14-0197.1
In salinity coordinates (Fig. 7a), there is an inflow both at low salinities, primarily owing to a net freshwater input from river runoff (from the E term), and at high salinities, owing to an input of Atlantic water. In between there is a more complex signal with outflow at lower salinities interrupted by a net inflow at the range of Pacific water followed by outflow at intermediate salinities. The total volume exchange in salinity coordinates shows the estuarine character of the Arctic Ocean, where inflowing warm and salty Atlantic water is transformed by the surface processes as well as Pacific water input to eventually exit the Arctic back to the North Atlantic as Polar Surface Water. The features of the M(S) exchange in the present model are similar to those found by Pemberton et al. (2014) in a regional coupled sea ice–ocean model.
In temperature coordinates it is seen (Fig. 7b) that the total and boundary exchange M(T) is mainly directed out of the Arctic Ocean for T < 1°C and into the Arctic for higher temperatures. The freshwater exchange E(T) shows an input predominantly at the very low temperatures, which is expected as most of the sea surface in the Arctic Ocean is near the freezing temperature (see, e.g., Fig. 6f).
From the cumulative salt balance it is seen (Figs. 8a,b) that the surface processes SE yield a flow toward lower salinities for S < 31 g kg−1 and toward higher salinities in the range 
The process-by-process balance for the salinity coordinate case: (a) the cumulative salt budget (106 g kg−1 m3 s−1), (b) the water mass transformation balance (Sv), and (c) the surface term 
Citation: Journal of Physical Oceanography 45, 4; 10.1175/JPO-D-14-0197.1
Figure 8b clearly shows that the volume balance of Eq. (12) has two different regimes. At low salinities S < 31 g kg−1, the balance is between the surface term 
To further examine the role of the different freshwater sources and sinks in the Arctic Ocean, we have decomposed the 
Figures 9a and 9b show the cumulative heat balance in temperature coordinates. Here, the surface heat exchange yields a transformation toward lower temperatures due to a net heat loss for T < 6°C, where most of the Arctic Ocean water mass can be found (see Fig. 6f). For low temperatures the diffusive cumulative heat fluxes yield a transformation toward higher temperatures and for high temperatures a flow toward lower temperature. Thus, similar to the cross-isohaline diffusive fluxes, the cross-isothermal diffusive fluxes induce a transformation that acts to decrease the temperature range. The cumulative advective heat exchange in temperature coordinates represents an overall import of heat occurring over a wide range of temperatures.
The process-by-process balance for the temperature coordinate case: (a) the cumulative heat budget (PW), (b) the water mass transformation balance (Sv), and (c) the surface term 
Citation: Journal of Physical Oceanography 45, 4; 10.1175/JPO-D-14-0197.1
The volume balance of Eq. (14) in temperature coordinates is shown in Fig. 9b. It is seen that the surface heat flux term 
Figures 8a and 9a both show that the residuals are typically smaller than the most dominating terms in the cumulative salt and heat equations; however, the budgets are not fully closed. The 
Figure 10 illustrates two limiting situations for Arctic Ocean water mass transformations in salinity coordinates. For low salinities, the balance is primarily between opposing transformations because of the changes in freshwater input 
A sketch showing the dominating balance of Eq. (12) in the Arctic Ocean in the case of (left) low salinity and (right) high salinity. Note that the E term is usually small.
Citation: Journal of Physical Oceanography 45, 4; 10.1175/JPO-D-14-0197.1
e. Inflow distributions in S–T coordinates
The Arctic Ocean water mass transformations viewed in salinity or temperature coordinates yield a simple leading-order picture. In temperature space, the advective exchange term M(T) shows how warm, inflowing waters are essentially transformed to cold, outflowing waters. In salinity coordinates, M(S) yields a similar picture; saline inflowing waters are chiefly transformed toward less saline outflowing waters. Looking more closely at M(S), one can identify a Bering Strait inflow signature at lower salinity and Barents Sea and Fram Strait inflow signatures. However, some features of the water mass transformations tend to be obscured when only using T or S frameworks, and here the S–T framework can provide more detailed information about the transformations. One reason to use a S–T framework is that the Atlantic water inflows and cold dense outflows are not well separated in salinity, and in temperature the Atlantic and Pacific inflows occupy similar temperature ranges. Further, a S–T framework should better resolve surface flux–induced transformations, which in the Arctic Ocean tend to occur in a small range of S–T values near the freezing line.
Thus, we now proceed to analyze the Arctic Ocean water mass transformations in S–T coordinates. To begin with, we focus on the boundary exchange distributions m(S, T) at the different gateways to the Arctic Ocean, which we here refer to as inflow distributions. We have also calculated the mean volume transports (Table 1) as well as the transport-weighted mean salinities and temperature (Table 2) at the different gateways, using the m(S, T)dSdT distributions as weights.
Mean volume transports (Sv) for the different gateways to the Arctic Ocean, calculated by summing the m(S, T)dSdT distributions. We have also included a number of recent observational estimates from the literature, most of which are compiled in Beszczynska-Möller et al. (2012). Note that the observational estimates are given within the parentheses.
Transport-weighted mean inflow and outflow temperatures and salinities for the different gateways to the Arctic Ocean. Note that the weighting is done with the m(S, T)dSdT distributions.
Figure 11a clearly shows the signature of water mass transformations occurring in the Arctic Ocean. Two distinct water types flow into the Arctic: the warm and salty Atlantic water and the slightly fresher Pacific water. This leads to a transport-weighted mean of T = 2.9°C and S = 34.3 g kg−1 for the inflowing waters. These source waters are then generally cooled and freshened in the Arctic Ocean, leading to a mean outflow characterized by T = −0.7°C and S = 33.6 g kg−1.
Net boundary exchange distributions −m(S, T) [106 m3 (s °C S)−1] for (a) all gateways, (b) Fram Strait, (c) Barents Sea Opening, (d) Bering Strait, (e) Barrow Strait, and (f) Nares Strait. Note that a positive value (red colors) means a net inflow to the Arctic region. In (a), the transport-weighted mean inflow (circle) and outflow (cross) S–T coordinates are also shown.
Citation: Journal of Physical Oceanography 45, 4; 10.1175/JPO-D-14-0197.1
We also note from Table 2 that the volume transport in the model is generally in good agreement with recent observational estimates compiled in Beszczynska-Möller et al. (2012) as well as with the inverse model study of Tsubouchi et al. (2012). However, the simulated Fram Strait inflow of 1.1 Sverdrups (Sv; 1 Sv ≡ 106 m3 s−1) is lower than the observed estimate of 3.0–6.6 Sv by Schauer et al. (2008) and Beszczynska-Möller et al. (2012). Likewise, the simulated Fram Strait outflow of 2.8 Sv is lower than their observational estimates of 4.5–8.6 Sv. This gives a simulated Fram Strait net volume transport of −1.7 Sv that is within the observed ranges of −1.6 ± 3.9 by Tsubouchi et al. (2012) and the −2.0 ± 2.7 Sv by Schauer et al. (2008). The simulated Barents Sea Opening net inflow of 2.7 Sv is also slightly higher than the 2.0 Sv estimated from observations by Smedsrud et al. (2010). In addition, it is also seen that the simulated inflow of 1.3 Sv through the Bering Strait is higher than the observed 0.8 ± 0.2 Sv estimated by Woodgate et al. (2005). Across the Canadian Arctic Archipelago the simulated net outflow of 0.6 Sv through the Barrow Strait is in line with the 0.7 Sv from observations by Prinsenberg et al. (2009). While at the Nares Strait the simulated outflow of 1.9 Sv is much higher in the model compared to the 0.6–0.9 Sv estimated from observations by Münchow et al. (2007) and Münchow and Melling (2008). It should be noted, however, that the model only has two gateways (the Barrow and Nares Straits) in the Canadian Arctic Archipelago, whereas observational volume budgets (e.g., Beszczynska-Möller et al. 2012) usually also include Cardigan Strait and Hell Gate with an additional volume transport of −0.3 Sv (Melling et al. 2008).
f. Arctic Ocean water mass transformations in S–T
Figure 12 shows 
The total transformation vector J and the boundary exchange distributions −m(S, T) [106 m3 (s °C S)−1] for the Arctic Ocean.
Citation: Journal of Physical Oceanography 45, 4; 10.1175/JPO-D-14-0197.1
A water parcel can undergo a transformation in S–T space because of a number of different surface and interior processes, summarized in Fig. 13. To study how the different processes contribute to the total transformation we decompose 
Schematic based on Groeskamp et al. (2014a) showing how different surface and internal processes act to transform a water parcel in S–T coordinates. Note that the description of the processes is based on how they are formulated in the model and that γ are neutral density lines.
Citation: Journal of Physical Oceanography 45, 4; 10.1175/JPO-D-14-0197.1
Figure 14 shows the transformation vector decomposed into its major components. An immediate question is what processes transform the generally warm and saline inflow waters to the cold and fresher outflow waters (see Fig. 11). In this perspective, the most striking feature of the transformations, at least in the S–T regions away from the freezing line, is that the surface processes primarily transform the Arctic Ocean water masses in the T direction toward colder temperatures and that the vertical mixing transforms in the S direction toward lower salinity. The reason is that the significant transformation toward lower salinity occurs in a S–T range that occupies a small surface area fraction of the Arctic Ocean (see Fig. 6). Thus, these water masses are only to a small degree directly influenced by the surface freshwater flux. Close to the freezing line, the surface processes act to either cool and salinify or cool and freshen the water mass. Here, the transformation is generally directed away from the narrow band of temperature–salinity classes that occupy the largest area at the sea surface. Thus, the surface fluxes strive to broaden the S–T distribution at the surface. This is partly balanced by the vertical mixing, which strives to warm and salinify the cold and freshwater. It is also seen that the isoneutral mixing has a less important role for most parts of the Arctic Ocean water mass in this model. However, it is important in a narrow salinity range 
The process-by-process decomposition of the time-mean transformation vector J showing (a) the total transformation, (b) surface processes, (c) vertical mixing, and (d) isoneutral mixing. For (a),(c), and (d), the vectors are plotted on top of the time-mean υ(S, T) {log10 [m3 (°C S)−1]}, while (b) is plotted on top of the a(S, T). The upper color bar is for the υ(S, T), and the lower color bar is for the a(S, T) distributions.
Citation: Journal of Physical Oceanography 45, 4; 10.1175/JPO-D-14-0197.1
To further examine the transformations close to the freezing line, we compute the time-mean transformations for the winter (October–March) and summer (April–September) seasons from our simulation. Figure 15 shows that the net transformation vector 
The process-by-process decomposition of the seasonal time-mean J showing (a),(b) the total transformation, (c),(d) surface processes, (e),(f) vertical mixing, and (g),(h) isoneutral mixing. For (a), (b), and (e)–(h), the vectors are plotted on top of the seasonal υ(S, T) {log10 [m3 (°C S)−1]}, while (b) and (c) are plotted on top of the seasonal a(S, T). (left) Winter conditions (October–March) and (right) summer conditions (April–September). The upper color bar is for the υ(S, T), and the lower color bar is for the a(S, T) distributions.
Citation: Journal of Physical Oceanography 45, 4; 10.1175/JPO-D-14-0197.1
The divergence of the transformation vector yields the net formation 
(a) The time-mean boundary exchange distribution −m(S, T) for all gateways enclosing the Arctic Ocean, (b) the total divergence 
Citation: Journal of Physical Oceanography 45, 4; 10.1175/JPO-D-14-0197.1
To further examine the role of the surface and internal processes, we decompose the divergence as 
It is also clear that there are regions where there is a divergence that does not balance the m(S, T). Analysis of the neglected e(S, T) term (not shown) does not compensate for this inconsistency. Model drift of the υ(S, T) could also have contributed, but in our case it is small. Instead, we assume that the inconsistency is because of the models’ linear free-surface treatment, errors induced by sampling and discretization in S–T space, and possibly numerical diffusion.
g. Model deficiencies and water mass transformations in S–T coordinates
We have analyzed the water mass transformation in the Arctic Ocean using a global ocean circulation model. Because of the model deficiencies, some aspects of the results are idiosyncratic to the model in use and might not be representative of the real ocean. For instance, Figs. 3 and 4 show that the Atlantic water core temperature is too cold and that the cold halocline is not well represented in the model. Holloway et al. (2007) found similar problems when analyzing the Arctic Ocean hydrography in a suite of different models, including both global and regional configurations. Below we briefly discuss how the Walin framework approach may reveal information on which model features and processes cause the differences between the observational and model-simulated hydrographic distribution.
When comparing model simulations and observations, the volume and area distribution functions are useful complements to traditional S–T diagrams. Figure 6 reveals that the model has too much water in a ridgelike S–T band that extends from S ~ 34.5 g kg−1 and T ~ 0°C toward S ~ 30 g kg−1 and T ~ −1.8°C. This water mass is not present in the observations, where the maximum in υ(S, T) in this range is encountered closer to the freezing line, forming a curve-shaped feature for 
Figure 14 suggests that vertical mixing between inflowing Atlantic water and colder and fresher surface waters contribute to form the spurious “too warm” halocline waters in the model; the vertical mixing causes excessive transformation toward lower salinity. Inspections of the model fields reveal that the Barents Sea branch of the Atlantic inflow is too cold when entering the St. Anna Trough and that there is no cyclonic Arctic boundary current in the Canada basin. In addition, Figs. 9b and 14 show that the isoneutral mixing together with surface heat loss are the major components contributing to a transform toward lower temperatures for Atlantic water, and Fig. 8b shows that isoneutral and vertical mixing dominate transformations toward lower salinities in the Atlantic water salinity range. These features also contribute to the cold bias of the Atlantic water in the model.
The absence of a cold halocline in the model seems thus to be partly related to excessive mixing of heat into the upper ocean. However, another cause could be insufficient sea ice–related formation of near–freezing point water in the model. Aagaard et al. (1981) proposed that the strong wintertime surface heat loss and sea ice formation on the shallow shelves are important processes for creating cold halocline water as well as cold, denser water. Figures 15c and 16b indicate that near–freezing point water is formed during winter in the model. However, Fig. 8b shows that the freshwater flux due to the restoration of the sea surface salinity results in a freshening that counteracts and reduces the salinification associated with sea ice formation for 
4. Summary and conclusions
In this study, we have investigated water mass transformations in the Arctic Ocean using the S–T Walin framework developed by Hieronymus et al. (2014). The method has been applied to the global general circulation model NEMO, run in the ORCA1 configuration. By diagnosing the surface and internal diffusive fluxes, we have studied the resulting water mass transformations in S–T space. In particular, we have studied how the inflowing waters, encompassing both relatively warm and salty Atlantic water and fresher Pacific water, are transformed within the Arctic Ocean into polar mixed layer and halocline waters, which compose the outflowing water masses. As anticipated, the most dominant water mass transformation is a cooling and freshening of the inflowing waters (e.g., Rudels 2009; Tsubouchi et al. 2012). The calculated water mass transformation vector 
By decomposing 
For S–T regions close to the freezing line, the transformations are more complex because of the seasonality of the surface fluxes and the growth/melt of sea ice. During the winter season, the surface fluxes yield a net transformation toward colder temperatures and higher salinity in this S–T region, reflecting sea ice formation and heat loss to the atmosphere. During summer, on the other hand, there is mainly a transformation toward lower salinities and slightly lower temperatures, reflecting ice melt and some surface heat input that reduces the cooling of the surface water. However, for waters that are slightly warmer than the freezing temperature, there is a pronounced transformation toward higher temperatures. Away from the freezing line, the annual-mean transformation is qualitatively similar to the wintertime transformation. However, for the coldest water below salinities of about S ~ 32 g kg−1, the annual-mean transformation more closely resembles the summertime transformation. This illustrates the importance of the seasonal cycle for the annual-mean water mass transformation.
The Arctic Ocean water transformations show many similarities with those of the global ocean. For instance, the surface fluxes tend to deplete water in the S–T classes that occupy the largest surface area, thereby creating the extremes, whereas the mixing processes act to reduce the temperature and salinity ranges, as was found in the study of global water mass transformations by Hieronymus et al. (2014). However, unlike the global case where in each S–T interval the formation of water masses due to surface fluxes and mixing must exactly cancel each other in a steady state, this is not required in the Arctic Ocean where flows across its boundaries introduce sources and sinks of water masses. Thus, for the Arctic Ocean the net water mass transformation due to surface fluxes and mixing is significant and necessary for connecting the sinks and sources of water masses that are associated with the exchange with the Atlantic and Pacific Oceans.
We believe that the water mass transformations diagnosed from the present ocean circulation model qualitatively capture the broad features of the water mass transformations in the real Arctic Ocean. However, there are model deficiencies in processes that are important for the water mass transformations and the use of sea surface salinity restoring creates spurious transformation. In addition, problems related to salt conservation (partly related to sea ice processes and free-surface treatment) results in an uncomfortably large residual in the S-coordinate salt budget. Accordingly, some of the more detailed features of the water mass transformation in S–T space are unrealistic in the present simulation. However, we argue in section 3g that to compute and analyze the water mass transformation in an ocean circulation model can highlight the performance of parameterized subgrid processes that ultimately cause the transformations.
It is of worth to briefly comment on observationally based application of water mass transformation studies of the Arctic Ocean. Data applications of the Walin formalism have mainly focused on water mass transformations due to air–sea fluxes, for example, Andersson et al. (1982), Tziperman (1986), and Speer (1993). In the Arctic Ocean, the transformations due to air–sea fluxes are difficult to compute because of the limited data, but crude estimates should be obtainable. The observations needed for computing the net inflow as a function of temperature and salinity are presumably better and a few computations have been made for the Fram Strait flow (e.g., Rudels 1987; Nilsson et al. 2008; Rudels et al. 2008) and for all circum-Arctic gateways over a 32-day period (Tsubouchi et al. 2012). Thus, there is some potential for the estimating of the water mass export and the water mass formation due to surface fluxes in S–T coordinates for the Arctic Ocean. Assuming a steady state, this would allow the water mass formation due to interior mixing 
Acknowledgments
P. Pemberton and H. E. M. Meier were supported by the project Advanced Simulation of Arctic Climate Change and Impact on Northern Regions (ADSIMNOR, 214-2009-389) funded by the Swedish Research Council for Environment, Agricultural Sciences, and Spatial Planning (FORMAS). J. Nilsson acknowledges support from the Knut and Alice Wallenberg Foundation (via the SWERUS-C3 program) and the Swedish National Space Board. The authors would like to thank Jan D. Zika and an anonymous reviewer for comments that helped improve the presentation and content of the manuscript.
APPENDIX A
Definitions
Following Hieronymus et al. (2014), we here consider a region in the ocean bounded by the sea surface, the sea floor, and an interior vertical boundary B (see Fig. 1). To describe the state and evolution of the water properties in the region, we introduce the following variables and flows:
APPENDIX B
Basic Relations
Based on the definitions above, we will now formulate equations describing the conservation of volume, heat, and salt for a region 
APPENDIX C
Salinity- or Temperature-Only Coordinates (Walin’s 1D Frameworks)
The equations above are related to the 1D frameworks by Walin (1977, 1982), and we will now describe how they are recovered from the S–T framework. The salinity-only coordinate case of Walin (1977) can be recovered by letting 
Here, the diffusive heat flux across the isothermal surface T is balancing the net surface heat loss over the part of the ocean surface where the temperature is less than T and the boundary heat flux 
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In this study temperature, denoted by T, refers to potential temperature as this is conserved by the numerical model used.
