1. Introduction
The global ocean circulation is of great importance for the earth’s climate system through its heat transport and the cycling and storage of carbon. Understanding the underlying physical processes that drive the global ocean circulation is essential for our understanding of the earth’s climate system and our ability to model it accurately. However, observing and modeling the global ocean circulation remains a challenge.
A component of the ocean circulation is buoyantly or density-driven due to thermohaline forcing and is often referred to as thermohaline circulation. Here, thermohaline forcing refers to boundary freshwater and heat fluxes and salt and heat fluxes by diffusive mixing. In this paper, we develop a description of the thermohaline circulation using its unambiguous relationship to the thermohaline forcing. The use of thermodynamic coordinates for understanding the relationship between the circulation and thermodynamic forcing was first made clear by Walin (1982). He showed that the area-integrated surface heat flux between two outcropping isotherms could be used to calculate the diathermal advection in a steady-state ocean.
Speer and Tziperman (1992) applied Walin’s framework to isopycnals instead of isotherms, which together with many subsequent studies (Marshall 1997; Marshall et al. 1999; Nurser et al. 1999; Sloyan and Rintoul 2000, 2001; Iudicone et al. 2008; Badin and Williams 2010; Nikurashin and Ferrari 2013) allowed an understanding of ocean circulation driven by thermohaline forcing. Using this framework, Nurser and Marsh (1998) showed that the total diapycnal transport can be expressed as a sum of a streamfunction difference and nonsteady component. The diapycnal transport can be fully expressed as a streamfunction only when the nonsteady component is small.
Streamfunctions have been widely used as a diagnostic to study ocean circulation. The advantage of scalar streamfunctions lies in their ability to represent the complex three-dimensional and time-varying ocean circulation in two dimensions, allowing new insight into the ocean circulation. A classic example is perhaps the meridional overturning streamfunction Ψλz, representing the zonally averaged ocean circulation in latitude λ and depth z coordinates. Because ocean currents tend to follow isopycnal surfaces rather than surfaces of constant depth, Döös and Webb (1994) calculated a streamfunction in latitude and potential density σ coordinates Ψλσ. They identified circulation cells related to the Atlantic overturning, the subtropical gyres, and the Antarctic Bottom Water circulation and showed that the Deacon cell, which is a strong circulation cell visible in Ψλz, almost entirely disappeared in λ–σ coordinates. From observations, Marsh (2000) used Walin’s framework to derive a streamfunction in latitude and density ρ coordinates Ψλρ. A more thermodynamic streamfunction was presented by Nycander et al. (2007), who constructed a streamfunction in density and depth coordinates Ψρz. This study showed that certain ocean circulation cells are either mechanically forced, buoyantly forced, or forced by a combination of both. This clearly illustrates that streamfunctions provide a different representation of the ocean circulation for each choice of coordinates.
Simultaneously, Zika et al. (2012) and Döös et al. (2012, hereafter referred to as ZD12) constructed the thermohaline streamfunction, a streamfunction in salinity S and temperature T coordinates ΨST. The ΨST is essentially a two-dimensional extension of Walin’s framework, applied in S–T coordinates. However, ZD12 calculated ΨST, using a model’s three-dimensional velocity field instead of using the thermohaline forcing. Therefore, their ΨST represented only advection normal to S–T isosurfaces and not necessarily net water mass transformation rates. ZD12 identified similar circulation cells and obtained estimates for circulation time scales and diapycnal freshwater and heat transports. A recent study by Zika et al. (2013) shows the influence of the magnitude of the Southern Ocean winds with circulation in different coordinates, including S–T coordinates.
Although ZD12 were the first to calculate ΨST, Speer (1993) used salt and heat fluxes, in Walin’s framework, and projected the water mass transformation rates in S–T coordinates. This provided a distinction between transformation of different water masses and their locations. They emphasized that they were unable to distinguish if this transformation was associated with either local changes in density without actual motion of water or due to advective fluxes. Kjellsson et al. (2014) analyzed the atmospheric circulation in dry and moist isentropic coordinates to construct the hydrothermal streamfunction. They considered both the effect of Eulerian advection and local changes of properties and found that the latter was negligible for these coordinates.
Here we derive the complete ocean circulation in S–T coordinates (section 2), namely, the diathermohaline circulation. We show that the diathermohaline circulation is composed of an advective component and a component due to local changes in S–T values, without fluid motion in geographical space. The advective component is due to ocean circulation normal to isohaline and isothermal surfaces and can be expressed as an advective thermohaline streamfunction (section 3). The local component is due to local changes of the S and T values, expressed as geographical displacements of isohalines and isotherms. This results in changes in the ocean volume distribution in S–T coordinates and can be expressed as a local thermohaline streamfunction, after removing a trend (section 4). The sum of the advective and local thermohaline streamfunctions is the diathermohaline streamfunction and represents the nondivergent diathermohaline circulation in S–T coordinates and is the novel aspect of this paper (section 5). The analysis of a numerical model and observational climatology in S–T coordinates shows that the local thermohaline streamfunction is a significant component of the ocean circulation in S–T coordinates and cannot be ignored (section 6). We suggest that the diathermohaline streamfunction provides a tool for the analysis of, and comparison among, ocean models and observation-based gridded climatologies (sections 7 and 8).
2. Circulation in SA–Θ coordinates
Here, we construct a formalism to calculate circulation in Conservative Temperature Θ and Absolute Salinity SA coordinates. Conservative Temperature is proportional to potential enthalpy (by the constant heat capacity factor 
a. Thermohaline forcing
Surface radiative and sensible heat fluxes cause movement in the Θ direction (Fig. 1). Precipitation results in movement in the negative SA direction and evaporation results in movement in the positive SA direction and simultaneously movement in the negative Θ direction due to the related latent heat loss (Fig. 1). Mixing acts to reduce both the stratification and the SA–Θ range of the fluid parcels. Hence, the initial range enclosed by an isolated fluid parcel in SA–Θ coordinates will never be increased by mixing processes. In the absence of external forcing, loss of salt, heat, or mass, the initial range will eventually be reduced to a point in SA–Θ coordinates. Mixing depends on the magnitude and orientation of geographical gradients of SA and Θ (Fig. 1). In geographical coordinates, mixing occurs as downgradient tracer diffusion due to epineutral mesoscale eddies or as small-scale vertical turbulent diffusion (Gent et al. 1995; Griffies 2004). However, the latter is in fact small-scale isotropic (rather than vertical) turbulent diffusion (McDougall et al. 2014).
Schematic describing how fluid parcels are displaced in SA–Θ coordinates by different thermohaline forcing, that is, (top) surface fluxes and (bottom) diffusive mixing, with γn referring to a neutral surface. The representation of mixing in this diagram is idealized, showing an isolated volume only influenced by (left) isotropic turbulent diffusive mixing or (right) along-isopycnal eddy diffusive mixing, reducing the volume’s spread in SA and Θ in an isotropic or isopycnal manner, respectively.
Citation: Journal of Physical Oceanography 44, 7; 10.1175/JPO-D-13-0213.1
b. The diathermohaline velocity
A fluid parcel that moves in SA–Θ coordinates must cross isohalines and/or isotherms, leading to a diahaline or diathermal velocity and related volume transport. For example, consider a volume V, with uniform Θ. If the Θ increases, this volume will be displaced, leading to a diathermal volume transport, in the positive Θ direction in SA–Θ coordinates. Equivalently, if the SA of V increases, this volume will be displaced, leading to a diahaline volume transport in the positive SA direction in SA–Θ coordinates. We reserve the use of the prefix “dia” for the net displacement through a surface (for a discussion on a diasurface velocity, refer to Griffies (2004, 138–141).
Schematic of the diathermohaline velocity 
Citation: Journal of Physical Oceanography 44, 7; 10.1175/JPO-D-13-0213.1
Construction of the diahaline velocity 
Citation: Journal of Physical Oceanography 44, 7; 10.1175/JPO-D-13-0213.1
3. The advective thermohaline streamfunction
4. The local thermohaline streamfunction
We separate 
For a conceptual description, imagine a control volume containing a motionless fluid with fixed volume Vcontrol and uniform SA–Θ values that (uniformly) change over time. Changing the SA–Θ properties of the fluid in Vcontrol over time leads to a volume transport in SA–Θ coordinates. We now consider different changes of the SA–Θ values of Vcontrol to analyze and understand the resulting motion in SA–Θ coordinates.
a. The diathermohaline trend
First, consider heating the control volume from time t1 to t2. When the fluid with volume Vcontrol is heated, it may cross several isotherms and the related volume transport through these isotherms, in positive Θ direction, will be Vcontrol/Δt, where Δt is a constant time step (Fig. 4a, cycle 1). Equivalently, a change in SA causes the properties of Vcontrol to cross isohalines, resulting in a similar volume transport in the positive SA direction (Fig. 4a, cycle 2). Although the fluid in the control volume has not moved in geographical space, its SA–Θ values have changed, resulting in motion in SA–Θ coordinates. The resulting volume transport can be calculated by analyzing the total changes of the SA–Θ values of the fluid, rather than analyzing the displacements of the isohalines and isotherms (see the appendix).
Circulation in SA–Θ coordinates due to a shift of the ocean’s volume distribution in SA–Θ coordinates, with (a) no net transport or (b) net transport. Arrows indicate through which isotherms (between a certain SA interval) and isohalines (between a certain Θ interval) the volume transport is assigned. Two arrows in opposite direction cancel out. Cycle 1 shows heating (t1 → t2) and cooling (t2 → t3), and Cycle 2 shows salinification (t1 → t2) and freshening (t2 → t3). Cycle 3 shows heating and salinification (t1 → t2) and cooling and freshening (t2 → t3). Cycles 4 and 5 show net transport due to a diathermohaline trend and or cyclic motion, respectively. Gray arrows of Cycle 4 show an incomplete cycle causing the diathermohaline trend, which will be closed when subtracting a trend, to define the cyclic component.
Citation: Journal of Physical Oceanography 44, 7; 10.1175/JPO-D-13-0213.1
A net displacement of fluid in SA–Θ coordinates can be understood as a diathermohaline trend (Fig. 4b, cycle 4). However, if this displacement is continued over multiple time steps, we can obtain both a diathermohaline trend and a time-averaged steady-state and nondivergent component, which we will refer to as the diathermohaline cycle.
b. The diathermohaline cycle
The diathermohaline cycle in SA–Θ coordinates takes place when changes of SA–Θ values in the control volume returns to their initial SA–Θ values over time, but the heating and cooling (freshening and salinification) takes place at a different SA (Θ), such that the net transports through isohalines for a certain Θ range and isotherms for a certain SA range do not exactly cancel out (Fig. 4b, cycle 5). This cycle results in a net volume transport of Vcontrol/Δt, across isohalines, for different Θ ranges, and net volume transports across isotherms, for different SA ranges. Note that any cycle in which there are (simultaneous) changes of SA–Θ values of the fluid in the control volume over time, which causes a transport across exactly the same isohalines and isotherms when moving away from and returning back to its initial state, results in no net transport over time (Fig. 4a, cycles 1, 2, and 3 from t1 to t3).
For example, consider a volume in a motionless ocean, enclosed by a pair of isotherms and a pair of isohalines that change position with time (Fig. 5). For illustrative purposes we consider only the dynamics of three volumes that are within our grid indicated with a–d: 1) the volume VΘ, of which Θ changes; 2) the volume 
Schematic of movement of isohalines and isotherms that change the ocean’s volume distribution in SA–Θ coordinates. Events i, ii, iii, and iv indicate displacement of the isotherms or isohalines due to heating, salinification, cooling, and freshening, respectively. The motion of VΘ, 
Citation: Journal of Physical Oceanography 44, 7; 10.1175/JPO-D-13-0213.1
c. The local thermohaline streamfunction
We have argued that diathermohaline volume transports can be decomposed into a diathermohaline cycle and trend. The diathermohaline trend represents net changes in the ocean’s volume distribution in SA–Θ coordinates. A trend can be the result of 1) the net change of the geographical position of the bounding isohalines and isotherms induced by a net change in local SA–Θ values, and 2) a nonzero integral of u in the direction normal to the bounding isohalines and isotherms, over the surface area enclosing a volume.
5. The diathermohaline streamfunction
6. Application to model- and observational-based hydrography
In the following, we calculate 
a. Description of used model and observations
We use the final 10 yr of a 3000-yr spinup simulation of the University of Victoria Climate Model (UVIC). This model is an intermediate complexity climate model with a horizontal resolution of 1.8° latitude by 3.6° longitude, 19 vertical levels, and a 2D energy balance atmosphere [Sijp et al. (2006), specifically their case referred to as GM]. The ocean model is the Geophysical Fluid Dynamics Laboratory Modular Ocean Model, version 2.2 (MOM2), with Boussinesq and rigid-lid approximations applied (Pacanowski 1996). We use the monthly averaged potential temperature θ(°C) and practical salinity SP.
The observation-based climatology we use is the Commonwealth Scientific and Industrial Research Organisation (CSIRO) Atlas of Regional Seas (CARS) 2009. This is a global, except for the boundary at 75°S, high-resolution (0.5° × 0.5° grid spacing, 79 vertical levels) seasonal atlas of in situ temperature (i.e., T), practical salinity (i.e., SP), and several other properties (Ridgway et al. 2002; Ridgway and Dunn 2003). At higher latitudes, observations are limited and biased to the summer state. In summary, CARS provides a gridded, time-continuous standard year value of SP and T on each grid point. To be able to compare the results with UVIC, we use monthly averaged values.
We have used the Thermodynamic Equation of Seawater—2010 (TEOS-10) software (IOC et al. 2010; McDougall and Barker 2011) to convert both the UVIC output and the CARS data to SA and Θ. The practical details of the calculations of the different variables from both model and observations are provided in the appendix.
b. The thermohaline volume transports and diathermohaline trend
The diathermohaline volume transport in SA–Θ coordinates for volumes with a certain SA and Θ grid size can be calculated and compared for the advective and local thermohaline streamfunction and the diathermohaline trend (Fig. 6). The diathermohaline trend shows maximum values on the order of 1 Sverdrup (Sv; 1 Sv ≡ 106 m3 s−1), which is small compared to those of the advective and local streamfunctions, as expected from an equilibrated climate model. Note that, using the Student's t test, we found that none of these trends are significant within the 95% level. Hence, for UVIC 
(left) Diahaline and (right) diathermal volume transports (Sv) of UVIC for (top) 
Citation: Journal of Physical Oceanography 44, 7; 10.1175/JPO-D-13-0213.1
Climate trends (e.g., long-term warming of the ocean) lead to a permanent change in the positions of isohalines and isotherms, thereby shifting the ocean’s volume toward a different state. Diathermohaline trend terms that do not stem from a climate change complicate the interpretation of the diathermohaline trend. For example, the time period over which we average to analyze the diathermohaline trend is chosen to include an integer amount of closed cycles of the dominant cyclic motions in SA–Θ coordinates. Climate variability modes that do not fit in the selected time period will cause a net shift of the ocean’s volume in SA–Θ coordinates. Rounding errors due to time and spatial averaging of model or observational data, numerical diffusion, and other possible sources of error also lead to a diathermohaline trend in SA–Θ coordinates.
c. The advective thermohaline streamfunction
The 
The three dominant circulation cells shown by 
UVIC’s (top) 
Citation: Journal of Physical Oceanography 44, 7; 10.1175/JPO-D-13-0213.1
d. The local thermohaline streamfunction
We have calculated 
The 
Citation: Journal of Physical Oceanography 44, 7; 10.1175/JPO-D-13-0213.1
The ocean’s surface SA–Θ values from a full year of CARS, distributed in SA–Θ coordinates. Color indicates geographical location as shown by the inset. The 1-Sv contours of 
Citation: Journal of Physical Oceanography 44, 7; 10.1175/JPO-D-13-0213.1
An anticlockwise-rotating cell is found in an area in SA–Θ coordinates associated with equatorial surface waters (Fig. 9). It shows strong freshening due to precipitation, associated with the seasonal variability of the surface freshwater and heat fluxes related to the position and strength of the intertropical convergence zone (ITCZ), and is named the precipitation cell.
A clockwise-rotating cell is mainly related to evaporation over high SA-valued water masses (Fig. 9), which are most likely the formation regions of South Pacific and Indian Ocean Subtropical Mode Water (Hanawa and Talley 2001) and high-salinity evaporation areas such as the Mediterranean, Persian Gulf, Red Sea, and tropical Atlantic, and is named the evaporation cell.
There is a clear separation in SA–Θ coordinates between the evaporation E and precipitation P cells and the Southern Hemisphere (SH) and North Pacific (NP) radiative cells, which are dominated by radiative heating and cooling (Fig. 9). The anticlockwise-rotating SH radiative cell stretches over a wide temperature range in SA–Θ coordinates. This is due to summer radiative heating and winter radiative cooling in the Southern Ocean and adjacent ocean basins at subtropical latitudes (Fig. 9). The curved shape of the SH radiative cell can be explained by a change in the E–P fluxes from being dominated by freshening (precipitation dominating evaporation and possible cryospheric processes) at cold temperatures, to being dominated by salinification (evaporation dominating precipitation) at slightly warmer temperatures. As a result the streamfunction changes direction on the SA axis, leading to the observed shape. The latter also explains the anticlockwise-rotating NP radiative cell, due to a combination of the cryospheric processes and seasonal radiative heat fluxes. The NP radiative cell is separated from the SH radiative cell by the fresh North Pacific surface waters.
The clockwise-rotating cryosphere cell represents a circulation at high latitudes. We remind the reader that CARS is based on limited high-latitude observations, biased toward summer and extending only to 75°S. This might reduce the magnitude and spread of the cryosphere cell in SA–Θ coordinates and complicate the interpretation. However, we suggest the cryosphere cell represents cryospheric processes as we find that warming (cooling) is associated with freshening (salinification), with the minimum influence of seasonal radiative heat fluxes (Fig. 9).
Comparing 
The reduced spread of the UVIC precipitation cell suggests an incorrect simulation of the ITCZ freshwater and heat fluxes. The evaporation cell also shows a reduced magnitude and spread at higher salinities suggesting a problem with the formation and properties of the South Pacific and Indian Ocean Subtropical Mode Water and the tropical Atlantic surface waters.
Areas covered by the evaporation and precipitation cells in SA–Θ coordinates are expected to diverge in time on the SA axis, if relatively salty water increases its salinity and relatively freshwater reduces its salinity (Durack et al. 2012). Such dynamics can be analyzed from climatological trends and are related to changes in the surface freshwater and heat fluxes of these particular areas.
In UVIC, both SH and NP radiative cells have merged in SA–Θ coordinates, suggesting that the surface freshwater pool in the North Pacific is not correctly modeled and coincides with the SH salinities. Differences in the SH surface freshwater fluxes between CARS and UVIC suggest that the transition between the evaporation- to precipitation-dominated regime for decreasing temperatures for the SH radiative cell is not captured by the model. Finally, the UVIC cryosphere cell has an increased spread and magnitude compared to CARS, which has a bias toward the summer and lacks Arctic data.
7. Discussion
We have presented the derivation of the diathermohaline streamfunction 
Diapycnal transport of (top) heat (1015 W) and (bottom) freshwater (Sv) through potential density surfaces (σ0) for UVIC for 
Citation: Journal of Physical Oceanography 44, 7; 10.1175/JPO-D-13-0213.1
We have used surface SA–Θ properties to provide understanding of the observed circulation of 
Ballarotta et al. (2013) showed that temporal and spatial averaging applied to construct the overturning streamfunction significantly influences the observed circulation and requiring care with the interpretation. Zika et al. (2012) showed that the parameterized eddies have significant influences on 
8. Conclusions
We have introduced the diathermohaline circulation, driven by boundary freshwater and heat fluxes and mixing processes (thermohaline forcing). The time-averaged nondivergent component of the diathermohaline circulation in SA–Θ coordinates is quantified by the diathermohaline streamfunction 
Currently, 
Acknowledgments
SG was supported by the joint CSIRO–University of Tasmania program in quantitative marine science (QMS) and the CSIRO Wealth from Oceans flagship and through the Office of the Chief Executive (OCE) Science Team Postgraduate Scholarship Program. BMS was supported by the Australian Climate Change Science Program, jointly funded by the department of Climate Change and Energy Efficiency and CSIRO. JDZ is supported by the U.K. National Environment Research Council.
We thank two anonymous reviewers for their helpful comments that have improved the paper. We thank Willem Sijp for providing the UVIC output and associated discussion, Ken Ridgway for providing useful discussion about the CARS climatology, and we acknowledge numerous discussions with Paul Barker. We thank Kristoffer Döös, Jonas Nycander, Johan Nillson, and Leo Maas for valuable discussions on this work. Finally we thank Walter Munk for inspiration and encouragements to continue this study in an “unfashionable” area of oceanographic research.
APPENDIX
Calculating 
In this appendix, we will explain the technical details of how to calculate the thermohaline volume transports and related streamfunctions using ocean hydrographic data of a model and observation-based product as described in section 6.
a. Discretization processes
We calculate 
In addition to the geographical discretization there is also a discretization in SA–Θ coordinates. Consider volume ΔV, bounded by a pair of isotherms that are separated by 2dΘ and a pair of isohalines that are separated by 2dSA. The volume’s Θ ranges between Θ ± dΘ and SA ranges between SA ± dSA. While ΔV may have any shape in Cartesian coordinates, it covers a square grid in SA–Θ coordinates (Fig. 2).
A position in SA–Θ coordinates is given by 
b. Calculating 
Consider ΔVi,j,k and the associated
Then consider ΔVi,j,k and the associated
If
The volume transport
- For volume ΔVi,j,k, we repeat this for n = 1: N time steps, and we will then take the time average of all contributions. This will also be applied to all volumes in space, such that we obtain
The shortest route concept. The volume transport V/Δt, related to a displacement of a volume V in SA–Θ coordinates in time, has to be assigned to the correct SA (Θ) interval of the isotherms (isohaline) that V has crossed, as indicated by the gray dots. These intervals are obtained when drawing a straight line between the initial grid and the final grid that V occupies. When the line crosses a midpoint between isohalines and isotherms, half of the transport is assigned to both directions.
Citation: Journal of Physical Oceanography 44, 7; 10.1175/JPO-D-13-0213.1
c. Calculating 
Consider
Consider
If
- Repeat this for all (xi, yj, zk, and tn) locations and also for the y and z directions and take their sum. Then take the time average over all available time steps to obtain
d. Calculating 
As 
For a grid with 
The advective thermohaline streamfunction 
Citation: Journal of Physical Oceanography 44, 7; 10.1175/JPO-D-13-0213.1
REFERENCES
Badin, G., and R. G. Williams, 2010: On the buoyancy forcing and residual circulation in the Southern Ocean: The feedback from Ekman and eddy transfer. J. Phys. Oceanogr., 40, 295–310, doi:10.1175/2009JPO4080.1.
Ballarotta, M., S. Drijfhout, T. Kuhlbrodt, and K. Döös, 2013: The residual circulation of the Southern Ocean: Which spatio-temporal scales are needed? Ocean Modell., 64, 46–55, doi:10.1016/j.ocemod.2013.01.005.
Döös, K., and D. J. Webb, 1994: The Deacon cell and the other meridional cells of the Southern Ocean. J. Phys. Oceanogr., 24, 429–442, doi:10.1175/1520-0485(1994)024<0429:TDCATO>2.0.CO;2.
Döös, K., J. Nilsson, J. Nycander, L. Brodeau, and M. Ballarotta, 2012: The World Ocean thermohaline circulation. J. Phys. Oceanogr., 42, 1445–1460, doi:10.1175/JPO-D-11-0163.1.
Durack, P. J., S. E. Wijffels, and R. J. Matear, 2012: Ocean salinities reveal strong global water cycle intensification during 1950 to 2000. Science, 336, 455–458, doi:10.1126/science.1212222.
Ferrari, R., and D. Ferreira, 2011: What processes drive the ocean heat transport? Ocean Modell., 38, 171–186, doi:10.1016/j.ocemod.2011.02.013.
Gent, P. R., J. Willebrand, T. J. McDougall, and J. C. McWilliams, 1995: Parameterizing eddy-induced tracer transports in ocean circulation models. J. Phys. Oceanogr., 25, 463–474, doi:10.1175/1520-0485(1995)025<0463:PEITTI>2.0.CO;2.
Graham, F. S., and T. J. McDougall, 2013: Quantifying the nonconservative production of Conservative Temperature, potential temperature, and entropy. J. Phys. Oceanogr., 43, 838–862, doi:10.1175/JPO-D-11-0188.1.
Griffies, S. M., 2004: Fundamentals of Ocean Climate Models.Princeton University Press, 518 pp.
Hanawa, K., and L. D. Talley, 2001: Mode waters. Ocean Circulation and Climate: Observing and Modelling the Global Ocean, International Geophysics Series, Vol. 77, Academic Press, 373–386.
IOC, SCOR, and IAPSO, 2010: The international thermodynamic equation of seawater—2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission Manuals and Guides 56, 196 pp. [Available online at http://www.teos-10.org/pubs/TEOS-10_Manual.pdf.]
Iudicone, D., G. Madec, and T. J. McDougall, 2008: Water-mass transformations in a neutral density framework and the key role of light penetration. J. Phys. Oceanogr., 38, 1357–1376, doi:10.1175/2007JPO3464.1.
Kjellsson, J., K. Döös, F. B. Laliberté, and J. D. Zika, 2014: The atmospheric general circulation in thermodynamical coordinates. J. Atmos. Sci., 71, 916–928, doi:10.1175/JAS-D-13-0173.1.
Marsh, R., 2000: Recent variability of the North Atlantic thermohaline circulation inferred from surface heat and freshwater fluxes. J. Climate, 13, 3239–3260, doi:10.1175/1520-0442(2000)013<3239:RVOTNA>2.0.CO;2.
Marshall, D., 1997: Subduction of water masses in an eddying ocean. J. Mar. Res., 55, 201–222, doi:10.1357/0022240973224373.
Marshall, J., D. Jamous, and J. Nilsson, 1999: Reconciling thermodynamic and dynamic methods of computation of water-mass transformation rates. Deep-Sea Res. I, 46, 545–572, doi:10.1016/S0967-0637(98)00082-X.
McDougall, T. J., 2003: Potential enthalpy: A conservative oceanic variable for evaluating heat content and heat fluxes. J. Phys. Oceanogr., 33, 945–963, doi:10.1175/1520-0485(2003)033<0945:PEACOV>2.0.CO;2.
McDougall, T. J., and P. M. Barker, 2011: Getting started with TEOS-10 and the Gibbs Seawater (GSW) oceanographic toolbox. SCOR/IAPSO WG127 Rep., 34 pp. [Available online at http://www.teos-10.org/pubs/Getting_Started.pdf.]
McDougall, T. J., D. R. Jackett, F. J. Millero, R. Pawlowicz, and P. M. Barker, 2012: A global algorithm for estimating Absolute Salinity. Ocean Sci., 8, 1123–1134, doi:10.5194/os-8-1123-2012.
McDougall, T. J., S. Groeskamp, and S. M. Griffies, 2014: On geometrical aspects of interior ocean mixing. J. Phys. Oceanogr., doi:10.1175/JPO-D-13-0270.1, in press.
Millero, F. J., R. Feistel, D. G. Wright, and T. J. McDougall, 2008: The composition of standard seawater and the definition of the reference-composition salinity scale. Deep-Sea Res. I, 55, 50–72, doi:10.1016/j.dsr.2007.10.001.
Nikurashin, M., and R. Ferrari, 2013: Overturning circulation driven by breaking internal waves in the deep ocean. Geophys. Res. Lett., 40, 3133–3137, doi:10.1002/grl.50542.
Nurser, A. J. G., and R. Marsh, 1998: Water mass transformation theory and the meridional overturning streamfunction. International WOCE Newsletters, No. 31, WOCE International Project Office, Southampton, United Kingdom, 36–39.
Nurser, A. J. G., and M.-M. Lee, 2004: Isopycnal averaging at constant height. Part I: The formulation and a case study. J. Phys. Oceanogr., 34, 2721–2739, doi:10.1175/JPO2649.1.
Nurser, A. J. G., R. Marsh, and R. G. Williams, 1999: Diagnosing water mass formation from air–sea fluxes and surface mixing. J. Phys. Oceanogr., 29, 1468–1487, doi:10.1175/1520-0485(1999)029<1468:DWMFFA>2.0.CO;2.
Nycander, J., J. Nilsson, K. Döös, and G. Broström, 2007: Thermodynamic analysis of ocean circulation. J. Phys. Oceanogr., 37, 2038–2052, doi:10.1175/JPO3113.1.
Pacanowski, R., 1996: MOM2 version 2 documentation, user’s guide, and reference manual. NOAA/GFDL Ocean Tech. Rep. 3.2, 329 pp. [Available online at http://gfdl.noaa.gov/cms-filesystem-action/model_development/ocean/manual2.2.pdf.]
Ridgway, K. R., and J. Dunn, 2003: Mesoscale structure of the mean East Australian Current system and its relationship with topography. Prog. Oceanogr., 56, 189–222, doi:10.1016/S0079-6611(03)00004-1.
Ridgway, K. R., J. R. Dunn, and J. L. Wilkin, 2002: Ocean interpolation by four-dimensional weighted least squares—Application to the waters around Australasia. J. Atmos. Oceanic Technol., 19, 1357–1375, doi:10.1175/1520-0426(2002)019<1357:OIBFDW>2.0.CO;2.
Sijp, W. P., M. Bates, and M. H. England, 2006: Can isopycnal mixing control the stability of the thermohaline circulation in ocean climate models? J. Climate, 19, 5637–5651, doi:10.1175/JCLI3890.1.
Sloyan, B. M., and S. R. Rintoul, 2000: Estimates of area-averaged diapycnal fluxes from basin-scale budgets. J. Phys. Oceanogr., 30, 2320–2341, doi:10.1175/1520-0485(2000)030<2320:EOAADF>2.0.CO;2.
Sloyan, B. M., and S. R. Rintoul, 2001: The Southern Ocean limb of the global deep overturning circulation. J. Phys. Oceanogr., 31, 143–173, doi:10.1175/1520-0485(2001)031<0143:TSOLOT>2.0.CO;2.
Speer, K. G., 1993: Conversion among North Atlantic surface water types. Tellus, 45A, 72–79, doi:10.1034/j.1600-0870.1993.00006.x.
Speer, K. G., and E. Tziperman, 1992: Rates of water mass formation in the North Atlantic Ocean. J. Phys. Oceanogr., 22, 93–104, doi:10.1175/1520-0485(1992)022<0093:ROWMFI>2.0.CO;2.
Walin, G., 1982: On the relation between sea-surface heat flow and thermal circulation in the ocean. Tellus, 34, 187–195, doi:10.1111/j.2153-3490.1982.tb01806.x.
Zika, J. D., M. H. England, and W. P. Sijp, 2012: The ocean circulation in thermohaline coordinates. J. Phys. Oceanogr., 42, 708–724, doi:10.1175/JPO-D-11-0139.1.
Zika, J. D., W. P. Sijp, and M. H. England, 2013: Vertical heat transport by the ocean circulation and the role of mechanical and haline forcing. J. Phys. Oceanogr., 43, 2095–2112, doi:10.1175/JPO-D-12-0179.1.
