Thermohaline Circulation

The thermosteric effect clearly dominates the halosteric effect. 

In the marine boundary layer, atmospheric pressure adjustment to sharp sea surface temperature gradients lead to a surface wind convergence, which anchors a narrow band of precipitation along the Gulf Stream. 

Wind-Driven Surface Currents in February and March

1. enhancement of the hydrological cycle. -> salty gets saltier and fresh gets fresher

2. Adiabatic vertical shifts (or heave) of density surfaces driven by wind changes will cause salinity change on a pressure surface without any real change to the ocean freshwater inventory or water masses.

above the reasons and beneath the main results :

1. Subsurface salinity changes on pressure surfaces are attributable to both isopycnal heave and real water mass modification of the temperature- salinity relationship. 
2. Broad-scale surface warming and the associated poleward migration of isopycnal outcrops drive a clear and repeating pattern of subsurface isopycnal salinity change in each independent ocean basin. 
3. Qualitatively, the observed global multidecadal salinity changes are thus consonant with both broad-scale surface warming and the amplification of the global hydrological cycle. 

In the strongly warming tropical and subtropical Atlantic Ocean, deepening isopycnals drive strong salinity increases on pressure surfaces above 500 dbar.

subtropics and tropics becoming saltier and polar regions fresher. 

here are three different results:

1. Surface flow balances E-P over the ocean and P-E over land: no additional groundwater flow required
2. The total flux of submarine groundwater discharge to the Atlantic Ocean is similar in volume to the riverine flux
3. groundwater discharge 3 to 4 times greater than river discharge, but largest amount is salty water showing strong interaction between land and ocean. 

three components:

1. sensible heat flux in the Oceans
2. sensible heat flux in the atmosphere 
3. latent heat flux in the atmosphere-ocean coupled system 

• In the subtropics, oceanic sensible heat flux is the dominating contributor
• mid latitudes, latent heat flux is the dominating contributor 
• at high latitudes, atmospheric sensible heat flux is the dominating contributor

S.590

• The annual variations in temperature decrease with depth and are rarely perceptible below 100 to 300 m. 
• The maxima/minima at the sea surface occurs at the end of the warming/cooling season.
  • Below the sea surface, the times of occurrence of the maxima and minima are delayed by as much as 2 months relative to the times at the surface. 

As sea water evaporates the salt remains behind, only the freshwater is transferred from the ocean to the atmosphere. A region of excess evaporation, such as the subtropics tend to become salty, while the areas of excess rainfall become fresher. Salinity reflects the workings of the hydrological cycle: the movement of freshwater through the earth/ocean/atmosphere system.

• Water warmer than 10°C dominate the sea surface but do not extend much below 500m in the ocean. 
• The thermocline is the sharp drop off in temperature with depth and marks the boarder between the surface zone (mixed layer) and the deep zone. 
• Deeper cold waters derive their properties at the sea surface during winter at high latitude. 

1. bowl-shaped isothermals in the subtropical Ocean around 30° off the equator and a few 100m below the sea surface. 
2. subsurface maximum of the vertical temperature gradient -> main thermocline 
3. strong front from the sea surface to the deep Ocean in the Southern Ocean.
   1. strong circumpolar current seperates cold water from the south and relative warm water from the north
4. cold water formed near the edge of Antarctica spreads northwards as bottom water 
5. northern source of cold water formation

1. bowl-shaped isothermals in the subtropical Ocean around 30° off the equator and a few 100m below the sea surface. 
2. subsurface maximum of the vertical temperature gradient -> main thermocline 
3. strong front from the sea surface to the deep Ocean in the Southern Ocean.
   1. strong circumpolar current seperates cold water from the south and relative warm water from the north
4. cold water formed near the edge of Antarctica spreads northwards as bottom water 

1. bowl-shaped isothermals in the subtropical Ocean around 30° off the equator and a few 100m below the sea surface. 
2. subsurface maximum of the vertical temperature gradient -> main thermocline 
3. strong front from the sea surface to the deep Ocean in the Southern Ocean.
   1. strong circumpolar current seperates cold water from the south and relative warm water from the north
4. cold water formed near the edge of Antarctica spreads northwards as bottom water 

• In the North Atlantic Ocean, there is a tongue-like feature of high salinity, starting from the upper ocean and pentrating vertically to the depth of 2km. 
• At the 2km level, the core of this high-salinity tongue extends southward and across the equator.
  • This salinity tongue is mostly the signature of the high-salinity Mediterranean Water. 
  • Since it is a subsurface maximum it is not directly connected to the surface salinity along this section. 
  • In fact, it is produced by a westward lateral transport of high salinity at a depth of roughly 1km. 
• In the Southern Hemisphere, an outstanding tongue of low salinity, originating from the sea surface at 50° S, extends to a depth of of 1km. 
  • This is the Antarctic Intermediate Water (AAIW)
• The relatively low salinity below the level of 4km is associated with Antartic Bottom Water (AABW) formed near the edge of the Antartic continent. 

The tongue-like features cannot be interpreted as flow directions since many other processes are involved!

• relatively high salinity in the upper 400m in the subtropics
• between 500m and 1,5km the salinity distribution is dominated by tongues of relatively low salinity from high latitudes. 
  • In comparison with the Atlantic section, the low salinity tongue from the south (AAIW) is less prominent.
• In contrast to the Atlantic section, here the AABW appears as slightly saltier water spreading northward in the deep ocean below 4km. 

• The low-salinity tongue associated with AAIW is the dominant feature in the Souther Hemisphere, similar to the Atlantic section. 
• The relatively high-salinity intrusion from the north dominates the depth between 2 and 4 km in the Souther Hemisphere. 
• In the North Indian Ocean, the influence of high-salinity water from the Red Sea can be seen clearly at the depth of 1km. 

• points on the T-S diagram are water types and lines on the T-S diagram are water masses
• Water types aquire the properties at the sea surface at special locations. Therefore not an abitrary combination of properties can occur
• After subduction temperature and salinity of the water becomes conserved and with that the definition of water masses via T-S diagram meaningful. 
• The mixing triangle shows the area in which water masses resulting out of the mixing of three water types can occur!

The net surface heat flux and evaporation minus precipitation result in temperature and salinity changes at the sea surface. This can be written as a surface density flux:

\(F_\rho =\rho_0(-\alpha_TF_T+\alpha_SF_S)\;\;\left[\frac{kg}{m^2s}\right]\)

with \(\alpha_T=-\frac{1}{\rho}(\frac{\partial \rho}{\partial T})_{pS}\)is the coefficient of thermal expansion and \(\alpha_S=\frac{1}{\rho}(\frac{\partial \rho}{\partial S})_{Tp}\)is the coefficient of haline contraction

The thermal density flux is:

\(F_T=\frac{Q_\sum}{\rho_0c_p}\;\;\left[\frac{mK}{s}\right]\)

The haline density flux is:

\(F_S=(E-P)S\;\;\left[\frac{m}{s}\right]\)

Instead of density often we use buoyancy of sea water:

\(b=-g\frac{\rho'}{\rho_0}\;\;\left[\frac{m}{s^2}\right]\)

Then the buoyancy flux is:

\(B=-\frac{g}{\rho_0}F_\rho\;\;\left[\frac{m^2}{s^3}\right]\)

If there is a surface density increase, then we have a surface buoyancy decrease. 

The change in surface buoyancy is equal to the area of the \(\rho\)-z diagram, which is bounded by the density of the process start and process end.  

• The density varies mostly with depth due to the weak compressibility of water. Although, the density varies mostly due to pressure changes, which is dynamical irrelevant. Do get dynamical relevant density variations one often takes the potential density.
• The problem with the potential vorticity is that the non-linearity of the equation of state introduces artificial features to the stratification.
• One solution is to choose the reference point as close to the discussed depth as possible, but this doesn't work if you consider the whole depth range.

Another solution is the introduction of the neutral surface or neutral density 

1. The local pressure is used as a reference point
2. the neutral surface is defined as a surface whose normal is in the direction of \(-\alpha\Delta\Theta+\beta\Delta S\) where \(\alpha\) is the thermal expansion and \(\beta\) is the haline contraction. 
3. Unfortunately, this surface is a helical surface. This means that arbitrarily closed trajectories on the surface are not possible. 
4. To solve this a algorithm was developed by Jackett and McDougall. It uses global maps of observed temperature, salinty and pressure. The surface defined in this way are approximately neutral and they stay within a few tens of meters of an ideal surface anywhere in the world. 

• This figure overestimates volume of the high latitudes due to meridian convergence
• undererstimating volume of the deep ocean. 

One can see: permament thermocline, the seasonal and tropical thermoclines and the various surface convergences and divergences with major water masses. 

• moderate density -> sinks to relatively shallow water depths
• The name "mode water" reflects the fact that these sources of water mass are not uniformly distributed in the temperature-salinity space; instead owing to specific sea surface conditions favorable for the formation of these water masses, they appear in clusters in the parameter space. 
• appears as local distribution maxima in the (T,S) space and as local minimum in potential vorticity. 

Mode water formation commonly occurs through subduction taking place in the upper ocean. Subduction of mode water from the late-winter mixed layer into the permanent thermocline of the subtropical basin interior is realized through the combined effects of vertical pumping and lateral induction.

• Vertical pumping is related to Ekman pumping and produced by the surface wind stress
• lateral induction is due to horizontal advection of the wind-driven gyre and the horizontal gradient of the late-winter mixed layer depth.
• lateral induction is the major player!  

graphic shows the basic elements of subtropical mode water formation

1. Background circulation: transports newly formed mode water away from the formation site.
2. Strong seasonal cycle of the mixed layer depth: Strong cooling due to cold and dry air blowing over relatively warm water (for example gulf stream region) generates huge volumes of mode water with nearly homogenous properties. The rapid retreat of mixed layer depth in early spring seals it with a shallow, strongly stratified layer on top, thus completing the formation of mode water. 
3. Large horizontal gradient of winter mixed layer depth: This combines with strong horizontal advection of the wind-driven gyre, giving rise to a strong lateral induction. 

The upper ocean is divided into four layers:

1. Ekman layer
   1. In the subtropical basin, the convergence gives rise to Ekman pumping, and in the subpolar basin the divergence gives rise to Ekman sucking (upwelling).
2. the mixed layer
   1. The mass exchange between the mixed layer and the seasonal pycnocline is called entrainment/detrainment.
3. the seasonal pycnocline 
   1. The mass exchange between the seasonal pycnocline and the permament pycnocline is called subduction/obduction.
4. the permanent pycnocline 

The annual mean subduction rate is defined as the total amount of water going from the mixed layer, passing through the seasonal pycnocline, to the permanent pycnocline irreversibly in one year. Excludes the contribution due to the so-called temporal detrainment, which re-enters the mixed layer downstream. 

The annual mean obduction rate is defined as the total amount of water going from the permanent pycnocline, passing through the seasonal pycnocline, to the mixed layer irreversibly in one year.  

In the upper ocean, there exists a thin boundary layer below the sea surface where the wind stress is balanced by frictional force due to vertical-shear-induced turbulence and pressure force. 

The structure of the Ekman layer in the ocean is much more complicated and includes surface waves, wave breaking, turbulence, and other dynamical processes, such as Stokes drift and the Langmuir cell. 

Nevertheless: Classical theory by Ekman (1905)

starting with equations of motions for homogeneous density and quasi-steady state ocean.

equations for a relatively thin surface layer, on the order of e few tens of meters, where the vertical shear of turbulence force is a dominating factor in the dynamic balance. 

\(-fv=-\frac{1}{\rho_0}\frac{\partial p}{\partial x}+\frac{\partial }{\partial z}(A\frac{\partial u}{\partial z})\\ fu=-\frac{1}{\rho_0}\frac{\partial p}{\partial y}+\frac{\partial}{\partial z}(A\frac{\partial v}{\partial z})\)

For boundary conditions we choose:

1. velocity vanishes at large depths
2. vertical stress on the sea surface match wind stress imposed on the ocean

\((u,v)\rightarrow0,\;\;as\;z\rightarrow\;-\infty\\ A\frac{\partial u}{\partial z}=\tau^x/\rho_0,\;\;A\frac{\partial v}{\partial z}=\tau^y/\rho_0\)

taking the ageostrophic part of the velocity only:

\(-fv_e=\frac{\partial }{\partial z}(A\frac{\partial u_e}{\partial z})\\ fu_e=\frac{\partial}{\partial z}(A\frac{\partial v_e}{\partial z})\)

Integrating this set vertically brings:

\(\mathbf{U_e}=-\mathbf{z}\times\mathbf{\tau} /f\rho_0\)

Where \(\mathbf{U_e}\) is the total volume flux integrated over the whole depth. Therefore, wind stress in the upper ocean drives a volume flux, the so-called Ekman transport, which is 90° to the right of wind-stress direction (NH). 

The rate of Ekman pumping can be calculated from the continuity equation: 

\(u_x+v_y+w_z=0\)

Using the upper boundary condition of w=0 at z=0, the vertical velocity at the base of the Ekman layer is:

\(w_e=\int\limits^0_{-H}(u_x+v_y)dz=\frac{\partial}{\partial x}\int\limits^0_{-H}u_e dz+\frac{\partial}{\partial y}\int\limits^0_{-H}v_edz\)

\(.\\w_e=\frac{1}{f\rho_0}[\frac{\partial \tau^y}{\partial x}-\frac{\partial \tau^x}{\partial y}]+\frac{\beta\tau^x}{f^2\rho_0}\)

The Ekman pumping rate consists of two parts:

1. wind stress curl 
2. beta effect

• Ekman pumping at the subtropical basin: westerly winds north and easterly winds south -> anticyclonic wind stress curl -> w_e<0 -> Ekman pumping. 
• Ekman sucking at the subpolar basin
• Strong along -shore winds can drive strong upwelling/downwelling in coastal areas. For instance the Coast of California, where strong equatorward  trade winds drive strong offshore Ekman transport in the upper ocean. 

For large scale steady state wind-driven circulation int the ocean interior, the nonlinear advection terms are negligible:

\(-fV=-P_x/\rho_0+\tau^x/\rho_0+F_x\\fU=-P_y/\rho_0+\tau^y/\rho_0+F_y\\U_x+V_y=0\)

where \((U,V)\) are the depth-integrated flux and Fare the forces due to bottom or lateral friction, which are assumed to be negligible except within the western boundary. 

cross-differentiating brings the Sverdrup relation:

\(\beta V=-(\partial \tau^x/\partial y-\partial \tau^y/\partial x)/\rho_0\)

The Sverdrup relation presents the basic vorticity balance in the wind-driven circulation!

In the ocean interior the planetary vorticity gradient is balanced by the wind-stress curl!

For example, in the subtropical basin the wind stress curl gives rise to negative wind stress torque. Under this negative vorticity drive, water parcels move equatorward and thus create the anticyclonic gyres in the world oceans. 

1. The ventilation by Iselin 
2. The Stomme demon

Stommel postulated in 1979 that a demon is working so that only the late-winter properties are selected. i.e. water that actually enters the permament thermocline is the water formed at the time when the mixed layer is deepest and the density is the highest. 

is a process that selects only the late-winter water for actual subduction into the permament pycnocline. This meachnism is called the Stommel demon

Indeed, if we want to simulate the annual mean wind-driven circulation, we should select the late-winter thermohaline boundary conditions at the sea surface, including mixed layer density and depth; however, the wind stress forcing, or the Ekman pumping rate, should be the annual mean because we are concerned about the annual mean movement of the particles in the thermocline. 

Subsurfaces are not in direct contact with atmospheric forcing. So how shall their motions be explained? 

Ventilation can put subsurface layers into motion. That is:

Many isopycnaly outcrop in poleward parts of the oceans. When a outcrops, it is exposed to the atmospheric forcing directly. Thus, the outcropping layer is in motion under the wind stress forcing, and it should continue its motion even after it has been subducted under the other layers. 

The basic idea ist that, within the subtropical gyre, water is pushed downward into the thermocline by Ekman pumping and then downwells along isopycnals as it moves southward, induced by Sverdrup dynamics. The motion of the particles after their rejection from the base of the mixed layer is confined within the corresponding isopycnal surfaces, because mixing is relatively weak below the mixed layer and above the rough topography (as observations also show). 

Now the process described by Iselin is called "ventilation by Ekman pumping", since there are several other types of ventilation. 

Luyten, Pedlosky and Stommel (1983) formulated a multi-layer model for the ventilated thermocline and applied this to the North Atlantic. 

The model:

1. The model is formulated for the ocean interior, excluding the western boundary region and the Ekman layer. 
2. several layers of constant density which outcrop at different latitudes. 

The uppermost layer is directly driven by Ekman pumping. After subduction, water particles retain their potential vorticity and continue their southward motion. Along the eastern boundary, the model predicts that water moving in a subsurface layer has to depart from the wall in order to maintain its potential vorticity. 

The model is driven by a simple sinusoidal Ekman pumping. 

There a four different dynamical regions in the second layer:

1. north of the outcropline: second layer is directly exposed to the Ekman pumping 
2. three different regions south of the outcropping line:
   1. pool region: water comes from the western boundary region 
   2. ventilated region: water continous its southward motion
   3. eastern region: consists of a shadow zone below the moving uppermost layer. 

Discontinuities in layer slope and velocity across the boundary of the shadow zone indicate changes in dynamics across this boundary. 

Basic assumptions: geostrophy for the horizontal momentum, hydrostatic approximation, and mass conversation. 

After subduction the potential vorticity of a parcel is conserved due to weak diffusivity. It follows that along a streamline the potential vorticity is conserved. 

It can be shown that the contourlines for layer thickness h are streamlines and lines of constant potential vorticity.