Thermohaline Circulation

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. 

The no-zonal flux condition requires the thickness of the subsurface layers to be constant along the eastern boundary. The constant layer thickness implies that the potential vorticity is non-constant along the eastern boundary because f varies along the meridional wall. Since potential vorticity should be conserved along streamlines in subsurface layers, the eastern boundary cannot be a streamline in these layers. Thus, the region next to the eastern boundary should be a shadow zone for the subsurface layers where fluid is stagnant, and motions must be confined to the uppermost layer that is directly exposed to the Ekman pumping. 

The existence of such a shadow zone near the eastern boundary is consitent with the observation that oxygen content in depth range of 600-800 m near the eastern boundary in the subtropical basin is the lowest in the whole basin. 

1. Warmer mixed-layer reducing the capacity to store oxygen
2. Decrease in the exchange between surface waters and the ocean interioe as a consequence of increased stratifaction caused by warmer surface water. 
3. Shallower ventilation in the tropics.
4. Enhanced consumption due to increased CO2
5. Regional circulation variability. 

The effective detrainment period is marked by the Langrangian trajectories of water particles released from the base of the mixed layer. 

The mixed layer reaches its annual maximum density and depth in late winter, so there is a very thick layer of almost veritcally homogenized water. When spring comes, the mixed layer shoals very quickly and leaves the homogenized water behind, so that the water subducted has properties very close to those of the late-winter mixed layer. 

The instantaneous detrainment rate is defined as the volume flux of water leaving the base of the mixed layer per unit horizontal area: 

\(D=-(w_{mb}+\vec{v}_{mb}*\nabla h_m+\partial h/\partial t)\)

where \(w_{mb}= w_e-\frac{\beta}{f}\int^0_{-h}vdz\) and \(\vec{v}_{mb}\) are the vertical and horizontal velocity at the base of the mixed layer and \(h_m\) is the mixed layer depth. 

\(w_{mb}\) is slightly smaller than the Ekman pumping rate due to geostrophic flow in the mixed layer. 

If there were no seasonal cycle, the subduction rate should equal the detrainment rate:

\(S=D=-(w_{mb}+\vec{v}_{mb}*\nabla h_m )\)

In the praxis we calculate the annual subduction rate as above but with \(h_m\)beeing the mixed layer thickness at late winter. 

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. 

• deep water
• mode water

1. Cold water on the bottom is formed around Antarctica, primarily in the Weddell Sea and Ross Sea. 
   1. Cold water mass formed around the edge of the Antartctic continent that sinks to the bottom of the world's ocean is called Antarctic Bottom Water (AABW)
2. Cold bottom water spreads northward in each basin, and there is a tendency for the cold water to pile up in the western side of the basin.
3. Bottom water temperature in the South Atlantic Ocean is the coldest among all basins. 
4. In the South Atlantic Ocean, only the Brazil Basin receives AABW directly. The eastern basin (Angola basin) does not receive AABW directly but through a narrow gap near the equator. 
5. At the northern end of the North Atlantic Basin there is a source of relatively cold water, which originates from the Norweign Sea and Greenland Seas. The North Atlantic Deep Water (NADW).
6. There is no deep water source in the North Pacific

1. Formation in the open Ocean 
   1. The Norweign/Greenland Seas
   2. The Labrador Seas
2. Formations along margins of the sea 
   1. Strong cooling along the edge of a continent creates favorable conditions for dense water mass formation in the marginal sea.
   2. The Weddel Sea
   3. The Ross Sea

North Atlantic Deep Water is formed in the northern Atlantic Ocean throught two processes, including open-ocean deep convection and boundary convection associated with the horizontal gyre. 

Deep water formed in the Norwegian and greenland Seas overflows the Denmark Strait and enters the open North Atlantic Ocean.

During the process of overflow, substantial entrainments take place, enhancing the total volumetric flux of the deep water. 

In the open North Atlantic Ocean, deep water appears as the deep western boundary current moving southward along the eastern coast of the American continent, gradually sending its water mass to the oceanic interior. 

Although NADW may lose lose its mass through upwelling in the interior to the Atlantic Basin, one of the major pathways of NADW is through the wind-driven upwelling associated with the southern westerly and the subsequent northern return flow in the form of the Ekman flux. 

In addition, in the Southern Ocean, deep water from the northern source (NADW) meets the bottom water from the  southern source (AABW).

The major sites of Deep Convection include the northwestern Mediterranean, the Labrador Sea, and the Greenland Sea. 

process can be roughly classified in the following major processes:

1. Preconditioning: Strong cyclonic wind stress curl in early winter enhances the Ekman upwelling in the center of the cyclonic gyre, leading to dome-shaped isopycnal structure. Within the center of the cyclonic gyre, stratification is very weak, and this can facilitate deep convection. 
2. Deep convection: Strong buoncy loss due to cooling and evaporation further reduces the stratification in the upper ocean within the central regime of the cyclonic gyre. Further cooling eventually sets in the deep convection, which consits of clusters of small- scale downward plumes (with a horizontal scale of 1 km or less) and eddies (with a horizontal scale of 10 km). Water in the small plumes moves downward with vertical velocity on the order of 0.1 m/s. Plumes and eddies from the mixed patch with a horizontal scale on the order of 100km. 
3. Lateral exchange and spreading: A few days after the onset of cooling, the dominating mode of heat exchange is shifted from vertical to horizontal through eddy activities on the geostrophic scale.
4. Final stage: The chimney-like density structure associated with deep convection is gradually closed up and leaves behind a dome-shaped isopycnal structure, with a layer of cold water which settles at depth. 

Two parameters play a major role in deep convection: 

1. buoyancy (Brunt-Väisälä frequence), which is also a measure of the frequency of internal gravity waves.
   1. the ocean is normally stable stratified, however small areas in the upper ocean can become temporarily unstable 
2. Rossby deformation radius, which is a measure of how far inertial gravity waves can travel over an inertial period
   1. horizontal scales much smaller than the deformation radius, geostrophic and hydrostatic balance break down. 

Old picture: 

• In the North Atlantic deep water is formed in the Norweign Sea and Greenland Seas. 
• the warm Atlantic inflow is depicted by solid arrows, and deep water formed at these locations overflows the Denmark Strait and the Faroe Bank Channel, forming the sources of the deep western boundary current (open arrows) which can be observed along the eastern coast of the North American Continent. 

According to the classical theory, NADW primarily orginate from deep convection in the middle of the Norweign Sea and Greenland Sea. Recent studies suggest that the primary source of the NADW is fro the gradual cooling within the rim current in the Norweign Sea and Greenland Sea. 

There are also other signs for the wrongness of the old theory:

1. No significant vertical volume flux in midbasin. Dominant component of the downwelling limb of the thermohaline circulation probably takes place in regions where convective mixing is found adjacent to steep topography. 
2. A significant vertical volume flux in midbasin at high latitudes would have to be accompanied by a very large horizontal circulation. 
   1. within planetary geostrophic dynmaics, the horizontal mass flux divergence reults only from variations in f:
   2. \(\beta v=f\frac{\partial w}{\partial z}\)
   3. for typical mixing regions f does not vary sufficiently to allow significant downwelling. 

• Regional and temporal distribution of sea surface height variance shows enhanced eddy activity near the West Greenland Current with maximum in winter. 
• The eddy maximum is not associated with the convective patch. 
• EKE (eddy kinetic energy) maximum appear each year during Dec/Jan at the West Greenland shelf and propagates southward into the central Labrador Sea. 
• Studies suggest barotropic instability of the Western Greenland Current as the source of the EKE maximum
• Later studies also highlighted the role of baroclinic instability
• WGC eddies transport warm and salty Irminger Water from the boundary to the central Labrador Sea that result in the deep warming.  As a result, stratification remains strong in the northern Labrador sea. -> no deep convection there. 

No. 

Observations (mooring time series) started during period of strongest convection- warming represents a recovery of similiar conditions found before that period 

Positive NAO index (low/Island; high/Azores) leads to strong cooling and convection in the Labrador over Winter time. 

We had a shift from negative NAO to pistive NAO over the late 60's and early 90's with decrease of the potential temperature of the LSW and largen convection depths. 

The classical theory has been the following: winter deep convection in the Iceland and Greenland Seas produces cold and dense water that sinks to the deep part of the Norweign Basin. As deep water accumulates and fills up to a level higher than the sills connecting the Norweign Basin with the open northern North Atlantic Ocean, deep water overflows the sills and becomes the source of NADW. 

Such a theory has some problems:

1. Existing estimates of deepwater formation rate are much smaller than the estimates of dense water overflows through the Greenland-Scotland Ridge.
2. This scenario implies that the overflow rate may have noticeable seasonal and interannual cycles. 
   1. For example, observations indicate that the production of deep water in the Greenland Sea was greatly reduced in the 1980s. However, there are no clear signs that the overflow rate changes much over such time scales. 

In fact, Atlantic Water in the northward flowing Norwegian Atlantic Current becomes gradually denser due to heat loss, filling up the shallow and intermediate depths along the rim of the basin. This water mass flows over the sills and becomes the source of the NADW. 

Tritium concentration analysis indicates that overflow water should come from a depth shallower than 1000m. As a matter of fact, three sills connecting the Norweign Sea to the North Atlantic Ocean are relatively shallow:

• Faroe-Shetland Channel (850m)
• Denmark Strait (600m)
• Iceland-Faroe Ridge (500m)

Therefore, deep water overflowing these sills should be primarily from the relatively shallow sources along the rim of the basin. Thus, cooling-induced convection along the rim current in the Norweign-Greenland Sea may be the major source of NADW. 

Similarly, deep convection in the Labrador Sea contributes very little to the overall meridional overturning circulation in the North Atlantic Ocean, and the most important pathway of water mass formation in the Labrador Sea is the gradual transition of water properties within the boundary current around the basin. 

Hard facts of the three 

1. Open ocean deep convection occurs in the Greenland Sea gyre, but is largely shielded by topography

2. Intermediate depth waters (convective and Atlantic Water) are laterally exhanged with the East Greenland Current entering the Nordic Seas via Fram Strait

3. Upwelling of deep water contributes to the Faroe Bank Channel overflow, but, as in Denmark Strait, the major part is derived from intermediate water masses.

    

    

    

• Atlantiv inflow: 7.5 Sv
• Dense overflow: 6 Sv
• Overflow passages from left ro right:
  1. Denmark Strait: 600m depth
  2. Faroe-Bank Channel: 850m depth
     1. the deepest and accounts for 1/3 of the total overflow
  3. Iceland-Faroe Ridge: 500m depth
• On large scale the exchange flow is in geostrophic balance  
• Interface between inflow and outflow tilts downwards from west to east. 

• No trends in overflow transport, which agrees well with downstream measurements of the Deep Western Boundary Current.
• Temperature increase of the inflow.
• Temperature decrease at the sill of DSOW and temperature increase at the sill of ISOW.
• Yet unclear if water mass changes due to changes in the source water masses, associated with long-term trends, or interannual variability.  

'Streamtube' model by Smith 1975 or the Reduced Gravity Plume Model 

1. Without rotation: 
   1. Plume is symmetric in cross-stream direction 
   2. Plume develops a head with large layer thickness
2. with rotation and friction:
   1. Under very low friction the flow turns to right and produces an almost geostrophic flow following the depth contours. 
   2. With increasing friction the downslope velocity component becomes more and more important. 

1. Rotating sector experiments

The theory of deep circulation was first developed in the late 1950s and early 1960s. 

Stommel et al. 1958: pie-shaped experimental tool, which rotated uniformly. The circulation was observed with release of dye. 

The parabolic-shaped upper surface of the water in the rotating experiments produces a dynamical effect equivalent to the \(\beta\)-effect. 

For an ocean with uniform depth on the surface of earth, potenital vorticity \(f/h\) is low a t low latitudes; therefore, the rim of the rotating pie corresponds to the low-latitude ocean on the earth. 

From the potential vorticity argument, the system allows three types of motion only:

1. Geostrophic flow along circle of constant radius
2. Radial flow in the interior is possible only if there is a source or sink. 
3. A western boundary current going northward or southward. Similiar to the wind-driven circulation, balancing potential vorticity in the whole model basin rules out the possibility of closing the circulation by an eastern boundary current. 

An increase/sink of water level (source/sink) corresponds to an upwelling leaving the abyssal layer. Thus, a source or sink implies stretching which must be balanced by radial flow as required by the linear vorticity balance! 

The circulation driven by a point source/sink in a basin confined by two meridians is particularly interesting because the western boundary current induced by source-induced interior flow can be very non-intuitive. 

Realisitc Case: Point source at the pole: In the basin interior there is a cyclonic poleward flow, and there is an equatorward western boundary current. 

In general of a point source at the western boundary: There is an interior upwelling driven by the source, so that there is always the same cyclonic flow in the basin interior. However, the transport of the western boundary current may very depending on the exact location of the source.

Therefore, the western boundary current transport is quite non-intuitive, owing to mass balance of the model and the special nature of spherical coordinates.

Based on theoretical reasoning, Stommel (1958) postulated a framework of deep circulation in the world's oceans. Accordingly, deep circulation in the world's oceans is driven by point sources of deep water in the northern North Atlantic Ocean and the Weddell Sea. 

Stommel 1958:

1. Deep circulation in the world's oceans is driven by point sources of deep water in the northern North Atlantic Ocean and Weddell Sea. 
2. With this distribution of the deep water source, there is a southward western boundary current in the Atlantic Basin which transports deep water away from the source. 
3. On it's southward path, it gradually loses its mass to the ocean interior. 
4. At the southern edge of the world's oceans there is a simple circumpolar current around the edge of Atnartica and deep western boundary currents moving northward and deep western boundary currents moving northward in individual basins which transport deep water from the southern source to the interior of the worlds oceans. 
5. In the interior of each basin water moves uniformly upward, as assumed in the model, and this model-assumed uniform upwelling drives poleward flow, as dictated by the linear vorticity balance. 

Stommel (1958) and Stommel and Aron (1960) developed a model for the explanation of Deep Western Boundary Currents.

1. The model is driven by a distriputed upward transfer of fluid through the main thermocline. 
   1. The themrocline is remarkably sharp everywhere in mid to low latitudes. Because turbulence in the thermoclinetransport heat downwards, the thermocline should become much weaker after many years. Because this is not happening, there should be a balance between upward advection of cold water and downward diffusion of heat. 
2. This sink is supplied by interior geostrophic transport
3. The upward water transfer is balanced by a concentrated source representing downward flow of cold fluid generated in a small area at high latitude. 
4. The abyssal circulation is composed of a single layer that is steady and geostrophic everywhere in the ocean interior, except at the western boundary where a narrow, intense boundary current is permitted to depart from geostrophy. 

A good marker for LSW water is its very low potenital vorticity, through nearly homogenous water. 

the three principle spreading routes of LSW:

1. to Irminger Sea: 0.5 years
2. to the North Atlantic interior: 2-3 years
3. along the deep western boundary current: 1 years 

Along the deep western boundary current

problem: DWBC mooring arrays indicate a strong reduction of LSW at the coast of New-foundland. Is the a continous DWBC? 

Othe survey with RAFOS floats drifting at 700 and 1500m depths brings the following result: Most of the floats leave the DWBC due to interactions with meanders of the NAC. 

ausgelassen. sehr kompliziert! 

The bottom layer of the world's ocean is filled with a thick layer of very cold water with potential temperature lower than 2°C. 

The origin of this water are a few sites along the contiental margin of Antarctica, where cold water is formed during Southern Hemisphere winter:

1. very cold wind from glacial ice on Antarctica blows over the coastal ocean adjacent, driving sea ice away from the coasts and thus creating coastal polynyas (small open water areas surrounded by ice). 
2. Strong cooling over polynyas produces more sea ice, and salt rejection during sea ice formation creates cold dense water with high salinity. 
3. this dense water overflow the continental slope. 
4. The offshore transport of the newly formed bottom water is compensated by the onshore flow of water in the subsurface layer. 
5. During the descent along the slope, it entrains the water in the environment; thus, it is slightly warmed up from -2°C to -1°C. Eventually, it sinks to the bottom with a temperature of nearly 0°C. 
6. Due to virgorous entrainment, the total volume flux of the final product is greatly increased. 

Meridional circulation pattern of the Southern Oceanis dominated by the upwelling of a warm, salty water mass called Circumpolar Deep Water and its transformation into Antarctic Surface Water, which ultimately sinks to become Antarctic Intermediate Water and Antarctic Bottom Water. The circulation is driven by wind and the exchange of heat and freshwater between the ocean and the atmosphere.

sensible heat polynyas: thermdynamically driven: occur when warmer water upwells

latent heat polynyas: formed through action of wind, tides, or ocean currents

...are found in many locations around the coastline and ice shelf edge. 

Three polynya regions are most productive of AABW:

1. the southern Weddel Sea (68%)
2. the Ross Sea (8%)
3. Adelie Land (24%)

Sea Ice production is large in latent heat polynayas, so productions maps can help to indentify latent heat polynya spots!

• Warming can be followed along the path of AABW from the Weddel Sea into the Altantic. 
• Warming below 4000m contributes 16% to the total ocean heat uptake. 
• thermal expansion of water below 4000m contributes 9% to sea level rise.