Definition of overflow

The mixed bottom layer of the FBC is where the actual overflow takes place, being fed by inflow of cold and fresh North Atlantic Water, Modified North Atlantic Water, Norwegian Sea Deep Water and Norwegian Sea Arctic Intermediate Water.^[9] These water masses have different temperatures (between -0.5 and 7.0 °C) and salinities (between 34.7 and 35.4 g/kg).^[9] Therefore, it may be complicated to exactly define which water entering the FBC contributes to the actual overflow. Four definitions are possible, two of which depending on the overflow velocity, one depending on the overflow flux, and one depending on the overflow water properties.

The simplest definition is in terms of velocities: water with a velocity in northwestern direction is then termed Faroe-Bank Channel overflow.^[1] At the sill, velocities can grow up until 1.2 m/s, accelerating when flowing downwards the deepening bathymetry.^[9] In this respect, high velocities are associated with strong mixing and highly turbulent flows. In the stratified layer at the top of the channel, velocities become negative (i.e., in southeastern direction), which makes these water no part of the overflow.

Another option is to take into account the barotropic (i.e., horizontal sea-surface height gradients determine currents) and baroclinic (i.e., horizontal density gradients determine currents) pressure gradients at the overflow depth between both sides of the GSR:

$${\displaystyle \Delta P_{trop}=g\Delta h}$$

$${\displaystyle \Delta P_{clin}=g\Delta H{\frac {\Delta \rho }{\rho }}}$$

where ${\textstyle \Delta h}$ is the decrease in sea-surface height and ${\textstyle \Delta H}$ is the decrease in interface height from upstream areas to the sill.^[10] Processes like mixing, circulation and convection contribute to these pressure gradients. The overflow velocity, then, scales as follows with the pressure gradient between the basins north and south of the ridge:

$${\displaystyle v={\sqrt {2\left(\Delta P_{trop}+\Delta P_{clin}\right)}}}$$

This velocity can then be used to define the total overflow flux in the FBC.^[11] A third definition is so-called kinematic overflow: the water flux from the bottom of the channel up to the interface height, being the level where the velocity in northwestern direction measures one half of the maximum velocity in the profile.^[10] The overflow flux is then calculated through

$${\displaystyle Q_{k}(t)=\int _{x_{1}}^{x_{2}}v_{0}(x,t)\left(h_{0}(x,t)-h_{B}\right)\operatorname {d} \!x+\int _{x_{1}}^{x_{2}}q_{B}\left(x,t\right)\operatorname {d} \!x}$$

where ${\displaystyle v_{0}}$ is the average profile velocity, ${\displaystyle h_{0}}$ is the interface height, ${\displaystyle h_{B}}$ is the height of the layer below the lowest measurement station in the channel, and ${\displaystyle q_{B}}$ is the volume flux per unit width of the channel.^[10]

Lastly, overflow can also be defined on the basis of hydrographical properties: namely as water that flows through the FBC having a temperature lower than 3 °C,^[10] or having a potential density higher than 27.8 kg/m³.^[12] This definition is most often used when estimating values for the magnitude of the FBCO.

Periodicity

Temperature and salinity profiles as well as current speeds in the FBC vary strongly on a day-to-day basis. The dense water forms domes that move through the channel with a period of 2.5 to 6 days.^[2] At the ocean surface, this periodicity can be observed in the form of topographic Rossby waves at the sea surface, which are caused by mesoscale oscillations in the velocity field.^[13] The resulting eddies are the consequence of baroclinic instabilities within the overflow water, which then induce the observed periodicity.^[14]

On a greater timescale, atmospheric forcing also causes periodic changes in the FBCO. When the atmospheric circulation governing the Nordic Seas is in a cyclonic (anticyclonic) regime, the source of the deep water predominantly comes via a western (eastern) inflow path, and the FBCO will be weaker (stronger).^[5] The eastern inflow path is called the Faroe-Strait Channel Jet. This transition from a cyclonic to an anticyclonic regime takes place on an interannual timescale, but the atmospheric forcing also shows a seasonal cycle. During summer the weakened cyclonic winds are associated with a higher FBCO transport. This indicates a fast barotropic response to the wind forcing.^[5]

Measurements

From 1995 onwards, FBCO has been monitored by a continuous Acoustic Doppler current profiler (ADCP) mooring, measuring volume transport, hydrographic properties and the density of the overflow.^[17] The kinematic overflow, derived from the velocity field, showed a non-significant positive linear trend of 0.01±0.013 Sv/yr between 1995 and 2015, whereas the coldest part of the FBCO warmed in that same period with 0.1±0.06 °C (which made density decrease), causing increasing transport of heat into the AMOC.^[18] This warming, however, is accompanied by an observed salinity (and therefore density) increase, which results in no net change in density.^[18]

Model simulations

Climate models have shown an overall decreasing trend in the baroclinic component of the overflow between 1948 and 2005; the barotropic pressure gradient, however, shows an increasing trend of equal magnitude. These processes compensate each other; as a result the pressure difference at depth does not show a significant trend over time.^[11]

Global inverse modelling, ocean hydrographic surveys, chlorofuorocarbon (CFC) inventories, and monitoring of the AMOC from 2004 to present have shown that the AMOC has slowed down in the past decades.^[6] As explained, density of FBCO waters did not significantly change in that time period, so changes in FBCO cannot (fully) explain the changes in the AMOC.^[19]