Ocean stratification

The density of water in the ocean, which is defined as mass per unit of volume, has a complicated dependence on temperature (${\displaystyle T}$), salinity (${\displaystyle S}$) and pressure (${\displaystyle p}$), which in turn is a function of the density and depth of the overlying water, and is denoted as ${\displaystyle \rho (S,T,p)}$. The dependence on pressure is not significant, since seawater is almost perfectly incompressible.[3] A change in the temperature of the water impacts on the distance between water parcels directly. When the temperature of the water increases, the distance between water parcels will increase and hence the density will decrease. Salinity is a measure of the mass of dissolved solids, which consist mainly of salt. Increasing the salinity will increase the density. Just like the pycnocline defines the layer with a fast change in density, similar layers can be defined for a fast change in temperature and salinity: the thermocline and the halocline. Since the density depends on both the temperature and the salinity, the pycno-, thermo-, and haloclines have similar shapes. The difference is that the density increases with depth, whereas the salinity and temperature decrease with depth.

The halo-, thermo-, and pycnocline at 10E, 30S. For this image the annual means of the year 2000 from the GODAS Data[4] has been used.

In the ocean, a specific range of temperature and salinity occurs. Using the GODAS Data,[4] a temperature-salinity plot can show the possibilities and occurrences of the different combinations of salinity and potential temperature.

Potential temperature - salinity plot. This plot was generated using the GODAS Data[4] of 2020.

Occurrences of combinations of potential temperature and salinity in the ocean. This plot was generated using the GODAS Data[4] of 2020.

The density of ocean water is described by the UNESCO formula as:[5]

$${\displaystyle \rho ={\frac {\rho (S,T,0)}{1-{\frac {p}{K(S,T,p)}}}}.}$$

The terms in this formula, density when the pressure is zero, ${\displaystyle \rho (S,T,0)}$, and a term involving the compressibility of water, ${\displaystyle K(S,T,p)}$, are both heavily dependent on the temperature and less dependent on the salinity:

$${\displaystyle {\begin{aligned}\rho (S,T,0)=\rho _{SMOW}+B_{1}S+C_{1}S^{1.5}+d_{0}S^{2},&\qquad K(S,T,p)=K(S,T,0)+A_{1}p+B_{2}p^{2},\end{aligned}}}$$

The surface temperature, surface salinity and surface potential density calculated and plotted using the annual mean over the year 2000 of the GODAS Data.[4]

with:

$${\displaystyle {\begin{aligned}{}&\rho _{SMOW}=a_{0}+a_{1}T+a_{2}T^{2}+a_{3}T^{3}+a_{4}T^{4}+a_{5}T^{5},\\{}&B_{1}=b_{0}+b_{1}T+b_{2}T^{2}+b_{3}T^{3}+b_{4}T^{4},\\{}&C_{1}=c_{0}+c_{1}T+c_{2}T^{2},\\\end{aligned}}}$$

and

$${\displaystyle {\begin{aligned}{}&K(S,T,0)=K_{w}+F_{1}S+G_{1}S^{1.5},\\{}&K_{w}=e_{0}+e_{1}T+e_{2}T^{2}+e_{3}T^{3}+e^{4}T^{4},\\{}&F_{1}=f_{0}+f_{1}T+f_{1}T+f_{2}T^{2}+f_{3}T^{3},\\{}&G_{1}=g_{0}+g_{1}T+g_{2}T^{2},\\{}&A_{1}=A_{w}+(i_{0}+i_{1}T+i_{2}T^{2})S+j_{0}S^{1.5},\\{}&A_{w}=h_{0}+h_{1}T+h_{2}T^{2}+h_{3}T^{3},\\{}&B_{2}=B_{w}+(m_{0}+m_{1}T+m_{2}T^{2})S),\\{}&B_{w}=k_{0}+k_{1}T+k_{2}T^{2}.\end{aligned}}}$$

In these formulas, all of the small letters, ${\displaystyle a_{i},b_{i},c_{i},d_{0},e_{i},f_{i},g_{i},i_{i},j_{0},h_{i},m_{i}}$ and ${\textstyle k_{i}}$ are constants that are defined in Appendix A of a book on Internal Gravity Waves, published in 2015.[5]

The density depends more on the temperature than on the salinity, as can be deduced from the exact formula and can be shown in plots using the GODAS Data.[4] In the plots regarding surface temperature, salinity and density, it can be seen that locations with the coldest water, at the poles, are also the locations with the highest densities. The regions with the highest salinity, on the other hand, are not the regions with the highest density, meaning that temperature contributes mostly to the density in the oceans. A specific example is the Arabian Sea.

Ocean stratification can be defined and quantified by the change in density with depth. The Buoyancy frequency, also called the Brunt-Väisälä frequency, can be used as direct representation of stratification in combination with observations on temperature and salinity.

The Buoyancy frequency, ${\displaystyle N}$, represents the intrinsic frequency of internal gravity waves.[1] This means that water that is vertically displaced tends to bounce up and down with that frequency.

The Buoyancy frequency is defined as follows:

$${\displaystyle N^{2}={\frac {-g}{\rho _{0}}}{\frac {\partial \rho }{\partial z}}.}$$

Here, ${\displaystyle g}$ is the gravitational constant, ${\displaystyle \rho _{0}}$ is a reference density and ${\displaystyle \rho }$ is the potential density depending on temperature and salinity as discussed earlier. Water is considered to have a stable stratification for ${\displaystyle \partial \rho /\partial z<0}$, leading to a real value of ${\displaystyle N}$. The ocean is typically stable and the corresponding ${\displaystyle N}$-values in the ocean lie between approximately ${\displaystyle 10^{-4}}$ in the abyssal ocean and ${\displaystyle 10^{-3}}$ in the upper parts of the ocean. The Buoyancy period is defined as ${\displaystyle 1/N}$. Corresponding to the previous values, this period typically takes values between approximately 10 and 100 minutes.[6] In some parts of the ocean unstable stratification appears, leading to convection.

If the stratification in a water column increases, implying an increase of the value ${\displaystyle N^{2}}$, turbulent mixing and hence the eddy viscosity will decrease.[7] Furthermore, an increase of ${\displaystyle N^{2}}$, implies an increase of ${\displaystyle |\partial \rho /\partial z|}$, meaning that the difference in densities in this water column increase as well. Throughout the year, the oceanic stratification is not constant, since the stratification depends on density, and therefore on temperature and salinity. The interannual fluctuations in tropical Pacific Ocean stratification are dominated by El Niño, which can be linked with the strong variations in the thermocline depth in the eastern equatorial Pacific.[1]

Furthermore, tropical storms are sensitive to the conditions on the stratification and hence on its change.[8] On the other hand, mixing from tropical storms also tends to reduce stratification differences among layers.

Temperature and salinity changes due to global warming and climate change alter the ocean density and lead to changes in vertical stratification.[2] The stratified configuration of the ocean can act as a barrier to water mixing, which impacts the efficiency of vertical exchanges of heat, carbon, oxygen, and other constituents. Thus, stratification is a central element of Earth's climate system. Global upper-ocean stratification continued its increasing trend in 2022 and was among the top seven on record.[2]

In the last few decades, the stratification in all of the ocean basins has increased. Furthermore, the southern oceans (south of 30°S) experienced the strongest rate of stratification since 1960, followed by the Pacific Ocean, the Atlantic Ocean, and the Indian Ocean.[1] When the upper ocean becomes more stratified, the mixed layer of surface water with homogeneous temperature may get shallower, but projected changes to mixed-layer depth by the end of the 21st century remain contested.[9] The regions with the currently deepest mixed layers are associated with the greatest mixed layer shoaling, particularly the North Atlantic and Southern Ocean basin.[9]

By looking at the GODAS Data[4] provided by the NOAA/OAR/ESRL PSL, the Buoyancy frequencies can be found from January 1980 up to and including March 2021. Since a change in stratification is mostly visible in the upper 500 meters of the ocean, very specific data is necessary in order to see this in a plot. The resulting plots from the GODAS Data might indicate that there is also a decrease in stratification looking at the differences of the stratification between the years 1980, 2000 and 2020. It is possible to see that the change in stratification is indeed the biggest in the first 500 meters of the ocean. From approximately 1000 meters into the ocean, the stratification converges toward a stable value and the change in stratification becomes almost non-existent.

Annual and latitudinal means of ${\displaystyle N^{2}}$ for different ocean basins. This plot was generated using the GODAS Data[4] of 1980, 2000 and 2020.

Change in annual and latitudinal means of ${\displaystyle N^{2}}$ for different ocean basins. This plot was generated using the GODAS Data[4] of 1980, 2000 and 2020.

In many scientific articles, magazines and blogs, it is claimed that the stratification has increased in all of the ocean basins (e.g in Ecomagazine.com[10] and NCAR & UCAR News [11]). In the figure below, the trends of the change in stratification in all of the ocean basins have been plotted.[1] This data shows that over the years the stratification has drastically increased. The changes in stratification are greatest in the Southern Ocean, followed by the Pacific Ocean. In the Pacific Ocean, the increase of stratification in the eastern equatorial has found to be greater than in the western equatorial.[1] This is likely to be linked to the weakening of the trade winds and reduced upwelling in the eastern Pacific, which can be explained by the weakening of the Walker circulation.[1]

This figure shows the global change in stratification ${\displaystyle N^{2}}$ since the year 1960 until 2018 from 0 to 2000 meters.[1] (a) Global, (b) Pacific Ocean, (c) Atlantic Ocean, (d) Indian Ocean and (e) Southern oceans. The thin grey lines indicate the interannual variations. The small plot in (a) shows the rates of ${\displaystyle N^{2}}$ for the global case and for the basins. This is calculated by centered differences of the smooth time series (Glb: Global, Pac: Pacific, Atl: Atlantic, So: Southern, Ind: Indian). The trends have been plotted for various datasets, indicated by the different lines.

The surface mixed layer is the uppermost layer in the ocean and is well mixed by mechanical (wind) and thermal (convection) effects. Turbulence in this layer occurs through surface processes, for example wind stirring, surface heat fluxes and evaporation, The mixed layer is inherently the layer most connected to the atmosphere and affects and is affected by all weather systems, especially those with strong winds such as hurricanes.[16]  Heat stored in the mixed layer in the tropical western Pacific plays a vital role in El Nino development.

The depth of the mixed layer is associated with physical, chemical and biological systems and is one of the most important quantities in the upper ocean.[16] Throughout the year, the depth of the mixed layer varies. The thickness of the layer increases in wintertime and decreases in the summer. If the mixed layer is really deep, less light can reach the phytoplankton. Phytoplankton have been shown to be important in the global carbon cycle.[17] Furthermore, since phytoplankton are at the bottom of the food chain, a decrease in phytoplankton can have consequences on a very large scale.

An exact relation between an increase in stratification and a change in the mixed layer depth has not yet been determined and remains uncertain. Although some studies suggest that a thinner mixed layer should accompany a more stratified upper ocean,[18][19][20] other work reports seasonal deepening of the mixed layer since 1970.[21] There is literature substantiating the statement that in the years from 1970 to 2018, the stratification in the basis of the mixed layer as well as the depth of the mixed layer have increased. Contradicting this result, other literature states a decrease of the depth of the mixed layer partly as a result of the increase of upper-ocean stratification.[22] It has been found that the mixed layer in the extension of the Kuroshio Current, at the west side of the North Pacific, has decreased more than 30 meters. This shoaling is caused by weakening of wind and a reduction of seasonal vertical mixing. Furthermore, there exists research stating that heating of the surface of the ocean, and hence an increase in stratification, does not necessarily mean an increase nor decrease in the mixed layer depth.[23] Using the GODAS Data[4] it can be seen that the depth of the mixed layer has increased as well as decreased over time.

Between 1970 and 2018, the summertime mixed-layer depth (MLD) deepened by 2.9 ± 0.5% per decade (or 5 to 10 m per decade, depending on the region), and the Southern Ocean experienced the greatest deepening.[21][23] However, there is limited observational evidence that the mixed layer is globally deepening, and only under strong greenhouse gas emissions scenarios do global mixed-layer depths shoal in the 21st century.[9] Although it is virtually certain that upper ocean stratification will increase through the 21st century, scientists express low confidence in how the mixed-layer depth will evolve.[9]

Annual means and change in annual means of the mixed layer depth of 1980, 2000 and 2020. This plot was generated using the GODAS Data.[4]

Identification of regions with increase and decrease of annual means of the mixed layer depth of 1980, 2000 and 2020. This plot was generated using the GODAS Data.[4]

• Lake stratification – Separation of water in a lake into distinct layers
• Ocean heat content