Significance of σt Surfaces
The density of sea water at atmospheric pressure, expressed as σt = (ρs,ϕ,0 − 1) × 103, is often computed and represented in horizontal charts or vertical sections. It is therefore necessary to study the significance of σt surfaces, and in order to do so the following problem will be considered: Can water masses be exchanged between different places in the ocean space without altering the distribution of mass?
The same problem will first be considered for the atmosphere, assuming that this is a perfect, dry gas. In such an atmosphere the potential temperature means the temperature which the air would have if it were brought by an adiabatic process to a standard pressure. The potential temperature, θ, is
Consider two air masses, one of temperature ϕ1 at pressure p1, and one of temperature ϕ2 at pressure p2. If both have the same potential temperature, it follows that
With regard to the ocean, the question to be considered is whether surfaces of similar characteristics can be found there. Let one water mass at the geopotential depth D1 be characterized by salinity S1 and temperature ϕ1, and another water mass at geopotential depth D2 be characterized by salinity S2 and temperature ϕ2. The densities in situ of these small water masses can then be expressed as σs1,ϑ1,D1 and σs2,ϑ2,D2.
Now consider that the mass at the geopotential depth D1 is moved adiabatically to the geopotential depth D2. During this process the temperature of the water mass will change adiabatically from ϕ1 to θ1 and the density in situ will be σs1,θ1,D2. Moving the other water mass adiabatically from D2 to D1 will change its temperature from ϕ2 to θ2. If the two water masses are interchanged, the conditions
The adiabatic change in temperature between the geopotential depths of 200 and 700 dyn meters is 0.09°, and thus θ1 = 13.82, θ2 = 8.01. By means of the Hydrographic Tables of Bjerknes and collaborators, one finds
It should also be observed that the mixing of two water masses that are at the same depth and are of the same density in situ, but of different temperatures and salinities, produces water of a higher density. If, at D = 700 dyn meters, equal parts of water S1 = 36.01 ‰, ϕ1 = 13.82°,
This discussion leads to the conclusion that in the ocean no surfaces exist along which interchange or mixing of water masses can take place without altering the distribution of mass and thus altering the potential energy and the entropy of the system (except in the trivial case that isohaline and isothermal surfaces coincide with level surfaces). There must exist, however, a set of surfaces of such character that the change of potential energy and entropy is at a minimum if interchange and mixing takes place along these surfaces. It is impossible to determine the shape of these surfaces, but the σt surfaces approximately satisfy the conditions. In the preceding example, which represents very extreme conditions, the two water masses were lying nearly on the same σt surface (σt1, = 27.05, σt2 = 26.97).
Thus, in the ocean, the σt surfaces can be considered as being nearly equivalent to the isentropic surfaces in a dry atmosphere, and the σt surfaces may therefore be called quasi-isentropic surfaces. The name implies only that interchange or mixing of water masses along σt surfaces brings about small changes of the potential energy and of the entropy of the body of water.