Preferred Citation: . The Oceans, Their Physics, Chemistry, and General Biology. New York:  Prentice-Hall,  c1942 1942.

Theory of Distribution of Variables in the Sea

The Principle of Dynamic Equilibrium

Experience shows that in a large body of water comparable, say, to the body of water in the Mediterranean Sea, the average conditions do not change from one year to another. The average distribution of temperature remains unaltered year after year, and the same is true as to the average salinity, oxygen content, and contents of minor constituents. If time intervals longer than a year are considered, say ten-year periods, it is probable that even the average number of different species of organisms remains unaltered, provided that the nonaquatic animal, man, does not upset conditions by exterminating certain species and depleting the stock of others. These unchanging conditions represent a state of delicate dynamic equilibrium between factors that always tend to alter the picture in different directions.

In dealing with conservative concentrations, diffusion and advection are at balance except at the sea surface, where external processes contribute toward maintaining the concentration at a certain level. This was illustrated when discussing the general distribution of surface salinity (p. 125), which was shown to depend on two terms, one that represents the external processes of evaporation and precipitation, and one that represents the internal processes of diffusion and advection. Similarly, the surface temperature depends upon heating and cooling by processes of radiation and by exchange with the atmosphere and upon conduction and advection of heat.


In a study of the subsurface distribution of temperature and salinity, it is not necessary to know the processes that maintain the surface values, but it is sufficient to determine these values empirically. If this could be done and if the processes of diffusion and the currents were known, the general distribution of temperature and salinity could be computed. Conversely, if these distributions were known, information as to diffusion and currents could be obtained. In oceanography only the latter method of approach has been employed.

When nonconservative concentrations are dealt with, the principle of a dynamic equilibrium implies that the effects of diffusion, advection, and biological processes cancel. Of the nonconservative concentrations, only the dissolved gases are greatly influenced by the contact with the atmosphere, and other nonconservative concentrations are practically unaltered by external processes.

Application of the principle of dynamic equilibrium can be illustrated by considering the distribution of oxygen. Below the euphotic zone, biological processes that influence the oxygen content always lead to a consumption of oxygen, and the processes of diffusion and advection therefore must lead to a replenishment that exactly balances the consumption. No further conclusions can be drawn. This obvious consideration has been overlooked, however, and some authors have interpreted a layer of minimum oxygen content as a layer of minimum replenishment (Wüst, 1935), while others have considered it a layer of maximum consumption (Wattenberg, 1938).

Conclusions as to the rapidity of consumption (and replenishment) could be drawn from the known distribution of oxygen only if the consumption depended upon the absolute content of oxygen, but the consumption appears to be independent of the oxygen content until this has been reduced to nearly nil (ZoBell, 1940). When all oxygen has been removed, consumption and replenishment must both be zero, and even this obvious conclusion should not be overlooked.

In certain instances a relation may exist between the oxygen distribution and the character of the current. Assume that a nearly horizontal internal boundary exists which separates currents flowing in opposite directions, that diffusion takes place in a vertical direction only, and that the coefficient of diffusion is independent of z. When dynamic equilibrium exists, equation (V, 9) is then reduced to

Since the consumption equals — R and is always positive, the curvature of s is positive when plotted against z. The curvature cannot remain positive at all depths, and therefore it is probable that s, the oxygen content, must be at a minimum near the boundary surface. Thus, a
minimum in the vertical distribution of oxygen may indicate the presence of a boundary surface at which there are no currents, but such a minimum can also develop under entirely different conditions (Seiwell, 1937).

Similar reasoning is valid when dealing with compounds that are removed from the water by organisms for building up their tissues and are returned to solution as metabolic products or by decomposition of organic tissues. A balance is maintained, but in many cases it is not correct to speak of “replenishment” by advection and diffusion, as in the case of oxygen, because the biological processes may lead to a net replenishment, in which case the physical processes must take care of a corresponding removal. Thus, in the deeper layers phosphates and nitrates are added to the water by decomposition of organic matter and removed by diffusion and advection.

When dealing with populations, similar considerations enter. It must be emphasized especially that the number of organisms present in unit volume of water gives no information as to the processes that operate toward changing the number. A small population of diatoms, say, may divide very rapidly without increasing in number, owing to the presence of grazers that consume diatoms. On the other hand, a large population of diatoms may not indicate a rapid production of organic matter, because further growth may be impossible owing to lack of nutrient salts in the water. The terms “population” and “production” have to be clearly defined and kept separate. (“Population” represents concentration, whereas “production” represents one of the processes that alter the concentration.

Another warning appears to be appropriate—namely, a warning against confusion between individual and local changes (p. 157). From the fact that a local population remains unaltered, it cannot be concluded that the population within the water which passes the locality of observation also remains constant—that is, that the individual time change is zero. Similarly, if a sudden change in population is observed in a given locality, it cannot be concluded that the processes which have been active in that locality have led to a rapid growth, because it is equally possible that a new water mass of other characteristics is passing the locality.

If the external influences were clear, if processes of diffusion and advection were known, and if biological and organic chemical processes were fully understood, the distribution of all concentrations could be accounted for. It would then be possible not only to explain the average distribution but also to account for all periodic and apparently random changes. This is the distant goal, but when working toward it one must be fully aware of the limitations of the different methods of approach.

Thus, complete description of the oxygen distribution below the euphotic zone is theoretically possible if the oxygen content in the surface

layers, the processes of diffusion, the currents, and the oxygen-consuming processes of decomposition were known. On the other hand, information as to oxygen consumption can be obtained not only by an examination of the processes of decomposition but also by a computation of the replenishment of oxygen by diffusion and advection. So far, all of our knowledge as to oxygen consumption below the euphotic zone is based on such computations and not on any consideration of biochemical processes.

The dynamic equilibrium, the importance of which has been stressed, exists only insofar as average conditions within a large body of water and over a considerable length of time are concerned. During any part of the day or year the external or internal processes may be subject to periodic or random variation such that at a given moment no equilibrium exists (∂ s/∂ t ≢ 0). At the surface, heating periodically exceeds cooling, and cooling periodically exceeds heating, as a result of which the surface temperature is subjected to diurnal and annual variations that by processes of conduction are transmitted to greater depths. It is possible that longer periods exist which are related to periodic changes in the energy received from the sun, but these long-period variations are of small amplitudes. In many areas, shifts of currents lead to local changes of the temperature which are periodic in character if the shifts are associated with the seasons, or nonperiodic if they are related to apparently random events. In the discussion of the annual variation of temperature (p. 131) the effect of these different processes was illustrated. Similar reasoning is applicable to periodic and random variations of salinity and also to variations of nonconservative properties.

From what has been stated it is evident that in the discussion of the distribution of concentrations in the sea it is as yet impossible to apply a method of deduction based on knowledge of all processes involved in maintaining the distribution. Instead, one has to follow a winding course, discuss processes and their effects whenever possible, discuss actual distributions if such have been determined, and either interpret these distributions by means of knowledge gained from other sources as to acting processes or draw conclusions as to these processes from the distribution. In some instances the processes that maintain the boundary values can be dealt with at considerable length, but otherwise the observed boundary values have to be accepted without attempts at explanation. In all cases, however, it is essential to bear in mind that one is dealing with concentrations in a continuous medium and that general considerations as set forth here are always applicable.

Theory of Distribution of Variables in the Sea

Preferred Citation: . The Oceans, Their Physics, Chemistry, and General Biology. New York:  Prentice-Hall,  c1942 1942.