In Art. 4.04 the discussion was restricted to constituents whose concentration is altered by advection and diffusion only, except perhaps at the boundaries of the fluid. The resulting equations are applicable to salinity or any of the major constituents such as chloride, sodium, sulfate, magnesium, etc. In fact, the equations of Art. 4.04 are applicable to any inert or conservative constituents. Dissolved nitrogen gas in another example.
Constituents such as phosphate, nitrate, and other nutrients, and
dissolved oxygen, carbon dioxide, etc. are non-conservative from the
physical standpoint, since the concentrations of these quantities
are altered locally by chemical action associated with the life
processes within the sea. Strictly speaking, these processes-
consumption, photosynthesis, respiration, and reduction by the
plant, animal and bacteria populations of the sea-represent
localized boundary processes. However, the boundaries are neither
fixed, permanent, nor predictable, except in a statistical sense.
The marine life, particularly the planktonic forms and
micro-organisms which comprise the bulk of the productive mass
of the sea, must be considered just as much a part of the fluid
which we will call sea water as the salinity, phosphate, etc. In
other words, the living phytoplankton, zooplankton, micro-organisms
and the detrital matter are further examples of non-conservative
constituents.
The total concentration of any of these non-conservative constituents
in a given mass of fluid which moves with the fluid velocity can be
altered by one or more of the abovementioned processes in addition
to diffusion.
If we let 
represent the concentration of any one of the
non-conservative constituents, then for a moving volume of
constant mass
where it is assumed that the function
can be defined such that its
volume integral for any arbitrary volume represents the most
probable net rate of production of the constituent N per
unit time by the statistical ensemble of discrete sources
contained within the volume at the instant t. The quantity
represents the diffusive flux of N, and
the outward unit normal to the boundary as before.
The value of 
can of course be either positive or negative
depending upon the constituent and the process; 
is production, 
is consumption.
By making use of Eq. (I-3) and the divergence theorem, and considering that the volume is arbitrary in size, it can be shown that Eq. (24) reduces to
If we introduce the diffusion velocity of N defined by
and add Eq. (I-1) multiplied by N to Eq. (IIA-1) we get the analouge to Eq. (II-4)
In the case of the non-living constituents such as phosphate,
it is observed that the 
is controlled principally
by the gradient of the concentration, the diffusion current being
directed towards the regions of low concentration. The value of
is positive below the euphotic zone of the sea where
bacterial action on detrital matter produces this nutrient; in the
surface layers it is generally negative and the magnitude must be
dependent upon the concentration of plant life, radiation, temperature,
etc. A detailed discussion of the production and consumption for
the various non-conservative constituents is well beyond the scope
of these notes. It may be remarked, however, that through relations
of the type (IIA-2) much can be learned with regard to the nature
of as a supplement to the more direct measurements.
The important thing to note is that a measure of N alone,
representing the so-called standing crop of the constituent,
is inadequate by itself in respect to ascertaining the rate of
production or consumptionof N. In a region where the
constituent N is virtually uniform then the advective and
diffusive terms contribute very little to the change of N with
time, and hence a direct measure of the local rate of change of
the concentration N represents a good approximation of .
Under conditions of an equilibrium where the standing
concentration is steady then must must balance the
dispersion of N by advective and diffusive processes. The magnitude
of N in this case, like the size of ones bank account, does
not serve as a direct reflection of the rate of turnover.
In passing, it is of interest to inquire into the meaning of
Eq. (IIA-2) if applied to marine life which does have means
of locomotion. The equation may concievably apply if we
regard as a statistical mean applying to the
relative migrations of the creatures in question. The factor
controlling the in this case is quite different
from that in the case of the inanimate constituents, and seems
to be in fact just the opposite-the tendency being for grouping together
rather than for dispersion. However, the migratory motion of the
groups as a whole is dependent upon the physiological adaptation
to the environment as well as upon the apparently psychological
controls. The diurnal, vertical migrations of the so-called
scattering layer, which is evidently a grouping of marine
life capable of locomotion, is a case in point.