A Simplified Physical Model for Studying
Assimilative Capacity
W. E. GATES, Assistant Professor
F. G. POHLAND, Associate Professor
School of Civil Engineering
Georgia Institute of Technology
Atlanta, Georgia
K. H. MANCY, Assistant Professor
F. R. SHAFIE, Research Fellow
School of Public Health
The University of Michigan
Ann Arbor,  Michigan
INTRODUCTION
Considerable effort has been expended in an attempt to define and evaluate
the assimilative capacity of natural waters. Most of these endeavors have utilized dissolved oxygen depletion and/or replenishment as the indicating parameter.
Consequently, when dealing with streams, it is generally accepted that the assimilative capacity refers to the oxygen which is available to the biosphere, from or
through the hydrosphere, within selected constraints.
Because the dissolved oxygen content of the hydrosphere is a renewable resource, assimilative capacity is primarily controlled by the rates, the relative
rates, and the changes in the rates which dictate the oxygen transfer from the atmosphere to the hydrosphere (surface reoxygenation) and from the hydrosphere to
the biosphere (deoxygenation). The net effect of the interplay of these factors is
usually considered to produce the classical concept of the oxygen sag curve (Figure
1). The sag curve, thus, reflects the impact which the deoxygenation processes
have on the dissolved oxygen concentration of the hydrosphere when the buffering
capability of reoxygenation is considered. If the rates of deoxygenation exceed
those of reoxygenation the curve demonstrates a negative slope, and if the magnitude of the rates is reversed, a positive slope prevails. The minimum point,
which is an inherent characteristic of such curves, represents the dissolved oxygen
concentration which must be compared with the selected constraints.
When the dissolved oxygen concentration of a slug of water in a stream is
measured at different times as the slug travels downstream, the resulting values
represent the actual balance which is being effected between the deoxygenation
and reoxygenation processes. However, as with any engineering problem, the emphasis is not on measuring the event, but on being able to predict it accurately. If
the sag curve can be adequately predicted, then the required degree of waste water treatment becomes known and it is then also possible to make Doth an optimum
use and equitable allocation of the oxygen resources of a stream.
In order to be able to predict exact values of the oxygen sag curve requires
that one also be able to predict the rates of reoxygenation and deoxygenation. The
latter implies that the parameters which control these rates are both identifiable
and determinable. As previously mentioned, in situ measurements are excellent
for describing the balance which is produced, however, they provide very little
information as to the exact nature of the two component processes. That is, such
determinations relate only indirectly to the separate processes and, also, they represent the results of studying a unique set of environmental conditions. It would be
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