The document discusses limitations of the dissolved oxygen (DO) sag equation model for streams. It lists four main limitations: 1) The model assumes steady state conditions while streams have varying flows, velocities, geometries and temperatures over time. 2) The model assumes plug flow while natural stream geometries are irregular with wide and narrow areas. 3) The model does not include the important role of algae in producing oxygen, which varies with sunlight. 4) The model only considers oxygen demand from suspended organisms, not from bottom-dwelling benthic organisms which account for significant oxygen demand, especially when organic material settles out.

1. PLUME
BEHAVIOUR

20. ESIMATION OF PLUME RISE

24. DISSOLVED OXYGEN MODEL
FOR STREAMS

53. Limitations of the DO Sag Equation
As with all mathematical models, certain simplifications have been made in the derivation of the DO sag
equation. Before reading on, look at the model derivation, think about the situation, and try to make a list of
limitations yourself.
Steady state -- Streams aren't steady state. Flows, velocities, geometries, and temperatures all vary with
time. Dividing the stream into smaller reaches reduces this limitation, but steady state conditions are still
assumed inside each reach. To the extent that the reach is not steady state, inaccuracies will be introduced.
Plug flow -- Streams aren't really plug flow. The geometries of natural streams are not regular -- there are
wide spots, pools, narrow chutes, sand bars, rocks -- so the flow doesn't move as a plug.
Algae -- The model doesn't include algae which are a very important source of oxygen. Note that the effects
of algae are very dependent on sunlight, which changes through the day. Modeling algae accurately would
require a nonsteady-state model.
Benthic organisms -- The model assumes that all the oxygen demand is from suspended organisms (i.e.,
bacteria living in the water column like they were in the BOD bottle). In fact, most natural bacteria live
attached to surfaces in "biofilms" -- slimy coatings on rocks or soil particles. So a significant portion of the BOD
is due to bottom-dwelling (benthic) organisms. The effect of benthic demand is especially strong if much of
the organic material is in the form of particles that settle out. Benthic effects are not included in the model
either.

56. pollutants of greater environmental concern. In addition,
by this way pollutants can more easily reach other sites
or environmental compartments way from the source.
Primarily, this involves leaching processes, i.e., a process
by which pollutants are released from solid phase into
the aqueous phase under the influence of dissolution and
desorption of pollutants from their support-phases. As
mentioned above, this is dependent on several factors,
such as, soil pH, redox conditions, biotic action, and the
amount of water percolating the soil, which will carried
out the pollutants to surface or groundwater
repositories. The aerobic conditions of Distribution,
Transport and Fate of Pollutants 49 surface waters and
the anaerobic conditions of groundwaters may have a
great influence in the dissolved transport, which may
result in the precipitation of pollutants by changes in
redox state. 2.3.2 Processes involved in pollutants
transport 2.3.2.1 Advection, dispersion, and diffusion
The transport of dissolved pollutants can occur due to
three processes: advection, dispersion, and diffusion.
Advection involves transport with flowing direction and
is associated with the mean velocity of the fluid. This
transport may be explained by Darcy’s Law that relates
the hydraulic gradient with the bulk properties of the
materials (porosity). The advection can be considered as