McKay, Donald. "Front matter" Multimedia Environmental Models ...

particles (aerosols), or biota in water]. In some cases, the phases may be similar
chemically but different physically, e.g., the troposphere or lower atmosphere, and
the stratosphere or upper atmosphere. It may be convenient to lump all biota together
as one phase or consider them as two or more classes each with a separate phase.
Some compartments are in contact, thus a chemical may migrate between them (e.g.,
air and water), while others are not in contact, thus direct transfer is impossible (e.g.,
air and bottom sediment). Some phases are accessible in a short time to migrating
chemicals (e.g., surface waters), but others are only accessible slowly (e.g., deep
lake or ocean waters), or effectively not at all (e.g., deep soil or rock).
Some confusion is possible when expressing concentrations for mixed phases
such as water containing suspended solids (SS). An analysis may give a total or bulk
concentration expressed as amount of chemical per m3
of mixed water and particles.
Alternatively, the water may be filtered to give the concentration or amount of
chemical that is dissolved in water per m3
of water. The difference between these
is the amount of chemical in the SS phase per m3
of water. This is different from
the concentration in the SS phase expressed as amount of chemical per m
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of particle.
Concentrations in soils, sediments, and biota can be expressed on a dry or wet weight
basis. Occasionally, concentrations in biota are expressed on a lipid or fat content
basis. Concentrations must be expressed unambiguously.
2.3.1 Homogeneity and Heterogeneity
A key modeling concept is that of phase homogeneity and heterogeneity. Well
mixed phases such as shallow pond waters tend to be homogeneous, and gradients
in chemical concentration or temperature are negligible. Poorly mixed phases such
as soils and bottom sediments are usually heterogeneous, and concentrations vary
with depth. Situations in which chemical concentrations are heterogeneous are
difficult to describe mathematically, thus there is a compelling incentive to assume
homogeneity wherever possible. A sediment in which a chemical is present at a
concentration of 1 g/m3
at the surface, dropping linearly to zero at a depth of 10 cm,
can be described approximately as a well mixed phase with a concentration of 1 g/m3
and 5 cm deep, or 0.5 g/m
3
and 10 cm deep. In all three cases, the amount of chemical
present is the same, namely 0.05 g per square metre of sediment horizontal area.
Even if a phase is not homogeneous, it may be nearly homogeneous in one or
two of the three dimensions. For example, lakes may be well mixed horizontally
but not vertically, thus it is possible to describe concentrations as varying only in
one dimension (the vertical). A wide, shallow river may be well mixed vertically
but not horizontally in the cross-flow or down-flow directions.
2.3.2 Steady- and Unsteady-State Conditions
If conditions change relatively slowly with time, there is an incentive to assume
“steady-state” behavior, i.e., that properties are independent of time. A severe mathematical
penalty is incurred when time dependence has to be characterized, and
“unsteady-state,” dynamic, or time-varying conditions apply. We discuss this issue
in more detail later.