Page 196 - Soil and water contamination, 2nd edition

Systems and models 183

lake (one store ) with a drain that discharges excess water as function of the lake volume: the
water discharge (flux) is proportional to the water volume in the lake:

Q k V (10.1)
out
3
-1
-1
where Q = discharge from the lake [L T ], k = rate constant [T ], and V = water
out
3
volume in the lake [L ]. Note that in this feedback mechanism, the rate of change of the
store , determined by Q , is controlled by the state of the store itself (V). Given a constant
out
inflow into the lake, the reservoir system evolves to a condition of steady state or dynamic
equilibrium , which means that the inputs and outputs are in balance, so that the state of the
system (water level) does not change. If an additional amount of water is instantaneously
added to the reservoir, the system tends to return to a state with a constant inflow and
outflow. By definition, the response time of the system is defined as 1/k, which corresponds
to the time needed to reduce the difference between the actual value and the steady state
value by 63 percent.
In contrast, a positive feedback mechanism exacerbates some initial change from the

steady state , leading to a ‘blow-up’ condition. For example, if in the same reservoir a crack
or hole occurs in the dam, the eroding power of the outflowing water enlarges the gap, so
the water discharge through the hole increases rapidly. It is only a matter of time before the
whole dam collapses. Eventually, when the reservoir is nearly empty the negative feedback
mechanism takes over, so a new steady state condition is reached for which the outflow
rate equals the inflow. The fact that the Earth has had water and an atmosphere for a very
long time suggests that our Earth system is dominated by negative feedback mechanisms.
Nevertheless, positive feedback mechanisms may be very important, since they have the
potential to bring about dramatic changes.
If we consider the hydrological cycle at the global scale , we may assume a closed system ,
i.e. a system that only exchanges energy with its surroundings; water does not enter or leave
the Earth system. The global hydrological cycle (see Figure 3.1) is driven by solar energy that
powers the evaporation and translocation by wind. The evaporated water is returned to the
Earth’s surface by precipitation, some of which falls on land. In most areas, more water enters
the land via precipitation than leaves it by evaporation. If the water is not temporarily stored
on the soil surface in the form of snow and ice, part of the excess water is discharged directly
into streams and lakes via overland flow . The rest infiltrates the soil and percolates to the
groundwater, which also ultimately discharges into surface waters. Rivers are the main routes
transporting water from land to sea.
Although the global hydrological cycle may be looked upon as a closed system , the water
cycle is often investigated at the smaller scale of a local groundwater system or single drainage
basin. The drainage basin as a hydrological unit can be envisaged as an open system receiving

mass (in the form of water) and energy from the weather over the basin and losing them
by evaporation and water discharge through the basin outlet. Therefore, the drainage basin
provides a useful framework for studying the phenomena related to the transport and fate of
contaminants.
Groundwater transports chemicals that are produced by internal weathering and
dissolution reactions or delivered to the soil surface via atmospheric deposition (e.g. acid
rain ) or anthropogenic immissions (e.g. application of manure , fertiliser, and pesticides in
agriculture). River water transports materials produced by erosion processes on hill slopes
and river banks and by internal production of organic matter , as well as dissolved ions
originating from natural or anthropogenic sources. The fine fraction of sediments, which
consists mainly of clay minerals and organic matter, is particularly able to bind various
chemicals; this fraction is therefore considered to be a very important vector for transporting
nutrients and a large variety of contaminants, including heavy metals and organic pollutants.

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