80 Ecology and Applied Environmental Science
In colder climates during the winter, surface water temperature can get as
low as almost 0°C (e.g. water immediately below a surface ice layer), whereas
in this case, the temperature of the deeper layers is near 4°C. In this way, a
winter layering is created that is much less marked and the reverse of the summer one. Temperature rise in the spring causes a smaller, spring inversion,
given that surface masses, getting warmer up to the temperature of maximum
density, tend to sink. Ultimately, the water acquires a uniform temperature
and density in all its depth, which favours a quite strong circulation.
The ecological significance of temperature layerings and seasonal inversions is great, since:
• Temperature changes directly affect organisms’ activities.
• Summer layering obstructs mixing; consequently the oxygen that
is absorbed by the atmosphere basically circulates only in the epilimnion, whereas the hypolimnion tends to be deprived of oxygen.
During autumn inversion, though, the hypolimnion’s masses come to
the surface and become enriched with oxygen.
• During seasonal inversions, nutrients get mixed and redistributed.
Nutrients that had sunk to low water masses rise to the surface where
they are now available for photosynthesis and other metabolic processes.
4.5.3 Mathematical Model of a lake
The mathematical model of a lake that follows is simplified and aims at
aiding the understanding of some main function mechanisms of aquatic
ecosystems and showing the general principles of mathematical simulation
of those mechanisms.
A non-stratified lake of a volume V is examined, with the assumption of
complete mixture, i.e. with the assumption that nutrients and organisms
are uniformly scattered in volume V. Therefore the study can be conducted
on the basis of concentrations (mass/volume) of organisms and nutrients
that are spatially stable. It is also accepted that the limiting factor of the
ecosystem is phosphorus. Carbon, nitrogen and the other nutrients, as well
as solar energy, are abundant for the whole duration of the phenomenon
under study (e.g. from May to September). The course of the phenomenon
is examined in temporal steps of 24 hours, on the basis of the average
24 hours solar radiation.
In reality, when the organisms die they sink to the bottom, decompose
and supply again the water body with phosphorus and other nutrients. This
recycling of phosphorus is not taken under consideration.
During the time t = 0, the concentrations of inorganic phosphorus,
producer organisms, and consumer organisms in the lake are C 0, X p0, Χ c0
correspondingly. In the time t = 0, inflow of inorganic phosphorus in the
lake begins, with a speed (mass/volume/time) that equals L. Speed L is a
In colder climates during the winter, surface water temperature can get as
low as almost 0°C (e.g. water immediately below a surface ice layer), whereas
in this case, the temperature of the deeper layers is near 4°C. In this way, a
winter layering is created that is much less marked and the reverse of the summer one. Temperature rise in the spring causes a smaller, spring inversion,
given that surface masses, getting warmer up to the temperature of maximum
density, tend to sink. Ultimately, the water acquires a uniform temperature
and density in all its depth, which favours a quite strong circulation.
The ecological significance of temperature layerings and seasonal inversions is great, since:
• Temperature changes directly affect organisms’ activities.
• Summer layering obstructs mixing; consequently the oxygen that
is absorbed by the atmosphere basically circulates only in the epilimnion, whereas the hypolimnion tends to be deprived of oxygen.
During autumn inversion, though, the hypolimnion’s masses come to
the surface and become enriched with oxygen.
• During seasonal inversions, nutrients get mixed and redistributed.
Nutrients that had sunk to low water masses rise to the surface where
they are now available for photosynthesis and other metabolic processes.
4.5.3 Mathematical Model of a lake
The mathematical model of a lake that follows is simplified and aims at
aiding the understanding of some main function mechanisms of aquatic
ecosystems and showing the general principles of mathematical simulation
of those mechanisms.
A non-stratified lake of a volume V is examined, with the assumption of
complete mixture, i.e. with the assumption that nutrients and organisms
are uniformly scattered in volume V. Therefore the study can be conducted
on the basis of concentrations (mass/volume) of organisms and nutrients
that are spatially stable. It is also accepted that the limiting factor of the
ecosystem is phosphorus. Carbon, nitrogen and the other nutrients, as well
as solar energy, are abundant for the whole duration of the phenomenon
under study (e.g. from May to September). The course of the phenomenon
is examined in temporal steps of 24 hours, on the basis of the average
24 hours solar radiation.
In reality, when the organisms die they sink to the bottom, decompose
and supply again the water body with phosphorus and other nutrients. This
recycling of phosphorus is not taken under consideration.
During the time t = 0, the concentrations of inorganic phosphorus,
producer organisms, and consumer organisms in the lake are C 0, X p0, Χ c0
correspondingly. In the time t = 0, inflow of inorganic phosphorus in the
lake begins, with a speed (mass/volume/time) that equals L. Speed L is a