5. EUTROPHICATION OF LAKES. Like winds and sunsets, wild things were taken far granted until progress began to do away with them. - Aldo Leopold, A Sand County Almanac. 5.1. INTRODUCTION.
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Like winds and sunsets, wild things were taken far granted until progress began to do away with them.
- Aldo Leopold, A Sand County Almanac
Thermal stratification causes a high concentra-tion of oxygen in near-surface waters, but the dissolved oxygen cannot mix vertically, and deep water eventually becomes anoxic. Anoxic conditions in the bottom waters and sediments cause anaerobic decomposition and the release of nutrients (phos-phate, ammonia, dissolved iron).
Figure 5.2. Regulation of the chemical composition of natural waters by algae.
Ratio of nitrate to phosphate in surface ocean waters.
Assuming the stoichiometric relationship for algal protoplasm, estimate the nutrient uptake rate for nitrate and CO2 in Lake Ontario. It was observed that 5µg per liter of phosphate was removed from the euphotic zone during the month of May in Lake Ontario. What is the rate of phytoplankton production in biomass, dry weight?
Solution: Use stoichiometric ratios to convert from phosphorus to biomass.
(31 days) (18.5 μgL-1 d-1) = 573 µg L-1 algae
0.57 mg L-1 of algae grew during the month of May in Lake Ontario
μmax – maximum growth rate, S – substrate or nutrient concentration, Ks – half-saturation constant.
and a multiplicative analogue:
Figure 5.4. Response curves of algal growth rates to limiting nutrients, light, and temperature.
Estimate the resulting growth rate for diatom phytoplankton in the Great Lakes by three different methods for the following data if the maximum growth rate is 1.0 per day.
- Liebig’s law of the minimum.
- Electrical resistance analogy.
- Multiplicative algorithm.
Solution: a) Monod kinetic expressions:
Liebig: the min growth rate is the appropriate choice the answer is 0.2 d-1.
All three nutrients contribute to an overall growth rate.
c) Multiplicative algorithm:
The multiplicative law also includes limitation due to all three nutrients, and it result in the lowest predicted growth rate of all three methods.
Experiment studies with all three nutrients in combination would be needed to confirm which model is most accurate.
V – lake volume; P – total phosphorus concentration; Qin – inflow rate; Pin – inflow total phosphorus concentration; ks – first-order sedimen-tation coefficient, Q – outflow rate.
α – ratio of particulate P to total P, vs – mean particle settling velocity, H – mean depth of the lake
τ – hydraulic detention time.
Lake Lyndon B. Johnson is a flood control and recreational reservoir along a chain of reservoirs in central Texas along the Colorado River. It has an average hydraulic detention time of 80 days, a volume of 1.71 × 108 m3, and a mean depth of 6.7 m. The ratio of particulate to total phosphorus concentration in the lake is 0.7, and the mean particle settling velocity is 0.1 m d-1. If the flow-weighted average inflow concentration of total phosphorus to Lake LBJ is 72 µg L-1, estimate the average annual total phosphorus concentration in the lake.
A plot of the fraction of total P remaining in any lake as a function of the dimensionless number ksτ is given by Figure 5.5. The fraction of total P removed to the lake sediments is equal to 0.454 (1 - P/Pin); the mass of total phosphorus entering the lake is 152 kg d-1 and the mass outflow is 83 kg d-1 (Figure 5.6).
Figure 5.5. Fraction of total P remaining in a lake as a function of the sedimentation coefficient ks times the detention time τ
Figure 5.6. Total P mass balance for Lake Lyndon B. Johnson in central Texas
νs – mean apparent settling velocity of total phosphorus.
ρ – hydraulic flushing rate of the lake (1/τ).
qs – surface overflow rate for the lake (Q/Asurf)
Figure 5.8. Relationship between summer levels of chlorophyll a and measured total phosphorus concentration for 143 lakes.
Figure 5.9. Dynamic model simulation of total phosphorus in the Great Lakes by Chapra.
Figure 5.12 illustrates a double phytoplankton bloom in Lake Ontario.
Schematic of an aquatic ecosystem
Flowchart for phosphorus kinetics in a dynamic ecosystem model
A dynamic eutrophication model calibration for Lake Ontario with two phytoplankton species (diatoms and nondiatoms)
Figure 5.13. Transport regime for a compartmentalized lake ecosystem model. Large arrows represent current flow (advection) and double; small arrows – mixing (dispersion) between compartments.
Vj – volume of the j-th comp.;
Cj – concentration of a conservative tracer in the j-th comp.;
Qij – flowrate from the j-th to the i-th adjacent comp.;
Eij – bulk dispersion coefficient between the j-th and the i-th adjacent comp.;
Aij – interfacial area between the j-th and the i-th adjacent comp.;
Ci – concentration of a conservative tracer in the i-th comp.;
lij – half-distance (connecting distance between the middle of the two adjacent compartments).
Figure 5.14. Ecosystem model for eutrophication assessments. Boxes represent state variables; solid arrows are mass fluxes; and dotted lines represent external forcing functions.
Rate Constants and Stoichiometric Coefficients for Dynamic Ecosystem Models