Alum Treatment for a Shallow Eutrophic Lake
A 40-hectare shallow lake has a mean depth of 2.5 m. Summer monitoring gives total phosphorus (TP) 85 µg/L, chlorophyll a 45 µg/L and Secchi depth 0.6 m. A farm ditch delivers an estimated 60 kg P per year. Sediment-core incubations suggest an internal phosphorus load of 180 kg P per year, with an uncertainty of about ±50%. The council proposes dosing the lake with alum at 25 g Al per cubic metre to 'lock up' the sediment phosphorus and reduce TP to 30 µg/L. Alum works best when the water is well buffered and oxygenated near the sediment. The lake stratifies in summer, and bottom dissolved oxygen falls below 1 mg/L. The council has not committed to reducing the ditch load.
1. Calculate the lake volume and the total mass of aluminium proposed. Check whether the dose is internally consistent with the stated figure.
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Area = 40 ha = 40 × 10,000 = 400,000 m². Mean depth = 2.5 m, so volume = 400,000 × 2.5 = 1,000,000 m³.
At 25 g Al/m³, total Al = 25 × 1,000,000 = 25,000,000 g = 25,000 kg = 25 t Al. The stated dose and the lake dimensions are consistent: 25 g/m³ over one million cubic metres gives 25 tonnes of aluminium.
That is the mass of aluminium, not the mass of alum product. Alum is a hydrated aluminium sulfate; the product mass will be several times larger because aluminium is only a fraction of the formula mass. The council's tender and budget must use the product mass and assay, not the aluminium mass. The calculation also assumes the whole lake is treated at the same dose; deeper holes or inflows may need different dosing. Before dosing, the council should measure alkalinity and pH, because alum consumes alkalinity and can acidify poorly buffered water.
2. A councillor says: 'The internal load is 180 kg P per year and the lake currently holds 85 kg P, so removing 180 kg will bring TP down to 30 µg/L.' Evaluate this reasoning and state what else must be known.
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The reasoning confuses a load with a standing stock. TP of 85 µg/L in 1,000,000 m³ is 85 µg/L × 1,000,000 L = 85,000,000 µg = 85 kg of phosphorus in the water column at the time of sampling. The 180 kg/year figure is a flux from the sediment, not a quantity stored in the lake. Subtracting 180 from 85 is dimensionally invalid and would give a negative number.
To predict the response, the council needs the water residence time, the external load, the settling rate of phosphorus and the fraction of the internal load that alum can actually bind. If the lake flushes quickly, the external load of 60 kg/year may dominate; if it flushes slowly, sediment release can keep TP high. Alum may reduce sediment release, but it does not stop the ditch input. The lake also stratifies and bottom oxygen falls below 1 mg/L, which can release phosphorus from sediment even after treatment. The ±50% uncertainty on the internal load means the true value could be 90–270 kg/year.
A defensible statement is: 'Alum may reduce internal loading, but it cannot be expected to reach 30 µg/L unless the external load is also controlled and the lake's flushing and oxygen conditions are accounted for.'
3. Design a two-year monitoring programme to judge whether the alum treatment worked. Include at least three variables and explain what result would count as success.
Read the worked answer
Monitor before treatment for at least one full year, then after treatment for one year, at the same deep-water station and at least one shallow station. Sample at fixed intervals (fortnightly in summer, monthly in winter) and at the same depth for TP, chlorophyll a and Secchi depth. Measure dissolved oxygen and temperature profiles to track stratification, and pH and alkalinity to check for alum side effects. Measure dissolved aluminium after treatment. Continue measuring ditch flow and phosphorus concentration to estimate the external load.
Success should not be defined only as a single TP value. A reasonable success criterion is a sustained summer mean TP below 30 µg/L, with chlorophyll a reduced and Secchi depth increased, and no increase in dissolved aluminium or decline in alkalinity beyond agreed limits. Because the internal load estimate has ±50% uncertainty, the programme should report confidence intervals and compare pre- and post-treatment medians rather than single samples.
A result showing lower TP only in the first summer, followed by a return to 85 µg/L, would suggest temporary binding or continued external loading, not success. The monitoring should therefore continue long enough to detect that rebound.