Lake Vellore: hitting a phosphorus target with a legacy in the sediment
Lake Vellore is an 8.4 km² reservoir supplying 190,000 people and hosting a cage farm producing 1,200 t of tilapia a year. August monitoring gives total phosphorus (TP) 45 µg/L, chlorophyll a 22 µg/L, Secchi depth 0.9 m, and hypolimnetic dissolved oxygen 2.1 mg/L during a two-week cyanobacterial bloom. A load apportionment attributes 55% of phosphorus to the wastewater treatment plant, 30% to agriculture and 15% to urban runoff; the cage farm is not listed. The regulatory target is TP 25 µg/L. The options costed are: tertiary phosphorus stripping at the treatment plant, US$12 million capital plus US$400,000 a year, removing 70% of that source; 30 m riparian buffer strips at US$2.1 million, removing 20% of the agricultural load; and alum dosing at US$600,000 a year, removing 40% of the internal load. Mean water residence time is 3.5 years.
1. Calculate whether the treatment plant upgrade alone reaches the 25 µg/L target. Show your working and state the assumption your calculation depends on.
Read the worked answer
Treat the apportionment as proportional to the 45 µg/L:
- Treatment plant share: 0.55 × 45 = 24.75 µg/L.
- Removed at 70%: 0.70 × 24.75 = 17.3 µg/L.
- New TP: 45 − 17.3 = 27.7 µg/L.
27.7 µg/L is above the 25 µg/L target, so the upgrade alone fails by about 2.7 µg/L.
Adding buffer strips: agricultural share 0.30 × 45 = 13.5 µg/L; 20% removed = 2.7 µg/L. New TP = 45 − 17.3 − 2.7 = 25.0 µg/L.
So the target is met exactly, but only if both measures are funded, and with zero margin.
Assumptions, all contestable: the lake responds linearly and immediately; phosphorus is the only limiting nutrient; there is no internal loading; and the apportionment is complete. The last is clearly false - the cage farm is missing. At a feed conversion ratio of 1.6, 1,200 t of fish consumes about 1,920 t of feed, and the phosphorus not retained in harvested fish is a real load. The plan is therefore optimised against an incomplete budget, and any omitted source pushes the achieved TP back above 25 µg/L.
2. A councillor argues for the cheaper buffer strips alone, since they act immediately. Evaluate that proposal and the treatment plant upgrade against the lake's physical and biological evidence.
Read the worked answer
Buffer strips alone: 2.7 µg/L reduction gives 42.3 µg/L, far short of 25. They are cheap (US$2.1 million one-off against US$12 million capital plus US$400,000 a year), fast to install, and deliver multiple benefits (sediment, habitat, flood peak). But on the phosphorus question they are a 6% improvement against a 44% requirement - a useful component, not a policy.
Treatment plant upgrade: it addresses the largest single source and is the only option that removes 17 µg/L. But it is capital-heavy and it will not show results quickly: with a 3.5-year residence time the lake integrates load over years, so no improvement should be promised before roughly 2029–2031.
The decisive evidence against a purely external fix: hypolimnetic DO of 2.1 mg/L means the sediment is anoxic and releasing stored phosphorus. Cutting the external load reduces the input to that store but does not empty it, so TP can plateau above target for a decade. Alum dosing binds sediment phosphorus and buys that time, at US$600,000 a year recurring.
Judgement: buffer strips plus treatment plant, with alum as a time-limited bridge and a phosphorus cap on the cage farm; set the interim target below 25 µg/L because the calculation has no margin and ignores internal loading. Judge success on chlorophyll a and hypolimnetic DO, not TP alone.
3. Design the monitoring and review structure that would tell the authority whether to continue paying for alum after five years.
Read the worked answer
Baseline variables: TP (compliance), chlorophyll a (ecological response), hypolimnetic DO (the driver of internal loading), Secchi depth, and inflow TP load from each source. Sample fortnightly in summer, monthly in winter, at three depths and two stations, with a fixed protocol so years are comparable.
Trigger for stopping alum: sediment iron is no longer reduced, hypolimnetic DO stays above roughly 4 mg/L through stratification, and summer chlorophyll a falls below an agreed ecological target for three consecutive years. If those are met, the sediment store has shrunk enough that external control alone should hold the lake.
Trigger for continuing or escalating: TP plateaus above 25 µg/L while external loads are demonstrably down, or chlorophyll a rises despite falling TP (indicating internal loading). In that case the farm cap and buffer width should be strengthened before more alum is bought.
Why five years: it matches roughly one and a half residence times, the minimum period in which a load reduction can be expected to show in the lake rather than in the inflow. Reviewing annually would be reading noise.
The key design principle is that the review must have pre-agreed numerical triggers, because the politically easy default is to keep paying for a treatment that is quietly not working.