Irrigation Water Allocation Under a Falling Water Table
A district agricultural office in a semi-arid province must allocate a fixed seasonal canal supply of 1,200,000 cubic metres among three command areas before the planting window closes in 18 days. Area A (400 ha) grows wheat and needs about 4,500 m³/ha per season; Area B (300 ha) grows melons, needs 6,000 m³/ha, and returns 2.5 times the net income per hectare of wheat; Area C (250 ha) grows wheat on saline soil where yields fall 15 percent unless a 500 m³/ha leaching dose is added. The water table in Area A has dropped 1.2 m over five years, and farmers there have already sunk 30 private tube wells. The canal authority can deliver at most 70,000 m³ per day, and the office must publish a written allocation that farmers can challenge.
1. Compute the water each area needs at full planting, compare with the available supply, and state whether a shortfall exists and how large it is.
Read the worked answer
Area A: 400 ha × 4,500 m³/ha = 1,800,000 m³. Area B: 300 ha × 6,000 m³/ha = 1,800,000 m³. Area C: 250 ha × (4,500 + 500) m³/ha = 1,250,000 m³. Total demand at full planting = 4,850,000 m³. Supply = 1,200,000 m³, so the shortfall is 3,650,000 m³ - roughly 75 percent of demand. No allocation can satisfy everyone; the office must choose which areas to prioritize and by how much to cut the others.
Check delivery feasibility too: 1,200,000 m³ ÷ 70,000 m³/day ≈ 17.1 days of pumping, which barely fits the 18-day window, so any delay in starting shrinks the usable supply.
2. Propose a defensible allocation rule. Justify the trade-off between economic return and the falling water table in Area A.
Read the worked answer
A defensible rule ranks uses by net return per cubic metre, not per hectare, then applies a sustainability constraint.
Net return per m³ for B is (2.5 × wheat return/ha) ÷ 6,000, versus wheat ÷ 4,500 for A. Per m³, B yields 2.5/6,000 = 0.000417 wheat-units per m³, while A yields 1/4,500 = 0.000222 - B is about 1.9 times more valuable per cubic metre. So a pure efficiency rule favors B.
But Area A's falling water table (1.2 m in five years, 30 private wells) means canal water there substitutes for groundwater that would otherwise be mined. Cutting A's canal share pushes farmers back onto declining wells, which is a hidden cost not captured in the per-m³ comparison. A reasonable compromise: fully serve B (1,800,000 m³ is already more than supply, so this is impossible) - instead, cap B at a share that keeps melon income high while leaving A enough to reduce well pumping.
A workable published rule: allocate first to C's leaching dose because salinity damage is irreversible; then split the remainder between A and B so that A receives at least enough to cover its wheat crop's critical stages, with the balance to B. State the numeric shares explicitly and explain that the rule protects the aquifer and prevents soil degradation, which are public costs, even at some loss of private income.
3. Farmers in Area C object that the leaching dose wastes water. How should the office respond, and what evidence would settle the dispute?
Read the worked answer
The office should explain that the 500 m³/ha leaching dose is not waste but an investment: without it, yields drop 15 percent, so the effective cost is 500 m³/ha against the value of 15 percent of the wheat crop. Compare: 15 percent of 4,500 m³/ha equivalent yield is worth more than the 500 m³/ha of water if wheat value per m³ exceeds roughly one-ninth of the leaching cost - which it does in most settings. Skipping the dose saves water this season but accumulates salt, raising future doses.
Evidence to settle it: soil salinity readings (EC) before and after leaching on a few test plots, plus yield records from plots with and without the dose. If measured yield loss without leaching is under about 11 percent (500 ÷ 4,500), the dose is marginal; if it is 15 percent as assumed, the dose pays. Publish the test-plot numbers so the challenge can be evaluated on data rather than assertion.