Rainwater Tank Sizing by Stochastic Reliability Simulation: Storage-Reliability Design Curves for a Semi-Arid and a Monsoon Climate

Household rainwater tanks are commonly sized by rules of thumb that never state the reliability they deliver. This paper replaces the rules with storage-reliability design curves from a daily water-balance simulation driven by a first-order Markov rainfall generator with gamma-distributed wet-day amounts (seed 20261110, 249 evaluation years per configuration), for two synthetic-but-representative climates (realised 520.7 mm/yr semi-arid and 1511.5 mm/yr monsoon, each with a 4-month wet season), roof areas 40/80 m2, demands 20/50 L/day, and storage 0.5-20 m3. The interpolated size for 90% reliability spans 0.85 m3 (monsoon, 80 m2, 20 L/day) to 17.30 m3 (semi-arid, 40 m2, 50 L/day). One configuration is supply-limited (semi-arid, 40 m2, 50 L/day: supply-to-demand ratio 0.91), so even 20 m3 delivers only 91.0% reliability and 98% is unreachable at any size. Audited on the same weather, the one-month-of-demand rule delivers 50.1-84.8% reliability and the largest dry-spell deficit rule delivers 87.7-100.0% at up to four times the necessary size. All results are simulated, not measured; the rainfall is a stated synthetic model, not gauge data. Computations are reproducible from the deposited compute.py and results.json.