Each treatment barrier removes a fraction of the (oo)cysts in the water. Removal is measured in log₁₀ reduction: 1‑log = 90% removed, 2‑log = 99%, 3‑log = 99.9%. Barriers stack additively in log space, so the plant's total performance is:
LRV_total = LRV_coag + LRV_filter + LRV_UV
C_out = C_in · 10^(−LRV_total)
Coagulation/flocculation — alum (Al₂(SO₄)₃) hydrolyses to form aluminium‑hydroxide flocs that enmesh cysts and eggs so they settle or filter out more easily. Removal rises with dose up to a practical ceiling (over‑dosing wastes coagulant without extra credit):
LRV_coag ≈ min(1.6, dose_mg/L / 12.5)
Rapid sand filtration — smaller effective grain size packs the bed tighter and traps more particles by straining and interception, at the cost of higher headloss. This mirrors EPA "credit" tables for conventional filtration (typically 2–3 log for Cryptosporidium):
LRV_filter ≈ clamp(3.0 − 1.7·(size_mm − 0.45), 0.3, 3.0)
UV disinfection — UV‑C photons (254 nm) damage the parasite's DNA/RNA so it can no longer infect a host, even though the (oo)cyst itself is still intact. Inactivation follows the dose–response curve used in the US EPA UVDGM for Cryptosporidium (roughly 12 mJ/cm² for 4‑log, 5.8 for 3‑log):
LRV_UV ≈ min(4.5, dose_mJcm2 / 2.7)
The compliance banner checks the combined LRV against the commonly cited 3‑log Giardia / Cryptosporidium removal‑or‑inactivation benchmark used by multi‑barrier drinking‑water regulations (e.g. US EPA LT2ESWTR, EU Drinking Water Directive risk‑based approach). Spheres in the tank represent individual cysts/oocysts entering at the left; each one rolls the barrier's removal probability as it crosses a zone and is captured (fades out) or continues to the tap.