Industry: Environmental Product: ModelRisk Application: Detection power and sampling-network design for soil and groundwater monitoring
A regulator approved a former industrial parcel for redevelopment on the strength of a nine-well groundwater monitoring grid that read clean. The deterministic logic looked airtight: the typical plume on a site like this peaks near 91 ug/L of TCE — well above the 50 ug/L action level — so any plume "would obviously be detected." A Monte Carlo simulation of the plume's uncertain location, size and the measurement error at each well told a different story: that nine-well grid had only a 68% chance of detecting a real exceedance, leaving a 32% probability of missing a genuine hotspot. Reaching the regulator's 95% detection target took 64 wells, not nine — and where the wells went mattered almost as much as how many there were.
The mistake in the deterministic view is subtle. It compares the plume's peak concentration to the action level and concludes "detectable." But a monitoring well does not sample the peak — it samples one point on a 200 m × 200 m parcel, at whatever distance it happens to sit from a plume whose centre is unknown. What matters is the concentration at the well, after measurement error, not the concentration at the plume core.
We modelled the plume as a radial Gaussian-decay field, C(d) = C_peak · exp(−(d/rho)²), where the peak concentration C_peak is LogNormal (median 90 ug/L, sigma_log 0.85) — skewed, with a long upper tail and occasional near-clean sites — and the decay radius rho is Triangular(18, 35, 70 m): most plumes moderately compact, some diffuse. Each well's reading is the true concentration at its distance multiplied by LogNormal(0, 0.35) analytical-plus-sampling error. A well detects when that reading is at or above 50 ug/L.
Crucially, every well on a given site sees the same plume realisation — one shared peak and one shared decay radius drawn per site. That common factor is what turns detection probability into a distribution across sites rather than a single number. Conditioning on the shared regime makes the point obvious: on strong, wide-plume sites the nine-well grid detects 100% of the time, but on weak, compact-plume sites it detects only 26% of the time — a 74-percentage-point spread driven entirely by the latent plume regime. A model that treated each well as an independent draw would average that away and badly understate how often a whole network comes up empty over a real hotspot.
Restricting to sites that genuinely contain an exceedance, the highest reading the nine-well grid returns has a median of 73 ug/L — but a P10 of just 24 ug/L and a P90 of 223 ug/L. On 32% of contaminated sites the entire network reads below the 50 ug/L action level: the plume exists, but no well is close enough to its core to register it. That shaded body to the left of the action line is the missed-detection rate the peak-concentration estimate could not see.
Doubling the well count is expensive; spending the same wells better is not. At 16 wells, a regular grid achieves 82% detection against 69% for randomly sited wells of the same count — a 14-percentage-point advantage purely from layout. The gap is widest in the mid-range (9–25 wells) where coverage is the binding constraint; once the site is saturated (81+ wells) grid and random converge, because almost any layout finds almost any plume.
Against the nine-well baseline miss probability of 32%, the plume decay radius — how compact the contamination is — moves the miss rate more than any other input (±7.0 points): a tight plume is a small target and is missed far more often than a diffuse one. The number and density of wells is second, well placement third. Measurement error and the exact action-level threshold barely move the number — a useful result, because it says the agency's money is better spent on more and better-placed wells than on a marginally more precise lab method.
A monitoring network does not detect the contamination it is over; it detects the contamination a well happens to sit close enough to read — and the only honest way to report that is as a probability with a known set of drivers, not as a clean bill of health.