Four Uncertain Inputs, Sampled Together
The take estimate depends on four inputs, none of which are known precisely. Rather than pick point estimates and pretend the answer is certain, we sample all four simultaneously across 200 draws and propagate the uncertainty through the full RAM PE pipeline.
| Input | Distribution | Range | Why Uncertain |
|---|---|---|---|
| Bottom grain size (phi) | Uniform | 0.5 – 4.5 | Site-specific geology varies within lease area |
| Attenuation multiplier | LogNormal | 0.3 – 3.0× | Hamilton’s regression has known scatter |
| Density multiplier | LogNormal | 0.5 – 5.0× | Roberts model versions differ by 2.6× |
| Mitigation (dB reduction) | Uniform | 6 – 15 dB | Bubble curtain performance varies by site and conditions |
Each draw runs through the RAM PE propagation model and density overlay to produce a take count. The 200 draws produce a distribution of takes.
With 200 draws, exceedance probabilities carry approximately ±3% sampling uncertainty (binomial standard error). Central estimates (median, mean) are stable; tail statistics (P95, exceedance) should be interpreted with this margin.
Note: The Bayesian inversion (Investigation 08) subsequently found an effective bottom grain size of φ = 6.5 ± 0.8, outside the prior range used here (φ 0.5–4.5). Re-running with the posterior parameters reduces the median take by approximately 30%. The estimates above are therefore conservative.
How Much Attenuation Is Enough?
The table below shows how the take distribution changes with increasing bubble curtain performance. The IHA typically authorizes 7 Level B takes. The question is: what mitigation level keeps P(exceed 7) below an acceptable threshold?
| Mitigation Level | Median Takes | P95 Takes | P(Exceed 7) |
|---|---|---|---|
| No mitigation (0 dB) | 50.4 | 126.9 | 100% |
| 6 dB (IHA standard) | 10.4 | 26.2 | 81.5% |
| 9 dB | 4.7 | 11.9 | 27.5% |
| 10 dB (measured typical) | 3.6 | 9.1 | 11.5% |
| 10.5 dB (required target) | 3.2 | 8.0 | 7.5% |
| 12 dB | 2.1 | 5.4 | 1.5% |
| 15 dB (CVOW measured range) | 0.97 | 2.4 | 0% |
At the IHA’s assumed 6 dB, the median take estimate is 10.4 — already above the IHA limit. P95 is 26.2, and there is an 81.5% chance of exceeding the authorization. The standard assumption is dangerously optimistic.
When mitigation reaches 9 dB, the median drops to 4.7 (below 7), but P(exceed) is still 27.5%. Only at 10.5 dB does exceedance drop below 10% (7.5%), making it the defensible performance target.
10.5 dB for 10% Exceedance
To bring P(exceed 7) below 10% requires 10.5 dB of noise reduction. This is the defensible target — a 90% confidence that the project stays within its authorization on any given pile driving event.
CVOW measured 14–17 dB of bubble curtain attenuation during its 2023–2024 installation campaign. The measured performance exceeds the 10.5 dB requirement by a comfortable margin. The technology works — but only if the IHA’s assumed performance (6 dB) is replaced with measured performance.
The gap between assumed and measured performance matters. At 6 dB, P(exceed) = 26.5%. At the measured 14–17 dB, P(exceed) drops below 3%. IHAs that use conservative assumptions about mitigation performance overestimate the take risk — but they also miss the opportunity to show that the technology is working.
Which Whale Density Is Right?
The Roberts et al. habitat-based density model is the standard source for NARW density in IHA applications. But the 2024 update produces densities 2.6× higher than the 2017 version for the southern New England lease areas.
Most active IHAs were prepared using Roberts 2017 densities. If the 2024 densities are more accurate — and they incorporate more recent sighting data and refined habitat variables — then current IHA take authorizations may underestimate actual exposure by a factor of 2–3×.
The Monte Carlo samples the density multiplier as a LogNormal distribution spanning both model versions. This is not a modeling choice — it is an honest representation of how uncertain the density input actually is.
Per-Event Risk and Season Totals
Not every pile driving event encounters a whale. During the allowed construction months (June–October), the per-event probability of a NARW being within the Level B harassment zone is 3–10%, depending on month (highest in June at ~10%, lowest in August at ~3%).
Over a full construction season of 60–80 pile installations, the probability of at least one take event is high. But the probability of a completely clean season — zero takes across all piling events — is approximately 45% at 10 dB mitigation. Roughly half of construction seasons would complete with no takes at all.
This is the value of the Monte Carlo framing: instead of asking “how many takes will we have?” we can ask “what is the probability that the season exceeds the authorization?” — a question that maps directly to regulatory risk.
200 Monte Carlo draws · 4 uncertain inputs sampled simultaneously · RAM PE propagation · Roberts et al. 2024 NARW density · Vineyard Wind site geometry
The Full Uncertainty
The Monte Carlo produces a distribution, not a point estimate. The CDF shows the probability that annual takes will be at or below any given value. The IHA authorizes 7 takes — there is a 26.5% probability of exceeding that limit.
Lognormal fit to 200 MC draws. 4 uncertain inputs sampled simultaneously: bottom grain size (phi), bottom attenuation, NARW density, bubble curtain performance. All levels SPL_rms (dB re 1 μPa).