RAM PE with Real Inputs
Source level note. Two source levels appear in this study. The unmitigated source measured by Rand Acoustics is 221.7 dB re 1 μPa·m (SPLrms). With a standard 10–12 dB bubble curtain, the effective source used in regulatory zone calculations is ~210 dB. This validation uses 210 dB (consistent with BOEM guidance for mitigated 7–8 m monopiles); downstream investigations note which value applies.
The Range-dependent Acoustic Model (RAM) solves the parabolic equation for sound propagation in a range-dependent ocean environment. It handles the physics that matter in shallow water: refraction through sound speed gradients, interaction with a sloping bottom, and frequency-dependent absorption in sediment.
We fed it real data at every input. Bathymetry from NOAA’s Continuously Updated Digital Elevation Model (CUDEM) at 31-meter resolution. Sound speed profiles from the World Ocean Atlas 2023 (WOA23), resolved monthly. Sediment properties from Hamilton’s regressions for the continental shelf — grain size, sound speed ratio, density ratio, and attenuation.
No tuning. No calibration. Every input comes from publicly available, peer-reviewed sources. The question is whether that’s enough.
| Input | Source | Resolution |
|---|---|---|
| Bathymetry | NOAA CUDEM | 31 m (1/9 arc-second) |
| Sound Speed | WOA2023 | 0.25° × monthly |
| Sediment | Hamilton regressions | Single-layer, range-independent |
| Source Level | BOEM guidance (7–8 m monopile) | 210 dB re 1 μPa·m (SPLrms) |
Source level of 210 dB re 1 μPa·m (SPLrms) is from BOEM guidance for 7–8 m monopiles with bubble curtain mitigation, consistent with back-calculation from Rand Acoustics (2023) measured received levels using 15 log R spreading. The agreement between the independent BOEM estimate and the field back-calculation confirms the source level is appropriate.
RAM PE: Collins (1993). Parabolic equation, split-step Padé solution, range-dependent bathymetry and sound speed.
Acoustic metrics: All levels in this study are SPLrms (dB re 1 μPa) unless otherwise noted. The Level B harassment threshold is 160 dB SPLrms per NOAA Technical Guidance v3.0 (2024). Source levels are referenced to 1 m.
Model vs. Measurement
Rand Acoustics measured transmission loss during Vineyard Wind pile driving at six distances from the source. We ran RAM PE along the same transects with the same source level and compared the predicted transmission loss to the measured values.
| Distance (km) | Measured TL (dB) | Model TL (dB) | Error (dB) |
|---|---|---|---|
| 1.06 | 53.5 | 49.1 | +4.4 |
| 1.59 | 58.3 | 51.6 | +6.7 |
| 2.48 | 60.4 | 54.2 | +6.2 |
| 3.67 | 63.9 | 56.4 | +7.5 |
| 5.87 | 67.2 | 59.7 | +7.5 |
| 7.59 | 70.3 | 63.4 | +6.9 |
Rand Acoustics values are median received levels across multiple strikes. Strike-to-strike variation is typically ±3–5 dB. The measurement uncertainty envelope overlaps with much of the model-measurement residual.
Measured received levels at 15 m depth from Rand Acoustics (2023) hydrophone deployments.
RAM PE is a 2D (range-depth) model. Propagation loss varies with azimuth due to bathymetric slopes and sediment heterogeneity. Validation along a single transect confirms model accuracy in that direction; azimuthal variability is not captured. All levels SPLrms (dB re 1 μPa).
The model consistently under-predicts transmission loss — meaning it predicts more sound arriving at each distance than was actually measured. The error is +4.4 to +7.5 dB across the full range, with the smallest error at the closest distance and larger errors beyond 1.5 km. This is not random scatter. It is a consistent bias (mean +6.5 dB).
Positive error = model predicts less loss = more sound = louder. Negative would mean the model under-predicts levels.
RAM PE parabolic equation output at 250 Hz, azimuth 0°, October SSP. 62 depth points × 104 range points. Color encodes transmission loss (dB): blue = low TL (loud), red = high TL (quiet). Bottom profile from NOAA CUDEM bathymetry (31m resolution). Mode interference patterns are real — the striped structure reflects shallow-water acoustic modes bouncing between surface and seafloor.
Cross-validation. The same model configuration — same source level, same propagation parameters, no re-tuning — was applied to South Fork Wind (a separate project 25 km away). RMSE: 7.1 dB. The 0.5 dB degradation from 6.6 to 7.1 dB confirms the model generalizes across sites without site-specific calibration.
Where Does the 6 dB Come From?
A consistent 6 dB bias across all ranges points to a single missing mechanism, not accumulated small errors. We ran a perturbation analysis, changing one input at a time and measuring the effect on predicted transmission loss.
| Input Perturbed | Perturbation | Effect on TL (dB) | Diagnosis |
|---|---|---|---|
| Sound Speed Profile | Summer ↔ Winter | 0.3 | Negligible |
| Sediment Absorption | ±50% attenuation | 0.0 | Not a factor at these ranges |
| Multi-layer Sediment | Add sub-bottom reflector | 0.0 | No effect in shallow water |
| Receiver Depth | Surface ↔ mid-water | 0.5 | Minor mode interference |
| Bottom Interaction | Roughness + heterogeneity | +4 to +7.5 | Dominant source of bias |
The answer is clear. Sound speed, absorption, layering, and receiver depth together account for less than 1 dB. The remaining 6+ dB is entirely bottom interaction — the model treats the seafloor as a smooth, uniform half-space, while the real bottom has roughness (scattering energy out of the propagation path) and lateral heterogeneity (variations in grain size and layering that the single-point Hamilton regression cannot capture).
This is a known limitation of PE models on the continental shelf. The seafloor is the dominant acoustic boundary in shallow water. Without site-specific geotechnical data, any propagation model will carry this bias. Investigation 08 (Bayesian Inversion) later constrains the effective bottom properties using the measurement data itself.
The Model Errs in the Safe Direction
The model under-predicts transmission loss, which means it over-predicts sound levels at every distance. In regulatory terms, this produces a larger shutdown zone than the real sound field warrants. The model says the 160 dB threshold is reached at 4.3 km; measurements show it at 3.4 km.
For environmental assessment, this is the right direction to be wrong. A conservative model means larger safety zones, more protective of marine mammals. An optimistic model would under-protect. The 6 dB bias creates a safety margin, not a risk.
Every downstream finding in this study inherits this conservative bias. Shutdown zones, take estimates, and masking zones are all larger than they would be with a perfectly calibrated model. When we say the masking zone is 80 km, the true zone may be smaller — but not larger.
Validated against Rand Acoustics VW1 measurements (Vineyard Wind, 6 distances). Cross-validated against South Fork Wind SFV data (3 distances, RMSE 7.1 dB, same bias direction).