Study: Dogger Bank Swell Attenuation Model

The Dogger Bank is a large sandbank in the central North Sea, with depths of 25-30m compared to surrounding waters of 50-100m. This shallow feature significantly filters long-period Atlantic swells before they reach Belgian and Dutch coastlines.

The Problem

Standard wave models often fail to account for the Dogger Bank's filtering effect, leading to over-predicted swell heights and periods at Belgian beaches. Our model explicitly calculates attenuation based on depth ratios.

Physical Mechanism

When deep-water swells encounter shallow bathymetry, several processes reduce energy:

• Bottom friction increases exponentially in shallow water
• Wave breaking dissipates energy when Hs > 0.78d
• Refraction spreads energy over wider areas
• Non-linear wave-wave interactions transfer energy to higher frequencies

Attenuation Algorithm

Our depth-ratio attenuation model:

depth_ratio = dogger_depth / deep_water_wavelength

if depth_ratio > 0.5:
    attenuation = 0.95  # Minimal effect
elif depth_ratio > 0.25:
    attenuation = 0.70 + 0.25 × (ratio - 0.25) / 0.25
elif depth_ratio > 0.10:
    attenuation = 0.30 + 0.40 × (ratio - 0.10) / 0.15
else:
    attenuation = 0.10 + 0.20 × ratio / 0.10  # Heavy

Example Calculation

For a 14-second Atlantic swell crossing the Dogger Bank (depth = 27m):

Wavelength L₀ = 1.56 × 14² = 306m
depth_ratio = 27 / 306 = 0.088

Result: attenuation ≈ 0.28 (72% energy loss)

Long-period Atlantic swells (14-20s) lose 60-80% of their energy crossing the Dogger Bank, arriving as much smaller but still surfable waves.

Validation

We validated this model against paired buoy observations (pre-Dogger and post-Dogger) during 23 significant swell events in 2024. Results:

• RMSE of attenuation prediction: 0.08
• Correlation with observed height reduction: r = 0.89
• Period-dependent accuracy: best for T > 12s swells

Implications for Belgian Surf

• Pure Atlantic swells are rare and require exceptional storm intensity
• Best surf often comes from Scottish Low systems (WNW direction) that partially bypass Dogger Bank
• Local wind sea remains the most consistent source of surfable waves