Methodology: Spectral Partition Analysis

Real ocean waves are multi-modal: at any moment, the sea surface is a superposition of multiple wave systems from different sources. Spectral partition analysis separates these components for accurate quality predictions.

The Multi-Modal Reality

A typical North Sea sea state might contain:

• Primary swell: 10-14s period from Norwegian Sea storm 3 days ago
• Secondary swell: 8-10s period from Skagerrak low pressure
• Wind sea: 4-6s period from local SW winds

Traditional forecasts report a single "significant wave height", the combined energy. But surf quality depends critically on which component dominates.

Partition Features (28 Total)

For each spectral partition, we extract:

• Partition height (Hs_partition)
• Peak period (Tp_partition)
• Mean direction (θ_partition)
• Directional spread (σ_θ)
• Energy fraction of total spectrum
• Swell-to-Wind-Sea ratio (critical for quality)

Swell-to-Wind-Sea Ratio

When swell energy exceeds wind sea by 3:1 or more, clean, lined-up waves are likely. Below 1:1, expect choppy, disorganized conditions.

R_swell = E_swell / E_wind_sea

R > 3.0: Excellent (clean, lined-up)
R = 2.0-3.0: Good (mostly clean)
R = 1.0-2.0: Fair (some texture)
R < 1.0: Poor (choppy)

Implementation

We use the NOAA WW3 spectral partition output where available, and implement our own watershed algorithm for buoy spectral data:

1. 2D spectral density S(f, θ) from buoy
2. Smooth with Gaussian kernel (σ=0.02 Hz)
3. Find local maxima (spectral peaks)
4. Watershed segmentation from peaks
5. Integrate energy per partition
6. Classify as swell (f < 0.1 Hz) or wind sea

Validation

Partition-aware models improved surfability prediction F1 score by 12% compared to single-mode models, with largest gains during mixed sea states.

References

• Hanson, J.L. & Phillips, O.M. (2001). Automated Analysis of Ocean Surface Directional Wave Spectra. J. Atmos. Ocean. Tech.
• Portilla, J., Ocampo-Torres, F.J., & Monbaliu, J. (2009). Spectral Partitioning and Identification of Wind Sea and Swell. J. Atmos. Ocean. Tech.