Use the range slider at the bottom to zoom all panels to a specific time period.

rogue_ratio = Max Wave / Signif Wave. Values > 2.0 define a rogue wave event. gust_ratio = Gust / Wind. Values > 1.5 indicate a rogue gust.

Use the range slider at the bottom to zoom all panels to a specific time period.

gust_ratio = Gust / Wind. Values > 1.5 define a rogue gust event.

Comparing wave rogue events (Max Wave / Signif Wave > 2.0) with gust rogue events (Gust / Wind > 1.5).

Comparison of confidence interval methods for GPD return levels: delta-method (asymptotic, from standard errors) vs block bootstrap (resampled, 500 replicates, block size 48h). Format: estimate [lower, upper].

The Generalized Pareto Distribution has CDF for exceedances \(y = x - u\) above threshold \(u\):

with two parameters:

Return levels for T-year event:

where \(n_y\) = observations per year, \(\lambda\) = exceedance rate.

Threshold sensitivity: GPD results depend on threshold choice. Lower thresholds give more data but may violate asymptotic theory. The mev package provides diagnostics.

Note: Limited sample size (n~8 years). The pooled GEV analysis below is illustrative only due to few annual maxima. The per-station GPD approach above is preferred.

Bayesian approaches: The mev package supports profile likelihood and Bayesian methods for improved uncertainty quantification.

Storm propagation: Cross-correlation lag analysis between stations could enable offshore-to-nearshore prediction with lead times.

Positive optimal lag means the first station leads (predicts) the second.

M6 is 320km offshore in the deep Atlantic. Waves reaching M6 will propagate toward coastal stations over several hours.

• Positive lag means M6 observations precede coastal observations
• R² > 0.5 indicates useful predictive skill
• Stations facing the Atlantic (M5, M2, M3) should have better predictions
• M4 (southeast) may have lower skill due to different storm exposure

Extreme = top 5% of wave heights at each station.

P(Station B extreme | Station A extreme) - probability of extreme at B given extreme at A:

Copulas model the dependence structure, especially in the tails (extremes).

• λU = 0: Extremes are independent (one station’s extreme doesn’t predict the other’s)
• λU > 0: Extremes are asymptotically dependent (joint extremes more likely than by chance)
• λU → 1: Perfect dependence in the tail (extremes always occur together)

For ocean buoys, λU > 0.3 indicates that storm events affect multiple stations simultaneously.

1. Forecasting: If M6 (offshore) shows large waves, can we predict when they’ll reach coastal stations?

2. Risk assessment: During storms, are all stations simultaneously at risk, or do waves propagate sequentially?

3. Rogue wave correlation: Do rogue wave events at one station predict increased risk at others?

Waves travel at the group velocity, which depends on wave period:

For typical swell with period T = 10s: \(v_g \approx 15.6\) m/s \(\approx 56\) km/h

For longer period swell (T = 15s): \(v_g \approx 23\) m/s \(\approx 84\) km/h

wave_height ~ wind_speed + gust + wind_speed_lag1 + wave_height_lag1 + wave_height_lag2 + wave_height_lag3 + wave_period + 
    atmospheric_pressure + pressure_change + wind_dir_sin + wind_dir_cos + hour + month

=== Wave Height Prediction Model Report ===

MODEL PERFORMANCE
----------------
Training R^2: 0.986
OOB RMSE: 0.193 m
Test RMSE: 0.226 m
Test MAE: 0.145 m
Test R^2: 0.983
Test samples: 80989

TOP PREDICTORS
--------------
1. wave_height_lag1 (importance: 155084.8)
2. wave_height_lag2 (importance: 113520.9)
3. wave_height_lag3 (importance: 91137.0)
4. wave_period (importance: 66892.2)
5. gust (importance: 24582.1)

PERFORMANCE BY WAVE HEIGHT
--------------------------
Low (0-2m): RMSE=0.11m, MAE=0.07m (n=28523)
Moderate (2-4m): RMSE=0.19m, MAE=0.14m (n=34218)
High (4-6m): RMSE=0.30m, MAE=0.23m (n=13758)
Extreme (>6m): RMSE=0.55m, MAE=0.37m (n=4477)